CLINICAL ORTHOPAEDICS AND RELATED RESEARCH Number 355S, pp S41-S55 0 1998 Lippincoti Williams & Wilkins

Mechanobiology of Skeletal Regeneration

Dennis R. Carter, PhD*; Gary S. Beauprt!, PhD*; Nicholas J. Giori, MD, PhD*; and Jill A. Helms, DDS, PhD**

Skeletal regeneration is accomplished by a cas- cade of biologic processes that may include dif- ferentiation of pluripotential tissue, endochon- dral ossification, and bone remodeling. It has been shown that all these processes are influ- enced strongly by the local tissue mechanical loading history. This article reviews some of the mechanobiologic principles that are thought to guide the differentiation of mesenchymal tissue into bone, cartilage, or fibrous tissue during the initial phase of regeneration. Cyclic motion and the associated shear stresses cause cell prolifer- ation and the production of a large callus in the early phases of fracture healing. For intermit- tently imposed loading in the regenerating tis- sue: (1) direct intramembranous bone forma- tion is permitted in areas of low stress and strain; (2) low to moderate magnitudes of ten- sile strain and hydrostatic tensile stress may stimulate intramembranous ossification; (3) poor vascularity can promote chondrogenesis in an otherwise osteogenic environment; (4) hy- drostatic compressive stress is a stimulus for

From the *Biomechanical Engineering Division, Me- chanical Engineering Department, Stanford University, Stanford CA and the Veterans Affairs Health Care Sys- tem, RR&D Center, Palo Alto, CA; and the **Molecu- lar and Cell Biology Laboratory, Department of Or- thopaedic Surgery, University of California, San Francisco, CA. Supported by the Department of Veterans Affairs through Merit Review Project A.501-4RA. Additional support from NIH grant K08-HD01079 was given to Jill Helms, MD. Reprint requests to Dennis R. Carter, PhD, Biomechani- cal Engineering Division, Mechanical Engineering De- partment, Stanford University, Stanford, CA 94305-3030.

chondrogenesis; (5) high tensile strain is a stim- ulus for the net production of fibrous tissue; and (6) tensile strain with a superimposed hy- drostatic compressive stress will stimulate the development of fibrocartilage. Finite element models are used to show that the patterns of tis- sue differentiation observed in fracture healing and distraction osteogenesis can be predicted from these fundamental mechanobiologic con- cepts. In areas of cartilage formation, subse- quent endochondral ossification normally will proceed, but it can be inhibited by intermittent hydrostatic compressive stress and accelerated by octahedral shear stress (or strain). Later, bone remodeling at these sites can be expected to follow the same mechanobiologic adaptation rules as normal bone.

Mechanobiology is the study of how mechan- ical or physical conditions regulate biologic processes. In considering the role of mechanobiology in fracture healing, it is use- ful to think about three overlapping phases in skeletal repair. In the first phase, there is a rapid proliferation of pluripotential tissue, which can differentiate into cartilage, bone, or fibrous tissue, thereby forming the fracture callus. The proliferation and differentiation of this tissue is under the influence of biologic growth and differentiation factors and af- fected by epigenetic chemical factors such as the local oxygen tension. Proliferation and differentiation also are affected strongly by the mechanical environment of the regenerat-

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S42 Carter et al Clinical Orthopaedics and Related Research

ing tissue, although the interactions between mechanical and biologic factors in the differ- entiation process are unclear.8

The second phase involves the endochon- dral ossification of the cartilage formed at the fracture site. This process, like endo- chondral ossification of the skeletal anlagen, will proceed in tissue that is not mechani- cally loaded. However, the speed of endo- chondral ossification can be influenced by the mechanical loading.6,10.1*,51 Intermittent hydrostatic compressive stress will slow or stop endochondral ossification, and intermit- tent octahedral shear stress (or strain) will accelerate ossification.

The third phase in secondary fracture healing entails the remodeling of the in- tramembranous and endochondral bone that is formed. This bone remodeling probably is regulated by the loading history in the same manner as bone during development and functional adaptation.3-7.50

This article addresses primarily the first phase of the fracture healing process in which preosseous pluripotential tissue dif- ferentiates into cartilage, bone, or fibrous tis- sue. Continuum material tissue level differ- entiation concepts are used to relate the distribution of stress and strain histories to the tissue differentiation patterns in the ini- tial phases of skeletal regeneration in a long bone. Then by the use of finite element com- puter models, the spatial patterns of tissue differentiation expected in normal fracture healing and distraction osteogenesis are pre- dicted. These patterns are compared with classic observations of fracture healing and

also with recent results from a mouse tibia distraction osteogenesis experiment.

CONCEPTUAL FRAMEWORK FOR SKELETAL MECHANOBIOLOGY

Levels of Consideration The role of physical factors in skeletal regen- eration can be addressed on the organ, tissue, cellular, and molecular levels (Table 1). These roughly parallel the levels of organi- zation described previously by Petersen34 and de RicqlCs et al.37

Organ level mechanical signals can be characterized in terms of loading history, which includes varying records of such quantities as force, displacement, and defor- mation. For example, the rigidity of a frac- ture fixation device and the physical activi- ties of a patient result in a clinical history of forces and motion at the fracture site. This history then may be correlated with the speed and efficacy of fracture healing. The organ level loading history also can be used as a basis for investigating the mechanobiol- ogy of skeletal regeneration at the tissue level.

At the tissue level, researchers trying to understand mechanical signaling, assuming that the differentiating tissue is a continuous material, characterize the mechanical stimu- lus in terms of engineering quantities such as stress and strain. Based on physical tests of tissue material properties and approxima- tions of tissue loading, these quantities can be calculated throughout the tissue, and have been related to various patterns of tissue dif-

TABLE 1. Levels of Consideration in Mechanobiology

Organ Tissue Cel I u lar Molecular ~~~~

Force Stress and strain Cell pressure Cytoskeletal changes Displacement Hydrostatic stress and strain Cell shape changes Stretch activated ion channels Stiffness Shear stress and strain Cell-matrix interactions lntegrins Failure load Strain energy density Oxygen and nutrient supply Growth factors Loading rate Fatigue damage Electrical potentials Cytokines Loading history Stress and strain history Temperature Receptors

Number 355s October, 1998 Mechanobiology of Skeletal Regeneration s43

ferentiation.9.'6,'7.30.32.33 Pressure, distortion, pressure gradients, and energy dissipation are other tissue level quantities that can be quantified and related to tissue responses.

Mechanical signaling also can be studied at the cellular level. In vitro studies have re- lated such cellular level signals as cell shape changes,',22.42.44 cell pressure,4J9324.43 and lo- cal oxygen tensionIlJ3 to patterns of produc- tion and assembly of characteristic extracel- lular matrix components and matrix degrading enzymes. Other cellular level sig- nals that have been investigated include cil- ium bending,35 temperature changes,25 and localized electrical potentials.28

The molecular level is the most specific level for the study of mechanical signaling. Molecular level signals may include cy- toskeleton damage or disruption, integrin binding, growth factors, and stretch acti- vated ion channel activity. Many of these molecular level signals also have been asso- ciated with changes in specific cell activi-

Understanding the overall process of me- chanical signaling requires an appreciation for these various levels of study and a knowledge of how one level relates to the next. For example, it can be observed at the organ level that fracture instability leads to delayed fracture healing. At the tissue level, fracture instability relates to increased stress and strain in the differentiating tissue and different forces lead to different spatial dis- tributions of stress and strain in the tissues. At the cellular level, local tissue stress and strain may cause changes in cell pressure or shape. At the molecular level, cell shape changes may cause a disruption of the actin cytoskeleton. This may be a molecular signal for the initiation of a certain pattern of pro- tein synthesis that on the organ level results in delayed fracture healing.

Mechanobiologic Concepts at the Tissue Level Pauwels,30 drawing on ideas of Roux38 and Benninghoffs in the early 1900s, studied dif-

ties. 1.22.39.40

ferentiation patterns in many normal and ex- perimental in vivo situations. He developed general concepts for explaining mechanical influences on skeletal tissue differentiation by estimating the applied loads in these situ- ations and inferring local stress and strain levels in the loaded tissue.

Stress and strain are tensor quantities de- fined by specifying six components and a reference coordinate system. Pauwels30 rec- ognized that the important information for tissue mechanical signaling appeared to be contained in the stress and strain invariants, which are scalar quantities independent of the coordinate system (thus invariant). These scalars can be calculated from the full stress and strain tensors. Two stress invariants are octahedral shear (or distortional) stress and hydrostatic stress. Two strain invariants are octahedral shear (or distortional) strain and volumetric strain. In a compressible, elastic, isotropic material, hydrostatic stress causes a change in material volume, or volumetric strain, but no distortion. Conversely, octahe- dral shear stress (also called distortional stress) causes material deformation, or dis- tortional strain, but no change in volume. Pauwels also realized that distortional stress and its resulting distortional strain always in- volves material elongation in some direction, and therefore is associated with a tensile strain in that direction (Fig 1).

Pauwels30 developed his ideas on the ef- fects of tissue distortion by examining par- ticular cases of localized fibrous tissue de- velopment from mesenchyme in oblique pseudarthroses and angulated fractures, and by observing the development of transverse collagen fibers in the cartilage between frac- ture surfaces. Making some simple assump- tions about tissue loading in these cases, he reasoned that the cell and extracellular matrix elongation associated with distortional stress constitute a specific stimulus for the develop- ment of collagen fibers. He also saw that in other regions of oblique pseudarthroses and angulated fractures, the tissue differentiated into cartilage.

Clinical Orthopaedics S44 Carter et al and Related Research

Hydrostatic Deformation +

Shear Deformation

/ \

FIG 1. Schematic representation of the defor- mation caused by hydrostatic stress and octa- hedral shear (or distortional) stress.

Making other assumptions about tissue loading in each of these cases, Pauwels con- cluded that hydrostatic compression is a spe- cific stimulus for cartilage formation, but he could not determine a mechanical stimulus that guided bone formation. He thus believed that “There is no specific mechanical stimu- lus for the formation of bony tissue. This proceeds on the basis of a rigid framework (connective tissue, cartilage, or bone).”30

Pauwels’ tissue differentiation ideas are represented graphically in Figure 2A.26329 He used the terms compression and deformation as axis labels. It is clear from his writings that in the context of tissue differentiation, Pauwels used the term compression to mean hydrostatic compressive stress. Hydrostatic tension was not depicted because he believed that hydrostatic tension could not be created in skeletal tissues. His use of the term defor- mation was meant to indicate stretching of the tissue in some direction. Regarding elon- gation occurring in addition to hydrostatic stress, Pauwels envisioned the formation of collagen fibers interposed with cartilage, and

thus the formation of fibrocartilage. Pauwels believed that when the tissue experienced low magnitudes of tensile strain and hydro- static stress, there was insufficient mechani- cal stimulus to guide the tissue differentia- tion process.

Perren32 and Perren and C ~ r d e y ~ ~ devel- oped the concept of interfragmentary strain to explain various characteristic fracture healing patterns and to provide a theoretical basis for evaluating fracture treatment strategies. Their approach was based on a consideration of the strain magnitude cre- ated in the differentiating tissue at the frac- ture site. One basic idea formed the basis for their theory: A tissue that ruptures or fails at a certain strain level cannot be formed in a region of precursor tissue experiencing strains greater than this level. These studies focused on strain rather than stress as the tis- sue level quantity describing mechanical stimulation because strain describes the ac- tual physical phenomenon of tissue elonga- tion, which can be related closely to tissue damage in soft biologic tissues. The inter- fragmentary strain tissue differentiation concept of Perren32 and Perren and Cordey33 was used to describe primary and secondary fracture healing.

Building on the foundation developed by Pa~wels,29~30 Perren,3* and Perren and Cordey,33 Blenman et a1,6 Carter et a1,g.g and Giori et al,16J7 further developed the con- cepts relating tissue differentiation to me- chanical loading (Fig 2B). They specifically discussed the importance of cyclic tissue loading and proposed a method to calculate a local stress or strain history. In this formu- lation, compressive hydrostatic stress his- tory guides the formation of cartilaginous matrix constituents, and tensile strain his- tory guides connective tissue cells in their production and turnover of fibrous matrix constituents. Fibrocartilage is formed in re- gions of tensile strain with superimposed hydrostatic compressive stress. Direct bone formation is permitted in regions exposed to neither significant compressive hydrostatic

Number 3558 October, 1998 Mechanobiology of Skeletal Regeneration S45

stress nor significant tensile strain. How- ever, osteogenesis requires a blood supply, and preosseous tissue can be diverted down a chondrogenic pathway in regions of low oxygen tension.* Using this basic concep- tual framework, the first author of the cur- rent study, along with his colleagues, previ- ously investigated the tissue differentiation patterns in fracture healing,6.* tissue differ- entiation at the bone implant interface,gJ7 and fibrous tissue modulation in tendons.16

The emphasis on stress and strain history is meant to allow the incorporation of a broad range of cyclically applied loads applied to the tissue over time. The best mathematical forms to represent the daily hydrostatic stress history and strain history are yet to be deter- mined. Current research in many laboratories is aimed at establishing the optimum loading history for bone repair. Results of such stud- ies likely will lead to a refinement of the ba- sic concepts presented here and suggest ap- propriate mathematical expressions for representing the loading history.

The mechanobiologic concepts presented must be viewed with a consideration of the biologic factors that initiate and influence the bone repair process. When bone initially is fractured or traumatized, a flood of chemi- cal factors are released to the local region of

A

Compression

tissue damage. These factors are responsible for initiating the sometimes massive tissue proliferation and differentiation cascade as- sociated with skeletal tissue regeneration. Cell proliferation in this early stage of regen- eration is increased additionally by intermit- tent motions at the site of regeneration. It seems likely that the cyclic shear (or tensile) strains created by motion serve as a stimulus to growth of the callus tissue. The differenti- ation of this regenerating tissue results in di- rect intramembranous bone formation, pro- vided the regenerating tissue is well vascularized and minimal mechanical forces or motions are imposed. The extent of prolif- eration and bone induction at a site of bone regeneration clearly is related to the diffu- sion and convection characteristics of chem- ical factors and the mechanical environment. The greatest amount of regenerating tissue therefore is expected at the location of great- est bone and soft tissue trauma.

The examples that follow show how the application of mechanical forces at the site of tissue regeneration can influence significantly the basic bone induction process described. Finite element models were used for making predictions about patterns of bone, cartilage, and fibrous tissue in a regenerating long bone based on mechanobiologic concepts pre-

FIG 2A-B. Phase diagrams. (A) Pauwel’s view of the role played by tissue mechanical stimuli in tis- sue differentiation (adapted with permission from Pauwels F: Biomechanics of the Normal and Dis- eased Hip. Berlin, Springer-Verlag 1976.) (B) The view of the current authors concerning the role of tissue mechanical loading history on skeletal tissue regeneration.

S46 Carter et al Clinical Orthopaedics and Related Research

Callus/Medullary Tissue Diaphyseal Bone

FIG 3. Finite element model used to calculate tissue stresses and strains in fracture healing (compression forces applied) and in the initial period of distraction osteogenesis (tensile forces applied).

sented (Fig 2B). By imposing simplified load- ing histories consisting of a repeatedly ap- plied unit compression or tension axial force, the histologic patterns expected in normal secondary fracture healing and distraction os- teogenesis were predicted and compared with documented histologic observations.

MATERIALS AND METHODS

Finite Element Model of Fracture Healing An axisymmetric finite element model was cre- ated to represent a long bone fracture or os- teotomy site in the initial stage of fracture healing (Fig 3). This same model was used to represent the geometry and histology of the mouse distrac- tion osteogenesis model (described later) before the initiation of distraction. The cortical bone was considered to act as a rigid boundary because it is much stiffer than other tissues represented at the site of regeneration. All other tissues were as- sumed to be linearly elastic and isotropic, as a simple first approximation. The assigned elastic properties of pluripotential callus and medullary tissue were E (elastic modulus) = 1.0 and v (Pois- son’s ratio) = 0.49.

It is assumed that with long bone fracture heal- ing in a cast or brace, intermittent compressive axial forces will be imposed at the fracture site as a result of muscular activity and perhaps partial

weightbearing. To simulate this loading in the au- thors’ model, a unit axial force was applied and the patterns of tensile strain and hydrostatic stress in the regeneration tissue were determined. These patterns were compared with the well docu- mented patterns of tissue differentiation observed in normal secondary fracture healing.

Distraction Osteogenesis Experiment and Finite Element Model A mouse tibia1 lengthening scheme was used to in- vestigate the molecular and cellular events that characterized tissue regeneration during distrac- tion osteogenesis.45 The treatment protocol con- sisted of a 7-day latency period followed by a phase of active distraction. Animals were sacri- ficed after 6 and 10 days of distraction osteogene- sis. Decalcified paraffin sections were prepared using standard histologic techniques and in situ hybridization, which included 35s labeled anti- sense riboprobe corresponding to collagen Type 11.

The finite element model of fracture healing (Fig 3) was used to calculate stress and strain pat- terns for the initiation of distraction before any tissue regeneration simply by applying a tensile force to the model instead of a compressive force.

A second axisymmetric finite element model was created based on the geometry and histologic analysis of the mouse model after 6 days of dis- traction (Fig 4). At that time, tissue regeneration is occurring in response to daily distraction, and the geometry has changed because of distraction and the presence of newly formed bone. The ma- terial properties of the loose connective tissue in the distraction gap of this model were E = 5.0 MPa and v = 0.49, and the newly formed bone was assigned the values E = 100 MPa and v = 0.30. The patterns of tensile strain and hydrostatic stress were determined for an applied unit tensile force and compared with the histologic and mole- cular findings in the sacrificed animals.

RESULTS

The distributions of maximum tensile strain and hydrostatic stress in the regenerating tis- sue were calculated. These data were inter- preted using the conceptual framework that has been presented (Fig 2B) to predict the distribution of tissue differentiation. The re-

Number 3558 October, 1998 Mechanobiology of Skeletal Regeneration 547

FIG 4. Finite element model representing the mouse tibia distraction osteogenesis exper- iment after 6 days of distraction at the rate of 0.42 mm twice per day. 0

Diaphyseal Bone Loose Connective Tissue

CalludMedullary Tissue Newly Mineralized Bone

sults then were compared with observed his- tologic and gene expression patterns.

Normal Secondary Fracture Healing With compression loading, the highest levels of hydrostatic compression were calculated directly in the fracture gap region between the bone ends (Fig 5). This gap region also experienced the highest level of tensile strain, suggesting that fibrocartilage would be ex- pected to form in the fracture gap between the bone ends. At all bone surfaces and re- gions outside the fracture gap, the hydrostatic stresses and tensile strains are relatively lower in magnitude. Direct intramembranous bone formation therefore will be permitted on most periosteal and endosteal surfaces, pro- vided an adequate blood supply is present. However, on endosteal surfaces near the frac- ture gap and in the intramedullary tissues, in- termediate to high levels of hydrostatic com- pression are created. This pressure may encourage cartilage formation at the endos- teum and in the medullary cavity at the frac- ture site. The mechanobiologic stimulus for endosteal cartilage formation at the fracture site probably is reinforced by vascular dam- age caused by the fracture trauma.

This tissue differentiation prediction is consistent with the documented nature of tis-

sue distributions in healing fractures (Fig 6). Direct bone formation often is observed on the endosteal and periosteal surfaces near the fracture gap. The amount of intramembra- nous bone formed generally is greater pe- riosteally than endosteally. Fibrocartilage cartilage and cartilage usually forms in the gap and medullary cavity at the fracture site.

At the periosteal surfaces near the gap, the hydrostatic stresses are actually slightly ten- sile, and intermediate levels of tensile strain are created outside the gap on the endosteal and periosteal surfaces (Fig 5). Because the magnitude of these tensile strains is rela- tively low, fibrous tissue would not be ex- pected to form on these surfaces. There are some indications, however, that low to mod- erate tensile hydrostatic stresses and strains actually may enhance bone formation. This periosteal region directly adjacent to an os- teotomy gap loaded in compression often is observed to have the most exuberant in- tramembranous osteogenic activity18 (Fig 7). The possible interactions between bone in- duction factors and mechanical environmen- tal factors in this area of low to moderate tensile strain and tensile hydrostatic stress remains an area for additional research.

When cartilage or fibrocartilage is created in the callus, it can undergo endochondral

Clinical Orthopaedics S48 Carter et al and Related Research

FIG 5. The patterns of maxi- mum principal tensile strain and hydrostatic stress calculated in the regenerating tissue at the fracture site when an axial com- pression force is applied.

ossification. This process is regulated by me- chanical stress history in a manner analogous to endochondral ossification of the cartilage anlagen during skeletogenesis.5~6~'0312 Endo- chondral ossification is delayed or prevented by intermittent hydrostatic compressive stresses and accelerated by octahedral shear stresses (or strains).

Osseous bridging of the fracture site gen- erally is initiated at the periphery of the cal- lus, a site of insignificant hydrostatic pres- sure. Once this osseous bridging occurs, the bridging bone carries much of the loading across the fracture site, effectively shielding the softer tissues of the callus from stress. The magnitudes of hydrostatic compressive stresses imposed on any cartilage in the frac- ture gap therefore are reduced. This reduc- tion in hydrostatic stress magnitudes then fa- cilitates endochondral ossification, which proceeds from the outer ossified callus to- ward the center line of the bone.

If the fracture site is not well immobi- lized, bending and torsional displacements may result, creating high intermittent hydro- static compression in the gap tissue and very high tensile strains in the regenerating tissue around the fracture gap. This loading also could cause direct physical damage to the or- ganizing tissue and the newly forming capil- laries at the fracture site. There would be sig- nificant tissue proliferation, and the high tensile strains would stimulate fibrous tissue formation. The continued motion and associ- ated damage would delay or prevent an ef- fective vascularization of the callus between the fracture fragments.

In this avascular, high compressive hy- drostatic stress environment, the fracture fragments could start to form articulating cartilaginous caps. This combination of a gliding motion and intermittent hydrostatic compression at this site might result in pseudarthrosis,s much in the same manner

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FIG 6A-B. Patterns of (A) initial tissue differentiation (reprinted with permission from Trueta J: Studies of the Development and Decay of the Human Frame. Philadelphia, WB Saun- ders 1968.) and (B) fracture bridging (reprinted with permis- sion from Urist MR, Johnson RW: The healing of fractures in man under clinical conditions. J Bone Joint Surg 25:375-426, 1943.) that have been docu- mented for normal fracture healing.

as described in the adventitious cartilage ex- perimental studies of Ha11.20 The loading con- ditions and mechanobiologic factors associ- ated with delayed union and pseudarthrosis show strong parallels to the mechanobiology of joint morphogenesis.12

Distraction Osteogenesis In the initial stages of distraction osteogene- sis, the tensile strain patterns in the regener- ating tissues are identical to those calculated in the fracture healing model. The patterns of hydrostatic stresses are identical to those in the fracture healing model, but reversed in sign because a tensile force rather than a

compressive force is applied. The fracture gap tissue is exposed to tensile strains and tensile hydrostatic stresses (Fig 8). If dis- traction is kept at a low level, bone could form in this region. However, if the distrac- tion rates are too high, however, fibrous tis- sue formation in the gap would be expected. The small regions on the periosteal surface near the gap that experience tensile hydro- static stresses during fracture healing are ex- posed to low magnitude hydrostatic com- pression during distraction. It is conceivable that the tissue in these periosteal areas would be stimulated down a chondrogenic pathway during distraction.

Clinical Orthopaedics S50 Carter et al and Related Research

FIG 7A-C. Radiographs of healing in an osteotomy gap treated in a sheep tibia. (A) Cyclic axial forces were imposed using an external fixator immediately after operation; (6) 2 weeks after opera- tion; and (C) 10 weeks after operation. In the center figure, tufts of bone can be seen forming on the periosteal surface near the osteotomy gap. (Reprinted with permission from Goodship ARE, Ken- Wright J: The influence of induced micromovement upon the healing of experimental tibia1 fractures. J Bone Joint Surg 67B:650-655, 1985)

The finite element models for distraction after 10 days predicted a region of moderate to high tensile strain in the distraction gap (Fig 9). This mechanical state likely is associ- ated with bone, fibrous tissue formation, or both depending on the strain magnitude. Near the surface of the new bone at the middle of the gap, the tensile strains are low to moder- ate, indicating a greater propensity for bone formation than at the high tensile strain region near the center of the gap. Tensile hydrostatic stresses calculated in the distraction gap (Fig 9) are consistent with predictions of bone for- mation. The histologic studies showed that the gap was characterized by a central growth interzone bordered by new bone (Fig 10A). The vascular sinusoids in the interzone were arranged approximately parallel to the calcu-

lated tensile strains. Pluripotential cells and blood populated the interzone.

Small areas of hydrostatic compressive stress (pressure) were calculated periosteally near the gap site (Fig 9). It has been proposed that this mechanical stimulus is chondrogenic (Fig 2). Safranin 0 and fast green staining and in situ hybridization with collagen Type I1 showed that cartilage formation was lim- ited to these small discrete regions at the pe- ripheries of the distraction gap adjacent to the osteotomy ends (Fig IOB).

DISCUSSION

The same theoretical framework used in pre- dicting the tissue differentiation patterns ob- served in fracture healing also can serve to

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FIG 8A-B. The patterns of (A) maximum principal tensile strain and (B) hydrostatic stress calculated in the regen- erating tissue at the site of dis- traction osteogenesis when a tensile distraction force is ap- plied initially.

predict the differentiation patterns observed in distraction osteogenesis. The mechanical and biologic results indicate that the stress and strain states and the tissue differentiation patterns in distraction osteogenesis are mir- ror images of those in fracture healing. The regions of initial bone formation in distrac- tion osteogenesis are regions of cartilage for- mation in fracture healing and, vice versa, the regions of initial cartilage formation are regions of initial bone formation in fracture healing. These findings support the basic mechanobiologic concepts that bone forma- tion is permitted (and perhaps promoted) in areas of low to moderate tensile strain, fi- brous tissue is promoted in areas of moderate to high tensile strain, and chondrogenesis is promoted in areas of hydrostatic compres- sive stress (pressure).

This presentation has focused only on the initial phases of tissue regeneration in frac- ture healing and distraction osteogenesis. In

the latter stages of healing, tissue growth and maturation occur, thereby altering the dis- tributing of stresses and strains in the tissues. The subsequent mechanobiologic aspects of endochondral ossification and bone remod- eling in these bone regeneration processes could be explored additionally using models in which geometry, material properties, and loading conditions evolve with time.6.11

The tissue level finite element simulations presented in this article used an elastic mate- rial model to represent the differentiating tis- sue. In an elastic formulation the terms hy- drostatic compressive stress and hydrostatic pressure are used synonymously. With a more complex material model such as a two phase (solid-fluid) poroelastic model, the to- tal hydrostatic stress in the tissue consists of a hydrostatic stress in the solid phase and a hydrostatic pressure in the fluid phase.27

In developing soft tissues, the extracellu- lar matrix is soft, so the total hydrostatic

Clinical Orthopaedics S52 Carter et al and Related Research

FIG 9A-B. The patterns of (A) maximum principal tensile strain and (B) hydrostatic stress calculated in the regenerating tissue during the sixth day of distraction in the mouse distrac- tion osteogenesis experiment.

stress consists mainly of pressure in the fluid phase (at physiologic loading frequencies). The cells experience this pressure and may transduce this mechanical signal into bio- logic events.52 Stress or pressure gradients are not considered in the mechanically based tissue differentiation concepts presented. Possible flow related cellular level mecha- nisms of mechanical signal transduction such as electrical streaming potential are not incorporated in these models, although oth- ers have proposed that flow related mecha- nisms could be important influences in tissue differentiation.36

In addition to having direct effects on cell mitosis, biosynthesis, and gene expression, hydrostatic pressure and changes in cell shape may alter tissue differentiation patterns in vivo by altering the blood and nutrient sup- ply to the tissue.2,10J9,22 Low vascularity or

low oxygen tension levels have been shown to shunt undifferentiated mesenchymal cells into a chondrogenic pathway.2.21,23,31,41,4* Be- cause capillary hydrostatic pressure is ap- proximately 0.0023 MPa,46 even low levels of tissue hydrostatic pressure may decrease blood and nutrient supply significantly by a direct physical effect. It also is conceivable that cyclic hydrostatic pressure may regulate the expression of angiogenic factors or anti- invasion factors and/or their receptors. A me- chanically mediated influence on angiogene- sis would critically affect intramembranous and endochondral osteogenesis.10

In the case of tissue deformation, re- searchers have made quantitative observa- tions relating tissue level tensile strains to associated cell elongation and cell shape change~.13J4>15~22 A study by Carter and Giori9 showed that, consistent with the tissue

Number 3558 October, 1998 Mechanobiology of Skeletal Regeneration S53

The fundamental concepts introduced here are applicable to virtually all or- thopaedic procedures that result in skeletal tissue regeneration. The response of pluripo- tential tissue to mechanical stimulation is clearly of importance in fracture healing, distraction osteogenesis, neochondrogenesis, and tissue differentiation at implant inter- faces. Additional studies exploring the rela- tions between tissue loading histories and cell biology and gene expression will lead to a better understanding of how mechanobio- logic and biological factors interact during skeletal regeneration.

Acknowledgments The authors thank Bobby Tay, MD, for insight in the mouse distraction osteogenisis experiment, and Jeff Lotz, PhD, for help with computer mod- eling.

FIG 10A-B. Histologic patterns at the sixth day of distraction in the mouse distraction osteogen- esis experiment. (A) Alkaline phosphatase stain to illustrate the distraction geometry associated with the finite element model of Figure 4. (B) Safranin 0 and fast green stain showing carti- lage formation (red) at periosteal surface near the gap. (Reprinted with permission from Tay BK, Le AX, Gould S, Helms JA: Biomechanical and molecular analyses of distraction osteogenesis in a mouse model. J Orthop Res [In press].)

differentiation concepts outlined earlier, cell flattening of chondrocytes and fibroblasts in vitro generally results in increased fibrous matrix synthesis and deposition, whereas the removal of the distorting stimulus leads to decreased fibrous matrix production.

Cell flattening also generally is related to increased mitosis.22 The increased tissue proliferation associated with motion at a fracture site may be related partly to the in- termittent cell flattening caused by tensile strains and distortions in the regenerating tis- sue. The upregulation of growth and differ- entiation factors by physical damage to this tissue also may play an important role in the proliferation of the callus.

References 1. Aggeler J, Frisch SM, Werb Z: Changes in cell shape

correlate with collagenase gene expression in rabbit synovial fibroblasts. J Cell Biol98:1662-1671, 1984.

2. Bassett CAL, Herrmann I: Influence of oxygen con- centration and mechanical factors on differentiation of connective tissues in vivo. Nature 190:460-461, 1961.

3. Beaupr6 GS, Orr TE, Carter, DR: An approach for time-dependent bone modeling and remodeling: Theoretical development. J Orthop Res 8:651461, 1990.

4. Begg DA, Salmon ED, Hyatt HA: The changes in structural organization of actin in the sea urchin egg cortex in response to hydrostatic pressure. J Cell Biol97:1795-1805, 1983.

5. Benninghoff A: Experimentelle Untersuchungen iiber den Einfluss verschiedenartiger mechanischer Beanspnrchung auf den Knorpel. Verh Anat Ges 33:194, 1924.

6. Blenman PR, Carter DR, Beauprk GS: Role of me- chanical loading in the progressive ossification of the fracture callus. J Orthop Res 7:398407, 1989.

7. Carter DR: Mechanical loading history and skeletal biology. J Biomech 20:1095-1109, 1987.

8. Carter DR, Blenman PR, Beaupr6 GS: Correlations between mechanical stress history and tissue differ- entiation in initial fracture healing. J Orthop Res 6:736-748, 1988.

9. Carter DR, Giori NJ: Effect of Mechanical Stress on Tissue Differentiation in the Bony Implant Bed. In Davies JE (ed). The Bone-Biomaterial Interface. Toronto, University of Toronto Press 367-379, 1991.

10. Carter DR, Orr TE, Fyhrie DP, Schurman DJ: Influ- ences of mechanical stress on prenatal and postnatal

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