OPTIMIZING IMAGE ACQUISITION AND RECONSTRUCTION FOR A NOVEL

ROBOTIC CONE-BEAM COMPUTED TOMOGRAPHY IMAGING SYSTEM

By

MICHAEL C. HERMANSEN

A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL

OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT

OF THE REQUIREMENTS FOR THE DEGREE OF

DOCTOR OF PHILOSOPHY

UNIVERSITY OF FLORIDA

2019

© 2019 Michael C. Hermansen

To mommy and daddy

4

ACKNOWLEDGMENTS

I would like to acknowledge first and foremost my advisor and committee chair, Dr.

Frank Bova, for taking me on as one of his graduate students. It has been an honor and a

privilege to work under his tutelage. He sincerely makes a point to teach me at every

opportunity. I have learned more from our short meetings than all the time I have spent in

lectures combined. He challenges me and tests me in order to expand my understanding and skill

sets. I am profoundly grateful to have the opportunity to work on this project and for the faith Dr.

Bova has in me to complete it.

Secondly, I would like to acknowledge the other members of my committee, Dr. Arreola,

Dr. Banks, and Dr. Entezari. They have each expressed excitement and confidence in me to

complete this proposed project successfully. They will surely each be invaluable to its

completion.

Lastly, I would like to acknowledge the love of my family. My family’s love has

continued to carry me while on the other side of the country. Their prayers have strengthened me

in every step of this journey far more than they will ever know.

5

TABLE OF CONTENTS

page

ACKNOWLEDGMENTS ...............................................................................................................4

LIST OF FIGURES .........................................................................................................................9

LIST OF ABBREVIATIONS ........................................................................................................13

ABSTRACT ...................................................................................................................................15

CHAPTER

1 INTRODUCTION ..................................................................................................................17

Clinical Problem .....................................................................................................................17 Literature Review ...................................................................................................................18

Robotic Imager Solution .........................................................................................................19 Hypothesis ..............................................................................................................................19 Aims ........................................................................................................................................19

2 BACKGROUND ....................................................................................................................23

Physics of X-Ray Interactions with Matter ............................................................................23

Photoelectric Effect .........................................................................................................23

Compton Effect ...............................................................................................................23

Scatter ..............................................................................................................................24 X-Ray Transmission Imaging .................................................................................................24

Imaging Modalities ..........................................................................................................24 Projection radiography .............................................................................................24 Projection fluoroscopy .............................................................................................25

Computed tomography .............................................................................................25 Cone-beam computed tomography ..........................................................................26 Current robotic imaging systems ..............................................................................26

Digital Image Reconstruction ..........................................................................................27 Simple back projection .............................................................................................27 Filtered back projection ............................................................................................27

Feldkamp-Davis-Kress algorithm ............................................................................28

3 MATERIALS AND METHODS ...........................................................................................33

CT Phantom Image Sets .........................................................................................................33 Catphan Phantom .............................................................................................................33

Anatomical Phantom .......................................................................................................33 Anatomical Phantom with Pedicle Screws ......................................................................33 Lucite/Bone Block Phantom ............................................................................................34

Imaging Platforms ..................................................................................................................34

6

MATLAB® .............................................................................................................................35

Virtual X-Ray System .............................................................................................................35

Attenuation Computation ................................................................................................36 Projection Dimensions .....................................................................................................37 Projection Geometry Simulation .....................................................................................37 Scatter Analysis ...............................................................................................................39

Reconstruction ........................................................................................................................40

Dimensions ......................................................................................................................40 Algorithms .......................................................................................................................40 Hounsfield Units Conversion ..........................................................................................40

Projection Generation to Reconstruction Workflow ..............................................................41 Image Quality Analysis ..........................................................................................................42

Quantitative Analysis ......................................................................................................42

Effective slice thickness ...........................................................................................42 Root mean square error ............................................................................................42

Modulation transfer function ....................................................................................43

Qualitative Analysis ........................................................................................................43 Soft tissue and bone contrast ....................................................................................43 Photon starvation artifact .........................................................................................43

Scan Acquisition Combinations .............................................................................................43 Anatomical Motions ........................................................................................................44

Oblique Motions ..............................................................................................................44 Oblique’s Plus Orthogonal Anatomical OLASCs ...........................................................45 Circular Motions ..............................................................................................................45

2PI Solid Angle Projections ............................................................................................45

4 AIM 1 – RESULTS OF QUANTITATIVE IMAGE ANALYSIS ........................................56

Effective Slice Thickness .......................................................................................................56 Root Mean Square Error .........................................................................................................56

Algorithm ........................................................................................................................56 Single Arc Scan Motions .................................................................................................56

Anatomical motions .................................................................................................56

Circular motions .......................................................................................................57 Double OLASCs ..............................................................................................................57

Anatomical combinations .........................................................................................57 Oblique combinations ..............................................................................................57

Circular combinations ..............................................................................................58 Triple OLACs ..................................................................................................................58

Anatomical combinations .........................................................................................58

Oblique’s plus orthogonal anatomical ......................................................................58 Circular combinations ..............................................................................................59

Coplanar Arc Projections vs 2PI solid angle projections ................................................59 Modulation Transfer Function ................................................................................................59

Algorithm ........................................................................................................................59 Single Arc Scan Motions .................................................................................................59

Anatomical motions .................................................................................................59

7

Circular motions .......................................................................................................60

Double OLASCs ..............................................................................................................61

Anatomical combinations .........................................................................................61 Circular combinations ..............................................................................................61

Triple OLASCs ................................................................................................................61 Anatomical combinations .........................................................................................61 Oblique’s plus orthogonal anatomical ......................................................................62

Circular combinations ..............................................................................................62 Coplanar Arc Projections vs 2PI Solid Angle Projections ..............................................62

Quantitative Conclusion .........................................................................................................62

5 AIM 2 – RESULTS OF QUALITATIVE IMAGE ANALYSIS OF BONE AND SOFT

TISSUE CONTRAST .............................................................................................................77

Single Arc Scan Motions ........................................................................................................77 Algorithm ........................................................................................................................77

Circulars ..........................................................................................................................77 Orthogonal Limited Arc Scan Combinations .........................................................................78

Double OLASCs ..............................................................................................................78 Anatomical combinations .........................................................................................78 Oblique combinations ..............................................................................................78

Circular combinations ..............................................................................................79 Triple OLASCs ................................................................................................................79

Anatomical combinations .........................................................................................79 Oblique’s plus orthogonal anatomical ......................................................................80

Circular combinations ..............................................................................................80 Coplanar Arc Projections vs 2PI solid angle projections .......................................................81

Qualitative Conclusion ...........................................................................................................81

6 AIM 3 – RESULTS OF QUALITATIVE IMAGE ANALYSIS OF PHOTON

STARVATION ARTIFACTS ................................................................................................91

Algorithm ................................................................................................................................91 Orthogonal Limited Angle Scan Combinations .....................................................................92

Double Anatomical OLASCs ..........................................................................................92

Circular combinations ..............................................................................................92 Triple OLASCs ................................................................................................................93

Anatomical combinations .........................................................................................93 Oblique’s plus orthogonal anatomical ......................................................................93 Circular combinations ..............................................................................................94

Coplanar Arc Projections vs 2PI solid angle projections .......................................................94 Qualitative Photon Starvation Conclusion..............................................................................95

7 DISCUSSIONS AND CONCLUSION ................................................................................102

Discussions ...........................................................................................................................102 Quantitative and Qualitative Results .............................................................................103

8

Algorithm comparison ............................................................................................103

Anatomical OLASCs ..............................................................................................103

Double oblique OLASCs .......................................................................................104 Circular OLASCs ...................................................................................................104 Oblique’s plus orthogonal anatomical ....................................................................105 Coplanar arc projections vs 2PI solid angle projections ........................................105

Qualitative Photon Starvation Artifact Results .............................................................106

Algorithm comparison ............................................................................................106 Anatomical OLASCs ..............................................................................................106 Circular OLASCs ...................................................................................................106 Coplanar arc projections vs 2PI solid angle projections ........................................107

Final Optimized Recommendations from Results .........................................................107

Limitations .....................................................................................................................108

Scan acquisition and reconstruction parameters ....................................................108 Reconstruction times ..............................................................................................109

Comparison with Modern CBCT Systems ....................................................................110

Future Work ...................................................................................................................110 Conclusion ............................................................................................................................113

LIST OF REFERENCES .............................................................................................................114

BIOGRAPHICAL SKETCH .......................................................................................................118

9

LIST OF FIGURES

Figure page

1-1 Images showing the space occupied by intraoperative medical scanners and

physicians trying to work around them ..............................................................................21

1-2 Graphic showing the OBI for a linac. The green field is the kV imaging field used for

CBCT. ................................................................................................................................21

1-3 Diagrams showing how x-ray projections typically follow along the long axis of

pedicle screws.. ..................................................................................................................22

1-4 Photo of an intraoperative CBCT reconstruction of pedicle screws showing typical

photon starvation artifacts. .................................................................................................22

2-1 An example of a common C-arm fluoroscopy unit. ..........................................................30

2-2 An example of a modern helical CT scanner. ....................................................................30

2-3 The left side shows a CT thin fan beam on a curved detector compare to a CBCT

cone-beam on a flat panel detector. ...................................................................................31

2-4 Image of the Artis zeego eco by Siemens Medical. The mounting of the c-arm on a

robotic arm adds additional degrees of freedom. ...............................................................31

2-5 Image of the Multitom Rax dual robotic imaging system. The x-ray tube and image

receptors are on separate robotic arms to be manipulated as necessary. ...........................32

2-6 A diagram of how the projection views are SBP through the image space to

reconstruct the original image. ...........................................................................................32

3-1 The Catphan phantom used for evaluating the spatial resolution and contrast of

reconstructive x-ray imaging systems. ...............................................................................47

3-2 The anatomical phantom which consists of a pig cadaver spine encased in ballistic

gel. ......................................................................................................................................47

3-3 Slice of anatomical phantom with pedicle screws added digitally. ...................................48

3-4 Comparison of the photon starvation artifact.....................................................................48

3-5 The Lucite/bone block phantom which consists of stacked blocks of Lucite around a

solid bone block to evaluate the level of scatter in CBCT imaging. ..................................49

3-6 Example of a fluoroscopic x-ray projection generated by the virtual x-ray system for

a CT image set. ..................................................................................................................50

3-7 Comparison of photon starvation artifact ..........................................................................50

10

3-8 The scatter analysis process for generating the projections ...............................................51

3-9 CBCT of Catphan® phantom’s four 23 degree ramps. .....................................................52

3-10 Slice of input Catphan Phantom image set with metal bead, identified by an orange

arrow, to provide point source for computing MTF. .........................................................52

3-11 Slice of anatomical phantom used to qualitatively evaluate the soft tissue and bone

contrast. ..............................................................................................................................53

3-12 Views of all three anatomical scan acquisitions. The arrows trace out the path of the

x-ray source with image receptor following an opposite path ...........................................53

3-13 Views of two separate sets of double oblique OLASCs ....................................................54

3-14 Views of two sets of triple oblique’s plus orthogonal anatomical OLASCs .....................54

3-15 Views of the circular scan acquisitions at a cone angle Θ .................................................54

3-16 Diagrams of 125 projections evenly over spaced a 2PI solid angle ..................................55

4-1 Graphs of EST as a function of arc size and projection density for reconstruction

algorithms ..........................................................................................................................65

4-2 RMSE values with arc length and projection density for reconstruction algorithms. .......65

4-3 RMSE values with arc length and projection density for scan motion ..............................66

4-4 RMSE values with cone angle and projection density for single circular motions ...........66

4-5 RMSE values with arc length and projection density for double anatomical OLASCs ....67

4-6 RMSE values with arc length and projection density for double oblique OLASCs ..........67

4-7 RMSE values with total projections per arc at various cone angles for double circular

OLASCs .............................................................................................................................68

4-8 RMSE values with arc length and projection density for triple anatomical OLASCs

at various projection densities. ...........................................................................................68

4-9 RMSE values with arc length and projection density for triple obliques plus

orthogonal anatomical ........................................................................................................69

4-10 RMSE values with number of projections per arc for various cone angles of triple

circular OLASCs. ...............................................................................................................69

4-11 RMSE values with total number of coplanar arc projections and 2PI solid angle

projections. .........................................................................................................................70

11

4-12 MTF curves with arc length and projection density for single axial scan motions by

reconstruction algorithms...................................................................................................70

4-13 MTF curves with arc length and projection density for single anatomical axial arcs .......71

4-14 MTF curves with arc length for axial scan motions at projection density .........................71

4-15 MTF curves of circular scan motions with 15 degree cone angle for various rotations ....72

4-16 MTF curves of circular scan motions with 30 degree cone angle for various rotations ....72

4-17 MTF curves of circular scan motions with 45 degree cone angle for various rotations ....73

4-18 MTF curves for double anatomical OLASCs at .5 projections per degree ........................73

4-19 MTF curves for double circular arcs at 25 projections per arc for various cone angles ....74

4-20 MTF curves for triple anatomical OLASCs.......................................................................74

4-21 MTF curves with arc length and projection density for sagittal oblique’s plus axial

OLASC ..............................................................................................................................75

4-22 MTF curves of triple circular arcs at 25 projections for various cone angles. ...................76

4-23 MTF curves of reconstructions using coplanar arcs via FDK and ASD-POCS and 2PI

solid angle ..........................................................................................................................76

5-1 Slices of the Catphan and anatomical phantoms reconstructed with 200 degree axial

arc length and 360 projections ...........................................................................................83

5-2 Slices of the Catphan and anatomical phantoms reconstructed with 150 projections at

45 degree cone angle ..........................................................................................................83

5-3 Slices of the Catphan and anatomical phantoms for double OLASCs ..............................84

5-5 Slices of the Catphan and anatomical phantoms for double circular OLASCs at 45

degrees with 50 projections per arc ...................................................................................85

5-6 Comparison of the same slices of the Catphan and anatomical phantoms for triple

OLASCs reconstructions ...................................................................................................86

5-7 Slices of Catphan and anatomical phantoms at 90 degrees arc length and 90

projections per degree ........................................................................................................87

5-8 Slices of Catphan and anatomical phantoms of triple circular OLASCs at 45 cone

angle ...................................................................................................................................88

5-9 Comparison of slices of the Catphan and anatomical phantoms of the 125 projections ...89

12

6-1 Comparison of same slice of anatomical phantom with pedicle screws

reconstructions of axial CBCT scans at 200 degree arc length and 360 projections .........98

6-2 Comparison of the same slice of the anatomical phantom with pedicle screws

reconstructed by the double anatomical OLASCs at 90 degree arc length and 90

projections per arc ..............................................................................................................98

6-3 Comparison of the same slice of the anatomical phantom with pedicle screws

reconstructed by the double circular OLASCs at 45 degree cone angle with 50

projections per arc ..............................................................................................................99

6-4 Slice of the anatomical phantom with pedicle screws reconstructed by the all three

anatomical OLASC at 90 degree arc length and 90 projections per arc. ...........................99

6-5 Same slices of the anatomical phantom with pedicle screws reconstructed by

OLASCs with 90 degree arc length and 90 projections per arc .......................................100

6-6 Slice of the anatomical phantom with pedicle screws reconstructed by the triple

circular OLASC at 45 degree cone angle with 50 projections per arc. ............................100

6-7 Slice of anatomical phantom with pedicle screws reconstructed with 125 projections ...101

13

LIST OF ABBREVIATIONS

2D Two-Dimensional

3D Three-Dimensional

AP Anterior-Posterior

ASD-POCS Adaptive-Steepest-Descent Projection on Convex Sets

Ax Axial

BYU Brigham Young University

CBCT Cone-Beam Computed Tomography

cm Centimeter

CT Computed Tomography

DDR Digitally Reconstructed Radiograph

DTF Discrete Fourier Transform

EM Electromagnetic

EST Effective Slice Thickness

FBP Filtered Back Projection

FDK Feldkamp-Davis-Kress

FFT Fast Fourier Transform

FWHM Full Width at Half Max

HU Hounsfield Unit

Lat Lateral

Linac Linear Accelerator

mm Millimeter

OBI On-Board Imager

OID Object to Image Distance

OLASC Orthogonal Limited Arc Scan Combination

14

ROI Region of Interest

SBP Simple Back Projection

SID Source to Image Distance

SOD Source to Object Distance

TIGRE Tomographic Iterative GPU-based Reconstruction Toolbox

TPS Treatment Planning System

TV Total Variation

UF University of Florida

Z Atomic Number

15

Abstract of Dissertation Presented to the Graduate School

of the University of Florida in Partial Fulfillment of the

Requirements for the Degree of Doctor of Philosophy

OPTIMIZING IMAGE ACQUISITION AND RECONSTRUCTION FOR A NOVEL

ROBOTIC CONE-BEAM COMPUTED TOMOGRAPHY IMAGING SYSTEM

By

Michael C. Hermansen

May 2019

Chair: Frank J. Bova

Major: Medical Sciences–Medical Physics

Modern intraoperative cone-beam computed tomography (CBCT) systems rely on a

support structure for the x-ray source and the image receptor and are restricted to rotating around

the patient in a single axial plane. These support structures can obstruct access during the

operative procedures. A solution to this lack of scan acquisition space and restrictive surgical

access has been addressed through a robotic imaging design.1 A proposed novel intraoperative

robotic CBCT system places both the x-ray source and image receptor on separate robotic arms

that can move in concert to acquire projections with full six degrees of freedom. Non-axial

CBCT scan acquisitions are proposed for acquiring unique orthogonal projection data to augment

traditional axial CBCT.

Modern intraoperative CBCT systems primarily rely on the Feldkamp-Davis-Kress

(FDK) algorithm for cone-beam filtered back projection based reconstruction.2 However, FDK

has not been adapted for reconstruction of multi-axial scan acquisitions nor for arc lengths much

less than 180 degrees. Modern techniques for reconstruction of limited arc length CBCT

projection sets rely on iterative algorithms such as total-variation (TV) minimization3 to provide

diagnostic quality reconstructions. However, effects of limited arc scans on quality of CBCT

reconstruction have not been fully investigated.

16

In this work, combinations of multiple orthogonal limited arc length scan acquisitions

were simulated for their effect on the quality of reconstruction of anatomical detail. Orthogonal

limited arc scan combinations (OLASCs) were simulated and reconstructed via iterative TV

minimization to evaluate the parameters of scan geometry, arc length, and projection density.

OLASCs were also used to image pedicle screws in order to reduce photon starvation artifacts.

17

CHAPTER 1

INTRODUCTION

Clinical Problem

Intraoperative image guidance systems provide the physician with real-time images of a

patient’s region of interest (ROI). The main goal of intraoperative image guidance systems is to

provide a targetable anatomic spatial map of the subject during the procedure. This is especially

critical when a rigid target attached to external fiducials is not available. With intraoperative

image guidance, physicians can better navigate to a region of tissue for removal or position

hardware or localize planning target volumes in radiotherapy. However, the gantries of modern

x-ray intraoperative image guidance systems, which house both the x-ray tube and image

receptor, occupy significant workspace that can restrict the physician’s workspace. Physicians

are left with the decision of sacrificing space and comfort for valuable real-time image guidance.

In radiotherapy, the gantry makes image guidance nearly impossible to utilize for non-coplanar

beams that require rotation of the treatment couch.

Most modern intraoperative imaging systems rely on CBCT geometry to image as much

volume as possible without the need to translate the patient. Figure 1-1 shows the obstructive

geometries of both intraoperative O-Arm CBCT and C-Arm imaging systems. These gantries

only allow for axial plane rotations of the x-ray tube and image receptor.

In radiotherapy, the on-board imaging (OBI) CBCT system is constrained by being

attached to the linear accelerator (linac). The OBI’s x-ray tube and image receptor are also

restricted to only rotating axially around the patient as shown in Figure 1-2. The x-ray tube and

image receptor arms extend from the linac gantry and do not allow rotation of the couch to

acquire non-coplanar projections. Also, the x-ray image field is oriented perpendicular to the

radiation field limiting the viewing angles available during radiotherapy.

18

Literature Review

There is a need for new versatile intraoperative imaging techniques to expand the

capabilities of current CBCT imaging systems. A single robotic arm with a rigidly mounted C-

arm structure has shown to improve on traditional axial scans by acquiring multi-axial

tomosynthesis scans.4 The combinations of dual elliptical scans has shown to limit truncation

along the axial in CBCT.5 FDK based CBCT reconstructions algorithms have been expanded

beyond circular scan motions after Katsevich developed spiral CBCT.6 This lead to further non-

coplanar FDK adaptation to circle-line-arc variations7 and sinusoidal.8

However, non-axial scan motions that are limited in arc length and number of

projections, are not conducive for the use of FDK. Therefore, modern techniques for

reconstruction of limited projection CBCT sets rely on iterative algorithms like TV

minimization,3 prior image compressed sensing,9-11 and recently deep learning.12 Each of these

algorithms have only been previously tested over complete arcs of 360 degrees. The effects of

limited arc lengths on quality of CBCT reconstruction has not been fully investigated.

Particularly, there is a need to better image metal objects. For example, pedicle screws sit

with their long axis in the axial plane of rotation of current imaging systems which maximizes x-

ray attenuation, as shown in Figure 1-3. Figure 1-4 is a CBCT image acquired on an

intraoperative O-Arm which shows typical photon starvation artifacts generated by pedicle

screws. Regardless of the photon starvation artifacts generated, intraoperative CBCT scans are

being increasingly used for both the placement and evaluation of spinal instrumentation.13-25 But

in these settings, the composition of the hardware as well as its orientation can result in

significant artifacts, often obscuring the anatomy of concern.26

19

Robotic Imager Solution

At the University of Florida (UF), a novel robotic CBCT imaging system that decouples

the x-ray tube from the image receptor removing all the geometric limitations of gantry housing

has been proposed.1 Unlike modern x-ray systems with a gantry that connects the x-ray tube and

image receptor, this new design places each on a separate robotic arms that can be independently

positioned with six degrees of freedom along any path not restricted by the patient or patient

support system. UF’s robotic imager has near complete freedom of movement through 4PI

around the patient to acquire projections.

The robotic CBCT imager is not limited to the axial rotation paradigm. This opens the

possibility for non-axial and non-coplanar imaging. Therefore, there is an enormous space

available from which to acquire projections at positions currently unavailable by current imaging

systems. It is proposed that combining multiple orthogonal limited angle scan combinations

(OLASC) will reduce artifacts caused by limited arc scans and provide adequate anatomical

detail. In this work, various OLASCs were investigated.

Hypothesis

Hypothesis: Decoupling of the x-ray source and image receptor will provide

intraoperative projection views that preserve anatomical detail as well as reduce the effects of

photon starvation in CBCT.

Aims

Aim 1: Evaluate the effects of limited arc scan motions and orthogonal scan motion

combinations on quantitative image quality metrics to determine the optimal arc length and

projection density.

Aim 2: Demonstrate qualitatively that OLASCs can provide bone and soft tissue contrast.

20

Aim 3: Demonstrate qualitatively that OLASCs can reduce artifacts due to photon

starvation.

21

Figure 1-1. Images showing the space occupied by intraoperative medical scanners and

physicians trying to work around them. A) shows how an O-arm CT and B) shows a

fluoroscopy unit positioned under the operating table. Source: Bourgeois, et al.

2015.27

Figure 1-2. Graphic showing the OBI for a linac. The green field is the kV imaging field used

for CBCT. Source: Varian Medical Systems Newsroom.

22

Figure 1-3. Diagrams showing how x-ray projections typically follow along the long axis of

pedicle screws. Source: http://www.partmedical.com/articles/medical-articles/spinal-

column-a-brain/93-some-important-notes-about-spinal-screw-insertion.html.

Figure 1-4. Photo of an intraoperative CBCT reconstruction of pedicle screws showing typical

photon starvation artifacts. Photo courtesy of author.

23

CHAPTER 2

BACKGROUND

Physics of X-Ray Interactions with Matter

The x-ray energies used for transmission imaging are in the range of about 15 keV to 512

keV. The principal photon-matter interaction mechanisms within this energy range are

photoelectric effect and Compton scattering.28 Both interaction mechanisms describe the

attenuation of photons as they interact particularly with electrons. Attenuation is the percent

reduction of photons in the original radiation beam as the photons are either absorbed or scatter

in matter.

Photoelectric Effect

The photoelectric effect involves the complete absorption of a photon by an orbital

electron. The electron is subsequently ejected from the atom with energy equal to the difference

in the energy of the incident photon and the binding energy of the electron.28 The probability of a

photon undergoing a photoelectric interaction is dependent on the cube of the ratio of the atomic

number (Z) of the atom to the energy of the photon. Therefore, the photoelectric effect is more

likely at lower energies since it is inversely proportional to the photon energy cubed.28

Compton Effect

Compton interactions involve the collision of a photon with a valence electron. Scattering

due to Compton interactions results in the valence electron being ejected from the atom and the

photon being deflected (scattered) at an angle with an energy loss equal to the energy gained by

the ejected electron.28 The trajectories of the ejected electron and scattered photon are governed

by the laws of conservation of energy and momentum. The probability of a Compton interaction

occurring increases with the energy of the incident photon above the minimum electron binding

energy. Also, the probability of a Compton event is approximately proportional to the density of

24

electrons in the medium.29 The angle of deflection of the electron is inversely proportional to the

energy of the incident photon.28

Scatter

Photoelectric interactions are the desired mechanism in x-ray transmission imaging

because the photon is completely absorbed, rather than scattered. Scattered photons that reach

the image receptor degrade the image since the path the photon took does not follow a straight

line connecting the point of detection to the source point.29 For soft tissue, the effective Z is a

relatively low 7.22, therefore, photoelectric interactions dominate interactions below photon

energies of 26 keV, while Compton interactions dominate at energies above 26 keV.30 Typical x-

ray transmission imaging modalities operate with a maximum photon energy range of 60 keV to

140 keV, but the average photon energy is about a third of the maximum.29

X-Ray Transmission Imaging

Imaging Modalities

X-ray transmission imaging began by taking single projections of objects to form

radiographs. With significant advancement in the speed of image acquisition and the use of

multiple projection radiographs intraoperative image guide for surgeons became possible via

fluoroscopy.

The imaging by sections or slices is referred to as tomography.29 X-ray tomographic

imaging involves taking multiple radiographs at specific distances and angles by which

reconstructive algorithms can produce the 2D projections that are combined to reproduce the 3D

object imaged. The main tomographic modalities are computed tomography (CT), and CBCT.

Projection radiography

Radiography is the detection of the transmitted x-ray photons through an object. X-ray

absorption through an object depends on the amount of and composition of the object, and the

25

photon energy.29 The result of a radiograph is a 2D image of the x-ray shadow of the internal

structure of the object. Radiographs show structures along the same x-ray path superimposed on

top of each other, which can make distinguishing internal structures difficult. Modern

radiography leverages the advent of image receptors with digital detectors to not only generate

images quicker, but also allow for post-processing to improve image quality.

Projection fluoroscopy

Fluoroscopy takes advantage of image receptors fast enough to take multiple radiographs

and display each sequentially to produce a type of x-ray transmission movie in real-time.29

Computed tomography

CT was a monumental advancement in the field of medical imaging. CT scans involve

the acquisition of multiple thin fan beam radiographs from specified distances and angles that are

then used to reconstruct the 3D object that was imaged.29 After reconstruction, CT scans generate

tomographic slices of an object that reveal the 3D internal structure of the object.

The first clinical CT scanner was developed by Godfrey Hounsfield in 1968 with a planar

beam geometry.31 Modern CT scanners have adopted a thin fan beam geometry onto a curved

thin collimated detector. The thin fan beam produces less scatter and the thin detector lowers the

probability that a scattered photon will reach the detector, thus, heavily reducing the effects of

scatter.

Modern CT scanners also acquire images of the subject in a helical motion where the

subject lays on a table that is translated through a circular bore around which the x-ray tube and

image receptor quickly rotate. As the patient is translated through the bore, the x-ray tube and

image receptor sit at fixed distance and spin around the patient. The curved image receptor

continuously acquires thin slice projections as the patient is translated through the bore.

26

Cone-beam computed tomography

CBCT utilizes a full cone x-ray beam geometry rather than a thin fan beam as in CT.

Similarly to CT, the x-ray tube and image receptor for CBCT scans are also set at a fixed

distance and rotate around the subject. However, the full fan beam allows a CBCT to acquire a

large volume in just one rotation. CBCT utilize a large cone-beam to scan large volumes where it

is not possible to translate the subject axially through the scanner. Furthermore, the image

receptor for CBCT scanners is typically a flat panel rather than curved like CT image receptors,

so as to also acquire planar radiographs.29

CBCT image quality suffers significantly from scatter as compared to fan beam CT. In

CT, the thin fan beam and thin detector make it difficult for scatter to reach the image receptor.

The larger cone-beam generates more scatter than a thin fan beam and the larger area of the flat

image receptor increases the probability for scatter to reach the image receptor and degrade the

quality of image.

CBCT scanners have recently been coupled to the gantries of radiotherapy linacs to

provide on-board imaging support. Linacs have the need to acquire a large 3D data set without

having to translate the subject because the linac structure blocks movement of the subject.

Therefore, CBCT works well to image a large volume of the subject with one fixed rotation of

the x-ray tube and image receptor.

Current robotic imaging systems

UF’s robotic imager will go further than other robotic system currently available.

Siemens Medical (Erlangan, Germany) has developed two commercial imaging systems that

utilize robotic positioning. The Atris zeego eco, shown in Figure 1-3, is a c-arm fluoroscopy

system mounted on a single robotic arm for manipulation. The Artis zeego eco, however, the x-

ray source and the image receptor are still connected by a gantry system.

27

Siemens Medical has also developed another robotic imager called the Multitom Rax

twin robotic imaging system. The Multitom Rax places the x-ray tube and image receptor on

separate robotic arms much in the same way the robotic imager, as shown in Figure 2-5. It is also

designed to perform multiple modalities including radiography and tomography. However, being

mounted to the ceiling of the room would prevent it from being used in conjunction with a linac

for radiotherapy.

UF’s robotic imager design will allow the x-ray source to be attached to an operating

table or the treatment couch of a linac. UF’s robotic imager will perform multiple modalities like

the Multitom Rex, but it will not have long manipulating arms attached to the ceiling to act as

obstacles.

Digital Image Reconstruction

The advent of digital detectors and the recent increase in computing power has fueled the

growth of x-ray imaging modalities that rely entirely on digital image acquisition and the

computationally heavy task of digital image reconstruction. The reconstruction times for CT, and

CBCT have all been reduced from hours to minutes or even less for some scans.

Simple back projection

The simplest method of reconstruction is simple back projection (SBP). SBP involves

summing the intensity values along the ray path connecting the pixel to the x-ray source point for

each pixel through the 3D volume. SBP reconstruction suffers from an inverse distance blurring

that results in poor images.29

Filtered back projection

The solution to the inverse blurring characteristic of SBP is to undo the blurring via

deconvolution. The blurred image resulting after SBP is caused by the convolution of the image

with the geometry of SBP reconstruction, which is an inherent characteristic. The deconvolution

28

is applied to the Fourier Transform of the image. The Fourier Transform decomposes a function

into the frequency components that comprise it. Projection images are comprised of discrete

pixel values, so the Discrete Fourier Transform (DTF) is needed to compute the Fourier

Transform of an image. The one-dimensional DTF and its corresponding inverse function, the

Inverse DTF, are given by equations 2-1 and 2-2 below;

For k = 0, …, N-1

𝑋𝑘 = ∑ 𝑥𝑛𝑒−2𝜋𝑖𝑘𝑛/𝑁

𝑁−1

𝑛=0

(2-1)

For n = 0, …, N-1

𝑥𝑛 = ∑ 𝑋𝑘𝑒2𝜋𝑖𝑛𝑘/𝑁

𝑁−1

𝑘=0

(2-2)

where the 𝑋𝑘 represents the DTF of 𝑥𝑛; N is the total number of discrete data points. It is quickly

noted that for a set of N data points, a total number of N2 calculations are required to compute the

DTF. This led to the development of the Fast Fourier Transform (FFT). The FFT is a clever

method for computing the DTF in much fewer calculations. The FFT is the principal algorithm

used to compute the Fourier Transform of an image data set.

After obtaining the Fourier Transform of the image set, a filter is applied to the Fourier

Transform of the image which undoes the inverse distance blurring.29 The filter itself is the

Fourier transform of the inverse distance blurring function. This technique is thus referred to as

filtered back projection (FBP). It is widely utilized in modern imaging modalities as the primary

reconstruction algorithm.

Feldkamp-Davis-Kress algorithm

The full cone-beam geometry of CBCT requires a modification to FBP in order to

reconstruct the 3D volume. Feldkamp, Davis, and Kress modified the FBP algorithm to be

29

applied to full fan beam geometry on a flat panel image receptor.2 The FDK algorithm accounts

for the geometric divergence of the cone-beam onto a flat panel detector. The FDK algorithm is

widely used for reconstruction of CBCT. The FDK algorithm formulation is given in equation 2-

3 below;

𝑉 = ∑ 𝐵[𝐻(𝑃𝛽)]𝛽∈𝑆

(2-3)

where 𝑉 is the reconstructed volume; 𝛽 is the scan angle from the projection angles set 𝑆; 𝑃𝛽 is

the projection data set at angle 𝛽; H represents the filter operator applied to the Fourier

Transform of the projection data set; B represents the back projection operator.32

30

Figure 2-1. An example of a common C-arm fluoroscopy unit. Source: GE Healthcare,

https://www.gehealthcare.com/en/products/surgical-imaging/oec-9900-elite.

Figure 2-2. An example of a modern helical CT scanner. Source: Siemens Medical,

https://usa.healthcare.siemens.com/computed-tomography/dual-source-ct/somatom-

force.

31

Figure 2-3. The left side shows a CT thin fan beam on a curved detector compare to a CBCT

cone-beam on a flat panel detector. Source: Scarfe, et al.33

Figure 2-4. Image of the Artis zeego eco by Siemens Medical. The mounting of the c-arm on a

robotic arm adds additional degrees of freedom. Source: Siemens Medical,

https://www.healthcare.siemens.com/refurbished-systems-medical-imaging-and-

therapy/ecoline-refurbished-systems/angiography-ecoline/artis-zeego-eco.

32

Figure 2-5. Image of the Multitom Rax dual robotic imaging system. The x-ray tube and image

receptors are on separate robotic arms to be manipulated as necessary. Source:

Siemens Medical, https://usa.healthcare.siemens.com/robotic-x-ray/twin-robotic-x-

ray/multitom-rax.

Figure 2-6. A diagram of how the projection views are SBP through the image space to

reconstruct the original image. Source: Smith SW, The Scientist and Engineer’s

Guide to Digital Signal Processing.34

33

CHAPTER 3

MATERIALS AND METHODS

CT Phantom Image Sets

The virtual x-ray simulator relied on digital image sets acquired via CBCT. The virtual x-

ray simulator uses the Hounsfield units for each voxel in the CBCT image set to predict the

attenuation of each voxel. To verify the accuracy of the reconstructed 3D data sets, specific

CBCT phantoms were chosen to test certain aspects of the reconstruction process.

Catphan Phantom

The Catphan® 504 model is a CBCT phantom used for image analysis. Its 23 degree

ramps were used to compute the effective slice thickness (EST) of the reconstructed image sets.

The Catphan phantom was also used to convert the attenuation coefficients of the reconstructed

image sets to Hounsfield Units (HUs) from the known HU values of the Catphan phantom. A bi-

linear fit was applied for conversion of attenuation coefficients to HUs.

Anatomical Phantom

The anatomical phantom is comprised of a pig vertebra as a proxy for a human spine

encased in ballistic gel. The anatomical phantom was used to demonstrate the reconstruction of

boney anatomy with the ballistic gel that provides a scattering media. The dimensions of the pig

spine phantom are 17 cm x 28.5 cm x 38.5 cm.

Anatomical Phantom with Pedicle Screws

The anatomical phantom was modified digitally by adding cylinders that mimic pedicle

screws. The screws were added digitally in order to generate a phantom with no inherent photon

starvation artifacts from which to generate projections. The screws were placed in the axial plane

and tilted +20 degrees and -20 degrees laterally. Furthermore, the HUs of voxels outside the

34

FOV were increased to better match anatomical phantoms dimensions since that whole phantom

is not contained within the scanner FOV.

The HUs of the pedicle screws were determined by comparing photon starvation artifacts

of the reconstructions of the anatomical phantom with pedicle screws with various HUs to the

photon starvation artifacts of an OBI scan of a similar phantom of pig vertebrae with pedicle

screws in ballistic gel. Figure 3-4 compares the photon starvation of reconstruction with various

HU values for the pedicle screws. Figure 3-4 demonstrates that reconstructions with the digital

screws set to 6500 HUs best reproduces the photon starvation artifacts. Therefore, digital screws’

HUs were set to 6500.

Each digital screw consists of two cylinders: head and body. The dimensions of each

digital screw’s head are a length of 16 mm and a diameter of 12 mm. The dimensions of each

digital screw’s body are a length of 45 mm and a diameter of 5 mm. Furthermore, the

background beyond the Field of view was set to -356 HUs in order to increase the attenuating

size of the phantom to better match the real size of the anatomical phantom.

Lucite/Bone Block Phantom

The Lucite/Bone phantom consists of stacked blocks of Lucite and solid bone. It was

used to compare the effect of scatter on image reconstructions in CBCT versus CT. The Lucite

provides uniform attenuation and the solid bone provides scatter.

Imaging Platforms

The imaging platforms that were used to acquire image sets to serve as digital phantoms

were a Siemens CT scanner and the Varian On-Board Imaging (OBI) CBCT system on a Varian

Clinac 21EX linear accelerator. The CT scanner was operated at 100 kilovolts (kV) with

modulated milliamps-seconds (mAs). The OBI CBCT was operated at three presets labeled

‘Standard Dose Head,’ ‘High-Quality Head,’ and ‘Pelvis Spotlight,’ whose parameters are

35

100kV/145mAs, 100kV/720mAs, and 125kV/720mAs respectively. Each of these presets

acquires about 360 projections over an axial arc length of 200 degrees.

A Varian OBI CBCT scan of the Lucite/Bone phantom with the ‘Pelvis Spotlight’ served

as the input image set to the x-ray simulator for the scatter analysis. A Varian OBI CBCT scan of

the Catphan Phantom with the ‘Standard Dose Head’ preset was used as the input image set to

the virtual x-ray simulator for the quantitative image analysis. A Varian OBI CBCT scan of the

anatomical phantom with the ‘Pelvis Spotlight’ served as the input image set to the x-ray

simulator for all the qualitative image analysis.

MATLAB®

The principal computational language used in this work is MATLAB®. MATLAB® is a

very powerful tool in the reconstruction process because it contains many important elements of

the reconstruction process already available. MATLAB® scripts and toolboxes are used in this

work extensively. Scripts have been written to simulate the geometry of each projection for each

modality, which is the input for the virtual x-ray simulator. The projection image sets returned by

the virtual x-ray simulator for reconstructive modalities are then used as the input for

reconstruction.

Virtual X-Ray System

Since a prototype of the robotic imager is not yet available to test, a virtual x-ray system

developed by Dr. Didier Rajon was used generate digitally reconstructed radiographs (DRRs) to

simulate radiographic projections. This virtual x-ray system allows the user to specify the

locations of the x-ray source point and image receptor, along with the orientation of the image

receptor to define its 2D plane within 3D virtual image acquisition space. The virtual image

receptor modeled is as a flat panel. A CBCT image set is then loaded into the virtual x-ray

system to define the 3D image acquisition space.

36

Attenuation Computation

The virtual x-ray simulator predicts the exposure of each pixel on the image receptor for

rays that originate at the x-ray source and pass through the CBCT image set. The virtual x-ray

simulator models the attenuation of monogenetic photons through the CBCT image sets’ voxels

along the ray path from the virtual x-ray source point to each pixel on the virtual image receptor.

The attenuation coefficient for each voxel is determined from the CT number or Hounsfield units

(HU) specified in the CBCT image set is given by,29

µ 𝑣𝑜𝑥𝑒𝑙 = µ𝑊𝑎𝑡𝑒𝑟𝐶𝑇𝑉𝑜𝑥𝑒𝑙−𝐶𝑇𝑎𝑖𝑟

𝐶𝑇𝑤𝑎𝑡𝑒𝑟−𝐶𝑇𝑎𝑖𝑟 (3-1)

where µ𝑊𝑎𝑡𝑒𝑟 is equal to 0.195 cm-1; 𝐶𝑇𝑎𝑖𝑟 and 𝐶𝑇𝑤𝑎𝑡𝑒𝑟 are equal to -1000 HUs and 0

HUs respectively. The percent attenuation of a ray is given by,29

𝑃𝑒𝑟𝑐𝑒𝑛𝑡 𝐴𝑡𝑡𝑒𝑛. = 1 − ∏ 𝑒−µ𝑖𝛥𝑥𝑖𝑁𝑖=1 (3-2)

where 𝑁 is the total number of voxels traversed by the ray; µ𝑖 and 𝛥𝑥𝑖 are the attenuation

coefficient of and the distance the ray travels through the 𝑖𝑡ℎ voxel respectively.

Once the percent attenuation value is computed, the virtual x-ray simulator maps the

value between 0 and 1000 based on user inputs of the maximum and minimum percent

attenuation values. These values acts as a window and level for the final projection. The

minimum percent attenuation value was set to zero and the maximum percent attenuation value

was determined by using a phantom of solid bone with pedicle screws in ballistic gel to find the

maximum percent attenuation value that reproduce a similar level of photon starvation artifact

with the OBI scan with the same 200 degree arc length, 360 total projections and FDK for

reconstruction. Figure 3-7 shows the OBI reconstruction compared to simulator projections

based reconstructions at various maximum percent attenuation values. Figure 3-7 demonstrates

that a maximum percent attenuation value of .9975 best reproduces the photon starvation.

37

Therefore, the user reconstructed image set percent attenuation values of 0 to .9975 were mapped

to the scale 0 to 1000.

Projection Dimensions

Each DRR’s geometry was set to match the geometry of the Varian OBI used to acquire

the input image sets; source to object distance (SOD) of 100 cm and a object to image (OID)

distance of 50 cm. Pixel dimensions were also chosen to match the PaxScan 4030CB digital

image receptor which are .388 x .388 mm2.

Projection Geometry Simulation

The input for the virtual x-ray simulator is a file that defines the geometry for each

projection. There is a separate projection geometry simulation MATLAB® script for each

imaging modality. The projection geometry simulation MATLAB® script inputs include the

SOD, the OID, the angle and direction of the scan arc, and the number of projections. The script

then generates a file with lines of values that define each projection’s setup geometry. The values

in each line define the locations of the x-ray source and center of the image receptor in the 3D

CT image set space, the image receptor normal vector, and the image receptor view up vector.

The projection geometry simulation MATLAB® script computes the orientation of the

virtual 2D image receptor plane in the 3D CT image set space. The locations of the x-ray source,

image receptor and their orientation are obtained by applying rotation matrices that move each

element to its proper location depending on the necessary movement. For isocentric CBCT,

rotation vectors about the anterior-posterior (AP), lateral (Lat), and axial (Ax) are applied. The

rotation vectors are dependent on the angle of rotation, 𝜃. The rotation matrix for each axis is

given in equations 3-3 through 3-5 below.

𝑅𝐴𝑃 = [cos (𝜃) 0 sin (𝜃)

0 1 0−sin (𝜃) 0 cos (𝜃)

] (3-3)

38

𝑅𝐿𝑎𝑡 = [1 0 00 cos (𝜃) sin (𝜃)

0 −sin (𝜃) cos (𝜃)] (3-4)

𝑅𝐴𝑥 = [cos (𝜃) sin (𝜃) 0

−sin (𝜃) cos (𝜃) 00 0 1

] (3-5)

For linear based tomosynthesis and radiographs, the linear translation vectors along the

AP, Lat, and Ax scan axis are dependent on the angle rotation, 𝜃, and the distance, D, from the

center of rotation to the central axis of the object, which for the x-ray source is the SOD and for

the image receptor is the OID. The linear translation vector for each direction are given in

equations 3-6 through 3-8 below.

𝑅𝐴𝑃 = [0

𝐷 ∗ tan (𝜃)0

] (3-6)

𝑅𝐿𝑎𝑡 = [𝐷 ∗ tan (𝜃)

00

] (3-7)

𝑅𝐴𝑥 = [00

𝐷 ∗ tan (𝜃)]

(3-8)

Circular tomosynthesis rotation vectors are a linear combination of linear translation

vectors. They are dependent on the angle of rotation, 𝜃, and the radius of the circular arc, R. The

circular tomosynthesis rotation vectors for each axis are given in equations 3-9 through 3-11

below.

𝑅𝐴𝑃 = [𝑅 ∗ cos (𝜃)

0𝑅 ∗ sin (𝜃)

] (3-9)

39

𝑅𝐿𝑎𝑡 = [

0𝑅 ∗ cos (𝜃)𝑅 ∗ sin (𝜃)

]

(3-10)

𝑅𝐴𝑥 = [𝑅 ∗ cos (𝜃)𝑅 ∗ sin (𝜃)

0

] (3-11)

With the virtual x-ray source and image receptor defined within the 3D CT image set

space, the virtual x-ray simulator can compute the ray path from the virtual x-ray source to each

pixel on the virtual image receptor.

Scatter Analysis

The simulator computes the primary beam’s attenuation, but does not add scatter to the

DDR, a critical image degrading parameter in CBCT imaging. The addition of scatter to digital

phantoms typically relies on convolving the digital image with burring functions.35-39 To account

for scatter, the input image sets were acquired on the OBI CBCT. This provided scatter to the

input image set without the need to artificially degrade the images.

To demonstrate that using a CBCT image set as the input for the simulator provides

scatter to the DRRs, 1-D line profiles of anterior-posterior DRRs with CT and CBCT input

image sets and raw OBI projections were compared. The CT input image set was acquired at

100kV with modulated mAs and the OBI CBCT image sets were acquired using the ‘Pelvis

Spotlight’ preset. The 1-D line profiles were sampled across Lucite and bone on the DRR and

then normalized to the profile’s mean across the uniform Lucite regions adjacent to the solid

bone. The contrast was plotted as the ratio of the profile to the mean Lucite signal minus one to

give the fraction contrast difference above the mean Lucite signal, as shown in Figure 3-8.

Figure 3-8 demonstrates that the simulator DRR from the OBI CBCT input image set has

40

significantly less contrast and thus has more scatter than both the simulator DRR from the CT

input image set and the raw OBI projection. This shows that the simulator generated DRRs from

OBI CBCT image sets represent a worst-case scenario for in the inclusion of scatter.

Reconstruction

Dimensions

Each image set reconstructed from simulator DDRs was set to match the high-resolution

voxel sizes and dimensions of the input image set. The OBI CBCT generated Catphan

reconstructions have a voxel size of 0.4883 x 0.4883 x 1 mm3 at 512 x 512 x 164 voxels. The

OBI CBCT generated anatomical phantom reconstructions have a voxel size of 0.46875 x

0.46875 x 1 mm3 at 512 x 512 x 174 voxels. By matching the reconstructions’ pixel size and

dimensions with its corresponding input image set, the reconstructions and their corresponding

input image set can more easily be compared pixel by pixel.

Algorithms

An open source MATLAB® toolbox, Tomographic Iterative GPU-based Reconstruction

Toolbox (TIGRE), was used to reconstruct each image set.40,41 TIGRE has been adapted to back

and forward project non-coplanar projections. Within TIGRE, the reconstruction algorithms used

were FDK and iterative TV based adaptive-steepest-descent projection on convex sets (ASD-

POCS).42 ASD-POCS has shown to be effective for limited arc sizes and limited number

projection sets. Each ASD-POCS reconstruction was performed with 50 or more iterations. The

ASD-POCS tuning parameter, as TIGRE defines them, and values used for each reconstruction

were 𝜖 = 1000, 𝑛𝑔 = 25, 𝛼 = 0.002, 𝛼𝑟𝑒𝑑 = 0.9, 𝜆 = 1, 𝜆𝑟𝑒𝑑 = 0.98, 𝑟𝑎𝑡𝑖𝑜 = 1.

Hounsfield Units Conversion

For each reconstructed image set, the image analysis was performed after the

reconstructed image set’s attenuation coefficients were converted to HUs. The HU conversion

41

was performed using the original OBI Catphan phantom reconstruction via FDK. The attenuation

coefficients of the inserts with various density of the Catphan reconstructed image sets were

directly compared to the HUs of the corresponding inserts in the original OBI Catphan phantom

reconstruction. The corresponding attenuation coefficients and HU values were plotted, and then

a bilinear fit was applied to plot. The bilinear fit provides the scaling from attenuation

coefficients to HUs. Each unique combination of reconstruction algorithm, projection geometry,

scan motion(s), arc length, and number of projections has a unique bilinear fit. For each

anatomical phantom with or without screws image set, the attenuation coefficients were scaled

using the bilinear fit obtained via a Catphan image set reconstruction that matches all the

reconstruction parameters.

Projection Generation to Reconstruction Workflow

The workflow from the generation of projection data to producing the 3D reconstructed

image set begins by selecting the projection generation simulator MATLAB® script for the

modality to be simulated. The geometry of each projection is defined within the script. The

projection geometry MATLAB® simulation script then produces for each projection the locations

of the x-ray source and image receptor points, and the orientation vectors for the image receptor.

The projection geometries and the CBCT image set are the inputs of the virtual x-ray

simulator. The virtual x-ray simulator computes the exposed image of the CBCT image set onto

the virtual image receptor assuming a cone-beam geometry. The virtual x-ray simulator then

outputs each DRR as a separate file.

The DRR files generated by the virtual x-ray simulator are then read together into TIGRE

to reconstruct the 3D image set. The image set is then converted from its raw attenuation

coefficients to HUs via a bilinear fit for the exact same parameters of the reconstruction

generated form the Catphan phantom. Subsequently, specific MATLAB® scripts perform the

42

image quality analysis. The image quality analysis scripts compute the EST, root mean square

error (RMSE), and modulation transfer function (MTF). The images are also evaluated for

qualitative image quality.

Image Quality Analysis

Quantitative Analysis

Effective slice thickness

The Catphan phantom’s 23 degree ramps were used to compute the EST of reconstructed

image sets, as shown in Figure 3-9. The Phantom Laboratory’s formula, which has been used in

literature,43 for the EST using the Catphan phantom computes the full width at half max

(FWHM) of the 23 degree ramps in an image slice, and subsequently multiplies the FWHM by

0.42. The EST for each image set is the average EST for at least two of the four 23 degree ramps

per slice over five slices. The measured EST of the input CBCT acquired on the Varian OBI with

the ‘Standard Dose Head’ preset was 1.16mm. Only single axial arcs were evaluated for EST.

Root mean square error

The RMSE was used to compare the reconstructions of the Catphan voxel by voxel with

the input Catphan image set for regions of interest. The Catphan regions of interest included five

slices of the various density inserts and two slices of the spatial resolution bar pattern. The

RMSE is given by,44

𝑅𝑀𝑆𝐸 = √∑ (𝑥𝑖𝑜𝑟𝑖−𝑥𝑖𝑟𝑒𝑐)

2𝑁𝑖=1

𝑁 (3-12)

where N is the total number of voxels, 𝑥𝑖𝑜𝑟𝑖 and 𝑥𝑖𝑟𝑒𝑐

are the values of the 𝑖𝑡ℎ

corresponding input image set and reconstructed voxels respectively.

Since the RMSE value is a measure of the global difference in the pixel values of two

image sets, the lower the RMSE value the more similar the image sets are. In order to preserve

43

scatter, the OBI CBCT Catphan Phantom image set served as the ground truth against which all

RMSE values were computed. Image sets that produced RMSE values set less than or equal to

100 when compared to the input Catphan image were subjectively considered diagnostic quality.

Modulation transfer function

The MTF was used to evaluate each 3D reconstructed image set’s spatial frequency

response. The MTF was computed using the Catphan’s metal bead which served as a point

source, the tiny dot near the middle Figure 3-10. The MTF was computed by sampling the point

spread function (PSF) of the metal bead and then following traditional MTF protocol.45

Qualitative Analysis

Soft tissue and bone contrast

The anatomical phantom was used to show the qualitative reconstructive performance of

each OLASCs. Attention was paid to contrast between bone and gel, and artifacts due to the

limited angle arcs. Attention was also paid to the texture of the soft tissue background provided

by the ballistic gel of the anatomical phantom as shown in Figure 3-11.

Photon starvation artifact

The anatomical phantom with pedicle screws was used to evaluate the effects of photon

starvation artifacts caused by the high attenuation of the metallic pedicle screws. Attention was

paid to dark and bright streaks that are caused by photon starvation.

Scan Acquisition Combinations

OLASCs were divided into to three groups of orthogonal scan acquisitions with various

combinations within each group evaluated. All scan acquisitions comprising a two or three

OLASCs were acquired with arcs of equal lengths at certain projection densities.

44

Anatomical Motions

The first group consists of scan acquisitions where the x-ray source and image receptor

rotate within each anatomical plane (i.e. axial, coronal, and sagittal), as shown in Figure 3-12.

The coronal and sagittal scan acquisitions are geometrically limited in arc length to account for

potential collisions with the patient support unit or patient. Single axial arcs were used to

evaluate the effects of arc length and projection density on EST. Single axial arcs were evaluated

until the input Catphan EST of 1.16mm was reach or the EST leveled off. Every OLASC of two

anatomical plane arcs, as well as the OLASC consisting of all three anatomical plane arcs were

evaluated in terms of RMSE and MTF curves. For each anatomical plane OLASC, projection

densities were set at .5, 1, 2, and 3 projections per degree, and the arc lengths were increased by

10 degree at each projection density.

Oblique Motions

The second group consists of two sets of double oblique OLASCs as shown Figure 3-13.

The oblique axial OLASC is formed by two axial plane acquisition that are tilted 45 degrees

caudally and distally to maintain orthogonality between the two scan motions, as shown in

Figure 3-13A. Oblique axial OLASC can each theoretically be a complete 360 degree arc

depending on the patient and the angle of tilt. The oblique sagittal OLASC is formed by two

sagittal plane acquisition that are tilted 45 degrees left and right laterally, as shown in Figure 3-

13B. Oblique sagittal OLASCs are also limited in arc length to account for restrictions usually

presented by the patient support unit or patient. Oblique OLASC consisting of the two oblique

axial arcs and of the two oblique sagittal arcs were evaluated. Projection densities and arc lengths

were varied in the same manner as anatomical plane OLASCs.

45

Oblique’s Plus Orthogonal Anatomical OLASCs

Both double oblique OLASCs maintain full orthogonal motion with one anatomical scan

motion as shown in Figure 3-14. The sagittal oblique’s are orthogonal with the axial anatomical

scan motion, and axial oblique’s are orthogonal with the sagittal anatomical scan motion.

Projection densities and arc lengths were varied in the same manner as anatomical plane

OLASCs.

Circular Motions

The third group consists of circular scan acquisitions. Circular arcs are formed by the x-

ray source and image receptor rotating in circles around the same anatomical axis (i.e. Ax, AP,

and Lat) in separate parallel planes, as shown in Figure 3-15. Both the x-ray source and image

receptor are rotating at a specified cone angle relative to the anatomical axis. Single Circular

scan acquisitions were used to evaluate the effects of cone angle and total projections on RMSE

and MTF. Every two circular OLASCs, as well as the all three circular OLASCs were evaluated.

For each circular OLASC, the total number of projections was set at 25, 50, 100, and 150, and

the cone angles were set to 15, 30, and 45 degrees at each total number of projections. Con

angles of greater than 45 degrees were not investigated since as the cone angle exceeds 45

degrees is essentially approaches coplanar projections scans that are currently used.

2PI Solid Angle Projections

The last scan motion is expanding the coverage of evenly spaced projections over an

entire 2PI solid angle as shown in Figure 3-16. This case represents the theoretical limit of

projection imaging by acquiring projections from every position along a 2PI solid angle around

an object. The real challenge is evenly spacing the projections over a curved surface. There is no

exact solution available. I settled on an approximation that relies on using the Golden Ratio to

determine the angle and spacing relative to the preceding position.46 The total number of

46

projections evenly spaced over 2PI was set at 25, 50, 100, 125, and 150. The central projection

was centered along the anterior-posterior axis.

47

Figure 3-1. The Catphan phantom used for evaluating the spatial resolution and contrast of

reconstructive x-ray imaging systems. Source: Phantom Laboratory,

https://www.phantomlab.com/catphan-500.

Figure 3-2. The anatomical phantom which consists of a pig cadaver spine encased in ballistic

gel. Photo courtesy of author.

48

Figure 3-3. Slice of anatomical phantom with pedicle screws added digitally.

A) B)

Figure 3-4. Comparison of the photon starvation artifact of the A) OBI scan reconstruction, then

the reconstructions with the digital screws’ HU values of B) 5000, C) 6500, and D)

8900.

49

C) D)

Figure 3-4. Continued

Figure 3-5. The Lucite/bone block phantom which consists of stacked blocks of Lucite around a

solid bone block to evaluate the level of scatter in CBCT imaging. Photo courtesy of

author.

50

Figure 3-6. Example of a fluoroscopic x-ray projection generated by the virtual x-ray system for

a CT image set. Photo courtesy of the author.

A) B)

Figure 3-7. Comparison of photon starvation artifact of the A) OBI scan reconstruction, then

reconstructions with simulator projections with maximum percent attenuation values

of B) .99, C) .9975, and D) .9999.

51

C) D)

Figure 3-7. Continued

A) B)

Figure 3-8. The scatter analysis process for generating the projections is given in the A) block

diagram, and the results given in B) 1-D profiles plotted as percent difference of

contrast above mean Lucite signal.

CBCT Simulator

DRR (Blue)

CT Simulator

DRR (Red)

OBI CBCT

Projection (Green)

CT Scan

OBI CBCT

Scan Lucite/Bone

Phantom OBI CBCT

Reconstruction

CT

Reconstruction

Virtual X-

Ray

Simulator

52

Figure 3-9. CBCT of Catphan® phantom’s four 23 degree ramps.

Figure 3-10. Slice of input Catphan Phantom image set with metal bead, identified by an orange

arrow, to provide point source for computing MTF.

53

Figure 3-11. Slice of anatomical phantom used to qualitatively evaluate the soft tissue and bone

contrast.

Figure 3-12. Views of all three anatomical scan acquisitions. The arrows trace out the path of

the x-ray source with image receptor following an opposite path that is not shown: A)

axial, B) sagittal, and C) coronal.

54

Figure 3-13. Views of two separate sets of double oblique OLASCs being A) sagittal oblique’s,

and B) axial oblique’s.

Figure 3-14. Views of two sets of triple oblique’s plus orthogonal anatomical OLASCs being A)

sagittal oblique’s plus axial, and B) axial oblique’s plus sagittal.

Figure 3-15. Views of the circular scan acquisitions at a cone angle Θ: A) coronal view of a

lateral circular scan acquisition, B) sagittal circular scan acquisition, and C) coronal

view of an axial circular scan acquisition.

55

A) B)

Figure 3-16. Diagrams of 125 projections evenly over spaced a 2PI solid angle that show A)

how the projections on a spherical surface, and B) the polygon spaces between

projections.

56

CHAPTER 4

AIM 1 – RESULTS OF QUANTITATIVE IMAGE ANALYSIS

Effective Slice Thickness

The effect of single axial arc length on EST for FDK and ASD-POCS is given in Figures

4-1. For FDK reconstructions at .5 projections per degree, the input Catphan image set EST limit

of 1.16 mm and leveling off at 160 degrees. While FDK reconstruction ESTs at 1, 2, and 3

projections per degree are nearly identical across all arc lengths by leveling to 1.37 mm at 80

degrees, then steadily decreases to 1.18 mm at 180 degrees. For ASD-POCS reconstructions, at

.5 projections per degree, the input EST limit is reached at 140 degrees, but does not level off. At

1 projection per degree, the input EST limit is reached at 120 and then decreases to 1.01 mm at

130 degrees and levels off. At 2 projections per degree, the input EST limit is reached at 80

degrees and then decreases to 1.01 mm at 110 degrees and levels off. At 3 projections per degree,

the input EST limit is reached at 70 degrees and levels off to 1.01 mm at 100 degrees.

Root Mean Square Error

Algorithm

The effect of single axial arc size on RMSE for FDK and ASD-POCS is given in Figure

4-2. For FDK reconstructions, the RMSE is nearly equivalent for each projection density for all

arc sizes by steady decreasing, except for .5 projections per degree which slowly diverges for the

for larger arc sizes. For ASD-POCS reconstructions, the RMSE for each projection densities

decreases until they all converge at about 130 degrees, and subsequently slowly decreases.

Single Arc Scan Motions

Anatomical motions

The effect of single arc scan motion with arc length on RMSE values for coronal and

sagittal scan motions are given in Figures 4-3. The single axial scan motion analysis is given in

57

Figure 10B. Both the coronal and sagittal scan motions, the RMSE decrease steadily as the arc

length is increased and there is effect from projection density.

Circular motions

The effect of single circular scan acquisitions on RMSE for 15, 30, and 45 degree cone

angles is given in Figure 4-4. For single circular axial reconstructions, with a 15 degree cone

angle, the RMSE drops to 340 at 200 projections and levels off. With a 30 degree cone angle, the

RMSE slowly decreases to 377 at 250 projections. With a 45 degree cone angle, the RMSE

increases to 340.6 at 200 projections. For single circular sagittal reconstructions, with a 15

degree cone angle, the RMSE slowly increases to 383.8 at 150 projections and then levels off.

With a 30 degree cone angle, the RMSE slowly decreases to 254 at 250 projections. With a 45

degree cone angle, the RMSE decreases to 157.8 at 50 projections and levels off. For single

circular coronal reconstructions, with a cone angle of 15 degrees, the RMSE steadily increases to

413.9 at 250 projections. With a cone angle of 30 degrees, the RMSE slowly decreases to 302.3

at 250 projections. With a cone angle of 45 degrees, the RMSE steadily decreases to 150.8 at 250

projections.

Double OLASCs

Anatomical combinations

The effect of double anatomical OLASCs with arc length on RMSE values at one and

two projections per degree is given in Figures 4-5. At both one and two projections per degree,

the RMSE values for the axial/coronal OLASC for all arc lengths are significantly lower than the

axial/sagittal and coronal/sagittal OLSCs.

Oblique combinations

The effect of double oblique OLASCs with arc length on RMSE at various projection

densities is given in Figures 4-6. For the sagittal oblique’s, varying the projection density has

58

little to no effect on the RMSE for nearly all arcs lengths. For axial oblique’s, as the arc length

increases the .25 and .5 projections per degree have lower RMSEs than 1 and 2 projections per

degree.

Circular combinations

The effect of each double circular OLASCs with number of projections per arc at various

cone angles is given in Figure 4-7. For both Ax/AP and Ax/Lat OLASCs, the 30 and 45 degree

cone angles are equivalent from 25 to 100 projections per arc after which the 30 degree cone

angle becomes superior. For the AP/Lat OLASCs, the 45 degree cone angle is significantly

superior to 15 and 30 degree cone angles for all numbers of projections per arc. Figure 4-7 shows

that across double circular OLASCs for 45 degree cone angle the RMSE values are very similar.

Triple OLACs

Anatomical combinations

The effect of triple anatomical OLASCs with arc length on RMSE for various projection

densities is given in Figure 4-8. For small arc lengths, .5 and 1 projections per degree is superior

until about 80 degrees for each arc, after which higher projection densities are superior.

Oblique’s plus orthogonal anatomical

The effect of triple oblique’s plus orthogonal anatomical OLASCs with arc length on

RMSE values for various projection densities is given in Figure 4-9. For sagittal oblique’s plus

axial OLASCs, Figure 4-9A shows that at 60 degree arc lengths projection density has a

significant effect with lower RMSE values with increasing projection density. At 90 degree arc

lengths, one projection per degree has the lowest RMSE value. For arc lengths greater than 90

degrees, there is little to no effect for projection density as RMSE values converge. For axial

oblique’s plus sagittal OLASCs, Figure 4-9B shows the for all arc lengths higher projection

values give lower RMSE values.

59

Circular combinations

The effect of triple circular OLASCs on RMSE values for various cone angles is given in

Figure 4-10. From 25 to 100 projections per arc, the 30 and 45 degree cone angles are equivalent,

after which the 30 degree cone angle is superior.

Coplanar Arc Projections vs 2PI solid angle projections

For the comparison of reconstructions via coplanar arc projection and evenly over spaced

2PI solid projections, Figure 4-11 shows that the RMSE values for coplanar arc reconstructions

via ASD-POCS are slightly lower than evenly spaced over 2PI surface projections. The coplanar

arc projections’ and 2PI solid angle projections’ RMSE values are very closer until they

converge at 200 total projections at the RMSE value of about 50. After which, they diverge at

200 projections with coplanar arc projections being superior.

Modulation Transfer Function

Algorithm

The effect of the reconstruction algorithm on MTF curves for single axial scan motions

compared to the input Catphan image set MTF curve is given in Figure 4-12. For FDK, an

increase in arc length at one projection per degree actually gives a worse MTF curves. For ASD-

POCS, an increase in arc length at one projection per degree gives better MTF curves with a 180

degree arc giving an MTF curve that matches the input Catphan image set MTF curve.

Single Arc Scan Motions

Anatomical motions

The effect of single axial arc length on single axial anatomical MTFs at various

projection densities is given in Figure 4-13. At .5 projections per degree, the 120 degree arc’s

MTF curve is nearly equivalent to the input Catphan image set MTF curve. At one projection per

degree, only the 120 degree arc’s MTF curve is equivalent to the input Catphan image set MTF

60

curve. At two projections per degree, the 90 and 120 arcs’ MTF curves are equivalent to the

input Catphan image set MTF curve with the 60 degree curve nearly equivalent.

The effect of projection density on single axial anatomical MTFs at various arc lengths is

given in Figure 4-14. For 60 degrees, the two projections per degree arc’s MTF curve is nearly

equivalent to the input Catphan image set MTF curve. At 120 degrees, the two projections per

degree arc’s MTF curve is equivalent to the input Catphan image set MTTF curve. At 180

degrees, the one and two projection per degree MTF curves are equivalent to the input Catphan

image set with the .5 projection per degree curve nearly equivalent.

Circular motions

The effect of single circular arcs on MTF curves for various axes of rotation for a 15

degree cone angle at 25 and 50 projections is given in Figure 4-15. At 25 projections, only the

axial rotation is able to match the input Catphan image set MTF curve. At 50 projections, the

axial and AP rotations are able to match the input Catphan image set MTF curve.

The effect of single circular arcs on MTF curves for various axes of rotation for a 30

degree cone angle at 25 and 50 projections is given in Figure 4-16. At 25 projections, none of the

rotations are able to match the input Catphan image set MTF curve. At 50 projections, the axial

and AP rotations are able to match the input Catphan image set MTF curve.

The effect of single circular arcs on MTF curves for various axes of rotation for a 45

degree cone angle at 25 and 50 projections is given in Figure 4-17. At 25 projections, only the

axial rotation is able to match the input Catphan image set MTF curve. At 50 projections, each

rotation is able to match the input Catphan image set MTF curve.

61

Double OLASCs

Anatomical combinations

The effect of double OLASCs on MTF curves at .5 projections per degree and their

comparison to the input Catphan image set MTF curve is given in Figure 4-18. For double

anatomical axial/coronal OLASCs, the MTF curve matches the input Catphan image set MTF

curve at all angles. For double anatomical axial/sagittal OLASCs, the 90 and 120 degree arcs’

MTF curves are equivalent to the input Catphan image set MTF curve with the 60 degree curve

nearly equivalent. For double anatomical coronal/sagittal OLASCs, only the 120 degree arc’s

MTF curve is equivalent to the input Catphan image set MTF curve. For all subsequent

projection densities, for each double anatomical OLASC the MFT curve is equivalent or nearly

equivalent to the input Catphan image set MTF curve.

Circular combinations

The effect of double circular OLASCs on MTF curves for various cone angles at 25

projections is given in Figure 4-19. At 15 degree cone angles, the Ax/AP and Ax/Lat OLASCs

were able to match the input Catphan image set MTF curves. At 30 degree cone angle, only the

Ax/AP OLASC is able to match the input Catphan image set MTF curve. At 45 degree cone

angle, each OLASC is able to match the input Catphan image set MTF curve.

Triple OLASCs

Anatomical combinations

The effect of triple anatomical OLASCs on MTF curves for various arc lengths is given

in Figure 4-20. At 60 degrees for each arc, the MTF curves at each projection density are nearly

equivalent to the input Catphan image set MTF curve. At 90 degrees for each arc, the MTF

curves at each projection density are equivalent to the input Catphan image set MTF curve.

62

Oblique’s plus orthogonal anatomical

The effect of oblique’s plus orthogonal anatomical OLASCs on MTF curves for various

arc lengths and projection densities is given in Figure 4-21. For sagittal oblique’s plus axial

OLASc, Figure 4-21A shows at just 60 degrees arc lengths nearly all projection densities give

MTF curves that match the input Catphan image set MTF Curve. At 90 degrees arc lengths,

Figure 4-21B shows all projection density MTF curves match the input Catphan image set MTF

curve. For axial oblique’s plus sagittal OLASC, Figure 4-21C shows at just 60 degree arc lengths

the MTF curves for all projection densities match the input Catphan image set MTF curve.

Circular combinations

The effect of triple circular OLASCs on MTF curves for various cone angles is given in

Figure 4-22. For all cone angles at 25 projections per arc, the triple OLASCs were able to match

the input Catphan image set MTF Curve.

Coplanar Arc Projections vs 2PI Solid Angle Projections

The effect of coplanar arcs and 2PI solid angle projections on MTF curves for various

total projections is given in Figure 4-23. At 25 total projections, only the 2PI solid angle

projection reconstruction was able to match the input Catphan image set MTF curve. At 50 total

projections, the coplanar arc via FDK and the 2PI solid angle projection reconstructions were

both able to match the input Catphan image set MTF curve, while the coplanar arc via ASD-

POCS was close to matching the input Catphan image set MTF curve. At 100 total projections,

each coplanar arc via FDK and ASD-POCS and the 2PI solid angle projection reconstructions

were able to match the input Catphan image set MTF curve.

Quantitative Conclusion

The quantitative effects of various single scan arcs and multi-arc orthogonal limited angle

scan combinations on root mean square error and modulation transfer function curves were

63

evaluated in this chapter. The scan combination groups of anatomical, circular, oblique, and 2PI

solid angle were each evaluated based on RMSE and MTF curves. Firstly, the evaluation of

reconstruction algorithm on limited scan arc lengths shows that iterative asymmetric steepest

descent projection on convex sets is superior to traditional Feldkamp-Davis-Kress for shorter

limited arc length axial scans. Iterative ASD-POCS consistently generated lower RMSE values

with MTF curves that more closely match the input Catphan image set MTF curve.

The quantitative image analysis shows that the optimal anatomical OLASC is the double

axial/coronal combination at 90 degrees and 90 projections per arc. This combination produced a

very low RMSE value comparable to the triple anatomical OLASCs for similar arc lengths and

projection densities. Therefore, there was little benefit from adding the third orthogonal sagittal

arc which would increasing the total number of projections by 50%. The axial/coronal OLASC

also produced an MTF curve that was equivalent to the input Catphan image set MTF curve.

Therefore, the axial/coronal OLASC at 90 degree and 90 projections per arc produced the best

quantitative image analysis metrics with the shortest arc lengths and lowest projection density.

The quantitative analysis of the circular scan motions shows that all three double circular

OLASCs at 45 degree cone angle and 25 projections can effectively produce low RMSE values

and MTF curves that match the input Catphan image set MTF curve. The triple circular OLASC

at 45 degree cone angle and 25 projections, similarly of the triple anatomical OLASCs, provides

marginally better quantitative results. Therefore, each double circular OLASCs can be

recommended over the triple circular OLASC of the same cone angle and number of projections.

The quantitative analysis of 180 degree coplanar projection arc reconstructions compared

to evenly spaced 2PI solid angle projection reconstructions gives near identical RMSE values

and MTF curves. This suggests that quantitatively reconstructions from equal number of

64

projections in a 180 degree coplanar arc approximate the projections evenly spaced over a 2PI

solid angle.

65

A) B)

Figure 4-1. Graphs of EST as a function of arc size and projection density for reconstruction

algorithms A) FDK, B) ASD-POCS.

A) B)

Figure 4-2. RMSE values with arc length and projection density for reconstruction algorithms

A) FDK, and B) ASD-POCS.

66

A) B)

Figure 4-3. RMSE values with arc length and projection density for scan motion A) coronal, and

B) sagittal.

A) B) C)

Figure 4-4. RMSE values with cone angle and projection density for A) circular axial, B)

circular sagittal, and B) circular coronal scan acquisitions.

67

A) B) C)

Figure 4-5. RMSE values with arc length and projection density for double anatomical OLASCs

at A) .5 projections per degree, B) 1 projection per degree, and C) 2 projections per

degree.

A) B)

Figure 4-6. RMSE values with arc length and projection density for A) sagittal oblique’s, and B)

axial oblique’s at various projections densities.

68

A) B) C)

Figure 4-7. RMSE values with total projections per arc at various cone angles for double

circular OLASCs A) Ax/AP, B) Ax/Lat, and C) AP/Lat.

Figure 4-8. RMSE values with arc length and projection density for triple anatomical OLASCs

at various projection densities.

69

A) B)

Figure 4-9. RMSE values with arc length and projection density for A) sagittal oblique’s plus

axial, and B) axial oblique’s plus sagittal.

Figure 4-10. RMSE values with number of projections per arc for various cone angles of triple

circular OLASCs.

70

Figure 4-11. RMSE values with total number of coplanar arc projections and 2PI solid angle

projections.

A) B)

Figure 4-12. MTF curves with arc length and projection density for single axial scan motions by

reconstruction algorithms A) FDK, and B) ASD-POCS.

71

A) B) C)

Figure 4-13. MTF curves with arc length and projection density for single anatomical axial arcs

at A) .5 projections per degree, B) 1 projection per degree, and C) 2 projections per

degree.

A) B) C)

Figure 4-14. MTF curves with arc length for axial scan motions at projection density of A) 60

degrees, B) 120 degrees, and C) 180 degrees.

72

A) B)

Figure 4-15. MTF curves of circular scan motions with 15 degree cone angle for various

rotations at A) 25 protections, and B) 50 projections.

A) B)

Figure 4-16. MTF curves of circular scan motions with 30 degree cone angle for various

rotations at A) 25 protections, and B) 50 projections.

73

A) B)

Figure 4-17. MTF curves of circular scan motions with 45 degree cone angle for various

rotations at A) 25 protections, and B) 50 projections.

A) B) C)

Figure 4-18. MTF curves for double anatomical OLASCs at .5 projections per degree for A)

axial/coronal, B) axial/sagittal, and C) coronal/sagittal combinations.

74

A) B) C)

Figure 4-19. MTF curves for double circular arcs at 25 projections per arc for various cone

angles of A) Ax/AP, B) Ax/Lat, and C) AP/Lat rotations.

A) B)

Figure 4-20. MTF curves for triple anatomical OLASCs at A) 60 degrees and B) 90 degrees.

75

A) B)

C) D)

Figure 4-21. MTF curves with arc length and projection density for sagittal oblique’s plus axial

OLASC at A) 60 degree and B) 90 degree arc lengths, and for axial oblique’s plus

sagittal OLASC at C) 60 degree and D) 90 degree arc lengths.

76

Figure 4-22. MTF curves of triple circular arcs at 25 projections for various cone angles.

A) B) C)

Figure 4-23. MTF curves of reconstructions using coplanar arcs via FDK and ASD-POCS and

2PI solid angle with total projection of A) 25, B) 50, and C) 100.

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CHAPTER 5

AIM 2 – RESULTS OF QUALITATIVE IMAGE ANALYSIS OF BONE AND SOFT TISSUE

CONTRAST

Single Arc Scan Motions

Algorithm

The qualitative effect of the reconstruction algorithm is demonstrated in Figure 5-1.

Images from OBI CBCT image sets of A) Catphan and D) anatomical phantoms reconstructed

from a 200 degree arc and about 360 projections via FDK. They are the ground truths against

which all reconstructions were compared qualitatively. Figure 5-1 B) and E) show that the FDK

reconstructions based on simulator generated projections can reproduce both the Catphan and

anatomical phantoms to nearly identical quality to the original CBCT OBI Catphan and

anatomical image sets. This principally validates that the virtual x-ray simulator projections are

equivalent to OBI generated projections after reconstruction. Figure 5-1 C) and F) show that

iterative ASD-POCS reconstructions are superior to FDK reconstruction based on visual analysis

of how the image has better background texture with less noise.

Circulars

The quantitative RMSE image analysis of Chapter 4 revealed that single circular scan

motions produced relatively high RMSE values. Figure 5-2 shows the reconstructions of the

various single circular rotations at 45 degree cone angles and 150 projections. Figure 5-2

demonstrates clear consistency with the high RMSE values that correlate with the streak artifacts

that are present in each single circular rotation. Furthermore, each of the rotations produces a

background texture with significant light and dark streaking. None of the circular scan motions

provides diagnostic quality bone and soft tissue contrast.

78

Orthogonal Limited Arc Scan Combinations

Double OLASCs

Anatomical combinations

The quantitative image analysis of Chapter 4 provides the beginning set of scan motions

parameters. From RMSE values, the axial/coronal OLASC at 90 degree arc length and 90

projections per arc produced an adequately low RMSE value for relatively short arcs and few

projections. Figure 5-3 shows all three double OLASC combinations at 90 degree arc length and

90 projections per arc qualitatively. Figure 5-3 demonstrates clear consistency qualitatively with

the RMSE results. The axial/coronal OLASC slices shown in A) and D) are superior in image

quality to the axial/sagittal OLASC slices show in B) and E), and coronal/sagittal OLASC show

in C) and F). The axial/coronal OLASC has very limited streak artifacts due to the limited arc

lengths, as opposed to the serious streak artifacts present in the axial/sagittal and coronal/sagittal

OLASCs. Only the axial/coronal OLASC reconstruction provides diagnostic quality bone and

soft tissue contrast with the best soft tissue background texture.

Oblique combinations

The quantitative RMSE image analysis revealed that the double oblique OLASCs

produced relatively high RMSE values. Figure 5-4 shows the reconstructions of the Sagittal and

Axial oblique’s at 100 degree arc length and 100 projections per arc. Figure 5-4 demonstrates

clear consistency with the high RMSE values that correlate with the streak artifacts that are

present in both sagittal (A and C) and Axial (B and D) oblique’s. Each of the double oblique

OLASCs produces a background texture with significant light and dark streaking. The streak

artifacts in the axial oblique’s reconstructions are significantly less than the sagittal obliques’

reconstructions. Neither the double sagittal nor the double axial oblique’s provides diagnostic

quality bone and soft tissue contrast.

79

Circular combinations

The quantitative RMSE image analysis revealed that the double circular OLASCs

produced low RMSE values. Figure 5-5 shows the reconstructions of the double circular

OLASCs of Ax/AP, Ax/Lat, AP/Lat at 45 degree cone angle and 50 projections per arc. Figure

5-5 demonstrates consistency with the low quantitative RMSE results for double circular

OLASCs as it shows very good reconstructions of both the Catphan and anatomical phantoms for

all three combinations. All three double circular OLASCs have similar reconstructed image

quality which provide diagnostic quality bone and soft tissue contrast and excellent soft tissue

background texture.

Triple OLASCs

Anatomical combinations

The quantitative RMSE image analysis gives low values for triple anatomical OLASCs.

Figure 5-6 shows the reconstructions of all three anatomical OLASCs at 60 degree arc length and

60 projections per arc and 90 degree arc length and 90 projections per arc. Figure 5-6 shows how

at the triple anatomical OLACS at 60 degrees with 60 projections per arc has significant streak

artifacts, but at the triple anatomical OLASC at 90 degrees with 90 projections is producing a

near artifact free reconstruction. Figure 5-6 shows similar image quality of the triple anatomical

OLASC at 90 degree arc length with 90 projections per arc to the double anatomical

axial/coronal at 90 degrees arc length with 90 projections per arc, which is consistent with the

RMSE values present in Chapter 4. The RMSE analysis showed the triple anatomical OLASC

produce a slightly lower RMSE value than the double axial/coronal OLASC. That result is

presented here by a slight improvement in image quality of the triple anatomical OLASC over

the double axial/coronal OLASC. Figure 5-6 also demonstrates the triple anatomical OLASC

reconstructions have very clear agreement with the original OBI CBCT image sets of the

80

Catphan and anatomical phantoms. The triple anatomical OLASC provides diagnostic quality

bone and soft tissue contrast, as well as soft tissue background texture.

Oblique’s plus orthogonal anatomical

The quantitative RMSE image analysis for triple oblique’s plus orthogonal anatomical

OLASCs gave RMSE values not as low at the triple anatomical OLASCs, but adequate. Figure

5-7 shows the reconstruction of both sagittal oblique’s plus axial and axial oblique’s plus sagittal

OLASCs at 90 degree arc length and 90 projections per arc. The image quality presented in

Figure 5-7 is actually better than what the RMSE quantitative analysis suggests. Both the sagittal

oblique’s plus axial and axial oblique’s plus sagittal OLASCs provide diagnostic quality bone

and soft tissue contrast, as well as excellent soft tissue background texture.

Circular combinations

The quantitative RMSE image analysis for triple circular OLASCs at 45 degree cone

angle gave low RMSE values. Figure 5-8 shows the reconstruction of triple circular OLASCs at

45 degree cone angle with 25 and 50 projections per arc. Figure 5-8 shows how at both triple

circular OLACS at 45 degrees with 25 and 50 projections per arc are nearly streak artifact free,

but the reconstruction with 50 projections has a more consistent background texture. Figure 5-8

shows similar image quality of the triple circular OLASC at 45 degree arc length with 50

projections per arc to the double circular OLASCs at 45 degrees arc length with 50 projections

per arc, which is consistent with the RMSE values present in Chapter 4 and similar to the little

difference between the axial/coronal and triple anatomical OLASCs. The RMSE analysis showed

the triple circular OLASC with a slightly lower RMSE value than the double circular OLASC.

That result is presented here by a slight improvement in image quality of the triple OLASC over

the double circular OLASC. Figure 5-8 also demonstrates the triple circular OLASC

reconstructions have very clear agreement with the original OBI CBCT image sets of the

81

Catphan and anatomical phantoms. The triple circular OLASC provides diagnostic quality bone

and soft tissue contrast, as well as excellent soft tissue background texture.

Coplanar Arc Projections vs 2PI solid angle projections

The quantitative RMSE image analysis of coplanar arc via ASD-POCS and 2PI solid

angle projection reconstructions gave similar results for both. Figure 5-9 shows the

reconstruction of the Catphan and anatomical phantoms of 125 projections along a 180 degree

coplanar axial arc via ASD-POCS and 2PI solid angle. Figure 5-9 demonstrates that coplanar

projections and 2PI solid angle projections have nearly identical image quality. This is consistent

with the RMSE results that showed near identical RMSE values for both reconstructions. Both

reconstructions provide diagnostic quality bone and soft tissue contrast, as well as excellent soft

tissue background texture.

Qualitative Conclusion

The qualitative analysis of various single scan arcs and multi-arc orthogonal limited angle

scan combinations on bone to soft tissue contrast, and background texture were evaluated in this

chapter. The scan combination groups of anatomical, circular, oblique, and 2PI solid angle were

each evaluated based on bone to soft tissue contrast, and background texture. Firstly, the

evaluation of reconstruction algorithm on limited scan arc lengths shows that iterative

asymmetric steepest descent projection on convex sets is superior to traditional Feldkamp-Davis-

Kress for shorter limited arc length axial scans. Iterative ASD-POCS consistently produced

reconstructions of the Catphan and anatomical phantoms that have superior bone to soft tissue

contrast, and better background texture.

The results of the qualitative analysis closely followed expectations generated by the

quantitative results. The axial/coronal OLASC at 90 degree arc length and 90 projections per arc

provides adequate bone and soft tissue contrast compared to all other anatomical OLASCs

82

comprised of either larger arc lengths, greater projection densities, or more arcs. Similarly, each

double circular OLASC provides adequate bone and soft tissue contrast compared to other

circular OLASCs comprised of either larger cone angles, greater projection densities, or more

arcs.

The qualitative analysis of 180 degree coplanar arc projection reconstructions via ASD-

POCS compared to 2PI solid angle projection reconstructions gives near identical bone and soft

tissue contrast. This further suggests that 180 degree coplanar arc approximate the projections

over a 2PI solid angle for equal number of projections.

83

A) B) C)

D) E) F)

Figure 5-1. Slices of the Catphan and anatomical phantoms reconstructed with 200 degree axial

arc length and 360 projections of the A) & D) original OBI CBCT FDK

reconstructions, B) & E) FDK reconstructions using virtual x-ray simulator

projections, and C) & F) ASD-POCS reconstructions using virtual x-ray simulator

projections.

A) B) C)

Figure 5-2. Slices of the Catphan and anatomical phantoms reconstructed with 150 projections

at 45 degree cone angle for rotations A) & D) AP, B) & E) axial, and C) & F) lateral.

84

D) E) F)

Figure 5-2. Continued

A) B) C)

D) E) F)

Figure 5-3. Slices of the Catphan and anatomical phantoms for double OLASCs of A) & D)

axial/coronal, B) & E) axial/sagittal, and C) & F) coronal/sagittal at 90 degrees arc

length and 90 projections per degree.

85

A) B)

C) D)

Figure 5-4. Slices of the Catphan and anatomical phantoms for double oblique OLASCs of A)

and C) sagittal oblique’s, and B) and D) axial oblique’s at 100 degrees and 100 projections per

arc.

A) B) C)

Figure 5-5. Slices of the Catphan and anatomical phantoms for double circular OLASCs at 45

degrees with 50 projections per arc for rotations of A) Ax/AP, B) Ax/Lat, and C)

AP/Lat.

86

A) B) C)

Figure 5-5. Continued

A) B)

Figure 5-6. Comparison of the same slices of the Catphan and anatomical phantoms for triple

OLASCs reconstructions at A) and C) 60 degree arc length and 60 projections per

arc, B) and D) 90 degree arc length and 90 projections per arc.

87

C) D)

Figure 5-6. Continued

A) B)

Figure 5-7. Slices of Catphan and anatomical phantoms at 90 degrees arc length and 90

projections per degree for A) and C) sagittal oblique’s plus axial, and B) and D) axial

oblique’s plus sagittal OLASCs.

88

C) D)

Figure 5-7. Continued

A) C)

Figure 5-8. Slices of Catphan and anatomical phantoms of triple circular OLASCs at 45 cone

angle with A) 25, and B) 50 projections per arc.

89

A) B)

Figure 5-8. Continued

A) B)

Figure 5-9. Comparison of slices of the Catphan and anatomical phantoms of the 125 projections

along A) and C) a 180 degree coplanar axial arc, and B) and D) 2PI solid angle.

90

C) D)

Figure 5-9. Continued

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CHAPTER 6

AIM 3 – RESULTS OF QUALITATIVE IMAGE ANALYSIS OF PHOTON STARVATION

ARTIFACTS

The following qualitative data presented is not as exhaustive as either the quantitative

data presented in Chapter 4 or the qualitative data presented in Chapter 5. The quantitative and

qualitative results of the pervious chapters informed the decision of which scan motions and

accompanying parameters in terms of arc length and projections per arc. Therefore, the scope of

qualitative photon starvation analysis presented below will be limited to those parameters proven

to be most advantageous in the quantitative and qualitative analysis of the previous chapters.

Algorithm

The effect of reconstruction algorithm on photon starvation artifact from the current

CBCT axial scan motion of a 200 degree arc length and 360 projections of the anatomical

phantom with pedicle screws is presented in Figure 6-1. Figure 6-1 shows slices of A) the

original anatomical phantom with pedicle screws, the anatomical phantom with screws

reconstructed via B) FDK, and reconstructed via C) ASD-POCS. 6-1B shows the typical photon

starvation artifacts that arises from current axial CBCT scan motions. It is important to pay

attention to the dark streaks extending along the long axes of both screws, between the screws,

the bright streaks coming off the screws nearly isotopically, and the loss of pedicle screw shape

and detail. B) will serve as the benchmark against which all subsequent reconstructions of the

anatomical phantom with screws are compared. C) shows how ASD-POCS significantly limits

the bright streak and lightly limits the dark streak photon starvation artifacts compared the FDK

reconstruction of B). However, each reconstruction produces a background texture with

significant light and dark streaking, although the ASD-POCS reconstruction background suffers

from less soft tissue background streaks.

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Orthogonal Limited Angle Scan Combinations

Double Anatomical OLASCs

The effect of double OLASCs with 90 degree arc length and 90 projections per arc on the

photon starvation artifact of the anatomical phantom with pedicle screws is shown in Figure 6-2.

Figure 6-2 demonstrates that all three double OLASCs can significantly limit the bright streaks

photon starvation artifact and improve the shape and detail of the pedicle screws. A) shows how

the axial/coronal OLASC has the best pedicle screw to bone to soft tissue contrast with very little

photon starvation artifact between the screws. However, the dark streak photon starvation

artifacts are only lightly reduced. B) shows how the axial/sagittal OLASC has good pedicle

screw shape and detail, but very little bone and soft tissue contrast. C) shows how

coronal/sagittal OLASC produces the best pedicle screw shape and detail and removes the dark

streak photon starvation artifact, but has poor bone and soft tissue contrast with a loss of soft

tissue background texture.

Circular combinations

The effect of double circular OLASCs at 45 degree cone angle with 50 projections per

arc on the photon starvation artifact of the anatomical phantom with pedicle screws is given in

Figure 6-3. Figure 6-3 demonstrates how each double circular OLASC at 45 degree cone angle

with 50 projections per arc produces a nearly photon starvation artifact free reconstruction of the

anatomical phantom with pedicle screws. All the bright streaks were eliminated with only a

minor dark streak remaining in between the screws. The shape and detail of the pedicle screws is

excellent as well. Notably, the bone and soft tissue contrast is excellent with excellent texture to

the soft tissue background.

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Triple OLASCs

Anatomical combinations

The effect of triple anatomical OLASC with 90 degree arc length and 90 projections per

arc on the photon starvation artifact of the anatomical phantom with pedicle screws is presented

in Figure 6-4. Figure 6-4 demonstrates the triple anatomical OLASC with 90 degree arc length

and 90 projections per arc appears to be very similar to the axial/coronal OLASC with the same

arc length and projections per arc in terms of pedicle screws to bone to soft tissue contrast. The

triple anatomical OLASC has slightly reduced photon starvation compared to the axial/coronal

OLASC. The shape and detail of the pedicle screws is excellent as well. The bone and soft tissue

contrast and the soft tissue background is adequate. This is consistent with the quantitative

RMSE analysis of Chapter 4 and the qualitative analysis of Chapter 5.

Oblique’s plus orthogonal anatomical

The effect of oblique’s plus orthogonal anatomical OLASCs with 90 degree arc length

and 90 projections per arc on the photon starvation artifact of the anatomical phantom with

pedicle screws is presented in Figure 6-5. Figure 6-5 demonstrates the how the axial oblique’s

plus sagittal OLASCs (6-5A) produces a nearly photon starvation artifact free reconstruction of

the anatomical phantom with pedicle screws. All bright and dark streak photon starvation

artifacts are nearly eliminated while at the same time providing adequate bone and soft tissue

contrast. Notably, the shape and detail of the pedicle screws is excellent. Furthermore, the soft

tissue background texture is adequate with some light and dark streaks. In contrast, the sagittal

oblique’s plus axial OLASC has significantly reduced bright streak photon starvation artifact

adequate pedicle screw shape and detail, but the dark streaks are only slightly reduced.

This result is not consistent with neither the previous quantitative RMSE analysis nor the

qualitative analysis with the anatomical phantom because they showed near identical results

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between the reconstructions of the axial oblique’s plus sagittal OLASC and the sagittal oblique’s

plus axial OLASC. However, this result shows a large difference in the quality of the

reconstruction of the pedicle screws with the axial oblique’s plus sagittal OLASC being far

superior to the sagittal oblique’s plus axial OLASC reconstruction.

Circular combinations

The effect of triple circular OLASCs at 45 degree cone angle with 50 projections per arc

on the photon starvation artifact of the anatomical phantom with pedicle screws is given in

Figure 6-6. Figure 6-6 demonstrates how the triple circular OLASC at 45 degree cone angle with

50 projections per arc produces a nearly photon starvation artifact free reconstruction of the

anatomical phantom with pedicle screws. All the bright streaks were eliminated with only a

minor dark streak remaining in between the screws. Notably, the pedicle screws to bone to soft

tissue contrast and pedicle screws shape and detail are all excellent with a perfect texture to the

soft tissue background, which is clearly diagnostic quality.

It is also notable that, similarly to the anatomical OLASCs, the triple circular OLASC

provides only marginal improvement in qualitative image quality. The addition of the extra

projections of the third circular arc do not appear to be justified since there is little added

qualitative benefit.

Coplanar Arc Projections vs 2PI solid angle projections

The effect of coplanar 180 axial arc via ASD-POCS and 2PI solid angle projection

reconstructions on the photon starvation artifact of the anatomical phantom with pedicle screws

is presented in Figure 6-7. Figure 6-7 demonstrates the effectiveness of only 125 2PI solid angle

projections to perfectly reconstruct the anatomical phantom with pedicle screws compared to the

180 degree coplanar projections. The 2PI solid angle projections reconstruction eliminated nearly

all photon starvation artifacts except for minor dark streaks along the long axis of the left screw,

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while the coplanar projections reconstruction suffers from severe photon starvation artifact. The

2PI solid angle projections reconstruction also provides the superior pedicle screw shape and

detail, as well as the superior bone and soft tissue contrast with the pedicle screws present.

Furthermore, the 2PI solid angle soft tissue background texture is excellent.

This result is also not consistent with neither the previous quantitative RMSE analysis

nor the qualitative analysis with the anatomical phantom because they both showed nearly

identical results between the 180 degree arc with 125 coplanar projection reconstruction and the

evenly spaced over 2PI 125 projections. However, this result shows a large difference in photon

starvation artifacts with the 125 2PI solid angle projections producing a superior reconstruction

with pedicle screws compared to 125 coplanar arc projections.

Qualitative Photon Starvation Conclusion

The qualitative analysis of various single scan arcs and multi-arc orthogonal limited angle

scan combinations on photon starvation artifacts were evaluated in this chapter. The scan

combination groups of anatomical, circular, oblique, and 2PI solid angle were each evaluated

based on qualitative photon starvation artifacts. Firstly, the evaluation of reconstruction

algorithm on limited scan arc lengths shows that iterative asymmetric steepest descent projection

on convex sets lessens the effects of photon starvation artifacts than traditional Feldkamp-Davis-

Kress.

The results of qualitative photon starvation artifact analysis for anatomical OLASCs

proved that the double anatomical axial/coronal OLASCs can a give similar reduction in photon

starvation artifacts compared to triple anatomical OLASCs. Among the double anatomical

OLASCs, the coronal/sagittal OLASC gave the best pedicle screw shape and detail while the

axial/coronal OLASC gave the bone and soft tissue contrast. This result, consistent with the

quantitative RMSE results of Chapter 4 and the qualitative results of Chapter 5, suggests that

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there is little improvement gained from adding the third orthogonal anatomical scan motion.

Therefore, the axial/coronal OLASC is adequate.

Similarly, the qualitative photon starvation artifact analysis for circular OLASCs proved

again that double circular OLASCs can give nearly equal reduction in photon starvation artifact

compared the triple circular OLASC. What was unique to the circular OLASCs case compared to

the anatomical OLASC is that each double OLASC was nearly equivalent to the triple OLASC,

which was expected from the quantitative RMSE results of Chapter 4 and the qualitative results

of Chapter 5. This also suggest for circular OLASCs that the third scan motion is not necessary.

The qualitative effects of anatomical oblique’s plus an orthogonal anatomical OLASCs

on photon starvation artifact were proven to be extremely effective in reducing photon starvation

artifacts, which is consistent with the quantitative results of Chapter 4 and qualitative results of

Chapter 5. In particular, the axial oblique’s plus sagittal OLASC eliminated all bright and dark

streak photon starvation artifacts entirely while also providing very good bone and soft tissue

contrast. The sagittal oblique’s plus axial OLASC produced a slight reduction in photon

starvation artifact, and bone and soft tissue contrast over the triple anatomical OLASC, but not

nearly as effective as the axial oblique’s plus sagittal OLASC. The effectiveness of the axial

oblique’s plus sagittal OLASC was surprising as the previous results of Chapters 4 and 5 did not

indicate it would be particularly effective.

The use of 2PI solid angle projections for reconstruction was suggested from the

quantitative results of Chapter 4 and the qualitative results of Chapter 5 to be equivalent to axial

coplanar arc reconstructions. However, the 2PI solid angle projection reconstructions has

produced definitely superior photon starvation artifact reduction over coplanar axial arc

reconstructions, as well as, over each anatomical and oblique OLASCs. The 2PI solid angle

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projection reconstructions eliminated nearly all bright and dark photon starvation artifact with

similar image quality to the axial oblique’s plus sagittal OLASC, while also producing superior

bone and soft tissue contrast that is nearly equivalent to the input anatomical phantom CBCT

scan. This analysis proves definitively that 2PI solid angle projection reconstructions can

effectively eliminate photon starvation artifact and preserve the bone to soft tissue contrast better

then coplanar arc projections.

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A) B) C)

Figure 6-1. Comparison of same slice of anatomical phantom with pedicle screws

reconstructions of axial CBCT scans at 200 degree arc length and 360 projections of

the A) original OBI CBCT, B) FDK with simulator projections, and C) ASD-POCS

with simulator projections.

A) B) C)

Figure 6-2. Comparison of the same slice of the anatomical phantom with pedicle screws

reconstructed by the double anatomical OLASCs at 90 degree arc length and 90

projections per arc for A) axial/coronal, B) axial/sagittal, and C) coronal/sagittal.

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A) B) C)

Figure 6-3. Comparison of the same slice of the anatomical phantom with pedicle screws

reconstructed by the double circular OLASCs at 45 degree cone angle with 50

projections per arc for rotations A) Ax/AP, B) Ax/Lat, and C) AP/Lat.

Figure 6-4. Slice of the anatomical phantom with pedicle screws reconstructed by the all three

anatomical OLASC at 90 degree arc length and 90 projections per arc.

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A) B)

Figure 6-5. Same slices of the anatomical phantom with pedicle screws reconstructed by

OLASCs with 90 degree arc length and 90 projections per arc for A) axial oblique’s

plus sagittal, and B) sagittal oblique’s plus axial.

Figure 6-6. Slice of the anatomical phantom with pedicle screws reconstructed by the triple

circular OLASC at 45 degree cone angle with 50 projections per arc.

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A) B)

Figure 6-7. Slice of anatomical phantom with pedicle screws reconstructed with 125 projections

by A) 180 degree coplanar arc, and B) non-coplanar evenly spaced over 2PI solid

angle.

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CHAPTER 7

DISCUSSIONS AND CONCLUSION

Discussions

This work evaluated the effects of various orthogonal limited angle scan combinations on

image quality metrics. OLASCs will be acquired by the novel intraoperative robotic CBCT

system. With a full six degrees of freedom available to rotate through, the robotic imager has

limitless possible scan motions and combinations available. In order to begin investigating this

space, we began by evaluating scan motions orthogonal to the traditional axial scan motion.

However, the obvious issue of collision with the patient support system for non-axial scan

motions arises. Therefore, it was necessary to investigate the quality of reconstructions for limit

arc length scan motions. Scan motions limited in arc length and number of projections,

necessitate the use of iterative reconstruction algorithms that are proven to better reconstruct the

image from limited arc lengths and fewer projections than traditional Feldkamp-Davis-Kress

based algorithms.

Quantitative EST analysis cannot be done using the Catphan phantom for non-axial scan

motions since the 23 degree ramps are designed specifically for axial scan motions. Therefore,

for OLASCs comprised of non-axial scan motions, the principal quantitative metrics used to

evaluate all OLASCs are root mean square error values and modulation transfer function curves.

Qualitative image analysis was based on the effect of OLASCs on the bone and soft

tissue contrast. Attention was also paid to the background texture of the soft tissue. Furthermore,

the effect of OLASCs on photon starvation artifacts caused by pedicle screws were also

qualitatively analyzed.

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Quantitative and Qualitative Results

Algorithm comparison

Quantitative image analysis of how single axial limited arc lengths affect the

reconstructed image effective slice thickness showed that iterative asymmetric steepest descent

projection on convex sets outperforms FDK for all projection densities except for .5 projections

per degree at very short arc lengths. Interestingly, the analysis showed that EST for FDK

reconstructions of limited arc lengths is independent of projection density and could not

reproduce the input Catphan image set EST for any arc length less than 180 degrees. Only the

ASD-POCS reconstructions at .5 projections per degree failed to reach the input Catphan image

set EST. In a similar fashion as with the EST analysis, the analysis of how single axial limited

arc lengths affect the reconstructed image RMSE values shows ASD-POCS is superior to FDK

for projection densities greater than or equal to one.

Anatomical OLASCs

Anatomical OLASCs demonstrated significant improvement over single axial limited arc

scans by generating lower RMSE values for shorter arc lengths and with lower projection

densities. Comparing RMSE values of double and triple anatomical OLASCs shows that the

axial/coronal OLASC has RMSE values nearly as low an as triple anatomical OLASCs at the

same arc length and projection density, but with a two-thirds as many projections. The

axial/coronal OLASC produces an MTF curve that matches the input Catphan image set MTF

curve, as well as produces very good bone to soft tissue contrast with good background texture.

This leads to the recommendation of using the axial/coronal OLASC at 90 degrees arc length

with 90 projection per arc over all other double and triple anatomical OLASCs.

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Double oblique OLASCs

Double oblique OLASCs reconstructions generate high RMSE values, which was

confirmed by qualitative analysis which shows that the reconstructions suffer heavily from

blurring along the projections’ paths for limited arc lengths regardless of projection density.

Therefore, double oblique OLASCs are not recommended for use.

Circular OLASCs

Single circular scan motions generated high RMSE values for each cone angle and each

total projections. This was also confirmed by the qualitative analysis which shows that the single

circular scan motions suffer from blurring along the projection paths. Therefore, they are not

recommended for use.

Each double orthogonal circular scan motion with cone angles of 30 or 45 degrees

produced low RMSE values which were confirmed by the qualitative analysis which showed

reconstructions with no blurring. The double circular OLASCs produce MTF curves that match

the input Catphan image set MTF curve, as well as produce very good bone to soft tissue contrast

with good background texture. The optimum projections per arc is 50. Similarly, to the

anatomical OLASCs, the triple circular OLASCs produced marginal improvement over the

double circular OLASCs for the same cone angle and projections per arc. Therefore, each double

circular OLASCs at 45 degrees with 50 projections per arc are recommended over the triple

circular OLASC.

Realistically, the cone angle of circular axial scan motions brings the x-ray source and

image receptor closer to the patient increasing the likelihood of a collision with the patient or the

patient support system. As the cone angle decrease, the closer the x-ray source and image

receptors will be to the patient or the patient support system. Thus, a circular cone angle of no

less than 45 degrees is recommended for axial circular scan motions. If collision is an issue even

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with a 45 degree cone angle, the only option available to avoid a collision is to increase the OID

and the SOD. The AP and Lat circular rotations do not suffer from these collision problems, and

thus are preferred over the axial circular scan motion. Therefore, the AP/Lat circular OLASC

with a 45 degree cone angle with 50 projections each is recommended as neither the AP nor Lat

rotation suffer from the collision considerations of the Ax rotation.

Oblique’s plus orthogonal anatomical

The oblique’s plus orthogonal anatomical OLASCs produced low RMSE values which

were confirmed by the qualitative analysis that showed reconstructions with no blur and

excellent bone and soft tissue contrast. The oblique’s plus orthogonal anatomical OLASCs

produce MTF curves that match the input Catphan image set MTF curve, as well as produce very

good bone to soft tissue contrast with good background texture. The axial oblique’s plus sagittal

and the sagittal oblique’s plus axial OLASCs produced comparable RMSE values and image

quality. Both OLASCs of 90 degree arc length with 90 projections are recommended for use.

Coplanar arc projections vs 2PI solid angle projections

2PI solid angle projection and 180 degree coplanar arc projection reconstructions

produced comparable RMSE values which were confirmed by the qualitative analysis. They both

also produced comparably excellent bone and soft tissue contrast and background texture. They

also both produced MTF curves that match the input Catphan image set MTF curve, as well as

produce very good bone to soft tissue contrast with good background texture. This suggests that

a 180 degree coplanar arcs approximate 2PI solid angle projection scans with equivalent total

projections. Therefore, the 180 degree coplanar projections are recommended over the evenly

spaced over 2PI solid angles projections for simplicity of acquisition.

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Qualitative Photon Starvation Artifact Results

Algorithm comparison

The addition of high attenuating pedicle screws to the anatomical phantom gave

interesting results for all the OLASCs. Single axial arcs produced reconstructions with typical

bright and dark streaks from photon starvation. Single axial arcs reconstructed via ASD-POCS

had less significant bright and dark streaks than FDK reconstructions. However, neither can

adequate reduce the bright and dark photon starvation artifacts. The subsequent OLASCs

reconstructions were compared to these single axial reconstructions since they represent the

current state of image quality of pedicle screws.

Anatomical OLASCs

The anatomical OLASCs demonstrated that they can effectively reduce, but not

eliminate, the dark and bright photon starvation artifacts, and provide excellent pedicle screw

detail. The pedicle screw to bone to soft tissue contrast is improved as well. Similar to the

quantitative and qualitative analysis, the triple anatomical OLASC does not significantly reduce

the bright and dark photon starvation artifacts compared to the double axial/coronal OLASC.

Therefore, the axial/coronal circular OLASC at 90 degree arc length with 90 projections per arc

is recommended.

Circular OLASCs

Each double circular OLASC produced a near artifact free reconstruction of the pedicle

screws, as well as perfect pedicle screws shape, detail, contrast to bone and soft tissue, and

background texture. As discussed in the quantitative and qualitative analysis, the axial circular

scan motion would present difficulty in avoidance of a collision with the patient or the patient

support system. Thus, of the three possible double circular OLASCs, the AP/Lat double circular

OLASC at a cone angle of 45 degrees with 50 projections per arc is recommended over the other

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two double circular OLASCs which comprise and Ax rotation. Similarly to the quantitative and

qualitative analysis, the triple circular OLASC does not significantly reduce the bright and dark

photon starvation artifacts compared to the AP/Lat circular OLASC. Therefore, the AP/Lat

circular OLASC at 45 degree cone angle with 50 projections per arc is recommended.

Coplanar arc projections vs 2PI solid angle projections

The largest deviation in the qualitative photon starvation analysis from the expectations

generated by the previous quantitative and qualitative analysis arises with the use of 2PI solid

angles projections. Previous quantitative and qualitative analysis produced the comparable

results between coplanar arc projections and 2PI solid angle projections, but the introduction of

highly attenuation pedicle screws causes severe bright and dark photon starvation artifacts to the

coplanar arc projections. In contrast, the 2PI solid angle projections produced a near artifact free

reconstruction with perfect pedicle screw shape and detail, as well as perfect pedicle screw to

bone to soft tissue contrast and background texture. Therefore, 125 2PI solid angle projections

are recommended over 125 coplanar arc projections to eliminate bright and dark photon

starvation artifacts.

The excellent 2PI solid angle projection reconstructions significantly deviated from

previous results, but were not unexpected as it was hypothesized that projections from all angles

would best mitigate photon starvation artifacts by limiting the attenuation ray paths of many of

the projections. Ironically, the surprising result was that in the previous quantitative and

qualitative analysis no significant difference in coplanar arc projections and 2PI solid angle

projections were a significant difference was expected.

Final Optimized Recommendations from Results

The quantitative and qualitative analysis, including the qualitative photon starvation

artifact analysis, has resulted in the optimized recommendation for the double circular AP/Lat

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OLASC at 45 degree cone angle with 50 projections per arc. The circular AP/Lat OLASC at 45

degree cone angle with 50 projections per arc produced a low RMSE value, an MTF curve that

matched the input Catphan phantom MTF curve, excellent pedicle screw to bone to soft tissue

contrast, and completely eliminated the bright and dark photon starvation artifacts with only 100

total projections.

Although, it should be noted that circular rotations would likely be more difficult to

acquire than simpler anatomical arc scan motions. The double anatomical axial/coronal OLASC

at 90 degree arc length and 90 projections produced a low RMSE value, an MTF curve that

matched the input Catphan phantom MTF curve, and excellent bone to soft tissue contrast, but

only marginally reduced the bright and dark photon starvation artifacts of the pedicle screws.

Therefore, the anatomical axial/coronal OLASC at 90 degree arc length and 90 projections could

be an adequate substitute for the circular rotations if the circular rotations prove difficult to

perform in practice. For the imaging of pedicle screws, the axial oblique’s plus sagittal OLASC

at 90 degree arc length with 90 projections per degree can also almost completely eliminate

bright and dark photon starvation artifacts using arc that could also be easier to acquire.

Furthermore, 125 2PI solid angle projections also gave near artifact free reconstructions of the

pedicle screws and may be another alternative for pedicle screw imaging over the circular

AP/Lat OLASC, but they could also be the most complicated set of projections to acquire in

practice.

Limitations

Scan acquisition and reconstruction parameters

In this work, each scan acquisition was simulated with the SOD and the OID set to 100

cm and 50 cm respectively to mimic the geometry of the Varian OBI. The simulated image

receptor also matched the PaxScan 4030CB on the Varian OBI. The Varian OBI is a commonly

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used CBCT scanning system, so it provided all the input CBCT image sets for this work, as well

as good set of parameters for acquisition. These parameters were not changed because the

resulting reconstructed image sets would not be so comparable to the current image sets

produced by the Varian OBI. Furthermore, changing the SOD, OID, or the image receptor

parameters would have required orders of magnitude more data acquisitions to adequately

analyze the effects. Since this work was already dealing with the parameters of scan motions, arc

length, and projections density, the SOD and OID were kept constant to limit the numbers of

parameters and thus the amount of data necessary to properly characterize the effects. Also, for

each multi-arc OLASC the arc lengths were not varied for arc within a multi-arc OLASC

combination because this would further amplify the amount of data to gather. For a similar

reason, only a single set of parameters were used for tuning the iterative ASD-POCS algorithm.

It would have taken orders of magnitude more reconstructions to tune the algorithm’s parameters

to each combination of scan motion, arc length, and projection density.

Reconstruction times

The use of iterative ASD-POCS does lead to significantly longer reconstruction times

even when the algorithm is computed on a graphics procession unit (GPU). The open source

TIGRE MATLAB® toolbox is not optimized for speed as it is designed to allow for easy

algorithm development by the open source community. Therefore, reconstruction times were not

considered is this work, but rather focused on iterative ASD-POCS’s potential for generating

reconstructions that are diagnostic quality with limited arc lengths and limited projection sets.

With optimization for computational time and more powerful GPUs, reconstruction times can

certainly be reduced significantly, but such hardware analysis was outside the scope of this work.

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Comparison with Modern CBCT Systems

The anatomical and circular OLASCs provide vital bone and soft tissue contrast for

intraoperative image guidance as shown by reconstructions of the anatomical phantom using

shorter arc lengths and fewer projections than current intraoperative systems like the Medtronic®

O-Arm, which uses a full 360 degree arc with 391 or 745 projections or the Varian OBI which

uses a 200 degree arc with 360 projections. The double circular AP/Lat OLASC, which has been

shown to be the most effective OLASC, produced reconstructions with excellent quantitative and

qualitative results comprises 50 projections for each arc totaling 100 projections. Particularly, the

double circular AP/Lat OLASC effectively eliminated all photon starvation artifacts caused by

pedicle screws. The optimized 2PI solid angle projections reconstruction consisted of 125

projections in total, and was also very effective in producing excellent quantitative and

qualitative results, especially in eliminating photon starvation artifact. The triple axial oblique’s

plus sagittal OLASC comprised 90 projections per arc for total of 270 projections which is still

two-thirds of the number of projections acquired by the OBI CBCT. Also, for simple scan not

involving highly attenuation objects, the double anatomical axial/coronal OLASC at 90 degrees

with 90 projections per arc for a total pf 180 projections has proven to be effective with half the

total projections necessary for an OBI CBCT acquisition.

Future Work

As discussed in the previous Limitations section, the number different parameters

investigated was limited so that an unrealistic amount of data would not need to be acquired.

Therefore, the very next step would be to investigate the effects of altering the SOD and OID,

and asymmetric arc length OLASCs. However, it would be most advantageous to first tune the

ASD-POCS parameters for the optimized OLASCs determined in this work. In regard

particularly to the investigation of asymmetric arc length OLASCs, the anatomical coronal scan

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arc has proven to be effective in combination with traditional axial scan motion with each arc

being the same length. It is proposed that a complete axial arc length can be augmented with a

coronal arc to correct artifacts inherent to axial scan motions.

In theory, complete sampling of projections over 2PI solid angle is the image acquisition

limit for CBCT imaging. The qualitative image analysis of the anatomical phantom did show that

for objects containing highly attenuating objects, a 180 coplanar projection arc does adequately

approximate the same number of 2PI solid angle projections. The investigation of 2PI solid

angles projections proved that they can effectively eliminate photon starvation artifacts when

coplanar arc projections suffer from severe photon starvation artifacts. However, the feasibility

of acquiring projections over 2PI would presumably be very difficult. Thus, investigation into

determining an optimized subset of projections of a complete 2PI set of projections would reduce

the difficulty in acquisition of 2PI projections.

This work has evaluated several different OLASCs, but it is not entirely clear which is

the best for each situation. It has been revealed that for situations without highly attenuating

objects, anatomical double axial/coronal OALSCs can provide projections that adequately

reconstruct the volume. As for situations with highly attenuating objects, the triple axial

oblique’s plus sagittal, the double circular AP/Lat, and the 2PI Solid angle projections OLASCs

can each provide excellent reconstructions. What can be noted of these three options is that they

almost entirely avoid projections that follow directly along the long axis of the pedicle screws.

This may explain why the triple sagittal oblique’s plus axial OLASC continued to suffer from

photon starvation artifacts. The anatomical axial motion includes projections that would follow

the long axis of the pedicle screws. The 2PI solid angle projections will have projections that are

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along the long axis of the pedicle screws, but they are not of the same density along the axial

motion as an axial coplanar projection scan motion.

This leads to the supposition that an algorithm could be devised to properly predict the

most advantageous projections among the 2PI solid angle options to best limit the effects of

photon starvation artifacts due to pedicle screws or any other metal object. The key goal of the

algorithm would be to limit the projections through the metal object that maximize attenuation.

First, the algorithm should identify the metal object via its high HUs. Secondly, the algorithm

should identify any asymmetry of the object in order to determine the minimum and maximum

attenuation paths. Lastly, the algorithm should select projections that follow along the minimum

attenuation paths and avoid paths of maximum attenuation.

The quantitative analysis performed in this work relied on the Catphan phantom which is

specifically designed for axial scan motions. Therefore, there is a need for a phantom specifically

designed for evaluating image quality metrics for non-axial and non-coplanar projections. A

phantom design has already been proposed and evaluated in literature for diverse CBCT orbit

geometries.47 This phantom would provide a more accurate assessment of quantitative image

quality metrics.

Furthermore, the OLASCs presented could be adapted to the available space around

patients receiving radiotherapy treatment with non-coplanar beams. Currently, the imaging for

non-coplanar beams is very limited because they operate strictly with the traditional axial CBCT

paradigm. Non-coplanar radiotherapy beams requiring a rotation of the couch do not fit it the

traditional axial paradigm, and thus, have no image guidance. Any attempt to provide image

guidance to non-coplanar radiotherapy beams will presumably have to rely on non-axial arcs

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severely limited in length. Combinations of non-axial arcs in and OLASC frame work may be

able to provide adequate image guidance.

Conclusion

In conclusion, this work has proven that the newly available scan motions, currently

unavailable with modern CBCT imaging systems, and their combinations via the novel robotic

imager can provide superior image quality with shorter arc lengths and fewer projections

compared to current CBCT imaging systems. This was accomplished largely due to the ability of

iterative ASD-POCS to recover the image from limited arc lengths and limited projection sets.

Particularly, the double circular AP/Lat OLASC was shown to perfectly reconstruct anatomical

bone and soft tissue, as well as effectively eliminate the photon starvation artifacts caused by

pedicle screws. In addition, the double anatomical axial/coronal and the triple axial oblique’s

plus sagittal OLASCs were showed to be effective in reconstructing anatomical bone and soft

tissue, as well as reducing photon starvation artifacts. Interestingly, 2PI solid angle projections

also were shown to effectively eliminate photon starvation artifacts of pedicle screws that are

typically present in traditional coplanar arc projection reconstructions.

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BIOGRAPHICAL SKETCH

Michael C. Hermansen was born in Logan, Utah to Chris and Kristine Hermansen in

1986. He grew up in Moorpark, California where he graduated from Moorpark High School in

2004. After completing his freshman year of college at Brigham Young University (BYU) in

Provo, Utah, he left for two years to serve a full-time mission for the Church of Jesus Christ of

Latter-day Saints in Rosario, Argentina in September of 2005.

After his return from Argentina, he resumed his studies at BYU. He completed his

Bachelor of Science in applied physics in April of 2012. He was accepted by the J. Crayton

Pruitt Family Department of Biomedical Engineering at the University of Florida and

subsequently began a Master of Science in biomedical engineering with a concertation in

medical physics in August of 2013. He completed is Master of Science in medical physics in

December of 2015, under advisor Dr. Frank J. Bova. He has continued his Ph.D. work under Dr.

Frank J. Bova’s direction in the Radiosurgery and Biology Lab.