Optimization of Beam Spectrum and Dose for Lower-Cost CT. Mary Esther Braswell. Graduate Program in Medical Physics Duke University.

Transcription

1 Optimization of Beam Spectrum and Dose for Lower-Cost CT by Mary Esther Braswell Graduate Program in Medical Physics Duke University Date: Approved: James Dobbins, Supervisor Anuj Kapadia Robert Reiman Paul Segars Thesis submitted in partial fulfillment of the requirements for the degree of Master of Science in the Graduate Program in Medical Physics in the Graduate School of Duke University 2016

2 ABSTRACT Optimization of Beam Spectrum and Dose for Lower-Cost CT by Mary Esther Braswell Graduate Program in Medical Physics Duke University Date: Approved: James Dobbins, Supervisor Anuj Kapadia Robert Reiman Paul Segars An abstract of a thesis submitted in partial fulfillment of the requirements for the degree of Master of Science in the Graduate Program in Medical Physics in the Graduate School of Duke University 2016

3 Copyright by Mary Esther Braswell 2016

4 Abstract In many parts of the developing world, easy access to volumetric imaging is not available. A Lower-Cost CT setup was proposed and found feasible by Dobbins et al. [1], but was not yet optimized to maximize image quality while minimizing radiation dose to the patient. A combination of spectrum modeling and Monte Carlo simulations were used to compare x-ray beam parameters to determine which combination was optimal. The beam parameters considered were filter type, filter thickness, and tube peak kilovoltage (). The optimization was based on the differential signal-to-noise ratio (dsnr) and the dose, using a factor referred to as dsnr Efficiency. After the three different filter materials at three different thicknesses were compared across five different values, it was determined that one half-value-layer (HVL) of copper was the best filter type and thickness to achieve maximum image quality for minimal patient dose. In order to verify that a good dsnr efficiency using the spectrum modeling and Monte Carlo meant that the system would provide useable images, the extended cardiac-torso (XCAT) phantom was used to simulate CT images, using a ray tracer, and estimate dose, using a full LCCT Monte Carlo simulation. The ray-tracer produced x-ray projections of the XCAT phantom which were then run through a Feldkamp reconstruction algorithm to produce CT images. The full LCCT Monte Carlo simulation iv

5 modeled the LCCT setup using the XCAT phantom to determine the dose to the patient. From the reconstructed CT images, it was determined that for image studies that favor air contrast higher values, such as 140, are optimal. For studies that favor bone contrast, however, the lower values, such as 60 or 80, are optimal. For 140 images, the average effective dose, calculated using the ICRP 103 protocol, was '( msv per mas. The average effective dose for 60 was '+ msv per mas, and the average effective dose for 80 was '( msv per mas. Further work is needed to determine optimal mas values for different imaging studies. The LCCT setup can provide volumetric imaging to developing parts of the world that currently have no volumetric imaging, which would greatly improve the quality of readily available medical care. v

6 Dedication This thesis is dedicated to my parents, Randy and Claire Braswell, for their unconditional love and support through every stage of my life; my siblings, Sarah, Luke and his wife, Brianne, and Anna Braswell, for always looking out for me and pushing me to be my best; and my countless friends, for being there when I needed them. This thesis is also dedicated to my nephew Elijah, to hopefully inspire him to never let anything get in the way of his dreams. vi

7 Contents Abstract... iv List of Tables... ix List of Figures... x List of Abbreviations... xiii Acknowledgements... xiv 1. Introduction Lower-Cost CT Image Quality Contrast Signal to Noise Ratio Resolution Image Quality and Dose Spectrum Modeling Monte Carlo XCAT Parameter Optimization Spectrum Modeling Methods DXSPEC Penelope Spectrum Modeling Results vii

8 2.2.1 Dose, Signal, and Noise Results dsnr and dsnr Efficiency Results Spectrum Modeling Discussion and Conclusions DXSPEC and Penelope Dose, Signal, and Noise Comparisons DXSPEC and Penelope dsnr Comparisons Final Spectrum Modeling Discussion and Conclusions CT Dose Simulation and Image Reconstruction Simulation and Reconstruction Methods XCAT Projector Methods Image Reconstruction Methods LCCT Simulation Methods Simulation and Reconstruction Results Imaging Results Simulation Results Simulation and Reconstruction Conclusions and Discussion Conclusions References viii

9 List of Tables Table 1: 1 and 2 HVL thicknesses for copper, aluminum, and gadolinium Table 2: XCAT Projector Input Parameters Table 3: XCAT Phantoms used in the XCAT projector Table 4: MATLAB CT reconstruction input parameters Table 5: TCM Simulation Input Parameters Table 6: Dose to Lung and Effective Dose results for each phantom and value combination ix

10 List of Figures Figure 1: Example DXSPEC output file Figure 2: Example projection from XCAT projector Figure 3: Example reconstructed CT image from 180 XCAT projections Figure 4: Penelope geometry setup from both the (a) beam s eye view and (b) the side. 21 Figure 5: The dose to 25 cm of tissue from an x-ray beam filtered by 1 HVL of aluminum Figure 6: Dose to 25 cm tissue from an x-ray beam filtered by 1 HVL of copper Figure 7: Dose to 25 cm of tissue from an x-ray beam filtered by 1 HVL of gadolinium. 25 Figure 8: Dose to 25 cm of tissue from an unfiltered beam Figure 9: Dose to the detector for the tissue setup and 1 HVL aluminum filter Figure 10: Dose to the detector for the tissue setup and 1 HVL copper filter Figure 11: Dose to the detector for the tissue setup and 1 HVL gadolinium filter Figure 12: Dose to the detector for the tissue setup and no filter Figure 13: Dose to the detector for the bone setup and 1HVL aluminum filter Figure 14: Dose to the detector for the air setup and 1HVL aluminum filter Figure 15: Dose to the detector for the bone setup and 1HVL copper filter Figure 16: Dose to the detector for the air setup and 1HVL copper filter Figure 17: Dose to the detector for the bone setup and 1HVL gadolinium filter Figure 18: Dose to the detector for the air setup and 1HVL gadolinium filter Figure 19: Dose to the detector for the bone setup and no filter Figure 20: Dose to the detector for the air setup and no filter x

11 Figure 21: Tissue setup detector noise for 1 HVL aluminum filter Figure 22: Tissue setup detector noise for 1 HVL copper filter Figure 23: Tissue setup detector noise for 1 HVL gadolinium filter Figure 24: Tissue setup detector noise for no filter Figure 25: dsnrbone values for 1 HVL aluminum filter Figure 26: dsnrbone values for 1 HVL copper filter Figure 27: dsnrbone values for 1 HVL gadolinium filter Figure 28: dsnrbone values for no filter Figure 29: dsnrair values for 1 HVL aluminum filter Figure 30: dsnrair values for 1 HVL copper filter Figure 31: dsnrair values for 1 HVL gadolinium filter Figure 32: dsnrair values for no filter Figure 33: Calculated dsnrbone Efficiency values from DXSPEC for 1 HVL filters Figure 34: Calculated dsnrbone Efficiency values from Penelope for 1 HVL filters Figure 35: Calculated dsnrair Efficiency values from DXSPEC for 1 HVL filters Figure 36: Calculated dsnrair Efficiency values from Penelope for 1 HVL filters Figure 37: Calculated dsnrbone Efficiency values from DXSPEC for 2 HVL filters Figure 38: Calculated dsnrair Efficiency values from DXSPEC for 2 HVL filters Figure 39: Combined dsnrbone efficiencies for 1 HVL filters Figure 40: Combined dsnrair efficiencies for 1 HVL filters Figure 41: Reconstructed CT images for Female 1 phantom for (a) 60, (b) 80, (c) 100, (d)120, and (e) xi

12 Figure 42: Reconstructed CT images for Female 2 phantom for (a) 60, (b) 80, (c) 100, (d)120, and (e) Figure 43: Reconstructed CT images for Male 1 phantom for (a) 60, (b) 80, (c) 100, (d)120, and (e) Figure 44: Reconstructed CT images for Male 2 phantom for (a) 60, (b) 80, (c) 100, (d)120, and (e) Figure 45: dsnrbone Efficiencies calculated using lung dose for each phantom Figure 46: dsnrbone Efficiencies calculated using effective dose for each phantom Figure 47: dsnrair Efficiencies calculated using lung dose for each phantom Figure 48: dsnrair Efficiencies calculated using effective dose for each phantom xii

13 List of Abbreviations CT OECD LCCT CBCT Gy SNR dsnr ma s CsI XCAT NCAT NURBS ED msv Computed Tomography Organization for Economic Co-operation and Development Lower-Cost CT Cone-Beam CT Gray Peak Kilovoltage Signal to Noise Ratio Differential Signal to Noise Ratio Milliamperes Second Cesium Iodide Extended Cardiac-Torso Phantom 4-D NURBS-Based Cardiac-Torso Phantom Nonuniform Rationale B-splines Effective Dose Millisievert xiii

14 Acknowledgements I would like to express my sincerest thanks to: Dr. James Dobbins for being my advisor; Dr. Anuj Kapadia for being my co-advisor; Dr. Paul Segars for helping me with the XCAT phantom and serving on my committee; Dr. Robert Reiman for serving on my committee; Dr. Jered Wells for helping me with CT reconstructions; Dr. Greeshma Agasthya, Yakun Zhang, and Wanyi Fu for helping me with Penelope; Brian Harrawood for helping me fix computer problems; Karen Kenna for scheduling all my meetings with Dr. Dobbins and for being an encouragement every time I saw her; and finally, the Duke Medical Physics and RAI Lab communities for fostering a collaborative work environment. Thank you. xiv

15 1. Introduction The advances in healthcare in the past century have been phenomenal. In just the last fifty years, specifically in the area of medical imaging, many new imaging modalities have been invented and implemented in state-of-the-art healthcare facilities [2]. One of the most notable of these modalities is Computed Tomography (CT). CT is a volumetric imaging modality that uses x-rays to acquire projection images at different angles around the patient, then uses a reconstruction algorithm to produce an image in the transverse plane. With CT images, physicians can distinguish between structures that would appear overlapped and indistinguishable on conventional x-ray radiograph images. For some cases, an x-ray radiograph is sufficient to diagnose patients; however, there are many cases in which the x-ray radiograph does not have enough information to correctly diagnose a patient. Volumetric imaging, specifically CT imaging, provides better patient care through better diagnostic abilities. Most healthcare facilities in the United States have access to at least one CT scanner; in fact, according to data from the Organization for Economic Co-operation and Development (OECD), in 2013 there were 43.4 CT scanners per million people in the United States [3]. Compared to the other countries surveyed by OECD in 2013, the United States had the second highest number of CT scanners per million people, second only to Australia. The trend of easily accessible CT scanners is a common theme in the developed world; the developing world, however, does not have this capacity at 1

16 present. According to the Global Health Observatory through the World Health Organization, in 2013 out of the 37 African countries surveyed only 9 countries had 1 or more CT scanners per million people and 3 countries had no CT scanners at all [4]. CT scanners are less predominant in developing countries primarily because of their cost. A state-of-the-art CT scanner can cost upwards of $2.5 million. However, people in the developing world often don t have easy access to a CT scanner which limits the ability to provide optimum medical care for them unless they travel great distances to a facility that does have CT. These trips can be costly and difficult and cause hardships for the patients and their families. The proposed solution to this problem is a Lower-Cost CT (LCCT), which would make volumetric imaging more easily accessible in the developing world. 1.1 Lower-Cost CT One of the most expensive parts of a CT scanner is the slip-ring gantry which allows the x-ray source to rotate continuously around the patient. A potential solution has been proposed: instead of using a fan beam and rotating the source and detector around the patient, use a stationary source and detector and rotate the patient between the source and the detector, acquiring the images with cone beam CT (CBCT) [1]. The rotation is accomplished through a rotating stage, which a patient stands or sits on, which makes 1 rotation in approximately 10 seconds. The source and detector are set up like a conventional x-ray setup, with the rotating stage in the middle. Previous work [1] 2

17 on this design has found that this is a feasible setup; however, when the initial feasibility study was performed, there were two main concerns. The first concern is patient motion. One patient rotation takes 10 seconds, which makes it very difficult for the patient to remain completely still. Patient motion can cause artifacts in the image, which could potentially cause the images to be no more or possibly even less useful than conventional x-ray images. An algorithm has been developed that reduces image artifacts due to patient movement [5]. This algorithm uses markers on the patient to track patient movement, then makes the adjustments in the reconstruction, so the images appear as if the patient had not moved. The second concern is patient dose. Absorbed dose is defined as the amount of energy absorbed in a unit mass of a tissue and has units of gray (Gy). Effective dose (ED), which is a better index of overall risk to the patient, is a weighted average of organ absorbed doses. It is important to know if the LCCT setup delivers a dose that falls within an accepted clinical dose range. In order to help the system operate within these dose limits, the spectrum can be optimized to achieve the best image quality for the lowest dose to the patient. 1.2 Image Quality In order to optimize the dose, the beam parameters that affect dose have to be optimized. However, the beam parameters that affect dose also affect the image quality. 3

18 By definition, image quality is a measurement of the usability of an image. There are several different measures of image quality Contrast One measure of image quality is the contrast. Contrast is defined as the relative difference between the measured signal in an object and the measured signal in the background, as seen in Equation 1. Contrast allows the differentiation of objects in an image. The higher the contrast the more easily objects can be distinguished from other objects. Signal in Target Signal in Background Contrast = Signal in Background 1 The amount of the x-ray beam that reaches the detector and gets measured as signal is determined by how much of the beam gets attenuated in the body. Attenuation coefficients for tissues are greater at lower energies than at higher energies [6]. This means that at lower beam energies, the contrast is higher than it is at high energies. The beam energy is determined by the x-ray tube peak kilo-voltage () and the amount of filtration in the beam, from both the externally imposed filter material and the patient. Although the contrast increases as decreases, if the is too low, most of the photons from the x-ray beam are attenuated in the patient and few make it to the detector. This means there is not enough signal to create a useful image unless dose is unnecessarily high. 4

19 1.2.2 Signal to Noise Ratio Another measure of image quality is the signal to noise ratio (SNR). The SNR compares the signal of the image to the amount of noise in the image, as seen in Equation 2. Image noise limits the ability to discern objects of interest the image. Usually noise makes an image look grainy, or mottled, which is caused by the fluctuations of incident photons on the detector [7]. Noisy images are not very useful because the noise makes it difficult to distinguish objects in an image. Raw Signal SNR = Noise 2 SNR is a good measure of image quality; it provides information on the visibility of the actual image compared to the noise in that image, but it doesn t provide any information on the difference between the signal in two different objects in the image. The differential SNR (dsnr), as seen in Equation 3, measures the difference between signal in an object and its background, or between two objects, and then compares that difference in signal to the noise in the image, providing information about the SNR of the anatomical object of diagnostic interest. Signal in Object 1 Signal in Object 2 dsnr = Noise 3 The signal in the detector is affected by the x-ray tube output. The parameters that contribute to x-ray tube output are the, tube current, measured in milliamperes (ma), and how long the beam stays on, measured in seconds (s). In diagnostic imaging, the product of tube current and beam time is referred to as the mas. 5

20 Since the noise increases as the raw signal increases, in order to generate the best images, the optimal dsnr must be found. The optimal dsnr will maximize the differential signal while minimizing noise Resolution Spatial resolution is a measure of how easily small features that are close together can be distinguished from each other. At high spatial resolution small features are more easily distinguished than those same features are at low spatial resolution. Although spatial resolution is important, it was not considered in this spectrum optimization study Image Quality and Dose As stated earlier, the same parameters that affect image quality also affect dose. Patient dose depends on tube output parameters, such as and mas. Other parameters that affect dose and image quality are beam filter type and beam filter thickness. Putting a filter in the beam can harden the beam by removing the low-energy portions of the x-ray spectrum that is produced by the x-ray tube, or, in the case of a k- edge filter, can lower the average beam energy. Beam hardening increases the beam mean energy, which decreases the dose for a given detected signal, because greater absorption of lower energy photons in the filter reduces their absorption in the patient. The filter type and thickness determine how much of the beam is removed from the spectrum. 6

21 In order to find the optimal spectrum, there must be a way to compare the image qualities of different x-ray spectra while also taking into consideration the amount of radiation dose the patient is receiving. One way to do this is to calculate the efficiency, which is defined here as the ratio of the squared dsnr to the patient dose This factor is referred to as dsnr efficiency. This efficiency value allows for simultaneous optimization of image quality and dose. 1.3 Spectrum Modeling The x-ray beam spectrum affects both image quality and patient dose. The beam spectrum represents the number of photons found at each energy in the x-ray beam. The shape of the spectrum is effected by the filter material, the filter thickness, the tube, and the tube mas. Each parameter produces a spectrum that has a different shape. These different shapes cause the beam to interact differently through the patient. For example, a spectrum that has a peak at lower energies, has a lower mean energy which causes a higher patient dose and lower signal than if the peak in the spectrum had been at a higher energy. The spectrum needs to be optimized in order to reduce unnecessary patient dose and achieve the best image. In order to compare many different beam parameter combinations and determine the optimal dsnr Efficiency without having to physically run each combination, a spectrum modeling program can be used. A spectrum modeling program uses a mathematical method to estimate the x-ray spectrum based on given parameters. The 7

22 mathematical method uses tabulated attenuation coefficients of the relevant materials in the beam to determine the beam spectrum as it passes through the various filters and the patient. DXSPEC is a spectrum modeling program designed specifically for diagnostic x-ray spectra developed by Ergun et al. in 1977 [8]. DXSPEC accounts for Compton and coherent scattering and photoelectric effect. DXSPEC also models secondary interactions, such as k-fluorescence and single Compton cascades. Originally DXSPEC was used to model a general x-ray tube x-ray spectrum including bremsstrahlung and characteristic x-rays, but was later modified by Dobbins to include empirical tube spectra that had been modeled by Boone and Seibert [9, 10]. Dobbins also modified DXSPEC to generate an estimate of expected noise, calculated by summing the energy weighted variances from each energy bin [9]. The modified version of DXSPEC can be used to estimate the signal, noise, and dose for any filter combination. DXSPEC outputs the attenuated exposure, fluence, and mean energy; the transmitted exposure, fluence, and mean energy; and the energy absorption noise, dose, and mean energy for each material placed in the beam as seen in Figure 1. DXSPEC considers every material placed in the beam a filter. By inputting the target material, thicknesses of various tissues, and detector composition, such as cesium iodide (CsI), the dsnr can be calculated from the values that DXSPEC outputs. 8

23 Figure 1: Example DXSPEC output file. DXSPEC outputs absorbed energy (*) and absorbed energy (**) estimates for each filter. The absorbed energy (*) value assigns the absorbed energy to the bin of the incident photon, while the absorbed energy (**) value assigns absorbed energy to the composite total of estimated initial and secondary absorption events. This means that the expected dose and signal in real-life will likely fall between these two points. In previous studies using DXPEC, DXSPEC was found to be accurate for attenuation values, but the noise and tissue dose values had not been validated. Since the dose values had not been validated, and dose is a very important aspect of this work, it was necessary to validate the DXSPEC dose results. An established technique to accurately estimate dose is Monte Carlo. 9

24 1.4 Monte Carlo The Monte Carlo method uses random numbers to model very complex mathematical processes. The term was first used by scientists in the 1940s who were working on nuclear weapons. Monte Carlo is used in many fields, including physics, to model complex equations and problems. In physics it can be used to model the path of a particle through a material. Monte Carlo simulations can use the probability distribution of interactions between a particle and a material to estimate the interactions of multiple particles. The Monte Carlo code is set up to use a random number each time something different could happen. For example, a Monte Carlo code following a photon interacting in water would use a random number to determine the energy of the photon, then use another random number to determine whether the photon was absorbed in the water, then another random number to determine if there were any secondary reactions, and so on until there are no more possible interactions. The decisions made by the random numbers are based on the probabilities supplied to the Monte Carlo code. For example, consider the interaction of an x-ray beam with water. The energy of each randomly-generated photon would be determined from the input spectrum, and whether the photon was absorbed by the water would be determined using the probability distribution of the photoelectric and Compton attenuation coefficients for water. 10

25 Many Monte Carlo packages, which are already set up to model interactions of particles with materials, are available. One available Monte Carlo package is PENELOPE, which stands for Penetration and Energy Loss from Positrons and Electrons. PENELOPE was developed in 2001 by Salvat et. al. to model electron and photon transport [11]. PENELOPE is very useful for diagnostic imaging and radiation therapy dosimetry simulations because it effectively models photon and electron transport through the body at those energies to high accuracy. Like everything, Monte Carlo has limitations. The main limitation of PENELOPE is that it is not an ideal way to acquire projection data because it would take much longer than other programs, such as ray tracing programs, to simulate enough particles to generate an image. Since DXSPEC does not produce as sophisticated a model of dose as does Monte Carlo methods, PENELOPE can be used to model the same simple setup as DXPEC to produce a more accurate measurement of dose. This allows the dsnr efficiency to be a more accurate measure than if only DXSPEC was used in its calculation. PENELOPE can also be used to model the entire LCCT setup, so that an estimate of dose to a phantom from a LCCT scan can be obtained. The PENELOPE simulation can be set up to model a CBCT x-ray tube output to rotate around a phantom and take projections at 180 different angles. This allows the dose to the phantom to be calculated. The geometry package that is included with PENELOPE allows a user to specify geometries made of quadratic surfaces. This geometry package makes it difficult to 11

26 generate complicated phantoms, such as the human body, however, PENELOPE can also use a pre-generated voxelized phantom. This means that an anthropomorphic phantom can be incorporated into the simulation and the dose to a person can be estimated with high precision. 1.5 XCAT There are three main types of anthropomorphic phantoms: mathematical, voxelized, and hybrid. The mathematical phantom can model motion, but is a very crude rendering of human anatomy. Voxelized phantoms, on the other hand, are developed from patient CT data, so they model human anatomy very well, but they do not model motion and they do not exist for a wide variety of patient body types and sizes. The hybrid phantom is made up of the best qualities of the mathematical and voxelized phantoms; it models human anatomy very well and models motion. One such hybrid phantom developed by Segars et al. is called the extended Cardiac-Torso (XCAT) phantom [12]. The XCAT is an extended version of the 4-D NURBS-Based Cardiac-Torso (NCAT) phantom. NURBS, or nonuniform rational B- splines, are used in computer graphics to model complicated surfaces, making it possible to model complex anatomical structures correctly. The NCAT phantom was developed using the Visible Human data from the National Library of Medicine. The NCAT only models the torso, but allows for cardiac and respiratory motion. The NCAT can be male or female; however, was only modeled from the male Visible Human data 12

27 set. The female phantom adds breast models to the male torso. The NCAT has the ability to model different patient sizes by scaling the anatomy of the Visible Human data set. The XCAT expands the NCAT to include the entire body. Although it was also modeled using the Visible Human data, there are variations of the XCAT to model different humans, based on clinical CT data. The XCAT models anatomical surfaces better than the NCAT by using subdivision surfaces along with NURBS surfaces. The subdivision surfaces better model certain structures in the brain and breast by taking a rough polygon mesh and subdividing it until the surface becomes smooth. A female XCAT was developed from the female Visible Human data and patient CT scans, and better breast models have been developed through high resolution dedicated breast CT data. The XCAT phantom also improves the NCAT phantom by using a higher resolution heart motion data set and a higher resolution lung motion data to model heart and respiratory motion. The XCAT can easily be used in Monte Carlo simulations, like PENELOPE, and can be easily imaged. A CT simulation for the XCAT phantom has been developed by Segars et al. [13]. The CT simulation uses ray tracing to produce projections of the XCAT phantom from different angles. This CT simulation models parallel, fan, and cone beam CT. The CT parameters can be changed to simulate any CT setup, including the LCCT [12-14]. An example projection image of the XCAT CT simulation can be found in Figure 2. 13

28 Figure 2: Example projection from XCAT projector. The projections from the CT simulator can be used to generate a CT image using a CT reconstruction algorithm, such as a Feldkamp algorithm [15]. The Felkamp algorithm developed by Feldkamp et al. in 1984, is a filtered back projection reconstruction algorithm specifically designed for CBCT. The Feldkamp reconstruction algorithm generates volumetric images using x-ray projection data. The XCAT CT simulator projections are run through the Feldkamp algorithm to produce CBCT images such as the image in Figure 3. 14

29 Figure 3: Example reconstructed CT image from 180 XCAT projections. 15

30 2. Parameter Optimization The first part of this work was to determine the optimal beam parameters using spectrum modeling. The spectrum modeling program DXSPEC was used as well as the penmain program included in the 2006 version of Penelope. 2.1 Spectrum Modeling Methods Previous work with DXSPEC determined that the optimal and filter for x- ray imaging for chest radiography using a CsI detector are 100 and 1 half-value layer (HVL) copper (Cu) filter. [9] Taking these findings into consideration, the following parameters were tested for the LCCT setup: filter type, filter thickness, and. One main parameter that affects image quality that was not tested was mas, however, mas is limited by the tube loading. This means that the optimal mas will have to be determined after the LCCT system is operational. The different filter types tested were aluminum, copper, and gadolinium. Aluminum and copper were used because they are inexpensive and are common filter materials. Gadolinium was chosen because it has a k-edge of 50.3 kev that creates a spectrum with two well-defined peaks, which could impact the image quality and dose. These filters provide a varying range of attenuation, with aluminum being the least attenuating and gadolinium being the most attenuating per filter thickness. 16

31 These filters were simulated with thicknesses of 0 half value layer (HVL), 1 HVL, and 2 HVL. An HVL thickness is the thickness of material it takes to attenuate half of the particles incident on that material. For monoenergetic sources the HVL can be found by HVL = ln 2 μ (4) where µ is the linear attenuation coefficient. This equation is derived from the attenuation equation N = N O e 'PQ (5) where N0 is the number of photons incident on the material, N is the number of photons that are transmitted through the material, and x is the thickness of material. For polyenergetic beams, the HVL must be found experimentally. 0 HVL means no attenuation, 1 HVL thickness of material attenuates half of the incident photons, and 2 HVL thickness of material attenuates three fourths of the incident photons. Using these thicknesses provides a good range of attenuation. The values that were simulated were: 60, 80, 100, 120, and 140. At kilovoltage values lower than 60, most of the beam is attenuated by the patient which means that usable signal per patient dose is not optimum for most imaging needs. At s higher that 140, the dsnr does not greatly improve because contrast is greater at lower energies. 17

32 2.1.1 DXSPEC After the parameters that would be tested were chosen, the HVL for each filter was found for each value. Since DXSPEC outputs the attenuated fluence and the transmitted fluence, the HVL can be found fairly easily. First the material was specified in DXSPEC as a filter with a thickness of several centimeters, broken into 0.1 cm steps. DXSPEC was run for each value, then using the output files, the attenuated and transmitted fluence at each 0.1 cm step were examined to find the thickness where the difference between the attenuated and transmitted fluence was minimized. The 0.1 cm step that had the closest transmitted and attenuated fluence was rerun through DXSPEC at 0.01 cm increments, then cm increments, so that the HVL to the nearest 0.01 mm could be found. The HVLs found by DXSPEC can be found in Table 1. This method was not the most efficient method to find the HVL thicknesses. The standard protocol and more efficient way is to test several thicknesses, plot the transmission vs. thickness, and interpolate using a logarithmic curve fit to find the HVL; however, the former approach is potentially more accurate when significant spectral shaping occurs. 18

33 Table 1: 1 and 2 HVL thicknesses for copper, aluminum, and gadolinium. Material Energy () 1 HVL (mm) 2 HVL (mm) Copper Aluminum Gadolinium After the HVLs for each filter type and were found, the optimization was started. Each filter type, filter thickness, and combination was run through three different setups in DXSPEC. The first setup included the filter, then 25 cm of tissue, then the detector. This setup was the tissue setup. The second setup had the filter, 24 cm of tissue, 1 cm of bone, then the detector. This setup was the bone setup. The final setup was the air setup, it had the filter, 24 cm of tissue, then the detector. After each filter type, filter thickness, and combination was run through DXSPEC for each setup, the dsnrs were calculated. The dsnr for tissue vs. bone contrast, or dsnrbone was found by dsnr STUV = I STUV I XYZZ[V N XYZZ[V (6) 19

34 where Ibone is the dose to the detector, or signal, for the bone setup, Itissue is the signal for the tissue setup, and Ntissue is the detector noise for the tissue setup. Likewise, the dsnr for tissue vs. air contrast, or dsnrair was found by dsnr ]Y^ = I ]Y^ I XYZZ[V N XYZZ[V (7) where Iair is the signal in the air setup. The dsnr Efficiencies could then be calculated by Efficiency = dsnrc D XYZZ[V (8) where the Dtissue is the Dose to the tissue in the tissue setup. After the dsnr Efficiencies are calculated, the different parameters can be compared to each other Penelope The Penelope subroutine, included with Penelope 2006, called penmain was used to validate the DXSPEC results. The DXSPEC signal results have been previously experimentally validated [9], however, the dose results have not. DXSPEC gives results in kev/(kj*cm 2 ), so in order to model the three DXSPEC setups in Penelope, the same thicknesses were used, but each thickness had a face that was 1 cm by 1 cm. The geometry can be found in figure 4. Figure 4a shows the setup in the beam s eye view, while Figure 4b shows the setup from the side. 20

35 Figure 4: Penelope geometry setup from both the (a) beam s eye view and (b) the side. In order to be consistent, the x-ray tube output spectrum, the spectrum with nothing in the beam, from DXSPEC was used as the energy spectrum of the photons in Penelope. Unlike DXSPEC, which outputs energy per tube output per square centimeter, Penelope results are in units of energy per photon, specifically ev per photon. To make the results comparable, the results from Penelope were multiplied by the fluence of the tube output in number of photons per tube output energy per square centimeter and ev was converted to kev, this made all the results in the same units: kev/(kj*cm 2 ). This is not a conventional unit for dose, however, it can be easily converted. The units for dose 21

36 are gray (Gy), where 1 Gy equals 1 J/kg. Converting kev/(kj*cm 2 ) to Gy/kJ, or dose per tube output begins by converting kev to J, then cm 2 must be converted to kg. The conversion factor for kev to J is kev equals 1.602*10-16 J. The square centimeters can be converted to grams by using the depth of material and the density as shown in equation (6). cm c depth cm density g cmh = mass g (9) Mass in grams can then be converted to kg. The complete conversion can be found in equation (7). Results J kev 'kl kj cm c kev g depth cm density cm h.001 kg g = Results Gy kj (10) Even though units of Gy are more conventional, the units for this part of the project were left in units of kev/(kj*cm 2 ), because the doses were only used for comparisons. Unlike DXSPEC, Penelope does not output a measure of noise, so in order to find the dsnr values from Penelope, the noise had to be calculated. Within the Penelope input file, an energy detector can be defined from one of the objects in the geometry file. The energy detector output gives the probability density of photons in defined energy bins. This probability density can be used to calculate the theoretical noise. Finding the standard deviation of the number of photons detected gives an estimate of noise. By definition, the standard deviation is the square root of the variance. In counting, or Poisson, statistics, the variance of a number of counts equals the number of counts. Since 22

37 each energy bin has its own counts, the variance for each energy bin was calculated. The total Penelope noise was then calculated using Noise = E Y c σ Y c (11) where Ei is energy of an energy bin and si is the standard deviation in that energy bin. After the noise was calculated for Penelope, the dsnr and dsnr efficiency values could be calculated and compared to the dsnr and dsnr efficiency values for the corresponding DXSPEC setups. The propagation of error can then be used to find the uncertainty in the noise and dsnr. 2.2 Spectrum Modeling Results Dose, Signal, and Noise Results Figures 5 through 8 display the dose results for DXSPEC absorbed energy (*), DXSPEC absorbed energy (**), and Penelope for the 1 HVL Aluminum, 1 HVL Copper, 1 HVL Gadolinium, and no filter cases, for 25 cm of tissue. The DXSPEC absorbed energy (*), absorbed energy (**), and Penelope results for the tissue setup dose to the detector, or signal, for 1 HVL aluminum filter, 1 HVL copper filter, 1 HVL gadolinium filter, and 0 HVL, or unfiltered, can be found in Figures 9 through 12, respectively. 23

38 Dose to 25 cm Tissue 1 HVL Aluminum Filter Dose (kev/(kj*cm^2)) 3.00E E E E E E E+00 Absorbed Energy (**) Absorbed Energy (*) PENELOPE Figure 5: The dose to 25 cm of tissue from an x-ray beam filtered by 1 HVL of aluminum. 3.00E+10 Dose to 25 cm Tissue 1 HVL Copper Filter Dose (kev/(kj*cm^2)) 2.50E E E E E E+00 Absorbed Energy (**) Absorbed Energy (*) PENELOPE Figure 6: Dose to 25 cm tissue from an x-ray beam filtered by 1 HVL of copper. 24

39 Dose to 25 cm Tissue 1 HVL Gadolinium Filter Dose (kev/(kj*cm^2)) 3.00E E E E E E E+00 Absorbed Energy (**) Absorbed Energy (*) PENELOPE Figure 7: Dose to 25 cm of tissue from an x-ray beam filtered by 1 HVL of gadolinium. 7.00E+10 Dose to 25 cm Tissue 0 HVL Dose (kev/(kj*cm^2)) 6.00E E E E E E+10 Absorbed Energy (**) Absorbed Energy (*) PENELOPE 0.00E+00 Figure 8: Dose to 25 cm of tissue from an unfiltered beam. 25

40 Dose (kev/(kj*cm^2)) Tissue Setup Detector Dose 1 HVL Aluminum Filter 5.00E E E E E E E E E E E+00 Absorbed Energy (**) Absorbed Energy (*) PENELOPE Figure 9: Dose to the detector for the tissue setup and 1 HVL aluminum filter. Tissue Setup Detector Dose 1 HVL Copper Filter Dose (kev/(kj*cm^2)) 5.00E E E E E E E E E E E+00 Absorbed Energy (**) Absorbed Energy (*) PENELOPE Figure 10: Dose to the detector for the tissue setup and 1 HVL copper filter. 26

41 Dose (kev/(kj*cm^2)) Tissue Setup Detector Dose 1 HVL Gadolinium Filter 4.50E E E E E E E E E E+00 Absorbed Energy (**) Absorbed Energy (*) PENELOPE Figure 11: Dose to the detector for the tissue setup and 1 HVL gadolinium filter. Tissue Setup Detector Dose 0 HVL Filter Dose (kev/(kj*cm^2)) 8.00E E E E E E E E E+00 Absorbed Energy (**) Absorbed Energy (*) PENELOPE Figure 12: Dose to the detector for the tissue setup and no filter. The detector doses for both the air setup and the bone setup followed the same trends as the tissue setup. The only difference is that for the air setup, the doses are 27

42 shifted slightly higher, and for the bone setup, the doses are shifted slightly lower. The detector doses for the bone and air setups are displayed in Figures Bone Setup Detector Dose 1 HVL Aluminum Filter Dose (kev/(kj*cm^2)) 4.50E E E E E E E E E E+00 Series1 Series2 Series3 Figure 13: Dose to the detector for the bone setup and 1HVL aluminum filter. 6.00E+08 Air Setup Detector Dose 1 HVL Aluminum Filter Dose (kev/(kj*cm^2)) 5.00E E E E E E+00 Absorbed Energy (**) Absorbed Energy (*) PENELOPE Figure 14: Dose to the detector for the air setup and 1HVL aluminum filter. 28

43 Dose (kev/(kj*cm^2)) Bone Setup Detector Dose 1 HVL Copper Filter 4.50E E E E E E E E E E+00 Absorbed Energy (**) Absorbed Energy (*) PENELOPE Figure 15: Dose to the detector for the bone setup and 1HVL copper filter. 6.00E+08 Air Setup Detector Dose 1 HVL Copper Filter Dose (kev/(kj*cm^2)) 5.00E E E E E E+00 Absorbed Energy (**) Absorbed Energy (*) PENELOPE Figure 16: Dose to the detector for the air setup and 1HVL copper filter. 29

44 Bone Setup Detector Dose 1 HVL Gadolinium Filter Dose (kev/(kj*cm^2)) 4.00E E E E E E E E E+00 Absorbed Energy (**) Absorbed Energy (*) PENELOPE Figure 17: Dose to the detector for the bone setup and 1HVL gadolinium filter. 6.00E+08 Air Setup Detector Dose 1 HVL Gadolinium Filter Dose (kev/(kj*cm^2)) 5.00E E E E E E+00 Absorbed Energy (**) Absorbed Energy (*) PENELOPE Figure 18: Dose to the detector for the air setup and 1HVL gadolinium filter. 30

45 Bone Setup Detector Dose 0 HVL Filter Dose (kev/(kj*cm^2)) 8.00E E E E E E E E E+00 Absorbed Energy (**) Absorbed Energy (*) PENELOPE Figure 19: Dose to the detector for the bone setup and no filter. Air Setup Detector Dose 0 HVL Filter Dose (kev/(kj*cm^2)) 1.00E E E E E E E E E E E+00 Absorbed Energy (**) Absorbed Energy (*) PENELOPE Figure 20: Dose to the detector for the air setup and no filter. 31

46 The calculated noise from Penelope and the noise results from DXSPEC for 1 HVL of aluminum, 1 HVL copper, 1 HVL gadolinium, and no filter can be found in Figures 21 through 24, respectively. The noise is only shown for the tissue setup because the noise in the other two setups is not used to compute the dsnr or dsnr efficiency. Tissue Setup Noise 1 HVL Aluminum Noise (kev/sqrt(kj*cm^2)) 1.80E E E E E E E E E E+00 Absorbed Energy (**) Absorbed Energy (*) PENELOPE Figure 21: Tissue setup detector noise for 1 HVL aluminum filter. 32

47 Noise (kev/sqrt(kj*cm^2)) Tissue Setup Noise 1 HVL Copper 1.80E E E E E E E E E E+00 Absorbed Energy (**) Absorbed Energy (*) PENELOPE Figure 22: Tissue setup detector noise for 1 HVL copper filter. Tissue Setup Noise 1 HVL Gadoliinium Noise (kev/sqrt(kj*cm^2)) 1.80E E E E E E E E E E+00 Absorbed Energy (**) Absorbed Energy (*) PENELOPE Figure 23: Tissue setup detector noise for 1 HVL gadolinium filter. 33

48 Tissue Setup Noise No Filter Noise (kev/sqrt(kj*cm^2)) 2.50E E E E E E+00 Absorbed Energy (**) Absorbed Energy (*) PENELOPE Figure 24: Tissue setup detector noise for no filter dsnr and dsnr Efficiency Results The results of the DXSPEC and Penelope dsnrbone calculations for 1 HVL of each filter type and no filter can be found in Figures The dsnrair calculations for 1 HVL of each filter type and no filter can be found in Figures

49 dsnr bone 1 HVL Aluminum Filter dsnr Absorbed Energy (**) Absorbed Energy (*) PENELOPE Figure 25: dsnrbone values for 1 HVL aluminum filter. dsnr bone 1 HVL Copper Filter dsnr Absorbed Energy (**) Absorbed Energy (*) PENELOPE Figure 26: dsnrbone values for 1 HVL copper filter. 35

50 dsnr bone 1 HVL Gadolinium Filter dsnr Absorbed Energy (**) Absorbed Energy (*) PENELOPE Figure 27: dsnrbone values for 1 HVL gadolinium filter. dsnr bone No Filter dsnr Absorbed Energy (**) Absorbed Energy (*) PENELOPE Figure 28: dsnrbone values for no filter. 36

51 dsnr air 1 HVL Aluminum Filter 620 dsnr Absorbed Energy (**) Absorbed Energy (*) PENELOPE Figure 29: dsnrair values for 1 HVL aluminum filter. dsnr air 1 HVL Copper Filter 620 dsnr Absorbed Energy (**) Absorbed Energy (*) PENELOPE Figure 30: dsnrair values for 1 HVL copper filter. 37

52 dsnr air 1 HVL Gadolinium Filter 620 dsnr Absorbed Energy (**) Absorbed Energy (*) PENELOPE Figure 31: dsnrair values for 1 HVL gadolinium filter. dsnr air No Filter dsnr Absorbed Energy (**) Absorbed Energy (*) PENELOPE Figure 32: dsnrair values for no filter. 38

53 The dsnrbone efficiencies for 1 HVL filters from DXSPEC and Penelope can be found in Figures 33 and 34. The dsnrair efficiencies for 1 HVL filters from DXSPEC and Penelope can be found in Figures 35 and E-06 dsnr bone Efficiencies DXSPEC 1 HVL Filters Efficiency ((kj*cm^2)/kev) 5.00E E E E E E+00 Aluminum Copper Gadolinium No Filter Figure 33: Calculated dsnrbone Efficiency values from DXSPEC for 1 HVL filters. 39

54 Efficiency ((kj*cm^2)/kev) dsnr bone Efficiencies Penelope 1 HVL Filters 9.00E E E E E E E E E E+00 Aluminum Copper Gadolinium No Filter Figure 34: Calculated dsnrbone Efficiency values from Penelope for 1 HVL filters. 1.20E-05 dsnr air Efficiencies DXSPEC 1 HVL Filters Efficiency ((kj*cm^2)/kev) 1.00E E E E E E+00 Aluminum Copper Gadolinium No Filter Figure 35: Calculated dsnrair Efficiency values from DXSPEC for 1 HVL filters. 40

55 dsnr air Efficiencies Penelope 1 HVL Filters 2.50E-05 Efficiency ((kj*cm^2)/kev) 2.00E E E E E+00 Aluminum Copper Gadolinium No Filter Figure 36: Calculated dsnrair Efficiency values from Penelope for 1 HVL filters. The 2 HVL filter thicknesses were run on DXSPEC, analyzed, then only the best filter was run through Penelope. The 2 HVL DXSPEC dsnr efficiencies can be found in Figures 37 and

56 dsnr bone Efficiencies DXSPEC 2 HVL Filters Efficiency ((kj*cm^2)/kev) 7.00E E E E E E E E+00 Aluminum Copper Gadolinium Figure 37: Calculated dsnrbone Efficiency values from DXSPEC for 2 HVL filters. 1.20E-05 dsnr air Efficiencies DXSPEC 2 HVL Filters Efficiency ((kj*cm^2)/kev) 1.00E E E E E E+00 Aluminum Copper Gadolinium Figure 38: Calculated dsnrair Efficiency values from DXSPEC for 2 HVL filters. 42

57 2.3 Spectrum Modeling Discussion and Conclusions DXSPEC and Penelope Dose, Signal, and Noise Comparisons The DXSPEC and Penelope results for the dose, signal, and noise results were considered in light of anticipated findings. For the dose to the tissue, it was expected that DXSPEC absorbed energy (*) would underestimate dose, and DXSPEC absorbed energy (**) would overestimate dose. When comparing the results from the DXSPEC runs and the Penelope runs, the Penelope dose fell in between the two DXSPEC doses, thus confirming expected results. When the DXSPEC code was previously validated, the results showed that the signal measured in DXSPEC was lower than the signal measured experimentally [9]. This was attributed to incomplete modeling of Auger electrons and other secondary reactions within the detector thickness. The signal results from Penelope showed a greater signal in the detector than the two sets of DXSPEC results. This is due to the better modeling of Auger electrons and secondary reactions over short distances in Penelope than in DXSPEC. The calculated noises from Penelope for 60, 80, and 100 are slightly higher than the noises calculated within DXSPEC; however, the noises calculated in Penelope for 120 are very similar to the DXSPEC absorbed energy (**) noise calculations, and the 140 calculated noise from Penelope falls between the absorbed energy (*) and 43

58 the absorbed energy (**) noises. The noise calculated from Penelope for each filter type followed this trend DXSPEC and Penelope dsnr Comparisons As seen in Figures 25 through 32 above, the dsnr values vary more between the different beam filters than any of the other results. The dsnr values, both bone and air, from DXSPEC follow the same general shape for each filter, but the Penelope results do not. The Penelope dsnrbone values for both 1 HVL of copper and 1 HVL of aluminum follow very closely with the calculated dsnrbone values from DXSPEC absorbed energy (**). In fact, for these two filters, the absorbed energy (**) dsnrbone values lie within the error bars of the Penelope dsnrbone values. The dsnr error was calculated using the propagation of error. The propagation of error for a given function R=R(x,y, ) is defined as, σ o = R x σ Q c + R y σ s c + (12) where sr is the error, or standard deviation in the function R, sx is the standard deviation of x, and sy is the standard deviation of y. Applying this to the dsnr equation, the error in the dsnr is defined as σ uvwo = 1 N S σ x c + 1 N S σ x S c + I I S N S c σ ws c (13) where I refers to the signal in the target, Ib refers to the signal in the background, Nb refers to the noise in the background, and s refers to standard deviation. The target 44

59 refers to either the bone or air setup and the background refers to the tissue setup. The statistical uncertainty within the Penelope results was used as the standard deviation for each signal measurement, while the standard deviation of the noise was calculated based on the propagation of error of the calculated noise. The dsnrbone values for both 1 HVL gadolinium filter and no filter don t follow either DXSPEC result closely, instead, the lowest values show the Penelope dsnrbone values to be closer to the absorbed energy (*) results. At 80, the Penelope dsnrbone values and the absorbed energy (**) dsnrbone values are almost equal, but then for 100, 120, and 140 the Penelope dsnrbone values are higher than the absorbed energy (**) values. The 1 HVL gadolinium and no filter Penelope dsnrair values follow the same trend as the dsnrbone values for the same filter materials. The 1 HVL aluminum and copper Penelope dsnrair have the same basic shape as the gadolinium and no filter, only shifted to above the absorbed energy (**) values Final Spectrum Modeling Discussion and Conclusions The major source of difference between the Penelope dsnr calculations and the DXSPEC dsnr calculations is the noise estimation from Penelope. Although the DXSPEC signal results were shown to be too low, the ratios between the results have previously been validated [9]. On the other hand, Penelope Monte Carlo is a wellestablished way to calculate dose, while the DXSPEC dose calculations have not been previously validated. This means, that in order to get a better understanding of dsnr 45

60 Efficiency, the dsnr values from DXSPEC can be used in equations (3) and (4) with the dose values from Penelope. Combining the two different methods gives dsnr efficiencies that can be found in Figures 39 and E-06 Combined dsnr bone Efficiencies 1 HVL Filters Efficiency ((kj*cm^2)/kev) 7.00E E E E E E E E+00 Aluminum Copper Gadolinium No Filter Figure 39: Combined dsnrbone efficiencies for 1 HVL filters. 46

61 Efficiency ((kj*cm^2)/kev) 1.60E E E E E E E E E+00 Combined dsnr air Efficiencies 1 HVL Filters Aluminum Copper Gadolinium No Filter Figure 40: Combined dsnrair efficiencies for 1 HVL filters. Figures 39 and 40 clearly show that copper has the highest dsnr efficiency for all but one value. For this reason, copper was chosen as the optimal filter to use for both the full CT dose simulations and image acquisition and reconstruction. After copper was chosen to be the best for all of the 1 HVL filters, it could be compared to 2 HVL copper filter. The DXSPEC dsnr values for the 2 HVL filters as seen in figures 37 and 38, shows copper to be the best 2 HVL filter. Comparing 1 HVL of copper to 2 HVL of copper does show a slight increase in the dsnr efficiencies. However, doubling the filter thickness would mean having to douple the tube loading, which for the LCCT system is not feasible. Therefore, a 1 HVL copper filter was determined to be the optimal filter for the LCCT system. 47

62 3. CT Dose Simulation and Image Reconstruction After the optimal filter type and thickness were found, the CT images could be acquired using the XCAT projector, reconstructed using a Feldkamp algorithm, and the dose could be calculated using Penelope. 3.1 Simulation and Reconstruction Methods XCAT Projector Methods The XCAT projector developed by Segars et al. [13] is an accurate way to acquire projection images, which can then be used to reconstruct CT images. The projector uses computer graphic ray tracing techniques to accurately calculate the CT projections for the XCAT phantom. The projector program uses input parameters to model different CT scanners and setups. This allowed for the XCAT projector to produce projections for the LCCT setup. The required CT setup input parameters and corresponding LCCT parameters can be found in table 2. The LCCT setup source to patient distance is 153 cm and the source to detector distance is 180 cm, which means that the patient to detector distance is 27 cm. The detector used is 41 cm by 41 cm, this models an available detector that can be used with the LCCT setup. The number of rows and channels determine the number of pixels in the detector, and using 512 by 512 will be sufficient for the purpose of this study. The fan angle of the LCCT system is degrees; this was calculated from the LCCT setup to irradiate 40 cm of the patient. The mas per projection was set at As 48

63 stated above, this project included no mas optimization, because of power and tube loading constraints that will be present for the actual system. Because of this, a low value of mas was chosen and used for each value so that the all of the images could be compared. The geometric efficiency of the detector was set to 0.8, the detector shift was set to -0.25, the electronic noise was turned off by setting the variance to 0, and the subvoxel index was set to 1. Table 2: XCAT Projector Input Parameters LCCT Parameter Value Needed Projector Input Parameter 0 :output_type(0=log_transformed,1=intensity_output,2=both) 0 :organ_to_center_projection(0=body) 1530 :distance_to_source(mms) 270 :distance_to_detector(mms) 410 :height(mms) 410 :width(mms) 512 :num_rows 512 :num_channels 7.48 :Half_fan_angle 0.05 :mas_per_projection 0.8 :Geometric_efficiency_detector :detector_shift 0 :variance_of_electronic_noise 1 :subvoxel_index In order to produce a projection with the XCAT projector, along with the parameter file that defines the above parameters, a phantom file, a spectrum file, and a projection angle are needed. The phantom file is generated from the XCAT phantom. The desired phantom can be scaled or shifted as desired. For the LCCT system, four different XCAT phantoms were chosen: two female and two male. The phantoms chosen 49

64 can be found in Table 3. These phantoms were chosen to model a range of diverse patient sizes. Table 3: XCAT Phantoms used in the XCAT projector. Label Age Weight (kg) Weight Percentil Height (cm) BMI Female Female Male Male The spectrum files that were used as inputs for the projector, were the spectra generated by DXSPEC for 60, 80, 100, 120, and 140 beams filtered by 1 HVL of copper. The projector was run for even angles from 0 to 358. Previous work with the LCCT setup determined that a sufficient image could be reconstructed from 180 projections, and the fewer projections taken, the lower the dose Image Reconstruction Methods After all of the projections had run, there were 180 projections for each value for each patient. These projections were then reconstructed using a Feldkamp algorithm. The Feldkamp algorithm has been implemented into a MATLAB TM (MathWorks, Natick, MA) code. This MATLAB code was used to generate all the CT images for this thesis. The MATLAB Feldkamp code needed inputs are shown in Table 4 with the corresponding LCCT parameters. The projection angles in Table 3 start at 90 and end at because the XCAT projector and the reconstruction algorithm have a different definition of 0 degrees and rotate in the opposite directions. 50

65 Table 4: MATLAB CT reconstruction input parameters. Variable LCCT Value Variable Explination theta 90:-2:-270 Projection Angles u_off Location of the center in the u direction v_off Location of the center in the v direction weights 1 Weight of each projection N_proj 180 Number of projections N_row 512 Number of rows N_col 512 Number of Columns du Pixel Thickness in the u direction dv Pixel Thickness in the v direction SAD 153 Source to Pt. Center Distance SDD 180 Source to Detector Distance IAD 27 Pt. Center to Detector Distance After the input parameters and the projection data are put into MATLAB the filtered back projection Feldkamp reconstruction algorithm for flat panel detectors was run and the CT images were acquired LCCT Simulation Methods The Penelope code used to model the full LCCT setup was a modified version of the tube current modulation (TCM) code developed and validated. The adaptations of the TCM code were made in the input files. The TCM Penelope code was designed to simulate CT scans in which the tube current is modulated across the patient to reduce dose. For the LCCT simulation, the modulation was turned off and the other parameters were changed to reflect the LCCT setup. First, the four phantoms that were used in the image acquisition, were reconfigured to be compatible with the TCM simulation package. The phantoms were saved as two raw files, one with the organ labels 51

66 embedded and the other with the material labels embedded. The updated input parameters can be found in Table 5. Table 5: TCM Simulation Input Parameters Variable Value Explination # patient pt001 Patient Identifier -- unique for each simulation inplane_resmm 3.45 Phantom Pixel Dimensions longaxis_resmm 3.45 Phantom Pixel Dimensions Norg 53 Number of Organs orgfile Female1_org_202_475_101.raw Organ File Nmat 24 Number of Materials matfile Female1_mat_202_475_101.raw Material File matdata 42pts.mat Material Data Ystart 128 Starting Pixel Location in the Y direction start_offset (cm) 1 Yend 128 Ending Pixel location in the Y direction end_offset (cm) 1 gantry_angle_dist_file na Modulation File 60 spcfile 60Cu1HVL.txt Spectrum File SID(cm) 153 Distance from the Source to Center of the Pt. FanAng(deg) Full Fan Angle colli (mm) 0 Collimation Thickness EffBeamWidth(mm) 402 Effective Beam Width at the Center of the Pt. pitch 0 sta_ang(deg) 0 Start Angle Xdim 202 Phantom Dimensions Ydim 475 Phantom Dimensions Zdim 101 Phantom Dimensions Xcenter 101 Center X Pixel Zcenter 50 Center Z Pixel The patient identifier was changed for each run of the simulation. The phantom pixel dimensions were in reference to the phantom used in the simulation. Because this 52

67 simulation usually models traditional CT, the y-direction is the direction from head to foot, which in the LCCT setup is the z-direction. The modulation was turned off, so the modulation file was not included. The spectrum file and values changed to run the simulation through each of the five values for each of the four phantoms. The collimation was originally used to determine scan length, but for the LCCT system, the scan length is zero because there is no patient translation throughout the scan. The effective beam width is the width of the beam at the center of the patient. Each phantom/ combination was run through the simulation 15 times in parallel, to reduce overall run time. The dose results from the 15 runs were then averaged together to produce the final dose results for each phantom/ combination. The dose in units of mgy per mas, was then converted to msv per mas using the tissue weighting factors from ICRP Simulation and Reconstruction Results Imaging Results The reconstructed CT images for the phantom Female 1 are found in figure 41. The reconstructed CT images for Female 2 are found in figure 42. Male 1 reconstructed CT images are found in figure 43. Male 2 reconstructed CT images are displayed in figure

68 Figure 41: Reconstructed CT images for Female 1 phantom for (a) 60, (b) 80, (c) 100, (d)120, and (e) 140. Figure 42: Reconstructed CT images for Female 2 phantom for (a) 60, (b) 80, (c) 100, (d)120, and (e)

69 Figure 43: Reconstructed CT images for Male 1 phantom for (a) 60, (b) 80, (c) 100, (d)120, and (e) 140. Figure 44: Reconstructed CT images for Male 2 phantom for (a) 60, (b) 80, (c) 100, (d)120, and (e)