Development and Application of a 4-Dimensional
Computed Tomography Simulator
by
Alan Chu
S.B., Electrical Engineering and Computer Science, Massachusetts
Institute of Technology, 2006
Submitted to the Department of Electrical Engineering and Computer
Science
in partial fulfillment of the requirements for the degree of
Master of Engineering in Electrical Engineering and Computer Science
at the
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
May 2007
c Massachusetts Institute of Technology 2007. All rights reserved.
Author . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Department of Electrical Engineering and Computer Science
May 25, 2007
Certified by . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
George T.Y. Chen
Director, Radiation Physics Division, Department of Radiation
Oncology, Massachusetts General Hospital, Professor of Radiation
Oncology, Harvard Medical School
Thesis Supervisor
Certified by . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
William M. Wells
Research Scientist, MIT CSAIL, Associate Professor of Radiology,
Harvard Medical School and Brigham and Women’s Hospital
Thesis Supervisor
Accepted by . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Arthur C. Smith
Chairman, Department Committee on Graduate Theses
Certified by . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Gregory C. Sharp
Radiation Physicist, Department of Radiation Oncology,
Massachusetts General Hospital
Instructor, Harvard Medical School
Thesis Supervisor
Certified by . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
John A. Wolfgang
Radiation Physicist, Department of Radiation Oncology,
Massachusetts General Hospital
Instructor, Harvard Medical School
Thesis Supervisor
2
Development and Application of a 4-Dimensional Computed
Tomography Simulator
by
Alan Chu
Submitted to the Department of Electrical Engineering and Computer Science
on May 25, 2007, in partial fulfillment of the
requirements for the degree of
Master of Engineering in Electrical Engineering and Computer Science
Abstract
This thesis presents the development and application of a 4-Dimensional Computed
Tomography (4D CT) simulation program. The simulation is used to understand
and quantify the sources of image artifacts that arise from irregular patient breathing
during 4D CT. Performance of the simulation is validated by comparing the simulation results with those of phantom experiments with CT scanners. The program
simulates 4D CT scanning of objects of arbitrary size and shape and is extended
to investigate the accuracy of gated radiotherapy. Experiments are performed using
realistic breathing patterns from patients, in addition to synthetic ones for various
studies. The simulation is used to study the effects of scan start time shift, breathing
trace baseline drift, and hysteresis of internal organ and abdominal surface motion
on the quality of 4D CT images.
While 4D CT significantly reduces artifacts from helical scans of the thoracic
and abdominal areas, a variety of different sources can still contribute to motioninduced artifacts in 4D CT. Since 4D CT is used to determine target margins for
radiotherapy, proper precaution should be taken so that image artifacts do not lead
to inaccurate treatment planning. Finally, this thesis discusses improvements in 4D
CT and suggests additional methods to improve treatment planning for radiotherapy.
Thesis Supervisor: George T.Y. Chen
Title: Director, Radiation Physics Division, Department of Radiation Oncology,
Massachusetts General Hospital, Professor of Radiation Oncology, Harvard Medical
School
Thesis Supervisor: William M. Wells
Title: Research Scientist, MIT CSAIL, Associate Professor of Radiology, Harvard
Medical School and Brigham and Women’s Hospital
3
4
Acknowledgments
First, I would like to thank Dr. George Chen for his support and guidance on this
research. He is an extremely busy person, but always finds the time to see his students.
It was through his support that I was able to work at Massachusetts General Hospital,
and I learned a great deal from him not only about medical physics and imaging, but
about graduate research as well.
The contributions of Dr. Sandy Wells were also very helpful for this thesis. I was
fortunate enough to take a class taught by him, and I received useful ideas from my
experiences there. I thank him for all the edits he made in preparing this thesis.
Dr. Greg Sharp and Dr. John Wolfgang provided a great deal of technical expertise in 4D CT. Whenever I was confused about an issue, a conversation with one of
them would clear things up dramatically. I thank John for repeatedly answering all
my questions. Greg provided a lot of useful code to me, and also provided knowledgeable answers to my numerous questions about 4D CT and radiotherapy. I would
also like to thank Kit Mui for providing helpful code and the Boston Medical Center
for the use of their CT scanner.
Last but not least, I thank my parents for their never-ending support.
5
6
Contents
1 Introduction
17
1.1
Brief History of CT Scanning . . . . . . . . . . . . . . . . . . . . . .
17
1.2
Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
18
1.2.1
Role of 3D Anatomical Imaging in Radiotherapy . . . . . . . .
18
1.2.2
Problems with 3D CT . . . . . . . . . . . . . . . . . . . . . .
19
1.2.3
4D Radiotherapy . . . . . . . . . . . . . . . . . . . . . . . . .
20
Goals and Purposes . . . . . . . . . . . . . . . . . . . . . . . . . . . .
20
1.3
2 Background and Theory of 4-Dimensional Computed Tomography 21
2.1
2.2
2.3
Introduction to 4D CT . . . . . . . . . . . . . . . . . . . . . . . . . .
21
2.1.1
Origins and Purpose of 4D CT
. . . . . . . . . . . . . . . . .
21
2.1.2
Overview of the 4D CT Algorithm . . . . . . . . . . . . . . .
22
Hardware Configurations . . . . . . . . . . . . . . . . . . . . . . . . .
24
2.2.1
Scanners . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
24
2.2.2
Respiratory Monitors . . . . . . . . . . . . . . . . . . . . . . .
25
Reconstruction Approaches
. . . . . . . . . . . . . . . . . . . . . . .
26
2.3.1
General Electric Scanner - Cine Mode . . . . . . . . . . . . . .
26
2.3.2
Philips Scanner - Sorting in Sinogram Space . . . . . . . . . .
27
3 Methods
3.1
29
Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
29
3.1.1
General Electric CT Scanner . . . . . . . . . . . . . . . . . . .
29
3.1.2
Philips CT Scanner . . . . . . . . . . . . . . . . . . . . . . . .
31
7
3.2
3.3
3.1.3
Breathing Traces . . . . . . . . . . . . . . . . . . . . . . . . .
31
3.1.4
Breathing Trace Analysis . . . . . . . . . . . . . . . . . . . . .
33
3.1.5
Error Quantification . . . . . . . . . . . . . . . . . . . . . . .
34
4D CT Simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . .
35
3.2.1
General Electric Scanner Experiment Simulations . . . . . . .
35
3.2.2
Comparison of Simulations to Experiments . . . . . . . . . . .
37
3.2.3
Time Shift Simulations . . . . . . . . . . . . . . . . . . . . . .
39
3.2.4
Hysteresis . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
40
3.2.5
Baseline Drift . . . . . . . . . . . . . . . . . . . . . . . . . . .
41
3.2.6
Arbitrary Object Simulations . . . . . . . . . . . . . . . . . .
43
Radiation Treatment Simulations . . . . . . . . . . . . . . . . . . . .
44
4 Results
47
4.1
Breathing Trace Analysis . . . . . . . . . . . . . . . . . . . . . . . . .
47
4.2
Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
50
4.2.1
General Electric CT Scanner . . . . . . . . . . . . . . . . . . .
50
4.2.2
Philips CT Scanner . . . . . . . . . . . . . . . . . . . . . . . .
55
4.2.3
Comparison of General Electric and Philips Scanners . . . . .
55
4D CT Simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . .
65
4.3.1
Comparison of Simulations to Experiments . . . . . . . . . . .
65
4.3.2
Time Shift Simulations . . . . . . . . . . . . . . . . . . . . . .
67
4.3.3
Hysteresis . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
69
4.3.4
Baseline Drift . . . . . . . . . . . . . . . . . . . . . . . . . . .
69
4.3.5
Arbitrary Object Simulations . . . . . . . . . . . . . . . . . .
74
Radiation Treatment Simulations . . . . . . . . . . . . . . . . . . . .
77
4.3
4.4
5 Concluding Remarks
81
5.1
Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
81
5.2
Suggestions and Future Work . . . . . . . . . . . . . . . . . . . . . .
84
5.2.1
4D CT Algorithm Improvements . . . . . . . . . . . . . . . .
84
5.2.2
Simulation Improvements . . . . . . . . . . . . . . . . . . . .
85
8
5.2.3
Alternative Methods of Quantifying 4D CT Error . . . . . . .
A Glossary of Terms
87
89
9
10
List of Figures
2-1 Diagram for phase-based 4D CT image reconstruction at the exhale
phase. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
24
3-1 Phantom positioned on the computer-driven sled, which was used in
the 4D CT experiments. . . . . . . . . . . . . . . . . . . . . . . . . .
30
3-2 Breathing traces 2563 (displayed using a scale factor of 3) and 2567
(displayed using a scale factor of 2). The peaks of the traces correspond
to exhale and the valleys correspond to inhale. . . . . . . . . . . . . .
32
3-3 Diagram for volume computation. . . . . . . . . . . . . . . . . . . . .
37
3-4 Diagram for computation of the acquisition amplitude of the first fourslice section that slices through Sphere 1. . . . . . . . . . . . . . . . .
39
3-5 Example of baseline drift in a breathing trace. The black trace is the
original sinusoidal breathing trace. The red dotted trace has a positive
slope, resulting in baseline drift. The orientation of the traces is such
that the peaks correspond to exhale, and the valleys correspond to inhale. 42
4-1 Amplitude, phase, and amplitude phase correlation of traces 2563,
2567, and 2 cm peak to peak sine wave. The segments shown in the
figure correspond to segments where Sphere 1 was scanned by the GE
scanner. The internal-external motion scale factor is incorporated into
the amplitude plots, which correspond to the true motion of the phantom. 48
4-2 Using the GE scanner, (a) coronal slice of static phantom; coronal slice
of phantom at 50% (inhale) phase for (b) 2 cm sine, (c) 2563 trace, (d)
2567 trace. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
11
51
4-3 Using the GE scanner, (a) coronal slice of static phantom; coronal slice
of phantom at 0% (exhale) phase for (b) 2 cm sine, (c) 2563 trace, (d)
2567 trace. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
53
4-4 Volume of Sphere 1 for different traces as a function of respiratory
phase using the GE scanner. These volumes were computed using the
GE Sim4D tools. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
54
4-5 Using the Philips scanner, (a) coronal slice of static phantom; coronal
slice of phantom at 0% (inhale) phase for (b) 2 cm sine, (c) 2563 trace,
(d) 2567 trace. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
56
4-6 Using the Philips scanner, (a) coronal slice of static phantom; coronal
slice of phantom at 40% (close-to-exhale) phase for (b) 2 cm sine, and
at 50% (exhale) phase for(c) 2563 trace, (d) 2567 trace. . . . . . . . .
57
4-7 Image volume of Sphere 1 using the GE and Philips scanner as a function of respiratory phase for trace 2563. . . . . . . . . . . . . . . . . .
58
4-8 Image volume of Sphere 1 using the GE and Philips scanner as a function of respiratory phase for trace 2567. . . . . . . . . . . . . . . . . .
59
4-9 Image volume of Sphere 1 using the GE and Philips scanner as a function of respiratory phase for 1 cm sine trace. . . . . . . . . . . . . . .
60
4-10 Image volume of Sphere 1 using the GE and Philips scanner as a function of respiratory phase for 2 cm sine trace. Note that the Philips plot
only contains volumes for phases 0%, 10%, 20%, 30%, and 40%. . . .
60
4-11 Z-coordinate of Sphere 1 center of mass using the GE and Philips
scanner as a function of respiratory phase for trace 2563. X-coordinate
and y-coordinate are constant throughout all phases. . . . . . . . . .
62
4-12 Z-coordinate of Sphere 1 center of mass using the GE and Philips
scanner as a function of respiratory phase for trace 2567. X-coordinate
and y-coordinate are constant throughout all phases. . . . . . . . . .
63
4-13 Z-coordinate of Sphere 1 center of mass using the GE and Philips
scanner as a function of respiratory phase for 1 cm sine trace. Xcoordinate and y-coordinate are constant throughout all phases. . . .
12
63
4-14 Z-coordinate of Sphere 1 center of mass using the GE and Philips
scanner as a function of respiratory phase for 2 cm sine trace. Xcoordinate and y-coordinate are constant throughout all phases. Note
that the Philips plot only contains COMs for phases 0%, 10%, 20%,
30%, and 40%. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
64
4-15 (a) 4D CT simulation image of Sphere 1 using 2563 respiration trace
at inhale phase, (b) 2563 amplitude trace, and (c) corresponding phase
trace determined by RPM software. Inset (upper left) shows the original 4D CT reconstruction image of Sphere 1 from the phantom scan.
66
4-16 Time shift 4D CT simulation images of Sphere 1 using 2563 respiration
trace at inhale phase. Results of starting the scan at the (a) sixth couch
position, (b) seventh couch position, (c) eleventh couch position, and
(d) twelfth couch position. . . . . . . . . . . . . . . . . . . . . . . . .
68
4-17 Hysteresis 4D CT simulation images of Sphere 1 using 2563 respiration
trace at inhale phase. Results of using a hysteresis delay of (a) 31 ms,
(b) 63 ms, (c) 94 ms, and (d) 125 ms. . . . . . . . . . . . . . . . . . .
70
4-18 Hysteresis 4D CT simulation images of Sphere 1 using 2563 respiration
trace at inhale phase. Results of using a hysteresis delay of (a) 156 ms,
(b) 188 ms, (c) 219 ms, and (d) 250 ms. . . . . . . . . . . . . . . . .
71
4-19 Baseline drift 4D CT simulation images of Sphere 1 at inhale using a
2 cm sine wave with a slope of (a) 0 cm/s, (b) 0.0136 cm/s, (c) 0.0268
cm/s, and (d) 0.0400 cm/s. . . . . . . . . . . . . . . . . . . . . . . . .
72
4-20 Image volume of Sphere 1 at 50% (inhale) phase as a function of the
baseline drift slope of a 2 cm sine breathing trace. . . . . . . . . . . .
73
4-21 Coronal cut of a 3D static scan of Sphere 1, which is used as input to
our simulation of arbitrary objects. . . . . . . . . . . . . . . . . . . .
74
4-22 4D CT simulation image of Sphere 1 using 2563 respiration trace at
inhale phase. The input object is the static 3D scan of Sphere 1, shown
in Figure 4-21. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
13
75
4-23 The left side shows the 4D CT simulation image of Sphere 1 using
the 2563 respiration trace at 10% phase. The right side shows the
experimental result from the GE scanner at 10% phase. The input
object is the static 3D scan of Sphere 1, shown in Figure 4-21. . . . .
76
4-24 The left side shows the 4D CT simulation image of Sphere 1 using
the 2563 respiration trace at 80% phase. The right side shows the
experimental result from the GE scanner at 80% phase. The input
object is the static 3D scan of Sphere 1, shown in Figure 4-21. . . . .
77
4-25 Breathing trace of a patient undergoing gated radiation treatment.
The gating trace is in blue, dotted with red points where treatment
commenced. The amplitudes are not scaled by any factor, and an
amplitude of 0 is the mean of the entire breathing trace. . . . . . . .
78
4-26 Radiation treatment simulation using the breathing trace in Figure 425 with the tumor depicted as the smaller circle and the aperture as
the larger circle. The square wave denotes when treatment commenced
(1 = beam on, 0 = beam off). . . . . . . . . . . . . . . . . . . . . . .
14
79
List of Tables
4.1
Characteristics of 122 different breathing traces. No scale factor was
used. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
50
4.2
Image volumes of Sphere 1 in cm3 for the GE and Philips scanners. .
61
4.3
Z-coordinate of image center of mass (COM) of Sphere 1 in centimeters
for the GE and Philips scanners. . . . . . . . . . . . . . . . . . . . . .
15
64
16
Chapter 1
Introduction
This thesis presents the development and application of a 4-Dimensional Computed
Tomography (4D CT) simulation program. The simulation is used to understand
and quantify the sources of image artifacts that arise from irregular patient breathing
during 4D CT. Performance of the simulation is validated by comparing the simulation results with those of phantom experiments with CT scanners. The program
simulates 4D CT scanning of objects of arbitrary size and shape and is extended
to investigate the accuracy of gated radiotherapy. Experiments are performed using
realistic breathing patterns from patients, in addition to synthetic ones for various
studies. The simulation is used to study the effects of scan start time shift, breathing
trace baseline drift, and hysteresis of internal organ and abdominal surface motion
on the quality of 4D CT images.
1.1
Brief History of CT Scanning
Computed Tomography (CT) technology has greatly improved in image quality and
speed since the first scanner was built in 1972 by Godfrey Newbold Hounsfield. The
first generation of CT scanners used a single x-ray source, a single detector, and
a pencil x-ray beam to acquire a set of parallel projection data for each rotation
angle [14][22]. The second generation of CT scanners used multiple detectors and a
narrow fan beam, and was more efficient than the first generation. In the first two
17
generations, the source and detector translated and rotated around the patient to
acquire projections for reconstruction.
The third generation of CT scanners used a fan beam and detectors that could
measure the projection across an entire cross-section. Therefore, translation across
the patient was not needed, and a rotation of both the source and detector was
sufficient to capture an image. However, this setup produced many artifacts caused
by the loss of calibration in the detectors from rotational motion[22].
The fourth generation of CT scanners used a ring of fixed detectors and a rotating source. This arrangement eliminated most of the artifacts due to detector
performance. However, fourth generation scanners needed a larger number of detectors, which increased the cost of CT scanners. In addition, the fourth generation was
more sensitive to scatter radiation.
Helical CT scanning was a further improvement to CT scanners. In helical CT,
the couch moves smoothly through the rotating gantry during scanning. In previous
generations, the couch was stationary for the acquisition of one slice, after which
the couch would move to the next stationary position for the next slice. Helical CT
greatly improved the speed of scanning. In addition, many helical scanners have
multiple detector rings, allowing the acquisition of multiple slices with each gantry
rotation.
1.2
1.2.1
Motivation
Role of 3D Anatomical Imaging in Radiotherapy
3-Dimensional imaging is an important part of radiation treatment planning. Along
with physical examination, 3D imaging is used to determine the gross tumor volume
(GTV), which includes the gross disease [21]. The GTV is expanded to include areas
of high risk of disease into the clinical target volume (CTV). An internal margin is
added to the CTV to accommodate organ motion and variations in size and shape
of the CTV. This volume is called the internal target volume (ITV). Finally, a setup
18
margin around the ITV is included to compensate for the uncertainty involved in
day-to-day patient setup, resulting in the planning target volume (PTV).
The accuracy of tumor imaging becomes even more important when tumors are
located very near critical structures such as the heart, lung, or spinal cord. The
overall goal of radiotherapy is to control malignant cells through the use of radiation
while at the same time sparing as much of the surrounding tissue as possible. In
some situations, the target volume may only be a few millimeters away from a critical
structure. Inaccuracies in imaging may result in radiation toxicity to the patient if the
target is too large. On the other hand, if the target volume does not adequately cover
the diseased tissue, malignant cells may not be entirely irradiated and the disease
may spread to surrounding areas.
1.2.2
Problems with 3D CT
Helical CT scanning of thoracic and abdominal tumors can produce significant motion
artifacts in both clinical and phantom studies [7][10][23]. These artifacts are mainly
generated by respiratory-induced motion of the patient. In addition, image distortions
can be introduced by movement of the tumor during a gantry rotation. Since CT
images of tumors are used for radiation treatment planning, CT image artifacts can
significantly reduce the accuracy of target delineation.
3D CT operates under the assumption that the patient’s anatomy is motionless
during scanning, which can lead to respiratory-induced motion artifacts in the CT
images. Recently, 4D CT was developed to accommodate the respiratory motion of
the patient during scanning.
The clinical use of 4D CT for radiation treatment planning has been increasing [2][13]. The increase in 4D CT is due in part to the expectation that 4D CT
images of thoracic and abdominal tumors are much more accurate than those produced by 3D CT [8]. However, it is important to examine and quantify the accuracy
of 4D CT images using different breathing patterns to see if the images are adequate
for clinical use.
19
1.2.3
4D Radiotherapy
Radiotherapy suffers from respiratory motion induced problems when the tumor is
located in the chest or abdominal area. Even if the shape and size of the tumor
are known, the accuracy of tumor irradiation decreases because of target respiratory
motion. 4-Dimensional radiotherapy seeks to mitigate these problems by tracking the
tumor’s location during treatment.
In respiratory-gated radiotherapy, the treatment beam is turned on only when the
tumor reaches a specified location. Treatment can also be gated based on respiratory
phase; for example, the beam is turned on only at full exhale. This approach allows
the design of smaller apertures1 since the apertures do not have to cover the full
extent of tumor respiratory motion. In principle, 4D radiotherapy provides accurate
irradiation of the tumor while sparing more of the surrounding healthy tissue.
4D CT is especially useful for 4D radiotherapy since 4D CT provides images of
the tumor at different phases in the patient’s respiratory cycle. These images allow
radiation oncologists to examine the respiratory motion of the tumor and to design
an appropriate treatment plan for the patient.
1.3
Goals and Purposes
One objective of this research is to examine the feasibility of using 4D CT images
for radiotherapy. In order for target margins to be set accurately, the tumor images
used in planning need to be sufficiently truthful. The 4D CT simulation program
efficiently produces results without having to physically use the 4D CT scanning
equipment. This research takes advantage of the simulation by performing numerous
4D CT studies with varying scan parameters. Finally, this thesis presents ideas on
improving 4D CT through the use of simulation and alternative imaging techniques.
1
See Appendix A for the definition of aperture.
20
Chapter 2
Background and Theory of
4-Dimensional Computed
Tomography
This chapter provides a brief overview of 4-Dimensional Computed Tomography (4D
CT) and the different hardware and software components it uses. This chapter starts
out by introducing the problems in medical imaging that prompted the invention of
4D CT, and then covers some of the methods currently used in 4D CT.
2.1
2.1.1
Introduction to 4D CT
Origins and Purpose of 4D CT
Respiratory-induced motion of tumors and normal tissues can cause significant artifacts in images acquired by helical CT scanning [3]. 4D CT was invented as a way to
account for the respiratory motion during imaging, and to produce accurate images
of a tumor at different phases in the patient’s breathing cycle. 4D CT is an integral
step used in 4-Dimensional radiotherapy and has been used as part of the planning
process for radiotherapy in clinical settings [1][2][13][16][18].
For sinusoidal respiratory motion, 4D CT is able to produce images that are more
21
accurate than ones produced by helical CT [19]. The accuracy of these 4D CT images
can increase the accuracy of tumor delineation for radiation treatment.
Another advantage of 4D CT is that it provides information about the locations
of the tumor over a period of approximately 2 minutes. In other words, each image
is reconstructed from data that was acquired throughout a span of several minutes.
Since 4D CT produces images at a number of different phases in the patient’s breathing cycle, the images provide information on the “average” trajectory of the tumor
for a cycle of breathing.
2.1.2
Overview of the 4D CT Algorithm
4D CT uses information from the real-time monitoring of a patient’s breathing during
the scan. This monitoring can be performed using a number of different methods,
as described in Section 2.2.2, but the result is a waveform that approximates the
anterior-posterior position of the patient’s abdominal surface as a function of time.
An assumption is made that this abdominal surface waveform is directly correlated to
the cranial-caudal motion of the patient’s internal organs as a function of time. During
scanning, the acquisition time of each image slice is recorded so that the slices can
be selected based on their acquisition time once the scan is completed. Respiratory
phases (0 through 2π) are assigned to each point of the waveform. Phases can also
be specified as percentages of the radian phase, such as 0%, 10%, 20%, . . ., 90% of
2π.
4D CT uses a conventional 3D CT scanner coupled with a breathing monitor. In
cine mode 4D CT, the couch stops at one of multiple pre-defined couch positions1
while the scanner continuously acquires data. The duration of these stationary couch
positions are set for at least one period of the patient’s breathing, which is approximately 4 to 5 seconds. The x-ray beam is then turned off and the couch is moved
to the next position, where the process repeats. Couch translation limits are set to
cover the entire cranial-caudal imaging region of interest (ROI); couch positions do
not overlap areas of imaging.
1
See Appendix A for the definition of couch position.
22
Figure 2-1 shows a diagram that explains the general principles behind phasebased image reconstruction2 in 4D CT. In this figure, the circle represents a coronal
cut3 of the reconstructed image of a sphere. The patient’s breathing trace4 waveform
is shown above the image, along with a square wave indicating when the x-ray beam
turns on and off (1 for on, 0 for off). The square wave also indicates the couch
positions since the beam is turned on at a couch position, and the beam is turned off
while the couch is moved to the next position. The breathing trace is oriented such
that exhale corresponds to the peaks and inhale corresponds to the valleys.
The image in Figure 2-1 is reconstructed at the exhale phase. Crosses in the
amplitude plot indicate points within each couch position where data is used for
reconstruction. Since each image is time-stamped, the software can select the appropriate images to use for each cross. Each arrow points from a cross to the section
of the image that came from that cross. Since at each couch position a subsequent
section of the couch is scanned, data from each of the couch positions is sufficient to
image the entire object when assembled together as shown in the figure. It is important to note that the amplitude5 of the sphere is the same for all couch positions at
this phase. This way, the sphere is at the same position every time a different section
of it is scanned at this phase, resulting in a reconstruction free of motion artifacts.
One helpful way to visualize the 4D CT process is by viewing the couch as being
stationary, while the CT bore moves along the couch toward the patient’s feet. By
thinking this way, it is clear that each pair of horizontal lines in Figure 2-1 represent
a section taken from a different couch position. One can imagine the sphere moving
in the cranial-caudal direction according to the amplitude plotted above it, while the
CT bore inches its way down the couch.
2
See
See
4
See
5
See
3
Appendix
Appendix
Appendix
Appendix
A
A
A
A
for
for
for
for
the
the
the
the
definition
definition
definition
definition
of
of
of
of
reconstruction.
coronal cut.
breathing trace.
amplitude.
23
Figure 2-1: Diagram for phase-based 4D CT image reconstruction at the exhale phase.
2.2
Hardware Configurations
This section describes two different systems used in the 4D CT scanning experiments
in this thesis. One system involves a General Electric (GE) LightSpeed Qx/i fourslice CT scanner coupled with the Varian Real-time Position Management (RPM)
respiratory gating system. The other system involves a Philips Brilliance CT Big Bore
16-slice scanner coupled with the bellows (belt) device for respiratory monitoring.
2.2.1
Scanners
The General Electric (GE) LightSpeed Qx/i four-slice CT scanner captures images
in axial cine mode6 . One CT tube rotation takes 0.8 seconds, and each slice is
2.5 mm thick, resulting in a four-slice acquisition of approximately 1 cm. The 4D
CT scan produces approximately 1000 to 1500 images in the Digital Imaging and
Communications in Medicine (DICOM) format.
6
See Appendix A for the definition of cine mode 4D CT.
24
The Philips Brilliance CT Big Bore 16-slice scanner captures images in helical
mode7 , which is slightly different from the cine mode described in Section 2.1.2. In
helical mode, the couch positions are not stationary. The couch moves very slowly as
the Philips scanner continuously acquires projection data, and the x-ray imaging beam
is never turned off. Because the couch moves very slowly, this method approximates
the behavior of cine mode, where the couch is stationary during scanning. In helical
mode, the x-ray beam does not need to be turned off since the couch is slowly moving
to cover the next area of the patient.
2.2.2
Respiratory Monitors
The Varian Real-time Position Management (RPM) system tracks the abdominal
surface motion of the patient during 4D CT scanning [4][6][17][20]. The RPM system
uses a CCD camera and a small plastic marker box that has two infrared reflecting
dots on its surface. The marker box is placed on the patient’s abdomen during
scanning while the CCD camera uses an infrared filter to illuminate the reflective
dots on the box. The anterior-posterior trajectory of the RPM box is recorded, and
the respiratory phase of the trace is calculated by RPM software. The RPM software
transmits a transistor-transistor logic (TTL) signal to the scanner to indicate when
the x-ray beam is turned on or off.
In the Philips bellows (belt) system, a belt is wrapped around the patient’s abdominal surface as the patient is lying on the couch. The device allows the belt’s
circumference to expand and contract. The patient’s inhalation causes the belt to
expand, and the device is able to track and record the expansion distance of the belt,
which results in a breathing trace. The system also assigns respiratory phases to the
breathing trace and communicates with the scanner.
While the respiratory monitors mentioned above are used for our study, other
investigations have used different methods. One such method for tracking the abdominal surface motion of a patient during scanning uses a needle that travels up
and down as the abdominal surface expands and contracts [12]. The device is purely
7
See Appendix A for the definition of helical mode 4D CT.
25
mechanical and involves a weight that is attached to a needle by a hinge. The needle
is balance on a fulcrum so that when the weight moves up and down, the end of the
needle moves down and up, respectively. The device is arranged so that the patient’s
abdominal surface pushes the weight up and down, causing the needle to move. The
needle is positioned so that the CT scanner captures its position with each image
acquisition. As a result, the patient’s breathing trace can be seen directly on the CT
images themselves. The position of the needle indicates the amplitude of breathing.
The advantage of this method is that no complicated communication between
the breathing monitor and the CT scanner is required. In the previous methods,
the breathing monitors communicate with the CT scanner to indicate x-ray on and
off values, and possible delays of the information transfer can be problematic. In
addition, the needle device is purely mechanical and very low-cost, as it was developed
in-house.
Another approach uses a spirometer to indirectly measure internal organ movement from breathing [5]. This system uses the volume of air inspired and expired by
the lungs to measure movement.
2.3
2.3.1
Reconstruction Approaches
General Electric Scanner - Cine Mode
This section describes the 4D CT reconstruction method used by the GE scanner,
running in cine mode and coupled with the RPM system. The GE scanner produces
images in Digital Imaging and Communications in Medicine (DICOM) format. Each
image is an axial slice of the object, and contains a time-stamp of the acquisition in
its header.
Approximately 1000 to 1500 unsorted DICOM images are produced at the end of
a 4D CT scan. The user specifies up to 20 phases for image reconstruction. The user
also specifies the number of images to acquire during each couch position. However,
all images are acquired at evenly time-spaced points within each couch position. For
26
example, if the user specifies 10 phases for reconstruction and 14 images to acquire,
14 images will be acquired at equally time-spaced points within each couch position.
For each of the 10 phases, the algorithm will use the image that has a phase closest
to the desired phase for 4D reconstruction.
The RPM convention is that the peaks of the breathing trace are assigned a phase
of 0 = 2π radians. The phase-assignment software only assigns phases to points that
correspond to 0 = 2π, and the points in between are assigned a linearly interpolated
value between 0 and 2π. The reconstruction of the image at any given phase, say
30%, may or may not use data acquired when the phase of the trace was at exactly
30% of 2π, but at one of the equally time-spaced points that has a phase closest to
30% of 2π.
A directory is created for each requested phase, and the desired DICOM files from
the unsorted directory are copied into each of the sorted directories. The unsorted
DICOM images are numbered in the order they were acquired by the scanner.
The RPM software assigns phase to the breathing trace in real-time as the patient
is scanned. Consequently, it uses a predictive algorithm to predict when the trace will
reach a peak to assign it a phase of 0 or 2π. This predictive algorithm is not always
correct, especially for segments of extremely irregular breathing. Because of this
problem, the Radiation Oncology department staff at Massachusetts General Hospital
(MGH) manually edit the phase for these problematic segments before reconstruction
to improve the quality of the resulting images.
2.3.2
Philips Scanner - Sorting in Sinogram Space
The Philips scanner, running in helical mode and coupled with the bellows breathing
monitoring system, sorts images in sinogram space. Instead of reconstructing images
using only the data from evenly time-spaced points within each couch position, the
Philips system can use data acquired at a point with exactly the specified phase.
Therefore, the reconstruction of the image at any given phase, say 30%, uses data
from points within each couch position that have a phase of exactly 30% of 2π.
27
28
Chapter 3
Methods
This chapter provides an overview of the materials and methods used for the 4D CT
experiments and a description of the 4D CT software simulations. For the experiments, a phantom was constructed, consisting of six rubber spheres and a straight
edge set on a styrofoam block. A computer-driven sled moved the phantom to simulate patient breathing motion during scanning. Two different scanners were used to
perform the 4D CT experiments: a General Electric (GE) LightSpeed Qx/i four-slice
CT scanner located at Massachusetts General Hospital, and a Philips Brilliance CT
Big Bore 16-slice scanner located at the Boston Medical Center. The GE scanner
used the Varian Real-time Position Management (RPM) respiratory gating system
to track phantom motion, and the Philips scanner used the bellows (belt) device to
track motion.
3.1
3.1.1
Experiments
General Electric CT Scanner
The phantom consisted of spheres of known dimensions and a straight edge positioned
on a styrofoam block. The phantom was placed on a computer-driven sled, which was
positioned on the CT scanner couch. A breathing trace was then programmed into
the computer controlling the sled, and the sled moved the phantom along the track
29
in a 1-Dimensional back and forth motion according to the breathing trace. The
motion of the sled moved in a cranial-caudal direction along the CT scanner couch to
simulate internal organ motion during patient respiration. A second stepping motor
assembly synchronously translated a horizontal ledge in the vertical axis to simulate
abdominal surface motion during respiration. For the GE scanner experiments, the
Varian RPM system was used to track the motion. Figure 3-1 shows the phantom on
the computer-driven sled along with a Varian RPM marker box placed on the ledge.
Figure 3-1: Phantom positioned on the computer-driven sled, which was used in the
4D CT experiments.
In the experiments using the GE scanner, a Varian RPM marker box was placed
on the ledge of the motion simulator. As explained in Section 2.2.2, the RPM system
tracks the motion of this marker box to monitor breathing. 4D CT images were
reconstructed at ten phases of respiration, which are referred to as 0%, 10%, 20%,
. . . , 90% phase. The convention is that 50% phase is at full exhale, and 0% phase
is at full inhale in the respiratory cycle. However, when using the GE scanner, the
RPM software inverts this convention so that 50% is at inhale and 0% is at exhale.
30
In this thesis, any data dealing with the GE scanner will use the convention that 50%
phase is at inhale and 0% phase is at exhale.
3.1.2
Philips CT Scanner
The same phantom and computer-driven sled was used for the Philips scanner experiments as was used with the GE scanner experiments. However, a different breathing
monitor was used to track phantom motion. In the experiments using the Philips
scanner, the bellows device (belt) was wrapped around the bottom of the motion
simulator and the ledge. The vertical motion of the ledge caused the belt to expand
and contract, which allowed the bellows device to monitor the motion, as explained
in Section 2.2.2.
Similar to the GE experiments, 4D CT images were reconstructed at ten phases of
respiration, which are referred to as 0%, 10%, 20%, . . . , 90% phase. The convention
with the Philips scanner is that 0% phase is at full inhale, and 50% phase is at full
exhale in the respiratory cycle. Note that this convention is opposite that of the
convention used in this thesis for the GE scanner, as mentioned in Section 3.1.1.
3.1.3
Breathing Traces
The breathing traces used to simulate irregular breathing were previously recorded
from patients undergoing 4D CT scans using the GE scanner. As a result, these
recorded traces were stored in the RPM data file format. An RPM breathing trace
file is a text file that specifies the amplitude of the marker box as a function of the
recorded time. Along with some information about the CT scan in the header, the file
includes the RPM-assigned phase of the trace as a function of time and the instances
along the trace when the x-ray beam was enabled.
Two traces were used, each from a different patient, to simulate irregular respiratory motion, and they are identified as breathing trace 2563 and breathing trace 2567.
Although traces 2563 and 2567 were recorded using the RPM system and contained
phase and beam-on information from the patient scans, only the amplitude informa31
tion was used to drive the phantom for the experiments. The phase and beam-on
information were recalculated by the breathing monitor during or after the scan, for
the GE or Philips scanner, respectively.
The amplitude of each recorded RPM trace depends on the placement of the RPM
box on each patient’s abdomen. For example, the amplitude measured by the RPM
system may be smaller if the box is placed lower on the abdomen where motion due to
breathing is less pronounced. The internal organ motion obviously does not depend
on the placement of the box. However, if the box is placed at a location with greater
motion, the measured motion of the box is larger. Therefore, since the breathing
traces are used to drive the phantom (internal organ) motion, each breathing trace
is multiplied by a chosen scale factor in order to make the phantom motion more
realistic. A scale factor of 3 was used for the 2563 trace, and a scale factor of 2 was
used for the 2567 trace. These traces are shown in Figure 3-2.
Figure 3-2: Breathing traces 2563 (displayed using a scale factor of 3) and 2567
(displayed using a scale factor of 2). The peaks of the traces correspond to exhale
and the valleys correspond to inhale.
32
In addition, a 2 cm peak-to-peak sine waveform and a 1 cm peak-to-peak sine
waveform were used to drive the phantom. Since these sinusoidal traces were created
using a computer, they were already in the amplitude versus time format. Breathing
traces 2563, 2567, 2 cm sine, and 1 cm sine were used to drive the phantom for both
the GE scanner experiments and the Philips scanner experiments.
3.1.4
Breathing Trace Analysis
After performing the GE scanner experiments, the RPM breathing traces, which
contain the phase and x-ray beam-on information from the phantom scans, were
obtained. This enabled the amplitude-phase relationship to be plotted for each given
phase of reconstruction.
Furthermore, a study was performed on 122 different RPM breathing traces
recorded from patients in a scanning or treatment hospital environment. These traces
were analyzed to determine the average length of time for a cycle of breathing, average
baseline drift1 , and average variance of breathing cycle amplitudes.
To determine the average breathing period for each trace, the length of time of each
cycle of breathing was measured by using the phase information from each recorded
RPM trace to determine the breathing cycles for each trace. Then, all the breathing
periods were averaged for each trace, and then those averages were averaged to obtain
a single number.
To determine the baseline drift and breathing cycle amplitudes, each trace was
first normalized to its average amplitude since the amplitude can vary depending on
RPM box placement, as discussed in Section 3.1.3. The average amplitude of each
trace was computed similarly to the way the average breathing period was computed:
the amplitudes of the breathing cycles were averaged, where the breathing cycles were
defined by the phase information from the trace. The baseline drift was measured
in two ways. The first way was to take the difference between the maximum of the
peaks and the minimum of the peaks of the trace. The peaks of the trace were found
by examining each breathing cycle and taking the maximum amplitude of each cycle.
1
See Appendix A for the definition of baseline drift.
33
The second way to measure baseline drift was to measure the slope of the best fit line
of the peaks. Finally, the variance of the measured breathing cycle amplitudes for
each trace was computed, and then the variances were averaged.
3.1.5
Error Quantification
In order to quantify the image artifacts obtained from the experiments, the volume
of Sphere 1 in each image was calculated for comparison to the true volume of Sphere
1, which was computed using a caliper-measured diameter. Sphere 1 is the largest
sphere in the phantom shown in Figure 3-1 and is labeled with the number one in
Figure 4-2. The caliper-measured diameter of Sphere 1 is 5.461 cm, which yields a
volume of approximately 85.27 cm3 .
The image volume of Sphere 1 was calculated from the Philips scanner by first
thresholding the 3D image with a pixel value of 200 to create a binary image. The
connected objects in the binary image were then labeled by using the bwlabeln()
function in MATLAB with a 26-connected neighborhood. The volume of Sphere 1
was simply the number of voxels in the thresholded Sphere 1 image. To convert
number of voxels into cubic centimeters, a conversion factor was used that consisted
of the caliper-measured volume of Sphere 1 divided by the number of voxels in the
static 3D Philips scan of Sphere 1.
In addition to using the previous method to calculate the volume of Sphere 1 in
the GE scanner images, the GE Sim4D software tools, which presumably thresholds
the objects as well, were also used. However, when the volumes of Sphere 1 generated
by the GE scanner were compared to those generated by the Philips scanner, the
volumes calculated from the MATLAB method mentioned above were used.
The center of mass (COM) of Sphere 1 was also computed in each of the 4D
reconstructed images from both the GE and Philips scanners. The COM of Sphere
1 was computed by averaging the 3D coordinates of each voxel of Sphere 1. For
example, for the x-coordinate, the x-coordinates of all the voxels of Sphere 1 were
summed together, and then divided by the total number of voxels in Sphere 1. The
y-coordinate and z-coordinate of the COM were computed in a similar fashion. Since
34
each voxel is not a perfect cube, different conversion factors had to be used for each
coordinate of the COM to convert into centimeters. The x-coordinate, y-coordinate,
and z-coordinate conversion factors consisted of the caliper-measured diameter of
Sphere 1 divided by the number of voxels of the diameter of Sphere 1 in the xdirection, y-direction, and z-direction, respectively. The orientation of the coordinates
is as follows: the x-coordinate specifies the row of each axial slice from the DICOM
data, the y-coordinate specifies the column of each axial slice, and the z-coordinate
specifies the cranial-caudal direction.
3.2
3.2.1
4D CT Simulations
General Electric Scanner Experiment Simulations
Software in the MATLAB programming language was implemented to simulate the
4D CT scanning process used by the GE scanner. Figure 4-15 shows an example of
the end result of the simulation. In this simulation, a sphere surface moves along a
cranial-caudal trajectory specified by an RPM trace that is multiplied by the scale
factor and positioned so that the mean of the trace is at an amplitude of zero. The
sphere moves along the trace so that the very center of the sphere corresponds to the
given amplitude. The simulation shows an amplitude versus time plot and a phase
versus time plot for the duration in which data is acquired. In both of these plots,
data acquisition points are marked with crosses, and connected with a dotted line.
Couch positions, which are specified by the beam-on and beam-off information from
the RPM trace, are indicated in both plots by a square wave that fluctuates between
1 and 0. A value of 1 indicates beam-on and 0 indicates beam-off.
During the simulation, a small circle moves along the amplitude plot to indicate
the position of the sphere. An example of this is shown in Figure 4-17 where the small
circle is shown at the very end of the amplitude plot since the figure shows the end
results of the simulations. At each specified acquisition point when the small circle
on the amplitude plot meets a cross, the simulation captures a four-slice section of
35
the sphere and draws the appropriate section in the coronal view on the left of the
two plots. In addition to drawing this four-slice section, the simulation also draws a
circle surrounding the acquired section that indicates the true position of the sphere
at that data acquisition point. For simplicity, the rotation time of the x-ray source
in the simulation is 0 seconds, indicating instantaneous acquisition.
At each consecutive acquisition point, the couch is translated and images are
acquired at the next couch position. This process is simulated by slicing the sphere
at consecutively lower (caudal) positions. In other words, the simulation gives a
stationary couch view of the reconstructed object, while moving the scanning plane
in the caudal direction for each consecutive couch position. Finally, a scale is given
on the left of the reconstructed sphere that shows the true size of the reconstructed
object.
The GE scanner is a four-slice scanner, and the simulation allows the user to specify how thick each four-slice section will be. Other user inputs include the radius of
the sphere surface and the scale factor used to convert the RPM trace amplitude into
motion of the sphere, as discussed in Section 3.1.3. The user also specifies the exact
indices of the RPM trace where data acquisition occurs. Since couch positions are
simulated by slicing at consecutively lower (caudal) positions, the user also specifies
the acquisition amplitude2 of the first four-slice section. The very top (cranial) slice
of the four-slice section was specified to correspond to the acquisition amplitude.
The 4D CT simulation calculates the volume of the reconstructed surface by mathematically calculating the volume of each four-slice section. Each four-slice section
is essentially a cross section of the sphere. The radius of each slice of the four-slice
section was first calculated. Figure 3-3 shows a diagram that explains this process.
In this figure, the solid circle represents a coronal view of the sphere at an amplitude
of zero, and the dashed circle represents the sphere at a data acquisition point. The
horizontal line across the dashed circle represents one particular slice of a four-slice
acquisition. The objective is to find the radius x of this slice. The acquisition amplitude b is known, the amplitude a of the sphere at this acquisition point is known from
2
See Appendix A for the definition of acquisition amplitude.
36
the RPM trace, and the radius r of the sphere is known. A simple application of the
Pythagorean theorem yields x. Once the radius of the slice is computed, the volume
of that slice can be computed by approximating it as a perfect disk. The volume of
the reconstructed image is just the sum of the volumes of the slices.
The 4D CT simulation can produce a movie of the 4D CT process as the sphere
moves along the trace and data is acquired. The simulation also can produce images
corresponding to frames of the movie.
Figure 3-3: Diagram for volume computation.
3.2.2
Comparison of Simulations to Experiments
The reconstruction of Sphere 1 in the GE 4D CT experiments with breathing trace
2563 was simulated. A four-slice section thickness of 1 cm (4 × 2.5 mm), a scale
factor of 3, and a sphere surface with the same radius as that of Sphere 1 (2.3705 cm)
were used, and the sphere was driven using the RPM trace 2563 from the GE 4D CT
experiment.
In order to simulate the GE experiments closely, the exact indices of the RPM
trace where data acquisition of Sphere 1 occurred needed to be found. First, the
sorted DICOM images from the GE scanner that correspond to a given phase were
37
examined. As explained in Section 2.3.1, for each 4D CT scan, the GE scanner outputs
a set of unsorted DICOM images given in the order that each axial slice was acquired,
and also a set of sorted DICOM images for each phase. These sorted DICOM images
are essentially the 4D reconstructed image of the object, and are taken or sorted from
the unsorted DICOM image set. These sorted DICOM images do not contain the
information of where in the RPM trace they were acquired. However, the unsorted
DICOM images of the scan do contain that information. Therefore, for each phase,
the sorted DICOM images that sliced through Sphere 1 were selected and matched to
the corresponding image in the unsorted set. Once the unsorted DICOM images that
were used in the 4D reconstructed image of Sphere 1 were found, the time location
in the RPM trace where these slices occurred was computed.
Next, the acquisition amplitude of the first four-slice section that sliced through
Sphere 1, as explained in Section 3.2.1, needed to be found. This was done by
examining the very top (cranial) of the reconstructed image of Sphere 1 for each phase.
Since the GE scanner is a four-slice scanner, it acquires 4 slices at a time for a given
rotation; in other words, the first four DICOM images in a sorted set correspond to
one acquisition, DICOM images five through eight correspond to another acquisition,
and so on. Therefore, if the most cranial slice of Sphere 1 comes from a DICOM image
that is a multiple of four, 0.75 cm needs to be added to account for the fact that the
four-slice section missed the top of Sphere 1 in the first three slices. Similarly, if the
most cranial slice of Sphere 1 comes from a DICOM image n not equal to a multiple
of four, (n mod 4 − 1) ∗ 0.25 cm need to be added.
Figure 3-4 shows a diagram that explains this process. The solid circle represents a
coronal view of the sphere at an amplitude of zero, and the dashed circle represents the
sphere at the first data acquisition point. The horizontal lines across the dashed circle
represent the four-slice section, and the arrow points to the acquisition amplitude of
the first four-slice section, as explained in Section 3.2.1. To determine the acquisition
amplitude b of the first section, the RPM time location of acquisition of the most
cranial slice of Sphere 1 was found, which revealed the amplitude a of Sphere 1
at that point in time in the RPM trace. The radius r of Sphere 1 and the extra
38
space (if any) described earlier was then added to that RPM amplitude to obtain the
acquisition amplitude b of the first four-slice section of Sphere 1.
Figure 3-4: Diagram for computation of the acquisition amplitude of the first fourslice section that slices through Sphere 1.
3.2.3
Time Shift Simulations
The 4D CT simulation was extended to reconstruct images of Sphere 1 when shifting
the start time of scanning. The quality of a 4D CT image depends on the behavior
of the breathing trace during the scan, and a patient’s breathing trace can change
drastically over a two minute period. Therefore, an investigation of the effects of
shifting the start time of scanning was performed, since this time shift will cause the
x-ray beam to image Sphere 1 during a different segment of the trace.
This version of the simulation has a number of differences from the previous version. The user does not specify the exact indices of the RPM trace where data
acquisition of Sphere 1 occurs. Instead, he specifies one of ten phases (0%, 10%, 20%,
. . ., 90%) and the simulation chooses the data acquisition points using the phase and
beam-on information from the RPM trace. Basically, the simulation chooses the point
39
in each couch position that is closest to the desired phase. The user, however, still
needs to specify the acquisition amplitude of the first four-slice section that slices
through Sphere 1.
Another difference between this version of the simulation and previous versions
is that the user must specify the start time of scanning. The user chooses a point
in the RPM trace to start scanning from. If that point is within a couch position,
the simulation uses that couch position as the first one for data acquisition. If the
starting point is between couch positions, the simulation uses the very next couch
position as the first one.
The simulation also allows the user to shift the scanning of couch positions by
different amounts of time. The length of each couch position stays the same; each
one is just shifted over by the user-specified amount. However, this feature was not
explored for the time shift simulations done for this thesis. The couch positions
specified by the 2563 trace were used as the different starting points of scanning.
3.2.4
Hysteresis
One major assumption made by the simulation (and 4D CT in general) is that the
internal organ motion has a one-to-one correlation with the external motion of the
abdomen. In other words, the simulation assumes that, within a scale factor, anteriorposterior movement of the abdomen indicates the exact same internal organ movement
in the cranial-caudal direction. This is important because in 4D CT, images are
reconstructed based on the amplitude and phase information from external abdominal
motion. The true motion of the tumor may be slightly different from the external
motion.
Fluoroscopic studies have been performed on patients in order to study the relationship between the external abdominal motion and the internal organ motion during
scanning [9]. These studies indicate that hysteresis occurs between the internal and
external motion of a patient. In other words, the internal organ motion actually leads
the abdominal surface motion by a length of time up to approximately 220 ms. This
hysteresis was simulated by having the internal motion lead the external motion by
40
some length of time specified by the user. Therefore, the data acquisition points obtained by the simulation were based on phase information that was delayed in time
with respect to the true motion of Sphere 1. For example, if the desired reconstruction
phase was 50%, the amplitude of Sphere 1 at an acquisition point would correspond
to a point on the RPM trace that was actually a few ms after the true 50% point for
that couch position. Simulations using the 2563 breathing trace with delays of 31,
63, 94, 125, 156, 188, 219, and 250 ms were performed.
This version of the simulation that implements the hysteresis delay was based on
the previous time shift version described in Section 3.2.3. Therefore, the features and
overall algorithm of that simulation were incorporated into this version.
3.2.5
Baseline Drift
Since baseline drift was observed in the breathing traces of patients, the effect of
breathing trace baseline drift on the 4D reconstruction of Sphere 1 was studied.
Baseline drift introduces variation in amplitude for a given respiratory phase, even if
the assigned phase of the breathing trace is accurate. Figure 3-5 shows an example
of positive slope creating baseline drift in a breathing trace. In this figure, the exhale
points along the baseline drift trace have consecutively increasing amplitudes. If the
positive slope were increased, which would result in a more severe baseline drift, the
amplitude at the exhale points would increase at an even faster rate. The results of
using a breathing trace with varying amounts of positive slope was investigated.
Varying amounts of baseline drift were added to the 2 cm sine breathing trace
before using it for the 4D CT reconstruction of Sphere 1. This version of the simulation incorporated all the features of the previous versions described in sections 3.2.3
and 3.2.4, along with a user-specified input of baseline drift slope. Simulations using
the 2 cm sine trace with added drift slopes of 0, 0.0136, 0.0268, and 0.0400 cm/s were
performed, and the volumes of these reconstructed images were computed.
41
Figure 3-5: Example of baseline drift in a breathing trace. The black trace is the
original sinusoidal breathing trace. The red dotted trace has a positive slope, resulting
in baseline drift. The orientation of the traces is such that the peaks correspond to
exhale, and the valleys correspond to inhale.
42
3.2.6
Arbitrary Object Simulations
The 4D CT simulation was extended to reconstruct objects of arbitrary size and
shape. Previous versions of the simulation only had the capability of using a sphere
surface to simulate the tumor shape. Since tumors exist in a wide variety of shapes,
another version of the simulation was implemented that, in addition to the features
of scan start time shift, hysteresis of internal and external motion, and baseline drift,
was able to take in an arbitrary object and perform a 4D CT scan using an RPM
breathing trace.
The simulation takes in as input a 3-Dimensional matrix that represents the 3Dimensional object to be scanned. This 3-D matrix is a stack of axial slices of
the object, similar to the DICOM data retrieved from a CT scan. The simulation
moves the center of the object along the RPM trace. Similar to some of the previous
sphere surface simulations, the user chooses the thickness of each four-slice section, the
scale factor used to convert the breathing trace amplitude into actual object motion,
and the acquisition amplitude of the first four-slice section that slices through the
object, as described in Section 3.2.1. In addition, the user chooses a specific phase for
reconstruction, and the simulation picks the data acquisition points using the phase
and beam-on information from the RPM trace.
However, there are some additional input parameters specific to the arbitrary
object simulation. The simulation needs to know the true size of the input object along
the cranial-caudal direction. The simulation needs this information to determine how
much of the object is acquired at each four-slice section acquisition. Therefore, the
user specifies the number of voxels per centimeter along the cranial-caudal direction
of the object.
Although the simulation deals with an arbitrary 3-Dimensional object and produces a 3-Dimensional reconstructed image, it gives a coronal view of the image
similar to the previous surface simulations. The arbitrary object simulation allows
the user to specify the coronal plane of view during the simulation. Figure 4-22 shows
an example of the end result of the simulation. Like the previous surface simulations,
43
it includes the amplitude and phase plots along with the reconstructed coronal slice.
To see how the simulation would perform with respect to our experiments using
the GE scanner and to our previous simulations of Sphere 1, the static, 3D scan of
Sphere 1 was used as the input object to our simulation. RPM breathing trace 2563
was used to drive the arbitrary object simulation of Sphere 1 for a number of different
respiratory phases.
3.3
Radiation Treatment Simulations
Using the software framework implemented for the sphere surface 4D CT simulations,
a program that simulates the gated radiation treatment of a patient was developed.
During gated radiation treatment, sometimes the patient’s breathing is so irregular
that the staff moves the gating window to compensate for baseline drift or amplitude
variation. The goal was to use the simulation to determine if the tumor was still
being adequately irradiated with these gating window changes.
Figure 4-26 shows an example of the end result of this simulation. This simulation
takes in an RPM breathing trace recorded from gated radiation treatment and moves a
circle corresponding to the tumor along the trace. The RPM breathing trace obtained
from gated radiation treatment contains the amplitude and phase information of the
abdominal surface trajectory, and also the instances when the x-ray treatment beam
was on. Figure 4-25 is an example of the RPM trace obtained from gated radiation
treatment. The red dots indicate points where the treatment beam was enabled.
Since the treatment was gated based on amplitude, the discontinuities of the red dot
baseline indicate the instances when the gating window was shifted. For example,
there was a clear gating window change at approximately 70 to 80 seconds in Figure 425.
On the left side of Figure 4-26, the smaller circle represents the tumor while the
larger circle represents the aperture of radiation treatment. The larger circle remains
stationary, and both the circles start out as blue in color. When the beam is turned
on as specified by the RPM trace, the smaller circle representing the tumor turns
44
red. The smaller circle turns blue when the beam is off. The square wave in both
the amplitude and phase plots represents when the beam was turned on and off (1 =
on, 0 = off). A small circle moves along the amplitude plot to indicate the position
of the sphere during the simulation. Additionally, since the duration of treatment
is typically around 10 minutes, the amplitude and phase plots scroll along the trace
with a window of around 15 seconds, as shown in Figure 4-26. By examining the
position of smaller circle when it turns red, the user can easily view whether or not
the entire tumor area is being irradiated by the x-rays.
The simulation allows the user to specify the radius of the tumor and aperture
circles, the position (amplitude) of the aperture circle, and the scale factor used to
convert the breathing trace amplitude into actual tumor motion. The simulation also
allows time shifts of starting scan time, similar to how it was described in Section 3.2.3.
This simulation produces a movie of the entire radiation treatment process, and
optional images corresponding to specific frames of the movie. Simulations of gated
radiation treatment were performed with tumor and aperture radii of 3 and 3.5 cm,
respectively, an aperture amplitude of zero, and a scale factor of 1.
45
46
Chapter 4
Results
This chapter describes the experimental results of 4D CT using the General Electric (GE) scanner at Massachusetts General Hospital and the Philips scanner at the
Boston Medical Center. The breathing traces used to simulate patient breathing during scanning are analyzed. The simulation results are presented and compared to the
experimental results.
4.1
Breathing Trace Analysis
The quality of a 4D CT scan depends greatly on the characteristics of the breathing
trace. In order to capture the irregularities inherent in the breathing patterns of
humans, two breathing traces recorded from patients were used: trace 2563 and trace
2567. A perfect 2 cm sine wave breathing trace was used as a comparison. Segments
of the 2563, 2567, and 2 cm sine breathing traces, along with their RPM-assigned
phases, are shown in Figure 4-1. The segments of traces 2563, 2567, and 2 cm sine
in the figure represent the segments of time in which Sphere 1 was scanned by the
GE CT scanner. The amplitude plots are oriented such that exhale is at the peaks
of the wave, and inhale is at the valleys. In addition, the amplitude plots have been
scaled by the internal-external motion scale factor1 , discussed in Section 3.1.3, and
represent the true motion of the phantom during the experiments.
1
See Appendix A for the definition of scale factor.
47
Figure 4-1: Amplitude, phase, and amplitude phase correlation of traces 2563, 2567,
and 2 cm peak to peak sine wave. The segments shown in the figure correspond
to segments where Sphere 1 was scanned by the GE scanner. The internal-external
motion scale factor is incorporated into the amplitude plots, which correspond to the
true motion of the phantom.
48
The amplitude-phase correlation is shown in the third row of Figure 4-1. This
amplitude-phase correlation indicates the amplitude of the breathing trace depicted
in the first row at specific phases depicted in the second row. The amplitude-phase
correlation is a useful metric to determine the quality of a 4D CT scan based on
the breathing trace. Notice that the spread of the amplitudes at each phase for
the 2 cm sine trace is much smaller than the spread for the 2563 and 2567 traces.
This is expected since a perfect sine wave will have a very predictable amplitude at
each given phase of the trace. Additionally, the phase assignment was much more
accurate for the 2 cm sine trace due to the regularity of the trace. The accuracy of
phase assignment also contributed to the small spread of amplitudes at each phase.
Trace 2563 was chosen for the experiment because of its variation in inhale amplitude at different breathing cycles, while having a relatively stable baseline at exhale.
However, as shown in Figure 4-1, the segment of the trace in which Sphere 1 was
scanned by the GE scanner has a significant breathing irregularity at around 83 seconds. This irregularity made it very difficult for the phase assignment software to
obtain the correct phases at this point, and as a result, the spacing of the cycles
shown in the 2563 phase plot is incorrect. There are some outliers for several phases
in the 2563 amplitude-phase plot. Outliers for phases 20%, 30%, and 50% are especially prominent. These outliers are a direct result from the breathing irregularity
around 83 seconds. Because the assigned phases were incorrect at this irregularity,
the amplitude of Sphere 1 at that irregularity was different from the amplitude at the
other couch positions for phases 20%, 30%, and 50%. Therefore, even though trace
2563 exhibits a relatively stable baseline at exhale, the resulting 4D reconstructed
image at exhale is not guaranteed to be artifact-free because of the errors in phase
assignment.
Trace 2567, on the other hand, has significant baseline drift while maintaining a
somewhat regular breathing cycle amplitude. No significant breathing irregularities
occur during the GE scanning of Sphere 1, and the RPM software did not have
difficulty assigning phases, as shown in Figure 4-1. The spread of the amplitudes for
each phase is due to the varying baseline of trace 2567.
49
The amplitude plot for the 2 cm sine wave in Figure 4-1 is quite regular, and
the RPM software assigns the phases correctly. Looking at the amplitude-phase
plot for the 2 cm wave, the points have slightly more spread at phases between 0%
(exhale) and 50% (inhale). This is the most noticeable at phases 80% and 90%. This
slight variation in amplitude is due to the velocity of the phantom at these phases.
At around 0% and 50%, the phantom is changing direction and the velocity of the
phantom is around zero. The phantom is traveling the fastest at phases such as 80%
and 90%, making the amplitude at these phases vary slightly.
In addition, a study was performed on 122 different breathing traces recorded
from patients in a scanning or treatment hospital environment. The average breathing period was found to be approximately 3.961 seconds. Since the breathing trace
amplitude may vary from day to day due to RPM sensor placement on each patient,
the amplitude of each trace was normalized to the average breathing cycle amplitude
for that trace. The average baseline drift in terms of the peaks of the trace was
0.5634. The average baseline drift in terms of slope was 4.2642 · 10−4 . The average
variance of the breathing cycle amplitudes was 0.06303. No scale factor was used for
this analysis, and Table 4.1 summarizes these results.
Table 4.1: Characteristics of 122 different breathing traces. No scale factor was used.
Average Breathing Period
Average Baseline Drift (Peaks)
Average Baseline Drift (Slope)
Average Variance of Breathing Cycle Amplitudes
4.2
4.2.1
4.0 s
0.56 (no units)
4.3 × 10−4 s−1
0.063 (no units)
Experiments
General Electric CT Scanner
This section gives the results of 4D experiments using the moving phantom, GE
scanner, and Varian RPM system. Figure 4-2 shows coronal slices of the phantom
50
taken at 50% (inhale) phase for the 2 cm sine, 2563, and 2567 breathing traces, along
with a 3D scan of the static phantom. All images of the phantom were constructed
from sorted DICOM data from the scanner, and the coronal slices all intersect the
center of Sphere 1.
Figure 4-2: Using the GE scanner, (a) coronal slice of static phantom; coronal slice
of phantom at 50% (inhale) phase for (b) 2 cm sine, (c) 2563 trace, (d) 2567 trace.
The 2 cm scan in Figure 4-2b is free of artifacts and resembles the static scan in
Figure 4-2a. This is expected given the nature of the 2 cm breathing trace described
in Section 4.1. The 2563 scan in Figure 4-2c, however, has a number of significant
artifacts. The top section of Sphere 1 in the 2563 scan is smaller than it should be,
indicating that the amplitude of the sphere was too low at that data acquisition point.
The section of Sphere 1 that is second from the bottom is essentially a duplicate of
51
the very bottom of the sphere. These artifacts of Sphere 1 can be correlated to the
artifacts of the diagonal ruler in the same image.
The 2567 scan in Figure 4-2d appears to have less serious artifacts than those in
the 2563 scan. The top of Sphere 1 appears slightly pointed and elongated, and the
ruler is not as straight as it is in Figures 4-2a and 4-2b.
The 0% (exhale) phase scans using traces 2563 and 2567 shown in Figure 4-3
appear to have slightly fewer artifacts than the corresponding 50% (inhale) scans. In
fact, in Figure 4-3c, only the most bottom section of Sphere 1 appears out of place.
The headers of the DICOM image that produced the bottom section of Sphere 1 were
searched and it was discovered that this section was acquired during the breathing
irregularity of trace 2563, discussed in Section 4.1. Given that the amplitude of trace
2563 at exhale did not vary much, Sphere 1 would have been almost artifact-free
without the breathing irregularity that occurred during the scanning of the bottom
section.
The 0% (exhale) phase scan using trace 2567 in Figure 4-3 appears slightly better
than the inhale scan of 2567. Sphere 1 is slightly elongated and the ruler is not as
straight as in the static scan of the phantom, but the overall shapes of the phantom
are intact. Examining the 2567 breathing trace in Figure 4-1, the exhale baseline
starts a little high, but remains somewhat constant throughout the period of data
acquisition for Sphere 1. Figure 4-3 shows that the scan of Sphere 1 reflects the
behavior of the breathing trace: the top of Sphere 1 is a slightly elongated due to the
exhale baseline starting high, but the rest of the sphere has barely any artifacts due
to the exhale baseline remaining relatively constant.
The image volume of Sphere 1 was computed using GE Sim4D tools. Figure 4-4
shows these computed volumes at all ten phases using breathing traces 2563, 2567, 2
cm sine, and 1 cm sine. Variations in the volume range from +12% to -12% of the
ground truth volume for trace 2563, which was 85.2737 cm3 . Variations for trace 2567
were +6.1% to -6.2%. Sinusoidal breathing traces exhibited less respiratory phase
dependence; for a 2 cm amplitude peak to peak, the volume ranged from +7.9% to
-3.0%, while for a 1 cm amplitude, the volume ranged from +5.3% to -0.20%.
52
Figure 4-3: Using the GE scanner, (a) coronal slice of static phantom; coronal slice
of phantom at 0% (exhale) phase for (b) 2 cm sine, (c) 2563 trace, (d) 2567 trace.
53
Figure 4-4: Volume of Sphere 1 for different traces as a function of respiratory phase
using the GE scanner. These volumes were computed using the GE Sim4D tools.
54
4.2.2
Philips CT Scanner
A 3D static scan of the phantom was performed using the Philips scanner. A coronal
slice of this static scan is shown in Figure 4-5a. All coronal slices of the phantom in
this section intersect the center of Sphere 1. The reason this image is upside down
relative to the images from the GE scanner in Section 4.2.1 is because the phantom
was placed on the couch in the opposite direction when using the Philips scanner.
Given that the objects of interest in the phantom are spherical, it does not matter
which direction the phantom enters the scanner. Sphere 1 is located on the bottom
left of the image in Figure 4-5a. Note that the convention with Philips is that 0%
phase is the inhale phase, and 50% phase is the exhale phase, which is opposite of
the convention used in this thesis for the GE scanner.
Figure 4-5 shows coronal slices of a static 3D scan of the phantom using the Philips
scanner, and coronal slices of 4D CT scans at 0% (inhale) phase using traces 2563,
2567, and 2 cm sine. Compared to the inhale 2563 scans using the GE scanner in
Figure 4-2, the Philips scans have fewer and less serious artifacts.
Figure 4-6 shows coronal slices of a static 3D scan of the phantom using the Philips
scanner, and coronal slices of 4D CT scans at 40% (close-to-exhale) phase using 2
cm sine, and at 50% (exhale) phase using traces 2563 and 2567. The 2 cm and 2563
scans performed quite well, as there is almost no difference in shape of the 2cm and
2563 spheres as compared to the static 3D scan. There is, however, some elongation
to Sphere 1 for the 2567 scan in Figure 4-6d.
4.2.3
Comparison of General Electric and Philips Scanners
It is interesting to compare the scans from the GE scanner to those from the Philips
scanner since the two scanners use different methods for 4D data acquisition as described in sections 3.1.1 and 3.1.2. The same phantom with the same mechanical
device that moves the phantom according to a specified breathing trace was used.
However, the GE scanner used the Varian RPM system to track phantom movement,
and the Philips scanner used the bellows (belt) device. All volume and center of mass
55
Figure 4-5: Using the Philips scanner, (a) coronal slice of static phantom; coronal
slice of phantom at 0% (inhale) phase for (b) 2 cm sine, (c) 2563 trace, (d) 2567 trace.
56
Figure 4-6: Using the Philips scanner, (a) coronal slice of static phantom; coronal
slice of phantom at 40% (close-to-exhale) phase for (b) 2 cm sine, and at 50% (exhale)
phase for(c) 2563 trace, (d) 2567 trace.
57
calculations in this section are done using Sphere 1.
Figure 4-7 shows the image volume of Sphere 1 as a function of phase from the GE
and Philips scanners using trace 2563. Table 4.2 shows the volume values. Although
the volumes at 20% through 60% for the Philips scanner are very close to ground
truth, the volumes for the rest of the phases are almost all greater than the maximum
of the volumes using the GE scanner. It is expected that the volumes would differ
from ground truth the most for phases around inhale (0% for Philips and 50% for
GE) given a trace with little baseline drift, but breathing cycle amplitude variation.
While the Philips scan follows this trend, the GE scan does not. In the GE scan, the
volumes straddle the ground truth line and do not come significantly closer to ground
truth at exhale phases. This behavior is explained by the breathing irregularity in
trace 2563 shown in Figure 4-1. The breathing irregularity during the GE scanning
of Sphere 1 affected the image reconstruction at all ten phases and caused significant
variation in volume for all ten phases.
Figure 4-7: Image volume of Sphere 1 using the GE and Philips scanner as a function
of respiratory phase for trace 2563.
Figure 4-8 shows the image volume of Sphere 1 as a function of phase from the
GE and Philips scanners using trace 2567. Table 4.2 shows the volume values. In
terms of volumes, the GE scanner produced images that are more accurate than those
produced by the Philips scanner; the volumes for the Philips scanner are consistently
much greater than ground truth, while the volumes for the GE scanner are much
58
closer, especially around the exhale phase of 0%.
Figure 4-8: Image volume of Sphere 1 using the GE and Philips scanner as a function
of respiratory phase for trace 2567.
Figures 4-9 and 4-10 show the image volume of Sphere 1 as a function of phase for
the two scanners using the 1 cm and 2 cm traces, respectively. (Note that the 2 cm
Philips plot only contains volumes for phases 0%, 10%, 20%, 30%, and 40%. Philips
DICOM data using the 2 cm trace for the rest of the phases was lost.) Table 4.2 shows
the volume values. Due to the regularity of the sine wave traces, the image volume
of Sphere 1 should be close to ground truth, as it is for the 1 cm sine trace. However,
the volumes for the 2 cm trace vary more than expected. For the GE scanner, the
volumes are the closest to ground truth at phases 0% and 50%, when the velocity of
the phantom is zero. This is also true for both scanners using the 1 cm sine wave, as
shown in Figure 4-9. The greater velocity of the phantom in between the inhale and
exhale phases contributed to some amplitude variation, resulting in a volume that
was greater than ground truth for these phases.
Figures 4-11 through 4-14 show the z-coordinate of the image center of mass
of Sphere 1 as a function of phase for the two scanners using the 2563, 2567, 1
cm, and 2 cm traces, respectively. The orientation of the coordinates is as follows:
the x-coordinate specifies the row of each axial slice from the DICOM data, the ycoordinate specifies the column of each axial slice, and the z-coordinate specifies the
cranial-caudal direction. Table 4.3 shows the z-coordinate values of the image COM
59
Figure 4-9: Image volume of Sphere 1 using the GE and Philips scanner as a function
of respiratory phase for 1 cm sine trace.
Figure 4-10: Image volume of Sphere 1 using the GE and Philips scanner as a function
of respiratory phase for 2 cm sine trace. Note that the Philips plot only contains
volumes for phases 0%, 10%, 20%, 30%, and 40%.
60
Table 4.2: Image volumes of Sphere 1 in cm3 for the GE and Philips scanners.
Phase (%)
0
10
20
30
40
50
60
70
80
90
GE
Philips
GE
Philips
GE
Philips
GE
Philips
GE
Philips
GE
Philips
GE
Philips
GE
Philips
GE
Philips
GE
Philips
Breathing Trace
2563 2567 1 cm 2 cm
91.9
86.9
85.3
85.0
107.0 97.2
85.6
86.1
92.3
91.1
86.7
89.7
94.1
95.2
86.0
87.8
92.2
87.5
87.2
97.5
85.0
91.4
87.1
90.8
90.9
86.5
85.8
87.1
85.2
92.2
87.3
91.4
85.0
79.6
87.2
88.9
82.0
95.5
86.4
89.1
81.1
80.8
85.0
85.1
83.8
96.7
85.7
79.8
83.6
85.8
90.9
86.4
96.8
86.8
94.6
84.8
86.0
89.1
94.1
98.2
87.8
95.7
86.3
88.3
90.0
102.2 98.6
87.8
93.4
86.9
88.4
86.6
107.6 98.8
86.5
-
61
Mean
S.D.
87.3
94.0
90.0
90.8
91.1
88.6
87.6
89.0
85.2
88.2
83.0
88.7
85.0
90.0
88.6
93.4
90.1
96.2
88.8
97.7
3.2
10.2
2.4
4.6
4.9
3.1
2.3
3.3
4.1
5.7
2.4
7.0
4.6
5.9
4.4
5.2
4.0
7.5
3.2
10.6
of Sphere 1 in cm.
The x-coordinate and y-coordinate of the COMs stay constant throughout all the
phases, which indicates there was no motion in the anterior-posterior direction nor
the lateral direction when using any of the four breathing traces. Also note that
the z-coordinate plots for the GE scanner appear to be inverted with respect to the
z-coordinate plots for the Philips scanner. This inversion happened because when
using the GE scanner, the RPM software inverts the convention so that 50% phase
is inhale (and 0% is exhale), which is opposite that of the Philips scanner having 0%
phase at inhale (and 50% at exhale).
Figure 4-11: Z-coordinate of Sphere 1 center of mass using the GE and Philips scanner
as a function of respiratory phase for trace 2563. X-coordinate and y-coordinate are
constant throughout all phases.
62
Figure 4-12: Z-coordinate of Sphere 1 center of mass using the GE and Philips scanner
as a function of respiratory phase for trace 2567. X-coordinate and y-coordinate are
constant throughout all phases.
Figure 4-13: Z-coordinate of Sphere 1 center of mass using the GE and Philips scanner
as a function of respiratory phase for 1 cm sine trace. X-coordinate and y-coordinate
are constant throughout all phases.
63
Figure 4-14: Z-coordinate of Sphere 1 center of mass using the GE and Philips scanner
as a function of respiratory phase for 2 cm sine trace. X-coordinate and y-coordinate
are constant throughout all phases. Note that the Philips plot only contains COMs
for phases 0%, 10%, 20%, 30%, and 40%.
Table 4.3: Z-coordinate of image center of mass (COM) of Sphere 1 in centimeters
for the GE and Philips scanners.
Phase (%)
0
10
20
30
40
50
60
70
80
90
GE
Philips
GE
Philips
GE
Philips
GE
Philips
GE
Philips
GE
Philips
GE
Philips
GE
Philips
GE
Philips
GE
Philips
Breathing Trace
2563 2567 1 cm 2 cm
6.5
6.4
6.1
5.6
18.9
18.6
18.8
19.7
6.5
6.5
6.2
5.8
18.7
18.5
18.8
19.6
6.6
6.8
6.4
6.3
18.2
18.3
18.6
19.2
6.9
6.9
6.7
7.1
18.0
18.1
18.3
18.7
7.1
7.0
7.0
7.3
17.8
18.0
18.1
18.2
7.1
6.8
7.1
7.5
17.8
18.0
18.0
6.9
6.7
7.0
7.3
17.9
18.0
18.0
6.9
6.6
6.7
6.9
18.1
18.0
18.3
6.7
6.5
6.3
6.3
18.3
18.1
18.5
6.5
6.4
6.3
5.8
18.6
18.5
18.8
-
64
Mean
S.D.
6.2
19.0
6.3
18.9
6.5
18.6
6.9
18.3
7.1
18.0
7.1
17.9
7.0
18.0
6.8
18.1
6.4
18.3
6.3
18.6
0.4
0.5
0.3
0.5
0.2
0.5
0.1
0.3
0.2
0.1
0.3
0.1
0.2
0.1
0.2
0.1
0.2
0.2
0.4
0.1
4.3
4.3.1
4D CT Simulations
Comparison of Simulations to Experiments
The 4D CT simulation produced results that were visually close to the experimental
results of Section 4.2. Figure 4-15a shows the simulation-generated image of Sphere
1 using breathing trace 2563 at inhale. Figure 4-15b shows the section of the 2563
breathing amplitude trace when slices were captured by the GE scanner at this phase,
and Figure 4-15c shows the corresponding phase assigned by RPM software. The
square wave in Figure 4-15b-c denotes when the x-ray beam was enabled (1 = beam
on, 0 = beam off). Crosses identify image acquisition points for each couch position.
The 4D CT image of Sphere 1 from the GE scanner (Figure 4-2c) is shown as an
inset in Figure 4-15. The reconstructed image is bounded by a series of circles that
represent the true position of the sphere at the moment each four-slice section was
acquired by the GE scanner.
The similarity of the simulation-generated image and the image from the GE
scanner suggests that the simulation was able to reproduce experimental results well.
In both images, the upper section of object is small, resulting from an amplitude that
was lower than at the other slice times, as shown by the amplitude plot. The next
three segments of the image are relatively artifact-free due to the reproducibility of
breathing amplitude. However, in both the actual and simulated images, the fifth
segment shows a severe artifact, caused by an amplitude variation that was much
greater than at the other slice times. Figure 4-15b shows an irregularity in breathing
during acquisition of the fifth segment. This significant variation led to an RPM error
in assigning phase, and as a result, the amplitude of Sphere 1 was much higher than
at the other image acquisition points for this phase.
The circles overlapping the reconstructed image in Figure 4-15a identify excursions
of the sphere at this (inhale) phase. The envelope of these regions represents the ITV2
bounds at this phase due to irregular breathing. The 4D CT reconstructed image by
itself does not account for the true positions of the object at all acquisition times, and
2
See Appendix A for the definition of internal target volume (ITV).
65
Figure 4-15: (a) 4D CT simulation image of Sphere 1 using 2563 respiration trace at
inhale phase, (b) 2563 amplitude trace, and (c) corresponding phase trace determined
by RPM software. Inset (upper left) shows the original 4D CT reconstruction image
of Sphere 1 from the phantom scan.
66
hence could be misleading when using the image to compute the ITV for subsequent
radiotherapy.
Assuming exact correlation between internal and external motion, and no deformation, the magnitude of the excursions of the object superior and inferior to the
image can be computed from the RPM trace. The excursion of the object superior to
the imaged region is equal to the difference between the amplitude of the first acquisition point and that of the subsequent acquisition point (indicated by the crosses in
Figure 4-15b) with the greatest amplitude out of all the acquisitions for this phase.
If the amplitude of the first acquisition point is the greatest, there is no excursion of
the object beyond the superior bound of the image. Similarly, if the last acquisition
captures the inferior end of the object, the excursion inferior to the image is equal
to the difference between the amplitude of the last acquisition point and that of the
acquisition point with the lowest amplitude out of all the acquisitions for this phase.
Again, if the last acquisition has the lowest amplitude, then there is no margin inferior
to the image.
Note that it is essential for this analysis that the first and last acquisitions capture
the superior and inferior ends of the object, respectively. If this is not the case, other
methods involving image registration may be required to ascertain the excursions
superior and inferior to the image.
4.3.2
Time Shift Simulations
In this section the results of shifting the start time of scanning using the 4D CT
simulation are examined. Because the quality of a 4D CT scan depends heavily on
the breathing behavior of a patient during scanning, starting the scan at a different
point in time along the breathing trace may produce an image with different artifacts.
Figure 4-16 shows the 4D reconstructed image of Sphere 1 using the 2563 trace at
inhale phase for different start times of scanning. In the experiment, the GE scanner
started scanning Sphere 1 at the fifth couch position, and the corresponding simulated
image is shown in Figure 4-15a. Figures 4-16a and 4-16b show results after starting
at the sixth and seventh couch positions, respectively. The breathing irregularity
67
mentioned in Section 4.1 still affects these two images since the irregularity occurs
during the data acquisition of Sphere 1. In Figure 4-16a, the irregularity causes the
amplitude of the object to be too high for the fourth section of the image, resulting
in the two gaps along the sides. In Figure 4-16b, the artifact from the breathing
irregularity is less noticeable. However, it is clear that at the third acquisition point,
the amplitude of Sphere 1 is greater than that of the other acquisition points.
Figure 4-16: Time shift 4D CT simulation images of Sphere 1 using 2563 respiration
trace at inhale phase. Results of starting the scan at the (a) sixth couch position, (b)
seventh couch position, (c) eleventh couch position, and (d) twelfth couch position.
Figures 4-16c and 4-16d show results after starting at the eleventh and twelfth
couch positions, respectively. At these segments in time, the breathing irregularity
mentioned in Section 4.1 does not appear, and the phase assignment software does a
reasonable job of assigning the correct phases to the trace. However, because these
68
images are reconstructed at the inhale phase, artifacts still exist due to the patient’s
inability to precisely reproduce his inhale amplitude. As a result, there is some
variation in the amplitudes during data acquisition, and the image appears slightly
elongated in Figures 4-16c and 4-16d.
4.3.3
Hysteresis
In this section hysteresis between internal organ motion and the external motion of
the abdomen is examined. This hysteresis is simulated by having the internal motion
lead the external motion by an interval of 0 to 250 ms.
Results of leading by 31, 63, 94, and 125 ms are shown in Figure 4-17, using the
2563 trace at inhale phase. Results of leading by 156, 188, 219, and 250 ms are shown
in Figure 4-18, also using the 2563 trace at inhale phase. The amplitude plots in
these two figures correspond to the true (internal) motion of Sphere 1, which leads
the external motion. The phase plots remain unshifted so that they are actually the
phases of an unshifted amplitude plot. As seen from these two figures, the overall
shape of the reconstructed image is largely the same for all the different delays. This
similarity is also reflected in the image volumes; the mean of the volumes for these
eight images is 77.6243 cm3 with a standard deviation of 0.6540 cm3 . The image
volume without any delay is 77.7420 cm3 . Given that the standard deviation is less
than 1 cm3 and that the difference between the mean and the volume without delay
is only around 0.1 cm3 , it is clear that these hysteresis delays do not perturb the
reconstructed image volume to a great extent.
4.3.4
Baseline Drift
Baseline drift in a breathing trace can cause the absolute amplitude of the imaged
object to vary for any given phase of breathing, even if the phase assignment software
is sufficiently accurate. The simulation was used to examine the resulting 4D reconstructed images by varying baseline drift in a controlled manner. Figure 4-19 shows
the reconstructed image of Sphere 1 at inhale phase using a 2 cm sine wave with a
69
Figure 4-17: Hysteresis 4D CT simulation images of Sphere 1 using 2563 respiration
trace at inhale phase. Results of using a hysteresis delay of (a) 31 ms, (b) 63 ms, (c)
94 ms, and (d) 125 ms.
70
Figure 4-18: Hysteresis 4D CT simulation images of Sphere 1 using 2563 respiration
trace at inhale phase. Results of using a hysteresis delay of (a) 156 ms, (b) 188 ms,
(c) 219 ms, and (d) 250 ms.
71
slope of 0, 0.0136, 0.0268, and 0.0400 cm/s. The image volume of Sphere 1 at inhale
phase as a function of baseline drift slope is shown in Figure 4-20.
Figure 4-19: Baseline drift 4D CT simulation images of Sphere 1 at inhale using a 2
cm sine wave with a slope of (a) 0 cm/s, (b) 0.0136 cm/s, (c) 0.0268 cm/s, and (d)
0.0400 cm/s.
As shown in Figure 4-19, the image flattens as the slope of the trace increases.
The flattening occurs because each subsequent acquisition point has an amplitude
that is greater than the previous point, so that the scanner actually misses a section
of Sphere 1 when going from one acquisition point to another. The image volume of
Sphere 1 plotted in Figure 4-20 mirrors this trend since the volumes decrease as the
slope of the trace increases. It is important to observe that although the reconstructed
image flattens as the slope of the trace increases, the excursions of the object become
larger. The circles overlapping each reconstructed image in Figure 4-19 represent
72
Figure 4-20: Image volume of Sphere 1 at 50% (inhale) phase as a function of the
baseline drift slope of a 2 cm sine breathing trace.
73
the true position of Sphere 1 at each acquisition point, and the union of the circles
clearly increases as the slope of the trace increases. This behavior is very problematic
for image-guided radiotherapy since the tumor will look smaller, while the margin of
tumor motion will actually be greater than even the true size of the tumor.
4.3.5
Arbitrary Object Simulations
In order to extend the simulation beyond the reconstruction of a perfect sphere,
the simulation was further developed to reconstruct objects of arbitrary size and
shape. The simulation takes in as input a 3-Dimensional matrix that represents the
3-Dimensional object to be reconstructed. To see how the simulation would perform
with respect to our experiments using the GE scanner, the static, 3D scan of Sphere
1 was used as the input object to our simulation. This input object is shown in
Figure 4-21.
Figure 4-21: Coronal cut of a 3D static scan of Sphere 1, which is used as input to
our simulation of arbitrary objects.
Figure 4-22 shows the reconstructed image from the simulation of arbitrary objects
74
using the static scan in Figure 4-21 as input. This simulation used trace 2563 at a
phase of 50% (inhale), and is very similar to the results depicted in Figure 4-15, which
used a sphere surface for reconstruction, and also very similar to the experimental
results from the GE scanner, depicted in Figure 4-2.
Figure 4-22: 4D CT simulation image of Sphere 1 using 2563 respiration trace at
inhale phase. The input object is the static 3D scan of Sphere 1, shown in Figure 421.
Figures 4-23 and 4-24 show the simulation results alongside the experimental
results for phases 10% and 80%, respectively. Although the simulation-reconstructed
images of Sphere 1 are very similar to the experimental results in both these figures,
there are some slight differences. These differences are due to an inherent limitation
of the GE scanner; the GE reconstruction software specifies that acquisition points
occur at discrete, evenly spaced points in each couch position, and at these points,
the phase may not be exactly equal to the desired phase for reconstruction. This
75
limitation is precisely the reason why the acquisition points do not all occur at 50%
in Figure 4-15c. In the simulation of arbitrary objects, data acquisition points occur
at precisely the phase specified by the user. Figures 4-22, 4-23, and 4-24 reflect this
behavior as the data acquisition points all occur at exactly the same phase.
Figure 4-23: The left side shows the 4D CT simulation image of Sphere 1 using the
2563 respiration trace at 10% phase. The right side shows the experimental result
from the GE scanner at 10% phase. The input object is the static 3D scan of Sphere
1, shown in Figure 4-21.
Although a sphere was used as input for these results, the input object can be
any arbitrary object. For example, it is possible to use 3D data from the DICOM
images of a regular CT scan as input for the simulation. A breath-hold helical scan
of a tumor can serve as input to the simulation since the scan would capture the
true shape of the tumor. Therefore, only the patient’s breathing trace recorded over
a period of approximately 4 to 5 minutes would be needed to produce a 4D CT
image of the tumor at different phases of breathing. This way, the patient would only
be exposed to radiation from a regular helical CT scan, rather than from a 4D CT
scan. Given that 4D CT scans generally expose the patient to more radiation than
a regular 3D scan of the same area, this process would be beneficial to the patient.
Additional analyses could also be performed, such as scan start time shifts, using the
simulation. Also, since the breathing trace is read in by a computer, the trace can be
manipulated to obtain the results from including additional baseline drift and other
76
Figure 4-24: The left side shows the 4D CT simulation image of Sphere 1 using the
2563 respiration trace at 80% phase. The right side shows the experimental result
from the GE scanner at 80% phase. The input object is the static 3D scan of Sphere
1, shown in Figure 4-21.
breathing irregularities.
4.4
Radiation Treatment Simulations
The 4D CT simulation was altered to simulate gated radiation treatment, as described
in Section 3.3. Using the breathing trace shown in Figure 4-25, there were definitely
points where the tumor was irradiated while partially outside the aperture, as shown
in Figure 4-26. Of course, it is important to note that a scale factor of 1 was used
to convert the breathing trace into tumor motion. If the actual tumor motion corresponds to a scale factor greater than 1, then even more of the tumor will not have
been irradiated at instances such as the one depicted in Figure 4-26.
77
Figure 4-25: Breathing trace of a patient undergoing gated radiation treatment. The
gating trace is in blue, dotted with red points where treatment commenced. The
amplitudes are not scaled by any factor, and an amplitude of 0 is the mean of the
entire breathing trace.
78
Figure 4-26: Radiation treatment simulation using the breathing trace in Figure 4-25
with the tumor depicted as the smaller circle and the aperture as the larger circle.
The square wave denotes when treatment commenced (1 = beam on, 0 = beam off).
79
80
Chapter 5
Concluding Remarks
5.1
Summary
The primary use of 4D CT is to create images of thoracic and abdominal tumors for
the purposes of developing accurate treatment for radiotherapy. Although 4D CT
produces accurate images when the patient’s breathing is regular, artifacts can occur
with irregular breathing and the resulting images can be misleading when used to
determine target margins. The simulation results in Figure 4-15 show that breathing
irregularities can produce 4D CT images that do not adequately describe the full
envelope of tumor locations at a given respiratory phase.
In order for 4D CT images to be used accurately for target margins, the breathing
trace of the scan should be examined along with the reconstructed image. Using the
GE scanner, the data acquisition points for a given respiratory phase can be found
by using the sorted and unsorted DICOM data and the RPM breathing trace. Once
these points are obtained, one can see how similar the amplitudes are to each other.
If they are very similar, the 4D CT image represents the tumor more accurately than
if they are not. In addition, the excursions superior and inferior to the image can be
found by using the analysis described in Section 4.3.1.
Regular helical CT scans of thoracic and abdominal tumors while the patient is
holding their breath can produce images very close to the actual shape of the tumor.
It is possible to use breathing monitor equipment such as the RPM system to monitor
81
a patient’s breathing without actually using the CT scanner to acquire any images.
If the patient is a very irregular breather, target margins may be more accurately
obtained by not doing 4D CT, but instead performing a breath-hold scan and examining the breathing trace of the patient, assuming the scale factor could be obtained.
Since the breath-hold scan provides an accurate representation of the shape and size
of the tumor, the breathing trace can be used to determine correct target margins
for each respiratory phase. This can be done by moving the tumor shape along the
breathing trace and taking a snapshot of the tumor at a given respiratory phase,
similar to what the simulation did in Figure 4-15. A 4D CT scan would probably
not be very accurate given that the patient is a particularly irregular breather. In
addition, by not 4D CT scanning the patient, the patient’s exposure to potentially
harmful radiation is reduced.
The inability of most patients to precisely reproduce an inhale amplitude explains
the lack of amplitude-phase correspondence at 50% phase in Figure 4-1. However,
Figure 4-10 shows that even for a near-perfect 2 cm peak-to-peak sinusoid breathing
trace, image volume can vary significantly from the true volume for phases in between
inhale (50%) and exhale (0%). This discrepancy is caused by the velocity of the object
while traveling between the inhale and exhale positions. Therefore, given the velocity
of the object and the inherent problems with inhale amplitude reproducibility, the
exhale phase is normally the best phase for accurate 4D CT reconstruction.
The time shift simulations in Section 4.3.2 reveal that, to some extent, the quality
of 4D CT scans can depend largely on luck. The images in Figure 4-16c and 4-16d
show the true shape of Sphere 1 quite well, and also represent the true envelope of
Sphere 1 positions for the given phase. The images in Figure 4-16a and 4-16b, however, show that the excursions of Sphere 1 exceed the bounds of the reconstructed
image. The starting times of these sets of images only differ by around 20 to 30
seconds. In fact, had the GE scan experiment using the 2563 trace at 50% started
a minute later, the resulting image would not contain the artifact due to the breathing irregularity, as discussed in Section 4.3.1. Patient breathing irregularities can
occur at specific points in time during scanning, and the quality of the resulting im82
age can depend on whether or not data acquisition happens to occur during those
irregularities.
The hysteresis results in Section 4.3.3 indicate that the time delay of internal and
external motion during breathing is not largely responsible for the artifacts in 4D CT.
In terms of image volume, the reconstructed images for different lag times did not
vary much from the reconstructed image without any lag time. Also, by qualitatively
examining the images, the overall shape and artifacts of the sphere do not change
significantly for different lag times. These results are promising because current 4D
CT technology does not take into account this time delay, and probably does not
need to for the purposes of radiotherapy.
Although 4D CT images are generally the most accurate at the exhale phase, baseline drift can still introduce significant artifacts. As shown in Figure 4-20, significant
variation in volume can occur with baseline drift. What is even more troublesome is
that reconstructed images for these simulations became smaller, while the envelope
of sphere locations became larger. This effect of baseline drift is yet another reason
why 4D CT images should be validated by subsequent examination of the breathing
trace produced during scanning.
Another problem arises from the fact that a patient’s breathing patterns at 4D
CT scan time may not be the same at treatment time. A multitude of factors such as
nervousness and environment differences, are responsible for this behavior. Therefore,
even if a 4D CT scan is accurately done and represents the full envelope of tumor
positions for a given respiratory phase, breathing irregularities during radiation treatment may hinder the proper irradiation of the tumor. Section 4.4 highlights some
of these problems. In Figure 4-25, it is clear that the operators changed the gating
window amplitude several times during treatment due to the irregular nature of the
patient’s breathing. The simulation showed that for a spherical tumor with radius
3 cm and an aperture with radius 3.5 cm, the tumor was irradiated while slightly
outside the aperture at certain instances during treatment.
83
5.2
5.2.1
Suggestions and Future Work
4D CT Algorithm Improvements
Artifacts in 4D CT images arise from the variation in amplitude of the object at a
given respiratory phase. Therefore, one way to improve the quality of these images
is to perform a conventional phase-based 4D CT scan, and then discard the fourslice sections of the image that correspond to acquisition points where the object’s
amplitude varied significantly from its amplitude at the other acquisition points for
that phase. Then, using a breath-hold scan to obtain a truthful representation of
the tumor shape, replace the missing sections with the appropriate sections. The
replacement sections are obtained by shifting the breath-hold tumor image to the
correct amplitude for that phase and taking four-slice sections of it that correspond
to positions of the missing sections in the 4D CT scan.
One problem with the phase-assignment software used by the RPM system is that
the phases are assigned in real time as the patient is being scanned. The software
uses an algorithm that predicts, with limited accuracy, when the trace amplitude
reaches its peaks to assign the 0% phase to those points. This task is much easier and
more accurately done once the entire trace is available. In other words, it is better to
perform data acquisition and breathing monitoring beforehand, then retrospectively
assign phases and resort the data. This way, no prediction is involved during phase
assignment; the software merely picks the peaks of the trace and assigns them to 0%
phase.
Amplitude-based resorting has the potential to solve the amplitude-phase variation that causes artifacts in phase-based 4D CT. In amplitude-based 4D CT, the
operator specifies an amplitude, instead of a phase, for image reconstruction. During
each couch position, the scanner is continuously acquiring data, similar to phase-based
4D CT. During reconstruction, data from each couch position is used for each section
of the image only if the amplitude of the object reached the specified amplitude. The
drawback of this approach is that the object may not reach the specified amplitude
for a given couch position and result in a missing section in the image. To counter
84
this, if the object does not reach the desired amplitude for a given couch position, the
operator may keep the couch at the same position to try and re-scan the same area
during the next beam-on segment. However, if the object does not reach the desired
amplitude again, this technique may result in the patient receiving an increase in
radiation exposure due to re-scanning.
One way to incorporate the benefits of amplitude-based 4D CT while mitigating
the disadvantages is to perform phase-based scanning, but amplitude-based resorting.
In other words, data is acquired in the same manner as phase-based 4D CT, where
areas are not re-scanned even if the object does not reach the desired amplitude at
a given couch position. Once all the data is acquired, the algorithm reconstructs
the image by choosing the acquisition points whose amplitudes match the desired
amplitude the closest. This way, the quality of the image does not depend on the
software’s ability to assign the correct phases to a breathing trace. In addition,
amplitudes at a given phase can vary even when the phase assignment is accurate.
Although this method does not guarantee artifact-free 4D images, it minimizes the
problems with amplitude-phase variation. Artifacts will still occur when the object
does not reach the desired amplitude at some couch position. However, on the whole,
this retrospective amplitude-based resorting should perform better than pure phasebased resorting.
5.2.2
Simulation Improvements
Although most internal organ motion during breathing is in the cranial-caudal direction, there is some anterior-posterior and lateral motion that occurs. It would
be interesting to perform simulations with these added degrees of freedom of motion.
The 4D CT simulation outlined here can be extended to receive two additional breathing traces that correspond to motion in the anterior-posterior and lateral motions.
However, monitoring internal organ motion from patients in these two additional
directions is difficult, and requires additional technology such as ultrasound or fluoroscopy. Another option would be to use contrived sinusoids for the two additional
directions of movement.
85
In the sphere surface simulations described in Section 3.2.1, circles representing the
true positions of the sphere at data acquisition points are drawn over the reconstructed
image. This feature is useful for examining the envelope of tumor positions at a given
respiratory phase. It would be useful to add this functionality to the arbitrary object
simulation. One way is to produce a second image, along with the one shown in
Figure 4-22, with the same field of view as the one shown in Figure 4-22 and displays
snapshots of the arbitrary object overlapped on top of each other. For example, for
the first acquisition point, the image is saved while it is at that amplitude. For the
next acquisition point, a snapshot of the object is taken at that amplitude, and the
snapshot is overlapped onto the previously saved snapshot by taking the maximum
intensity value for each voxel between the two snapshots. Each subsequent acquisition
point is treated similarly. The resulting image should give an envelope of the positions
of the arbitrary object for the given respiratory phase.
Section 5.1 describes a method of using a breath-hold scan and a breathing trace
to determine an accurate target margin without the use of 4D CT. The arbitrary
object simulation, once it has the functionality of displaying the envelope of object
positions, could be used to automate this method. The simulation would accept,
among other parameters, the breath-hold scan, which is already in 3-Dimensional
format, the patient’s RPM breathing trace, and a respiratory phase for reconstruction,
and produce a 3-Dimensional envelope of tumor positions for each phase. The result
would provide radiation oncologists and dosimetrists with a good understanding of
the patient’s tumor motion.
One disadvantage of the 4D CT simulations that were implemented is that deformation of internal organs during breathing is not addressed. Deformation could cause
the tumor to change shape at different respiratory phases and affect the simulations’
accuracy. Deformation may be an inherent flaw of the simulations due to the difficult
nature of deformation simulation and prediction. A crude method of deformation
simulation would be to use image registration techniques to “squeeze” or “stretch”
the object into different sizes at different phases. For example, if it is known that
internal organs compress slightly at the inhale phase, the simulation could “squeeze”
86
the object by a slight amount before acquiring a four-slice section for reconstruction.
However, it is difficult to determine how much to adjust the object at different phases
until further research is completed.
5.2.3
Alternative Methods of Quantifying 4D CT Error
Image volume was primarily used to quantify error in the reconstructed 4D CT images.
However, there are some problems with using volume. It is possible for an image
to have a volume that is very close to the ground truth volume while still having
significant artifacts. For example, using the GE scanner, four-slice sections could be
acquired in such a way that the entire object is covered with no parts imaged more
than twice, but in the wrong order. In other words, the entire object is present, but
each four-slice section of it is stacked together in the wrong order. Of course, in the
case of tumors shaped like a perfect cylinder aligned in the cranial-caudal direction,
the reconstructed image would resemble the true size and shape of the tumor exactly.
However, it is very unlikely that many tumors will exhibit the perfect symmetry of
that situation.
Using the arbitrary object simulation, the error of reconstructed images could be
quantified by keeping track of image voxels in the input object, and by keeping track
of the order in which they are acquired. One way to implement this is to use a 3Dimensional matrix of zeroes with the same dimensions as the input object, and to
keep track of an “error count,” which starts out at zero. At each acquisition point,
the simulation adds one to each voxel in the zeroes matrix with coordinates the same
as a voxel that is being acquired in the input object matrix. In addition, at each
acquisition point, the simulation checks to see if there are any non-zero voxels inferior
(caudal) to the section being imaged. If there are, it adds the number of object
voxels1 contained in the current four-slice section to the error count. After the image
is reconstructed, the simulation counts the number of voxels with a value not equal
1
An object voxel is defined in this thesis as a voxel in the 3-D image that is part of the object.
Not all the voxels acquired during an image acquisition contain the actual object. Object voxel refers
to the ones that do.
87
to one, and adds this number to the error count.
Using this method of error quantification, a large error count would correspond to
an image containing many under-imaged or over-imaged voxels, and/or voxels imaged
in the wrong order. In the previous case where the volume of the reconstructed
image happens to be the same as ground truth, the artifacts can still be captured
and quantified by the simulation. Note that during each acquisition point, if there
are voxels inferior (caudal) to the current acquisition that were already imaged, the
simulation adds the number of object voxels in the current acquisition section to the
error count, and not the number of object voxels already imaged and inferior to the
current acquisition. Furthermore, it does not check the voxels superior (cranial) to
the current acquisition. These rules ensure that in the case where there is a large
contiguous chunk of the object that appears in the right order, the error count is less
than if more sections of the object are in the wrong order.
Another method of error quantification is to use non-rigid image registration to
match a 4D CT image to a static scan of the object. Images with more significant
artifacts would require a larger number of displacement vectors, and/or displacement
vectors with greater magnitude to register to the static scan. These displacements
would allow proper quantification of the error contained in a 4D CT image.
88
Appendix A
Glossary of Terms
acquisition amplitude. The acquisition amplitude of an axial four-slice section acquisition is the cranial-caudal position of that axial acquisition with respect to
the point on the couch that corresponds to an object amplitude of zero.
amplitude. The amplitude of an object at any given time is the amplitude of that
object along the scale factor included RPM breathing trace at that time. The
scale factor included RPM trace specifies the cranial-caudal (internal organ)
motion along the couch surface. Therefore, object amplitude refers to the motion
amplitude of the object and corresponds to the position of the object along the
couch surface.
aperture. In radiotherapy, the aperture refers to the cross-sectional area of the target
from the beam’s point of view that receives a radiation treatment beam.
baseline drift. Baseline drift in a breathing trace refers to the gradual change in
the baseline of the trace over time. Baseline drift is determined visually by
examining the exhale points along the trace. If the line connecting the exhale
points fluctuates to a certain degree (as opposed to being horizontal), the trace
exhibits baseline drift.
breathing trace. A breathing trace is a plot of the patient’s abdominal surface amplitude as a function of time. A Varian Real-time Position Management (RPM)
89
breathing trace is obtained in the form of a text file that contains the abdominal
surface amplitude for each point in time, the phase information of each point
in time, and x-ray on or off information for each point in time.
cine mode 4D CT. In cine mode 4D CT, the couch is stationary for approximately
5 seconds while the scanner continuously acquires CT projection data. The xray beam is turned off when the couch translates to the next position.
coronal cut. A coronal cut is a plane that transects a human body’s anterior from
its posterior. For example, a coronal cut of the head is a cut that travels from
ear to ear, parallel to the suture extending across the skull between the parietal
and frontal bones.
couch position. In cine mode 4D CT, a couch position is the position of the couch
when the scanner is acquiring data. Couch position can also refer to the interval
of time in which the couch is stationary and the x-ray beam is acquiring images.
helical mode 4D CT. In helical mode 4D CT, the couch moves very slowly as the
scanner continuously acquires projection data, and the x-rays are never turned
off. The x-ray tube traces a helical path around the patient.
internal target volume (ITV). The internal target volume (ITV) refers to the
volume formed by the Clinical Target Volume and an internal margin. The
ITV includes the gross tumor, additional areas of high risk of disease, and a
margin to accommodate organ motion.
reconstruction. In this thesis, 4D CT image reconstruction of an image or object
refers to the process of resorting the DICOM images from the scanner to form
a 4D CT image at a given phase. This is distinct from its meaning in CT
reconstruction from projection data.
scale factor. In 4D CT, anterior-posterior abdominal surface motion is assumed to
correlate well with the cranial-caudal motion of internal organs. Since the RPM
breathing trace tracks the patient’s abdominal surface amplitude as a function
90
of time, the RPM breathing trace is multiplied by a scale factor to convert it
into the cranial-caudal internal organ motion.
91
92
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