Transcript
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
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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.
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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.
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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.
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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
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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.
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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.
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