Joshua Bernick - Masters Thesis - A Preclinical Assessment ... · exhibits towards her research,...

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A Preclinical Assessment of Lithium to Enhance Fracture Healing

by

Joshua Hart Bernick

A Thesis Submitted in Conformity with the Requirements

For the Degree of Master of Applied Science – Biomedical Engineering

Institute of Biomaterials and Biomedical Engineering

University of Toronto

© Copyright by Joshua Hart Bernick 2013

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A Preclinical Assessment of Lithium to Enhance Fracture Healing

Joshua Hart Bernick

Master of Applied Science

Institute of Biomaterials and Biomedical Engineering

University of Toronto

2013

Abstract

Delayed or impaired bone healing occurs in 5-10% of all fractures, yet cost effective

solutions to enhance the healing process are limited. Lithium, a current treatment for bipolar

disorder, is not clinically indicated for use in fracture management, but has been reported to

positively influence bone biology. The objective of this study was to identify lithium

administration parameters that maximize bone healing in a preclinical, rodent femur fracture

model. Using a three factor, two level, design of experiments (DOE) approach, bone healing

was assessed through mechanical testing and µCT-image analysis. Significant improvements

in healing were found at a low dose, later onset, longer duration treatment combination, with

onset identified as the most influential parameter. The positive results from this DOE

screening focuses the optimization phase towards further investigation of the onset

component of treatment, and forms a crucial foundation for future studies evaluating the role

of lithium in fracture healing.

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Acknowledgements

I would like to thank my supervisors, Dr. Cari Whyne and Dr. Diane Nam, for all their

support and guidance throughout my project. They were always available to help me with

every hurdle that I encountered. The success of this thesis would not have been possible

without their knowledge and experience. Thank you Dr. Nam for your clinical guidance, for

your help with my thesis defense preparation, and for making sure that I always focused on

the big clinical picture of our research. I would like to especially thank Dr. Whyne, who I

feel tremendously fortunate to have worked with over the last two years. The dedication she

exhibits towards her research, her students and her entire lab makes her an incredible mentor

and teacher.

I would also like to thank all my colleagues at the Orthopaedic Biomechanics Lab at

Sunnybrook whom I have had the opportunity to work with over the last two years and who

have contributed to my project. It was a pleasure getting to know all of you. You have made

my time in the lab an unforgettable experience and I wish everyone much success with your

future endeavors. I would like to make special mention of Dr. Margarete Akens for her help

with the animal work, and to Edwin Wong for all the countless hours we spent together in the

mechanical testing room.

I would like to thank my committee members, Dr. Benjamin Alman and Dr. Albert Yee,

whose knowledge and experience undoubtedly contributed to the success of my thesis. Their

insightful questions and innovative suggestions helped to guide my research as it progressed,

and I feel very fortunate to have had the opportunity to work with two talented and educated

surgeons.

I would also like to thank everyone in the animal facility at Sunnybrook who helped care for

my animals throughout my project. All your hard work in ensuring that this component of

my project was executed smoothly is greatly appreciated. I want to especially thank Yufa

Wang, whose assistance with all the animal work was absolutely crucial for the success of

my project. This project could not have been completed without his help. His knowledge

and experience helped to guide my project and his company will certainly be missed. I

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learned much from Yufa regarding animal research and ethics, animal surgery and care, and I

can even go as far to say that I now know many more words in Mandarin than I did when I

first started my Masters two years ago.

I would like to thank the Canadian Institute of Health Research and the Ontario Graduate

Scholarship for helping to fund this work.

I would also like to thank my friends and family who have been there to support me

throughout this Masters and throughout my entire life. To Mom, Dad and Alana: Thank you

for always believing in me and for teaching me the value of hard work and dedication. I feel

incredibly fortunate to have such an amazing family, and I am truly grateful for the amazing

opportunities you have provided for me, both personally and academically. Finally, I would

like to thank Kayla, my better half, who has always been there for me in everything I do.

Thank you for always supporting me and for encouraging me to always follow my dreams.

You are my world, and it means so much knowing that I have you by my side.

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Table of Contents

Chapter 1: Background and Literature Review.............................................................1

1.1 Motivating Problem ...................................................................................................1

1.2 Long Bones: Anatomy, Composition and Biomechanics ..........................................2

1.3 Fracture Patterns ........................................................................................................5

1.4 Physiology of Fracture Healing .................................................................................6

1.5 Biomechanics of Fracture Healing ............................................................................9

1.6 The Wnt Pathway and Fracture Healing..................................................................11

1.7 Lithium: Properties and History ..............................................................................13

1.8 Lithium and its Application to Fracture Healing .....................................................15

1.9 Previous Work .........................................................................................................17

1.9.1 Preclinical Work............................................................................................................ 18

1.9.2 Preliminary Clinical Work: Lithium and Fracture Risk................................................ 22

1.10 Design of Experiments...........................................................................................24

1.11 Study Rationale and Project Overview..................................................................27

1.12 Significance ...........................................................................................................28

Chapter 2: Research Objectives and Hypothesis..........................................................29

2.1 Overall Study Goal ..................................................................................................29

2.2 Overall Research Question ......................................................................................29

2.3 Overall Research Hypothesis...................................................................................29

2.4 Master's Research Objective....................................................................................29

2.5 Master’s Research Question ....................................................................................30

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2.6 Master’s Research Hypothesis.................................................................................30

2.7 Master’s Specific Aims............................................................................................30

Chapter 3: Materials and Methods ................................................................................31

3.1 Overall Experimental Design...................................................................................31

3.2 Phase 1 Screening ....................................................................................................37

3.2.1 Sample Size Calculations .............................................................................................. 38

3.3 Experimental Methodology .....................................................................................39

3.4 In Vivo Fracture Model ............................................................................................41

3.5 Evaluation of Lithium Treatment ............................................................................43

3.5.1 Biomechanical Testing.................................................................................................. 43

3.5.2 µCT Imaging and Stereological Analysis ..................................................................... 46

3.5.3 CT Based Torsional Rigidity ........................................................................................ 50

3.6 Data Analysis ...........................................................................................................53

3.6.1 Design of Experiments System Modeling..................................................................... 53

3.6.2 Differences Between Treatment Groups and Control Groups ...................................... 54

3.6.3 Correlation Analysis...................................................................................................... 54

Chapter 4: Pilot Work and Optimization of the Experimental Protocols..................55

4.1 In Vitro Pilot Work: Optimization of the Fracture Jig.............................................55

4.2 In Vivo Pilot Work: Modifications to the 28 Day In Vivo Cycle .............................61

4.2.1 Modifications to the Method of Lithium Administration ............................................. 61

4.2.2 Modifications to the Maximum Dosage Level.............................................................. 63

Chapter 5: Results ...........................................................................................................65

5.1 Destructive Torsional Mechanical Testing ..............................................................66

5.2 µCT Based 3D Bone Stereology..............................................................................70

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5.3 CT Based Torsional Rigidity ...................................................................................72

5.4 Design of Experiments System Modeling ...............................................................74

5.4.1 Primary Outcome Response: Maximum Yield Torque................................................. 77

5.5 Experimental Groups vs. Controls...........................................................................92

5.6 Correlation Analysis ................................................................................................94

5.7 Contralateral Limbs .................................................................................................95

Chapter 6: Discussion......................................................................................................98

6.1 Outcome Response Measures: Trends and Correlations .......................................102

6.2 DOE System Modeling: Results and Application to Fracture Healing .................108

6.2.1 Primary Outcome Response: Treatment Onset ........................................................... 110

6.2.2 Primary Outcome Response: Treatment Dose and Duration ...................................... 114

6.2.3 Pharmacokinetics and Pharmacodynamics ................................................................. 118

Chapter 7: Future Direction.........................................................................................123

7.1 Phases Two and Three of the Design of Experiments ...........................................123

7.2 Serum Lithium Analysis ........................................................................................125

7.3 Lithium and Impaired, Pathologic Bone Healing ..................................................126

7.4 Clinical Translation................................................................................................127

Chapter 8: Conclusion and Significance .....................................................................129

References.......................................................................................................................131

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List of Abbreviations

AC Adenyl Cyclase

ANOVA Analysis of Variance APC Adenomatous Polyposis Coli

ATP Adenosine Triphosphate β-Cat β Catenin

BMC Bone Mineral Content BMD Bone Mineral Density

BMP Bone Morphogenetic Protein BSA Body Surface Area

BV Bone Volume BV / TV Bone Volume over Total Volume (Bone Volume Fraction)

Ca2+ Calcium Ion cAMP Cyclic Adenosine Monophosphate

CCN1 / Cyr61 Cyclin 1 / Cysteine-Rich Protein 61 CK-1α Casein Kinase 1α

ColI Type 1 Collagen CREB Cyclic Adenosine Monophosphate Response Element Binding

Protein CT Computed Tomography

CTRA CT Based Torsional Rigidity DKK Dickkopf Related Protein

DOE Design of Experiments DV1 Dishevelled

E Young’s Modulus ELISA Enzyme Linked Immunosorbent Assay

EO Endochondral Ossification ERK / MAP Extracellular Signal Regulated Kinases / Mitogen Activated

Protein Kinases F- Fluorine Ion (Fluoride)

FDA US Food and Drug Administration

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G Shear Modulus g Grams

GJ Torsional Rigidity GJavg Average Torsional Rigidity

GJmin Minimum Torsional Rigidity GPa GigaPascals

GSK-3β Glycogen Synthase Kinase - 3β IO Intramembranous Ossification

J Polar Moment of Inertia kg Kilograms

kN Kilonewtons kV Kilovolts

Li Lithium Li+ Lithium Ion

Lbs Pounds LRP 5/6 Low Density Lipoprotein Related Protein 5/6

m Meter mEQ/L Milliequivalents per liter

mg Milligram Mg2+ Magnesium Ion

mgHA Milligrams of Hydroxyapatite mgHA / ccm Milligrams of Hydroxyapatite per Cubic Centimeter

mm Millimeter MPa MegaPascals

MPCs Mesenchymal Progenitor Cells mRNA Messenger Ribonucleic Acid

MSDS Material Safety Data Sheet MTS Materials Testing System

N Newton OH- Hydroxyl Ion

OFAT One Factor at a Time OPCs Osteochondral Progenitor Cells

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OPPG Osteoporosis-Pseudoglioma Syndrome OVX Ovariectomize

PI3K Phosphatidyl Inositol 3 Kinase PKA Protein Kinase A

PKB Protein Kinase B PKC Protein Kinase C

PMMA Polymethylmethacrylate PO4

3- Phosphate Ion

r2 Coefficient of Determination RANKL Receptor Activator for Nuclear Factor k B Ligand

ROI Region of Interest Runx2 Runt Related Transcription Factor 2

SFRP Secreted Frizzled Related Protein σult Ultimate Strength

T3 Triiodothyronine T4 Thyroxine

TCF / LEF T Cell Factor / Lymphoid Enhancer Factor TMD Tissue Mineral Density

TV Total Volume µA Microampere

µCT Microcomputed Topography µM Micrometer

UK United Kingdom WIF Wnt Inhibitory Factor

Wnt Wingless/Int family wt Weight

° Degrees Ø Diameter

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List of Tables

Chapter 1: Background and Literature Review

Table 1.1 - The four biomechanical stages of fracture repair .....................................................10

Table 1.2 - Coded matrix for the design of experiments analysis ..............................................26

Chapter 3: Materials and Methods

Table 3.1 - Lithium dosing, onset and duration parameter levels used in screening.................31

Table 3.2 - Screening stage treatment groups..............................................................................37

Chapter 4: Pilot Work and Optimization of the Experimental Protocols

Table 4.1 - Body surface area method for converting dosage levels between species..............64

Chapter 5: Results

Table 5.1 - The experimental and control groups used in the primary screening stage. ...........65

Table 5.2 - A summary of the mechanical testing data from phase one screening ...................67

Table 5.3 - A summary of the bone stereology data from phase one screening........................70

Table 5.4 - A summary of the CT based torsional rigidity data from phase one screening......72

Table 5.5 - A summary of the DOE modeling on each of the eleven outcome responses........75

Table 5.6 - ANOVA sum of squares chart from the DOE analysis ...........................................83

Table 5.7 - ANOVA table for the maximum yield torque output response...............................85

Table 5.8 - The 95% confidence intervals for the model equation coefficients ........................87

Table 5.9 - T-test comparing maximum yield torque between group ten and controls.............92

Table 5.10 - T-test comparing maximum yield torque between group five and controls .........93

Table 5.11 - T-test comparing maximum yield torque between late onset and controls...........94

Table 5.12 - A summary of the Pearson correlation analysis .....................................................94

Table 5.13 - A summary of the mechanical testing data for the contralateral limbs .................96

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Table 5.14 - A summary of the bone stereology data for the contralateral limbs......................96

Table 5.15 - A summary of the CT based torsional rigidity data for the contralateral limbs....96

Chapter 7: Future Direction

Table 7.1 - Body surface area method for converting dosage levels between species............127

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List of Figures


Figure 1.1 - The basic anatomy of a long bone .............................................................................3

Figure 1.2 - The four most common fracture patterns seen clinically..........................................5

Figure 1.3 - The three biological phases of fracture repair ...........................................................7

Figure 1.4 - The fracture callus.......................................................................................................8

Figure 1.5 - The Canonical Wnt/β-Catenin signaling pathway ..................................................11

Figure 1.6 - Lithium's mechanisms of action as it relates to GSK-3β ........................................16

Figure 1.7 - Lithium's interaction with the Canonical Wnt/β-Catenin signaling pathway........17

Figure 1.8 - Design of experiments ..............................................................................................25


Figure 3.1 - The complete three staged experimental study design ...........................................36

Figure 3.2 - Experimental methodology flow chart ....................................................................40

Figure 3.3 - Custom drop weight apparatus used to generate a closed femur fracture..............42

Figure 3.4 - Mechanical testing setup used for destructive torsional testing .............................44

Figure 3.5 - Graphical definitions of the mechanical testing parameters...................................45

Figure 3.6 - Definition of the region of interest used in the stereological analysis....................47

Figure 3.7 - Pre processing steps conducted prior to the stereological analysis. .......................47

Figure 3.8 - Examples of raw and segmented images used in the stereological analysis .........49

Figure 3.9 - Graphical representation of the CT-based torsional rigidity...................................52


Figure 4.1 - Unmodified fracture jig ............................................................................................57

Figure 4.2 - The modified fracture jig used in the current study ................................................58

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Figure 4.3 - Fracture patterns generated using the original jig ...................................................59

Figure 4.4 - Fracture patterns generated using the modified jig .................................................60

Chapter 5: Results

Figure 5.1 - A sample torque vs. twist angle plot from one of the femurs tested ......................66

Figure 5.2 - Average maximum yield torque for each experimental group...............................68

Figure 5.3 - A box and whisker plot outlining the variation in maximum yield torque............68

Figure 5.4 - Sample images from two bones after mechanical testing was complete...............69

Figure 5.5 - 3D isosurface models of three rat femurs used in phase one screening.................71

Figure 5.6 - Average minimum CT based torsional rigidity for each experimental group.......73

Figure 5.7 - A box and whisker plot for the minimum CT based torsional rigidity measure ...73

Figure 5.8 - Raw scatter plots for maximum yield torque vs. dose, onset and duration ...........78

Figure 5.9 - Scatter plot for maximum yield torque vs. dose, colored by duration ...................79

Figure 5.10 - Normal percent probability plot of the output residuals before transformation ..80

Figure 5.11 - The Box-Cox power transformation plot ..............................................................81

Figure 5.12 - Normal percent probability plot of the output residuals after transformation .....82

Figure 5.13 - Pareto chart showing the magnitude and direction of each input effect ..............84

Figure 5.14 - Predicted vs. actual values for the maximum yield torque output response........86

Figure 5.15 - Main effect plot for dose ........................................................................................88

Figure 5.16 - Main effect plot for onset .......................................................................................88

Figure 5.17 - Main effect plot for duration ..................................................................................89

Figure 5.18 - Two-factor interaction plot between dose and duration .......................................90

Figure 5.19 - The predicted design space for the maximum yield torque output response.......91

Figure 5.20 - Average maximum yield torque for the contralateral limbs.................................97

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Chapter 6: Dicussion

Figure 6.1 - Definition of an object’s torsional rigidity.............................................................108

Figure 6.2 - Fracture healing in the rodent animal model.........................................................113

Figure 6.3 - The various physiological targets of the GSK-3β enzyme...................................120


Figure 7.1 - Phase two optimization study design.....................................................................124

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List of Equations


Equation 1.1 - Formula for calculating a given effect from the coded design matrix ...............26


Equation 3.1 - Relationship between scanner output intensity and ash density.........................50

Equation 3.2 - Relationship between apparent density and shear modulus ...............................51

Equation 3.3 - Modulus weight centroid for each cross sectional slice......................................51


Equation 4.1 - Equation used to convert dosing level between two different species...............64

Chapter 5: Results

Equation 5.1 - The predictive model equation for the maximum yield torque design space....87


Equation 7.1 - Equation used to convert dosing level between two different species.............128

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1.1 Motivating Problem

Skeletal fractures continue to increase in incidence, affecting over 2% of Canadians per year.

Yet the progression of effective treatment options remains relatively static (Cluett, 2010).

Peak bone mass is reached between 20 and 25 years of age, and then begins to slowly

deteriorate, continuing for the duration of one’s life. Consequently, as a person ages, bone

strength progressively weakens and the accompanying risk of fracture grows. Moreover, age

related bone diseases, such as osteoporosis, weaken bone even further, contributing to an

even greater risk of fracture. Osteoporotic related fractures are more common than heart

attack, stroke and breast cancer combined, and are predicted to occur in one in three women

and one in five men (Osteoporosis Canada, 2011). As the baby boomer generation

continues to age, it is estimated that by the year 2030 the number of seniors living in Canada

will reach nearly 11 million, more than double the current census (Statistics Canada, 2010).

As the population continues to expand, the number of debilitating fractures will inevitably

keep growing.

Currently, the regenerative process of fracture repair is quite complex and, in most cases,

requires several weeks of immobilization and/or surgery to achieve adequate healing. In

addition to the undesired cost, invasiveness and healing duration associated with traditional

methods of treatment, the extent of functional disability and lost productivity associated with

the recovery period are substantial both to the individual and at societal levels (Osteoporosis

Canada, 2011). Musculoskeletal disease and injury represents the largest component of total

economic cost of illness in Canada, with over two billion dollars per year being spent on the

treatment and maintenance of osteoporosis induced fractures (Osteoporosis Canada, 2011).

Even still, delayed or impaired healing generally occurs in 5-10% of all cases (Hoeppner,

Secreto, & Westendorf, 2009), often causing further disability, which requires additional

intervention to help restore proper function and mobility. Collectively, the morbidity from

skeletal fractures places a tremendous burden on society, and this will continue to worsen as

years progress.

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As such, there is an evident need to develop effective options to augment traditional methods

of treatment for bone fractures. Although research in fracture healing has identified several

potential therapeutic targets, there has been minimal progress to date of fracture repair

solutions that are non-invasive, cost effective and have the ability to clinically accelerate the

healing process. A successful, inexpensive and non invasive, pharmacological approach to

enhance fracture repair could potentially decrease the overall healing duration, reduce the

incidence of mal and non union, diminish the need for surgery and restore earlier function

and mobility leading to improved patient outcomes.

1.2 Long Bones: Anatomy, Composition and Biomechanics

There are four main classifications of bone shape found in the human skeleton -long, short,

flat and irregular –, and the shape of a given bone is generally indicative of its physiological

function. Long bones, such as the femur, are important for mobility and stability and are

subject to the majority of loading during daily activities. Their hollow cylindrical design,

depicted in Figure 1.1 on the following page, leads to a lightweight structure with optimal

strength, ensuring that any applied load can be effectively dissipated (Marieb & Mallatt,

1992). This distinct morphology helps long bones effectively support most of the body’s

daily locomotive activity.

Long bones are comprised of two different types of bony constituents that are differentiated

based on porosity and microstructure. The outer, hard layer, known as compact/cortical bone

(≃ 5-10% porous), is composed of densely packed bone tissue and forms the protective

cortex responsible for bone’s smooth and white appearance (Martin, Burr, & Sharkey, 2004).

Cortical bone is found mainly in the diaphysis, the bone shaft, which surrounds the

medullary cavity, the site of storage for yellow bone marrow. The inner, spongy layer,

known as trabecular/cancellous bone (≃ 75-95% porous), consists of loosely packed,

interconnected bone segments that are surrounded by red bone marrow, the site of

hematopoesis (Martin, Burr, & Sharkey, 2004). Trabecular bone is found in the epiphysis,

the proximal and distal ends of bone, and is encased by a thin, cortical shell. Cortical bone,

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being denser and less porous than its trabecular counterpart, is consequently harder, stronger

and stiffer, and is the major contributor to bone’s overall strength.

Figure 1.1 - The basic anatomy of a long bone. The diaphysis is primarily composed of compact bone that surrounds the medullary canal, while the epiphysis consists of cancellous bone encased within a thin compact shell. Bone is highly vascularized, receiving a constant blood supply via capillaries, and is surrounded by lymph vessels that drain into the lymphatic system. Bone is encased by a protective membrane known as the periosteum and is covered by articular cartilage on its surfaces that comprise the joints.

Bone is composed of both organic and inorganic components, which ultimately contribute to

different aspects of its mechanical properties. The organic component, accounting for about

30% of total bone volume, is primarily type I collagen, connective tissue that contributes to

bone's post yield mechanical properties, including its ultimate strength and fracture

toughness. The organic phase provides bone with the ability to accommodate plastic

deformation past its yield point. The inorganic component, or bone mineral, which accounts

for around 45% of total bone volume, consists of hydroxyapatite mineral composed mainly

of calcium phosphate crystals [Ca5(PO4)3(OH)]. These crystals are tightly packed into highly

ordered patterns within the collagen network and contribute to bone's elastic mechanical

properties, including its yield strength and Young's Modulus (Viguet-Carrin, Garnero, &

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Delmas, 2006; Martin, Burr, & Sharkey, 2004). The inorganic phase primarily contributes to

bone's compressive and tensile strengths prior to the yield point. Investigators have shown

that denaturing the organic collagen network significantly alters bone's post yield properties,

particularly its ability to absorb plastic strain energy, without affecting its elastic stiffness

(Wang et al., 2001).

Bone is a composite, anisotropic, viscoelastic material whose material properties are

dependent on the direction and nature of loading. Bone is generally described as a

transversely isotropic material with different material properties in its longitudinal versus

transverse directions. Bone is strongest when loaded longitudinally, showing increased

Young’s Modulus (E) and ultimate strength (σult) compared to transverse loading. Through

extensive testing, Reilly and colleagues (1974) determined that bone has an E and σult of

approximately 18 GigaPascals (GPa) and 135 GPa longitudinally, compared to significantly

lower values of 10 GPa and 53 GPa in its transverse orientation. Moreover, bone exhibits

different material properties depending on the type of loading. Through their work, Reilly

and colleagues (1974) quantified the compressive, tensile and torsional ultimate strengths of

bone to be approximately 195 MegaPascals (MPa), 135 MPa and 70 MPa respectively. The

significantly lower torsional ultimate strength highlights the importance of torsional testing

as a biomechanical benchmark to assess bone strength.

The viscoelastic nature of bone implies that its mechanical properties are strain rate sensitive.

The higher the loading speed, the greater bone’s elastic modulus, strength and ductility, and

the more strain energy it is able to absorb prior to fracture (Keaveny, Morgan, & Yeh, 2004;

McGee, Qureshi, & Porter, 2004). Physiologically, however, the viscoelastic influence of

bone is less important, as this phenomenon is only appreciable at loading rates that exceed

the normal physiologic range. For the majority of daily activities that tend to occur within a

narrow range of loading rates (0.01 - 1.0% strain/second), the viscoelastic strengthening of

bone, although present, is assumed to be minor (Cristofolini et al., 2009; Keaveny, Morgan,

& Yeh, 2004). Collectively, these factors highlight the difficulty surrounding the accurate

quantification of bone’s mechanical properties, and emphasize the importance of

understanding the type and nature of loading in order to predict the associated response.

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1.3 Fracture Patterns

Fractures occur when bone is forced to absorb an excess in strain energy that subsequently

leads to a break in its structural continuity. While there are many different types of fractures

that can be generated, the distinct pattern created is dependent on multiple factors, including

the characteristics of the applied forces and torques, as well as the geometry and mechanical

properties (Young’s Modulus, ultimate tensile strength and fracture toughness) specific to the

bone under scrutiny. The four most common long bone fracture patterns that arise clinically

are transverse, oblique, spiral and comminuted (Figure 1.2).

Figure 1.2 - The four most common fracture patterns seen clinically. The type of pattern generated is dependent on a combination of internal and external factors such as the nature of the applied load as well as the geometry and mechanical properties specific to the bone.

Transverse fractures can be identified by a fracture line that lies perpendicular to the

diaphysis of the bone. This type of fracture most commonly arises from failure under

bending loads, which place one side of the bone under tension and the other side under

compression. The fracture is initiated on the convex face of the bending bone, the site of

maximum tension, and leads to uniform crack propagation throughout (McGee, Qureshi, &

Porter, 2004).

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Oblique fractures are categorized by a fracture line that extends at an angle of 30-45˚ through

a single plane with respect to the longitudinal axis of bone. The angled fracture pattern

usually results from a combination of loads that generate a shear stress along an oblique

plane of the diaphysis, initiating a crack and propagating the fracture (Pierce, Bertocci,

Vogeley, & Moreland, 2004).

Spiral fractures differ from oblique ones in that the fracture pattern traverses through

multiple planes obliquely around the bone rather than through one single plane. Spiral

fractures occur when bone is subject to torsional loading, which creates shear stresses in both

vertical and horizontal directions. The horizontal shear can be resolved into planar

components of tensile and compressive force. Since bone is weaker in tension than

compression, and the tensile and compressive components are maximal on 45˚ planes

relative to the maximal shear, spiral fractures characteristically propagate at 45˚ in the

direction of maximum tension. The spiral pattern is generated via simultaneous 45˚

propagations on each axial plane of the bone (McGee, Qureshi, & Porter, 2004).

A comminuted fracture is different from the first three patterns discussed in that it does not

create a clean, distinctive fracture line, but rather, results in multiple, unorganized and

dispersed bone fragments. This type of fracture generally occurs when trauma is excessive,

and is indicative of a direct, high magnitude blow to the bone (Pierce, Bertocci, Vogeley, &

Moreland, 2004).

1.4 Physiology of Fracture Healing

Following a traumatic fracture to bone, the body immediately begins a healing response in

order to regenerate bone union, and restore mechanical strength and structural stability to the

injury site. This regenerative process of fracture healing contains three distinct biological

stages. A schematic outlining the general progression can be found in Figure 1.3 on the

following page.

7

Figure 1.3 - The three biological phases of fracture repair. The first stage is the inflammatory stage during which the cells responsible for repair are activated. In the second stage, known as the proliferative/repair phase, the actual repair of the fracture occurs. Once the proliferative phase is complete, and bone union has been achieved, the bone’s original contour and shape are restored. This final stage is known as remodeling (Figure reproduced courtesy of Dr. Benjamin Alman's Laboratory, The Hospital for Sick Children, Toronto, Ontario).

In the primary inflammatory phase, the fracture site is immobilized and a hematoma forms

within the medullary cavity. Systemic blood vessels dilate, and cells characteristic of the

inflammatory response, such as growth factors, cytokines and leukocytes are activated and

migrate towards the injury site. Through intercellular signaling, these inflammatory cells

then recruit other, more specialized cells, specific to bone repair, such as mesenchymal

progenitor cells (MPCs), to migrate to the hematoma (Buckwalter, Einhorn, & Marsh, 2006;

Frost, 1989).

In the proliferative stage that follows, MPCs proliferate into osteochondral progenitor cells

(OPCs), which then differentiate into either chondrocytes- precursors for cartilage formation-

or osteoblasts- precursors for bone formation- to initiate fracture repair. The lineage of OPC

differentiation depends on the presence of stimuli in the surrounding environment, including

the degree of vascularisation and the influence of growth factor signaling. The proliferative

phase can progress via two different pathways - endochondral ossification (EO) or

intramembranous ossification (IO) –, which is dependent on the degree of fixation and the

8

type of bone being repaired (Marsell & Einhorn, 2011; Buckwalter, Einhorn, & Marsh,

2006).

EO generally dominates in cases of non rigid fixation, including those fractures stabilized

through intramedullary nailing. EO is primarily responsible for the repair of long bones,

such as the femur, and is characterized by rapid chondrocyte differentiation. In EO, a

hyaline cartilaginous template is formed first by the chondrocytes, which is then

progressively replaced by lamellar bone that is laid by the osteoblasts. This heterogeneous

combination of cartilage and bone, characteristic of EO proliferative healing, is known as the

fracture callus (Figure 1.4).

Figure 1.4 - Located within the medullary hematoma, the fracture callus progressively transforms from soft to hard as it re-establishes union between the initial bone fragments (Reichert, et al., 2009). This figure is reproduced with permission from Elsevier (see Appendix).

In the early proliferative stage of long bone healing, the callus is considered “soft”,

composed primarily of cartilage. As healing evolves, the callus transforms from “soft” to

“hard” as the outer bony region grows laterally and the interior cartilage is replaced with

newly developing bone. This process, which progressively stabilizes the fracture site,

continues until the fracture gap is bridged and a bony union is achieved between the two

initial fragments. As such, in EO, rapid chondrocyte differentiation is initially required to

9

lay the cartilaginous template, and only as healing progresses does osteoblast activity

become imperative, effectively transforming the initial template into lamellar bone.

IO, on the other hand, is responsible for the repair of flat bones, such as the skull, and occurs

in healing with increased fixation. IO is characterized by rapid and immediate osteoblast

differentiation. There is no cartilaginous template present during the repair phase, and as

such, bone union is achieved without a fracture callus being generated (Marsell & Einhorn,

2011; Buckwalter, Einhorn, & Marsh, 2006).

Long bones generally heal through a combination of EO and IO, although due to the poor

fixation that usually accompanies the fracture, EO typically dominates. The central region of

a long bone fracture achieves re-connectivity through callus mediated EO healing, while the

peripheral portions of the fracture, closer to the intact diaphysis, generally heal through IO.

Evidently, both chondrocytes and osteoblasts are essential to normal fracture repair, and

impaired development of either can lead to improper bone healing (Marsell & Einhorn, 2011;

Buckwalter, Einhorn, & Marsh, 2006).

Once the repair phase is complete, and bone connectivity has been achieved, the final stage

of remodelling occurs. Osteoblasts, the bone building cells, and osteoclasts, the bone

resorbing cells, work in unison to remove the damaged components of the fracture, while

restoring the bone’s mechanical strength, stability, original contour and structure

(Buckwalter, Einhorn, & Marsh, 2006; Frost, 1989).

1.5 Biomechanics of Fracture Healing

Traditionally, long bone fracture healing has been divided into four distinct biomechanical

stages. These stages were first introduced by White III and colleagues (1977) in their work

that employed destructive torsional testing to investigate the mechanical properties and

healing patterns of rabbit tibia fractures. Examining characteristics such as the maximum

torsional moment sustained, the location of failure, and the observed fracture pattern, the

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authors quantified four distinct, biomechanical phases of fracture repair. They are

summarized in Table 1.1 below.

Table 1.1 - The four biomechanical stages of fracture repair. This table is based on the work of White III, Panjabi, and Southwick (1977).

Stage Characteristics

Stage I Low stiffness, rubbery/elastic pattern Bone fails through the original fracture site only

Stage II High stiffness, hard-tissue pattern Bone fails through the original fracture site only

Stage III High stiffness, hard-tissue pattern Bone fails partially through the original fracture site and partially through intact bone

Stage IV High stiffness, hard-tissue pattern Bone fails through intact bone only

In their results, the authors emphasize two important transitions evident during the phases of

bone healing. The first transition, occurring between stages I and II, is when the fracture site

morphology changes from rubbery and elastic to hard tissue and rigid. During their

experimentation, this transition occurred between days 21 and 27 of bone healing, and

signified the initiation of callus transformation from soft to hard. The authors highlight this

as a significant checkpoint during bone healing because this feeling of high resistance

associated with fracture fixation and stabilization can be determined clinically through hands

on, physical assessment. The second transition, occurring between stages II and III, is when

mechanical testing causes failure through intact bone in addition to the original fracture site.

During their experimentation, this checkpoint occurred around day 49, and was the primary

sign that bone union had been recreated and mechanical properties had been more uniformly

re-established. While the timing of these transitions is likely different in other species, such

as humans, who exhibit different rates of bone healing, fracture healing ultimately still

proceeds through these four distinct stages. As such, even in humans, the correlation

between each phase and its associated biomechanical characteristics still exists, indicating

that bone stiffness and strength increases as the fracture callus progresses and bone union is

re-established.

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1.6 The Wnt Pathway and Fracture Healing

Molecular mechanisms that regulate skeletal tissue formation during embryological

development are known to be recapitulated during various physiological regenerative

processes in adulthood, such as fracture healing. The canonical Wnt/β-Catenin signaling

pathway, seen in Figure 1.5 below, is an important example of cellular signaling system

activated during fracture healing, with proper activity believed to be imperative for

successful bone repair.

Figure 1.5 - The Canonical Wnt/β-Catenin signaling pathway, a molecular mechanism activated during fracture repair that is believed to be critical for proper bone healing. (A) Depicts the result of the pathway when Wnt ligands are not present. In this situation, β-Catenin is destroyed by proteolysis and transcription is inhibited. (B) Highlights the outcome of the pathway when Wnt ligands are present, as is the case during normal fracture repair. In this situation, the Wnt ligands bind to Frizzled and LRP5/6, two G protein-coupled receptors specific to this pathway. Once these receptors are stimulated, a cascade of secondary messenger steps leads to the detachment and inactivation of the Wnt destruction complex (Axin/APC/GSK-3β/CK-1α). This ultimately frees β-Catenin, allowing it to trans-locate into the nucleus and bind to the TCF/LEF family of transcription factors to initiate transcription of Wnt target genes. Many of the Wnt target genes that are transcribed through this pathway are prerequisites for proper osteoblast differentiation. This figure is reproduced and adapted with permission from Springer (see Appendix).

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When functioning properly, as depicted in Figure 1.5B on the previous page, the Wnt

mechanism stimulates nuclear transcription of Wnt target genes. β-Catenin (β-cat) is a

crucial component of this pathway because it is the primary regulatory enzyme that

determines biochemical functionality. If active, its biological function is to bind to a group

of transcription factors of the T-Cell Factor / Lymphoid Enhancer Factor (TCF/LEF) family

in the nucleus and initiate transcription; if inactive, TCF/LEF binds to its nuclear co-

repressor Grouch and transcription is inhibited. A complete collection of discovered Wnt

target genes show many to be prerequisites for proper osteoblast differentiation and

metabolic activity, including runt-related transcription factor 2 (runx2) (Komori, 2010),

osteocalcin (Kahler & Westendorf, 2003), the receptor activator for nuclear factor k B ligand

(RANKL) (Spencer et al., 2006) and cyclin 1/cysteine-rich protein 61 (CCN1/Cyr61) (Si, et

al., 2006). In the context of fracture repair, stimulation of β-Catenin will initiate

transcription of Wnt genes and lead to osteoblast differentiation, which will actively

contribute to the repair process by promoting successful bone growth (Wu & Pan, 2010;

Secreto, Hoeppner, & Westendorf, 2009; Silkstone, Hong, & Alman, 2008). Osteoblasts are

imperative to long bone healing, as they are needed to successfully convert the fracture site

from its initial "soft" cartilaginous template to its final "hard" lamellar bone state.

The Wnt pathway is regulated by a destruction complex that is composed of a series of

enzymes including glycogen synthase kinase-3β (GSK-3β), tumour suppressor adenomatous

polyposis coli (APC), axin and casein kinase -1α (CK-1α). When the frizzled and low

density lipoprotein related protein 5/6 (LRP 5/6) surface co-receptors are not stimulated, and

the pathway remains inactive, β-Catenin is targeted for ubiquitination by the destruction

complex. CSK-1α phosphorylates β-Catenin at its serine 45 location, which primes β-

Catenin for subsequent phosphorylation by GSK-3β at its threonine 41 and serine 33 and 37

locations. Phosphorylation at serine 33 and 37 is recognized by β-transduction repeat

containing protein, which tags β-Catenin for proteolysis by proteosomal machinery 26S

(Valenta, Hausmann, & Basler, 2012). This leads to β-Catenin degradation and ultimate

downstream inhibition of nuclear transcription. However, when Wnt ligands are present, and

the pathway is activated, as is the case during normal fracture repair, dishevelled (Dv1)

becomes phosphorylated and recruits axin to its cytoplasmic tail. This disturbs the normal

regulatory activity of the destruction complex and inhibits the phosphorylation, and

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subsequent proteolysis, of β-Catenin. In this situation, β-Catenin remains in its de-

phosphorylated state, enabling it to accumulate in the cytoplasm and trans-locate into the

nucleus, where it binds to nuclear TCF/LEF to initiate transcription (Chen & Alman, 2009).

With the Wnt/β-Catenin pathway being implicated in bone regeneration and fracture repair,

research has explored therapeutic strategies to externally stimulate pathway activity and

harness its bone anabolic potential. There are various mechanisms by which the Wnt/β-

Catenin pathway can be stimulated, including promoting cell surface receptor activity,

blocking naturally occurring extracellular pathway antagonists, interfering with the

regulatory activity of the intracellular destruction complex and promoting the nuclear

binding of transcription factors β-Catenin and TCF/LEF. Collectively, stimulation of Wnt

signaling by any of these proposed mechanisms will enhance β-Catenin activity and lead to

increased transcription of Wnt implicated osteoblast precursor genes. If up regulated during

fracture repair, this mechanism of action should theoretically result in greater than normal

bone cell activity at the fracture callus. This suggests that bone healing should occur at a

faster rate, and should result in a more uniformly healed structure with increased strength and

stability (Wu & Pan, 2010; Secreto, Hoeppner, & Westendorf, 2009; Silkstone, Hong, &

Alman, 2008).

1.7 Lithium: Properties and History

Lithium (Li) is a soft, silver white alkaline metal that belongs to group one of the Periodic

Table of Elements. It has an atomic number of three, and consists of three protons and three

electrons in its neutral state. Lithium has a standard atomic mass of 6.941 AMU due to the

existence of several naturally occurring stable isotopes: 6Li, with three neutrons, is found in

roughly 7.5% abundance, and 7Li, with four neutrons, is found in approximately 92.5%

abundance. Similar to other alkaline metals, lithium has only one valence electron, which it

readily gives up to become a Li+ cation eager to form ionic bonds. Due to its small atomic

radius and willingness to give up this lone valence electron, lithium is a prominent conductor

of heat and electricity, and is a highly reactive element.

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Lithium was discovered as a chemical element by Swedish chemist Johan August Arfvedson

in 1817. Its name, derived from the Greek word lithos, meaning stone, was given to reflect

the fact that it was first found as a solid mineral comprising part of petalite ore. Petalite was

discovered earlier in the 18th century by Brazilian scientist Jose Bonifacio de Andrada,

however, at the time of its discovery, its exact composition was unknown. Years later,

Arfvedson was the first to confirm that lithium comprised part of the petalite mineral, a

compound now known to have the chemical formula LiAl(Si2O5)2. Although Arfvedson is

credited with the discovery of lithium, William Thomas Brande was the first person able to

successfully isolate elemental lithium, when, in 1821, he used the technique of electrolysis to

separate lithium oxide into its constituents (Winter, 2012).

Today lithium can be found in a wide range of applications. Lithium oxide is commonly

used as a flux for processing silica, and helps provide ceramics and glasses with optimal

properties and aesthetic glazes. Furthermore, due to its high electrochemical potential,

lithium has become an important anodic material, and lithium ion batteries are commonly

used for electrical applications. Moreover, lithium is used to manufacture all purpose,

lubricating greases that are frequently employed in high temperature, industrial applications

(Jaskula, 2012).

In addition to several of its major applications outlined above, lithium is also widely used in

the medical industry, with “lithium pharmacology” being a specific branch of therapy that

refers to the use of the lithium cation (Li+) as a drug. Lithium’s first appearance in medicine

was in 1847 where it was utilized as a treatment for gout, after English scientist Alfred

Baring Garrod discovered that it could dissolve excessive uric acid from the kidneys

(Shorter, 2009). Its role as a potential treatment for gout, however, was generally

unsuccessful and short-lived, and by the late 1930s, most of the products introduced on the

market for this purpose were removed. Today, lithium is better recognized for its role in

treating mental illness. Its entrance into mainstream, psychiatric medicine began in Australia

in 1949, when Dr. John Cade hypothesized that uric acid imbalance may be linked to a range

of psychotic disorders, and successfully treated ten of his manic patients with lithium citrate

and lithium carbonate supplements (Shorter, 2009). Building upon Cade's discovery, in 1967

Baastrup and Schou demonstrated the first systematic clinical evidence for lithium's use in

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psychotropic medicine through a non blinded trial; three years later, Baastrup and colleagues

confirmed previous findings in a randomized, double blind discontinuation trial (Marmol,

2008). Since then, lithium has become an integral pharmacological treatment for a wide

range of psychological disorders. It was clinically approved by the Food and Drug

Administration (FDA) in 1974 for treatment of bipolar disorder, and is still widely

recognized as the gold standard for this application (Martinsson, et al., 2013; Hirschowitz,

Kolevzon, & Garakani, 2010; Marmol, 2008). It is also used as a first line mono therapy for

acute mania, a prophylaxis for depression and a protective agent against suicidal behaviour

(Malhi et al., 2012). However, further advancements in the understanding of lithium’s

mechanism of action and pharmacodynamic activity within the body has hinted towards a

novel application for its use in modern medicine. Recently identified as a Wnt pathway

stimulator, lithium therapy is now believed to have anabolic effects on bone biology, and is

currently being explored as a potential treatment to enhance fracture healing.

1.8 Lithium and its Application to Fracture Healing

Lithium interacts with the Wnt/β-Catenin signaling pathway in a manner that makes it an

appealing therapeutic strategy to stimulate pathway activity. Mechanistically, lithium is a

well-characterized, reversible, competitive inhibitor of GSK-3β, competing with the

magnesium ion (Mg2+) at the GSK active site (Livingstone & Rampes, 2006; Meijer,

Flajolet, & Greengard, 2004; Doble & Woodgett, 2003; Jope, 2003; Stambolic, Ruel, &

Woodgett, 1996). Moreover, in addition to being a direct competitive inhibitor of GSK-3β,

lithium also indirectly inhibits GSK-3β activity by stimulating several other cell signaling

pathways, including the cyclic adenosine monophosphate / protein kinase A (cAMP/PKA)

pathway and phosphatidyl inositol / protein kinase B / protein kinase C (PI3K/PKB/PKC)

pathways, which collectively lead to the inhibitory phosphorylation of GSK-3β at its serine 9

location (Quiroz et al., 2010; Sarno, Li, & Jope, 2002). GSK-3β, as previously mentioned, is

one of the major enzymes comprising the destruction complex of the Wnt/β-Catenin

signaling system. As such, with its ability to both directly and indirectly inhibit GSK-3β

(Figure 1.6), lithium can interfere with GSK-3β's ability to phosphorylate β-Catenin at its

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threonine 41 and serine 33 and 37 target locations. This ultimately inhibits the proteolysis of

β-Catenin, promoting its translocation into the nucleus where it binds to its transcription

factor (TCF/LEF) to initiate transcription. This sequence will result in increased

transcription of Wnt target genes and, in the context of bone healing, should result in

increased activity of the bone building osteoblasts at the fracture callus. This should

theoretically increase the rate at which EO progresses, and long bones heal, as increased

osteoblast activity will lead to quicker bone formation and more efficient "soft cartilage" to

"hard bone" turnover at the site of the fracture callus (Figure 1.7). This mechanism of action,

ideal for bone healing, renders lithium therapy as an attractive, non invasive intervention to

enhance fracture repair.

Figure 1.6 - Lithium's mechanisms of action as it relates to GSK-3β. Lithium has the ability to both directly and indirectly inhibit GSK-3β activity, making it an appealing therapeutic strategy to stimulate Wnt/β-Catenin signaling. Direct inhibition occurs via competition with Mg2+ at the GSK-3β active site. Indirect inhibition occurs via serine 9 phosphorylation at the GSK-3β N-terminus.

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Figure 1.7 - When lithium inhibits GSK-3β , β-Catenin is stimulated and trans-locates into the nucleus where it promotes transcription of Wnt target genes. This leads to increased osteoblast differentiation, proliferation and survival, ultimately contributing to enhanced bone formation. This figure is reproduced and adapted with permission from Springer (see Appendix).

1.9 Previous Work

While lithium has played a significant role in mainstream, psychiatric medicine for the past

40 years, its application to bone biology and fracture healing is a fairly novel concept. Since

its discovery as a GSK-3β inhibitor in the 1980s, many investigators have explored potential

applications between lithium therapy, Wnt/β-Catenin signaling and bone biology.

Collectively, these studies have provided important insight into lithium’s potential as an

anabolic bone agent to enhance fracture healing, and have laid the foundation for future work

in this area. Many of these studies, both preclinical and clinical, are expanded upon below.

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1.9.1 Preclinical Work

Therapeutic strategies exploring the Wnt/β-Catenin pathway through signal modulation have

shown to influence fracture repair and stimulate bone growth. In one study, Komatsu et al.

(2010) demonstrated that LRP 5 receptor knockout mice displayed impaired fracture repair,

as evident by reduced callus area, decreased bone mineral density (BMD) and weaker

biomechanical properties compared to their wild type counterparts. Since LRP 5 is a major

G- protein coupled receptor of the Wnt/β-Catenin pathway, the authors concluded that

Wnt/β-Catenin signaling is crucial to bone growth and fracture repair, with activation

enhancing repair and inactivation impeding it. Various other studies have reported finding

an up regulation of Wnt pathway related components at the site of the fracture callus (Chen,

et al., 2007; Zhong et al., 2006; Hadjiargyrou, et al., 2002) further supporting the conclusion

that the Wnt pathway plays an active role during bone repair. In another study, Kulkarni and

colleagues (2007) demonstrated that daily administration of a known GSK-3β inhibitor

(#603281-31-8) increased bone formation and restored bone volume in ovariectomized,

osteopenic rats. From their results, the investigators concluded that Wnt pathway modulation

through GSK-3β inhibition has an anabolic effect on cells of mesenchymal origin, such as

osteoblast and chondrocytes, and that this is a potential therapeutic target for bone healing.

The theoretical relationship between lithium, GSK-3β inhibition and Wnt/β-Catenin

signaling has been confirmed in several studies that have all commonly reported a positive

connection between lithium administration and bone formation. A recent study by Warden

and colleagues (2010) investigated the effects that various psychotropic drugs have on the

skeleton. The results from this study elucidated the anabolic effect that lithium treatment has

on bone biology, as treated mice displayed a significant increase in BMD and bone formation

compared to healthy, untreated controls. The authors attributed their findings to the

inhibitory activity that lithium has on GSK-3β and the subsequent stimulation that this has on

Wnt/β-Catenin pathway signaling. Correspondingly, Clément-Lacroix et al. reported similar

findings in their 2005 study, detailing how lithium chloride treatment restored bone volume,

bone mass, trabecular thickness and osteoblast number in two different strains of

ovariectomized, osteoporotic mice. Additionally, Meng and co investigators (2010)

described the protective effects that lithium chloride treatment had on bone loss in a hindlimb

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unloading rat model. The hindlimb unloading model is a well documented technique known

to induce skeletal muscle atrophy and regional bone loss; it is primarily used to investigate

physiological responses to a microgravity environment, such as those experienced during

spaceflight (Carvalho, Louzada, & Riso, 2007; Valentin et al., 2006; Morey-Holton et al.,

2005). In their study, Meng et al. reported an increase in BMD, trabecular related

histomorphometric indices, elastic modulus and β-Catenin expression in lithium treated

hindlimb unloading rats compared to hindlimb untreated controls, findings which they

attributed to lithium’s stimulation of the Wnt/β-Catenin pathway through GSK-3β inhibition.

Several studies have also investigated the effect that lithium has on bone cell activity, bone

turnover and bone metabolism. Spencer and colleagues (2005) investigated the effects of

treating mice cells with lithium chloride in vitro. Results showed that cells exposed to

lithium chloride exhibited elevated levels of nuclear β-Catenin and displayed increased

TCF/LEF mediated transcriptional activity compared to untreated controls. In addition,

marker gene assays illustrated that treatment of cells with lithium chloride increased

expression of Alkaline Phosphatase (a marker for immature osteoblasts) and ColI (a marker

for mature osteoblasts), and reduced mRNA expression of the Wnt target gene RANKL (a

marker for mature osteoclasts). Collectively, the authors concluded that lithium chloride

effectively modulates Wnt/β-Catenin signaling and influences bone cell metabolism by

promoting osteogenesis and inhibiting osteoclastogenesis. Similar observations are reported

in earlier published work, which also suggests that lithium therapy likely interferes with the

regulatory activity of bone cells. Broulik et al. (1984) found increased levels of alkaline

phosphatase in the serum of lithium treated patients compared to untreated controls, with

66% of lithium treated subjects displaying alkaline phosphatase activity well above the

normal therapeutic range. Since alkaline phosphatase is a hydrolytic enzyme secreted by

osteoblasts, and is a well documented biochemical marker of bone formation (Seibel, 2005;

Christenson, 1997), the authors concluded that lithium therapy stimulates bone cell activity,

leading to improved bone formation. Furthermore, Zaidi et al. showed in their 1989 and

1990 studies that lithium therapy in rats had the ability to augment regular osteoblastic

activity, as well as inhibit calcitonin mediated action on the osteoclasts. Finally, Pepersack

and colleagues (1994) illustrated that lithium treatment inhibited 1,25-dihydroxyvitamin D

mediated bone resorption in both human bone marrow cultures and foetal rat long bones.

20

Collectively, these studies strongly suggest that lithium influences bone metabolism at the

cellular level, possibly by creating an imbalance in bone turnover equilibrium.

There have also been several studies that have investigated the effect of lithium on bone

matrix. It is well known that many ions can substitute for the calcium (Ca2+), phosphate

(PO43-) and hydroxyl (OH-) ions of hydroxyapatite, and incorporate themselves into the

crystal lattice. For example, the fluorine ion, fluoride (F-), can substitute for the hydroxyl ion

in hydroxyapatite, generating fluorapatite, a modified crystal lattice structure with increased

strength and stability (Wei, Evans, Bostrom, & Grondahl, 2003; Jones, 2001). Early

literature suggests that lithium may have a comparable effect on bone matrix, possibly

substituting for the calcium ion in the hydroxyapatite lattice. Birch first found in his 1974

study that lithium accumulated in both rat and human bones after oral administration. This

finding complemented a previous study by this investigator (Birch & Jenner, 1973), which

showed that lithium treatment decreased bone calcium levels in rats. Later, Mayer et al.

(1986) showed that the lithium ion could substitute for calcium in a synthetic carbonated

hydroxyapatite; since then, other researchers have determined that incorporating lithium at

optimal levels into hydroxyapatite ceramics improves the microstructure and micro-hardness

of the compound (Shainberg, et al., 2012; Fanovich, Castro, & Porto Lopez, 1998). In

addition to the potential incorporation of lithium into the hydroxyapatite lattice through

substitution for calcium, it may also be possible that, due to its small ionic radius, lithium

could incorporate into the lattice as a point defect within the vacant interstitial spaces.

Several dental researchers have reported finding lithium present in teeth enamel

(Schamschula et al., 1978; Curzon & Losee, 1977; Brudevold et al., 1975), with one study

suggesting that lithium may even have a protective effect against dental caries (Schamschula

et al., 1981). The main inorganic mineral in dental enamel is hydroxyapatite (Mihu, Dudea,

Melincovici, & Bianca, 2008; Staines, Robinson, & Hood, 1981) - the same as that found in

bone-, which lends additional support to the possibility that lithium can biologically

substitute into the hydroxyapatite structure, although no definite mechanism has been

confirmed. While far from conclusive, these works seem to suggest that lithium could

become incorporated within the hydroxyapatite crystal lattice, either through calcium ion

substitution or as an interstitial point defect, and, at optimal levels, may potentially have a

positive influence by improving the mechanical properties of bone tissue.

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Based on the literature, which strongly suggests that lithium has an anabolic influence on

bone biology, a United States Patent Application was recently filed in December 2012 (US

Patent #0315310 A1) for a bone tissue implant coated with lithium ions (Hansson &

Petersson, 2012). In their document, the inventors reference many studies to support their

claim that lithium therapy enhances bone formation by stimulating osteoblast differentiation

via Wnt/β-Catenin activation. Based on related research, the inventors speculate that coating

a bone implant with lithium ions will result in increased local bone generation and will lead

to improved osteointegration between the implant and surrounding bone tissue. They see this

new device as having widespread impact on clinical care, creating a mechanically stronger

bond at the bone-implant interface, leading to more effective implant loading and improved

patient mobility. Although, to date, this novel implant has only been tested in a preclinical

rabbit model, this patent, nonetheless, may potentially represent a big step towards the

eventual integration of lithium into orthopaedic related clinical applications.

Finally, while there has been a lot of work done in vitro to try and understand lithium’s

influence on bone biology, little has been conducted in vivo to see how these principles

translate to living applications. A study by Chen and co workers (2007) marks one of the

first published works by investigators attempting to bridge the “translational gap” and

experimentally address the question of whether lithium treatment can be used as an anabolic

agent to enhance fracture repair in a living subject. In their paper entitled “Beta-Catenin

Signaling Plays a Disparate Role in Different Phases of Fracture Repair: Implications for

Therapy to Improve Bone Healing”, the authors administered lithium treatment to both wild

type and β-Catenin knockout mice, either before or after generating a tibia fracture, and

assessed lithium’s role in the healing process. Among other findings, results demonstrated

that lithium administration increased bone density, bone volume and bone healing in mice,

but only when treatment was given post fracture and the mice had the β-Catenin gene. If

lithium was given prior to fracture generation it was detrimental to the healing process; if

lithium was given to β-Catenin knockout mice, it had minimal affect on healing. Not only

was this study one of the first to concretely test lithium’s ability to enhance bone healing in a

preclinical animal model, but its discussion also presented two critical findings surrounding

lithium’s therapeutic potential as a treatment for fracture healing. First, this study confirmed

that lithium’s mechanism of action is through the Wnt/ β-Catenin pathway, and that

22

activation of this pathway is critical to enhancing bone repair. Second, and most important,

this study illustrated that lithium’s potential as an anabolic agent to enhance fracture healing

is likely temporal, and as such, determination of its ideal therapeutic window is key to

optimizing its benefits for this promising application.

1.9.2 Preliminary Clinical Work: Lithium and Fracture Risk

To date, there have been no clinical studies exploring lithium’s ability to enhance bone

healing in a human fracture patient. One pilot study launched in July 2010 at the University

of Maryland (Streeten & Ramirez, 2010) is currently investigating the use of lithium to treat

patients who have osteoporosis-pseudoglioma syndrome (OPPG). OPPG is an autosomal

recessive genetic disease caused from mutations in the LRP 5 gene of the Wnt/β-Catenin

pathway, which leads to blindness and fragile and brittle bones from birth (Gong, et al.,

2001). Preclinically, lithium treatment was able to restore bone mass and bone strength in a

mouse model with a genetically induced OPPG phenotype (Clément-Lacroix, et al., 2005).

As such, the investigators are hopeful that similar trends will surface in this study, although

results have not yet been released.

Interestingly, a report published in the 2008 edition of the Journal of Medical Case Reports

presented the case of a 40 year old woman, taking lithium carbonate for severe bipolar

disorder, who suffered an oblique, mid-shaft fracture of the right tibia at 34 weeks gestational

age (Ahmad, Kuhanendran, Kamade, & Charalambides, 2008). Since the woman was

pregnant, clinicians opted to wait until post-partum to surgically stabilize the fracture. Four

weeks later, after the baby was born, and prior to planned surgical stabilization, radiographs

indicated clinical union of the woman’s tibia, with significant callus bridging of all four

cortices. The authors proposed that the accelerated healing response (less than half the time

expected for tibia shaft fracture union) was likely due to an increase in hormones, especially

oestrogens, that accompany the third trimester of pregnancy; they make no mention of the

fact that the patient was on lithium treatment throughout the duration of bone healing. Given

the ample evidence relating lithium, Wnt/β-Catenin signaling and bone anabolism, it is very

23

possible that the lithium therapy also contributed to the accelerated healing response seen in

this patient.

Several preliminary, clinical reports have highlighted a positive relationship between lithium

usage, increased bone strength and reduced fracture risk amongst psychiatric patients.

Vestergaard et al. (2005) explored the effects of lithium usage in the Danish population,

reporting a decreased fracture risk amongst lithium users for Colles, spine and hip fractures.

Moreover, the authors found that the risk for both Colles and spine fractures was further

reduced with increasing accumulated dosage of lithium, although this was not the case for

hip fractures. In a more recent report, Witling and colleagues (2007) investigated the

relationship between lithium usage and fracture risk amongst United Kingdom (UK)

residents by analyzing information from the UK General Practice Research Database.

Similar to the trend identified by Vestergaard and colleagues, this study also reported a

decreased fracture risk amongst lithium users. The authors found lithium’s protection to be

the greatest amongst current users; past users were identified as having a higher risk for

fracture, displaying an increasingly worse correlation with time since discontinuation. In a

third report presented by Bolton et al. (2008), the authors used data from the Manitoba

Department of Health and found a statistically significant relationship between lithium usage

and a lower fracture risk in subjects over the age of 50. Recently, Zamani et al. (2009) used

dual X-ray absorptiometry to assess bone mineral density amongst 150 people in the Iranian

population and found a 4.5-7.5% increase in bone mineral density at the spine, femoral neck

and trochanter in lithium users compared to healthy, matched controls. These results support

an earlier study by Nordenstrom et al. (1994) who found an increase in the bone mineral

density of the lumbar spine and femoral neck in long term lithium treated patients compared

to matched, untreated controls. Finally, in a recent report evaluating changes in bone mineral

density amongst post menopausal women using psychotropic medication, Bolton and

colleagues (2011) demonstrated a trend among lithium users towards lower risk of clinically

indicated osteoporotic bone mineral density. This finding is consistent with the work of

Cohen and colleagues (1998) who report that lithium therapy does not present as a risk factor

for osteoporosis.

24

While these five initial reports seem to provide support for lithium’s protective affect against

skeletal fractures, the evidence presented is far from conclusive. Serum lithium

concentrations were never calculated in any of the study subjects, and lithium exposure was

estimated based on the number of prescriptions purchased alone. This fact, coupled with

various other confounding variables across study subjects -including severity of mental

disorder, type, location and severity of fracture, variation in gender, height and weight and

polypharmacy- make it difficult to draw significant conclusions from these works.

Nonetheless, these studies all provide suggestive evidence for lithium’s anabolic properties

and protective influence on the skeleton, and advocate for future work in this direction.

1.10 Design of Experiments

Design of experiments (DOE) is a well established, robust technique that is used to

investigate the effects and interactions of multiple input factors in a system, and their

ultimate influence on producing an optimal response (Figure 1.8). It is especially useful for

study designs where parameter selection and optimization is the ultimate goal. DOE uses an

experimental setup that incorporates the analysis of variance (ANOVA) technique to

investigate how variations in system inputs ultimately affects system outputs. Generally, a

single primary output is established so that the system can be optimized to meet this pre-

determined design goal. DOE, and its associated ANOVA approach, was first pioneered in

the early 1900s by Sir Ronald Alymer Fisher for use in agricultural design situations

(Anderson & Whitcomb, 2007). However, given its very broad and easily repeatable

approach, DOE has since found a wide range of applications in the natural/social sciences

and engineering domains.

25

Figure 1.8 - In a design of experiment approach, system inputs are varied and the resultant output response is recorded. This type of experimental setup helps the researcher understand how variations in inputs affect the system outputs. Collectively, this approach can be used to determine an optimal design point for a given system.

Traditionally a one factor at a time (OFAT) approach has been implemented in biological,

preclinical study designs, whereby each factor is varied independently while all others are

kept fixed. OFAT approaches have several limitations when compared to their DOE

counterparts. First, because each factor is varied independently, OFAT approaches require a

larger number of samples and more experimental runs in order to achieve adequate statistical

power. With larger sample sizes and more required runs, OFAT designs necessitate more

time, resources and money in order to be completed. Second, because input factors are

varied independently, OFAT approaches are unable to investigate interactions that may arise

between factors. This can be very problematic because, in a study design aimed at

determining the optimal design point, OFAT approaches may actually miss the individual

input combinations that correspond to this point of optimization. DOE approaches address

many of these limitations associated with OFAT designs by allowing the experimenter to test

many factors simultaneously. Simultaneous factor comparison generates a larger inductive

basis, allowing for more precise estimations and predictions of the responses, more accurate

inferences on process variations, and better overall experimental efficiency (Anderson &

Whitcomb, 2007).

26

DOE analysis uses a coded matrix that shows whether main effects and interactions are at

high or low design levels. Interaction levels for each run are determined by multiplying the

levels of the respective parent terms for that specific run. A given main effect or factor

interaction is then quantified as the difference of average high (+1) responses to average low

(-1) responses on the output variable under investigation. Table 1.2 outlines a hypothetical

three factor, two level design, showing the coded main effects and factor interactions on a

given response R.

Table 1.2 – A complete coded matrix for a three factor- two level design, showing all main effects and interaction effects on a given response, R.

Run Main Effects Interaction Effects Response # A B C AB AC BC ABC R 1 -1 -1 -1 1 1 1 -1 R1 2 1 -1 -1 -1 -1 1 1 R2 3 -1 1 -1 -1 1 -1 1 R3 4 1 1 -1 1 -1 -1 -1 R4 5 -1 -1 1 1 -1 -1 1 R5 6 1 -1 1 -1 1 -1 -1 R6 7 -1 1 1 -1 -1 1 -1 R7 8 1 1 1 1 1 1 1 R8

Effect EA EB EC EAB EAC EBC EABC RAVG

Equation 1.1 - Formula for calculating a given effect from the coded design matrix.

Main Effect A = (Average [R2;R4;R6;R8]) – (Average [R1;R3;R5;R7])

A given effect is calculated using Equation 1.1 shown above. Main effect A, for example,

would be quantified as the difference of average responses from runs 2,4,6,8 (high/+ levels)

and average responses from runs 1,3,5,7 (low/- levels). Once all effects are quantified, the

ANOVA technique is then used to determine which main effect and interaction terms

significantly contribute to the system model.

The DOE approach is generally uncommon in biological literature, although it has been

successfully implemented in several biological studies pertaining to microarray protocol

optimization (Wrobel et al., 2003; Wildsmith et al., 2001), parameter selection for biological

27

assays (Coffey, Grevenkamp, Wilson, & Hu, 2013; Lutz, et al., 1996), and factor

characterization in systems biology (Liepe, Filippi, Komorowski, & Stumpf, 2013 ; Kreutz &

Timmer, 2009). To date, however, there have been no studies documented in the literature

examining the application of the DOE approach in an in vivo, preclinical, translational drug

study, as proposed in this work, to investigate treatment parameters, evaluate treatment

effects and explore optimized treatment regiments. As such, this study represents a novel

application for the use of design of experiments in preclinical, biological oriented research.

1.11 Study Rationale and Project Overview

With lithium studies producing promising results, there appears to be a role for the

application of this inexpensive and highly accessible pharmacological agent in enhancing

fracture repair. However, research to date is still lacking with respect to the administration

parameters of treatment dose, onset and duration that will optimize the potential benefits of

lithium on bone healing. Therefore, as a first step, a preclinical study is required to outline

and quantify the exact benefits of lithium on fracture healing. A three factor, three staged,

design of experiments approach will be used to evaluate the effects and interactions that

varying lithium treatment dosage, onset and duration has on femoral fracture healing in a rat

preclinical model. This will provide a systematic, engineering based approach for

determining optimal lithium administration parameters that enhance the quality of bone

healing. The evaluation of lithium as an effective fracture healing agent requires accurate

definition of these parameters before it can be studied further clinically, and hopefully

integrated within clinical practice.

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1.12 Significance

This study addresses current limitations in fracture healing through evaluation of a cost

effective, highly accessible and clinically promising solution. Previous work has confirmed

the positive anabolic effect that lithium has on Wnt/β-Catenin pathway signaling and

subsequent bone formation. Several pre clinical studies have shown that lithium

administration effectively induces bone growth in rodents, and many case-control

epidemiological studies report that patients taking lithium to manage their psychotic ailments

possess stronger bones with a reduced fracture risk. Thus, there is significant evidence

suggestive for the potential of using lithium as a treatment option for fracture healing.

However, before lithium can be studied in a clinical scenario, further work is required to

define the precise administration parameters of treatment dose, onset and duration that

optimally enhance the quality of bone healing. Therefore, this study represents an essential

preclinical step needed to properly assess lithium's role as a fracture healing agent. By

proper characterization of the effects of lithium on the structure and function of healing bone,

this study will form a foundation towards future translational studies focused on the potential

of lithium to enhance fracture healing and improve patient care.

29

Chapter 2: Research Objectives and Hypothesis

2.1 Overall Study Goal

The overall goal of the proposed research is to evaluate lithium’s role as a fracture healing

agent by investigating how variation of treatment parameters affects measures of bone

strength and stereology.

2.2 Overall Research Question

Can lithium administration post fracture be optimized to enhance the quality of bone

healing?

2.3 Overall Research Hypothesis

Lithium administration post fracture can be optimized to enhance the quality of bone healing.

2.4 Master's Research Objective

The objective of this Master’s thesis is to complete the initial screening phase of the overall

research study. This is the first of a three phased experimental design collectively aimed at

determining optimal administration parameters of lithium dosage, onset and duration that

enhance the quality of bone healing. Phase one screening is a three-factor, two level,

parametric analysis that investigates how variations in, and interactions amongst, the three

lithium treatment parameters affects the quality of bone healing.

30

30

2.5 Master’s Research Question

Which lithium treatment administration parameter (dose, onset or duration) has the most

prominent affect on enhancing the quality of bone healing?

2.6 Master’s Research Hypothesis

It is hypothesized that the initial screening phase will show lithium dosage as the most

critical parameter affecting the quality of fracture healing, followed by duration and onset.

2.7 Master’s Specific Aims

The proposed research aims to validate the ability of lithium treatment to enhance the quality

of fracture healing by determining optimal administration parameters of treatment dose,

onset and duration that maximize the study primary outcome measure in a preclinical rat

femoral fracture model. Using a DOE approach, quality of bone healing will be assessed

through evaluation of the biomechanical and structural characteristics of the healing fracture

callus. Eleven different outcome measures will be quantified:

A) Primary outcome measure:

a. Biomechanical strength of bone healing (maximum yield torque), as determined through destructive torsional mechanical testing

B) Secondary outcome measures:

a. Additional mechanical properties of the fracture callus (experimental torsional stiffness; twist angle at failure), as determined through destructive torsional mechanical testing

b. Micro-structural properties of the fracture callus (bone volume; total volume; bone volume fraction; average bone mineral density; average tissue mineral density; average bone mineral content), as determined through µCT-image based 3D bone stereological analysis

c. CT-based torsional rigidity of the fracture callus (minimum; average), as determined through µCT-image based techniques

31


3.1 Overall Experimental Design

Optimal lithium treatment parameters of administration dose, onset and duration will be

investigated using a methodological setup that combines a three factor design of experiments

approach and a response surface analysis. The experimental setup, depicted in Figure 3.1,

entails three distinct phases- screening, optimization and verification - that collectively study

the effects and interactions that varying lithium administration parameters has on study

outcome measures. Biomechanical strength of bone healing quantified via experimental,

mechanical testing will be used as the primary study outcome measure; this is the current

gold standard used to assess the quality of fracture healing in terms of the healing bone’s

ability to regain mechanical strength and bear load (Weis, Miga, Granero-Molto, & Spagnoli,

2010). Secondary outcome responses will include additional measures obtained through

mechanical testing, as well as pertinent parameters obtained through µCT-based 3D bone

stereology and µCT-based torsional rigidity analysis investigating the microstructure and

micro-properties of the fracture callus.

Phase one screening will investigate administration parameters at high, middle and low

factor levels outlined in Table 3.1. A total of 70 healthy, six week old, female Sprague

Dawley rats will be used during this stage of the study.

Table 3.1- The high, middle and low factor levels for lithium dosing, onset and duration parameters explored in this study.

Factor Level Dose mg/kg-wt/day

Onset days

Duration weeks

High 100 7 2 Middle 60 5 1.5

Low 20 3 1

Dosing range and treatment onsets were chosen based on previous studies that investigated

lithium administration in rodents. With regards to dosing, Clément-Lacroix and colleagues

(2005) highlighted that a lithium dose of 200 mg/kg-wt/day in mice produced plasma levels

32

comparable with treatment doses for humans with bipolar disorder. Moreover, both

Clément-Lacroix et al. (2005) and Chen and coworkers (2007) report successfully

administering approximately 200 mg/kg-wt/day of lithium to mice without issues. However,

because the current work investigated fracture healing in a rat, lithium dosing levels needed

to be properly translated for its application to this different species. Using the FDA

approved, normalization of body surface area approach presented by Reagan-Shaw and

colleagues (2007), a dosing level of 200 mg/kg-wt/day in a mouse was determined to be

equivalent to 100 mg/kg-wt/day in a rat. As a result, the maximum factor level of lithium

dosage was set as 100 mg/kg-wt/day. This dosing level was used in several previous rat

studies and was shown not to be lethal during the course of the experiment (Choudhary, et

al., 2008; Hamamura, et al., 2000). A dose of 20 mg/kg-wt/day was chosen as the lower

factor level based on the work of Hamamura and colleagues (2000), which demonstrated that

administration of lithium at 20 mg/kg-wt/day caused significant changes in protein

expression in cells of rat brains compared to saline treated controls. As such, the results from

this study confirmed that lithium therapy even as low as 20 mg/kg-wt/day can still be

considered large enough to cause a quantifiable effect that differs from non treatment.

Furthermore, a study by Ahmad and coworkers (2011) revealed signficiant differences in

blood serum chemistry between rats treated with oral lithium therapy ranging from only 15-

30 mg/kg-wt/day. Given that significant differences were seen in such a small dosing range,

this study provided additional support that the much larger dosing range of 20-100 mg/kg-

wt/day chosen for the current study would likely be sufficient for detecting significant

differences.

With regards to onset, Chen and coworkers (2007) showed that lithium treatment in mice

significantly improved bone healing when given four days post fracture, but was detrimental

to the healing process if administered pre fracture. In their study, the authors explain that for

lithium to have a positive influence on fracture healing, its therapeutic stimulation of Wnt/β-

Catenin signaling must occur only after mesenchymal precursors have committed to the

osteoblast lineage. As such, an onset range of three to seven days was chosen for the current

work in order to target the possible time range of this commitment, as well as to ensure that

the already tested onset of four days by Chen and colleagues would be incorporated within

the current factor range investigated. Three days was specifically chosen as the lower

33

boundary because this is the time point when the majority of undifferentiated mesenchymal

progenitor cells have migrated to the hematoma. Einhorn (1998) reported that at three days

post fracture, undifferentiated mesenchymal precursors stained the most intensely in areas of

soft callus. Further, several investigators have reported that levels of Interleukin-1 and 6,

two cytokines believed to be involved in the recruitment of mesenchymal precursors to the

fracture site, peak at day one post fracture, declining to nearly zero levels by day three

(Dimitriou et al., 2005; Cho et al., 2002). These findings can be attributed to the fact that by

day three post fracture, the majority of undifferentiated mesenchymal progenitor cells have

already migrated to the fracture site, and therefore, high levels of recruitment cytokines are

no longer needed. With the majority of mesenchymal precursors already present at the

fracture site by day three, this time point likely marks the beginning of when these cells have

the potential to undergo lineage commitment. A treatment onset of anything less than three

days, therefore, will likely have a minimal influence since the majority of precursors will

have not yet migrated to the fracture site. Seven days was specifically chosen as the higher

onset boundary based on evidence in the literature suggesting that the “soft” to “hard” callus

transition in a rat fracture model begins around the seven day mark (Marsell & Einhorn,

2011). With osteoblast activity being imperative for the “soft” to “hard” callus turnover, the

onset of this physiological transition is likely linked with a heavy increase in mesenchymal

precursor commitment to the osteoblast lineage.

Duration time was chosen based on research indicating that at four weeks post fracture, long

bone in younger rats is nearly healed and exhibits biomechanical properties approaching

those of intact standards (Meyer, Meyer, Phieffer, & Banks, 2001). Furthermore, according

to reviews by Histing and colleagues (2011) and O'Loughlin and colleagues (2008), which

outline the standards, tips and pitfalls of small animal models in fracture healing research,

four to five weeks post fracture is an appropriate time point for analyzing the later phases of

bone healing in the rat.

In the primary screening stage, parameters will be explored at all possible combinations of

high and low factor levels, as shown previously in Table 3.1. Given a three factor

(dose/onset/duration), two level (high/low) design, this corresponds to eight different

experimental groups representing the eight possible high/low factor combinations. A ninth

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experimental group will be included with all parameters set at middle factor levels so to

account for the possibility of non linear responses. Finally, two control groups will be

incorporated into screening, with one group receiving a sham treatment of saline instead of

lithium and the other group receiving no treatment at all.

Based on the results from the screening phase, the administration parameter(s) determined to

be the most influential on bone healing will be further explored in the optimization phase.

The DOE modeling conducted in screening will dictate how the next phase is designed,

including which factors are explored, at what combinations and intervals, and how many rats

are required for proper power. Figure 3.1 depicts a proposed optimization design in the case

when screening determines two factors as being much more important to the design than the

third. In this case, parameters are tested more thoroughly, using a rotatable surface design, at

intervals of one sixth, one third, one half, two thirds and five sixths, within the factor range.

For example, if dose is determined to be one of the most important factors in this scenario,

then in the two-factor optimization design it would be explored at factor levels of 33 (=1/6),

47 (=1/3), 60 (=1/2), 73 (=2/3) and 87 (=5/6) mg/kg-wt/day respectively. The analysis in this

proposed design will generate an output response surface similar to that depicted in Figure

3.1. A polynomial fit function (Anderson & Whitcomb, 2007) will be used to identify a

single point on that surface whose coordinates will represent the optimal lithium treatment

parameters.

Note that this optimization design is proposed solely on speculative screening results; the

exact design of phase two optimization is dependent on the results from phase one screening.

As such, not much can be definitively said with regards to the optimization phase until

screening is completed and main effects and factor interactions have been quantified. If, for

example, screening shows that only one, or all three, factors are crucial to the system, then

the proposed optimization design will need to be modified accordingly. Moreover, if the

results from screening suggest that an optimal factor level lies somewhere outside the tested

factor range (i.e.: the analysis suggests that the optimal input level for a certain factor is

either less than the minimum value tested in screening or greater than the maximum value

tested in screening), or the results are ambiguous - either due to methodology problems or

study power issues -, then optimization will need to be designed in such a way as to better

35

characterize the screening stage factors and re-establish the factor range. In the final stage,

verification, the optimal treatment parameters will be tested to confirm results for the

optimized treatment regimen. Figure 3.1 on the following page summarizes the overall

experimental design. Note, this Master’s thesis focuses only on completion of the initial

screening phase of the three-phased study design. The next phases of the study design

will be discussed in greater detail in the future direction section.

36

Figure 3.1 - This figure shows a schematic outlining the three stages of the experimental design. The primary screening stage will use a total of 70 rats to test factor levels at low, middle and high values. Each axis of the cube represents one of the three parameters under investigation, and each corner represents either a high or low factor value. A yellow circle indicates that a trial will be conducted at the treatment level specified by the circle’s location in the 3D cube, and the number within the circle represents the number of rats that will be tested. For example, the bottom left circle shows that a trial will be conducted on six rats with all factor levels set to a minimum (as indicated by the coordinates: dose = 20 mg/kg-wt/day, duration = 1 week, onset = 3 days). The blue circle in the center of the cube represents an experimental group with all parameters set to middle factor levels, and is included to evaluate lack of fit and account for the potential of non-linear responses. Based on the results of the DOE analysis from the initial screening phase, the parameter(s) determined to be most influential to the study design will be carried through to the optimization stage. The optimization design is completely dependent on the results obtained during screening, and thus, nothing can definitively be said about its design until the results from screening are obtained. The schematic above shows the proposed optimization design in the situation where two parameters are determined to be significant in screening, with the third factor, and all factor interactions, showing much less importance. In this case, a rotatable surface design is used to test the two factor levels at more thorough intervals ranging between the maximum and minimum boundaries previously tested in screening. The results of the optimization stage will generate a response surface, and a single point on this surface will be determined as the optimized location. The coordinates of this point will represent “optimal lithium treatment parameters”, the goal of the overall study. In the final stage, verification, four rats will be tested to confirm the optimized treatment regimen. More details on the actual design of the optimization phase will be provided in the future direction section.

37

3.2 Phase 1 Screening

This Master’s thesis is focused only on the completion of the initial screening phase of the

three-stage experimental design. A total of 70 healthy, six week old, female Sprague Dawley

rats were used in the screening phase, and were divided into 11 different experimental

groups. Eight groups (#1-5, #8-10) of six rats each were tested at a specific combination of

high/low factor levels; a ninth group (#7) of nine rats was tested at middle factor levels; two

control groups (#6, #11) of six and seven rats were exposed to either a sham or no treatment

respectively. A summary of the treatment groups used in the screening stage can be seen in

Table 3.2 below.

Table 3.2 - Experimental and control groups used in the primary screening stage. A total of 70 rats were divided into nine experimental and two controls groups, which collectively explore treatment parameters at combinations of minimum, middle and maximum factor values.

Screening Stage

Group Number

Group Type Number of Rats

Dose (mg/kg-wt/day)

Factor Level

Onset (days)

Factor Level

Duration (weeks)

Factor Level

1 Experimental 6 20 Min 3 Min 1 Min 2 Experimental 6 100 Max 7 Max 1 Min 3 Experimental 6 20 Min 3 Min 2 Max 4 Experimental 6 100 Max 7 Max 2 Max 5 Experimental 6 100 Max 3 Min 1 Min 6 Control 6 Saline - - 7 Experimental 9 60 Mid 5 Mid 1.5 Mid 8 Experimental 6 20 Min 7 Max 1 Min 9 Experimental 6 100 Max 3 Min 2 Max

10 Experimental 6 20 Min 7 Max 2 Max 11 Control 7 None - -

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3.2.1 Sample Size Calculations

The literature presents a wide range of data from torsional mechanical testing on healing rat

femoral fractures. Each study design is different, exploring different treatment interventions,

making it difficult to use previous findings to accurately predict study power and infer

sample size calculations. Nonetheless, data from four studies (Park, et al., 2013; Azuma et

al., 2001; Huddleston et al., 2000; Ekeland et al., 1981) was used as a general guideline to

determine sample size for the current study. While study designs and treatment interventions

differed, all four investigators conducted destructive torsional testing on healing femurs from

rats of similar weight (300 g) at similar study endpoints (25-28 days post fracture) as that

proposed in the current work.

The average maximum torque to failure of the healing femora from these four studies was

207 N-mm, with an average standard deviation of 49 N-mm. In order to enable detection of

a 20% difference in maximum yield torque (41 N-mm) with a 49 N-mm assumed standard

deviation, at a 0.05 two tailed significance and 80% power, a total of 48 subjects are

required for a two-level, parallel trial (Schoenfeld, 2010). With two levels per factor, this

implies that 24 subjects must be tested at each of the maximum and minimum levels

respectively. However, given a cubic study design with eight experimental groups total, each

factor level is essentially tested four times (four groups) throughout the duration of the

current study. For example, the minimum dosage level is tested in groups one, three, eight

and ten; while the maximum dosage level is tested in groups two, four, five and nine. As

such, with 24 total subjects required per factor level, and four different groups during which

each factor level is tested, this amounts to six total subjects per group. As such, a sample

size of six rats was chosen for each of the eight different experimental groups. To maintain

consistency, six rats were also allocated to each of the two control groups. With regards to

the middle factor level, eight rats were chosen based on DOE system design guidelines

stating that for every experimental combination tested, one centre point should be included.

As such, eight experimental groups necessitates eight middle points. Two extra rats were

provided with the animal shipment and were randomly assigned to groups seven and 11.

39

3.3 Experimental Methodology

The experimental methodology that was performed on each rat sample during the initial

screening phase is expanded upon on the following pages. It is important to note that this

procedure will be identical for both the optimization and verification phases to follow.

While the dosing, onset and duration parameters explored during these following two phases

will be different than those explored during screening, all steps pertaining to the

experimental methodology and data analysis will be identical.

The experimental methodology was divided into two main sections: the in vivo fracture

model and the evaluation of lithium treatment. In all rats, the in vivo portion of the project,

including femur fracture, lithium treatment and bilateral harvest, occurred over a 28 day

cycle. Following animal sacrifice and bone excision, evaluation of bone healing in each

sample was performed through a combination of mechanical testing and µCT based analysis.

A flow chart depicting the complete process that was applied to each sample is shown in

Figure 3.2 on the following page.

40

Figure 3.2 - Flow chart highlighting the chronology of the experimental procedures and analysis performed on each sample.

41

3.4 In Vivo Fracture Model

A closed mid-shaft unilateral femur fracture was induced in healthy, six week old female

Sprague Dawley rats (approximate weight = 300 grams) following the technique previously

published by Manigrasso and O'Connor (2004). After shaving and sterile preparation of the

right knee, a small incision was made anterior to the patella, and a 1.0 mm Ø intramedullary

steel pin was inserted into the femoral canal to pre-stabilize the bone. Once completed, the

soft tissues at the knee were closed with a deep 3-0 absorbable (Vicryl) suture followed by a

skin staple. A custom designed drop weight apparatus (Figure 3.3) was used to generate a

closed femur fracture under general gas anaesthesia. This type of apparatus was chosen

because it best replicated a high impact fracture model with associated trauma and

accompanying soft tissue damage. Post fracture, the animals were given appropriate

analgesics, allowed free, unrestricted weight bearing in their cages, and had full access to

food and water as needed. The fracture was allowed to heal over a 28 day period, during

which time the lithium treatment was administered. Daily oral gavage was used to deliver

the drug directly into the stomach as this was the only way to guarantee accurate dosing. In

order to minimize the stress related effects associated with daily gavage, the rats were given

light anaesthetic during administration, a technique published in the 2001 edition of

Contemporary Topics in Laboratory Animal Science (Murphy, Smith, Shaivitz, Rossberg, &

Hurn, 2001). As Histing and colleagues (2011) make note, inhalant anaesthesia exerts only

minimal stress on the animal, and thus, can be used in short intervals on a daily basis without

the risk of adverse effects. Immediately after lithium administration, two mL of saline

solution was injected subcutaneously in an attempt to flush the drug and keep the rats

hydrated. All animals were sacrificed at 28 days post fracture and femurs were harvested

bilaterally, removing the intramedullary pin. Bilateral harvest allowed for additional,

identical analysis on some of the intact femurs. This was used to establish a standard point

of reference to which the contralateral, healing femora were compared, and to help

understand the potential systemic impact of lithium therapy on intact bone tissue.

42

Figure 3.3 - Custom drop weight apparatus used to generate a closed femur fracture. The rat femur is centered beneath the blade and secured in place using the triangular locking clamps. A 380-gram weight is dropped from a height of 33 cm. The blade shaft is dampened by a spring so that when the tip makes contact with the bone it immediately rebounds back upwards. This ensures that the blade transfers minimal impact energy during collision and does not cause excessive trauma leading to comminution. The device is repeatable, and generates a consistent, mid shaft transverse fracture.

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3.5 Evaluation of Lithium Treatment

A combination of biomechanical testing, µCT-based 3D bone stereology and CT-based

torsional rigidity analysis were used to evaluate how variations in lithium treatment affected

the overall quality of bone healing. Biomechanical analysis provided an indication of the

healing femur’s ability to regain its load baring capabilities, while µCT image analysis was

used to quantify the micro-structural composition and micro-properties of the healing callus.

Between mechanical testing, µCT image based stereological analysis and CT based torsional

rigidity, eleven different outcome measures were obtained. All three components of the

analysis are explained in further detail below.

3.5.1 Biomechanical Testing

Biomechanical strength of bone healing was used as the primary study outcome measure to

assess the quality of fracture repair, as this is the current gold standard for quantifying the

competence of healing bone and its ability to bear load (Voide, et al., 2006). Specifically,

destructive torsional loading was chosen as the testing method for quantifying the

biomechanical parameters of the healing callus. Torsion was chosen because bone is known

to be approximately three times weaker in torsion than in bending, and so, would likely fail

in this loading scenario first (Nordin & Frankel, 2001). Moreover, compared to three point

bending, which predetermines the site of the maximum moment to be that directly below the

loading point, torsion places every section along the length of the bone under identical,

uniform loading conditions. Thus, whereas the location of failure in three point bending is

localized to the point where loading is applied, failure in torsion is not subject to these

predefined biases and will naturally occur at the weakest location over the entire specimen

length (Burstein & Frankel, 1971).

Torsional testing was conducted on an MTS Bionix 858 (MTS Systems, MN, USA)

materials testing system. Each femur was aligned longitudinally to the loading axis of the

MTS with its proximal and distal ends potted in bone cement (polymethylmethacrylate /

PMMA). The gauge length, which is defined as the distance between the two PMMA pots,

was kept at a constant of 15 mm between each sample. This value was chosen based on

44

visual inspection, ensuring that the callus was always captured between the two pots, and

was consistent with the protocols of Huddleston and coworkers (2000), Kasra et al., (1997)

and Wang and colleagues (1994) who also used this gauge length. A schematic of the testing

setup can be seen in Figure 3.4.

Figure 3.4 - Mechanical testing equipment setup used for torsional testing.

Applied torque was measured using a 1.4 N-m reaction torque transducer (Futek, CA, USA).

An angular displacement of 1.5˚/second was applied until evident failure occurred (identified

by a sudden, rapid, drop in torque reading), or until a maximum angular displacement of 50˚

was achieved. This loading rate was chosen based off the mechanical protocols of Sardone

and coworkers (2011) and Azuma et al. (2001) who also biomechanically analyzed rat femur

through destructive torsion testing at this loading rate. By analyzing load displacement

curves to failure, maximum yield torque, twist angle at failure, and experimental torsional

stiffness were determined. Maximum yield torque was defined as the maximum torsional

45

value sustained during the elastic portion of loading. This value, different from the ultimate

torsional moment, was used to represent the first point of failure during testing, where bone

yielding occurred, micro fractures were initiated and mechanical integrity was compromised.

Since a constant gauge length was used for every sample, experimental torsional stiffness

was defined as the slope of the linear, elastic portion of the applied torque-twist angle graph

generated during analysis. These two parameters are illustrated in Figure 3.5. Maximum

yield torque was used as the primary study outcome measure for DOE analysis purposes.

Figure 3.5 – Graphical definitions of maximum yield torque, twist angle at failure and experimental torsional stiffness. Maximum yield torque was defined as the primary study outcome measure, and was used to assess the quality of fracture healing.

46

3.5.2 µCT Imaging and Stereological Analysis

µCT-based 3D bone stereology was used to investigate the microstructure of the healing

fracture callus, and provided the basis for most of the secondary outcome measures for this

study. Prior to mechanical testing, each rat femur was imaged using a Scanco 100 µCT

scanner (Scanco Medical, Switzerland). Samples were scanned at an isotropic voxel size of

14.8 µm using a voltage of 55 kV, a current of 200 µA and a beam hardening correction

factor of 1200 mgHA/ccm. The scanner was pre-calibrated using a set of four

hydroxyapatite phantoms (100, 200, 400 and 800 mgHA/ccm) provided by Scanco, thus

allowing for the direct quantification of bone density from scan intensity output using an

assumed linear relationship. Once complete, the scans were reconstructed, exported as

Dicoms and imported into AmiraDEV 5.40 (Visage Imaging, CA, USA) for image

processing.

Once in AmiraDEV, the scans were cropped using the interactive crop editor tool to isolate

the region of interest (ROI) to be analyzed. Given a high impact, drop weight induced

fracture model, the location of fracture and the degree of fracture comminution inherently

varied across samples. As a result, the ROI was taken as a fixed distance from the midway

point of the lesser trochanter, proximally, to the start of the patellar notch, distally. A

schematic outlining the exact location of the ROI can be seen in Figure 3.6 on the following

page. Using this anatomically defined ROI ensured that the entire callus would always be

captured, regardless of its location, degree of comminution and resultant number of slices.

Since the ROI essentially spanned the entire femoral shaft, it also included parts of cortical

bone both proximally and distally from the callus boundaries. However, it was assumed that

this addition was consistent across samples, as all femurs were from rats with identical

genetic and biological characteristics. The images were then rotated using the transformation

tool to align the long axis of the bone with the vertical (z) axis of the software’s coordinate

system. A summary of the pre processing steps executed in AmiraDEV is depicted in Figure

3.7 on the following page.

47

Figure 3.6 - Definition of the region of interest (ROI) used in the stereological analysis.

Figure 3.7 - A summary of the pre processing steps conducted prior to the stereological analysis.

48

The images were exported as raw data and imported into a CT analyzer software (SkyScan,

Belgium), where a custom processing module was used to execute the stereological analysis.

This module combined processes including smoothing, filtering, de-speckling, contouring

and thresholding in order to first separate the ROI from external noise and then calculate

properties relating to geometry and mineralization. A fixed global threshold of 25% the

maximum native gray scale value, corresponding to a mineral density of 365 mgHA/ccm,

was used to differentiate mineralized tissue that was included in the analysis from un or

poorly mineralized tissue that was excluded. This value was chosen based on the work of

Morgan et al. (2009). Visual inspection confirmed that this value captured the callus volume

in its entirety.

In their paper entitled “Guidelines for Assessment of Bone Microstructure in Rodents Using

Micro-Computed Tomography”, Bouxsein et al. (2010) outline important stereological

parameters that should be considered when describing rodent bone morphology. Consistent

with these guidelines, as well as various other papers that have investigated fracture healing

in a rodent closed femur fracture model (Toben, et al., 2011; Morgan, et al., 2009; Nyman, et

al., 2009), stereological parameters including bone volume (BV, mm3), total volume (TV,

mm3), bone volume fraction (BV/TV, %), mean bone mineral density (BMD, mgHA/cm3),

mean tissue mineral density (TMD, mgHA/cm3) and mean bone mineral content (BMC,

mgHA) were calculated. CT-based torsional rigidity (CTRA, kN*mm2) was also calculated

and will be expanded upon in the following section. Collectively, these µCT derived

parameters were used to explore the microstructure of the healing fracture callus and

provided the basis for the majority of secondary outcome measures for this study.

For every µCT slice a pair of segmented images were generated similar to those

representatively shown in Figure 3.8 on the following page. These two different

segmentations were used in cohort to quantify all the stereological output parameters for

each µCT slice individually, as well as the complete ROI in its entirety. Figure 3.8B shows a

representative example of the segmentation used in the calculations of bone volume, mean

tissue mineral density and mean bone mineral content, while Figure 3.8C shows a

representative example of the segmentation used in the calculations of total volume and

49

mean bone mineral density. Bone volume fraction was denoted as the ratio of the bone

volume (Figure 3.8B) to the total volume (Figure 3.8C).

Figure 3.8 - A raw image (A) and the accompanying pair of segmented images (B, C) from a single µCT slice used in the stereological evaluation. Figure B was used in the calculations of BV, TMD and BMC, while Figure C was used in the calculations of TV and BMD. Bone volume fraction was denoted as BV/TV.

50

3.5.3 CT Based Torsional Rigidity

Torsional rigidity, also known as torsional stiffness, is a measure of an object’s resistance to

elastic, twisting deformation in response to an applied torque. This measure, represented by

the abbreviation GJ, takes into account both the geometry (J = polar moment of inertia) and

material properties (G = shear modulus) of an object, with a larger GJ value implying a

stiffer object that better resists deformation. Mechanically, torsional rigidity is defined as the

product of the slope of the linear portion of an object's torque vs. twist profile and the

object’s gauge length. While traditionally determined through direct experimental testing,

Nazarian and colleagues (2010) recently proposed a computational, CT-based method for

quantifying the torsional rigidity of healing long bones. This technique, outlined in their

paper “Application of Structural Rigidity Analysis to Assess Fidelity of Healed Fractures in

Rat Femurs with Critical Defects”, uses bone’s geometry and density profiles based on µCT

images in order to quantify its torsional rigidity. In the current study, this process, expanded

upon below, was implemented through a custom written .tcl code imported into the

AmiraDEV command port.

The first step in the analysis was to convert the intensity weighted scan into a density

weighted scan using the inherent scanner intensity/density calibration relating these two

measures. This linear relationship, shown in Equation 3.1, converts the scanner Hounsfield

intensity unit into a measure of ash density. Next, the ash density weighted scan was

converted into a measure of apparent density using a scaling factor of 0.654, identified as the

cortical bone volume conversion ratio for healthy, rat bone (Nazarian et al., 2009). This

apparent density weighted scan was then transformed into a shear modulus weighted scan

(G) using Equation 3.2 on the following page, relating apparent density and shear modulus in

the healthy rat femur (Nazarian et al., 2009).

Equation 3.1 - Relationship between scanner output intensity (Hounsfield Unit) and ash density.

51

Equation 3.2 – Relationship between apparent density (ρapp) and shear modulus (G).

The next step involved calculating the neutral axis of the bone, which is defined as the cross

sectional axis along which there are no longitudinal stresses or strains. To do this, the

modulus weighted centroid of each cross sectional slice was calculated using Equation 3.3.

The neutral axis was then defined as a line connecting the modulus weighted centroids of

each cross sectional slice.

Equation 3.3 - Equations used to calculate the X and Y coordinates of the modulus-weighted centroid for each cross sectional slice.

With the neutral axis defined, and each pixel in the µCT slice converted to its modulus

weighted form, the accompanying equation in Figure 3.9 was then used to calculate the

torsional rigidity of each axial slice. Xi and Yi represent the distances of each pixel from the

X and Y neutral axes respectively. The area of each pixel (14.8 µm x 14.8 µm = 219 µm2)

was used as the constant value for da. For each region of interest, the minimum torsional

rigidity (GJmin) and the average torsional rigidity (GJavg) were calculated. Since bone is only

as strong as its weakest cross section, GJmin was the primary parameter of interest.

52

Figure 3.9 – An illustration of the CT-based method for calculating the torsional rigidity (GJ) for the cross sections of axial long bones. Gi(ρ) is the modulus weighted value of each pixel, Xi and Yi are the distances of each pixel from the X and Y neutral axis respectively, and da is the cross sectional area of each pixel (Nazarian, et al., 2010). This figure is reproduced with permission from Springer (see Appendix).

53

3.6 Data Analysis

Once the eleven different outcome responses were obtained, data was organized into the

appropriate eleven treatment groups and reported as mean ± standard deviation. DOE

modeling was then executed on both primary and secondary outcome measures, followed by

a correlation analysis between mechanical testing parameters and µCT based imaging

parameters. The emphasis of the statistical analyses was paramount for the study and was

undertaken with the assistance of Dr. Ian Sigel, a DOE expert who aided in the development

of the original study design.

3.6.1 Design of Experiments System Modeling

Design of experiments system modeling was conducted on each of the eleven outcome

responses (maximum yield torque, twist angle at failure, experimental torsional stiffness,

bone volume, total volume, BV/TV, mean bone mineral density, mean tissue mineral density,

mean bone mineral content, GJmin, GJavg) using a commercially available, DOE-specific

statistical package (Design-Ease v7, Stat-Ease, MN, USA).

Raw data was imported into the software in coded matrix notation so that each response

would be allocated to the proper treatment group. Data normality was then confirmed by

plotting the output residuals on a normal percent probability plot, where a normal distribution

was assumed when the residuals displayed a linear pattern within a small residual range. In

the case when the data deviated from normality, an appropriate Box-Cox transformation

(logarithmic, square root or inverse square root) was applied to the output responses, as

recommended by the software, to help stabilize the variance. With the proper transformation

applied, and all factors in coded matrix notation, main effects and interactions were

calculated on the response. A sum of squares chart, showing standardized effect, sum of

square tally, and percent contribution, was then used to determine which terms were included

in the model space. Terms were excluded from the model if they showed less than a 10%

weighted contribution to the model space. However, if an interaction term was included in

the model, then both its parent main effects were also included -even if either showed a

weighted contribution of less than the 10% threshold- in order to avoid issues of model

54

hierarchy (i.e. If AB was included, then A and B were both included). A 10% threshold was

chosen based on the expert opinion of orthopaedic surgeons who suggested that a 20%

increase in mechanical properties of the healing femur would be a clinically relevant

outcome.

With the model defined, an analysis of variance (ANOVA) was then used to determine if the

model itself was significant, which effects and interactions were significant to the model, and

whether the model showed significant curvature, indicating a non linear or saturated response

within the cubic design space. In all cases, a p-value of 0.05 was taken as significant. A

regression analysis was then fit to the model space, and a coefficient of determination was

calculated in order to quantify the predictive nature of the model. A Pareto chart was

generated in order to visualize relative effect contributions of the input parameters, both in

magnitude and direction, while main effect plots and factor interaction plots were created to

show how variations in input parameters affected the output response.

3.6.2 Differences Between Treatment Groups and Control Groups

Based on the DOE system modeling, one treatment group was identified as being the "best",

and one treatment group was identified as being the "worst", with respect to maximizing the

primary study outcome measure of maximum yield torque. Independent samples, two tailed,

T-tests (SPSS, V18.0, Chicago, IL, USA) were used to determine if there were significant

differences between either of these two experimental groups and the controls. T-tests were

conducted with both control groups (6 and 11) pooled, as there was no significant difference

between these two groups (p=0.58). A p-value of 0.05 was taken as statistically significant.

3.6.3 Correlation Analysis

Pearson’s correlation analysis (SPSS, V18.0, Chicago, IL, USA) was used to determine the

strength of correlations between mechanical testing parameters and µCT based imaging

parameters. A p-value of 0.05 was taken as statistically significant.

55


Before beginning with phase one screening, pilot work was completed in order to confirm

that all experimental procedures could be implemented successfully. Through a combination

of in vitro and in vivo pilot work, several problems with the initially proposed protocols were

revealed, and appropriate modifications were implemented. This phase of the project is

expanded upon in further detail below.

4.1 In Vitro Pilot Work: Optimization of the Fracture Jig

Before beginning with any animal experimentation, important in vitro work was done to

modify the fracture jig so to make it applicable for the current fracture model. The jig was

initially designed for a study that required the generation of a tibia fracture in a mouse.

However, given that the current study investigated bone healing in a rat femur, several

modifications were implemented in order to reconfigure the jig for the current study.

First, since a rat is a significantly larger rodent than a mouse, the platform of the initial jig,

where the animal rests during fracture induction, was not spacious enough for the current

study. During preliminary testing using the original jig, it was found that when aligned

properly on the platform, the rat’s upper torso and head would completely overhang the edge.

To address this issue, a 6”x 6” aluminum platform, seen in Figure 4.2, was added as an

extension to the existing base. This extension eliminated the overhang and provided the

additional room needed to accommodate a rat.

Second, when using the previous jig on the mouse tibia, the user was required to manually

align the tibia centrally under the contact point of the drop weight and hold it in place during

fracture induction. This approach is problematic for several reasons. Firstly, it introduces

undesirable user variability into the experimental design. With a manual alignment

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approach, it is very challenging to obtain a consistent and repeatable mid-shaft transverse

fracture, as the impact of the drop blade and its positioning are dependent on the way the user

orients the bone. Since the goal of the current study centered around lithium’s ability to

improve fracture healing, it was imperative that a relatively consistent fracture be introduced

in order to ensure similar bone healing across all specimens. Secondly, the need for manual

alignment of the bone poses as a safety risk. With manual alignment required, the user’s

fingers are positioned, and remain, in very close proximity to the drop weight blade as it is

engaged to create the fracture. This is unsafe, as the user could slip and inadvertently be

struck by the blade.

To address both of these issues, a clamping mechanism, seen in Figure 4.2, was added to the

jig platform. The mechanism consists of two triangular clamps that rest and tighten over the

rat’s knee joint and abdominal cavity respectively. The clamps are tightened via two set

screws, allowing the user to control the tightening strength. This is important for two

reasons. First, if secured too tightly, the pressure may physically injure the animal. Second,

if clamped too tightly, the drop weight force will not be dissipated properly throughout the

bone, as some of the strain energy will undesirably be transferred to the clamps. The clamp

edges form a 90° angle, with the interior face machined to create a rough, friction filled

contact surface. This ensures that contact occurs on both faces of the clamp, which adds to

its ability to properly secure the femur in place. To use the clamping mechanism, the rat was

positioned supine with its right patellar joint located and locked centrally under the smaller

clamp. By positioning and locking in this orientation, the femur was secured with its mid-

shaft forced to lie directly underneath the blade of the drop weight, ensuring the blade made

contact in a similar location each time. This can be repeated across each sample by ensuring

that every rat is positioned with this patellar joint landmark in mind.

It is important to mention, however, that due to the high impact fracture model that the jig

was designed to replicate, as well as the inherent biological differences between each

sample- including variation in weight, muscular density surrounding the femur, and femoral

shaft length and curvature- it was impossible to ensure that an identically located, mid-shaft

transverse fracture occurred every time. An uncontrolled blunt impact to the bone is required

to replicate a traumatic fracture model and achieve surrounding soft tissue damage; yet, this

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comes with the trade-off of being unable to fully control the fracture pattern that is

subsequently generated. The modifications to the fracture jig, however, helped to minimize

this inherent error by introducing a more consistent and repeatable method for fracture

induction. In addition, by not requiring the user to hold the femur in place, the new clamping

mechanism significantly reduced the potential of an accident occurring. Figure 4.1 depicts

the original jig, while Figure 4.2 shows the modified jig used in the current study.

Figure 4.1 – Unmodified fracture jig. This device was used in a previous study to generate tibia fractures in a mouse model.

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Figure 4.2 – The modified fracture jig used in the current study. The new jig incorporated two major changes. First, a 6”x6” aluminum square extension was added to the existing base so to create a large enough platform to accommodate a rat. Second, a clamping mechanism was designed in order to eliminate the need to manually align the bone under the drop weight blade. This created more consistent, repeatable fractures across samples and eliminated significant user variability introduced into the experimental design.

59

Figures 4.3 and 4.4 show fluoroscopic images taken of fractures induced by the previous jig

and the modified jig respectively. Although biological variability made it difficult to achieve

identical fracture patterns, compared to the previous jig, the modified jig was better able to

create a consistent fracture pattern across samples.

Figure 4.3 – Using the original fracture jig it was difficult to achieve a consistent mid-shaft, transverse fracture. The fracture patterns obtained using the original jig were indicative of the one seen above. Generally, manual alignment resulted in a heavily oblique fracture pattern situated in the distal third region of the femur.

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Figure 4.4 – While the image above only shows one example, fracture patterns generated using the modified jig were significantly better than those observed before the jig was modified. However, due to the inherent difference between samples, and the fact that the jig was designed to simulate a non-controlled, high impact trauma to the bone, perfectly identical fracture patterns were nearly impossible to generate. Nonetheless, the modified jig had the ability to create a fairly transverse fracture pattern that was more consistently mid-shaft oriented. Using the patellar joint as an anatomical landmark, this pattern could be repeated across samples, eliminating much of the undesired user variability inherent with manual alignment.

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4.2 In Vivo Pilot Work: Modifications to the 28 Day In Vivo Cycle

The in vivo pilot stage was very important to the development of the materials and methods

of this study as it helped to identify two major problems with the initially proposed

experimental protocol. Using the results obtained from pilot work completed on ten rats, two

significant modifications to the 28 day in vivo protocol were implemented at the start of the

actual experiment. These changes, which are related to treatment administration and dosing

level, are explained in further detail below.

4.2.1 Modifications to the Method of Lithium Administration

Four rats were ordered in June 2012 for the first experimental trial to ensure that all

components of the 28 day in vivo cycle could be implemented without problems. Initially,

raspberry Jell-O was proposed as the vehicle for lithium chloride treatment. It was planned

that each day the rats would be given the required lithium dosage dissolved within a Jell-O

cube, and they would eat this treat at their own will. Food and water would be pulled 24

hours prior to Jell-O feeding, and during feeding, the rats would be isolated in a cage with

only their treatment. This method, however, immediately proved problematic because the

treatment Jell-O (with lithium) was never consumed. Jell-O cubes were left in cages for

hours at a time, with no success, to the point where they melted and could no longer be

consumed. In contrast, the control rats, who were given plain Jell-O lacking any lithium, ate

the cubes without hesitation. It was hypothesized that the rats did not eat the lithium Jell-O

because they could smell an unpleasant odour coming from the cube as a result of the drug,

which the raspberry flavour could not successfully mask. A related finding was published by

Loy & Hall (2002) in the Quarterly Journal of Experimental Psychology, reporting that rats

establish an aversion to lithium once introduced to the treatment by generating an association

between its salty taste and the subsequent aversive consequences -such as nausea and

dehydration- that it has on them.

Regardless of the reason, the Jell-O was discontinued after several days of trying, and other

treatment delivery methods, including syringe feeding, dissolving the lithium in drinking

water and oral gavage, were attempted. Syringe feeding proved unsuccessful because the

62

rats would resist during feeding, and most of the time would not swallow the lithium

solution, spitting it out once it was syringed into their mouths. Both the drinking water

technique and gavage feeding, however, yielded better results. With regards to the water, the

rats appeared to drink around 25 mL of water daily, and this did not differ between control

rats, who received regular water, or treated rats, who received a lithium-water solution.

However, since the rats were left to drink their water overnight without anyone monitoring

them, it cannot be confirmed that the full dose of the treated water was actually consumed.

There is the possibility that the water dripped excessively from the bottle, or, similar to the

syringe method, simply was not swallowed. Moreover, the amount of water that was gone

from the bottle each morning fluctuated by around ± 5 mL, which made it difficult to be

certain that this method could be used to successfully administer accurate and consistent

dosages. With regards to gavage, although the most stressful and unpleasant for the rats, this

technique allowed for accurate lithium dosage to be administered to the stomach on a daily

basis without fail. Many other groups who have administered lithium to rodents have found

success by dissolving the drug in their drinking water (Ahmad et al., 2011; Chen, et al.,

2007; Clément-Lacroix, et al., 2005; Dehpour et al., 2002). However, these studies were not

concerned with strict lithium dosages, but rather, were interested in a binary type setup

investigating differences between a lithium treated group and non lithium treated group.

Since accurate dosage is imperative for this study, it was decided that lithium must be

administered using gavage, as this is the only way to guarantee accurate dosing.

The four rats from this cycle were sacrificed after 28 days and their femurs were harvested.

From this cycle, two rats were saline treated controls, and two were suppose to be tested at

the initially proposed maximum factor levels (dose=200 mg/kg-wt/day; onset=7 days;

duration=2 weeks). However, it could not be certain that the two rats who were given

lithium received accurate dosage during each feeding. In fact, due to the complications

encountered with the various treatment methods, these rats probably received much less than

the 200 mg/kg-wt/day of lithium they were intended to receive. All that could be confidently

stated was that two rats definitely received some lithium while the other two rats definitely

received none. These specimens were used for pilot mechanical testing and µCT image

analysis purposes, and provided some preliminary observations comparing lithium treated vs.

non lithium treated bone healing.

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4.2.2 Modifications to the Maximum Dosage Level

With the gavage technique confirmed, six more rats were ordered as pilots in July 2012 to

ensure that a full 28 day in vivo cycle could be completed before beginning the actual

experiment. Initially, the dosing factor range was planned to span from a low level of 50

mg/kg-wt/day to a high level of 200 mg/kg-wt/day. In this pilot phase, two rats were tested

at the initially proposed high factor levels, two rats were tested at the initially proposed

middle factor levels and two rats were tested as untreated controls. Unfortunately, both rats

treated at high parameter levels (dose = 200 mg/kg-wt/day, onset = 7 days, duration = 2

weeks) passed away on days seven and ten of their respective treatments, prior to completion

of their full 28 day in vivo cycles. From their symptoms and nature of death, the hypothesis

from the chief veterinarian and animal technicians monitoring these rats was that they died

from toxic poisoning brought upon by excessive lithium ingestion. Although previous

papers do report successfully administering dosages of around 200 mg/kg-wt/day to mice

(Chen, et al., 2007; Clément-Lacroix, et al., 2005), these studies also elucidate that dosages

were only approximations due to the fact that the drug was administered through their

drinking water. Thus, even though these papers report mice receiving 200 mg/kg-wt of daily

lithium, in all likelihood, less than that would have been ingested during their respective

studies. In this pilot stage, the gavage technique was used as the method of drug delivery

since previous in vivo work confirmed it as the ideal method for ensuring accurate dosing.

Therefore, it can be certain that each rat received exactly 200 mg/kg-wt/day of lithium

delivered directly into the stomach, an over dosage that likely caused the toxicity.

The general rule when dealing with animal dosing is that the larger the animal the smaller the

required dosage to elicit a similar effect (Sharma & McNeill, 2009; Reagan-Shaw, Nihal, &

Ahmad, 2007). This is because larger animals generally have a slower metabolism, and thus

don’t require as much of a given drug for it to reach its therapeutic level in the serum. With

rats being larger than mice, it follows that the dosages they receive should be lower than

those previously reported in the literature for mice. Reagan-Shaw and colleagues (2007)

present an accurate method for translating dosing level between different species based on

the normalization of body surface area (BSA) approach presented and approved by the FDA

Draft Guidelines. Using a conversion factor, Km, representing the ratio of a species' average

64

body weight (kg) and its average body surface area (m2), proper dosing levels for any

particular drug can be converted from one species to another (Table 4.1). This is particularly

useful for extrapolating dosing results from preclinical animal drug studies to human phase I

and II clinical trials.

Table 4.1 - Body surface area method for converting drug dosage levels between two different species. Values are presented based off the work of Reagan-Shaw and colleagues (2007).

Species Weight (kg) BSA (m2) Km Factor Human: Adult 60 1.6 37 Human: Child 20 0.8 25 Rabbit 1.8 0.15 12 Rat 0.15 0.025 6 Mouse 0.02 0.007 3

Equation 4.1 - Equation used to convert dosing level between two different species.

With the conversion factor for a rat being twice as large as that for a mouse (Km rat = 6; Km

mouse = 3), Equation 4.1 implies that dosing in a rat should, therefore, be half of that in a

mouse. As such, high level dosage to be investigated in phase one screening was lowered

from 200 mg/kg-wt/day (tested in the pilot phase) to 100 mg/kg-wt/day, with the middle and

lower factor levels modified accordingly. Due to this change in dosage, the six rats tested in

this pilot phase were used only for pilot mechanical testing and µCT image analysis

purposes.

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Chapter 5: Results

In the following section, the results from the phase one screening study are presented.

Observations from six different sections will be summarized, including mechanical testing

data, µCT-based 3D bone stereology data, CT based torsional rigidity calculations, design of

experiments system modeling, experimental vs. control comparison, and correlation analysis.

Two rats had to be excluded from the complete analysis: rat 63, part of experimental group

four, died prematurely before completion of its 28 day in vivo cycle; rat 54, part of

experimental group ten, could not be used because its healing femur snapped prematurely

during bone harvest. One additional sample experienced complications during mechanical

testing (rat 14, part of experimental group six) and could not be used for this portion of the

analysis. Other than these three samples, no significant complications were experienced

warranting sample exclusion. Table 5.1 below shows an updated summary of the treatment

groups analyzed in the screening stage.

Table 5.1 - The experimental and control groups used in the primary screening stage. Two samples had to be excluded from analysis due to in vivo cycle complications, resulting in two groups (#4, #10) with five samples only. One sample encountered complications during the mechanical testing phase and had to be excluded from this portion of the analysis (6*); it was still analyzed using the µCT image based techniques. Extra samples were tested at middle (#7) and control (#11) levels as per the DOE study design.

Group Number

Group Type Number of Rats

Dose (mg/kg-wt/day)

Onset (days)

Duration (weeks)

1 Experimental 6 20 3 1 2 Experimental 6 100 7 1 3 Experimental 6 20 3 2 4 Experimental 5 100 7 2 5 Experimental 6 100 3 1 6 Control 6* Saline - - 7 Experimental 9 60 5 1.5 8 Experimental 6 20 7 1 9 Experimental 6 100 3 2

10 Experimental 5 20 7 2 11 Control 7 None - -

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5.1 Destructive Torsional Mechanical Testing

Through destructive torsional testing, the maximum yield torque, twist angle at failure and

experimental torsional stiffness were calculated for each sample. Figure 5.1 shows a

representative output of the data and post processing from one of the mechanical tests, while

Table 5.2 summarizes complete results. Experimental group ten possessed the highest

maximum yield torque and experimental torsional stiffness, while experimental group five,

its direct treatment opposite, showed the lowest maximum yield torque and one of the lower

experimental torsional stiffness outcomes.

Figure 5.1 - Torque vs. twist angle plot for one of the samples tested. The red highlighted point indicates the time during testing when failure was first initiated; its X and Y coordinates represent the twist angle at failure and the maximum yield torque respectively. Experimental torsional stiffness was quantified as the slope of the line of best fit through the linear, elastic region of the curve.

67

Table 5.2 - A summary of the mechanical testing data for the eleven different experimental groups. Average values are reported, with standard deviations given in parentheses. Maximum values for maximum yield torque and experimental torsional stiffness are bolded.

Group Dose (mg/kg-wt/day)

Onset (days)

Duration (weeks)

Maximum Yield Torque

(N-mm)

Twist Angle (°)

Torsional Stiffness (N-mm/°)

1 20 3 1 278.8 (108.1) 12.5 (4.0) 24.3 (8.8) 2 100 7 1 333.0 (124.2) 14.9 (5.1) 24.2 (8.6) 3 20 3 2 351.9 (89.6) 18.3 (3.3) 20.8 (5.2) 4 100 7 2 398.2 (244.5) 15.1 (5.3) 27.0 (11.7) 5 100 3 1 255.8 (89.1) 18.3 (7.6) 18.7 (7.6) 6 Saline Control 302.2 (159.7) 19.7 (6.9) 19.6 (14.1) 7 60 5 1.5 330.5 (147.1) 24.5 (10.9) 16.3 (8.8) 8 20 7 1 393.5 (169.3) 18.5 (11.4) 24.9 (12.6) 9 100 3 2 276.7 (77.0) 21.9 (11.2) 18.5 (11.9)

10 20 7 2 481.1 (104.0) 17.2 (9.0) 30.5 (5.8) 11 No Treatment Control 349.7 (125.2) 14.5 (4.8) 25.2 (6.3)

The primary study outcome response, maximum yield torque, is shown graphically in

Figures 5.2 and 5.3. Based on the column graph in Figure 5.2, note that experimental groups

one, five and nine, rats similarly treated at an earlier onset of lithium therapy, stand out as

possessing the lowest values for the maximum yield torque output response. In contrast,

experimental groups four, eight and ten, rats similarly treated at a later onset of lithium

therapy, stand out as possessing the highest values for the maximum yield torque output

response. The box and whisker plot in Figure 5.3 highlights the large variation evident in the

data, an outcome expected in biological based experimentation.

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Figure 5.2 - Average maximum yield torque to failure for each of the eleven experimental groups, including standard error bars.

Figure 5.3 - A box and whisker plot showing the distribution and variation of maximum yield torque within and across experimental groups.

69

As is expected with torsional mechanical testing, most samples broke through a single

oblique plane extending through the central location of the callus. Several samples (15-

20%), however, displayed unexpected braking patterns, including axial separation,

comminuted fragmentation and bone separation not within the callus. Figure 5.4 shows the

typical braking pattern that was encountered during testing.

Figure 5.4 - These are images taken from two different samples after mechanical testing was complete. Most samples broke through an oblique plane similar to the patterns shown above.

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5.2 µCT Based 3D Bone Stereology

Stereological measures of bone volume (BV), total volume (TV), bone volume fraction

(BV/TV), mean bone mineral density (BMD), mean tissue mineral density (TMD) and mean

bone mineral content (BMC) were calculated for each sample. Results are summarized in

Table 5.3 below. Interestingly, experimental group ten, which displayed the best mechanical

properties, showed lower stereological values on parameters quantifying both the amount

and mineralization of bone in the callus.

Table 5.3 - A summary of the bone stereology data for the eleven different groups. Average values are reported, with standard deviations given in parentheses.


Onset (days)

Duration (weeks)

BV (mm3)

TV (mm3)

BV/TV (%)

BMD (mgHA/ccm)

TMD (mgHA/ccm)

BMC (mgHA)

1 20 3 1 314.5 (53.1)

574.9 (92.9)

54.7 (2.3)

516.2 (25.2)

921.2 (18.7)

289.1 (44.0)

2 100 7 1 355.2 (32.1)

644.3 (80.3)

55.4 (4.6)

506.8 (52.1)

889.8 (29.1)

316.4 (33.8)

3 20 3 2 313.9 (33.2)

581.9 (115.7)

54.9 (6.9)

515.5 (62.2)

915.2 (18.4)

286.9 (26.2)

4 100 7 2 351.2 (46.8)

599.8 (102.8)

58.9 (3.5)

541.9 (41.5)

899.5 (31.8)

314.8 (32.4)

5 100 3 1 315.0 (31.7)

539.7 (31.3)

58.3 (4.0)

547.4 (37.2)

920.9 (17.4)

289.9 (27.7)

6 Saline Control 353.8 (36.1)

624.1 (56.6)

56.7 (3.5)

526.0 (34.5)

900.6 (13.0)

318.6 (32.0)

7 60 5 1.5 331.5 (76.9)

622.7 (142.6)

53.4 (4.4)

489.2 (39.5)

888.6 (28.9)

293.0 (59.5)

8 20 7 1 309.5 (51.5)

577.9 (129.7)

54.4 (5.5)

508.6 (66.1)

911.2 (37.6)

280.8 (40.2)

9 100 3 2 303.0 (30.0)

528.9 (77.7)

57.8 (5.2)

554.5 (60.6)

937.7 (38.9)

283.6 (22.7)

10 20 7 2 326.9 (57.2)

590.8 (65.3)

55.2 (6.4)

507.1 (57.9)

898.2 (21.0)

293.1 (48.1)

11 No Treatment Control 342.0 (62.0)

636.8 (175.6)

54.8 (5.3)

512.7 (64.6)

907.4 (47.6)

307.9 (40.6)

Representative 3D Isosurface based models can be seen in Figure 5.5 on the following page.

Collectively, these figures provide a representation as to the variation in healing patterns of

different experimental groups and highlight how lithium therapy at the best treatment

combination helped to improve bone healing.

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Figure 5.5 - 3D isosurface models of three rat femurs used in the study. (A) A healing femur from a rat part of experimental group ten, determined as the best combination of lithium treatment (low dose, later onset, longer duration). (B) A healing femur from a rat part of experimental group five, determined as the worst combination of lithium treatment (high dose, earlier onset, shorter duration). (C) An intact contralateral femur from a control rat part of experimental group six.

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5.3 CT Based Torsional Rigidity

For each region of interest, the minimum CT-based torsional rigidity (GJmin) and the average

CT-based torsional rigidity (GJavg) were calculated. Experimental group ten, which

displayed the best mechanical properties, previously summarized in section 5.1, was shown

to have the largest minimum CT-based torsional rigidity value. Experimental group five, its

direct opposite treatment, which displayed poor mechanical properties, was shown to have

one of the lowest minimum CT- based torsional rigidity values. Results are summarized in

Table 5.4 below. GJmin, the primary parameter of interest from this portion of the analysis, is

shown graphically in Figures 5.6 and 5.7.

Table 5.4 - A summary of the CT based torsional rigidity findings for the eleven different groups. Average values are reported, with standard deviations given in parentheses. The maximum value for GJmin is shown in bold.


Onset (days)

Duration (weeks)

GJmin (kN-mm)

GJavg (kN-mm)

1 20 3 1 253.0 (71.6) 432.8 (89.0) 2 100 7 1 292.1 (66.7) 561.5 (133.2) 3 20 3 2 238.6 (51.9) 460.8 (92.6) 4 100 7 2 268.0 (47.0) 509.6 (79.9) 5 100 3 1 225.8 (40.4) 415.0 (74.5) 6 Saline Control 280.4 (55.9) 547.9 (106.4) 7 60 5 1.5 261.2 (78.2) 516.0 (175.2) 8 20 7 1 275.4 (81.6) 556.8 (245.7) 9 100 3 2 198.5 (40.4) 410.2 (123.0)

10 20 7 2 310.7 (81.4) 510.9 (124.7) 11 No Treatment Control 269.2 (51.0) 494.9 (176.0)

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Figure 5.6 - Average minimum CT based torsional rigidity for each of the eleven experimental groups, including standard error bars.

Figure 5.7 - A box and whisker plot showing the distribution and variation of minimum CT based torsional rigidity within and across experimental groups.

74

5.4 Design of Experiments System Modeling

Based on the eleven outcome parameters calculated for each sample (maximum yield torque,

twist angle at failure, experimental torsional stiffness, BV, TV, BV/TV, BMD, TMD, BMC,

GJmin and GJavg) eleven different design of experiment models were analyzed. The results

from each model are summarized on the following pages. Maximum yield torque

represented the primary outcome measure for the current study, as biomechanical strength is

the current gold standard used to assess the effectiveness and functionality of long bone

fracture healing (Weis et al., 2010). The results from the maximum yield torque DOE model

are expanded upon in greater detail in the next section.

In each model five different outcomes are reported: the applied transformation used, the

terms included in the model space, the direction of their effect, the associated p-values, and

the overall model coefficient of determination.

The applied transformation was based on a recommendation from the software; it was used

to correct for non-normal behaviour amongst the response data, and helped to stabilize the

variance. Terms were only included in the model if they showed greater than a 10%

contribution to the model space, as quantified through the sum of squares tally. If a certain

interaction term was included in the model (because it showed greater than a 10%

contribution to the model space), then its parent main effects were included regardless, even

if they showed less than a 10% contribution to the model space. For example, in the twist

angle at failure response, duration, dose*onset and onset*duration were all included in the

model because these terms showed greater than a 10% contribution to the model space. Yet,

even though the dose and onset main effects presented with less than a 10% contribution to

the model space, they were still included in the model because their subsequent interaction

term (dose*onset) was also included. This inclusion criterion is why each of the eleven DOE

models has a different number of model terms included. For each term included in the model

the direction of its effect was also provided, denoting whether an increase in the term was

good or bad for the output response. For example, in the maximum yield torque response, a

negative effect for dose implied that increasing dose resulted in a decrease in the response,

whereas a positive effect for both onset and duration implied that increasing these terms

75

resulted in an increase in the response. The strength and significance of the effect was

determined by the associated p-value; the stronger the effect, the lower the p-value, with

p<0.05 denoting significance. For example, in the maximum yield torque model, the p value

for onset was less than 0.05 and much smaller than the p value for dose (p=0.0125 <

p=0.1109), collectively implying that the positive affect of onset was much larger than the

negative affect of dose, with increasing onset having a significantly positive affect on the

output response. For each term in the model, as well as for the model in its entirety, an

associated p-value was reported, denoting significance. Not all terms that were included in

the model were necessarily significant to its response. For example, in the GJmin response,

both dose and onset showed greater than a 10% contribution to the model space and so, both

were included in the model. However, while the model itself was determined as significant

(p<0.05), only the onset term showed significance (p<0.05), while the dose term did not.

Finally, the coefficient of determination for the overall model was reported, providing an

indication of the model’s predicative nature. No coefficient of determination in any model

exceeded 0.22, implying that none of the models could be used to make accurate predictions

on the response. Therefore, even though certain models were significant, suggesting that the

trends observed were true, no model could be used to quantifiably predict output responses in

terms of input factor levels. A summary of the DOE model for each of the eleven different

outcome responses is shown in Table 5.5.

Table 5.5 - A summary of the design of experiment system modeling for each of the eleven outcome response measures analyzed. For each system, the applied transformation, the model terms, their effect on the response, their statistical p value and the overall system coefficient of determination are provided. Significant terms are italicized and shown with an asterisk. Results for maximum yield torque, the primary study outcome measure, are bolded.

Outcome Response

Applied Transformation

Model Terms Effect P-Value Coefficient of Determination

(r2) Model 0.0168*

Dose Negative 0.1109 Onset Positive 0.0125*

Duration Positive 0.1409


(N-mm)

Square Root

Curvature Non Significant 0.7692

0.183

Model 0.3977

Dose Positive 0.7358 Onset Negative 0.5249

Duration Positive 0.2933

Twist Angle at Failure

(°)

Logarithmic

Dose*Onset Negative 0.1759

0.099

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Onset*Duration Negative 0.2090 Curvature Significant 0.0210*

Model 0.1667


Duration Positive 0.6714 Onset*Duration Positive 0.2796

Experimental Torsional Stiffness (N-mm/°)

None

Curvature Significant 0.0393*

0.121

Model 0.1227

Dose Negative 0.2238 Onset Negative 0.1224

Dose*Onset Negative 0.1419

Bone Volume (mm3)

Inverse Square Root


0.108

Model 0.1996

Dose Negative 0.9491 Onset Positive 0.1098

Dose*Onset Positive 0.1551

Total Volume (mm3)

None


0.088

Model 0.2938


Duration Positive 0.4842 Onset*Duration Positive 0.4208

BV/TV (%)

None


0.094

Model 0.1003


Bone Mineral Density

(mgHA/ccm)

None


0.086

Model 0.0391*

Dose Positive 0.9499 Onset Negative 0.0050*

Duration Positive 0.8046 Dose*Onset Negative 0.2006

Dose*Duration Positive 0.1695

Tissue Mineral Density

(mgHA/ccm)

None

Curvature Significant 0.0252*

0.211

Model 0.2233

Dose Positive 0.2284 Onset Positive 0.2399

Dose*Onset Positive 0.1897

Bone Mineral Content (mgHA)

None


0.083

Model 0.0080*


GJmin (kN-mm2)

Logarithmic


0.172

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Model 0.0111* Onset Positive 0.0114*

GJavg (kN-mm2)

Logarithmic


0.118

The design of experiments modeling results from the eleven different outcome measures

yielded a number of interesting findings. First, four models were determined to be

statistically significant (maximum yield torque, tissue mineral density, GJmin, GJavg), and in

each of these four models, onset was the only input parameter determined to be significant to

the model. In the maximum yield torque and both GJ models, increasing onset was

significantly positive for the response, whereas in the tissue mineral density model,

increasing onset was significantly negative for the response. Second, in the experimental

torsional stiffness model, onset was statistically positive for the response even though the

model itself was not significant. This result suggests that, consistent with other findings, a

later onset is likely beneficial for this response, however, due to the other terms included in

the model space, a definitive conclusion cannot be made. Third, seven of the eleven models

showed onset as being the input parameter with the largest affect on the output response. In

five models (maximum yield torque, experimental torsional stiffness, total volume, GJmin,

GJavg) increasing onset showed a positive effect, whereas in two models (bone volume, tissue

mineral density) increasing onset showed a negative effect. Fourth, eight of the eleven

models displayed non significant curvature, while only three models suggested that the

associated response may be non-linear or saturated. Finally, none of the models appear to be

adequate at predicting an output response, since all coefficients of determination are less than

0.22.

5.4.1 Primary Outcome Response: Maximum Yield Torque

In the following section, the complete results from the DOE modeling on the primary

outcome parameter of maximum yield torque are presented.

Data was organized into scatter plots in order to visualize how factor levels affected the

response. Figure 5.8 on the following page shows the rough scatter plots for maximum yield

torque vs. dose, onset and duration respectively, colored by trial run. These plots provide an

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indication of how the output response was distributed depending on the factor level. In the

onset scatter plot, more data points are clustered at an increased maximum yield torque for

the higher (seven day) factor level. Trends are less evident in both the dose and duration

plots.

Figure 5.8 - Scatter plots showing the distribution and variation of maximum yield torque output data depending on the dose (A), onset (B) and duration (C) factor levels. Plots are colored by run to show the raw result from every sample tested.

79

Interactions between factors were examined by plotting maximum yield torque vs. a given

factor, but coloring the plot by a second factor rather than by the trial run. An interaction

would have presented itself by showing localization of a given color in either the upper or

lower corners of the plot. If the colors were randomly dispersed within the grouped columns

then this was an indication that no interaction was present. None of the three interaction

scatter plots showed visual trends that suggested a two factor interaction was present. Figure

5.9 is a representative plot depicting the interaction between dose and duration.

Figure 5.9 - A scatter plot showing the distribution and variation of maximum yield torque output data depending on the dose, colored by duration. These color by factor plots were used to investigate potential interaction trends between input parameters. As seen, red and blue markers are fairly evenly dispersed across the columns, an indication that no interaction was occurring.

After plotting the data and looking for preliminary visual trends, statistical modeling was

initiated. First, the data was checked for normality. Figure 5.10 shows a normal percent

probability plot of the output residuals, and Figure 5.11 shows the accompanying Box-Cox

power transformation plot. As seen in the residuals plot, some of the data towards the upper

and lower extremes deviated from normality, as it was situated too far away from the guiding

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red line. In addition, residuals in the middle of the plot displayed a subtle, but evident “S-

curve” pattern centered about the guiding red line. Moreover, the residuals ranged by over

600 total units (-306, +321). With such a large variation, deviations from the red line of

normality and "S-curve" patterns become overly accentuated and result in the need for

variance stabilization. As such, the Box-Cox power transformation plot recommended

applying a square root transformation to the output response data to help stabilize the

variance. Normally distributed data and homogeneity of variance must be confirmed prior to

using ANOVA statistical methods.

Figure 5.10 - The normal percent probability plot of the output residuals for the maximum yield torque of each sample. This plot was used to check for the assumption of normality. As seen above, some points fall off the red line, and the residual distribution displays a subtle “S-curve” pattern, indicating deviation of the data from normality. With such a large range in the output residuals (>600 units), the software recommended applying a square root transformation to help stabilize the variance.

81

Figure 5.11 - The Box-Cox power transformation plot was used to transform the data if it deviated from normality. In this case, the software recommended a square root transformation in order to help stabilize the variance.

Figure 5.12 on the following page shows the normal percent probability plot of the output

residuals after the power transform was applied to help improve the data. While deviations

from the red line of normality were still evident, the residuals now only spanned a total of 18

units, making these deviations no longer an issue. Once the Box-Cox power transformation

was applied, normality was assumed and the homogeneity of variance assumption was

verified.

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Figure 5.12 – The normal percent probability plot of the output residuals for the maximum yield torque of each sample after the square root transformation was applied. The residuals now ranged only 18 units, making the assumption of normality valid.

Once a square root transformation was applied to the data, the sum of squares chart was used

to determine which terms to include in the model. Inputs showing greater than a 10%

weighted contribution to the model space were included. As seen from the sum of squares

chart shown in Table 5.6, dose, onset and duration were all included in the model, while the

other two factor and three factor interaction terms were applied to the residual error.

83

Curvature was always included in the model in order to check for a possible non-linear or

saturated output response within the cubic design space.

Table 5.6 - The sum of squares chart used to quantify the size of each effect and its percent contribution to the model space. Terms that showed less than a 10% contribution were excluded from the model and applied to the error. Bolded terms indicate those included in the model.

Term Effect Sum of Squares %

Contribution

% Contribution to the Model

Require Intercept Model A-Dose -1.70 33.29 4.27 21.58 Model B-Onset 2.72 84.91 10.90 55.05 Model C-Duration 1.57 28.29 3.63 18.34 Error AB -0.39 1.46 0.18 0.95 Error AC -0.72 6.01 0.77 3.90 Error BC 0.15 0.25 0.03 0.16 Error ABC 0.05 0.03 0.004 0.02

Model Curvature -1.10 0.63 0.08 Error Lack Of Fit 0 0 Error Pure Error 624.20 80.12

Lenth's ME 2.16

Lenth's SME 3.01

The sum of squares chart above shows that onset had the largest weighted contribution to the

model space (55%), followed by dose (22%) and then duration (18%). This trending is

consistent with the respective effect magnitude for each input factor, also shown in the table

above (onset = 2.72; dose = 1.70; duration = 1.57). Moreover, the direction associated with

each effect indicates that increasing onset and duration had a positive influence on the

maximum yield torque output response (+ effects), whereas increasing dose had a negative

influence on this outcome (- effect). Collectively, these effect patterns suggest that the

“best” treatment combination occurred at a lower dose, later onset and longer duration

(low/high/high) input factor combination, whereas the “worst” treatment combination

occurred when input factor were set to opposite extremes (higher dose, earlier onset, and

shorter duration; high/low/low). These factor effects are further supported by the Pareto

Chart shown in Figure 5.13 on the following page.

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Figure 5.13 - The Pareto chart shows both the size and direction of each input parameter as related to the output response. As seen above, B, A and C (representing onset, dose and duration respectively) were terms included in the model space (as indicated by the hollowed out bars), whereas the other four solid bars, representing the three two factor interactions and the one three factor interaction, were excluded from the model and applied to the error. B (onset) showed the largest effect, followed by A and then C. The tip of the onset bar extends beyond the t-value limit of 2.01, implying that this effect was considered statistically significant to the model space. Orange bars depict positive effects, whereas blue bars represent negative effects.

With the model defined, and all normality assumptions verified, the ANOVA technique was

then used to determine the statistical influence of all model inputs. As seen in Table 5.7, the

ANOVA showed that the model was statistically significant (p=0.02), and, consistent with

the Pareto Chart shown in Figure 5.13, onset was the only significant term in the model space

(p=0.01). In addition, the model was shown to have no significant curvature (p=0.77),

implying that the output responses displayed linear behaviour, showing no indication of

saturation within the cubic design space. Finally, a non significant lack of fit (p=0.97)

confirmed that the model error occurred due to random noise, rather than true model misfit.

Collectively, the results of the ANOVA confirmed that, with 95% confidence, the model

85

itself showed true, significant effects, and that increasing onset had a statistically positive

effect on the maximum yield torque output. Compared to pooled controls, rats treated at a

later onset showed a 21% increase in their maximum yield torque, while rats treated at the

“best” treatment combination of low dose, high onset and high duration showed a 46%

increase in their maximum yield torque.

Table 5.7 - The ANOVA table for the maximum yield torque output response. Terms included in the model are bolded. Significant findings are italicized with accompanying asterisk. As shown, the model was determined to be statistically significant, with onset being the only significant parameter in the design space.

Source Sum of Squares

Degrees of Freedom

Mean Square F Value

P-Value Prob > F

Model 141.79 3 47.26 3.74 0.02* A-Dose 33.29 1 33.29 2.63 0.11 B-Onset 84.91 1 84.91 6.72 0.01*

C-Duration 28.29 1 28.29 2.24 0.14 Curvature 1.10 1 1.10 0.09 0.77

Residual 631.96 50 12.64 Lack of Fit 7.76 4 1.94 0.14 0.97 Pure Error 624.20 46 13.57 Cor Total 774.85 54

Following the ANOVA, a regression analysis was executed to determine the predictive

ability of the model. While the ANOVA determined the model to be statistically significant,

the regression analysis confirmed that the model was a very poor predictive tool (r2= 0.183)

and could not be used to make a quantifiable prediction on the nature of the outcome

response given model inputs. A scatter plot depicting the relationship between actual and

predicted outputs is shown in Figure 5.14 on the following page. As seen, the points are

generally oriented on a pattern of zero slope and deviate far from the ideal line of r2=1 that is

shown. Hence, this plot highlights the poor correlation between the actual and predicted

output responses.

86

Figure 5.14 - A plot of the predicted vs. actual values for the maximum yield torque output, with accompanying r2 value. The model shows very poor predictive nature, as evident by the low r2 value and the generally flat slope of the data points.

The model equation in terms of coded factor levels (±1) is shown in Equation 5.1, along with

associated 95% confidence intervals on the equation coefficients (Table 5.8). The

confidence intervals further validate the results from the ANOVA. As seen, the range of

confidence indicates that one can be 95% certain that the coefficient associated with onset is

not zero, or less than zero, implying that onset does have a significantly positive effect on the

87

maximum yield torque output. However, the 95% confidence intervals for both the dose and

duration coefficients includes zero within the range. Therefore, one cannot be statistically

certain that these two terms have an effect on the model -since either coefficient could

theoretically be zero-, a result consistent with that found in the ANOVA.

Although Equation 5.1 presents a relationship between coded model inputs and the

maximum yield torque output, the low coefficient of determination for the overall model, as

shown previously in Figure 5.14, nonetheless implies that this equation is a very poor

predictive tool.

Equation 5.1 - The predictive coded model equation relating model inputs - dose, onset and duration - to the model output, maximum yield torque. Using model inputs as either high (+1) or low (-1) coded values, this equation provides an estimation as to what the maximum yield torque would be given different combinations of model inputs.

Table 5.8 - The 95% confidence intervals associated with the model equation coefficients from Equation 5.1 above. As seen, it is statistically certain that the onset coefficient is not zero, since zero is not included in the 95% confidence interval. However, both dose and duration include zero in their respective 95% confidence intervals, implying it cannot be statistically concluded that these terms have an effect on the model. This finding was also seen in the ANOVA, as the p values associated with both dose and duration were greater than 0.05, while the p value associated with onset was less than 0.05.

Factor Coefficient Estimate

Degrees of Freedom

Standard Error

95% CI Low

95% CI High

Intercept 18.20 1 0.53 17.14 19.25 A-Dose -0.85 1 0.53 -1.90 0.20 B-Onset 1.36 1 0.53 0.31 2.42

C-Duration 0.79 1 0.53 -0.27 1.84

On the following pages a variety of output plots are provided that were generated by the

software to supplement those results found from the statistical models. Collectively, these

plots give a pictorial indication of how variation in input parameter and their interactions

affected the maximum yield torque output response. All plots are in agreement, in that they

suggest that a lower dose, later onset, longer duration (low/high/high) treatment combination

is best for maximizing the primary outcome parameter of maximum yield torque.

88

Figure 5.15 - These two plots show how changes in dose affected maximum yield torque. The red points represent the actual design points, while the black squares indicate average values with accompanying least square difference error bars. As seen in both the left and right figures, representing different combinations of onset and duration factor levels, increasing dose ultimately decreased the maximum yield torque.

Figure 5.16 - These two plots show how changes in onset affected maximum yield torque. The red points represent the actual design points, while the black squares indicate average values with accompanying least square difference error bars. As seen in both the left and right figures, representing different combinations of dose and duration factor levels, increasing onset ultimately increased the maximum yield torque.

89

Figure 5.17 - These two plots show how changes in duration affected maximum yield torque. The red points represent the actual design points, while the black squares indicate average values with accompanying least square difference error bars. As seen in both the left and right figures, representing different combinations of dose and onset factor levels, increasing duration ultimately increased the maximum yield torque.

The six plots provided above are main effect plots at specific design points. The software

allowed the user to obtain graphs for any combination of input parameters within the design

space, even those not specifically tested. These six plots were chosen as representative

images highlighting opposite ends of the cubic design space.

Since no significant interactions were found, the two factor interaction plots relay the same

information that the three main effect plots collectively relay. Figure 5.18 shows the two

factor interaction plot between dose and duration. If an interaction had been present, the two

lines (black and red) would have intersected. However, because the lines remain parallel, no

interaction is observed.

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Figure 5.18 - The two-factor interaction plot for dose and duration at the two different onset factor levels. It can be seen that a low dose is ideal, as the black line (low dose) is positioned above the red line (high dose) in both plots. Moreover, it can be seen that increasing duration is ideal for increasing maximum yield torque, as both black and red lines show increasing, positive slopes. Finally, it is evident that a later onset is best for the response, as the late onset graph (right) shows a positive vertical shift upwards compared to the low onset graph (left). Collectively, this two factor interaction plot relays the same information as a combination of main effect plots, suggesting that low dose, high onset and high duration is the "best" treatment combination for maximizing the maximum yield torque output response.

The final, predicted design space is shown in Figure 5.19 on the following page. The small

red circles indicate the location of a specific combination of treatment parameters, and the

accompanying number represents the number of samples tested at that location. Values

reported at each corner are those based on the predicted, coded model equation found

previously in Equation 5.1. For example, at a low dose (-1), low onset (-1) and low duration

(-1) treatment combination, Equation 5.1 suggests a predicted output response of 285.6 N-

mm (front-bottom-left corner). Consistent with all other plots and statistical models, the

cubic design space highlights that the best response occurred at a lower dose (-A), later onset

(+B) and longer duration (+C) treatment combination. Its corresponding position is

underlined in red below. The worst treatment combination occurred at a higher dose (+A),

earlier onset (-B) and shorter duration (-C). Its corresponding position in the cubic design

space is underlined in blue. Moreover, a later onset, represented by the top face of the cube

91

(outlined in red), possesses four of the five largest outcome responses, whereas an earlier

onset, represented by the bottom face of the cube (outlined in blue), possesses four of the five

lowest outcome responses. Hence, the design space is in agreement with the results obtained

from the statistical models, which identified a later onset as being statistically positive for

this output response.

Figure 5.19 - The predicted design space for maximum yield torque. Values were determined based on the predicted model equation using coded (±1) input factors. As indicated by the red underline, the best location in the design space is at a low dose, later onset, longer duration (-A, +B, +C) treatment combination situated in the upper, back left corner of the cube.

92

5.5 Experimental Groups vs. Controls

Once the DOE model determined the “best” and “worst” treatment groups based on the

primary outcome measure of maximum yield torque, these two groups were compared to

pooled controls. Group ten, treated at a low dose, high onset and high duration treatment

combination (dose=20 mg/kg-wt/day; onset=7 days; duration=2 weeks) was determined by

the DOE system modeling to maximize the primary outcome response of maximum yield

torque, while group five, treated at a high dose, low onset and low duration treatment

combination (dose=100 mg/kg-wt/day; onset=3 days; duration=1 week) was determined by

the DOE system modeling to minimize this response.

A two tailed independent samples T-test revealed a significant difference (p = 0.042) for

maximum yield torque between the pooled controls and experimental group ten (Table 5.9).

Levene's test for equality of variances showed that there was no significant difference

between the variance of the two groups (F=0.50, p>0.05), confirming that the assumption of

equal variances could be used for the statistical test. Compared to pooled controls, this

combination of lithium administration significantly improved maximum yield torque by

46%.

Table 5.9 - An independent samples T-test comparing the maximum yield torque between group ten and the pooled controls. Assuming an equal variance, the results indicated that there was a significant difference between group ten and the pooled controls on the maximum yield torque outcome response. The test p value is reported (bolded) along with the 95% confidence interval for the difference in means.

Levene's Test for Equality of

Variances T-Test for Equality of Means (Maximum Yield Torque - Pooled

Controls, Experimental Group10) 95% Confidence Interval of the Difference

F Sig. t df Sig. (2-tailed)

Mean Difference

Std. Error Difference Lower Upper

Equal variances assumed

.50 .49 -2.22 15 .042 -151.17 68.16 -296.44 -5.89

Equal variances not assumed -2.49 9.9 .032 -151.17 60.80 -286.85 -15.48

In contrast, a two tailed independent samples T-test revealed no significant difference (p =

0.246) for maximum yield torque between the pooled controls and experimental group five

93

(Table 5.10). Levene's test for equality of variances showed that there was no significant

difference between the variance of the two groups (F=1.36, p>0.05), confirming that the

assumption of equal variances could be used for the statistical test. Compared to pooled

controls, this combination of lithium administration decreased maximum yield torque by

22%, although this result was not significant.

Table 5.10 - An independent samples T-test comparing the maximum yield torque between group five and the pooled controls. Assuming an equal variance, the results indicated that there was no significant difference between group five and the pooled controls on the maximum yield torque outcome response. The test p value is reported (bolded) along with the 95% confidence interval for the difference in means.

Levene's Test for Equality of

Variances T-Test for Equality of Means (Maximum Yield Torque - Pooled

Controls, Experimental Group 5) 95% Confidence

Interval of the Difference


Mean Difference



1.36 .26 1.20 16 .246 74.09 61.55 -56.38 204.56

Equal variances not assumed 1.39 14.48 .187 74.09 53.47 -40.24 188.42

Finally, since five of the eleven DOE models showed a later onset as having the largest

positive effect on the outcome response, including four models showing this effect as being

statistically significant, a two tailed independent samples T-test was conducted to determine

if there were any significant differences between rats receiving lithium treatment at a later

onset and pooled controls (Table 5.11). Levene's test for equality of variances showed that

there was no significant difference between the variance of the two groups (F=0.87, p>0.05).

Using an assumption of equal variances, rats receiving a later onset of lithium treatment

showed a 21% increase in their maximum yield torque compared to pooled controls,

although this difference was determined as non significant (p = 0.229). These results suggest

that even though the DOE modeling indicates that a later onset is significantly positive for

increasing the maximum yield torque output response, it is important to control the dose and

duration components of the treatment regiment otherwise this positive effect may be lost.

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Table 5.11 - An independent samples T-test comparing the maximum yield torque between rats receiving a later onset and the pooled controls. Assuming an equal variance, the results indicated that there was no significant difference between late onset rats and the pooled controls on the maximum yield torque outcome response. The test p value is reported (bolded) along with the 95% confidence interval for the difference in means.

Levene's Test for Equality of Variances

T-Test for Equality of Means (Maximum Yield Torque - Pooled Controls, Late Onset)

95% Confidence

Interval of the Difference


Mean Difference



.87 .36 1.23 32 .229 68.05 55.50 -45.00 181.10

Equal variances not assumed 1.30 26.60 .206 68.05 52.48 -39.70 175.80

5.6 Correlation Analysis

A correlation analysis revealed a significant, inverse correlation between maximum yield

torque and tissue mineral density (r = -0.281, p = 0.021), and a significant positive

correlation between maximum yield torque and minimum CT-based torsional rigidity (r =

0.242, p = 0.049). There were no other significant correlations between mechanical

parameters and µCT based imaging parameters, although several combinations demonstrated

trends nearing significance (0.1 > p > 0.05), including maximum yield torque and GJavg, (p =

0.069) and experimental torsional stiffness and TMD (p = 0.062), GJmin (p = 0.069) and GJavg

(p = 0.056). The complete correlation matrix is shown in Table 5.12. Significant

correlations are bolded with an asterisk.

Table 5.12 - Pearson correlation analysis between mechanical testing parameters and µCT-based stereology parameters. Pearson correlation coefficients and associated p-values are provided for each combination of parameters tested. Significant correlations are bolded with an asterisk.

BV TV BV/TV BMD TMD BMC GJ min

GJ avg

Pearson .109 .153 -.140 -.214 -.281 .054 .242 .224 Torque P-value .381 .217 .258 .082 .021* .666 .049* .069 Pearson -.164 -.171 .037 .032 .018 -.181 -.129 -.043 Angle P-value .184 .166 .768 .798 .888 .143 .297 .727 Pearson .170 .208 -.134 -.187 -.229 .138 .224 .235 Stiffness P-value .168 .090 .280 .130 .062 .265 .069 .056

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5.7 Contralateral Limbs

Contralateral, non-fractured femurs were analyzed in order to investigate lithium's affect on

the off-target limb. Six non fractured, contralateral femurs from group ten (dose=20 mg/kg-

wt/day; onset=7 days; duration=2 weeks), six non fractured, contralateral femurs from group

five (dose=100 mg/kg-wt/day; onset=3 days; duration=1 week) and six non fractured,

contralateral femurs from group six (saline control) were subject to identical biomechanical

torsion testing, µCT based bone stereology analysis and CT-based torsional rigidity

calculations. Groups five and ten were specifically chosen because DOE analysis on the

healing femurs revealed these two experimental groups to be on opposite ends of the cubic

design space, with group ten treatment parameters showing the most positive influence on

the primary outcome measure of maximum yield torque, and group five treatment parameters

showing the most negative influence on this response.

Mechanical testing data (Table 5.13), stereological results (Table 5.14) and CT-based

torsional rigidity calculations (Table 5.15) are presented for the three contralateral groups

tested. A two way ANOVA was used to compare the eleven different response measures

between the three contralateral groups tested, with p<0.05 considered significant. Results

confirmed no significant difference between groups on maximum yield torque, the primary

study outcome measure, or on any of the other mechanical parameters determined through

torsional testing. In the stereological analysis, a small but significant increase in TMD was

found in comparing group five to group ten (3.1%, p=0.03). No significant differences were

found between groups on any of the other image based secondary outcome parameters.

Collectively, these results seem to suggest that short term lithium treatment successfully

targets the healing femur and does not greatly influence the mechanical properties or the

micro-structure of the contralateral, intact limb. However, the small difference in TMD

suggests that systemic lithium still may incorporate into the bone matrix of the contralateral

limb, possibly through calcium substitution in the crystal lattice structure.

It is interesting to note that although no significant differences were found between groups,

trending seen in the healing femora data was similarly exhibited in the contralateral data.

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Group ten contralateral femurs showed the highest maximum yield torque and GJmin, while

displaying the lowest TMD, an identical trend seen in the group ten healing femur data.

Table 5.13 - A summary of the mechanical testing data for the three different contralateral limb groups tested. Average values are reported, with standard deviations given in parentheses.


Onset (days)

Duration (weeks)


(N-mm)

Twist Angle (°)

Torsional Stiffness (N-mm/°)

5 100 3 1 380.4 (107.9) 12.3 (1.5) 31.3 (7.6)

6 Saline Control 363.5 (123.5) 12.7 (3.4) 30.2 (14.1)

10 20 7 2 404.6 (87.9) 13.2 (7.4) 31.2 (7.4)

Table 5.14 - A summary of the bone stereology data for the three different contralateral limb groups analyzed. Average values are reported, with standard deviations given in parentheses.


Onset (days)

Duration (weeks)

BV (mm3)

TV (mm3)

BV/TV (%)

BMD (mgHA/ccm)

TMD (mgHA/

ccm)

BMC (mgHA)

5 100 3 1 181.8 (7.3)

277.2 (14.3)

65.7 (2.7)

718.2 (31.0)

1092.5 (7.5)

198.6 (7.5)

6 Saline Control 183.2 (13.5)

290.1 (26.8)

63.3 (2.1)

684.0 (35.1)

1078.2 (24.2)

197.3 (11.2)

10 20 7 2 187.9 (11.1)

298.2 (21.7)

63.1 (3.3)

670.8 (41.9)

1059.1 (22.4)

198.8 (8.6)

Table 5.15 - A summary of the CT based torsional rigidity findings for the three different contralateral groups tested. Average values are reported, with standard deviations given in parentheses.


Onset (days)

Duration (weeks)

GJmin (kN-mm)

GJavg (kN-mm)

5 100 3 1 103.9 (10.9) 165.7 (11.9)

6 Saline Control 108.6 (9.4) 172.2 (17.3)

10 20 7 2 116.1 (14.1) 177.9 (18.6)

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Comparison of the maximum yield torque between healing and contralateral femurs from the

three different groups investigated is shown graphically in Figure 5.20. It is interesting to

note that it is the healing limb, not the contralateral one, from group ten, which displayed the

largest maximum yield torque. In groups five and six, the contralateral limb was shown, as

expected, to be stronger than its healing counterpart.

Figure 5.20 - A comparison of the average maximum yield torque, with accompanying standard error, between healing and contralateral femurs from the three different groups investigated.

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Chapter 6: Discussion

There are over 346 million people currently populating North America (One World - Nations

Online, 2013) and approximately one third are expected to experience a debilitating fracture

in their lifetime (Hoeppner, Secreto, & Westendorf, 2009). In nearly 5-10% of those cases,

accounting for over five million people, the bone will fail to heal normally and result in a non

or mal union, leading to significant personal and economic consequences (Hoeppner,

Secreto, & Westendorf, 2009). As such, there remains an imminent need to find treatment

methods to aid in fracture healing.

To date, there are only two anabolic drugs approved for use in the United States that are

therapeutically aimed at stimulating bone growth: bone morphogenetic protein (BMP-2;

BMP-7) and Teriparatide (parathyroid hormone) . Previous work has shown these treatments

as individually effective for fracture healing (Barnes et al., 2008; Hak et al., 2006; Nakajima,

et al., 2002), while Morgan and colleagues (2008) reported that using both treatments in

combination enhanced healing even further. Despite positive evidence, these treatments

have not gained consensus indication for use in fracture management due to their significant

limitations. BMPs are expensive, costing around $6000 per delivery, have a very short half

life and must be implanted locally to have any effect. Teriparatide must be given daily via

subcutaneous, systemic injections, is also quite expensive, costing around $750 per month

(RxFiles, 2010) for all required daily treatments, and its usage time is restricted in certain

regions (18 month maximum in Europe; 24 month maximum in the United States) because of

serious safety concerns. Teriparatide has been known to cause acute hypercalcemia and

hypercalciuria (Khosla, Westendorf, & Oursler, 2008), while increased parathyroid hormone

levels have been linked to osteosarcoma in rats (Vahle, et al., 2002).

The canonical Wnt/β-Catenin pathway is a promising therapeutic target to stimulate bone

growth. A naturally occurring, biological cell signaling cascade, this pathway has been

confirmed to influence the osteoblast lineage, stimulating mesenchymal progenitor

precursors to differentiate into fully active, mature osteoblasts (Hoeppner, Secreto, &

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Westendorf, 2009; Khosla, Westendorf, & Oursler, 2008; Krishnan, Bryant, & MacDougald,

2006). As such, therapeutic strategies aimed at enhancing Wnt/β-Catenin pathway activity

have tremendous potential as anabolic interventions for bone growth, lending to possible non

invasive treatments for fracture repair.

There are two basic approaches to stimulate Wnt/β-Catenin pathway activity: adding

pathway agonists or blocking naturally occurring pathway antagonists. The former approach

is costly and not reasonable, as recombinant Wnts are glycoproteins that are both difficult

and expensive to purify (Hoeppner, Secreto, & Westendorf, 2009). The latter approach of

blocking naturally occurring antagonists is more feasible and is the current focal point of

Wnt/β-Catenin related research.

There are many possible therapeutic targets for blocking naturally occurring Wnt/β-Catenin

pathway antagonists, including using antibodies to block the action of extracellular Wnt

inhibitors - Sclerostin; Dickkopfs (DKK-1,2); secreted frizzled related proteins (SFRPs) and

Wnt inhibitory factors (WIFs) -, or targeting the action of intracellular pathway components,

such as the GSK3β-Axin-APC-CK1α destruction complex and the Chibby binding motif

(Kim, et al., 2013; Wagner, et al., 2011). However, it is the stimulation of pathway activity

through systemic, lithium induced GSK-3β inhibition that has been of particular interest,

with various investigators reporting on the positive anabolic affect that this approach has on

bone biology (Warden, et al., 2010; Chen, et al., 2007; Clément-Lacroix, et al., 2005).

Other therapeutic interventions targeting the Wnt/β-Catenin pathway, such as anti-Sclerostin

and anti-DKK antibodies, have similarly demonstrated positive anabolic effects in preclinical

models (Komatsu et al., 2010; Li, et al., 2009), and some of these drugs have even been

investigated (Padhi et al., 2011) and are currently being tested in Phase I/II clinical trials

(ClinicalTrials.gov identifier: NCT00896532; NCT00741377). However, these interventions

are fairly novel, their recombinant nature makes them quite costly, and the potential human

risks and their long term safety concerns have yet to be fully determined. In contrast, lithium

is an appealing therapeutic option for Wnt/β-Catenin pathway stimulation, as it has been

effectively used in mainstream, psychiatric medicine for over 50 years, with minimal long

term, serious safety risks and no known links to cancer. Moreover, although systemic

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toxicity can occur with over dosage, when the drug is closely monitored and maintained at its

therapeutic levels (0.6-1.2 mEQ/L), it has been proven to be a relatively safe intervention,

with only minor, temporal acute side effects. Finally, the generic, 1200 mg, oral-systemic,

once-a-day capsule of lithium treatment, currently used by the majority of bipolar disorder

patients, costs a mere $15 per month (RxFiles, 2010). Compared to other approved anabolic

treatment options (BMPs; Teriparatide) and other drugs aimed at harnessing the anabolic

potential of the Wnt/β-Catenin pathway (anti-Sclerostin antibody; anti-DKK antibody),

lithium presents as an attractive, non invasive and highly cost effective treatment option.

While lithium's mechanism of action is still under much scrutiny, a variety of propositions

have been presented in the literature, many of which show interconnectivity, with ample

crosstalk relating back to Wnt/β-Catenin signaling. For example, lithium is known to

activate the ERK/MAP kinase pathway, an important cell signaling pathway shown to

regulate cell division as well as neuronal and synaptic plasticity. In addition to

phosphorylating its nuclear receptor (CREB), stimulation of the ERK/MAP kinase pathway

is also known to inherently inhibit GSK-3β activity through serine 9 phosphorylation (Quiroz

et al., 2010; Doble & Woodgett, 2003). Similarly, lithium is known to stimulate cyclic

adenosine monophosphate (cAMP) mediated signal transduction by elevating basal adenyl

cyclase (AC) activity. AC catalyzes the conversion of adenosine triphosphate (ATP) to

cAMP, which, in turn, activates protein kinase A (PKA). In addition to downstream

activation of mitogen-activated protein kinases, it is well known that PKA also

phosphorylates GSK-3β at serine 9 leading to its inactivation (Quiroz et al., 2010; Fang et al.,

2000). Moreover, lithium is known to activate the phosphatidyl inositol cell signalling

cascade, which ends in downstream activation of protein kinase B (PKB) and certain

isoforms of protein kinase C (PKC). PKB and PKC have a diverse range of cellular targets,

which regulate many cellular processes including metabolism, protein synthesis, cell cycle

activity and cell survival. Both PKB and PKC have beem shown to inihibit GSK-3β activity

by phosphorylating this enzyme at its serine 9 location (Chaung, Wang, & Chiu, 2011;

Sarno, Li, & Jope, 2002). Therefore, while lithium is inherently a natural, direct inhibitor of

the GSK-3β enzyme, it also indirectly inhibits GSK-3β through stimulation of several cell

signaling pathways that, downstream, also inhibit GSK-3β via serine 9 phosphorylation.

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GSK-3β is a multifaceted enzyme phosphorylating many different cellular targets with a

wide variety of physiological implications. It is involved in embryogenesis, energy

homeostasis, cell signaling, cell life cycle regulation, gene expression, and much more

(Sutherland, 2011; Doble & Woodgett, 2003). With recent work elucidating the anabolic

affect that Wnt/β-Catenin pathway stimulation has on bone, and the ample evidence relating

lithium's mechanism of action to the Wnt/β-Catenin pathway through direct and indirect

GSK-3β inhibition, lithium's potential use in bone anabolic applications, such as fracture

healing, has a sound basis. Yet, while lithium therapy holds clinical promise for this

application, there has been minimal work to date focused on defining an actual treatment

regimen to optimize the healing process. Given the need for precise regulation of GSK-3β

levels, and the direct link between lithium and this enzyme, thorough preclinical

investigation of the lithium-GSK-3β -Wnt/β-Catenin signaling axis as it pertains to bone

healing is required before lithium can be considered for use in this clinical application.

As such, the goal of the current study was to complete phase one screening of the three

phased experimental design collectively aimed at determining the optimal combination of

lithium treatment that maximizes bone healing in a rodent preclinical, femur-fracture model.

Results suggested that a lower dose (20 mg/kg-wt/day), later onset (7 days), longer duration

(2 weeks) treatment combination was best for bone healing, as this combination maximized

the primary outcome response of maximum yield torque, demonstrating a significant 46%

increase over pooled controls (481.1 ± 104.0 N-mm vs. 329.9 ± 135.8 N-mm). In contrast,

the opposite combination of treatment parameters - higher dose (100 mg/kg-wt/day), earlier

onset (3 days), shorter duration (1 week) - was shown to be detrimental to bone healing,

demonstrating a 22% reduction in maximum yield torque compared to pooled controls (255.8

± 89.1 N-mm vs. 329. 9 ± 135.8 N-mm). Onset was shown to be the most significant

parameter influencing the maximum yield torque response, with a later onset being

statistically positive for improved healing, suggesting that the exact timing of treatment

administration is the most crucial factor in optimizing the treatment regimen. With bone

healing being such a highly coordinated and tightly regulated temporal physiological process,

this finding is not surprising.

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6.1 Outcome Response Measures: Trends and Correlations

The primary outcome response of maximum yield torque showed quite a large variation, with

standard deviations reaching nearly 50% of the mean in several of the treatment groups.

Large variations near 50% of the mean were also seen in the experimental stiffness data,

calculated from the slope of the applied torque-twist angle graph generated during

mechanical testing. Large variations are expected in biological focused research, especially

during biomechanical testing, where inherent, uncontrollable factors such as biological based

variability greatly influence the results. While large variations in biomechanical fracture

healing data have been reported by other investigators (Azuma et al., 2001; Yang, et al.,

1996; Ekeland et al., 1981), the variation seen in the data of our study was on the higher end

of what has been reported in the literature. One plausible explanation for such a large

variation stems from the inconsistent fracture patterns generated across samples. A closed,

drop weight induced, high impact fracture model was used in our study in order to mimic

trauma, and produce the associated soft tissue and muscular damage that accompanies it.

However, this type of fracture model comes with the trade-off of being unable to fully

control the fracture pattern generated, since once the drop weight is initiated, its trajectory

remains uninfluenced. While the modifications made to the jig in the in vitro optimization

phase of the project (section 4.1) were aimed at addressing this problem, the issue of

inconsistencies amongst fracture patterns still remained. Even though all rats were of the

same strain, sex, age and weight, variations in biological factors including muscular density

and limb length and curvature could have influenced the type of fracture pattern generated

and the nature of the local healing response initiated. For example, smaller, transverse

fractures will heal much faster and more efficiently than larger, comminuted patterns.

Similarly, a fracture situated perfectly mid-shaft will heal differently than a fracture located

heavily in the proximal or distal femur. Other fracture models could have better controlled

for fracture pattern (such as open osteotomies or more controlled three point bending jigs),

but these models would have sacrificed the high impact trauma and associated soft tissue

damage that accompanies a closed, drop weight approach. One possibility to improve the

repeatability of our closed drop weight fracture jig would be to drop a heavier weight from a

shorter distance, ultimately reducing the speed at which the fracture blade makes contact

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with the bone. In the current study, a mass of 380 grams was dropped from a height of 33

cm, transferring a total of 1.23 Joules of useable energy to the bone. In future work, a similar

amount of energy can be transferred to the bone by dropping a larger mass from a shorter

height. The reduction in kinematic properties of the blade, including impact speed, time

traveled and distance dropped, that will follow from dropping a heavier mass from a shorter

distance, may better help control the degree of trauma and improve the repeatability of the

fracture pattern generated.

Biomechanics represent an important clinical benchmark in fracture healing assessment,

superior from simple radiographic observation, as the fracture callus is considered to reach

clinical biomechanical standards well before callus mineralization becomes dense enough to

indicate complete healing on radiographs (Aspenberg, et al., 2009). While some

investigators report having used a three point bending test to investigate the biomechanics of

fracture healing in rodents (Fu et al., 2009; Nyman, et al., 2009; Yingjie, et al., 2007; Utvag

et al., 1999), other studies, including this work, used destructive torsional testing to assess

the biomechanical properties of the healing bone (Park, et al., 2013; Nazarian, et al., 2010;

Shefelbine, et al., 2005; Azuma, et al., 2001; Huddleston, et al., 2000). One of the major

limitations of three point bending is that it localizes the applied load, and therefore, initial

failure during testing is highly dependent on where the main load is applied. Moreover, three

point bending does not apply equally severe loading conditions at every cross section along

the bone’s length; by definition, the maximum moment occurs at the tensile and compressive

faces of where the load is applied, and decreases away from the point of application.

Therefore, for a fracture callus, which is a non homogenous biological structure, three point

bending leads to an inaccurate representation of its biomechanical properties and introduces

unnecessary experimental bias to its location of failure (Habermann et al., 2010). Torsion is

the ideal test choice, as it subjects each cross section to identical loading conditions, allowing

the bone to naturally fail at its weakest location (Burstein & Frankel, 1971).

CT-based torsional rigidity analysis, previously described by Nazarian and colleagues

(2009), was successfully implemented in the current study. Similar to findings reported in

their 2010 paper, we found a significant correlation between maximum yield torque and

GJmin (r=0.242, p<0.05), although this correlation was significantly weaker than what was

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previously reported (r=0.88) by the authors. Our data demonstrated no significant

correlation between mechanical testing outcomes and GJavg, a finding also reported by the

previous authors. Since bone is only as strong as its weakest cross section, and weakest, not

average, mechanical properties dictate failure behaviour, our findings validate the claim

made by the previous authors that GJmin is the better CT-based predictor of bone failure.

Moreover, our mechanical and stereological correlation results, indicating strongest positive

correlations between mechanical testing parameters and CT-based torsional rigidity values

(rather than other common µCT based measures), are consistent with those results reported

by Morgan et al. (2009). In their paper, Morgan and colleagues outline that the best

predictors of mechanical properties of bone are CT based outcomes that incorporate quantity,

distribution and mineral density into one measure. CT based torsional rigidity incorporates

all three of these factors, making it superior to other stereological indicators (such as BV/TV,

TV, TMD or BMC), which only take into account one factor at a time.

Interestingly, our findings show no significant correlations between torsional stiffness

assessed through mechanical testing and CT-based rigidity methods. This is in contrast to

Nazarian and colleagues (2010) who report this relationship to be moderate to strong for

GJavg (r2=0.63), and the strongest and most significant for GJmin (r2=0.81). This discrepancy

could potentially be explained by differences in study designs. First, in the Nazarian study,

femurs were harvested eight weeks after fracture, whereas in our study, femurs were

harvested four weeks post fracture. There are disagreements in the literature in terms of the

timing of rat bone healing. Meyer and coworkers (2001) report that in younger rats, bone is

nearly healed after four weeks, exhibiting biomechanical properties approaching those of

intact standards. Similarly, Habermann et al. (2010) state that the endochondral ossification

to remodelling phase transition in the rat occurs around day 21, asserting that differences in

bone healing can be detected by day 28. Moreover, both Histing, et al., (2011) and

O'Loughlin, et al., (2008) suggest that four to five weeks post fracture is the ideal time point

to investigate bone healing in the rat. This is in stark contrast to Ekeland et al. (1981) who

report in their study that rat femoral fractures only seemed mechanically healed after 13

weeks. Results from these studies suggest that fracture healing does not occur within a

predetermined, fixed time length, but rather, spans over a varying duration that is dependent

on a multitude of biological, physiological and external interconnected factors. As such,

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differences in healing times may have contributed to differences in mechanical properties

displayed, and differences in correlations observed. After only four weeks, fracture calluses

are likely more elastic and less progressive in their healing, implying that their response to

mechanical torsional testing would be much less predictive than an eight week callus, which

would likely be stiffer, more mineralized and closer, physiologically, to intact bone.

Second, in our study, the healing femurs were subject to systemic lithium treatment, whereas

in the Nazarian study they were exposed to local bone morphogenetic protein-2 vector

delivery. It is not known whether systemic lithium incorporates itself into the matrix of

bone, although several researchers have suggested that lithium may displace the calcium ion

in the hydroxyapatite lattice in a similar mechanism by which the fluoride ion displaces the

hydoxy ion (Mayer et al., 1986; Birch & Jenner, 1973). If this is true, then lithium’s

incorporation into the hydroxyapatite lattice of bone could alter bone's mechanical properties

by interrupting dislocation motion through the crystal structure, potentially affecting its

strength and stiffness. Moreover, if lithium replaces calcium in the hydroxyapatite lattice,

then it may also lower bone's calcium equivalent mineral density, a parameter used in the

calculations for CT based torsional rigidity. Hence, there is the possibility that lithium

therapy influenced both the mechanical and image based parameters of the healing femur in

our study, ultimately contributing to the variation in correlation data we observed.

Interestingly, we saw a decrease in tissue mineral density in rats treated at the "best"

combination of lithium therapy compared to pooled controls but an increase in tissue mineral

density in rats treated at the "worst" combination of lithium therapy compared to pooled

controls. While far from conclusive, these results seem to suggest that at optimal treatment

levels, lithium can incorporate into bone matrix, likely exchanging with calcium, improving

bone's mechanical properties and lowering its calcium equivalent tissue mineral density.

While not executed in this study, imaging techniques such as micro-beam X-ray diffraction

can be used to investigate the crystal structure of bone matrix and confirm the presence of

small ions within the hydroxyapatite lattice (Nakano et al., 2013; Rogers & Daniels, 2002).

Hence X-ray diffraction provides a plausible option for future work investigating lithium's

potential incorporation into bone matrix.

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Many studies have examined fracture healing in the rodent through biomechanical and µCT

based outcomes and have reported a diverse range of findings. For example, Nyman and

colleagues (2009) report a weak inverse correlation between TV and bone strength, and

BV/TV and bone strength, arguing that their results indicate that larger calluses are weaker

than smaller calluses. These results are in stark contrast to Morgan and colleagues (2009)

who report strong positive correlations between mechanical strength and both BV and

BV/TV, suggesting that these µCT derived measures are strong predictors of callus

mechanical properties. There are many reasons as to why the literature reports such

inconsistent results, including differences in the fracture model used, differences in the

animal model, different study endpoints and different mechanical testing methods employed

(Histing, et al., 2011; O'Loughlin et al., 2008). For example, a closed vs. open fracture

introduces different healing environments that could ultimately lead to differences in

outcome measures observed. Moreover, fracture healing in the femur will be very different

than that in the tibia, as the tibia has an asymmetric diameter and is mechanically influenced

by the fibula. Torsion vs. three point bending can provide variations in mechanical testing

data observed because of the different strengths and limitations pertaining to each type of

test. Analysis of bone healing at different time points post fracture can also alter findings.

Sigurdsen and colleagues further support this point in their 2011 paper by showing how the

correlations between maximum three point bending moment and several µCT based

parameters vary depending on the type of fracture fixation (internal vs. external) and the time

point of analysis (30 vs. 60 days). Nonetheless, high variances and correlations between

mechanical testing results and stereological parameters seen in our data are within the

bounds of previous data in the literature examining long bone fracture healing.

An interesting finding in our data was that maximum yield torque and tissue mineral density

displayed a significant, inverse correlation (r=-0.281, p=0.021), implying that those femurs

displaying enhanced mechanical properties had poorer bone quality. While most researchers

have commonly reported strong, positive correlations between these two parameters (Kim et

al., 2012; Morgan, et al., 2009; Nyman, et al., 2009), other studies conducted in our

laboratory (Nam, et al., 2012; Wright, Nam, & Whyne, 2012) have reported similar inverse

findings. One possible explanation for the inverse correlation observed is that the increased

mineralization of bone does not accurately describe its quantity or distribution within the

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callus. Even though the mineral density of the callus may be high, this does not imply that it

is structurally superior. Locations of very highly mineralized segments of bone may exist

within the callus that are not connected. Therefore, while these locations would contribute to

an increase in average callus mineral density, they would not provide increased structural

support or stiffness in comparison to less mineralized, connected bone segments. Another

possible explanation for this inverse correlation may be the result of lithium's potential

incorporation into bone matrix. If lithium replaces calcium in the crystal lattice structure, it

may subsequently improve bone's mechanical properties while simultaneously decrease its

calcium equivalent tissue mineral density.

The inverse significant correlation between callus mechanical properties and tissue mineral

density was also accompanied by a trend suggesting that stronger calluses displayed larger

total volumes. This finding implies that those calluses displaying better mechanical

properties in strength and stiffness were physically larger and more robust. As Nam and

colleagues (2012) similarly report, this makes sense from a mechanical perspective since a

wider deposition of bone from the neutral axis leads to an increased polar moment of inertia

and subsequent higher resistance to torsional deformation. Since torsional rigidity is linearly

proportional to an object’s material properties but second order proportional to its

geometrical distribution (Figure 6.1), there must be significant changes in an object’s

material properties to illicit as large of an effect that changes to its geometric distribution

would cause. In our study, minimum and maximum mean callus tissue mineral densities

varied by only 15% (835.9 – 982.4 mgHA/ccm). Therefore, with such a small variation in

callus density, and subsequent callus shear modulus, it was ultimately the bone distribution

and callus volume that had the most prominent influence on its resistance to deformation.

This provides a plausible explanation as to why physically larger calluses showed increased

mechanical properties, even though physiologically, larger calluses are generally indicative

of less progressive bone healing.

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Figure 6.1 – An object’s torsional rigidity is defined as the product of its shear modulus (G) and polar moment of inertia (JBB). G takes into account the object’s material properties, while JBB incorporates the object’s geometric distribution from its neutral axis.

6.2 DOE System Modeling: Results and Application to Fracture Healing

In the current study we investigated how variations in lithium treatment affected eleven

different outcome parameters, but focused on maximum yield torque, the primary study

outcome measure. As Sigurdsen and colleagues (2011) indicate, the torsional load at the

yield point is the most important clinical parameter for fracture healing assessment, as this

corresponds to the ability of a patient’s limb to resist high applied loading before irreversible

damage occurs. Results from our design showed that the maximum yield torque response

was maximized at a low dose, later onset, longer duration lithium treatment combination (20

mg/kg-wt/day, 7 days, 2 weeks). In addition to the overall model being statistically

significant, onset was determined as having a statistically significant, positive effect,

implying that a later, seven day onset was best for the output response. Thus, we were able

to conclude with 95% confidence that the combination of low dose, later onset and longer

duration lithium treatment (low/high/high factor levels) increased maximum yield torque, but

that only a later treatment onset was significant for this response.

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Even though the primary outcome response of maximum yield torque was used to

characterize the design space, a complete DOE analysis was still conducted on each of the

other ten secondary responses. Consistent with our findings from the primary response

model, we found that a later onset also significantly improved bone healing, as quantified by

several of the secondary outcome measures, including experimental torsional stiffness (p =

0.034; high onset: 26.5 ±9.7 N-mm/° vs. low onset: 17.7 ±7.6 N-mm/°; 49% increase), GJmin

(p = 0.0035; high onset: 286.3 ±67.8 kN-mm2 vs. low onset: 229.0 ±53.2 kN-mm2; 25%

increase) and GJavg (p=0.011; high onset: 536.9 ±153.0 kN-mm2 vs. low onset: 429.7 ±92.1

kN-mm2; 25% increase). Interestingly, we found that a later onset significantly reduced our

secondary outcome measure of tissue mineral density, as rats treated at a later onset showed a

2.7% decrease in their mean tissue mineral density compared to those who began treatment

earlier (p = 0.005; 889.7 ±29.7 mgHA/ccm vs. 923.7 ±24.8 mgHA/ccm). A much smaller

difference could be significantly detected on this measure, as its variance was significantly

smaller. This finding is consistent with the inverse correlation seen between maximum yield

torque and tissue mineral density, and further validates the hypothesis that lithium therapy, at

optimal levels, may substitute for calcium in the hydroxyapatite lattice, improving bone’s

mechanical properties while simultaneously reducing its calcium equivalent tissue mineral

density.

Beyond onset, which was determined to have a significant effect in five of the eleven DOE

models (maximum yield torque, experimental torsional stiffness, TMD, GJmin, GJavg), no

other input terms (dose, duration, two factor interactions, three factor interaction) were found

to be significant in any of the other DOE models. We observed no significant trending in the

secondary DOE models for bone volume, total volume, bone volume fraction or bone

mineral content. These results were expected, as many investigators (Nazarian, et al., 2010;

Nyman, et al., 2009; Gardner et al., 2006; Shefelbine, et al., 2005) have reported weaker, non

significant correlations between these stereological measures and callus strength and

stiffness, suggesting that these parameters are poor indicators for assessing fracture healing.

The treatment combination of low dose, later onset and longer duration that maximized our

primary outcome response of maximum yield torque was also shown to maximize our

secondary outcome response of experimental torsional stiffness. Since both maximum yield

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torque and torsional stiffness are parameters obtained through mechanical testing, these

results suggest that the lower dose, later onset, higher duration treatment regiment likely has

a significant influence on improving the mechanical properties of the healing fracture. As

biomechanical indices are the current gold standard for assessing the competence of fracture

healing, the consistent trends that we observed between these two mechanical based outcome

models supports the potential use of lithium to improve fracture repair.

6.2.1 Primary Outcome Response: Treatment Onset

Our finding that a later onset of lithium treatment was significantly positive for bone healing

is supported by results found in 2007 by Chen and colleagues. In their work, entitled “Beta-

Catenin Signaling Plays a Disparate Role in Different Phases of Fracture Repair:

Implications for Therapy to Improve Bone Healing”, the authors show how β-Catenin plays

a crucial, but disparate role in the fracture healing process. In the early stages of fracture

healing, β-Catenin is needed to properly direct mesenchymal progenitor cells into their

respected chondrocyte and osteoblast lineages. In doing so, β-Catenin levels must be tightly

regulated in order to ensure a proper balance between chondrocytes and osteoblasts, with too

high or too low levels creating a cellular imbalance that is disastrous to the healing process.

The authors assert that in the early stages of fracture repair it is the precise regulation of β-

Catenin that is crucial to healing, as opposed to its enhanced stimulation. The Wnt pathway

itself seems to inherently regulate early β-Catenin levels without the need for outside

intervention. There are several internal, negative feedback mechanisms functioning through

Wnt inhibitory proteins, DDK-1 and Sclerostin that help to ensure that the proper levels of

pathway components are maintained (Kim, et al., 2013; Wagner, et al., 2011; Kim, et al.,

2007). As such, therapies that enhance early Wnt signaling prior to distinctive mesenchymal

commitment are likely detrimental to the healing process.

In contrast, once mesenchymal cells have been committed to the osteoblast lineage, Chen

and colleagues (2007) show how increasing β-Catenin levels improves osteogenesis, leading

to enhanced fracture repair. Thus, the authors conclude that to have a positive influence on

fracture healing, stimulation of Wnt/β-Catenin signaling must occur only after mesenchymal

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precursors have been committed to the osteoblast lineage. Otherwise, if done prior to

commitment, improper β-Catenin levels will be detrimental to the healing process. To

validate their point, Chen and coworkers demonstrate that, in a mouse tibia fracture model,

lithium treatment pre fracture hindered bone healing (a time point prior to mesenchymal

commitment), but lithium treatment given four days post fracture enhanced bone healing (a

time point where some mesenchymal precursors have presumably been committed). This

conclusion regarding the temporal importance of Wnt/β-Catenin signal modulation has been

similarly reported by other investigators who have published works discussing the

therapeutic potential of the Wnt/β-Catenin pathway in fracture repair (Day & Yang, 2008;

Silkstone et al., 2008).

Based on the results of Chen and colleagues (2007), as well as evidence from the

physiological and transcriptional profiling of bone healing, we chose three days post fracture

as the low onset level for this study. With Chen et al. advocating that mesenchymal

precursors must be committed to the osteoblast lineage for lithium therapy to have a positive

effect, and with these authors reporting positive results when treatment was administered

four days post fracture, it follows that at least some of the precursor cells at the fracture site

must have already undergone lineage commitment by this time point. However, with

evidence suggesting that the majority of precursor cells have completed their migration to the

hematoma by day three post fracture, it is likely that some of these precursors will have

undergone their lineage commitment by this earlier time point as well. As such, with

physical evidence that a four day time point was beneficial, as well as suggestive evidence

that an even earlier onset could suffice, three days post fracture was tested as the low onset

factor level in our study.

Chen and colleagues only tested a single four day post fracture time point for lithium

treatment onset because their study goal was centered around proof of concept rather than

bone healing optimization. In our study, we purposely chose the lower onset prior to day

four so that this already proven time point would be captured within the factor range that we

tested. However, understanding on the timing of the various physiological phases of fracture

healing in the rodent and the temporal dependence of lithium’s interaction with these

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biological stages suggests that a later onset of lithium therapy, beyond four days, is likely

even more beneficial to fracture repair.

Fractured long bones generally undergo indirect healing, which is a combination of both

intramembranous and endochondral ossification processes. The majority of bone re-

connectivity is achieved through endochondral ossification, whereby a cartilinageous

template, or soft callus, is laid first by chondrocytes, and as healing progresses, the cartilage

is slowly replaced by newly developing bone, or hard callus, that is laid by osteoblasts.

Therefore, physiologically, chondrocytes are crucial to the early stages of healing, as they

mediate soft callus formation, and osteoblasts are imperative for the soft to hard callus

transition that occurs in the later stages of bone repair. As Chen and colleagues highlight, the

ideal therapeutic influence of lithium therapy must target the timing when mesenchymal cells

become committed to the osteoblast lineage, a cellular transition closely linked to the

physiological shift from soft to hard callus. Wnt/β-Catenin stimulation before this point is

detrimental to bone healing, whereas Wnt/-Catenin stimulation after this point stimulates

osteogenesis and enhances bone healing. While the exact timing is not conclusive, evidence

suggests that this soft to hard callus transition peaks sometime between days seven and 15

post fracture in the rodent.

Various researchers have presented approximate timelines of fracture healing in rodents, all

generally reporting similar findings. A timeline based off the work off Strohbach and

colleagues (2011) can be seen in Figure 6.2 on the following page, outlining the various

phases of bone healing in rodents and their approximate duration.

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Figure 6.2 – The various phases of fracture repair are presented, with the duration of each phase indicated by the length of the arrow. The center of the arrow represents the peak of each phase, while the beginning and ends of each arrow represent the approximate phase duration. As seen, chondrogenesis, or soft callus formation, spans from about day six to 17, peaking around day 11, while endochondral bone formation, or hard callus formation, spans form about day eight to 23, peaking around day 15. This implies that the "soft" to "hard" overlap spans somewhere around day eight to 15. This timeline is presented for the experimental mouse and rat rodent models.

This proposed timeline is in good agreement with what Marsell & Einhorn present in their

2011 review on the biology of fracture healing. In their article, the authors provide a general

overview of the four main phases of fracture repair with approximate timing of each. By

monitoring the expression of various stage dependant extracellular matrix markers, including

type II procollagen and proteoglycan of soft callus formation, hypertrophic chondrocytes of

soft callus termination, and type I procollagen, alkaline phosphatase, osteocalcin and

osteonectin of hard callus formation, the authors were able to conclude that soft callus

formation peaks approximately between days seven and nine, ending around day 13, and

hard callus formation begins approximately between days seven and nine, peaking near day

15. This pattern in protein marker expression is similar to what has been reported by others

investigating the physiology and cellular biology of fracture healing (Hadjiargyrou, et al.,

2002; Einhorn, 1998; Jingushi, Joyce, & Bolander, 1992). Collectively, these proposed

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timelines imply that days seven to 15 post fracture span the majority of "soft" to "hard"

callus transformation, the time point whereby the mesenchymal precursors must commit to

the osteoblast lineage to properly mediate this physiological transition. Therefore, lithium

therapy targeting this time range may be most effective. As such, in our study, we chose an

onset of seven days as our high factor range in order to target the beginning of this

physiologic transition.

The results from our study showed that a later onset was more beneficial to fracture repair, as

bone healing from rats treated at an onset of seven days presented as significantly better than

that from rats treated at an onset of three days. However, results from the curvature analysis

of the DOE model showed non significant curvature, implying that the outputs displayed an

increasing linear trend with no indication of saturation within the factor range tested. These

results suggest that the optimal design point likely lies somewhere outside the cubic design

space, and that an even later onset beyond seven days, possibly targeting a time point

between the seven to 15 day range of primary callus turnover, could potentially be more

beneficial for improving the mechanical properties of the healing fracture. This is something

that will explored in phase two optimization, and will be expanded upon in greater detail in

the future direction chapter to follow.

6.2.2 Primary Outcome Response: Treatment Dose and Duration

No benefit of higher lithium dose (100 vs. 20 mg/kg-wt/day) was found in this study. In

contrast to expectations, the lower dose showed a trend towards superior fracture healing (p

= 0.11), as rats treated at the lower dosage displayed a 19% increase in maximum yield

torque compared to those treated at the higher level (371.8 ±135.2 N-mm vs. 312.3 ±143.3

N-mm). Clinically, this is a very encouraging finding, as it suggests that patients may be

better off taking less lithium to maximize its positive influence on fracture healing.

Interestingly, De Boer and colleagues (2004) reported that lower concentrations of lithium

treatment enhanced Wnt/β-Catenin induced mesenchymal stem cell proliferation in vitro.

The authors concluded that lithium treatment may have a bimodal influence on cells of

mesenchymal origin, displaying a stimulatory effect at lower concentrations but an inhibitory

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effect at higher concentrations. Our findings are in support of a bimodal profile for lithium

therapy, as rats administered lower dosages of lithium displayed an increase in maximum

yield torque compared to pooled controls (371.8 ±135.2 N-mm vs. 329.9 ±135.8 N-mm),

whereas rats given higher dosages of lithium displayed a decrease in maximum yield torque

compared to pooled controls (312.3 ±143.3 N-mm vs. 329.9 ±135.8 N-mm).

With regards to duration, rats treated at a higher duration of two weeks showed a 17.8%

increase in maximum yield torque compared to those rats treated at the lower duration of one

week (371.3 ±149.9 N-mm vs. 315.3 ±129.6 N-mm). Similar to dosage, this trend was also

found to be non significant (p= 0.14).

The lack of significance on both of the dose and duration results may be due to an

underpowered study design. With each factor level being tested a total of 24 times (six times

per group x four different groups tested), there were a total of 48 animals tested at the two

distinct factor levels. Given the very large inherent variation that occurred in our mechanical

testing data (standard deviation from all samples = ±138.8 N-mm), a Post Hoc power

analysis revealed that, at 80% power and 95% confidence, our study was only able to detect a

minimum significant difference of 81 N-mm between groups. With the actual difference on

the maximum yield torque response being 59.4 N-mm between rats treated at low and high

dosage levels, and 56 N-mm between rats treated at low and high duration levels, we would

have required a total of 88 animals (44 per factor level) and 100 animals (50 per factor level)

for the dose and duration factors respectively, in order to detect these significant differences

at 80% power and 95% confidence.

As with any non natural drug intervention, lower doses are preferred in order to best

minimize any adverse accompanying consequences. This is especially important for lithium,

a drug that has a very narrow therapeutic range with potential accompanying side effects.

There are disagreements in the literature in terms of the optimal serum lithium level in the

treatment of bipolar disorder. Severus and colleagues (2008) argue for a very narrow range

between 0.6 and 0.75 mEQ/L, while others suggest that a broader range between 0.6-1.2

mEQ/L is adequate (Canan et al., 2008; American Psychiatric Association, 2002). Despite

this disagreement, there is a general consensus that serum levels must be tightly monitored,

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as anything above 1.2 mEQ/L is considered toxic. Exceeding this level can result in serious

neural and gastro-intestinal acute consequences, including induced nausea, delirium, tremor,

diarrhea and vomiting. There have also been studies linking toxic lithium levels to

cardiovascular abnormalities, including cardiac arrhythmias and irregular electrocardiogram

readings presented as non specific T wave flattening and prolonged QT intervals (Canan et

al., 2008; Mamiya et al., 2005). Levels above 2/L can be life threatening, and have been

associated with neurotoxicity, encephalopathy and both seizure and coma induction (Young

& Newham, 2006; American Psychiatric Association, 2002).

The toxicity of lithium has been well documented in the literature through various preclinical

animal studies. Choudhary and colleagues (2008) commented on the significant

neurobehavioral and neurochemical changes they found in the brains of rats given 100

mg/kg-wt/day of lithium over a two week duration. These results suggest that lithium

therapy could be dangerous at high dosage, short duration drug levels. In constrast, the

results of a study by Ahmad et al. (2011) suggest that lithium therapy could also be harmful

at lower dosage, longer duration drug levels, as rats administered 15 mg/kg-wt/day over

seven weeks showed signs of blood toxicity with accompanying liver and kidney issues.

In our study, we readily saw the toxic effects that systemic lithium treatment can have. In

our initial pilot phase, all rats given a dosage of 200 mg/kg-wt/day died prior to completing

their two week treatment. During their treatment, the animal technicians noted significant

behavioural changes in these rats, including more prominent spinal hunches, evident

piloerection and reduced eating patterns; the chief veterinarian attributed their deaths to

lithium induced toxicity. The 2010 material safety data sheet (MSDS) for lithium chloride

(ScienceLab, 2010) indicates that the lowest published lethal dose in the rat was 200 mg/kg-

wt administered orally for three days. As such, it is not surprising that the lithium treatment

combination that we administered during our first pilot phase was lethal. In our actual study,

even after lowering the maximal dosage to 100 mg/kg-wt/day, one rat receiving the drug for

two weeks died the day after finishing its treatment, prior to completing its 28 day in vivo

cycle. While inconclusive, the animal technicians suspected lithium to be at the root of this

rat's death as well. Given all the evidence indicating lithium overdose is toxic, our finding

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that lower doses show better trends for optimal bone healing is extremely promising for

clinical integration.

Most of lithium's significant side effects are acute and result when levels exceed those

therapeutically recommended. If serum levels are kept within the appropriate range, these

side effects can be properly controlled. Bipolar patients generally experience the most severe

side effects within the first few weeks of starting treatment as their body acclimatizes to a

new drug; beyond that, side effects are minor and temporal, generally increasing after the

first two hours of daily treatment when peak serum levels are achieved, quickly subduing

thereafter (Young & Newham, 2006; American Psychiatric Association, 2002). To help

control the temporal, acute side effects, most bipolar patients take a single oral dosage of

lithium before going to bed so that their serum levels peak while asleep.

While the acute symptoms can generally be managed, there are some concerns with the long

term effects that lithium therapy can have, especially on the kidneys. Lithium is a potent

inhibitor of anti-diuretic hormone, impairing the kidneys' ability to properly retain salt and

water. As a result, chronic, systemic lithium use leads to renal toxicity, characterized by

severe diabetes insipidus, polyuria and polydipsia (Malhi et al., 2012; Livingstone &

Rampes, 2006). Lithium is the most common cause of drug induced nephrogenic diabetes

insipidus, affecting over 10% of chronic lithium users (Livingstone & Rampes, 2006).

Moreover, between 10%-20% of patients on long term lithium therapy display morphological

changes in their kidneys, including interstitial fibrosis, tubular atrophy and glomerular

sclerosis (American Psychiatric Association, 2002). Beyond the major nephrogenic impact,

other chronic, endocrine related side effects have been noted in lithium treated patients.

Chornic lithium causes hyperparathyroidism and hypercalcemia by interfering with the

body’s homeostatic calcium sensing receptor system. Lithium inhibits the action of inositol

triphosphate - an important secondary messenger that regulates intracellular calcium levels -,

and also diminishes the cellular response to calcitonin, interfering with the body’s ability to

lower elevated serum calcium levels (Malhi et al., 2012; Livingstone & Rampes, 2006).

Chornic lithium also causes hypothyroidism by inihibting the release of thyroxine (T3) and

triiodothyronine (T4) from the thyroid gland and increasing the release of thyroid stimulating

hormone from the anterior pituatary (Malhi et al., 2012; Livingstone & Rampes, 2006).

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Finally, chornic lithium treatment has been associated with an increase risk of weight gain

(McKnight et al., 2012; Young & Newham, 2006).

However, the fact that lithium has been used in medicine for over 50 years, and is still

recognized today as the gold standard treatment for bipolar disorder, lends to its credibility as

a generally safe drug. In addition, while the chronic side effects of lithium therapy certainly

pose as serious concern for its long term use in psychotropic medicine, these issues become

clinically moot in its application to short-term bone healing. Lithium has a maximal four

week window to enhance fracture healing; if it takes any longer than this to have an effect,

then its use becomes less relevant clinically, as bone should naturally heal by itself.

Therefore lithium's potential in fracture healing is quite appealing, as the major problems

associated with its long term, chronic use are non issues for the proposed application.

6.2.3 Pharmacokinetics and Pharmacodynamics

Finally, examining both the pharmacokinetics and pharmacodynamics of lithium can provide

additional support as to why the low dose, later onset, longer duration treatment combination

presented as best for our primary outcome response. After oral ingestion, lithium is almost

completely absorbed by the gastro-intestinal system where it enters the systemic blood

circulation. Its bioavailability is quite high, with anywhere from 85-100% of the drug,

depending on the type of lithium salt administered, reaching the systemic circulation (Keck

Jr. & McElroy, 2002; Nielsen-Kudsk & Amdisen, 1979). Peak serum concentrations are

generally reached within one to three hours after oral ingestion. Once systemic, lithium can

take action on its targeted cellular receptor(s) or can enter the cell through the sodium

channels to take action on its intracellular targets. Lithium is not metabolized and is

exclusively removed by the kidneys, with nearly 95% of the drug being renally excreted at a

clearance half life of 24 hours (Keck Jr. & McElroy, 2002).

Generally a drug becomes much less effective once timing exceeds its pharmacokinetic half

life. A one to three hour peak serum concentration and 24 hour clearance half life imply that

lithium’s physiologic affect is quick acting, with a single dosage likely becoming moot

beyond a 24 hour threshold. Therefore, in order for lithium therapy to have a continuous

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lasting effect, daily treatment administration is required; bipolar patients currently using

lithium for treatment must take the drug daily for precisely this reason. Therefore, in its

application to bone healing, daily administration would certainly be required as well.

Moreover, the pharmacokinetics imply that to properly target a specific physiologic time

duration of bone healing, it is the treatment onset and duration components that must be

catered appropriately. With the multitude of evidence from Wnt/β-Catenin signaling biology

and the physiological phases of bone healing indicating that there is an ideal therapeutic

window for effective treatment, daily administration at an onset/duration combination

targeting this time range is well supported.

Lithium has various mechanisms of action, many of which are interconnected and relate back

to Wnt/β-Catenin signaling. This may be one possible explanation as to why a lower dosage

of lithium therapy is sufficient for improving fracture healing. In addition to direct,

competitive inhibition of GSK-3β, lithium is known to stimulate the ERK/MAP kinase

pathway, the cAMP mediated signal transduction pathway and the Phosphatidyl Inositol

PKB and PKC pathway, all of which end in downstream GSK-3β inhibition through

phosphorylation at its serine 9 location. Moreover, in addition to its role in Wnt/β-Catenin

signaling, GSK-3β has also recently been confirmed to be an active component of the

Hedgehog signaling pathway. Similar to its role in Wnt/β-Catenin signaling, GSK-3β

inhibition leads to hedgehog activation, resulting in the translocation of the Gli transcription

factor to the nucleus, where it initiates transcription of hedgehog related genes (Sutherland,

2011; Doble & Woodgett, 2003; Jope, 2003). Hedgehog signaling has been implicated in

osteoblast differentiation and endochondral bone development during embryogenesis

(Oliveria et al., 2012; Mak, et al., 2008; Hu et al., 2004), and like Wnt/β-Catenin, may also

play a crucial role in fracture healing. Therefore, lithium induced inhibition of GSK-3β, both

directly and indirectly, could have a biologically additive affect, functioning through a

variety of different mechanisms, implying that lower dosages of therapy could result in

amplificatory signaling that would be adequate to elicit a sufficient response.

There is also the possibility that higher levels of lithium may cause systemic poisoning,

which interferes with proper bone healing. Although a dosage of 100 mg/kg-wt/day of

lithium in a 300 gram rat is therapeutically equivalent to the regular maintenance dosage for

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a bipolar adult (900 - 1200 mg/day) (Lembke, 2009; Reagan-Shaw, et al., 2007), daily

administration of the drug in humans is still associated with a variety of side effects that are

temporally related to peak serum concentrations. As such, peak serum concentrations

achieved several hours after oral ingestion, may be associated with temporary systemic

toxicity, even at therapeutically indicated levels. In addition, GSK-3β has a multitude of

physiological targets beyond the Wnt/β-Catenin pathway, many of which are implicated in

cellular homeostasis and survival (Figure 6.3). Proper regulation of GSK-3β is imperative,

as both hyper or hypo phosphorylation of this enzyme on any of its downstream targets can

have disastrous cellular implications, including cytoskeleton instability, decreased cellular

plasticity, activation of oncogenic genes and induced cellular apoptosis (Sutherland, 2011).

As such, extensive inhibition of this enzyme caused by over dosage of lithium may

potentially result in systemic toxicity, through various cellular responses, that ultimately

interferes with proper bone healing.

Figure 6.3 – The various physiological targets of the GSK-3β enzyme.

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These plausible explanations are indicative of the “just right” notion of pharmacology, which

implies that there exists an optimal dosing level for every drug in order to maximize its

intended effects, with too high or too low levels being ineffective or detrimental. With

regards to lithium and its intended effect on Wnt/β-Catenin signaling, too much lithium can

cause over inhibition of GSK-3β that ultimately results in excessive cellular β-Catenin levels.

Too much β-Catenin can initiate an apoptotic cascade, ultimately diminishing any positive

effect that lithium therapy could potentially have on bone healing. Similarly, there exists a

lower threshold whereby too little lithium essentially becomes synonymous to no treatment.

As such, it follows that lithium must be administered at its “just right” level in order to

maximize its positive effects on fracture repair. The results from our study suggest that this

optimal dosing for lithium is found at much lower levels than those used clinically to treat

bipolar disorder; 20 mg/kg-wt/day in the rodent model, a level that translates to humans as

nearly four times lower than the regular maintenance dosage for a bipolar adult,

demonstrated a trend towards improved healing. Further work (additional samples) must be

completed in order to demonstrate if dosing has a significant impact on the outcome, and if

so, the factor range for this parameter would need to be more closely examined (i.e. even

lower dose levels) to optimize its performance.

Taken together, the results from our study are clinically promising. While a later onset was

the only parameter proven to be statistically significant for improving bone healing, trends

indicated that a lower dose and higher duration also had a positive effect on the healing

response. These results were supported by analysis of our primary study outcome measure

of maximum yield torque. Several of the secondary outcome measures (experimental

torsional stiffness; GJmin; GJavg) showed a later onset as being significantly positive to the

model, while the secondary outcome measure of total volume, an indication of callus size,

showed a later onset as being the most positively influential parameter, although the trending

was not significant. Moreover, a low dose, later onset and longer duration treatment

combination was also shown to maximize the secondary outcome response of experimental

torsional stiffness, possibly suggesting that this treatment regimen is best for improving the

mechanical based properties of the healing fracture. The results from our study are both

biologically and physiologically indicated through understanding of the temporal dependence

of fracture healing, lithium's mechanisms of action - particularly through the canonical

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Wnt/β-Catenin signaling pathway-, the therapeutic targets of GSK-3β inhibition and the

pharmacokinetics and pharmacodynamics of oral lithium therapy. However, given the toxic

implications of lithium, as well as the need to tightly regulate GSK-3β levels, more work is

required to better characterize lithium's optimal treatment point. This study represents only

the screening phase of the overall study design, but motivates the optimization and

verification stages to follow in order to identify optimal administration parameters. Lithium

therapy is emerging as a very promising option to enhance fracture healing, and the results

from our study form a critical foundation for future translational studies focused in this area.

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The future direction of this study involves four main components: the second and third

phases of the complete DOE study design, serum lithium analysis, investigating lithium

treatment in pathologic bone healing, and ultimately, clinical translation.

7.1 Phases Two and Three of the Design of Experiments

The next phase of the project, optimization, will expand upon the results found in screening

in two main domains. First, while the results from screening showed that a later onset of

seven days positively affected bone healing, analysis from the curvature component of the

DOE model suggested that a later onset, beyond seven days, might be even more beneficial.

As such, optimization will test two later onset time points, ten and fourteen days, to

investigate if delaying lithium treatment even further has a more positive effect. With the

ample evidence suggesting that the soft to hard callus transition occurs somewhere between

days seven and 15 post fracture, as well as the temporal correspondence of Wnt/β-Catenin

signaling to this physiological transition, identifying the optimal time point within this range

is an important task for optimizing the treatment regimen. Second, while the results from

screening demonstrated trends that a lower dose and higher duration of lithium therapy

improved bone healing, these findings were not statistically significant. We believe that,

because of the large variances associated with the data, the study was likely unpowered to

detect the smaller magnitude differences that we observed (17-20% differences in the mean).

As such, optimization will concurrently gather more information about the high and low

dose/duration combinations by testing the two new proposed onsets at each of the "best" (low

dose/ long duration) and "worst" (high dose/ short duration) dose/duration combinations. In

doing so, we will increase our sample size at these two specific design points, allowing us to

better understand the influence of these two factors.

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The proposed study design to be used in the next phase can be seen in Figure 7.1. Six rats

will be tested at each new combination of treatment dose, onset and duration, resulting in 24

total rats. An identical methodology used in phase one screening will be applied to the

upcoming optimization stage, with the only difference being the specific administration

parameters of lithium tested. We anticipate that by increasing the number of animals and

testing additional onset design points, we will be able to better characterize the lithium

administration parameters that optimize bone healing.

Once the optimal lithium administration parameters are determined, phase three verification

will be conducted to confirm findings. This phase, again, will use an identical methodology

to phase one screening and phase two optimization, except that all rats will be administered

lithium at the determined optimal treatment combination. In doing so, this phase will

hopefully validate the overall study goal, confirming that lithium therapy can be optimized to

improve bone healing in a rat, preclinical femur fracture model.

Figure 7.1 - The proposed study design for phase two optimization, testing lithium administration at four new dose/onset/duration combinations.

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7.2 Serum Lithium Analysis

In order to confirm that oral lithium administration reaches the systemic circulation as

hypothesized, rat serum will be analyzed for traces of lithium. Given the extremely high

bioavailability of lithium therapy, and the fact that we saw two pilot rats and one

experimental rat die from suspected systemic toxicity, we are fairly confident that oral

lithium ingestion in rats successfully makes it to their systemic circulation as expected.

However, the affect of daily anaesthetic accompanying treatment administration is unknown,

introducing the possibility that isoflurane gas interferes with the gastrointestinal absorption

of lithium. Serum analysis is the only way to definitively confirm systemic drug activity.

Serum lithium levels will be determined through the use of a commercially available, FDA

approved, lithium enzymatic assay (Diazyme, CA, USA) that can be adapted to our current

ELISA assay micro-plate reader. Six rats, identical to those used in phase one screening, will

be ordered to establish baseline serum lithium levels. Once baseline levels are established,

12 additional rats will be ordered for the serum analysis. Consistent timing will be used in

this stage of the project as was implemented in phase one screening. Once rats arrive at the

animal facility, they will remain in their cages for one week prior to the surgical procedure.

A sham fracture surgery will be conducted, where all steps of the procedure will be

replicated except for the physical fracture generation. After surgery, six rats will be given a

low dosage of lithium treatment (20 mg/kg-wt/day) and six rats will b e given a high dosage

of lithium treatment (100 mg/kg-wt/day) via daily oral gavage under light gas anaesthetic.

All 12 rats will begin treatment at a seven day onset and will continue for a duration of two

weeks, consistent with the onset/duration combination of the “best” treatment group as

determined from phase one screening. Sacrifice will occur immediately at the end of the two

week treatment mark via intra-cardiac injection. Cardiac blood will be collected and

preserved following the protocol of Diazyme Laboratories (2013) to ensure for proper serum

analysis. Analysis of the serum from these 12 rats will hopefully confirm lithium's systemic

activity, as well as highlight the range of serum concentrations achieved through levels of

high and low dosing.

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7.3 Lithium and Impaired, Pathologic Bone Healing

More than 80% of fractures in people over the age of 50 occur in individuals diagnosed with

osteoporosis, costing the Canadian Health Care System over two billion dollars per year

(Osteoporosis Canada, 2011). This significant problem, which is only going to worsen as the

population continues to age, motivates this future phase of the study.

Once optimal lithium administration parameters are determined and verified, the ideal

treatment regimen will be tested in an impaired fracture healing model of osteoporosis. The

use of a physically aged rat is one option for achieving an osteoporotic model, as female, 56

week old rats experience menopause-like symptoms, including cessation of their

reproductive cycles and associated hormonal patterns, and display decreased bone density.

Yet, several factors limit the use of physically aged rats in preclinical research, including

increased cost, limited availability and increased risk of disease transmission (Parhizkar,

Ibrahim, & Latiff, 2008). In contrast, ovariectomy (removal of the ovaries) in young, three

month old female rats has been shown to produce significant trabecular bone loss that

manifests by four weeks after the surgical procedure. As such, ovariectomy creates

phenotypic, skeletal changes in rats that replicate post menopausal bone loss caused by

osteoporosis (Kalu, 1991; Wronski, Lowry, Walsh, & Ignaszewski, 1985). This method is

currently the gold standard animal model for evaluating new therapies in both the prevention

and treatment of osteoporosis (Kharode, Sharp, & Bodine, 2008).

In this future stage of the project, bilateral ovaritectomies will be performed on three month

old female Sprague Dawley rats that follows the protocol of Parhizkar and colleagues (2008).

At four weeks post procedure, an identical methodology used in phase one screening will be

implemented, including fracture induction, 28 day in vivo cycle (lithium administration,

bilateral harvest) and lithium treatment evaluation. This phase of the project will assess the

ability of the optimal lithium treatment regimen to heal a fracture in an animal model of

pathologically impaired bone healing. As such, the findings from this part of the study will

hopefully highlight the tremendous potential of lithium therapy to manage osteoporotic

induced fractures and improve patient care for our aging and fragile population.

127

7.4 Clinical Translation

The ultimate goal of the current study is the eventual clinical translation of lithium as an

agent to improve fracture healing. This work, as described, aims to determine an optimal

lithium treatment regimen to improve fracture healing in a preclinical rat model.

Rats differ from humans with respect to their bone structure (they lack a haversian system),

and evidence suggests that the fracture healing process occurs much faster in these smaller

animals (Checa, Prendergast, & Duda, 2011; Histing, et al., 2011; O'Loughlin et al., 2008;

Nunamaker, 1998). The duration of fracture healing in rats is expected to last about four to

five weeks (Histing, et al., 2011; O'Loughlin et al., 2008), whereas in humans, proper bone

healing generally requires between 12 and 15 weeks (Marsell & Einhorn, 2010). However,

the distinct physiological phases, key biological stages and morphological changes of bone

healing (for example: mesenchymal precursor commitment, “soft” to “hard” callus turnover)

are similar between humans and rodents (Schmidmaier, et al., 2004), although one would

expect to see differences in the exact timing and levels of specific gene markers between

these different species. As such, the dosing, onset and duration levels for the optimal

treatment regimen will need to be appropriately determined for humans so that clinical

lithium therapy properly targets the timing of these biological stages.

Based on the work of Reagan-Shaw and colleagues (2007), lithium dosing can be translated

between different species through the normalization of body surface area (BSA) approach

(Table 7.1; Equation 7.1) that was first presented and approved by the FDA Draft Guidelines.

Using the ratio between a species’ approximate body weight and body surface area (Km),

appropriate drug levels can be translated from one animal to another.

Table 7.1 - Body surface area approach for converting drug dosage levels between two different species. Values are presented based off the work of Reagan-Shaw and colleagues (2007).

Species Weight (kg) BSA (m2) Km Factor Human: Adult 60 1.6 37 Human: Child 20 0.8 25 Rabbit 1.8 0.15 12 Rat 0.15 0.025 6 Mouse 0.02 0.007 3

128

Equation 7.1 - Equation used to convert dosing level between two different species.

For example, using Table 7.1 and Equation 7.1, the lower lithium dosage of 20 mg/kg-wt/day

given to rats in our study would translate to a clinical dosage of 3.24 mg/kg-wt/day in a

human. With the average male weighing roughly 80 kg (175 lbs), this amounts to a daily

lithium dosage of 260 mg, which is lower than the clinical starting dose for bipolar patients

(300 mg) and over four times less than the average maintenance dosage for a bipolar adult

(1200 mg). As such, while our preclinical study will determine an optimal treatment regimen

for lithium therapy in a rat, this regimen will need to be properly modified before lithium

therapy can be tested in a clinical fracture healing setting.

While this study focused on the systemic delivery of lithium for fracture healing, local

delivery of lithium at the fracture site within a time release system may represent a viable

future alternative, particularly in the treatment of open fractures. Local delivery would likely

reduce the potential for systemic side effects, but would require further investigation in order

to determine optimal dosing levels and release characteristics.

Sunnybrook Health Sciences Centre is the largest level one trauma center in Canada, with

musculoskeletal injuries of all types and severities, including fractures, being managed in the

Division of Orthopaedic surgery. With its diverse patient population and its clinical research

resources, Sunnybrook Health Sciences Centre and the University of Toronto provides an

ideal environment for future clinical trials investigating lithium’s ability to improve fracture

healing.

129

Chapter 8: Conclusion and Significance

Skeletal fractures remain one of the most significant challenges in orthopaedic medicine,

with approximately one third of individuals expected to experience a fracture in their

lifetime. In addition to the significant financial, social and economic burdens that

debilitating fractures place on both the individual and society, the significantly large number

of fractures, combined with prevalent rates of delayed healing and non union (5 – 10%),

motivates a need to find successful treatment methods that improve bone healing.

Lithium is the current gold standard treatment for bipolar disorder, having been used safely

and effectively for over 50 years. Although currently not indicated for fracture healing

management, it has recently gathered much attention for use in this application, particularly

due to its positive anabolic influence on bone biology, stimulating osteogenesis and

promoting bone growth. With the ample theoretical, preclinical and clinical evidence

advocating for lithium’s use as a pharmacological treatment to enhance fracture healing, the

current study addressed a significant gap in the literature pertaining to its precise treatment

regimen to optimize lithium’s benefits on bone healing.

The results from this study suggest that lithium administration at a low dose, later onset,

longer duration treatment combination is best for bone healing, with onset being the most

critical parameter to the optimized treatment regimen. These results are clinically promising

as they suggest that lower doses of treatment are better, an ideal finding given the narrow

therapeutic window and toxic implications of excessive lithium therapy. While more work is

needed to precisely optimize lithium treatment, the robust characterization of the effects of

lithium administration on the structure and function of healing bone generated in this study

will form a crucial foundation for future translational studies in this area.

When lithium was first discovered in 1817, Arfvedson had no idea the profound influence

that this tiny chemical element would one day hold in mainstream clinical care. Since its

first use in psychotropic medicine in 1949, lithium therapy has changed the lives of millions

of patients suffering from bipolar disorder. With lithium therapy now emerging as a highly

130

accessible, cost effective and clinically promising solution to enhance fracture healing, it

may not be long before this tiny chemical element is approved for another clinical use, with

an opportunity to potentially benefit the lives of even more individuals.

131

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