ABSORBED DOSE MEASUREMENTS AND MCNP MODELING FOR THE LEKSELL GAMMA KNIFE. A Thesis. the Degree Master of Science in the. Yipeng Li, B.S.

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1 ABSORBED DOSE MEASUREMENTS AND MCNP MODELING FOR THE LEKSELL GAMMA KNIFE A Thesis Presented in Partial Fulfillment of the Requirement for the Degree Master of Science in the Graduate School of The Ohio State University By Yipeng Li, B.S. ***** The Ohio State University 2002 Master s Examination Committee: Dr. Nilendu Gupta, Adviser Dr. Thomas E. Blue Approved by Adviser Nuclear Engineering Graduate Program

2 ABSTRACT The Leksell Gamma Knife is a radiosurgery device that uses 201 convergent photon beamlets to treat brain tumors. These narrow photon beams pose great challenges on the absorbed dose distribution measurements because of the existence of the sharp dose fall-off regions. The purpose of this thesis was to evaluate different dosimeters for the measurement of absorbed doses for the LGK and to create a Monte Carlo based model for the LGK. In this work, two newly available dosimeters, the EDR2 radiographic film and TLD-100H disks, were evaluated for absorbed dose distribution measurements for the Leksell Gamma Knife. The measurements with the EDR2 radiographic film showed that it can conveniently and accurately measure the absorbed dose profile in the isocenter. The work on TLD-100H disks showed that they can be used to ii

3 measure the absorbed dose received in the isocenter as well as the structure dose received in areas away from the isocenter with good accuracy. In this work, a MCNP model of the Leksell Gamma Knife for absorbed dose distribution calculation was also developed, which directly simulates photons from the source while avoiding the time-consuming transport in the radiation unit of the Gamma Knife. This work has laid the foundation for future work to create a system for computing and measuring absorbed doses to brain structure in the Gamma Knife radiosurgery using a structure segmented head phantom. iii

4 Dedicated to my grandmother iv

5 ACKNOWLEDGMENTS First and foremost, I would like to express my deepest gratitude to Dr. Nilendu Gupta for his support and guidance. Without his help, this work could not have been accomplished. I also would like to thank Dr. Thomas Blue for his invaluable comments on the work and for being a member of my examination committee. My thanks also go to Dr. Jeff Woollard for his help in the Gamma Knife modeling and MCNP simulation, Mr. Brent Albertson for his enthusiastic assistance in TLD irradiation, my fellow Mr. Chenguang Li for his help on the development of Gamma Knife modeling. My special thanks go to Mr. Andy Hawk for his help on TLD measurement and preparation of thesis defense. I also would like to thank Dr. Reinhard Gahbauer, the chairman of the Radiation Oncology Department at the Arthur G. James Cancer Hospital and v

6 Richard J. Solove Research Institute, for his support on funding this research. I also would like to thank Mr. Steve Fonseca for his encouragement and help on my life in the Unites States. Finally I would like to sincerely thank my parents for their consistent mental support and my brother for his unselfish help in the past years. vi

7 VITA March 24, Born Pucheng, China June, B.S. Engineering Physics, Tsinghua University Beijing, China September 2000 Present...Research Assistant The Ohio State University FIELDS OF STUDY Major Field: Nuclear Engineering Studies in Health Physics vii

8 TABLE OF CONTENTS Page Abstract ii Dedications iv Acknowledgment v Vita vii List of Tables xii List of Figures xiii List of Diagrams xvii Chapters 1 Introduction Objectives Introduction Scope of work Outline Background Gamma Knife viii

9 2.2 GammaPlan and absorbed dose profile Film dosimetry TLD dosimetry Thermoluminescence Lithium fluoride MCNP Comparison of dosimeters for LGK Previous work Film measurement Equipment Radiographic film EDR2 (Extended Dose Range) GAFCHROMIC TM film MD VXR-16 DosimetryPRO film digitizer Model radiochromic densitometer Data processing software OmniPro-Accept Measurement EDR2 Film Preparation Exposure MD-55 film Dose Profile acquisition Using automatic film scanner VXR-16 PRO Using the manual densitometer Model H&D curve measurement Dose profile measurement Data processing Error analysis Results and conclusion TLD measurement General description of the experiment Equipment Procedure Irradiation ix

10 Readout process Annealing Process Cooling process Calibration in MXE Equipment Experimental setup Readout Data processing Error analysis Calibration curve Calibration in LGK Dose profile measurements Results Error Analysis Conclusion MCNP calculation Tallies in MCNP Gamma Knife modeling A single channel in the gamma knife Full Gamma Knife modeling Surface disk source modeling Point source modeling Gamma Knife modeling with SOURCEX Results and comparison Conclusion Conclusion and future work Conclusions Suggestions for future work x

11 Reference APPENDICES Appendix A Dose profiles of 4 helmets in x and z directions Appendix B Beam data file and conversion code Appendix C Raw data of TLD measurements Appendix D MCNP input file for single channel modeling Appendix E Channel polar and azimuthal angles calculation Appendix F MCNP input file for 201 surface source Appendix G MCNP input file for energy distribution Appendix H SOURCEX code xi

12 LIST OF TABLES Table Page 3.1 Responsive Range Comparison for Films in the Kodak Ready-Pack Film Family Dose levels for H&D curve H&D curve data for MD FWHM and penumbra size comparison (4 and 18mm) FWHM and penumbra size comparison (8 and 14mm) Dose levels used for calibration Calculation of Disk Correction Factor SCF calculation Data processing for MU=380, SCF MU=380 = Dose levels and corresponding TLD readings Dose profile measurement using TLD disks Error for TLD absolute dose measurements Electron transport options in MCNP Helmet inlet and outlet diameters xii

13 LIST OF FIGURES Figure Page 2.1 Schematic view of a gamma knife Leksell Gamma Knife Model C Cross sectional view of LGK Coordinate system for dose profile measurement Dose profile of the 18mm helmet along x axis Dose profile of the 18mm helmet along z axis Dose response curve of EDR2 film MD-55 Film Calibration Curve Film holder Marks on the Film Measured H&D curve for EDR2 film H&D curve for MD-55 radiochromic film Averaging effect of the light detector with a 2-mm aperture Dose profiles along x-axis for 4mm helmet Dose profiles along y-axis for 4mm helmet xiii

14 3.10 Dose profiles along z-axis for 4mm helmet Dose profiles along x-axis for 8mm helmet Dose profiles along y-axis for 8mm helmet Dose profiles along z-axis for 8mm helmet Dose profiles along x-axis for 14mm helmet Dose profiles along y-axis for 14mm helmet Dose profiles along z-axis for 14mm helmet Dose profiles along x-axis for 18mm helmet Dose profiles along y-axis for 18mm helmet Dose profiles along z-axis for 18mm helmet LS drifting during the readout process Time-Temperature Profile used for TLD disks readout Effect of the shape of TTP on glow curve Sensitivity change due to the cooling process Calibration setup in MXE Calibration curve for TLD-100H disks A quarter of the film template Calibration curves for MXE and LGK Calibration curve with normal dose rate xiv

15 and lowered dose rate in MXE Angular dependency of TLD-100H disks Calibration curve from LGK for TLD-100H disks Averaging effect of TLD disks Dose profile along x axis (18mm) Dose profile along z axis (18mm) Cross-sectional view of a single channel with a 18mm helmet Photon spectrum in the outlet of the 18mm helmet Perpendicular-incident surface disk source Point source modeling Coordinate system rotation Position sampling scheme Intersection of a particle with the bottom surface Intersection of a particle with the outlet surface Single channel dose profile comparison (no air gap) Dose Profile Comparison along x (18mm, disk source) Dose Profile Comparison along z (18mm, disk source) Dose Profile Comparison along x (4mm, disk source) Dose Profile Comparison along z (4mm, disk source) xv

16 5.14 Dose Profile Comparison along x (18mm, point source) Dose Profile Comparison along z (18mm, point source) Dose Profile Comparison along x (4mm, point source) Dose Profile Comparison along z (4mm, point source) Dose Profile Comparison along x (SOURCEX, 18mm) Dose Profile Comparison along z (SOURCEX, 18mm) A.1 Dose profiles along x and z axes for the 18mm helmet A.2 Dose profiles along x and z axes for the 14mm helmet A.3 Dose profiles along x and z axes for the 8mm helmet A.4 Dose profiles along x and z axes for the 4mm helmet E.1 Polar angle calculation E.2 Azimuthal angle calculation xvi

17 LIST OF DIAGRAMS Diagram Page 4.1 TLD data processing SOURCEX sampling scheme xvii

18 CHAPTER 1 INTRODUCTION 1.1 Objectives The purpose of this study was to evaluate different dosimeters for the measurement of absorbed doses for the Leksell Gamma Knife 1 (LGK) and to create a Monte Carlo based model for LGK. The work performed in this project will lay the foundation for future work to create a system for computing and measuring absorbed doses to brain structure in the Gamma Knife radiosurgery using a structure segmented head phantom. The goals for the absorbed dose measurements comprised two sub-goals: I. Evaluate the suitability of a new film dosimeter, EDR2, for LGK absorbed dose measurements; II. Evaluate TLD-100H disks as dosimeters for structure dose measurements for LGK. 1 Leksell Gamma Knife, Elekta Instruments AB, Sweden 1

19 1.2 Introduction Small x-ray/gamma ray beams, such as encountered in LGK, present numerous difficulties in absorbed dose measurements. The lack of electron equilibrium particularly imposes challenges on dosimeters used in the radiation therapy (see section 2.6 for discussion). A newly available film dosimeter (Kodak EDR2 film 2 ) has a wider and approximately linear response range, which makes it potentially a suitable dosimeter for LGK dosimetry. New TLD dosimeters are also now available. Compared to previous available TLD disks, the new ones are doped with different impurities and show higher sensitivity to x-rays, which makes them capable of accurately measuring very low absorbed doses as countered in structure dosimetry for the LGK. They can be small and thin, therefore, can be easily sandwiched between the halves of the spherical phantom and used to measure absolute doses in the LGK [1]. The absorbed dose calculation algorithm used in LGK GammaPlan 3 is simplistic and semi-empirical. It assumes constant linear attenuation through different tissues and takes into account photon scattering simply by 2 EDR2 film, Eastman Kodak company, Rochester, NY, USA 3 Leksell GammaPlan, Elekta Instruments AB, Sweden 2

20 including a measured off-axis ratio into the absorbed dose calculation. Although general speaking the brain is homogeneous, heterogeneity exists in area containing low density air cavities and high density bones, which might perturb small beams in a way that the algorithm used in GammaPlan can not predict [2]. Another limitation of this algorithm is that the absorbed dose distribution within the patient s brain is calculated only inside a rectangular parallelepiped immediately surrounding the treatment volume. The reason for this is that the treatment planning system only allows for a limited matrix of dose points. Although the absorbed dose is calculated accurately within this volume, and the location of the volume is known accurately with respect to the helmet, absorbed doses outside of the rectangular parallelepiped are not calculated (except for doses at requested points outside the calculation matrix and dose statistics within explicitly drawn structure based on a sampled number of dose calculation points). Besides for cases involving multiple shots, the aggregated absorbed dose within the tumor is based upon the sum of several high dose gradient regions. The treatment planning system based upon a semi-empirical model of the measured dose distribution may involve accuracies from the measured absorbed dose fall-off, due to the difficulties in making such measurements, as well as the inaccuracies in the model. 3

21 However, Monte Carlo (MC) based algorithms calculate the absorbed doses in a fundamental way. They simulate the transport of a particle within the brain and calculate energy deposited; therefore, homogeneity assumption is not necessary. The contribution from scattered photons to the structure dose is also taken into account by the simulation. The flexibility of the MC based algorithms can be combined with images of the patient s brain to create a patient specific treatment planning, which will more accurately calculates absorbed doses received by the tumor as well as normal tissues. 1.3 Scope of work In this work, the absorbed dose profiles from GammaPlan were used as a standard for comparison of our measurements and calculations, since their accuracy inside and at locations just around the treatment isocenter has been validated. Different dosimeters were used to measure the dose profiles at the isocenter with different helmets. More specifically, EDR2 radiographic film and MD-55 radiochromic film measurements were conducted to get the absorbed dose profiles in the isocenter. Also the TLD-100H disks were used to measure the absolute absorbed doses as well as dose distributions around the isocenter. Besides, a full LGK Monte Carlo model was developed to compute the dose distribution. All the dose profiles obtained either by 4

22 measurements or by calculation were compared to the standard for verification. 1.4 Outline The outline of this thesis is as follows. Chapter one is the introduction to this thesis. This chapter discusses the objectives and scope of work of this thesis and introduces necessary background. It also provides an outline of the thesis. Chapter two contains the background material for the thesis. Specifically it discusses the dose profiles used as benchmark for all absorbed dose measurements and calculations. This chapter also includes a summary of previous work performed in this field. Chapter three describes the use of radiographic and radiochromic films to measure dose profiles at the isocenter. Chapter four describes the use of TLD-100H disk to measure the structure dose of LPK. Chapter five presents a single channel model and two simplified full LGK models. A promising full LGK model using SOURCEX feature of MCNP is also described in this chapter. 5

23 Chapter six presents the conclusion of the thesis and presents suggestions for future work. 6

24 CHAPTER 2 BACKGROUND 2.1 Gamma Knife A gamma knife is a stereotactic radiosurgery device, which delivers high radiation absorbed doses to small volumes within the brain using 201 convergent gamma-ray beams while providing good sparing of normal structures [1]. Figure 2.1 illustrates how a gamma knife works. Gamma rays emitted by radioactive sources are directed by channels drilled in a hemispherical tungsten helmet. These conical collimator channels shape and create highly focused gamma-ray beamlets that intersect at the target with high precision. 7

25 Figure 2.1: Schematic view of a gamma knife Figure 2.2 shows the Leksell Gamma Knife (model C), similar to that (model B) installed at the Arthur G. James Cancer Hospital and Richard J. Solove Research Institute at The Ohio State University. The unit comprises of three main parts: I. Radiation Unit: holds and provides the primary collimation for the 201 Co-60 sources with total radioactivity about 6000 Ci at the time of installation. The unit is shielded at the treatment end by a pair of shutters that remain closed when the LGK is not being used for 8

26 treatments; II. Helmets: 4 interchangeable helmets, 18, 14, 8 and 4mm, are used for final collimation. The size of the helmet denotes the nominal diameter of the gamma-ray beam from each collimator at the treatment isocenter; III. Patient Treatment Couch: carries a patient in and out of the radiation unit during treatment duration. The helmet is affixed to the couch and the patient s head is affixed to the helmet such that the center of the hemispherical helmet corresponds to the target to be treated. Figure 2.2: Leksell Gamma Knife Model C 9

27 The cross sectional view of the LGK, Figure 2.3, demonstrates the treatment process: I. The target is localized by medical imaging methods, such as MRI or CT with the help of a stereotactic frame attached to the patient s skull; II. Measurements for reconstructing the shape of the head of the patient, and the treatment target data from the medical imaging are fed into the LGK treatment planning system, GammaPlan. Based on the size, shape and position of the target, an experienced physician then decides the treatment plan that best delivers the intended radiation absorbed dose distribution. This treatment plan consists of the treatment locations, the helmet sizes for each location, and the treatment time for each location; III. After the treatment planning and review process is over, and some quality assurance checks are completed on the treatment unit to ensure its safety and accuracy, the patient is led to the treatment room and positioned appropriately on the patient couch with target at the center of the helmet. After the operators leave the room and the treatment time for that treatment is programmed at the treatment console outside the room, the portal door opens and the patient is sent into the radiation unit. 10

28 IV. When the treatment time is completed, the couch moves back and the treatment is complete. V. The treatment delivery is repeated for each of the planned treatment locations. Figure 2.3: Cross sectional view of LGK 2.2 GammaPlan and absorbed dose profile GammaPlan is the treatment planning system dedicated to the LGK. It calculates the absorbed dose distributions by super-imposing doses delivered by each of the 201 photon beams and for each treatment isocenter. The dose 11

29 calculations require the knowledge of the patient s skull geometry, the transverse absorbed dose profile for a specific helmet size, and the absorbed dose rate at the reference point in a water phantom. Then the dose delivered by each beam is calculated in a matrix centered on the region of interest [3]. In this algorithm, the photon scattering effect was taken into account by the transverse dose profile, which is the absorbed dose distribution along x, y or z axis in a spherical polystyrene phantom whose origin coincides with the isocenter. Since absorbed doses in areas distal to the isocenter mainly results from scattered photons, this profile is of importance for calculation of absolute dose received to those areas. The absorbed dose profiles are also used for quality assurance. During the LGK installation, the dose profile calculated by the GammaPlan was verified as part of the LGK acceptance test using radiographic film dosimetry [4] and is routinely checked to verify the accuracy and integrity of the system. Because of its importance in the dose calculation and quality assurance, the dose profile for each helmet has to be measured accurately. The lower part of Figure 2.4 shows the coordinate system used in all the measurements and 12

30 calculations: the origin is the isocenter; the x-y plane coincides with the bottom surface of the hemispherical helmet; the z-axis points into the superior aspect of the helmet (the upper part of Figure 2.4 is the top view and side view of a helmet; only a few of the 201 collimators are shown on the figure for illustrating their location better). The dose profile for the 18mm helmet along the x axis is shown in Figure 2.5 (dose profiles for other helmets are in APPENDIX A). 13

31 y z z x y x Figure 2.4: Coordinate system for dose profile measurement 14

32 relative dose(%) x (mm) Figure 2.5: Dose profile of the 18mm helmet along x axis When the absorbed dose at a designated point is to be calculated, the dose profile is used to find the off-axis factor, which is defined as the dose relative to the isocenter. Two parameters are used to characterize profiles of different helmets. FWHM (Full Width at Half Maximum) or the profile width determines the size of an area where high radiation will be delivered. 15

33 Penumbra, resulting from photon scattering, is defined as the lateral distance between 20% and 80% relative dose in the fall-off region outside the primary radiation area. The unbalanced channel configuration along the z axis results in the asymmetry of absorbed dose distribution, which is shown in Figure 2.6: relative dose (%) z (mm) Figure 2.6: Dose profile of the 18mm helmet along z axis 16

34 Since photons beams are incident only from the positive direction of z axis, the dose received in the negative z direction is less than that in the opposite direction. Therefore the symmetry of the dose profile in the z direction is compromised. Compared to the dose profile along x axis, the z-axis profile also has a sharper penumbra area due to the same reason mentioned. 2.3 Film dosimetry Radiation dosimetry based on radiographic and other films is widely used in the Radiation Oncology. Compared to other dosimeters, such as ion chambers, diodes and thermoluminescent dosimeters (TLDs), film dosimeters have the characteristic that they can be used for 2D spatial absorbed dose data acquisition and at higher resolutions than other dosimeters. The latter characteristic of film dosimeters make them ideal to measure the sharp dose gradient regions encountered in the absorbed dose distribution measurements for the Gamma Knife. The two types of films currently widely used are radiographic film and radiochromic film. They have different characteristics useful for dose distribution measurements under different conditions. The mechanism of action of the radiographic film is very similar in principle to that of 17

35 photographic film. The latent image formation results from decomposition of silver halides (AgCl, AgBr or AgI) due to the secondary electron from the gamma-rays. Radiographic film is also sensitive to visible light; therefore the film is usually either packaged in a light-tight readypack, or loaded into a light-tight cassette in a dark room. Just like photographic films, to fix the latent image a wet chemical developing process is required. Radiographic film for radiation oncology quality assurance measurement is available in various sizes, which make it suitable for performing measurements for different geometries and modalities. Also the radiographic film can be read out by densitometers equipped with any wavelength of light source. This last feature significantly reduces the requirement on the readout device. However, the wet processing procedure can contribute a significant part of uncertainty to the radiographic film dosimetry. Another disadvantage of this type of film is its strong energy dependence because of differences in sensitivity to photon energies in the KeV region [5]. In this study, EDR2 radiographic film was evaluated for the absorbed dose profile measurement (the details of EDR2 film was in section 3.1). Radiochromic film is based on a totally different mechanism. When it is exposed to ionizing radiation, it develops a distinctive and characteristic 18

36 color, whose darkness is proportional to the amount of absorbed dose [5]. It is therefore self-developing; no wet processing is required, which eliminates one of the greatest contributions to the uncertainty in film dosimetry. Also the radiochromic film is not sensitive to room light, except prolonged exposure to fluorescent light. This greatly facilitates the working with this film. Unlike the radiographic film, the radiochromic film has a wider usable dose range [5]. The absorbance spectrum of currently used radiochromic films has two peaks centered on 610nm and 670nm. Therefore specialized light source with wavelength close to these two peaks has to be used in order to achieve maximum sensitivity of measurements. This limitation puts higher requirement on the readout device. 2.4 TLD dosimetry 2.4.1Thermoluminescence The phenomenon of thermoluminescence is the basis of TLD dosimetry. It is believed that this phenomenon is closely related to the lattice defects in the crystal structure of a thermoluminescent material, such as thermal or intrinsic defects [6]. These lattice defects create, between the valence band and conduction band, intermediate energy levels, which serve as trap centers for electrons. 19

37 When a thermoluminescent material is exposed to ionizing or nonionizing radiation, electrons are excited from valence band and trapped in the trapping centers in the forbidden gap. If one heats the material, electrons will obtain enough energy and get released from the trapped centers. When these released electrons return to their ground state, excess energy is radiated in forms of visible or ultraviolet photons, whose number is proportional to the energy deposited in the material due to the radiation. With the multiplication effect of photomultiplier tube, the number of photons can be further proportionally increased and create detectable signal proportional to the energy deposited in that material Lithium fluoride LiF is the most widely used material in thermoluminescent dosimetry. It has several desirable features: its effective atomic number, Z eff is close to that of tissues; it is insensitive to light and the thermal fading is small (<5% in 12 weeks); it has weak energy dependency and wide useful range of exposures from few mr to10 5 R, with linear response up to 10 3 R. LiF based TLDs are available in three different types according to the different abundance of 6 Li in the LiF: TLD-100 (natural 6 Li abundance: 20

38 7.5% 6 Li and 92.5% 7 Li); TLD-600 (highly enriched 6 Li, 95.6%) and TLD-700 (very low 6 Li content, <0.01%). LiF dosimeters also come with different doping impurities. LiF TLDs doped with Mg, Cu and P are recently available commercially. These TLDs are denoted with an H appended to their names to distinguish them from those doped with Mg and Ti. For example, TLD-100H indicates that it is doped with Mg, Cu and P with natural 6 Li enrichment in the LiF. The TLD-100H disk used in our experiments has several features making it a suitable low dose dosimeter for LGK. Firstly, the disk size of this dosimeter is 3.6mm in diameter and the thickness is 0.60mm, which makes it very suitable sandwich it between the layers of a plastic phantom. Secondly, it can be used to measure doses as low as 1µGy and has a very good linear dose response range up to 10Gy. Its response is also independent on photons with energy higher than 100keV. 2.5 MCNP MCNP (Monte Carlo N-Particle transport code) utilizes the Monte Carlo method to solve radiation transport problems involving neutron, photon, electron and coupled neutron/photon/electron transport. For photon transport 21

39 problems, such as the one studied in this thesis, MCNP is especially suited to perform the calculation. The detailed photon physics treatment in MCNP allows for the accurate transport of photons through a geometry. During particle transport, this treatment accounts for the photoelectric effect, pair production, Compton scattering, incoherent (Thomson) scattering and fluorescence photons produced after photoelectric absorption. The Monte Carlo method is also most useful for geometrically complex transport problems which cannot be sufficiently modeled by codes that use deterministic method. The geometric modeling capabilities of MCNP allow for arbitrary three dimensional configurations of materials bounded by various surfaces. These capabilities allow for accurate modeling of the Gamma Knife. Additionally, the repeating structures feature in MCNP will facilitate modeling of the voxelized geometry of the patient obtained form the 3D imaging studies. MCNP also provides users the capability of arbitrary source distribution modeling by using SOURCEX, which can greatly simply the modeling (see Chapter 5). 2.6 Comparison of dosimeters for LGK [7] The main difficulties of LGK dosimetry are the steep dose gradients (penumbra area) and lateral electronic disequilibrium. Because of their 22

40 relative large size, ion chambers are not quite suitable, except for the absolute dose measurement at the isocenter for the 18mm helmet. Radiographic film dosimetry is capable of measuring doses for small fields, but many factors, such as energy dependency, processing conditions make it difficult to get reliable absolute doses. Radiochromic film has the advantages of better tissue equivalence, high spatial resolution, and room light handling, but the dose response is nonlinear in the clinical range. Silicon diodes are common choice in dosimetry of LGK beams because of their very small size, but they suffer from energy, dose rate, and the directional dependency. Currently none of the dosimetries for LGK are perfect. Therefore it is important to determine the advantages and disadvantages of new dosimeters as they emerge. 2.7 Previous work EDR2 film has been used for dose verification of IMRT by Zhu et al. and showed satisfactory results [8]. Radiochromic film also has been successfully applied in the dose distribution measurements for LGK [4, 9]. To our best knowledge, the new TLD-100H disks has not yet been used in the LGK dosimetry. 23

41 Monte Carlo-based LGK modeling has also been studied. Cheung et al. [10, 11, 12] did a series of calculations using EGS4 code. Their results showed that Monte Carlo method could be applied to evaluate the dose profile from the planning system. Recently Moskvin et al. [2] also reported their excellent results calculated by PENELOPE code [13]. Cheung simulated particles right from where they were born and also showed acceptable efficiency. Moskvin performed the simulation in two stages. In the first stage, the characteristics of photons beams at the outlet of each channel were calculated. Then equivalent surface sources with the same characteristics were created and the calculations were done with these virtual sources. This two-stage scheme can improve the efficiency in the sense that no transport inside the radiation unit is necessary once the surface sources are created. However in order to get the characteristics and apply them in the surface source creation, the outlet has to be segmented thus the values, such as photon flux and photon angular distribution have to be averaged. In this work, a direct but conceptually more accurate LGK modeling is developed and presented in Chapter 5. 24

42 CHAPTER 3 FILM DOSIMETRY This chapter describes in detail the absorbed dose profile measurements at the isocenter for all 4 helmets along x, y and z axes with radiographic film EDR2 and radiochromic film MD-55. Film dosimeters are especially suitable for these measurements because of their high resolution and the capability of 2D spatial absorbed dose distribution measurements. For radiographic film EDR2, absorbed dose profiles were readout by an automatic film scanner; while for radiochromic film, they were read out using a manual densitometer as well as the same automatic film scanner. All measured absorbed dose profiles were then compared to the corresponding standard, i.e. absorbed dose profiles from the GammaPlan, to determine the optimal combination of film and readout device for dose measurement. 25

43 3.1. Equipment Radiographic film EDR2 (Extended Dose Range) EDR2 film is the latest type of radiographic film in the family of Kodak Ready-Pack films which are widely used in radiation therapy departments. It was introduced by Kodak in response to the needs of the Radiation Oncology field for performing quality assurance checks for newer treatment modalities like Intensity Modulated Radiation Therapy (IMRT). The wider useable dose response range of the EDR2 film makes it especially suitable for absorbed dose measurements in the LGK. For example, the dose rate of the LGK at Arthur G. James Cancer Hospital, the Ohio State University was 2.319Gy/min (given by GammaPlan on 6/26/02); and the timer error of the machine, which corresponds to the extra absorbed dose received during the patient couch moves in and out of the treatment position, was minute. The dose fluctuation associated with this timer error would thus be 19.9 cgy, a significant fraction of the saturation dose for XV-2 film as indicated in Table

44 Responsive Range Approximate Saturation Exposure PPL cGy 10cGy XTL 1-15cGy 30cGy XV cGy 200cGy EDR cGy 700cGy Table 3.1: Responsive Range Comparison for Films in the Kodak Ready-Pack Film Family EDR2 film response is also approximately linear within the usable dose response range (Figure 3.1), which reduces the number of points required to constuct a calibration curve (H&D curve) for absolute and relative absorbed dose measurement. 27

45 Figure 3.1: Dose response curve of EDR2 film GafChromic TM film MD-55 1 Radiochromic film MD-55 was designed for measurement of absorbed dose for high-energy photons. It has a linear response range up to about 70Gy (Figure 3.2). 28

46 Figure 3.2: MD-55 Film Calibration Curve VXR-16 DosimetryPRO film digitizer 2 The VIDAR VXR-16 DosimetryPRO film digitizer supports 16-bit gray depth, providing better optical density resolution. It is also able to scan radiochromic film, which is not feasible by its predecessor VXR12. The spatial resolution can be as high as 285pixels/inch (8.9µm between two pixels). 1 GafChromic TM MD-55 film, Nuclear Associates, Carle Place, NY 2 VXR-16 DosimetryPRO Film Digitizer, VIDAR System Corporation, Herndon, VA 29

47 Model radiochromic densitometer 3 The Nuclear Associates Model radiochromic densitometer is a member of the family of transmission densitometers. It is especially suitable for MD-55 film dosimetry because it is equipped with an ultra bright red LED light source and a filter of 10nm bandwidth centered at 660nm±2nm that matches the absorption spectrum of GafChromic TM MD-55 (615nm and 675nm). The usable density range is from 0 to 4.00 with optical density resolution Since the positioning of the film for measuring the absorbed dose profiles are accomplished with a manually controlled stage for this transmission densitometer, an obvious disadvantage is that it requires a lot of tedious work to make measurements with this device. For example, in order to achieve 100µm spatial resolution for a complete dose profile of the 18mm helmet that spreads about 5 centimeters, one has to sequentially measure about 500 points, which will take about 1 and a half hours Data processing software OmniPro-Accept 4 The OminPro-Accept software works in conjunction with the VXR-16 DosimetryPro film scanner to provide automatic film densitometry and 3 Model radiochromic densitometer, Nuclear Associates, Carle Place, NY 4 OmniPro-Accept, IBA, Bartlett, TN,

48 dosimetry capabilities. The software provides not only the usual functionalities of a commercial film scanning software in radiation oncology, such as image displaying, dose profile extraction, isodose measurements from films, data manipulation and so on, but also the added flexibility on importing and exporting data. It supports text-based beam data files. One can create such a file by following its format. The data obtained by the manual densitometer therefore can be imported into the software for comparison of the profiles measured manually to those measured using the automatic film scanner Measurement EDR2 film Preparation EDR2 film comes in batches, each of which has 10 pieces, 12 by 10 in size. Within each batch, films are considered as identical in terms of response to radiation. Based on the design of the polystyrene cassette used for holding the film for the LGK quality assurance phantom, each film was further cut up into twelve 3 by 3 5 small pieces. For the measurements we conducted, 15 small pieces were used: seven for establishing the dose response curve for that film batch in conjunction with the film conditions on the day of the 31

49 experiment; seven for dose measurements in x-y and x-z planes of 4, 8, 14, 18mm helmet, respectively (for the dose profile in x-y plane of 18mm helmet, one of those 7 pieces for calibration was used). The last one was for background subtraction. The film handling and cutting was done in a darkroom because radiographic film is sensitive to visible light and the small cut pieces were kept in the darkroom. The seven points chosen for dose response (H&D) curve covers the whole useable response range of EDR2 film (Table 3.2). Based on the dose rate of the day,d, exposure time T was determined for each point. The real doses, D c, were corrected by the time error T err (Equation 3.1). D = D ( T + T ) (Equation 3.1) c err 32

50 Time(min) Dose(Gy) DoseCorrected(Gy) Table 3.2: Dose levels for H&D curve (D =2.412Gy/min on 3/5/02, T err =0.08min) The exposure time for all other small pieces except for the one used in background subtraction was 2.0 minutes. Since it is not convenient to develop films with small size in an automatic film processor, a film holder was fabricated on which the exposed small film pieces were mounted for processing. This film holder was fabricated by cutting rectangular holes in a developed blank normal medical film (Figure 3.3). The holes were smaller than films to be exposed but larger than the biggest spot from the highest dose of 18mm helmet. 33

51 Figure 3.3: Film holder Exposure The cut pieces of film were stored in an envelope marked Unexposed and kept in the darkroom all the times. When a measurement began, the polystyrene cassette was brought into the darkroom and a cut piece of film was mounted into the groove of the cassette with a non-residual tape. Inside the cassette, two lines had been drawn for the purpose of determining the isocenter. A pin was used to mark the film for the purpose of positioning the isocenter and indicating the film orientation (Figure 3.4). 34

52 Figure 3.4 Marks on the Film It was not necessary to mark on films the irradiated dose level because one could distinguish them easily by observing the shape, size and the darkness of the spots. After marking the film, the other half of the cassette was put back, closely against the first half. This light-tight cassette prevented the film from getting exposed by visible light during carrying the film from darkroom to the LGK room and, after exposure, carrying film back to the darkroom. 35

53 After the helmet of selected size was mounted onto the LGK, the cassette was inserted into the polystyrene phantom, and the phantom mounted onto the helmet with the trunions such that the center of the phantom was located at position X=100, Y=100 and Z=100 (X, Y, and Z are measured in the stereotactic frame coordinate system). The marked side of the film was set so that it faces the incidence of gamma rays in the case of x-y plane dose profile measurement. For x-z plane, the marked side is toward the positive direction of X axis. After the irradiation was done, the cassette was taken out of the phantom and carried to the darkroom where the film was unmounted and stored in an envelope marked as Exposed. After all films were exposed, they were mounted on film holders in the darkroom, 9 pieces for each film holder. Then the film mounted in the holder were developed using a standard medical automatic x-ray film processor MD-55 film For the work presented in this thesis with radiochromic film, we did not expose any new film. The film exposed as a part of the 2001 yearly quality 36

54 assurance checks for the gamma knife were used, but was re-processed using the radiochromic densitometer and the Vidar scanner Dose profile acquisition Using automatic film scanner VXR-16 PRO The developed EDR2 films mounted on the film holder were then scanned with VXR-16 PRO. Before measuring the dose profiles, the scanner was calibrated to read optical density in conjunction with the OmniPro software, using a calibrated step-wedge film that was provided by the manufacturer. This was followed by a dose response calibration for the EDR2 film, which was performed by scanning films had received known absorbed doses (7 pieces exposed in x-y plane using the 18mm helmet). The fog OD (obtained from the blank EDR2 film) was used for background subtraction. Then films for 4, 8, 14, 18mm helmets, both in x-y and x-z planes, were scanned and the inplane and crossplane dose profiles were excerpted. For plotting purpose, the data of all dose profiles were exported to KaleidaGraph for windows from Synergy Software. 5 KaleidaGraph, Synergy Software Technologies, Vermont, Canada 37

55 OD dose (Gy) Figure 3.5: Measured H&D curve for EDR2 film Figure 3.5 showed that this batch of film (assuming that variation of films within the same batch is negligible) had a linear dose range between 1Gy to about 5.5 Gy. Below and above this region, the film response showed some extent of nonlinearity. Because of the small size of MD-55 films, they were also mounted on another film holder with smaller holes to facilitate the scanning. Therefore 38

56 the same procedure used in the EDR2 film was applied except a new calibration curve was established for MD-55 film Using the manual densitometer Model H&D (Optical Density vs. Absorbed Dose) curve measurement The H&D curve for MD-55 radiochromic film was obtained by measuring the net optical density of films, which were exposed to predetermined absorbed doses using the 18mm helmet. Dose OD1 OD2 OD3 Averaged OD Background Net OD Table 3.3: H&D curve data for MD-55 In Table 3.3, the ODs at each dose point were measured near the visually estimated isocenter. The net OD was obtained by subtracting the background 39

57 (the OD of a blank film from the same batch) from the averaged OD of each dose level. The resultant H&D curve (for dose levels less than 60Gy) for MD-55 was shown in Figure 3.6. In order to take into account the known nonlinear effect at the low dose range of the radiochromic film, a fourth-order polynomial was used to fit the data (the third-order polynomial fit was also applicable; the second-order polynomial fit, however, showed slight nonlinearity in the high dose range). The linear dose response range is from about 5Gy up to 60Gy y = x x x x - 3E Dose(Gy) Net Optical Density Figure 3.6: H&D curve for MD-55 radiochromic film 40

58 Dose profile measurement Since no marks had been made for the MD-55 film, the isocenter had to be determined before a dose profile was measured. The following procedures were used to locate the position of the isocenter: 1. Get the maximum optical density (MOD) of a film by measuring the optical density of several points near the visually estimated center; 2. Move the x-ruler while fix the y-ruler of the manual densitometer; find two positions with optical density equal to MOD/2. It is better for these two positions away from each other as far as possible. Record coordinates of these two positions, (x 1, y 0 ) and (x 2, y 0 ); 3. Move the y-ruler while fix the x-ruler; repeat the same positioning described in step 2. Record coordinates of the new two positions, (x 0, y 1 ) and (x 0, y 2 ); 4. Calculate the coordinates of the isocenter, which is given by ((x 1 +x 2 )/2, (y 1 +y 2 )/2); 5. Fix y-ruler at (y 1 +y 2 )/2 and move x-ruler to measure ODs at different points along x-axis; this gives the dose profile along x axis; 6. Fix x-ruler at (x 1 +x 2 )/2 and move y-ruler to measure ODs at different points along y-axis; this gives the dose profile along y-axis. 41

59 For films exposed in the x-y plane, step 1 to 6 was repeated. The exposure spot in x-z plane is not symmetrical in all directions; instead it is more like an ellipse with long axis along x and short axis along z. However the isodose contour (relative dose greater than 0.8) is approximately a circle. Therefore the same procedure can be used with the modification that the optical density used for locating isocenter was chosen to be 90% of the MOD. After the measurement was done, the OD was converted to dose using H&D curve of the MD-55 film Data processing Dose profiles used as standard were obtained by sampling their continuous version stored in the GammaPlan TM. Then all data measured were fed into OmniPro-Accept for systematic comparison of profile parameters. For the EDR2 film, after an exposed film was scanned using VXR16-PRO, profiles along inplane and crossplane were extracted. The dose profile parameters, FWHM and penumbra, were automatically calculated. Then the dose profile was exported to KGraph for plotting. Before doing that, the dose profile was centered and re-normalized using menu options of the 42

60 software. Although other ways were applicable, the easiest way to export data was selecting a dose profile, choosing copy option from the menu and pasting to Excel. By this way, the dose profile data were shown as four columns indicating x, y, z coordinates and relative dose, respectively. The data block was then copied to plotting software. For dose profiles obtained by scanning MD55 film, the above procedure was also used. The data of MD55 by the manual densitometer were first converted to beam data files supported by OmniPro-Accept. The conversion code (APPENDIX B) basically generated a file having the same format as that in files generated by the software but with different data block. The format of a beam data file was carefully examined and also described in the APPENDIX B. After a dose profile was read in by the software, the same procedure used for scanned data was applied. The data from the GammaPlan were processed simply the same way as the manually obtained MD55 data Error analysis During the dose profile measurements, various factors may affect the accuracy of dose measurements. Because of the different imaging mechanisms of EDR2 and MD-55 films, the focus of error analysis are 43

61 different. For the EDR2 film, the error could be from the film itself, the non-uniformity of each film and the variation of response between different films, from the processing procedure and from the scanner like the positioning accuracy and the average effect due to the size of the light detector. But the two dominant recognized factors for radiographic film are the variation of processing procedure and the size of the light detector. In this case, films for dose measurements and films for calibration were from the same batch and processed at the same time, therefore the calibration curve could be considered as truly reflect the response of all films. The error introduced by processing procedure can be ignored. VXR-16 DosimetryPRO film scanner uses a CCD array to detect the light density change. Each CCD is very small (about 20µm). With 71dpi scanning mode, a block of 64 CCDs are mapped to a pixel with size of 356µm, which is small enough to ignore the averaging effect. However, even these two dominant error contributions were eliminated; it was still hard to give an error estimation for each point in the dose profile because of the difficulty in estimating all kinds of uncertainties in the process. For MD-55 film, its accuracy depends on the film uniformity, environmental stability, the scanning system used and so on. Here one of the main error 44

62 contributions associated with the finite size of the light detector is discussed. Manual densitometer Model used a detector with an aperture 2mm in size. This relative large window effectively averaged the optical density in that area. This effect would not affect the dose measurement in areas where delivered dose changed slowly or linearly, such as the flat area and the penumbra area of the dose profile. However, for those areas where dose changed nonlinearly, such as shoulders of a dose profile, the smoothing could give different dose values. This point was demonstrated in Figure 3.7, where the complete dose profile (dash line) was derived using cubic spline interpolation on the sampled dose profile (solid dotted line) that was from the GammaPlan. The dots were obtained by averaging the derived profile with a 2-mm long moving window. This picture showed that, generally, the 2-mm aperture of the densitometer did not introduce significant error to the system; the measurement of dose distribution in the shoulder area could have about 2% error. This conclusion also held for dose profiles of other helmets. 45

63 sampled dose profile interpolated dose profile smoothed dose profile Figure 3.7: Averaging effect of the light detector with a 2-mm aperture 3.6. Results and conclusion Dose profiles in x, y and z axes for 4, 8, 14 and 18mm helmets were shown from Figure 3.8 to Figure

64 Dose Profiles along x-axis for the 4mm Collimator Helmet Radiochromic Film with Manual Radiochromic densitometer Treatment Planning System Radiochromic Film with Automatic Film Scanner Radiographic Film (EDR2) with Automatic Film Scanner Distance in x-direction (mm) Figure 3.8: Dose profiles along x-axis for 4mm helmet 47

65 Dose Profiles along the y-axis for the 4mm Collimator Helmet Radiochromic Film with Manual Radiochromic densitometer Treatment Planning System Radiochromic Film with Automatic Film Scanner Radiographic Film (EDR2) with Automatic Film Scanner Distance in y-direction (mm) Figure 3.9: Dose profiles along y-axis for 4mm helmet 48

66 Dose Profiles along z-axis for the 4mm Collimator Helmet Radiochromic Film with Manual Radiochromic densitometer Treatment Planning System Radiochromic Film with Automatic Film Scanner Radiographic Film (EDR2) with Automatic Film Scanner Distance in z-direction (mm) Figure 3.10: Dose profiles along z-axis for 4mm helmet 49

67 Dose Profiles along x-axis for the 8mm Collimator Helmet Radiochromic Film with Manual Radiochromic densitometer Treatment Planning System Radiochromic Film with Automatic Film Scanner Radiographic Film (EDR2) with Automatic Film Scanner Distance in x-direction (mm) Figure 3.11: Dose profiles along x-axis for 8mm helmet 50

68 Dose Profiles along the y-axis for the 8mm Collimator Helmet Radiochromic Film with Manual Radiochromic densitometer Treatment Planning System Radiochromic Film with Automatic Film Scanner Radiographic Film (EDR2) with Automatic Film Scanner Distance in y-direction (mm) Figure 3.12: Dose profiles along y-axis for 8mm helmet 51

69 Dose Profiles along z-axis for the 8mm Collimator Helmet Radiochromic Film with Manual Radiochromic densitometer Treatment Planning System Radiochromic Film with Automatic Film Scanner Radiographic Film (EDR2) with Automatic Film Scanner Distance in z-direction (mm) Figure 3.13: Dose profiles along z-axis for 8mm helmet 52

70 Dose Profiles along x-axis for the 14mm Collimator Helmet Radiochromic Film with Manual Radiochromic densitometer Treatment Planning System Radiochromic Film with Automatic Film Scanner Radiographic Film (EDR2) with Automatic Film Scanner Distance in x-direction (mm) Figure 3.14: Dose profiles along x-axis for 14mm helmet 53

71 Dose Profiles along the y-axis for the 14mm Collimator Helmet Radiochromic Film with Manual Radiochromic densitometer Treatment Planning System Radiochromic Film with Automatic Film Scanner Radiographic Film (EDR2) with Automatic Film Scanner Distance in y-direction (mm) Figure 3.15: Dose profiles along y-axis for 14mm helmet 54

72 Dose Profiles along the z-axis for the 14mm Collimator Helmet Radiochromic Film with Manual Radiochromic densitometer Treatment Planning System Radiochromic Film with Automatic Film Scanner Radiographic Film (EDR2) with Automatic Film Scanner Distance in x-direction (cm) Figure 3.16: Dose profiles along z-axis for 14mm helmet 55

73 Dose Profiles along x-axis for the 18mm Collimator Helmet Radiochromic Film with Manual Radiochromic densitometer Treatment Planning System Radiochromic Film with Automatic Film Scanner Radiographic Film (EDR2) with Automatic Film Scanner Distance in x-direction (mm) Figure 3.17: Dose profiles along x-axis for 18mm helmet 56

74 Dose Profiles along the y-axis for the 18mm Collimator Helmet Radiochromic Film with Manual Radiochromic densitometer Treatment Planning System Radiochromic Film with Automatic Film Scanner Radiographic Film (EDR2) with Automatic Film Scanner Distance in y-direction (mm) Figure 3.18: Dose profiles along y-axis for 18mm helmet 57

75 Dose Profiles along z-axis for the 18mm Collimator Helmet Radiochromic Film with Manual Radiochromic densitometer Treatment Planning System Radiochromic Film with Automatic Film Scanner Radiographic Film (EDR2) with Automatic Film Scanner Distance in z-direction (mm) Figure 3.19: Dose profiles along z-axis for 18mm helmet 58

76 Qualitatively, in terms of shape all the measured profiles were in good agreement with benchmarks from the planning system. A further quantitative comparison of FWHM and penumbra size was made in Table 3.4 and 3.5. Generally, all the measured parameters were larger than those from GammaPlan. In terms of percentage, some of them are in fact quite high. For example, in the 4mm penumbra measurement, the smallest discrepancy was about 25%. However, most of the differences in absolute value were less than 0.5mm, smaller than the physical size of most of other dosimeters. Therefore, the results could be considered as reasonably good. 59

77 Gamma Plan Radiochromic - Manual Radiochromic VXR-16 EDR VXR-16 Dose Profile Parameters 4mm - X direction 50% Width Penumbra - Left Penumbra - Right Dose Profile Parameters 4mm - Y direction 50% Width Penumbra - Left Penumbra - Right Dose Profile Parameters 4mm - Z direction 50% Width Penumbra - Left Penumbra - Right Dose Profile Parameters 18mm - X direction 50% Width Penumbra - Left 10.1 N/A Penumbra - Right 10.1 N/A Dose Profile Parameters 18mm - Y direction 50% Width Penumbra - Left 10.1 N/A Penumbra - Right 10.1 N/A Dose Profile Parameters 18mm - Z direction 50% Width Penumbra - Left Penumbra - Right Table 3.4: FWHM and penumbra size comparison (4 and 18mm) 60

78 Gamma Plan Radiochromic - Manual Radiochromic VXR-16 EDR VXR-16 Dose Profile Parameters 8mm - X direction 50% Width Penumbra - Left 5.2 N/A Penumbra - Right 5.2 N/A Dose Profile Parameters 8mm - Y direction 50% Width Penumbra - Left Penumbra - Right Dose Profile Parameters 8mm - Z direction 50% Width Penumbra - Left Penumbra - Right Dose Profile Parameters 14mm - X direction 50% Width Penumbra - Left 8.2 N/A Penumbra - Right 8.2 N/A Dose Profile Parameters 14mm - Y direction 50% Width Penumbra - Left Penumbra - Right Dose Profile Parameters 14mm - Z direction 50% Width Penumbra - Left Penumbra - Right Table 3.5: FWHM and penumbra size comparison (8 and 14mm) 61

79 From the tables, it is hard to tell which combination of film and readout device is the best choice among these three LGK dosimetries. The criterion set here is that an ideal dosimeter should be accurate and convenient. As for this specific application, both EDR2 and MD-55 films can be used to accurately measure dose profiles. The automatic film scanner also greatly facilitates the readout process of exposed films and its performance on MD-55 is also satisfactory. The manual densitometer is accurate but not convenient in the sense of requiring a lot of tedious work. EDR2 film has a linear dose response in the clinical range and high precision can be achieved in this range. But the processing procedure somewhat complicates its usage. MD-55 film is easier to use for its self processing nature. In this sense, MD-55 radiochromic film is better than EDR2 radiographic film. Nonetheless, back to the first sub-goal of this study, the results clearly showed that EDR2 film can be used to accurately measure the dose profiles for the LGK. 62

80 CHAPTER 4 TLD MEASUREMENT This chapter describes the use of TLD-100H disks to potentially measure the structure doses for LKG. The high sensitivity to photons and excellent linearity down to few cgy make it suitable to accurately measure the dose in the low dose regions away from the treatment isocenter. In this study, 25 TLD disks were calibrated first and then used to perform measurements in the high and low absorbed dose regions to evaluate the TLD-100H disks as a dosimeter for the LGK. The major difficulty associated with TLD dosimetry is that many factors can significantly affect the reading of a TLD dosimeter, such as the stability of the TLD reader, the heating and cooling cycles in the reader and the annealing process. Also the sensitivity of the dosimeter may change from repeated use. This chapter addresses these issues in detail and describes some of the solutions we worked out to overcome them. 63

81 4.1 General description of the experiment Equipment The TLD dosimetry system used in this work consists of TLD-100H disks (Bicron, Solon, OH, with physical size 3.6mm in diameter and 0.60mm in thickness), a TLD reader with control software (Teledyne System 310) and an annealing oven (Thermolyne F47925 furnace) along with other accessories, including a vacuum tweezer, an oxidized aluminum annealing planchet with 100 depressions and a reading planchet Procedure Irradiation Different irradiation procedures were used for the calibration and measurements under different conditions. These are described in more details in later sections Readout process Since the fading of TLD-100H disks is negligible, the time interval between the irradiation and the readout is not crucial. Nevertheless, irradiated TLD disks were read out at least 16 hours after irradiation for all the measurements. 64

82 The warm-up time of the TLD reader was experimentally shown to be not important. In all the readouts, this time varied from 3 to 10 minutes. The software-controlled readout process consisted of two stages: system self-check and thermoluminescent (TL) cycle. At the first stage, the TLD reader automatically checked and recorded certain values affecting the system performance, such as LS (light source for tracing the gain drift of the photomultiplier tube, PMT) and DC (dark current). It was noticed that the LS consistently decreased as the readout process proceeded (Figure 4.1). Exact reason for this phenomenon was unknown. Probably it was because of the heat build-up from consecutive TL cycles, which affected the gain of amplifiers used in the PMT circuit. The important aspect of LS drifting was its effect on counting. The counts for the same disk with exactly the same exposure, assuming no degradation of the disk, were statistically different if LS differed during the readout process. Because of the drifting, the counts of disks undesirably depended on the order they were readout, which was observed in the measurements. Therefore, the LS value for each disk had to be recorded and used as a correction factor. It was noticed that the cross-chip variation after LS correction was within 2%, half of that before LS correction. 65

83 1900 LS June, CHIP # Figure 4.1: LS drifting during the readout process (readout order 1 30) The TTP (Time-Temperature Profile) used in the readout process was recommended by the TLD manufacturer and is shown in figure 4.2. The interval for integration of the TLD signals was chosen from 24 th to 48 th second. The preheat area (from 14 th to 24 th second) eliminates the effects of noise and other undesirable sources. The TTP in the reader was quite repeatable unless the thermal conductivity of the reading planchet changed. 66

84 , , , 240 Temperature(C) , , , Time(s) Figure 4.2: Time-Temperature Profile used for TLD disks readout (the first number of the data pair was time and the second was temperature) The thermal conductivity of the reading planchet was crucial for TLD readout. The edge of the planchet is easily easy to get rusted because of the repeating heating and cooling from each reading cycle as well as the friction of the reading planchet with the TLD reader when the planchet is inserted into the reader. The buildup rust would affect the uniformity of heat distribution of the planchet, resulting in the change of TTP which included 67

85 the change of heating slope and the stability of the temperature. The change of TTP could greatly affect the shape of the glow curve (Figure 4.3) and possibly the counting of a disk in the case that the peak(s) drifted out of the integral interval. Therefore it was important to sand the edge before each measurement (not necessary before each disk was readout). counts counts with rusted planchet counts with sanded planchet TTP with rusted planchet TTP with sanded planchet temperature time (1/10sec) 0 Figure 4.3: Effect of the shape of TTP on glow curve 68

86 The software equipped with System 310 controls the whole readout process and displays data and glow curve. The glow curve can be stored in the form of text file and used for further processing Annealing process Before the initial use, all disks were annealed twice with the recommended TTP. After that, when all TLD disks were readout, they were put on an oxidized aluminum annealing planchet, which then was put into the annealing oven for 10 minutes annealing in 240 C. This temperature could be manually set on the front panel of the oven. TLD-100H would be damaged in a higher temperature; therefore one had to make sure the 240 C limit was not exceeded Cooling process After 10 minutes annealing, these TLD disks could be cooled down in two different ways: slow cooling process and fast cooling process. By slow cooling the TLD disks were left in the oven, which was turned off after the annealing time was completed. Since the annealing oven was a very good adiabatic container, the disks were cooled down in a very slow and repeatable way. Another way was to let disks cool down in the air, i.e. taking 69

87 them out of the oven. Because of the huge difference of the disk temperature and the ambient temperature, this cooling process is much faster. However in the sense of repeatability, the latter process was difficult to guarantee every time the disks were cooled down in the same rate because the environmental temperature changed from time to time. A big gain with the fast cooling process was the increased sensitivity, about 100% higher than that with slow cooling process (Figure 4.4). It was also experimentally shown that the response of TLD disks with fast cooling process was reasonably good and reproducible. Considering the purpose of this experiment was to measure the low structure dose in the normal tissue, higher sensitivity was preferable, just as the reason to choose TLD-100H whose sensitivity to photons is only 1/15 of the former one. 70

88 fast cooling slow cooling counts time (1/10sec) Figure 4.4: Sensitivity change due to the cooling process 4.2 Calibration in MXE This section gives a detailed description of the TLD calibration process. Thirty TLD-100H disks were used for this purpose. Because of the different response of each disk, each disks was calibrated individually, i.e. every disk retained its identity during the whole calibration process. Since observable sensitivity change was found when fast cooling process was resumed after slow cooling process was tried, sensitivity change had to be corrected. For estimating the sensitivity drift, 5 disks with similar dose response were 71

89 irradiated with 2Gy each time when other disks were irradiated to other dose level. Then the sensitivity change detected by these five disks was used to correct the counts of other TLD disks. Finally the calibration curve was constructed based on the average response of all the rest 25 disks at each dose level Equipment MXE, a linear accelerator based photon and electron beam generator in the Radiation Oncology Department at the Arthur G. James Cancer Hospital and Richard J. Solove Research Institute, was used to deliver the designated dose to TLD disks. It was capable of accurately delivering radiation doses down to as low as 1 cgy, which was useful to construct the calibration curve in the low dose range. A Plexiglas irradiation plate with 40 depressions uniformly distributed along a circle was used to hold TLD disks. During the irradiation, three solid water blocks of dimension 30 by 30 by 5cm were used with 2 blocks below and 1 above to provide electronic and scatter Experimental setup The disks were placed on the Plexiglas sheet, and covered with a plastic wrap. Two buildup blocks were placed on the treatment table; the Plexiglas 72

90 was placed on top of them and then it was covered with the third buildup block. Using the linac patient laser alignment system, the distance between the Plexiglas sheet and the source was set as exactly 100cm. The center of the sheet coincided with the central axis of the beam. Thus a radical symmetry was obtained and each chip received the same dose (Figure 4.5). Figure 4.5: Calibration setup in MXE 73

91 The number of monitor units was calculated using the equation 4.1: MU ID TMR FF SADFactor OAR = (Equation 4.1) Where: ID = Irradiation dose in cgy TMR = Tissue Maximum Ratio FF = Field Factor SADFactor = Source to Axis Distance factor OAR = Off Axis Ratio For SAD=1m, a field size and r=7.5cm radius circle, other values could be found from the table used for MXE dose calculation: SADFactor=1, TMR=0.945, FF=1.058 and OAR= Then Equation 4.1 could be reduced to: ID MU = (Equation 4.2) As the MU had to be an integer, the MU values were determined first and 74

92 corresponding IDs were calculated using Equation 4.2. The values of MUs and IDs were listed in Table 4.1: MU Dose(cGy) MU Dose(cGy) Table 4.1: Dose levels used for calibration Readout After the irradiation, the TLD disks were readout using the procedures described in section 4.1.2, i.e. readout annealing fast cooling. Then another irradiation was performed and the same procedures repeated Data processing The data processing procedure used for TLD readings was shown in Diagram 4.1: 75

93 Diagram 4.1: TLD data processing First of all, the raw count (C i ) of disk i was corrected by LS: C LS i Ci = 1800, (Equation 4.3) LS i The scaling factor 1800 was close to the average of LS; however, its exact value was not important. DCF (Disk Correction Factor) was obtained by comparing the different responses of disks at absolute dose cGy (MU=190). Six irradiations 76

94 were performed at this level and the average count of each disk was calculated based on the LS-corrected values. Then the response of the first disk was set to 1 and DCFs for other disks were calculated using Equation 4.4 (also see Table 4.2): DCF i C LSi, = (Equation 4.4) C LS,1 These DCFs were used for all dose levels. Given the count of disk k at certain dose level, the modified count was: C C LS, k DCFk, = (Equation 4.5) DCFk 77

95 #1 #2 #3 #4 #5 #6 AVERAGE DCF (to be continued ) Table 4.2: Calculation of Disk Correction Factor (#n means the n th irradiation; each row was readings for a disk) 78

96 (continued from Table 4.2) #1 #2 #3 #4 #5 #6 AVERAGE DCF Considering the possible sensitivity drift between measurements due to the annealing process as well as the radiation damage to disks, an SCF (Sensitivity Correction Factor) was used for compensation. More specifically, in each measurement, 5 out of 30 disks were chosen to be irradiated with MU=190. The average count of these five disks (after LS correction and DCF correction) was then compared to the average value of the same 5 disks when all 30 disks were irradiated with MU=190. The ratio of these two values was defined as SCF (Table 4.3). The SCFs for MU=95, 190 and 285 were set to be Measurements at these levels did not take into account the sensitivity drift. However, they were carried out before the trial of switching fast cooling and slow cooling process when the readings were believed quite repeatable. The excellent linearity of the calibration curve also justified this simplification. 79

97 Therefore, the count after sensitivity compensation was (note that the SCF was not chip-specific; instead it was for all chips in a measurement; SCF D represents SCF for dose level D.): C SCF, k C DCFk, = (Equation 4.6) SCF D MU=3 MU=6 MU=12 MU=24 MU=48 chip # chip # chip # chip # chip # average SCF MU=71 MU=380 MU=475 MU=570 chip # chip # chip # chip # chip # average SCF Table 4.3: SCF calculation (reference value = ) 80

98 Finally for each dose level, the average response of all the 25 disks was taken as the count for that level (Equation 4.7). C D = N k = 1 C SCF, k N (Equation 4.7) This whole procedure was illustrated in Table 4.4: Error analysis Equation 4.3 to 4.7 could be combined and rewritten as Equation 4.8: C D = N Ck ( ) = LS DCF SCF N k 1 k k D (Equation 4.8) It was clear that the errors depend on not only the fluctuation of counts, but also LS, DCF and SCF. After the LS and DCF correction, the count for each disk, C DCF, k could be treated as a measurement of the true count, C D, of a TLD disk at dose level D. The SCF was a constant at that dose level. To simplify the analysis, the uncertainty of LS and DCF were ignored. Therefore the error of C D can be expressed as: 81

99 C = C ± SC ( ) (Equation 4.9) D D D where SC ( ) D = 1 N 1 N k= 1 ( C C ) SCF, k N D 2 (Equation 4.10) 82

100 Chip C i LS C Ci DCF CLS, k, = 1800 CDCFk, LS DCF LSi i C DCFk, = CSCFk, = k SCF Table 4.4: Data processing for MU=380, SCF MU=380 = Calibration curve: The counts at each dose level and the calculated standard deviation based on Equation 4.9 and 4.10 were listed in Table 4.5. The SDs were very small, 83

101 which showed the effect of correction factors. Dose Average SD(%) Counts Table 4.5: Dose levels and corresponding TLD readings The calibration curve was drawn on Figure 4.6 (the fitted line was forced to pass through point (0, 0); for dose level 98.78, and cGy, the average values were calculated using all the 30 disks instead of 25; in this case, N=30 instead of 25): 84

102 y = x R 2 = calibration fitted line counts absorbed dose(cgy) Figure 4.6: Calibration curve for TLD-100H disks With all the correction factors, the TLD disks showed a very good linearity in a large dose range (from about 3cGy to 6Gy). 4.3 Calibration in LGK In order to measure the absolute dose as well as the dose profile for the LGK, these TLD disks had to be fixed inside a cassette, which was then inserted 85

103 into the phantom. For this purpose, a film template was created to hold the disks. This rectangular template was made of a blank film with a sequence of holes along each central line, which coincides with the x or z axis of the LGK. The size of holes was slightly bigger than the disks so that the TLDs could be easily put in and yet were not able to move around. In order to measure the absorbed dose profiles, the holes needed to be as close as possible. However, due to the difficulty in drilling such small holes (3.7mm in diameter) close together in the film, an alternative scheme was used. Two films with the same dimension were prepared and a set of every other complementary holes were drilled in each film in such a way that they covered the area of a half dose profile with minimum overlap as illustrated in figure 4.7. In figure 4.7, the holes shown in solid were drilled in one film and the dotted holes in the second. When these disks calibrated at the MXE were used to measure the absolute dose at the isocenter with the 18mm helmet, the measured doses were 10% higher than the anticipated doses. This led to the re-calibration of these disks in the LGK as described below. 86

104 Figure 4.7: A quarter of the film template (solid circles are in one film and dashed circles are in the other; the number corresponds to the index of a TLD disk) During the calibration of the TLD s in the LGK, a disk was placed right in the center of the film template, which coincided with the isocenter of the LGK. The dose levels chosen covered the same range as that in the MXE. 87

105 For each dose level, two disks were exposed. For the count of each disk, the correction factor DCF was also used. (assume DCFs did not change in these two different calibration conditions). The average value of the counts of those two disks was used to construct the calibration curve for the LGK (Figure 4.8). counts MXE LGK y = x R 2 = y = x R 2 = absorbed dose(cgy) Figure 4.8: Calibration curves for MXE and LGK Figure 4.8 showed that for the same absorbed dose, the response of TLD-100H disks in the LGK was slightly higher than that in the MXE. 88

106 Three factors might contribute to the response deviation: different photon energy, different dose rates (the dose rate of LGK was 2.274Gy/min while that of MXE was Gy/min with the parameters mentioned in the section 4.3) and different irradiation geometry. According to the manufacturer s configuration sheets, there is no dependency on photon energy higher than 300keV. So the first factor could be eliminated. The check of dose rate dependency was also conducted. It turned out that the response deviation did not result from the difference of dose rates. For a quick check, a procedure similar to the one used for the calibration in the LGK was used, i.e., two disks for each dose level. The point was to obtain the same dose rate in the MXE as that in the LGK. The dose rate in MXE was changeable by adjusting the SAD (source to axis distance). The source in the MXE could be considered as a point source without losing accuracy. Therefore the dose rate in the axis was proportional to the inverse of the square of distance from the irradiation position to the source. Simply D1 2 D SAD1 2 SAD = 2 89

107 Given D 1=2.5995Gy/min (corresponds to 250MUs/min) for SAD 1=100cm, the SAD for D 2=2.274 (matching that in the LGK) is SAD 2 =106.9cm. Therefore by lowering the treatment table of the MXE from 100cm to cm away from the source, the dose rate will be the same as that of the LGK. A new calibration curve was created at this dose rate, which was shown in Figure 4.9: MXE MXE LOW_DOSE_RATE y = x counts y = x absorbed dose(cgy) Figure 4.9: Calibration curve with normal dose rate and lowered dose rate in MXE. 90

108 These two calibration curves overlapped right on each other as showed in Figure 4.9, which clearly demonstrated that the difference in dose rate did not contribute to the dose deviation. So it was very likely that the TLD response was sensitive to the irradiation geometry. At the MXE, the photon beam is primarily incident at right angles to the top of the TLD while in the LGK, the gamma ray beams are incident at different angles up to 0 degree (in the same plane as the TLD s). However, the exact reason for this difference is not clear. A quick check of the effect of irradiation geometry on TLD response was also conducted by irradiating the TLD s in a spherical phantom and rotating the gantry of the MXE so that photons were incident on the TLDs at different angles. Figure 4.10 showed the relative absorbed doses for five different angles. In the case of 0, the central axis of the photon beam from the MXE was perpendicular to the surface of TLDs; in the case of 90, the central axis of the beam was parallel to the surface of TLDs. It was clear from the figure that the responses of the TLD disks were dependent on the angle that photons incident. As the angle increases, the response also increases, which is consistent with higher response observed in the calibration performed in the LGK. 91

109 relative dose (%) angle (degree) Figure 4.10: Angular dependency of TLD-100H disks 4.4 Dose profile measurement The dose profile of the LGK was also measured using the TLD disks with the new calibration curve (The calibration curve was forced to go through point (0, 0) here, Figure 4.11). First, the film template was fixed in the polystyrene cassette and then TLD disks were carefully placed into holed according to their index. Finally, the whole set was inserted into the phantom and irradiated in LGK for 2.4 minutes with the 128mm helmet. 92

110 4.4.1 Results The coordinate of the center for each TLD disk, absolute dose and the relative dose of that disk were listed in Table counts y = x R 2 = absorbed dose(cgy) Figure 4.11: Calibration curve from LGK for TLD-100H disks 93

111 TLD TLD X(cm) AD(cGY) RD(%) Z(cm) AD(cGY) RD(%) index index Table 4.6: Dose profile measurement using TLD disks (AD: Absolute dose; RD: relative dose) Given the dose rate 227.6cGy/min on 8/7/02, the absolute dose received in the isocenter with irradiation time 2.4 minutes plus time error 0.08min was cGy. The measurement of TLD disk yielded cGy/min, only 1% less than the value from GammaPlan. The dose profile measurement had to take into account the smoothing effect resulted from the finite size of TLD disk, like the one discussed in the 94

112 manual densitometer. The diameter of TLD disks was 3.6mm, almost twice as big as the diameter of the aperture. Figure 4.12 showed the effect, which lowered and smoothed the shoulder but did not change other parts of a dose profile noticeably (the same procedure was used as that used in the chapter 3 except the moving window now had the width of 3.6mm) sampled dose profile interpolated dose 1 profile smoothed 0.95 dose profile Figure 4.12: Averaging effect of TLD disks The measured dose profiles were shown in figure 4.13 and 4.14, which 95

113 clearly showed the smoothing effect. The TLD results were in good agreement with the standard profile in most of the dose points sampled profile smoothed profile TLD measurement Figure 4.13: Dose profile along x axis (18mm) 96

114 sampled profile smoothed profile TLD measurement Figure 4.14: Dose profile along z axis (18mm) Error analysis According to the statistics for a single measurement, the uncertainty was given by the square root of the measurement. Table 4.7 showed errors for each disk. In the error calculation, the count of each disk was square rooted and then converted dose. As the absorbed dose increases, the count of a TLD disk recorded in the TLD reader increases corresponding, which yields a 97

115 smaller standard deviation because the standard deviation is proportional to the inverse of the square root of the measurement. TLD index AD (cgy) DV (cgy) SD (%) TLD index AD (cgy) DV (cgy) SD (%) Table 4.7: Error for TLD absolute dose measurements (AD: average dose; DV: deviation; SD: standard deviation) 4.5 Conclusion Although it turned out that the TLD-100H disks showed angular dependance and the calibration of these disks had to be done in the LGK instead of MXE, 98

116 the calibration procedure provided valuable opportunities to identify some issues not known to us before, such as the LS drifting and huge sensitivity change due to different cooling process. Correction factors, such as DCF and SCF, will be useful for compensating cross-disk deviation and sensitivity drifting from the annealing process. The TLD-100H disks showed a very good linearity on dose response in a wide dose range, which coud be seen in the calibration curve obtained from MXE. In the LGK, the calibration in low dose has to be established. For the absolute dose measurement, the measurement was very close the calculated value. Although the calculated value was not within one standard deviation of the measurement (558.58±0.66cGy, calculated value was cGy), this may be improved by carefully examining the behavior of TLD disks in the low dose. Forcing the calibration curve passing through (0, 0) may not be a reasonable procedure because the residual signal of a disk was not 0 after it was annealed. The dose profile measurements showed that TLD disks can be used to accomplish this task. The evaluation of the response in the low dose region, again, requires a more accurate low-dose calibration. 99

117 CHAPTER 5 Monte Carlo Modeling of the Leksell Gamma Knife In this chapter, Monte Carlo modeling of the LGK for performing absorbed dose calculation is described in detail. MCNP provides three types of tallies for energy deposition calculation. The differences between these tallies can affect the accuracy of dose calculation; therefore a thorough analysis of these three tallies is discussed. This is followed by descriptions of various methods for accomplishing the the gamma knife model. A single channel model is presented, which will be a building block or the first stage of the full Gamma Knife modeling. However, due to the fact that we were unable to obtain the detailed geometric configuration of a single channel from the manufacturer, this model was constructed based on the description from Vadim Moskvin et al., which may include some simplifying assumptions [2]. Nevertheless, the idea here is to enhance the understanding of MCNP modeling of the Gamma Knife. The process of modeling, the single channel geometry based on the above is presented in details. This model can be 100

118 easily updated with any changes in the geometry, as more accurate information on the geometry of the source and collimator channel is available from the manufacturer. The full LGK Monto Carlo model was implemented using two simplified single channel models. In one model, photons were considered as being generated from a disk source and perpendicularly incident on the spherical phantom, while in the other model, photons were treated as being emitted from a point source on the top of each channel. A full LGK model utilizing the customized source sampling technique of MCNP is also developed. This scheme is fundamental in the sense that it generates particles directly from the source and implicitly incorporates the geometry of a channel into its sampling algorithm. 5.1 Tallies in MCNP MCNP provides three types of tallies for dose calculation. F4:p is a track length estimator of photons which tallies the flux of all particles over a designated cell. F6:p tallies energy deposition averaged over a cell (MeV/g). It can be regarded as a special case of F4:p tally in the sense that it internally multiplies the flux with a heating function to get energy deposition. With the 101

119 flux-to-dose response function, represented by DE and DF cards in MCNP, F4:p tally can accomplish the same task. But the heating function and response function are not completely the same, which will result in slight difference in energy calculation. *F8:p, energy deposition tally, can be used to tally energy deposited by all particles in a cell instead of converting flux to energy deposition. When a *F8:p tally is used, MCNP follows exactly event to event and collects energy left by all events in that cell. MCNP also allows users to turn on or off the electron transport and to determine, when the electron transport is turned off, the way the non-transported electrons are to be treated. Table 5.1 gives a detailed description of options from MCNP. 102

120 MODE P E MODE P PHYS:P IDES=0 MODE P PHYS:P IDES=1 Electron transport is turned on; all electrons generated are banked and transported. Electron transport is turned off; TTB model is used. In TTB model, electrons are also generated, but they are assumed that they travel in the direction of the incident photon and are immediately annihilated. Bremsstrahlung photons produced by nontransported electrons are banked and then transported. Electron transport is turned off; all electron production is turned off too. All electron energy is assumed to be locally deposited. Table 5.1: Electron transport options in MCNP (TTB: Thick-Target Bremsstrahlung model) Deciding which tally to use and how electron is to be treated depends on the problem to be solved. As mentioned before, the dose profile in the isocenter indicates that there exists a sharp dose gradient region, where electron equilibrium condition is not fulfilled. Therefore the tally that can calculate dose accurately under these conditions is desirable. To pick the appropriate tally requires a good understanding of combinations of these three tallies and electron transport options used in MCNP. When a F4:p is used, along with DE and DF, to get the deposited energy in a cell, it does implicitly assume that the electron equilibrium is established in 103

121 that cell because this tally multiplies the response function specified by the following formula: R( E) = µ en = (1 G ph ) f ph 10 µ E µ ph en / ρ + (1 G ) f µ c c c + (1 G pp ) f pp µ pp For example, the term ( 1 G ) f µ calculates the energy deposited by ph ph ph interaction of an electron generated in photoelectric effect with surrounding media. This part of energy may not deposit locally in real situation because the electron can undergo interaction outside the cell where it is generated. However, when the flux is converted to dose by response function, that part of energy is always considered as locally dissipated. Primarily the F6:p tally has the same limitation although the heating function is slightly different to the response function. The only discrepancy between these two is that heating function does not take into account the energy carried away by electron-induced photons while the response function does. The *F8 tally is based upon a completely different tally algorithm. When variance reduction is absent, this tally exactly follows the transport of a 104

122 history and accumulates the energy deposited by this history in a cell. Passing through a cell does not necessarily contribute to the energy deposition in *F8. Therefore, *F8 does not assume conditions of electronic equilibrium. However, *F8 tally puts certain computational complexity in that collisions inside a small detector is quite rare. Forced collision variance reduction technique has to be used in order to achieve statistical confidence in the dose calculation. In this study, however, this elegant technique was not applied because it would not help if an accurate single channel model was not available. For all simulations performed in this study, F4 tally with DE and DF cards were used. 5.2 Gamma Knife modeling A single source channel in the gamma knife Although it is conceptually possible to model the LGK as a whole and transport the photons right from where they were born, such a Monte Carlo simulation is computationally very inefficient. The LGK radiation unit mostly comprises of shielding, which prevents photons coming out of the machine except through the channels formed by different collimators. The simulation of deep penetration of photons inside the radiation unit is time-consuming and, most importantly, not necessary. A common way is to 105

123 separate the whole simulation process into two stages. The first stage is to find the characteristics of particles coming out of the primary collimators of the LGK, such as energy, position and angular distribution of photons and electrons. Then the information obtained is used in the second stage to construct a surface source with the same spatial, energy and angular distribution. This surface source is only dependent on the size of a helmet; when completed, this surface source can be used to calculate doses either in a polystyrene phantom or a voxelized brain phantom. Because of the greatly improved computational efficient, this surface source can be used for a future MCNP based LGK planning system, our ultimate goal for the Gamma Knife modeling. However, this scheme was not the preferred model for use in this study because another more efficient, elegant, and direct approach for source modeling was developed. The reason we still investigated and performed calculations for a single channel model here was to have a simple method available to check the geometric description of the LGK source and collimator geometry. Figure 5.1 shows the cross-sectional view of a simplified single channel of the LGK (the configurations are from [2] except the air gap). At the top is the cast iron unit with a Co-60 radioactive source, which is surrounded by a 106

124 thin layer of air. As a photon directed towards the treatment isocenter is emitted from the source, it passes the 65mm-long primary stationary collimator that is made of 96% tungsten alloy, followed by the 92mm-long secondary stationary collimator that is made of lead. Finally it reaches the interchangeable helmet collimator, which is also made of 96% tungsten alloy and is 60mm in thickness. The sizes of inner and outer apertures of a channel in 4, 8, 14 and 18mm helmet are measured with a caliper and listed in Table 5.2. The precise configuration of a channel inside the stationary collimators is unknown; therefore these parameters were estimated based on the 18mm helmet. The diameter of the outer aperture of the secondary stationary collimator was assumed the same as that of the inner aperture of the helmet, i.e. 8.28mm. The channel in the secondary stationary and the primary stationary collimator is assumed to be a smooth cone. 107

125 ?? FDVWLURQ WXQJ SULPDU VWDWLRQDU\ FROOLPDWRU θ max? /HDG VHFRQGDU VWDWLRQDU\ FROOLPDWRU WXQJ LQWHUFKDQJHDEO KHOPHW?? XQLWPP Figure 5.1: Cross-sectional view of a single channel with a 18mm helmet 108

126 18mm 14mm 8mm 4mm Inner aperture Outer aperture Table 5.2: Helmet inlet and outlet diameters (mm) Each Co-60 source capsule is loaded with 20 small pellets stacked on each other, all 1mm in diameter and 1mm in height. Thus it can be viewed as a cylinder with 1mm in diameter and 20mm in height. This source modeling was adopted by many Monte Carlo based LGK simulations [2, 10, 11, 12]. Based on the geometry provided in the cross-sectional view, a simple input file was written to calculate the energy distribution of particles in the outlet of the 18mm helmet, which was shown in Figure 5.2 (The MCNP input file is in APPENDIX G). The photon energy was set at 1.25MeV. It was clear from the figure that the scattered photon flux was about three-order less than that of the uncollided photons. Based on this observation, one could conclude that most of photons coming out of the helmet were directly emitted by the source. In other words, if a photon underwent an interaction 109

127 with channel material, it would be removed from the primary beam and contribute nothing to the dose received in the isocenter. Moskvin et al [2] calculated the secondary electron flux spectrum. They found the low energy electron (less than 80~100KeV) flux was one order of magnitude less than that of photons. However electrons within this energy interval would not contribute to the total dose because its range in the air was shorter than the distance from the inner surface of the helmet to the patient. The flux of higher energy electrons (above 80~100KeV) was 2 orders of magnitude less than that of photons. Therefore, the dose in the isocenter was essentially from photons directly emitted by the source. This fact provided an opportunity to model the LGK directly instead of the normal two-stage scheme. 110

128 1 photon spectrum Energy (MeV) Figure 5.2: Photon spectrum in the outlet of the 18mm helmet Full Gamma Knife modeling Surface disk source modeling As mentioned before, one way to model the LGK was to consider photons as being parallel beams of uniformly distributed photons, emitted perpendicularly from 201 disk sources. Each disk corresponds to the diameter of the inner aperture of the secondary collimator for each helmet. 111

129 The 201 photon beams were directed such that their central axes all converged at the isocenter of the LGK (Figure 5.3). Figure 5.3: Perpendicular-incident surface disk source In order to let MCNP sample 201 disk sources, the coordinates of centers of these disks as well as planes where these surface sources lie on had to be determined (APPENDIX E). 112

130 The source term used in MCNP calculation was: Sdef sur=d202 pos=fsur d203 rad=d204 dir=-1 erg=1.25 sur=d202 specified MCNP that the surface was to be sampled according to distribution 202. The sampling of MCNP variable pos was dependent on the selection of surface. rad=d204 specified MCNP to sample the position where a particle was born in a way defined in distribution 204. dir=-1specified the flying direction of generated photons was the opposite of the normal to the source surface. In summary, this source definition modeled the LGK as a collection of 201 monoenergetic photon beams perpendicular to the inner surface of a helmet (the MCNP input file was presented in APPENDIX F) Point source modeling The point source scheme treated the Co-60 cylinder source as an isotropic point source and the size of the beam was simply determined by the cone formed by the stationary collimator and the helmet (Figure 5.4). Considering the small dimension of the source, this could be a reasonable simplification. 113

131 Figure 5.4: Point source modeling In this modeling, the positions of point sources had to be determined. This was done by calculating the vertex of the cone (see Figure 5.1). Simple calculation yielded the distance of this point source to the isocenter was 41.83cm for the 18mm helmet. For computational efficient, the point source was biased so that only particles toward the isocenter were generated. The biased angle was controlled by the cone, which can be easily calculated. 114

132 The source term used in the calculation was: sdef sur=d202 pos=fsur d203 dir=d205 erg=1.25 which was almost the same as the one used in the surface disk source modeling. Without defining rad variable in the source term, MCNP assumed the source was a point source. The angular distribution was specified in dir=d205. The parameters of surface were also changed (see APPENDIX G). 5.3 Gamma Knife modeling with SOURCEX A direct scheme to model the LGK was to sample partic les from the source. This scheme, as metioned, will be very inefficient because a significant part of computational time was wasted in transporting particles through the radiation unit. However, assuming that only uncollided photons contribute to the dose deposition for the LGK treatment, a new efficient source model was investigated using SOURCEX feature of MCNP, which let users generate their own source description that are more complicated than those offered by MCNP through the source cards. The SOURCEX subroutine was used as the engine to generate the starting position and starting direction of a particle. A particle was generated in the volume of the cylindrical source with a limited angular distribution. Then the trajectory of this particle inside the radiation unit and the helmet was predicted. If this particle could successfully escape 115

133 from the unit, then further transport was performed; otherwise, the particle was eliminated and a new particle was sampled. The transport of photons through the shielding material was avoided by the elimination algorithm, which also implicitly incorporated the single channel geometry. This scheme used in SOURCEX is described in Diagram 5.1: 6WHSFKDQQHO VHOHFWLRQ 6WHSSRVLWLRQ VDPSOLQJ 6WHSGLUHFWLRQ VDPSOLQJ Diagram 5.1 SOURCEX sampling scheme In step 1, one of 201 channels was selected with equal probability because there was no preference for a particle generating in certain channel. For this 116

134 purpose, a random number uniformly distributed in [0, 201) was generated and rounded down to an integer. This integer plus 1 was the channel within which a particle was going to be generated. In step 2, the position where a particle was born was sampled. For simplicity, one can rotate the coordinate system so that the new z axis coincided with the central line of the channel selected in step 1. More specifically, this was done by rotating x axis counterclockwise f radian about the z axis, and then rotating z axis counterclockwise? radian about the new y axis (Figure 5.5). z(z') r y' z r(z') y' θ θ O(O') ϕ y O(O') ϕ y x x' x x' Figure 5.5: Coordinate system rotation 117

135 In the new coordinate system x y z, the position was sampled uniformly within the source cylinder using the following scheme (also see Figure 5.6): a ' = ρcosθ b' = ρsinθ 1 1 c' = z + ( z z ) rand () 0 1 0? 1 was uniformly sampled in [0, 2p] and c in [z 0, z 1 ]. Since the probability 2 2 density function of? was f ( ρ) = ρ,? was sampled using ρ = R ξ, where 2 R R was the radius of the source cylinder and? a random number uniformly distributed in [0, 1). 118

136 VRXUFHF\OLQGHU z ' ρ ( a', b', c') θ 1 z 1 z 0 LVRFHQWHU Figure 5.6: Position sampling scheme In step 3, the direction of the particle was sampled, which basically was to sample the polar angle,? 2, and azimuthal angle, f 2, of the unit direction vector. The direction distribution by default was isotropic in SOURCEX, but for the gamma knife modeling, only the particles born directed toward the isocenter were computationally important. Based on the knowledge of the geometry of a single channel and the assumption of tracking only uncollied photons, the direction sampling was biased so that particles heading to the isocenter were favored. This biasing angle was determined by the maximum 119

137 polar angle a particle could travel through the channel without a collision (see cross-view of a single channel, Figure 5.1): tan θ = ( R+ R )/ d max out where R was the radius of the source cylinder, R out the radius of the inner aperture of a channel and d the distance from isocenter to the bottom of the source cylinder. In order to obtain a desired angular distribution, which is a uniform distribution within a solid angle, the cosine of the polar angle,? 2, was uniformly sampled in [-1, -cos? max ] and the azimuthal angle, f 2, is uniformly sampled in [0, 2p]. The particle was then examined to check whether or not it could travel through the channel without collision. The first step of checking was to see if it could travel through the wall instead of the bottom of the source cylinder. Assume the intersection of the course of the particle with the bottom surface of the source cylinder was (a 0, b 0, c 0 ). The coordinates of the intersection point and the born position of the particle had the following relation: 120

138 a' a' = l sinθ cosϕ b' b' = l sinθ sin ϕ c' c ' = l cosθ 0 2 where (a, b, c ) was the place where the particle was born; l was the distance between the born position and the intersection (Figure 5.7). z' ( a', b', c' ) θ 2 y' ϕ 2 l x' r' ( a' 0, b' 0, c' 0 ) Figure 5.7: Intersection of a particle with the bottom surface 121

139 c 0 had the value of 21.7cm because it was in the bottom surface of the source cylinder. Therefore the values of a 0 and b 0 could be calculated as: c' c' a' = a' + sinθ cosϕ cosθ2 c' c' b' = b' + sinθ sinϕ cosθ2 If r, the distance from the center of the bottom circle to the intersection was greater than the radius of the circle, then the particle would pass through the wall of the cylinder; therefore this particle had to be discarded and a new particle would be sampled. The second step of checking was done at the outlet of a channel (Figure 5.8). If the particle passed both tests, then the direction vector of this particle was used as a valid direction. 122

140 z' ( a', b', c') ϕ 2 θ 2 y' x' r' ( a' 0, b' 0, c' 0 ) Figure 5.8: Intersection of a particle with the outlet surface All the above sampling and calculations were done on the coordinate system x y z. The whole gamma knife model was built on a world coordinate system xyz, so the position and the direction sampled in x y z coordinate system had to be transformed back to xyz system. The transform of position was specified by the Equation

141 a a' b = Mz( ϕ) M y( θ) b' c c' (Equation 5.1) The effect of left multiplying M y (-?) was rotating the z axis clockwise? radian along the y axis. The followed left multiplying M z (-f) was rotating the x axis clockwise f radian along the z axis. Therefore the resulting coordinates were the starting position of a particle in the xyz system. M y (?) and M z (f) were defined as: M y M z cosθ 0 sinθ ( θ ) = sinθ 0 cosθ cosϕ sinϕ 0 ( ϕ) = sinϕ cosϕ The coordinates of unit direction vector in x y z system was: u ' = sinθ cosϕ v ' = sinθ sin ϕ w' = cosθ 2 2 2

142 The transform of direction was specified by Equation 5.2: u u' v = Mz( ϕ) My( θ) v' w w' (Equation 5.2) In Equation 5.1 and 5.2,? and f were the polar angle and the azimuthal angle of the center vector of the selected channel in xyz system, respectively. The 201 center vectors were calculated in advance and stored as a constant array in the SOURCEX. The calculation has been included in APPENDIX E. Given a selected channel, the center vector (x 0, y 0, z 0 ) was retrieved from the array and the polar angle and azimuthal angle are calculated as: θ = arccos x z 0 y z 2 0 ϕ = arccos x 2 0 x 0 + y 2 0 Finally the position and direction coordinates were assigned to MCNP 125

143 built-in variables and MCNP would transport this particle the same as when a source definition was presented in the input file (for SOURCEX code see APPENDIX H): xxx= ayyy, = bzzz, = c vvv = uuuu, = vwww, = w 5.4 Results and comparison Based upon the estimated geometry, the MCNP simulation for a single channel dose profile was performed and the result was shown in Figure 5.9 (the MCNP input file is in APPENDIX D). In this calculation, the phantom was a water cubic box centered in the isocenter instead of a polystyrene sphere and the dose calculated was for points 80mm underneath the water surface (the rest of resulted were obtained with a polystyrene phantom 80mm in diameter with its center coincident with the isocenter). 126

144 1 0.9 Dose Profile Comparison along X MCNP PS (single channel) Relative Dose X (cm) Figure 5.9: Single channel dose profile comparison (no air gap) The calculated curve had a less flat top and sharper penumbra. It was also shown that adding the air gap would decrease the slope of the penumbra but also increase the slope of the top. Enlarging the diameter of the cylindrical source had the same effect. This deviation was most probably due to the inaccurate modeling of a single channel. 127

145 The results of the full LGK modeling using surface disk sources are shown in Figures 5.10 to Dose Profile Comparison along X MCNP PS 0.7 Relative Dose X (cm) Figure 5.10: Dose Profile Comparison along x (18mm, disk source) 128

146 1 Dose Profile Comparison along Z relative dose (%) z (cm) Figure 5.11: Dose Profile Comparison along z (18mm, disk source) 129

147 Dose Profile Comparison along X MCNP PS X (cm) Figure 5.12: Dose Profile Comparison along x (4mm, disk source) 130

148 Dose Profile Comparison along Z MCNP PS Z (cm) Figure 5.13: Dose Profile Comparison along z (4mm, disk source) Although the result of the x-axis profile for the 18mm helmet matched the benchmark quite well, general speaking, the calculated dose profiles had a flatter top and sharper penumbra. These results were expected because, in 131

149 the real situation, photons beams were divergent instead of the assumed parallel beam. Figure 5.14 to 5.17 were the results of calculations with 201 point sources compared with profiles from the GammaPlan for the 18mm and 4mm helmets Dose Profile Comparison along X MCNP PS 0.7 Relative Dose X (cm) Figure 5.14: Dose Profile Comparison along x (18mm, point source) 132

150 Dose Profile Comparison along Z MCNP PS 0.7 Relative Dose Z (mm) Figure 5.15: Dose Profile Comparison along z (18mm, point source) 133

151 Dose Profile Comparison along X MCNP PS 0.7 Relative Dose X (cm) Figure 5.16: Dose Profile Comparison along x (4mm, point source) 134

152 Dose Profile Comparison along Z MCNP PS 0.7 Relative Dose Z (mm) Figure 5.17: Dose Profile Comparison along z (4mm, Point Source) The calculated dose profiles showed almost the same characteristics with those obtained with 201 perpendicular incident surface disk sources. The reason could be explained roughly as very slight difference exists between 135

153 the perpendicular incident beam and a beam incident with a very small solid angle. In the center of the phantom, these two beams was indistinguishable. The results were also consistent with those obtained by Xiaowei et al [14]. As a conclusion, the angular distribution in the outlet of a channel was important to smooth the dose profile and flat the penumbra. A surface-source LGK modeling must incorporate this distribution. The simulation with the scheme presented was also performed (only for 18mm in x and z axes) and the results were showed in Figure 5.18 and

154 Dose Profile Comparison along X MCNP PS 0.7 Relative Dose X (mm) Figure 5.18: Dose Profile Comparison along x (SOURCEX, 18mm) 137

155 Dose Profile Comparison along Z MCNP PS 0.7 Relative Dose Z (mm) Figure 5.19: Dose Profile Comparison along z (SOURCEX, 18mm) The scheme with SOURCEX was sensitive to the structure of a channel because the elimination criterion was completely based on the geometry. 138

156 Since we did not have the exact source geometry from the manufacturer, the geometry we used was probably different enough to cause these discrepancies in our results. We believe that if the accurate model for the source can be obtained, this method would give us the most efficient and accurate source model for the Gamma Knife. 5.5 Conclusion Two simplified full LGK models that we implemented indicated that the angular distribution of photons coming out of each channel needed to be taken into account to better predict the penumbra region of the dose profiles. An accurate single channel model was required to obtain such information. The single channel model presented here, although simple, seemed not be able to capture this distribution. The scheme applied by SOURCEX needs to be modified using the detailed and more accurate configuration of a single channel in order to get satisfactory results. 139

157 CHAPTER 6 CONCLUSIONS AND FUTURE WORK 6.1 Conclusions In this thesis, two newly available dosimeters, EDR2 film and TLD-100H disks, were evaluated. Two simplified models and an elegant full model of the LGK were also developed in this work. The results of EDR2 film measurement showed that it could be used to accurately measure the absorbed dose profile in dose range up to about 5.5Gy. The TLD-100H disks with some necessary corrections showed a very good linear response in a wide range When they are carefully calibrated in the right radiation geometry, TLD-100H disks can be used for accurate absolute absorbed dose as well as dose profiles measurement in the isocenter of the LGK. 140

158 MC based LGK model developed in this work using SOURCEX feature of MCNP indicates that an accurate single channel configuration is required to obtain satisfactory results. Although this model did not successfully reproduce the dose profile in the isocenter, its core idea, i.e., incorporating geometry in the sampling algorithm, is believed to be able to yield better results than the two-stage models, which have to discretize distributions that are continuous essentially Suggestions for future work: First of all, the full LGK model should be modified based on an accurate single channel geometry if it is available. In order to account the electron disequilibrium, variance reduction technique that is useful for *F8 tally, like forced collision, need to be investigated. For EDR2 film, one can further apply it on absolute dose measurements. TLD-100H disks requires better calibration in the low dose range in order to measure the structure dose. Finally, a systematic way to estimate error associated with measurements is necessary. 141

159 REFERENCE [1]. Leksell Gamma Knife Instruction for Use [2]. Moskvin, V., DesRosiers, C., Papiez, L., Timmerman, R., Randall, M., and DesRosiers, P., Monte Carlo simulation of the Leksell Gamma Knife : I. Source modeling and calculations in homogeneous media, Phys. Med. Biol. 47, , [3]. Wu, A., Lindner, G., Maitz, A. H., Kalend, A. M., Lunsford, L. D., Flickinger, J. C., and Bloomer, W. D., Physics of Gamma Knife approach on convergent beams in stereotactic radiosurgery, Int. J. Radiation Oncology Biol. Phys., Vol. 18, , [4]. Somigliana, A., Cattaneo, G. M., Fiorino, C., Borelli, S., Vecchio, A. D., Zonca, G., Pignoli, E., Loi, G., Calandrino, R., and Marchesini, R., Dosimetry of Gamma Knife and linac-based radiosurgery using radiochromic and diode detectors, Phys. Med. Biol , [5]. Radiochromic film dosimetry, Recommendations of AAPM Radiation Therapy Committee Task Group No. 55 [6]. McKinlay, A. F., Thermoluminescence dosimetry, Adam Hilger Ltd., Bristol BS1 6NX. [7]. Heydarian M., Hoban P. W., and Beddoe A. H., A comparison dosimetry techniques in stereotactic radiosurgery, Phys. Med. Biol. 41, ,

160 [8]. Zhu, X. R., Jursinic P. A., Grimm D. F., Lopez, F., Rownd J. J., and Gillin, M. T., Evaluation of Kodak EDR2 film for dose verification of intensity modulated radiation therapy delivered by a static multileaf collimator, Med. Phys. 29 (8), August 2002 [9]. Kellermann, P. O., Ertl, A., and Gornik, E., A new method of readout in radiochromic film dosimetry, Phys. Med. Biol , [10]. Cheung Y. C., Yu K. N., Ho R. T. K., and Yu C. P., Monte Carlo calculation of single-beam dose profiles used in a gamma knife treatment planning system, Med. Phys. 25 (9), , September [11]. Cheung Y. C., Yu K. N., Ho R. T. K., and Yu C. P., Monte Carlo calculation and GafChromic film measurements for plugged collimator helmets of Leksell Gamma Knife unit, Med. Phys. 26 (7), , July [12]. Cheung Y. C., Yu K. N., Ho R. T. K., and Yu C. P., Stereotactic dose planning system used in Leksell Gamma Knife model-b: EGS4 Monte Carlo versus GafChromic films MD-55, Applied Radiation and Isotopes, 53, , [13]. Salvat F., Fernandez-Varea J. M., Baro J., and Sempau J., 1996 PENELOPE, an algorithm and computer code for Monte Carlo simulation of electron-photon showers, Informes Tecnicos CIEMAT Report, No. 799 (Madrid: CIEMAT). [14]. Liu X. and Zhang C., Simulation of dose distribution irradiation by the Leksell Gamma Unit, Phys. Med. Biol. 44, ,

161 APPENDIX A DOSE PROFILES OF 4 HELMETS IN X AND Z DIRECTIONS x axis z axis relative dose (%) distance (mm) Figure A.1: Dose profiles along x and z axes for the 18mm helmet 144

162 x axis z axis relative dose (%) distance (mm) Figure A.2: Dose profiles along x and z axes for the 14mm helmet 145

163 x axis z axis relative dose (%) distance (mm) Figure A.3: Dose profiles along x and z axes for the 8mm helmet 146

164 x axis z axis 80 relative dose (%) distance (mm) Figure A.4: Dose profiles along x and z axes for the 4mm helmet 147

165 APPENDIX B BEAM DATA FILE AND CONVERSION CODE A sample beam data file used by OmniPro-Accept (.asc) containing two dose profiles: :MSR 2 # No. of measurement in file :SYS BDS 0 #Beam Data Scanner System # comment symbol # RFA300 ASCII Measurement Dump ( BDS format ) # # Measurement number 1 # %VNR 1.0 data from %VNR to %PRD can be found in the head data block of a film %MOD %TYP SCN %SCN PRO %FLD UDF %DAT %TIM 16:06:50 %FSZ %BMT PHO 6.0 %SSD 1000 %BUP 0 %BRD 1000 %FSH -1 %ASC 0 %WEG 0 %GPO 0 %CPO 0 %MEA 2 %PRD 0 %PTS 33 number of data points in the dose profile 148

166 %STS # start scan values in mm ( X, Y, Z ) %EDS # end scan values in mm ( X, Y, Z )!! # # X Y Z Dose # = each data line has strict format: = =TABSevenDigitTABSevenDigitTABSevenDigit = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = =

167 :EOM # End of Measurement # # RFA300 ASCII Measurement Dump ( BDS format ) # # Measurement number 2 indicating the second dose profile # %VNR 1.0 %MOD %TYP SCN %SCN PRO %FLD UDF %DAT %TIM 16:06:50 %FSZ %BMT PHO 6.0 %SSD 1000 %BUP 0 %BRD 1000 %FSH -1 %ASC 0 %WEG 0 %GPO 0 %CPO 0 %MEA 2 %PRD 0 %PTS 33 %STS # start scan values in mm ( X, Y, Z ) %EDS # end scan values in mm ( X, Y, Z )!! # # X Y Z Dose # = = = = = = =

168 = = = = = = = = = = = = = = = = = = = = = = = = = = :EOM # End of Measurement :EOF # End of File Conversion Code: #include "fstream.h" #include "stdlib.h" #include "string" #include "iostream.h" #include "iomanip.h" // // this progrom is used to generate output file for software OmniPro-Accept // format: ASCGenerator file1 file2 // file1: input file, containing data of coordinates and dose. 151

169 // the format must be four columns with x, y, z and dose in each column // this version supports multiple data block. blocks must be seperated by // blank lines. // suggestion: using excel to generate these four columns and copy to a //.txt file and save. because this program is very primitive, so the first // column must be the column containing the position information. // e.g // not // file2: file to be opened by OmniPro-Accept. the extension is.asc(not default). // int main(int argc, char* argv[]) { char ca_inputline[100]; char *cp_token; char *cp_inputfile = argv[1]; char *cp_outputfile = argv[2]; struct { float ProfileData[100][4]; // x, y, z and dose data int NumPoint; // number of points in the current profile float StartPos[3]; // start position of the profile float EndPos[3]; // end position of the profile }Data[10]; ifstream ins; ofstream outs; ins.open(cp_inputfile); outs.open(cp_outputfile); if(ins.fail()) { cout << "cannot open input file!!! " << endl; exit(1); } if(outs.fail()) 152

170 { } cout << "cannot open output file!!! " << endl; exit(1); int MeasurementCount = 0; // count the index of the current measurement. int PointCount = 0; // count the data point in each data block int TotalMeasurement = 0; // count the total number of measurement in the current file bool NewBlock = false; // read in data while(ins.eof() == 0) { while( NewBlock == false ) { if(ins.eof() == 1) { break; } ins.getline(ca_inputline, 100); if(ca_inputline[0] == '\0' ca_inputline[0] == 32) { NewBlock = true; break; } // New data block cp_token = strtok(ca_inputline, " \t"); Data[MeasurementCount].ProfileData[PointCount][0] = atof(cp_token); // x value cp_token = strtok(null, " \t"); Data[MeasurementCount].ProfileData[PointCount][1] = atof(cp_token); // y value cp_token = strtok(null, " \t"); Data[MeasurementCount].ProfileData[PointCount][2] = atof(cp_token); // z value cp_token = strtok(null, " \t"); Data[MeasurementCount].ProfileData[PointCount][3] = atof(cp_token); // dose if(pointcount == 0) { Data[MeasurementCount].StartPos[0] = Data[MeasurementCount].ProfileData[PointCount][0]; Data[MeasurementCount].StartPos[1] = 153

171 Data[MeasurementCount].ProfileData[PointCount][1]; Data[MeasurementCount].StartPos[2] = Data[MeasurementCount].ProfileData[PointCount][2]; } PointCount++; } // set EndPos Data[MeasurementCount].EndPos[0] = Data[MeasurementCount].ProfileData[PointCount-1][0]; Data[MeasurementCount].EndPos[1] = Data[MeasurementCount].ProfileData[PointCount-1][1]; Data[MeasurementCount].EndPos[2] = Data[MeasurementCount].ProfileData[PointCount-1][2]; Data[MeasurementCount].NumPoint = PointCount; MeasurementCount++; TotalMeasurement = MeasurementCount; PointCount = 0; } NewBlock = false; // output data outs << ":MSR " << setw(7) << TotalMeasurement << " " << "# No. of measurement in file" << endl; outs << ":SYS BDS 0 #Beam Data Scanner System" << endl; for(int i=0; i<totalmeasurement; i++) { outs << "#" << endl; outs << "# RFA300 ASCII Measurement Dump ( BDS format )" << endl; outs << "#" << endl; outs << "# Measurement number" << setw(7) << i+1 << endl; outs << "#" << endl; outs << "%VNR 1.0" << endl; outs << "%MOD " << endl; outs << "%TYP SCN " << endl; 154

172 outs << "%SCN PRO " << endl; outs << "%FLD UDF " << endl; outs << "%DAT " << endl; outs << "%TIM 16:06:50 " << endl; outs << "%FSZ " << endl; outs << "%BMT PHO 6.0" << endl; outs << "%SSD 1000" << endl; outs << "%BUP 0" << endl; outs << "%BRD 1000" << endl; outs << "%FSH -1" << endl; outs << "%ASC 0" << endl; outs << "%WEG 0" << endl; outs << "%GPO 0" << endl; outs << "%CPO 0" << endl; outs << "%MEA 2" << endl; outs << "%PRD 0" << endl; outs << "%PTS " << Data[i].NumPoint << endl; outs << "%STS " << setw(7) << Data[i].StartPos[0] << " " << setw(7) << Data[i].StartPos[1] << " " << setw(7) << Data[i].StartPos[2] << " # start scan values in mm ( X, Y, Z )" << endl; outs << "%EDS " << setw(7) << Data[i].EndPos[0] << " " << setw(7) << Data[i].EndPos[1] << " " << setw(7) << Data[i].EndPos[2] << " # end scan values in mm ( X, Y, Z )" << endl; outs << "! " << endl; outs << "! " << endl; outs << "#" << endl; outs << "# X Y Z Dose" << endl; outs << "#" << endl; for(int j=0; j<data[i].numpoint; j++) { outs << "= " << setw(7) << Data[i].ProfileData[j][0] << " " << setw(7) << Data[i].ProfileData[j][1] << " " << setw(7) << Data[i].ProfileData[j][2] << " " << setw(7) << Data[i].ProfileData[j][3] << endl; } outs << ":EOM # End of Measurement" << endl; } outs << ":EOF # End of File" << endl; } return 0; 155

173 APPENDIX C RAW DATA OF TLD MEASUREMENTS Exposure 5/24/2002 6/4/2002 4:10pm, 6/5/02 Warmup 1 12:30pm, 6/2/2002 1:50pm, 6/5/ :09pm, 6/6/2002 Read 2 12:40pm (95 3, ) 2:00pm (95, 30 1)1:33pm, (95, 30 21, 10 1, 20 11) Chip# RawCounts LS RawCounts LS RawCounts LS (to be continued ) 156

174 (continued from the previous page)

175 Exposure 4:00pm, 6/6/2002 4:00pm, 6/7/2002 4:30pm, 6/10/02 Warmup 12:07pm, 6/7/2002 2:55pm, 6/9/2002 1:08pm, 6/12/2002 Read 1:10pm (190, 1 30) 3:55pm (190, 1 30) 2:58pm (190, 1 30) Chip# RawCounts LS RawCounts LS RawCounts LS Exposure 4:00pm, 6/13/2002 4:00pm, 6/17/2002 4:00pm, 6/24/02 158

176 Warmup 10:30pm, 6/14/2002 9:00am, 6/18/2002 8:00am, 6/25/2002 Read 10:40pm (285, 1 30) 9:30am (285, 1 30) 8:16am (190, 1 30) Chip# RawCounts LS RawCounts LS RawCounts LS

177 Exposure 4:00pm, 6/25/2002 4:00pm, 6/26/2002 4:30pm, 7/3/02 Warmup 8:12am, 6/26/2002 8:25am, 6/27/ :51am, 7/4/2002 Read 8:23am (190, 1 15, ) 8:35am (190, 30 1)8:16am,7/5/2002 (190, 1 30, Slow 6 ) Chip# RawCounts LS RawCounts LS RawCounts LS

178 Exposure 4:00pm, 7/8/2002 4:30pm, 7/10/2002 4:00pm, 7/15/02 Warmup 8:30am, 7/9/ :13am, 7/11/2002 8:50am, 7/16/2002 Read 8:42am (190, 1 30, Slow*) 10:23am (190, 1 30) 9:00am (380, 1 30) Chip# RawCounts LS RawCounts LS RawCounts LS

179 Exposure 4:00pm, 7/16/2002 4:00pm, 7/17/2002 5:00pm, 7/18/02 Warmup 9:03am, 7/17/ :40am, 7/18/2002 9:20am, 7/19/2002 Read 9:13am (475, 1 30) 10:50am (570, 1 30) 9:30am (71, 1 30) Chip# RawCounts LS RawCounts LS RawCounts LS

180 Exposure 4:00pm, 7/25/2002 4:00pm, 7/26/2002 5:20pm, 7/30/02 Warmup 8:47am, 7/26/ :48pm, 7/27/2002 1:25am, 7/31/2002 Read 9:52am (12, 1 30) 12:52pm (6, 1 30) 1:28am (3, 1 30) Chip# RawCounts LS RawCounts LS RawCounts LS

181 Exposure 10:30pm,8/7/2002 4:00pm,8/14/2002 Warmup 10:40pm, 8/8/2002 9:30am, 8/15/2002 Read 10:43pm (1 30) LGK profile 9:33am (1 30) LGK profile Chip# RawCounts LS RawCounts LS

182 Exposure 8/16/2002 4:00pm,8/26/2002 Warmup 8/17/ :13am, 8/27/2002 Read (1 19) 10:15am (1 19) Calibration in LGK Calibration in MXE with lowed dose rate Chip# RawCounts LS RawCounts LS

183 Exposure 4:30pm, 9/10/2002 Warmup 11:05am, 9/11/2002 Read 11:10am, (2 10, 16) Angular dependency check Chip# RawCounts LS time to turn on the TLD reader 2 time to start reading 3 monitor unit (MU) 4 readout order 5 the TLD reader was turned off between the 15 th and 16 th readings. 6 slow cooling 166

184 APPENDIX D MCNP INPUT FILE FOR SINGLE CHANNEL MODELING gamma knife model with 201 sources c **************** Cell Card ********************** imp:p=1 $ air imp:p=1 $ tungsten imp:p=1 $ air imp:p=1 $ lead imp:p=1 $ air imp:p=1 $ tungsten imp:p=1 $ Co-60 source imp:p=1 $ cast iron: pure Fe imp:p=1 $ air gap #( ) imp:p= #( ) -20 #(-9 1-5) imp:p= imp:p= imp:p= imp:p= imp:p= imp:p= imp:p= imp:p= imp:p= imp:p= imp:p= imp:p= imp:p= imp:p= imp:p= imp:p= imp:p= imp:p=1 167

185 imp:p= imp:p= imp:p= imp:p= imp:p= imp:p= imp:p= imp:p= imp:p= imp:p= imp:p= imp:p= imp:p= imp:p= imp:p= imp:p= imp:p= imp:p= imp:p= imp:p= imp:p=1 c **************** Surface Card ******************** 1 PZ PZ PZ PZ PZ KZ $ cone surface c 7 CZ CZ $ primary collimator 8 CZ 0.05 $ Co-60 source cylinder 9 CZ 5 $ the cylinder containing the model c 11 so 8 $ the phantom R = 8cm 12 PX PX 8 14 PY PY 8 16 PZ PZ 8 168

186 20 so 50 $ the whole sphere 40 PZ PZ cz cz cz cz cz cz cz cz cz cz cz cz cz cz cz cz cz cz cz cz cz cz cz cz cz cz cz cz cz cz cz cz cz cz cz cz cz

187 c ************** Problem Type ************** mode p c c ************** Source Term ************** sdef POS= AXS=0 0 1 RAD=d1 EXT=d2 VEC=0 0-1 DIR=d3 ERG=1.25 c si si2 1 si sp3 0 1 c c *************** Tally ************************** f024:p f034:p f044:p f054:p f064:p c de df0 c e e e e e e e e e e e e e e e e e e-012 c ************* Material ******************* m $ air m $ cast iron: pure Fe m m $ lead $ tungsten c m $ for H c $ for C m c c ************* Energy Card **************** phys:p 2 c ************* Cutoff Card **************** nps

188 APPENDIX E CHANNEL POLAR AND AZIMUTHAL ANGLES CALCULATION According to the drawing (LEKSELL GAMMA KNIFE HELMET TEST TOOL, ref. 301) coming with the Gamma Knife, the polar angles of the five rings of channels were determined using the following method: θ 5 θ 2 θ 3 θ 4 d 1 d 2 θ 1 d 3 d 4 d 5 Figure E.1 Polar angle calculation Assume 171

189 π θ2 θ1 = θ3 θ2 = θ4 θ3 = θ5 θ4 = θ5 = θ 2 Therefore, θ d /2 5 sin = θ = rad 2 R θ θ θ θ θ π = 5θ = rad 2 π = 4θ = rad 2 π = 3θ = rad 2 π = 2θ = rad 2 π = θ = rad 2 The top view of the helmet showed that, if one fills out the A7, A18 and so on, the circle in the same ring could be assumed uniformly distributed. Therefore, the intervals between two adjacent centers were: 172

190 2π A: φ5 = = rad 48 2π B: φ4 = = rad 45 2π C: φ3 = = rad 40 2π D: φ2 = = rad 40 2π E: φ1 = = rad 36 With the polar and azimuthal angle information, MATLAB program, SourceCard.m, was created to generate the coordinates of the centers as well as the plane parameters. 173

191 Figure E.2: Azimuthal angle calculation SourceCard.m function [Source, Plane] = SourceCard() % this function is used to calculate the coordinates of the centers of % the 201 disk sources % the following constants may not equal in the real case: % R = 16.5; % cm R = 44.46; % for 4 mm helmet angle1 = ; % rad angle2 = ; angle3 = ; 174