Optimisation of eye plaque dosimetry using Monte Carlo method

Transcription

1 University of Wollongong Research Online University of Wollongong Thesis Collection University of Wollongong Thesis Collections 2011 Optimisation of eye plaque dosimetry using Monte Carlo method Julia Anne Green University of Wollongong Recommended Citation Green, Julia Anne, Optimisation of eye plaque dosimetry using Monte Carlo method, Master of Science thesis, University of Wollongong. School of Engineering Physics, University of Wollongong, Research Online is the open access institutional repository for the University of Wollongong. For further information contact Manager Repository Services:

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3 OPTIMISATION OF EYE PLAQUE DOSIMETRY USING MONTE CARLO METHOD A thesis submitted in partial fulfilment of the requirements for the award of the degree MASTER OF SCIENCE from UNIVERSITY OF WOLLONGONG by JULIA ANNE GREEN, BACHELOR OF MEDICAL AND RADIATION PHYSICS SCHOOL OF ENGINEERING PHYSICS 2011

4 CERTIFICATION I, Julia A. Green, declare that this thesis, submitted in partial fulfilment of the requirements for the award of Master of Science, in the School of Engineering Physics, University of Wollongong, is wholly my own work unless otherwise referenced or acknowledged. The document has not been submitted for qualifications at any other academic institution. Julia A. Green 14 th July 2011 ii

5 And so we say Hooray for eyes! Hooray, hooray, hooray... for eyes! (Theo. LeSieg) iii

6 ABSTRACT Cancer of the eye is a rare and challenging disease. Uveal melanoma is the most prevalent of ocular malignancies in adults, with Australia holding one of the highest rates of incidence worldwide. While rare, the consequences are serious and more often than not, the sufferer will incur vision loss as a result of treatment, or, in time, will face losing the eye. Brachytherapy using radioactive eye plaques is the preferred method of treatment for ocular melanoma, yielding the best results for the patient in terms of vision and survival. Currently, methods of plaque brachytherapy dosimetry are limited by the size and spatial resolution of detectors such as thermoluminescent dosimeters (TLDs), where steep dose gradients create significant challenges. It is not only the detector size but the complexity of source geometry that hinder accurate dosimetry further still. These limitations lead to incomplete dose distributions and inevitably, inaccurate treatment planning for the quality assurance of eye plaques before clinical use. Dose planning software for I-125 plaque brachytherapy using the 15mm ROPES plaque has been developed based on interpolation of data from the published dosimetric parameters of the Task Group No. 43 (TG43) AAPM revised protocol (Rivard et al., 2004). This application includes the ability to export dose maps in the format of a 256 x 256 pixel array analogous to the output of the Medipix2 silicon pixelated counting device recently used in physical measurements at the Centre for Medical Radiation Physics (CMRP). Using the Geant4 photon transport toolkit, Monte Carlo dosimetry was performed for a single I-125 model 6711 seed to optimise the dose rate distribution data calculated the software. Dose point data was obtained every millimetre up to 25mm in the radial direction and every five degrees in polar angle. Similarly, Monte Carlo method was used to compare dose distributions for the Ru-106 CCD plaque with those generated by the Plaque Simulator (BEBIG GmbH, Berlin, Germany). The cylindrical symmetry of the plaque allowed data to be obtained in toroids of radii in millimetre increments up to 25mm, and depth from the plaque surface also in millimetre increments up to 25mm. iv

7 The results of the I-125 simulation were used to calculate the TG43 dosimetric parameters and were in good agreement with the published data. Radial dose functions over the scoring range fell within 3% with a maximum deviation from TG43 data of only 2.8% (occurring 1mm away from the source on the plaque central axis). Anisotropy functions were obtained within 5% uncertainty for all polar angles. The Ru-106 plaque results differed considerably from the dose data generated by the Plaque Simulator with the most significant deviation occurring at very small distances from the plaque inner surface (within 1cm). Monte Carlo method is a useful technique for dosimetry of plaque brachytherapy sources used in the treatment of ocular melanoma. The Geant4 toolkit is capable of accurately scoring dose at defined small radial distances from the source previously unaccounted for. The dose point array obtained for the model 6711 seed can be input into the dose planning software for dose optimisation and combined with the results of recent physical measurements using the Medipix2, can achieve the quality assurance of eye plaque brachytherapy treatment. v

8 ACKNOWLEDGMENTS To my primary supervisor and teacher, Professor Anatoly Rosenfeld, thank you for your unrelenting passion and drive for research and knowledge that has been an inspiration for many in the field of Medical Physics. Professor Rosenfeld s commitment to his students is commendable and his love of physics has allowed me to see the universe in a new light. I wish to thank Professor Rosenfeld for his time and support throughout my postgraduate studies. Similarly, Dr Michael Lerch has been a key figure in my learning and achievement, his easy-going nature partnered with his wealth of expertise has made my time at the University of Wollongong both enjoyable and rewarding. Thank you to Dean Cutajar, whom without, this work would not be possible. Dean s exceptional high level of knowledge in the field of brachytherapy dosimetry and Monte Carlo physics has provided me with a strong foundation upon which to build my own knowledge. I would like to thank Dean in particular for his time, patience and assistance with the Geant4 Monte Carlo simulations and treatment planning software code of this thesis which was supported greatly by the work of his PhD thesis. Mr. Cutajar s support and encouragement of my research has been essential to my progress and is something I value greatly. Thank you also to Stephen Dowdell for his assistance with Geant4 code and expertise in Proton Therapy. I would like to acknowledge and thank the eye plaque dosimetry research team supported by a NHMRC grant; Mr. Michael Weaver, Dr Daniel Franklin and Dr Marco Petasecca for their support and experimental work with the Medipix2 device. In particular, thank you to Michael Weaver for his assistance with the Medipix dosimetry which is supported by the results of his PhD thesis. Finally, thank you to the Centre for Medical Radiation Physics at the University of Wollongong for their continual support and encouragement of postgraduate research students in the field of Medical Physics. vi

9 PUBLICATIONS Publications arising from this thesis include: Rosenfeld, A.B., Petasecca, M., Lerch, M.L.F., Cutajar, D., Franklin, D., Green, J., Weaver, M., Jakubek, J., Carolan, M.G., Conway, M., Pospisil, S., & Kron, T. (2009). Three-dimensional dosimetry imaging technique of I-125 plaque for eye cancer treatment. 11 International Workshop on Radiation Imaging Detectors June 28 - July 2, Prague. Cutajar, D., Petasecca, M., Lerch, M.L.F., Franklin, D., Green, J., Weaver, M., Jakubek, J., Carolan, M.G., Conway, M., Pospisil, S., & Rosenfeld, A.B. (2009). Threedimensional dosimetry imaging technique of I-125 plaque for eye cancer treatment. Engineers and Physical Scientists in Medicine, November 2009, Canberra. Weaver, M., Green, J., Petasecca, M., Lerch, M.L.F., Cutajar, D., Franklin, D., Jakubek, J., Carolan, M.G., Conway, M., Pospisil, S., Kron, T., Metcalfe, P., Zaider, M., & Rosenfeld, A.B. (2010). Three-dimensional dosimetry imaging technique of I-125 plaque for eye cancer treatment. Proceedings of the 11th International Workshop on Radiation Imaging Detectors. Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment, doi: /j.nima Cutajar, D., Green, J., Guatelli, S., & Rosenfeld, A.B. (2010). Monte Carlo generation of dosimetric parameters for eye plaque dosimetry. Engineers and Physical Scientists in Medicine, November 2010, Melbourne. vii

10 CONTENTS ABSTRACT... iv ACKNOWLEDGMENTS... vi PUBLICATIONS... vii CONTENTS... viii LIST OF FIGURES... xi LIST OF TABLES... xv Chapter One... 1 Introduction... 1 Chapter Two... 4 Literature Review Ocular melanoma in Australia and worldwide Treatment Episcleral plaque brachytherapy Description of plaques Eye Plaque Brachytherapy Dosimetry Current methods of dosimetry in eye plaque brachytherapy AAPM TG43 Brachytherapy Formalism Ru-106 Protocol of Measurements Treatment planning systems Limitations in dose planning software for eye plaque brachytherapy Radiation interactions with matter Photon interactions Electron interactions Monte Carlo Physics Geant4.9.3 Monte Carlo Toolkit Monte Carlo Dosimetry for Eye Plaque Brachytherapy Chapter Three viii

11 Dose Planning Software Software Development Plaque Geometry Dose Calculation Output Plaque Configuration Medipix Output Cross Section Depth Dose Distribution Isodose Discussion Chapter Four Iodine-125 based eye plaque dosimetry Monte Carlo Simulation of I-125 Source Simulation Geometry Physics Considerations Particle Generation Derivation of geometry function Results Discussion Chapter Five Ruthenium-106 based eye plaque dosimetry Monte Carlo Simulation of Ru-106 Source Simulation Geometry Physics Considerations Particle Generation Results Discussion Chapter Six Conclusion ix

12 REFERENCES APPENDIX A I-125 and Ru-106 dose array APPENDIX B Monte Carlo Code: Geometry APPENDIX C Monte Carlo Code: Particle Generation x

13 LIST OF FIGURES Figure 1. Anatomy of the uveal tract: ciliary body, iris, and choroid... 4 Figure 2. Intraocular melanoma: Iris with nodular melanoma (left) and large choroidal melanoma (right) (Shields & Shields, 2009)... 5 Figure 3. Three components of the 15mm ROPES plaque (Eye Physics, LLC see 12 Figure 4. Schematic diagram of the 15mm ROPES plaque (as per Eye Physics, LLC see 13 Figure 5. BEBIG Ru-106 plaque applicator types including notched type (left and middle) and schematic of plaque geometry (Eckert & Ziegler BEBIG GmbH, 2008) Figure 6. BEBIG Ru-106 opthalmic applicator range (Eckert & Ziegler BEBIG GmbH, 2008) Figure 7. Coordinate system used in calculating dosimetric parameters for a brachytherapy source as defined by the TG43 AAPM revised protocol (Rivard et al., 2004) Figure 8. Model 6711 Onco seed geometry (Rivard et al. 2004) Figure 9. Visualisation of the Plaque Simulator treatment planning software showing central axis and plaque positioned behind tumour on back of eye (Eye Physics, LLC see 30 Figure 10. Photoelectric effect Figure 11. Compton Scattering Figure 12. Pair Production Figure 13. Coherent scattering in photon transport calculations Figure 14. Photographic image of the 15mm ROPES plaque and acrylic insert fully loaded with ten 6711 model I-125 brachytherapy seeds Figure 15. Medipix 256 x 256 pixel map output Figure 16. Plaque coordinate system assumed in code Figure 17. Seed configuration in 15mm ROPES plaque showing the respective positions of seed numbers Figure 18. Coordinate system for dose calculation. Note that the seed is in the x-y plane xi

14 Figure 19. Relative point of measurement, R(x, y, z) at relative angle θ and distance r from the point of measurement to the centre of the seed Figure 20. Eyecan user interface and output Figure 21. a) Eyecan five seed pixel map, 12mm from plaque on central axis; b) Eyecan ten seed pixel map, 0mm on plaque central axis displaying the accuracy of seed geometry assumed by the software Figure 22. Cross sectional view in treatment volume at y = 0mm, through the centre of the eye, showing regions of high dose at the apex Figure 23. Depth dose curve on the central axis of the 15mm ROPES plaque loaded with ten I-125 seeds with activity of 0.4Ci per seed Figure 24. Isodose curves on the central axis of the 15mm ROPES plaque loaded with ten I-125 seeds of 0.4Ci activity per seed where blue represents dose points of 5Gy (±1%), green represents dose points of 50Gy (± 1.4%) and red represents dose points of 200Gy (± 2%) Figure 25. Depth dose Central axis depth dose (z = 0mm to z = 25mm) measured by Medipix2 compared with tabulated data from the TG43 protocol Figure 26. Longitudinal view of seed geometry assumed by Monte Carlo simulation as per Williamson (1988) Figure 27. Transverse view of seed geometry assumed by Monte Carlo simulation as per Williamson (1988) Figure 28. Toroid position relative to the centre of the source with every point of measurement the same distance, r and angle, from the source Figure 29. Geant4 visualisation of Monte Carlo simulation of model 6711 seed showing inner silver core (magenta), air gap (blue) and titanium shell (silver), and set of 50 concentric scoring toroids (red) positioned 1mm apart Figure 30. Geant4 visualisation of Monte Carlo simulation of single 6711 seed with scoring tubes (red) positioned every 1mm on the source central axis Figure 31. Surface generation geometry Figure 32. Endcap coordinates Figure 33. Endcap coordinate generation xii

15 Figure 34. Geant4 visualisation of Monte Carlo simulation of model 6711 seed showing the inner silver core (magenta), air gap (blue) and titanium shell (silver). Photon emission, represented in green, demonstrates the generation from the surface of the silver core, and electrons, in red (shown in the zoom window) demonstrate the generation of secondary particles in the physics model Figure 35. Coordinate system of seed showing the angle Beta relative to the centre of the seed Figure 36. Radial dose function demonstrating the Depth-dose delivered on the central axis compared with TG43 data Figure 37. Monte Carlo anisotropy functions compared with tabulated data provided by the TG43 protocol Figure 38. BEBIG Ru-106 CCD plaque Figure 39. Ru-106 CCD plaque geometry assumed by the Monte Carlo code Figure 40. Cross section of Ru-106 CCD plaque geometry assumed by Monte Carlo code Figure 41. Geant4 visualisation of Monte Carlo simulation of Ru-106 plaque showing silver curved surface (silver). Photon emission, represented in green, demonstrate the generation from the inner surface of the plaque. Generated electrons are absorbed in the silver window but secondary electrons, in red, are visible Figure 42. Geant4 visualisation of the Monte Carlo simulated Ru-106 plaque (silver) with scoring tubes (red) positioned 1mm apart from the inner surface of the plaque on the plaque central axis through the volume of the eye (blue) Figure 43. Geant4 visualisation of the Monte Carlo simulated Ru-106 plaque (silver) with scoring toroids (red) positioned 1mm apart on the plaque central axis (z = 12mm) through the volume of the eye (blue) Figure 44. Plaque surface geometry for particle generation Figure 45. Ring geometry Figure 46. Coordinate generation Figure 47. Monte Carlo derived Ru-106 CCD plaque central axis depth dose compared with central axis dose generated from the Plaque Simulator xiii

16 Figure 48. BEBIG Ru-106 plaque applicator schematic showing detailed geometric source specifications (Eye Physics, LLC, Los Alamitos, CA, USA see 92 xiv

17 LIST OF TABLES Table 1. I-125 spectra Table 2. Radial dose functions for the single Amersham health model 6711 seed Table 3. Anisotropy functions for the Amersham model Table 4. Ru-106 Photon contamination spectra* Table 5. Rh-106 Beta ray spectra* Table 6. Seed coordinates and direction vectors Table 7. I-125 source spectra Table 8. Comparatively tabulated radial dose function values, g(r), obtained from Monte Carlo (MC) simulation and TG43 data Table 9. Monte Carlo (MC) derived anisotropy functions, F(r,θ), comparison with TG43 tabulated data Table 10. Monte Caro and TPS derived depth dose on plaque central axis Table 11. Monte Carlo derived I-125 Dose Array Table 12. Monte Carlo derived Ru-106 dose array, were z(mm) is the distance along the central axis and r(mm) is the distance about the central axis xv

18 Chapter One Introduction Brachytherapy remains the most popular method of treatment for ocular melanoma today (Gragoudas, 2006; Skalicky et al., 2008; Shields & Shields, 2009). The treatment involves the surgical insertion of a radioactive plaque to the surface of the eye adjacent to the tumour. Brachytherapy for ocular melanoma can provide patients with a good longterm outcome in terms of local tumour control, however, metastases are a significant concern, often leading to vision or eye loss (Shields et al., 2002) and in many cases, fatality (Domato, 2006). The main objective of radiation therapy in the treatment of cancer is to deliver maximum dose to the tumour with minimum dose to normal tissue. Accurate dosimetry is crucial to the realisation of this goal. In the case of radiation treatment for ocular melanoma where the treatment volume is small, the steep dose gradients and close proximity to surrounding critical structures makes dosimetry particularly challenging. Dosimetry of eye brachytherapy sources has been well covered in the literature over the past two decades (Yoriyaz et al., 2005; Davelaar et al., 1992; Williamson & Li, 1995; Fluhs et al., 2004; Dolan et al., 2006; Beiki-Ardakani et al., 2008; Thompson & Rogers, 2010). The most popular experimental methods implement the use of thermoluminescent dosimeters (TLDs), which provide good results but are limited by their size and subsequent poor resolution (Rivard et al., 2004; Binder, Chiari & Aiginger, 1990; Davelaar et al., 1992). Monte Carlo methods of dosimetry are becoming increasingly useful in eye brachytherapy due to the ability to sample within a very small range from the surface of the source. The small distances from the source are of particular interest to researchers due to the published shortcomings of current dose calculation protocol at these points (Awan et al., 2007; Taylor & Rogers, 2008). 1

19 Experimental dosimetry in ocular radiotherapy, where tumours are small and can be close to critical structures such as the optical nerve, demands high spatial resolution dosimetry and high detector dynamic range due to the steep dose gradients involved. A new approach is required to provide real time, high spatial resolution, low dose rate dosimetry for eye plaque quality assurance. Experimental dosimetry of the I-125 and Ru-106 based plaques has been performed using the Medipix2 silicon pixelated counting device recently at the Centre for Medical Radiation Physics (CMRP), University of Wollongong. The Medpix2 device consists of a 256 x 256 pixel array that provides high spatial resolution dosimetry with a fast read-out. The unique output and capabilities of this detector demand a revised treatment planning system that caters to the output of the device. Accurate dose planning software based both on published data from the TG43 protocol and the Monte Carlo method will be designed and developed for direct comparison with the physical measurements. This software will include an output component based on the two dimensional pixel maps produced by the Medipix2. The Monte Carlo methods of dosimetry presented in this work aim to identify and describe unique methods of scoring dose from a single I-125 seed and the curved surface of the Ru-106 plaque. The dose delivered to the treatment volume of the eye will be measured and calculated using Monte Carlo applications based on the Geant4 Toolkit, and the results compared with commercial Treatment Planning Systems (TPS) and current literature. The accuracy of the results will rely heavily on the ability of the simulation to model a true and accurate representation of the I-125 and Ru-106 source based on specifications of construction and spectra in the literature. The goal of the Monte Carlo simulations is to obtain two individual dose rate arrays for I- 125 and Ru-106 respectively for input into the developed dose planning software. The dose rate arrays, in conjunction with the treatment planning system unique to the Medipix2 device, hopes to achieve optimized dosimetry for eye brachytherapy in a way not realised previously. The ultimate goal of this research and the collaborative research of CMRP, is to provide eye plaque quality assurance in a clinical setting in four refined steps: treatment planning based on three-dimensional (3D) imaging of the tumour 2

20 volume, customised eye plaque preparation according to the treatment plan, dose calculation using TG43 and Monte Carlo derived data; and finally, 3D dosimetric imaging with Medipix2 for quality assurance of the treatment plan and dose verification. 3

21 Chapter Two Literature Review 2.1 Ocular melanoma in Australia and worldwide Tumours of the eye develop in four main areas; the uveal tract, conjunctiva, eyelid and the orbit (Shields & Shields, 2009). The uveal tract or uvea, shown in Figure 1, is a vascular layer in the eye consisting of the iris, ciliary body and choroid (Shileds & Shields, 2009). All three compartments of the uvea are in close proximity to vital structures, such as the lens, retina, macula, fovea and optic nerve (see Fig. 1). Melanoma and squamous cell carcinoma are the most prevalent ocular malignancies in adults (Singh & Topham, 2003), with uveal melanoma being the most common form (Stickland & Lee, 1981; Egan et al., 1988; Wilkes et al., 1979; Zehetmayer et al., 2000). The choroid is the most frequent of sites in the uveal tract for the development of primary melanoma (see Fig. 2), followed by the ciliary body and then the iris (Peyman, Sanders & Goldberg, 1980). Figure 1. Anatomy of the uveal tract: ciliary body, iris, and choroid 4

22 Between 1993 and 1997, just under cases of eye cancer were recorded across five continents, translating to approximately cases per year worldwide (Parkin et al., 2002). More recently, American data, released by the Collaborative Ocular Melanoma Study (COMS) (Singh & Kivelä, 2005), reported approximately 5 in every million cases of uveal melanomas per year. Conjunctival melanoma is even more uncommon, with about 200 cases reported annually in the United States (Shields & Shields, 2009). Alarmingly, Australia has one of the highest incidence rates of ocular melanoma (Parkin et al., 2002). In 2006, there were a recorded 99 new cases of ocular melanoma in adults in NSW alone and another 81 new cases in 2007 (Cancer Institute NSW, 2009). This number is predicted to rise under our ever increasing population, with projected outcomes reported of over 100 new cases by the year (Cancer Institute NSW, 2009). Furthermore, sun exposure and environmental factors have been evidenced to increase the risk of choroidal and ciliary body melanoma in Australia (Vajdic et al., 2002). Figure 2. Intraocular melanoma: Iris with nodular melanoma (left) and large choroidal melanoma (right) (Shields & Shields, 2009). Patient survival is generally poor for those suffering with uveal melanoma (Singh & Topham, 2003; Scelo et al., 2006; Virgili, Gatta & Ciccolallo, 2008), having a reported 25% five-year mortality rate (Chang et al., 1998). Irrespective of treatment type, metastasis is the main cause of death in choroidal and uveal melanoma patients (Gragoudas et al., 1991; COMS, 2001; Fakiris et al., 2007; Shildkrot & Wilson, 2009,). For example, the Collaborative Ocular Melanoma Study group (COMS) showed no significant difference in 5 and 10-year mortality rates between patients with large tumours treated by episcleral plaque brachytherapy and enucleation (COMS, 2001). 5

23 Similarly, Gragoudas (2006) reported approximately one quarter of affected patients in the United States will eventually die from metastasis. This result highlights the need for optimised treatment when the primary tumour is confined to the eye (providing the tumour has a low T stage value ). In addition to metastasis, almost 50% of patients will lose vision or the eye due to the disease and/or the treatment (Damato, 2006; Granero et al., 2004). Hence, the most challenging aspects of the disease are in achieving successful early stage treatment as well as vision retention Treatment Ocular melanoma is typically treated by resection of the surgical mass or for progressed large tumours, via enucleation (removal of the eye) (Shields & Shields, 2009). These procedures are both highly invasive and result in permanent vision impairment. There are a number of conservative modalities available for the treatment of ocular melanoma, including; phototherapy, such as photocoagulation or transpupillary thermotherapy, radiotherapy, chemotherapy, immunotherapy and stereotactic radio surgery (Damato, 2006; Gragoudas et al., 1992; Shields et al., 1990). Phototherapy techniques are generally used in the treatment of tumours very small in size (Shields, Shields & Cater et al., 1998). The most common forms of eye-sparing treatment for medium to large sized tumours include episcleral plaque brachytherapy (Packer & Rotman, 1980; Lommatzsch, 1983; Finger et al., 1994) and charged particle radiotherapy (Castro et al., 1997; Fuss et al., 2001), in particular, proton beam therapy (Shildkrot & Wilson, 2009). Transpupillary thermotherapy (TTT) has been a nonsurgical treatment option for ocular melanoma for a number of years, however, in more recent times, this avenue is now seen almost purely as an adjunctive therapy for patients to improve local tumour control (Shields, Cater, Shields et al., 2002; Bartlema et al., 2003; Shildkrot & Wilson, 2009). T stage values are used to describe the presence and nature of the primary tumour in the patient s body and are part of the TNM (Tumour Node Metastasis) staging system developed by the American Joint Committee on Cancer (AJCC). Higher T numbers (1-4) indicate more extensive disease (e.g. greater size, wider spread etc.) (AJCC, 2002). 6

24 The treatment involves a continuous delivery of infrared light, heating the tumour to C until hyperthermia is reached (usually within seconds of exposure) (Domato, 2006). For choroidal melanomas, the treatment works over time to create an atrophic scar covering the treatment area via a series of burns (Domato, 2006). The most published complication arising from TTT, is high local reccurrence (Shields, Shields, Perez et al., 2002; Singh et al., 2004; Domato, 2006; Pan, Diddie & Lim, 2008). Shields, Shields, Perez, Singh and Cater (2002) reported an alarming 23% local recurrence within 3 years for patients treated with TTT alone. Regardless of reccurrence, there is a plethora of vision complications that accompany the treatment, such as retinal burns, iris burns, and distortion of the pupil and cataract (Domato, 2006), all of which result in significant visual field loss. Such complications have ultimately led to the demise of TTT as a stand-alone therapy for the treatment of uveal or choroidal melanoma. Gamma knife stereotactic radiosurgery is used less frequently than other non-invasive techniques, however, it has been shown to provide results comparable to more widely used treatments (Toktas et al., 2010; Zehetmayer et al., 2000). The procedure involves delivery of a single high dose of radiaition (Cobalt-60) via a large number of beams that are focused on a precision target in the patient using a specially designed highly shielding collimation system. This technology is accurate enough to treat target volumes of anywhere between 4mm and 4cm in diameter (Khuntia et al., 2009), making the technique ideal for treating ocular malignancies. The advantages of stereotactic radiosurgery are that it is non-invasive, it significantly reduces dose to normal tissue and is convenient for the patient, with treatment provided within a single day (Fakiris et al., 2007; Modorati et al., 2009; Khuntia et al., 2009). Toktas et al. (2010), analysed the outcomes of 35 uveal melanoma patients who underwent Gamma Knife surgery, having no previous treatment. The dose prescribed was 30Gy at 50% isodose field for all patients, with all the tumours being relatively small. Complications in follow up were significant, with 17.1% of patients experiencing retinal 7

25 detachment. After 12 months, 20 patients had experienced vision impairment and three required enucleation due to tumour progression into surrounding areas. Despite these complications, cumulative 1-year and 3-year local tumour growth control rates were 97% and 83% respectively, demonstrating that the long term outcomes of this method of treatment are similar to those of enucleation and brachytherapy. While this form of stereotactic radiosurgery is a potentially eye-saving procedure, the risk of secondary enucleation in follow-up is not uncommon (Zehetmayer et al., 2000). Furthermore, there is currently only one facility in the Australia with the ability to provide Gamma Knife treatment, and is specifically used for brain tumour patients. Thus, radiosurgery is not a possible treatment option for most Australians with ocular melanoma. Proton therapy is unique in its advantages due to the way in which protons deposit their energy in a medium. The dose profile of a proton beam is characterised by a low level entrance dose with a sharp increase in dose known as the Bragg peak, occurring at a depth that can be specified by the range of the protons through beam energy selection. After the Bragg peak, the dose drop-off is steep and approaches zero almost immediately. This fact makes proton therapy advantageous in the treatment of uveal melanoma due to the close proximity of vital structures situated behind the tumour. Both Gragoudas (2006) and Caujolle et al. (2010) demonstrate the advantages of proton therapy for the treatment of uveal melanomas through the high survival rates obtained from long-term studies of patients in the United States. Gragoudas (2006) studied 2069 patients undergoing proton therapy treatment for uveal melanoma since The five-, ten-, and fifteen- year survival rates were reported to be 86%, 77% and 73% respectively, and were comparable to those of other facilities. Similarly, Caujolle et al. (2010), studied 886 patients treated by proton beam therapy for uveal melanoma from 1991 to 2007 and found five- and ten- year survival rates of 92% and 86% respectively for T1 stage malignancies and 89% and 78% respectively for T2 stage malignancies. Gragoudas (2006) also reported a 90% probability of retaining the eye at five- and ten- years post irradiation. Both studies found these rates and results in agreement with those of patients after receiving I-125 plaque brachytherapy or enucleation. 8

26 While these results are extremely promising, proton beam therapy is limited by its availability. With only around 30 proton facilities worldwide, none of which located in Australia, the use of proton therapy for the treatment of ocular malignancies is not an option for many sufferers around the globe. Moreover, the financial burden of proton therapy to the community and the patient is large, only serving to hinder its availability and use further still. The current body of literature details a variety of procedures and therapies for the treatment of ocular melanoma, all of which are accompanied by their own risks and clinical benefit for the patient. Nevertheless, brachytherapy using radioactive plaque applicators remains the most widely used treatment for posterior uveal melanoma, having demonstrated higher local tumour control, lower short term reoccurrence rates and decreased long term vision loss. 2.2 Episcleral plaque brachytherapy Brachytherapy using radioactive eye plaques is the most widely used radiotherapy technique for the treatment of ocular melanoma (Lommatzsch, 1986; Packer, Rotman & Salanitro, 1984; Shields et al., 1982; Shields, Shields & Donoso, 1991; Shields, 1993; Skalickly et al., 2008; Shields & Shields, 2009). The procedure involves the surgical insertion (suturing) of a radioactive plaque to the sclera, close to the tumour. During treatment, the apex (deepest region) of the tumour will receive a dose ranging from between 80Gy to 100Gy depending on its size and location (Hokkenan et al., 1996; Granero et al., 2004). Brachytherapy treatment of uveal melanoma has been shown to yield good results in terms of tumour control as well as improved vision retention as enucleation is not necessary if treatment is successful. Nevertheless, normal tissue complication may arise due to the small and intricate nature of the eye itself and the subsequent irradiation of surrounding tissues and vital structures. 9

27 The treatment of ocular malignancies by insertion of radioactive seeds originated in the 1930 s when Moore (1930) published on the use of radon seeds for the treatment of choroidal melanoma. Three decades later, Stallard (1961, 1966) developed the application of removable conformal radioactive plaques in the treatment of ocular tumours. The first isotope used clinically in Stallard s methods was Cobalt-60, but was associated with high rates of morbidity and has since been supplanted by radionuclides such as Ir-192, Ru-106/Rh-106, Pd-103and I-125. Today, source selection is influenced by tumour size, thickness and location (Granero et al., 2004). Iodine-125 and Ruthenium- 106 plaques have become the preferred source in eye plaque brachytherapy today (Stallard, 1966; Packer, Rotman & Salanitro, 1984; Gragoudas, 2006). The use of I-125 seeds in eye plaque brachytherapy was first described by Packer and Rotman (1980) and has become the most widely used source today in this application (Chan et al., 2001). Since it is a low-energy photon emitter, I-125 delivers a lower dose to surrounding normal tissue in comparison to other radionuclides with higher energy emissions. Survival rates for patients treated with I-125 plaque brachytherapy are high and compare favourably to those of external beam radiotherapy (Char et al., 1993) or enucleation (COMS, 1998). For example, in 2001, the COMS group reported that survival rates for I-125 plaque therapy and enucleation were the same, and in 2006, the group confirmed this result with a report on twelve-year mortality rates and prognostic factors (COMS, 2001; COMS, 2006). Ru-106, a beta emitter, was incorporated into an ophthalmic applicator by Lommatzsh (1974, 1986) for the treatment of choroidal melanoma over forty years ago and has since been used to provide treatment with a 90% tumour control rate (Eichmann, Fluhs & Spaan, 2009). The German company, BEBIG GmbH, began marketing these applicators in the 1960 s (ICRU, 2004) and they are now predominantly used in Europe (Kleineidam, Guthoff & Bentzen, 1993). Being a beta emitter, the Ru-106 plaques provide less depth penetration and therefore have the advantage of normal tissue sparing (Wilkinson et al., 2008). For this reason, Ru-106 plaques are preferred for the treatment of small-sized tumours (Sanchez-Reyes et al., 1998; Wilkinson et al., 2008). For example, Wilkinson et 10

28 al. (2008) performed a dosimetric comparison of Ru-106 and I-125 plaques for shallow (less than 5mm) chorodial melanoma lesions. The authors determined the dose delivered to various regions of the eye during a Ru-106 and I-125 treatment using the Plaque Simulator (BEBIG, GmbH) TPS for 26 individual patients and compared the results with those provided by the COMS concluding that Ru-106 plaques may be capable of more accurate treatment for smaller tumours. Such results indicate the potential advantage of Ru-106 for reducing the risk to normal surrounding structures, and consequently, loss of vision. In terms of tumour control rate, it appears that with careful selection of cases, a tumour control rate of more than 95% may be achievable with Ru-106 plaques (Domato et al. 2005, as cited in Wilkinson, Kolar, Flemming & Singh, 2008). Despite these promising results for tumours small in size, Eichmann (2009) stressed the potential harm the higher dose rate of Ru-106 plaques may have on surrounding structures, in particular, the optic nerve and fovea. Hence, accurate dosimetry and treatment planning software is critical for small tumours and their intricate treatment volumes Description of plaques A number of plaques have been designed for use in eye brachytherapy by various groups (Packer & Rotman, 1980; Luxton et al., 1988; Moore, 1930; Stallard, 1961; Stallard, 1966; COMS, 1998; Eckert & Ziegler, 2008). The plaques are generally spherical in shape and are made of metal (usually gold alloy) (Astrahan et al., 1990). I- 125 and Ru-106 loaded plaques are the most popular choice for treatment of uveal melanoma worldwide (Chan et al., 2001). Hence, the two plaques used in the described dosimetry methods of this thesis were the 15mm ROPES (Radiation Oncology Physics and Engineering Services, Australia) plaque and the Ru-106 ophthalmic plaque manufactured by BEBIG (BEBIG GmbH). These plaque designs will be described in detail in the following sections. 11

29 ROPES plaque design The 15mm ROPES plaque (ROPES Ltd, Sydney, Australia) is commonly used today in I-25 based treatment and dosimetry (Walsh-Conway & Conway, 2009). This plaque, as the name suggests, is 15mm in diameter and has ten seed holes positioned in an acrylic insert that sits within the spherical stainless steel backing of the plaque (see Fig. 3). The stainless steel backing acts as a radiation shield to prevent the irradiation of normal tissue and vital structures. Figure 3. Three components of the 15mm ROPES plaque (Eye Physics, LLC see The stainless steel plaque has a spherical top sitting on a cylindrical shell 3mm in height (Granero et al., 2004). The acrylic insert is also spherical in shape and sits within the steel plaque such that it offsets the radioactive seeds 1mm from the sclera where it is attached (Granero et al., 2004). Figure 4 shows the schematic of the 15mm ROPES stainless steel plaque and acrylic insert. 12

30 Figure 4. Schematic diagram of the 15mm ROPES plaque (as per Eye Physics, LLC see BEBIG plaque design Ruthenium-106 opthalmic plaques are becoming an increasingly popular choice for the treatment of a variety of ocular melanomas and are particularly well accepted throughout Europe (Lommatzsch, 1983). The German designed BEBIG ruthenium-106 beta emitting plaques are popular in clinics across the world (Seregard, 1999; Hernandez et al., 1993). These plaques are spherical in shape with radii ranging from 12mm 14mm over a variety of plaque types. All plaques have a polished metal surface with the Ru-106 source encapsulated within 1mm thick pure silver sheets (Eckert & Ziegler BEBIG GmbH, 2008). The plaque contains a thin silver foil radiation window 0.1mm in thickness on the inside active surface and a 0.9mm backing on the outer convex surface that acts as a radiation shield, assumed to absorb approximately 95% of all beta radiation (see Fig.6) (Eckert & Ziegler BEBIG GmbH, 2008). 13

31 Figure 5. BEBIG Ru-106 plaque applicator types including notched type (left and middle) and schematic of plaque geometry (Eckert & Ziegler BEBIG GmbH, 2008) A total of 16 plaque designs are available to treat a variety of tumour types (see Fig. 5). Uveal and choroidal melanomas are typically treated with the CCA, CCB, CCC, CCD and CGD plaques unless the tumour is positioned close to the optic nerve, in which case the COB, COD, COE and COC designs would be employed (Eckert & Ziegler BEBIG GmbH, 2008). These plaques are notched on one side to conform to the tumour while avoiding the optic nerve. Small tumours, such as retinoblastomas are treated with the CCX, CCY, CCZ and CXS plaques while CIA, CIB and the CIB-2 plaques that have a shallow notch, are used to treat ciliary body melanomas or melanomas close to the iris (Eckert & Ziegler BEBIG GmbH, 2008). 14

32 Figure 6. BEBIG Ru-106 opthalmic applicator range (Eckert & Ziegler BEBIG GmbH, 2008) 2.3 Eye Plaque Brachytherapy Dosimetry Current methods of dosimetry in eye plaque brachytherapy rely heavily on the accuracy of standard recommendations provided by respected and established groups in medical physics. These recommendations are naturally under constant revision as treatment and dosimetry techniques become increasingly sophisticated in the current era of ever advancing and revolutionary technology. In this work, current standards in eye plaque brachytherapy dosimetry and treatment planning will be revised using Monte Carlo techniques, requiring a strong grasp of the methods and limitations of relevant protocol. The following sections will outline existing popular methods of dosimetry in eye plaque brachytherapy and the internationally recognised dose calculation protocol for dosimetry about I-125 and Ru-106 brachytherapy sources Current methods of dosimetry in eye plaque brachytherapy Dosimetry in eye brachytherapy is often considered an arduous task, due to the small volume of the eye and the geometry of the plaque designs in use today. A range of techniques have therefore been investigated for many of the available sources currently in 15

33 use. In particular, for I-125 and Ru-106 based plaque designs due to their popularity. Dosimetry for I-125 seeds using TLDs has been performed for a number of decades with success. Results have been shown to be particularly accurate at larger distances from the source (greater than 5mm) (Luxton et al., 1988; Duggan & Johnson, 2001; Wallace, 2002, as cited in Rivard, 2002; Muller-Runkerl & Cho, 1994, as cited in Williamson & Li, 1995). Dosimetry for beta emitting plaques, such as Ru-106, is particularly challenging due to the short range of radiation and steep dose gradients at close distances to the source that demands high spatial resolution geometry. Methods of dosimetry are limited by the size of detectors available and by the curved surface of Ru-106 plaques. A number of methods have been tested for accurate measurement of absorbed dose distributions from Ru-106 eye plaques over the last two decades. In the beginning stages of Ru-106 dosimetry, films, TLDs, diodes and plastic scintillators were used with success, however, limitations arose due to their size and the geometry of the plaque source. For example, Binder, Chiari and Aiginger (1990) performed dosimetry of Ru-106 opthalmic applicators using TLDs positioned behind a BEBIG CCB plaque on a tissue equivalent eye phantom. Over 120 TLDs were cut to a size small enough to obtain an adequate response from the surface of the plaque. Measurements covered the central area of treatment and demonstrated a significant underdose in comparison to what was expected during a typical treatment. The TLDs were unable to measure outside the treatment area or on the peripheral edges of the plaque. Similar to results with I-125, the TLDs are limited mainly in their spatial resolution, being particularly poor for measurements at close distances to the source. Extrapolation chambers are said to be the standard device for dosimetry of beta emitting sources such as Ru-106 (Soares et al., 2001) and do not require radiation calibration, which is a desirable characteristic. Nevertheless, the large and somewhat awkward geometry of the device makes accurate dosimetry in close range to the source extremely difficult and is the method s greatest limitation in this context (Soares et al., 2001). 16

34 Hence, these devices are mostly restricted for use in dosimetry of planar sources rather than curved. Radiographic and radiochromic films, and other thin detection materials have been used widely in Ru-106 dosimetry due largely to their accessibility (Wu & Krasin, 1990; Soares & McLaughlin, 1993, Taccini et al., 1997; Hjortenberg, Hansen & Wille, 1989; Davelaar et al., 1992). The major shortcoming of this method is the low sensitivity of the film being inadequate for measuring at larger distances from the source (Soares et al., 2001). More specifically, radiochromic films have large variations in thickness across their surface due to the materials of the backing, greatly decreasing the reproducibility of results (Soares et al., 2001). Fibre optic plastic scintillators have been used in dosimetry for quality assurance of Ru-106 plaques previously (Elchmann et al., 2009; Sliski et al., 2006). However, similar to TLDs for quality assurance of I-125 sources, the method is limited by the size of the device (1.0x5.0mm) and the resultant poor resolution (Elchmann et al., 2009; Sliski et al., 2006). Furthermore, the procedure involves a rather complex and slow scanning assembly to obtain the required two-dimensional (2D) dose distributions from the curved source. In recent years, three-dimensional semiconductor detectors such as the Medipix2 (Wilkins et al., 1996) and Timepix (Llopart et al., 2001) have been used successfully to provide high spatial resolution X-ray imaging, finding applications in radiography, neutronography, and micro-tomography (Wright et al., 2005; Jakubek et al., 2006). The Medipix2, developed at CERN (Llopart et al., 2001), is defined as a single-particlecounting pixel detector with a high detection efficiency and an unlimited dynamic range (Jakubek, 2007). With a 256 x 256 sensitive silicon pixel array, the Medipix2 device compares the charge collected at each pixel with a known threshold to provide real time intensity read-out of the incoming ionizing radiation (Jakubek, 2007). Jakubek et al., (2006) used a micron focused X-ray source and the Medipix2 detector to obtain threedimensional radiographic images of the soft tissues of plants and insects. Spectroscopic dosimetry, based on a silicon radiation detector used in spectroscopy mode has been used in low dose rate brachytherapy for point dosimetry with success (Cutajar et al., 2006) and 17

35 recently, the advantages of three-dimensional detectors such as the Medipix2, have also been utilised for radiation dosimetry in the quality assurance of brachytherapy sources. Weaver et al. (2010), obtained three-dimensional dosimetric images of the dose distribution from a 15mm ROPES plaque loaded with I-125 seeds and the Ru-106 CCD plaque using the Medipix2. The detector was placed below the plaque within a tissue equivalent phantom of eye matching dimensions and 2D dose maps were obtained in a range of depths. Three-dimensional dose distributions were then reconstructed from the series of 2D dose maps. The results of this work were high spatial resolution images acquired in real-time that can be used for the quality assurance of such plaques before clinical use. These results are relevant to a range of radiation therapy procedures in intricate volumes. Other recent studies are pushing the boundaries of dosimetry for eye brachytherapy, redeveloping old techniques to cater to the challenges and limitations presented by the eye and plaque geometries. For example, Eichmann, Fluhs and Spaan (2009) developed an advanced experimental dosimetry method for measurement of the dose distribution from a BEBIG Ru-106 plaque using a plastic scintillator system and a newly designed apparatus that guides the detector across the surface of the plaque at a constant, small distance. The plastic scintillator employed had a resolution of sub-millimetre range, water equivalence, high sensitivity, and a large dynamic range (Eichmann et al., 2009). The results were of high resolution and identified small sized areas of hot and cold activity. This study highlights the strength of new methods of dosimetry for eye plaque brachytherapy in achieving increased accuracy dose distributions for input into TPS for dose optimisation. Furthermore, new experimental methods such as the Medipix2 approach developed at the CMRP (Weaver et al., 2010) and the system proposed by Eichmann et al. (2009), necessitate new and improved Monte Carlo methods to compliment and verify the results of physical measurements for quality assurance in eye brachytherapy. 18

36 2.3.2 AAPM TG43 Brachytherapy Formalism In 1995, the American Association of Physicists in Medicine (AAPM) released a protocol for brachytherapy dose calculations, so named the AAPM Task Group No. 43 (TG43) Report. The protocol outlined specific recommendations for both 2D and onedimensional (1D) source-specific dose-rate calculations. In the years that followed, great advances were made in the field of brachytherapy treatment and dosimetry, and to accommodate for this, the AAPM published an updated protocol in This report not only corrects an error present in the original protocol, but provides guidelines for physicists conducting experimental and theoretical methods of dosimetry, including Monte Carlo derived dose-rate distributions, where the consistency in derivation of the parameters used in the TG43 formalism between groups is essential. Both the original and revised reports are based on the following five primary definitions as outlined in the TG43 Report (Rivard et al., 2004): 1) A source is defined as any encapsulated radioactive material that is or can be used in brachytherapy procedures, having no restrictions on size or symmetry. 2) A point source is a dosimetric approximation whereby radioactivity is assumed to be spherically symmetric through a dimensionless point at any given radial distance r. The effect of the inverse square law on the radiation distribution at any distance may be determined using 1/r 2. 3) For a cylindrically symmetric source, the transverse plane is that which bisects the radiation distribution perpendicular to the longitudinal axis of the source. 4) A line source is a dosimetry approximation whereby radioactivity is assumed to be uniformly distributed along a 1D line-segment of active length L. While this assumption does not accurately describe the radioactivity distribution of an actual brachytherapy source, it provides a simplified method of calculating distributions outside the range of tabulated TG43 data. 19

37 5) A seed is defined as a cylindrical brachytherapy source with active length, L, or effective length, L eff, less than or equal to 0.5cm. General 2D Formalism It is necessary to comprehend the geometry of brachytherapy sources as defined by the TG43 protocol in order to understand the described methods of calculating dose distributions. The coordinate system assumed in these calculations is shown in figure 7. Figure 7. Coordinate system used in calculating dosimetric parameters for a brachytherapy source as defined by the TG43 AAPM revised protocol (Rivard et al., 2004) The 2D dose rate distribution around a cylindrically symmetric brachytherapy source is defined by the TG43 formalism as (Rivard et al., 2004), G L r, D(r,θ) = S G L r 0, 0 g L r F r, (2.1) Where S K is the air kerma strength and Λ is the dose rate constant (both described later), r is the distance in centimetres from the center of the active source to the point of interest and θ is the polar angle identifying the point of interest, P(r, θ), relative to the longitudinal axis of the source. Both r 0 and θ 0 denote the reference point, defined as the 20

38 point at a reference distance r 0 of 1cm and a reference angle θ 0 of 90. The functions G L (r, θ) and G L (r 0, θ 0 ) are therefore the Geometry functions at the point of interest and the reference point respectively, g L (r) is the radial dose function and F(r, θ) is the anisotropy function. These functions will be described in detail in the following sections. The subscript, L, indicates the function is for a line source and may also be replaced with a P, for point source approximations. Air Kerma Strength Kerma is the energy transferred to charged particles as a result of indirect ionizing radiation (Attix, 2004). The air-kerma of a brachytherapy source is therefore simply a measure of its strength. Air-kerma strength, S K, has units of U where 1U = μ Gym 2 h -1 = 1cGycm 2 h -1 (Rivard et al., 2004). Air-kerma strength is defined by the TG43 protocol as the air-kerma rate, K δ (d), in a vacuum and due to photons of energy greater than δ, at distance d, multiplied by the square of this distance, d 2 (Rivard et al., 2004), S d d 2 (2.2) Where d is the distance from the centre of the source to the point Κ δ (d) specification. This point is generally (but not always) the same as the point of measurement and is located on the transverse plane of the source. The distance d must be large enough relative to the maximum linear dimension of the distribution to ensure geometry effects are excluded in the calculation. Photon scattering and attenuation values in air should be taken into account as well as in any other medium between the source and the point of measurement. Dose Rate Constant The dose rate constant is a ratio of the dose rate at the reference point and the air-kerma strength, S Κ (Rivard et al., 2004). It has units of cm -2, r0, S D 0 (2.3) 21

39 The value of the dose rate constant is therefore dependent on the radionuclide, the source model and the method used to determine the air-kerma strength. Geometry function The Geometry function, G L (r, θ), provides an inverse square correction for dose rate calculation based on an approximation of the spatial distribution of radioactivity within the source, including the geometrical effects of the source alignment relative to the point of measurement (Rivard et al., 2004). It is used to increase the accuracy of interpolation of data between tabulated dose rate values of the protocol and may be used in either 1D or 2D treatment planning calculations. For simplicity, the TG43 protocol recommends the geometry function be approximated using a point or line source model (Rivard et al., 2004). For a point source, the geometry function is simply the inverse square law for radiation intensity, however, the line source function must take into consideration the length of the source, L, the angle, θ of the point of calculation, P(r, θ) with respect to the source and the angle subtended by the ends of the source with the point of calculation, denoted as beta (figure 7) (Rivard et al., 2004). if 0 G L r, Lr sin (2.4) r L / 4 if 0 Radial Dose Function The radial dose function accounts for the fall-off in dose that occurs due to photon scattering and attenuation rather than geometry and distance. The radial dose function is defined as (Rivard et al., 2004), g r D r, 0 D r, 0 0 G G r, 0 r, 0 0 (2.5) The value of the function is equal to 1 at the reference distance, r 0 and angle, θ 0 =

40 Anisotropy Function The 2D anisotropy function, F(r, θ) describes the variation in dose as a function of polar angle in the transverse plane of the source due to the source encapsulation and is defined as (Rivard et al., 2004), D r, GL r, 0 F r, D (2.6) r, G, 0 L r Amersham Health Model 6711 Oncoseed The Amersham Health model 6711 Oncoseed contains a 3mm long silver rod inside a 4.6mm welded titanium capsule (Rivard et al., 2004). The capsule is 0.05mm thick with welded end caps (Rivard et al., 2004). The I-125 is absorbed onto the silver rod and the silver itself produces characteristic X-rays that affect the spectrum of the source. The silver carrier differs in size and shape between models and as such, dosimetry will be unique to each source. Figure 8 illustrates the construction and geometry of the model 6711 seed design. Figure 8. Model 6711 Onco seed geometry (Rivard et al., 2004) 23

41 I-125 is a photon-emitting source with a half-life of 59.4 days (Rivard et al. 2004). The photon spectrum consists of five main energies obtained from Attix (2004) which are listed along with their probabilities in Table 1 below. Table 1. I-125 spectra. Photon energy (kev) Photons per disintegration There are a number of source characteristics that can affect the photon spectrum of the seed and hence the dosimetry. Furthermore, source geometry, internal construction and activity vary greatly in accordance with the manufacturer. The AAPM Task Group 43 published values for the Amersham health model 6711 seed cover radial distances of up to 10cm from the source. The radial dose functions and anisotropy functions are listed in Table 2 and 3 respectively. These values were obtained using TLD measurements and are used for interpolation between dose points in I-125 brachytherapy treatment planning systems. Table 2. Radial dose functions for the single Amersham health model 6711 seed. Line source approximation r [cm] Amersham 6711 L = 3.0mm

42 The anisotropy functions (Table 3) are provided every 10 degrees for angles between 0 and 80 degrees about the source. Table 3. Anisotropy functions for the Amersham model Polar angle r [cm] θ (degrees) Ru-106 Protocol of Measurements In 2002, National Institute of Standards and Technology (NIST) developed the NIST traceable calibration protocol for dose rate calculation in Ru-106 eye plaque 25

43 brachytherapy (Astrahan, 2003), replacing the original protocol that had been in use over a number of decades with a reported uncertainty of up to 30% (Soares, 1998). BEBIG, the manufacturers of Ru-106 plaques, currently supply the updated protocol, commonly referred to as the 11 point Protocol of Measurements (Eichmann, 2009). This protocol consists of an 11 point depth dose curve on the central axis, from a distance of 0.6mm, then 1mm to 10mm from the centre of the plaque surface incremented every 1mm (Eichmann, 2009). The protocol also provides dose rate measurements of 33 points up to and close to the plaque surface (Astrahan, 2003). These measurements were performed using a plastic scintillator detector in a water phantom and have a reduced uncertainty of 20% (Astrahan, 2003). A number of studies have been published on a variety of alternative methods for measuring and determining dose rates, including 8 and 10 point protocols of measurement (Hokkanen et al., 1996; Cross et al., 2001; Wilkinson et al., 2008; Astrahan, 2003, Eichmann et al., 2009). Astrahan (2003) suggests a dose rate calculation method for Ru-106 eye plaques based on an adaptation of the TG43 protocol for brachytherapy sources. This method is simple and time efficient since it is fundamentally based on the familiarity of the TG43 formalism for dose rate calculation about a brachytherapy seed. The method involves the summing of a discrete number of uniformly distributed patch source dose functions over the surface of the plaque (Astrahan, 2003). The functions are derived from Monte Carlo modelling and empirical measurements (Astrahan, 2003), and calculations are made using the methods of the TG43 formalism altered for the geometry of the plaque surface. The central axis fits achieved using this method were within 2% for almost all plaque types used in the study. Astrahan s semi-emperical method makes calculating dose distributions from a Ru-106 source compatible with current TPS employing the TG43 formalism. While Monte Carlo methods, such as those described by Astrahan (2003), can reduce uncertainty in calculation significantly, they are time consuming and often laborious in nature. Hence today, the manufacturer s Protocol of Measurements remains the most widely used method of dose verification in Ru-106 brachytherapy. 26

44 Ru-106 Spectrum Ruthenium-106 is a fission product with a half-life of days (ICRU, 2004). The isotope decays via beta emission to Rhodium-106, which decays to the stable nuclide Palladium-106 (ICRU, 2004). The maximum energy of the Ru-106 electron spectrum is 39.4keV and the maximum photon energy is 1.56MeV (ICRU, 2004). The photon contamination spectra is shown in Table 4 and the beta spectra in Table 5. Table 4. Ru-106 Photon contamination spectra*. Energy (MeV) Photon emission probability (%) The main electron contribution to the spectrum comes from Rhodium-106 decay, which has a half-life of only thirty seconds. Since this transformation is fast, the daughter product, Rh-106, can be considered to be in equilibrium with the parent, Ru-106 (ICRU, 2004), and hence its decay spectra (shown in Table 5) is of great significance in dosimetry. Rhodium-106 has a maximum beta energy emission of 3.54MeV and an average energy emission of 1.41MeV (ICRU, 2004). Table 5. Rh-106 Beta ray spectra*. Energy (MeV) No. beta rays per disintegration

45 *Decay data for Ru-106/Rh-106 was obtained from Appendix A of the ICRU Report 72 (ICRU 2004). 28

46 2.4 Treatment planning systems A number of treatment planning systems are available for eye plaque brachytherapy, including the ROCS (Carlsbad, CA) eye software, PINNACLE (Koninklijke Phillips Electronics N.V.) and the Plaque Simulator (BEBIG GmbH, Berlin, Germany). The Plaque Simulator is widely used in eye plaque brachytherapy treatment planning and has been verified for dosimetry in a number of publications (Knutsen et al., 2001, Astrahan, 2003). The software package offers a real-time, interactive 3D simulation of the desired treatment plan with a colour graphic display interface (see Fig. 9). A number of sources (I-125, Pd-103, Ir-192 and Ru-106) and plaque types including the ROPES, COMS and BEBIG plaques are available to choose from. The program implements 3D computed tomography (CT) information of the eye based on patient specific anatomy (Astrahan et al., 1990). The Plaque Simulator calculates the dose distribution in any subregion of a transverse, sagittal or coronal planar cross-section of the eye, in any plane transecting the plaque and crossing the entire eye, or on a spherical surface within or surrounding the eye (Astrahan et al., 1990). The software allows for source activity to be specified and automatically accounts for isotope decay based on the assay date. A number of viewing perspectives over a range of angles are available as well as depth dose curve and isodose contour generation. 29

47 Figure 9. Visualisation of the Plaque Simulator treatment planning software showing central axis and plaque positioned behind tumour on back of eye (Eye Physics, LLC see Limitations in dose planning software for eye plaque brachytherapy Current treatment planning systems for use in I-125 brachytherapy rely on the radial dose functions provided by the AAPM TG43 protocol for calculating the dose distribution around a brachytherapy seed. These radial dose functions are adequate over a limited range of radii (0.1cm r 10cm) (Rivard et al., 2004), however, the distances by which these values are incremented are not consistent, leaving a number of values of r unaccounted for. Furthermore, the quality of the radial dose function fit for calculating dose data is reduced for values of r 0.5cm (Taylor & Rogers, 2008). At these small distances from the source, fits are said to suffer from non-physical fluctuations and significant inaccuracy for values of r 0.25cm (Taylor & Rogers, 2008). In the case of I- 125 eye plaque brachytherapy, where the dose gradient is steep, dose data at small distances (r 0.5cm) from the plaque is of utmost importance to the quality assurance of treatment (Awan et al., 2007). Tabulated dose rate data is provided by the TG43 protocol for a number of brachytherapy sources. More specifically (and for the purpose of this work), the protocol provides dose rate data for the single Amersham Health model 6711 source for radii between 0.5cm and 7cm. The protocol recommends care be taken when calculating dose rates for values of r outside the range of the tabulated data, in particular, for radii less than 0.5cm, due to reasons outlined above. 30

48 The BEBIG Plaque Simulator software for Ru-106 treatment planning has an in built Protocol of Measurement which consists of a depth-dose curve of 11 points from mm from the centre of the plaque surface. However, this is difficult to measure and verify physically since the region of interest falls within close proximity to the plaque surface and hence dose gradients are steep. These measurements are performed in a water phantom, 1mm away from the inner surface of the plaque using a cylindrical plastic scintillator detector, 1mm in diameter and 0.5mm in height (Eichmann et al., 2009). Since the dimensions of the detector are small, point dose measurements are made possible, however, measuring 1mm away from the surface of the source causes a loss in resolution which ultimately serves to decline the quality of the dose distribution (Eichmann et al., 2009). It has been reported that advanced novel Monte Carlo techniques provide suitable methods for calculating dose-rates at these small distances (Williamson & Li, 1995; Rivard, 2002; Rivard et al., 2004). At present, I-125 loaded eye plaques are the most popular for treating eye melanoma in Australia and worldwide (Chan et al., 2001). Furthermore, the Amersham Health model 6711 seed is the most widely used I-125 brachytherapy seed for permanent implantation (Rivard et al., 2004). The Ru-106 based plaques are particularly common for the treatment of small tumours (<5mm). Hence, in this work, a single Amersham Health model 6711 I-125 seed and a Ru-106 BEBIG CCD plaque was modelled using Monte Carlo method. The Geant4 version user-code was used for all Monte Carlo simulations in this study. The Monte Carlo derived dose distributions for this source can be used to build an array of input data to be incorporated into current TPS, such as those described in Chapter Three, for dose optimisation. 2.5 Radiation interactions with matter In order to perform accurate Monte Carlo dosimetry for brachytherapy or any form of radiation treatment, it is necessary to understand the type of interactions radiation can have with matter. Furthermore, an understanding of these interactions is crucial to the 31

49 evaluation of the radiobiological impact on the patient during treatment. In the case of eye plaque brachytherapy using I-125 and Ru-106 plaques, photons are the primary particles of interaction and must be included in the simulation. It is also necessary to consider electron interactions for I-125 and for electrons arising from the beta emission of Ru Photon interactions When a radioactive isotope, such as those described for use in episcleral plaque brachytherapy, undergoes radioactive decay, it may emit energy in the form of photons. These photons, despite having no charge, may interact with the medium through which they travel via four main processes; photoelectric absorption, Compton scattering, pair production and Rayleigh (coherent) scattering. In the first three processes, the photon may impart some or all of its energy to an electron within the medium and hence either be scattered into the medium or disappear completely (Knoll, 2000). The mode of interaction is completely dependent on the energy of the incident photon and the material of the medium. These photon interaction mechanisms will be discussed in depth in the following sections. Photoelectric absorption When a photon interacts with the particles of a medium it can transfer all of its energy to an electron occupying a bound shell of an atom within the medium. In doing so, the now photoelectron is excited enough to be ejected from its bound state in the shell and absorbed in the medium (see Fig. 10). The energy of the photoelectron is equal to the energy of the original incident photon minus the energy lost in interaction (the binding energy of the photoelectron to the shell). This process is known as photoelectric absorption and dominates at low photon energies. 32

50 Figure 10. Photoelectric effect E h E B (2.7) Where E is the energy of the photoelectron after interaction, hν is the initial incident photon wavelength (denoted by the product of h, Plank s constant and ν, photon frequency) and E B is the binding energy of the photoelectron. Compton Scattering The process of Compton scattering involves the partial delivery of the incident photon energy to an electron within the absorbing medium. When a photon comes close to an absorber electron of the medium, a fraction of its energy is transferred, causing the electron to recoil at some angle while part of its energy goes into scattering the photon off at a significant angle through the medium. Both the electron (assumed to be initially at rest) and the photon are scattered through an angle relative to its original direction (Knoll, 2000) as shown in Figure

51 Figure 11. Compton Scattering h h ' (2.8) h (1 ( )(1 cos )) 2 mc Where hν' is the photon wavelength after scattering, hν is the initial wavelength of the photon, m is the mass of the electron, c is the speed of light and θ is the subsequent scattering angle. The majority of photon interactions detected from gamma-ray emitting sources will be a result of Compton scattering, as it is the most probable of all mechanisms at these energies (Knoll, 2000). Pair Production Pair production is the most unlikely of interaction mechanisms to occur between photons and atoms of the absorbing medium. This is a result of the high photon energy required and therefore, will only be predominant at high energies. The phenomenon of pair production occurs only when the incident gamma photon energy exceeds twice the rest- 34

52 mass energy of an electron in the absorbing medium (1.02MeV). Consequently, the photon energy is completely transferred to the nucleus resulting in the production of an electron-positron pair and hence the complete disappearance of the photon. All remaining energy greater than the required 1.02MeV is transferred to the kinetic energy of the electron-positron pair (Knoll, 2000). As the electron-positron pair are slowed and absorbed by the medium (typically within only a few millimetres), the positron undergoes annihilation (Knoll, 2000), resulting in the production of two 511keV annihilation photons which are emitted simultaneously in opposite directions (See Fig. 12). Figure 12. Pair Production Coherent Scattering Coherent scattering is an elastic interaction between a photon and an atom of the absorber medium where the direction of radiation is altered and the absorber atom moves no more than what is required to conserve momentum (Attix, 2004). Although no energy is lost in 35

53 the interaction, coherent scattering adds to the attenuation coefficient, as, at each point of measurement, the average distance travelled by photons to the point is larger (see Fig. 13). The photon scattering angle is dependent on the atomic number of the medium as well as the initial photon energy where lower energies correspond to a greater angle of scatter (Attix, 2004). Therefore, this kind of interaction must be considered in photon transport calculations, particularly for low energies. Figure 13. Coherent scattering in photon transport calculations Electron interactions The interaction of electrons with matter is an important concept in the application of radiation in medicine, being the fundamental interaction considered in external beam radiation therapy and medical imaging. In the context of this work, it is necessary to understand electron interactions for brachytherapy dosimetry using I-125 and Ru-106 sources. The processes by which electrons interact with the atoms of a medium differ significantly from those of heavy charged particles, namely in the rate of energy loss being lower and the angle of deflection being larger for electrons through the medium (Knoll, 2000). The mass of an incoming fast electron, ignoring relativistic effects, is equal to the mass of the orbital electron of the nuclei of the absorbing medium (Knoll, 2000). The incident electron can therefore impart large amounts of energy in one interaction. Electrons are unique in that they may transfer energy to a medium not only 36

54 via coulomb interactions but also electromagnetic radiation. The electromagnetic radiation emanated by a fast electron is known as bremsstrahlung. Bremsstrahlung It is known that any charge, when accelerated, must radiate energy (Knoll, 2000). When an electron passes near the nucleus of an absorber atom of the medium, the electron is deflected and experiences an inelastic interaction in which an X-ray photon is emitted (Attix, 2004). These X-ray photons are referred to as continuous or bremsstrahlung X- rays. In this process, the electron imparts most, if not all of its kinetic energy to the photon and is slowed down in the medium. It is important to note that only fast electrons can have a significant yield of bremsstrahlung and that radiative losses are larger for high energy electrons and for absorber materials of high atomic number (Knoll, 2000). Positron Interactions Since a positron is of equal mass to an electron, it may undergo similar interactions to electrons of an atom despite the attractive forces it will experience. As described previously, after interaction, the positron annihilates producing two annihilation photons of 511keV in opposite directions. These photons then deposit their energy in the medium. Backscattering When an electron interacts with a medium via coulomb interaction or bremsstrahlung, it is scattered through an angle according to its energy. If the angle is significant enough to exceed the angle of incidence, the electron may be scattered out of the absorbing medium. This process is so named backscattering. It is important to comprehend the possibility of backscattering when performing dosimetry in order to determine how much energy will be deposited outside the treatment area. Backscattering is significant for low energy electrons and for absorbing materials of high atomic number (Knoll, 2000). 37

55 2.6 Monte Carlo Physics The development of the Monte Carlo method has had a major impact on radiation dosimetry and measurement over the past half century. Essentially, the method relies on probability to predict the solution to a complex problem using statistical sampling and is done so using fast computers (Metropolis & Ulam, 1949). While the principle of statistical sampling originated in the late 18th century (Hendricks, 1994), the method s potential for particle transport and tracking was not realised until the mid 1940 s, when Von Neumann and Ulam (1945) developed and adapted it to be used in the then, new, electronic computer. The Monte Carlo method calculates the most probable behaviour of a system by observing the outcomes of a large number of trials (Metropolis & Ulam, 1949). The trials are somewhat a game of chance (Hendricks, 1994), utilising random numbers, which simulates the physical events responsible for the probable behaviour of the system (Hendricks, 1994). It is most suited to describing a mixture of deterministic and stochastic processes (Von Neumann & Ulam, 1945, as cited in Metropolis & Ulam, 1949) and hence is of great relevance to the study of radiation transport. The Monte Carlo method is used in the study of radiation interactions with matter for medical applications (Hendricks, 1994; Williamson, 1988; Agostinelli et al., 2003). In recent decades, Monte Carlo based dosimetry for radiation therapy has become increasingly popular, being used in most modern experimental studies as a verification or theoretical comparison for results. The method can predict the outcome of a large number of particles in a defined medium based on the interactions it will have with objects of that medium, providing the probable behaviour of the particles. For this purpose, the user must describe the physical properties of the particle considered in the interaction, i.e. energy, process of interaction, cross-sections etc. In order to apply the Monte Carlo method to the system, a random sequence of numbers uniformly distributed between the interval of zero and one must be generated, meaning that every number in this interval has an equal probability of occurring in the sequence (Hendriks, 1994). When generated by a computer, these random numbers are given the name, pseudorandom numbers. 38

56 Pseudorandom numbers can influence the given energy and direction of particles generated to track through a medium. A number of particles and interactions may be considered by the Monte Carlo radiation transport calculation. Furthermore, the radiation may be of varying energy and originate from either a point source, line source or any specified geometry, albeit simple or intricate in nature. All particle, object, and medium information may be input by the user according to the problem. The objects used for detection within the simulation geometry are known as the sensitive detectors or scoring volumes, and these may be defined as either a combination of simple or complex geometries. Any number of details regarding the particles tracked may be defined and obtained from these sensitive volumes. This is one of the most desirable characteristics of the Monte Carlo method; any ideal situation involving radiation and matter may be created in the computer code and the outcome obtained, meaning that complex experimental scenarios may be tested with ease, providing all required input data is available to the user. The greatest drawback of Monte Carlo method for particle transport is the computational time required to achieve accurate results with reduced statistical uncertainty. The more particles simulated, the more events collected and the less associated uncertainty Geant4.9.3 Monte Carlo Toolkit There are a number of commercially and freely available toolkits designed for use with the Monte Carlo method. These toolkits have their own separate data libraries of particle information for the code to draw on during computation. The Geant4 Monte Carlo Toolkit (version 4.9.3) was the toolkit of choice for Monte Carlo photon transport calculations within this research. Geant4 (Geant4 Collaboration, CERN) is an open source code written in C++ available from the Geant4 website (Giani et al., 1998), and is in extensive use at the CMRP for a range of medical physics applications. The toolkit simulates the passage of particles through matter using Monte Carlo sampling. It is useful for complex simulation of physics detectors and physical processes due to the many physics models included to manage the interactions of particles with matter across a wide energy range. These models cover the physics of photons, electrons, muons, hadrons and 39

57 ions from 250eV up to PeV (1x10 5 GeV) (Agostinelli et al., 2003). The physics repository is under constant review and refinement by the Geant4 Collaboration. Geant4 is enhanced by range cuts that are region specific, so that if a user so desires, a process may suppress particles whose range falls below the specified value in non-vital areas (Agostinelli et al., 2003). This feature ultimately serves to reduce overall computation times. The user can define a number of components of the simulation process including system geometry, materials, fundamental particles of interest, generation of primary particles of events, the tracking of particles and their management, the response of the sensitive detectors and their output, and the visualisation of detectors and events (Agostinelli et al., 2003). Cross-sections are calculated using formulas, parameterisations or interpolation of data from included databases. Databases are separated such that different databases may be selected where more appropriate to the problem (Agostinelli et al., 2003). The user may define a number of volumes, each housing other volumes. The geometries of the volume may be simple (e.g. box, cylinders, and spheres) or complex (e.g. trapezoids and tori) and are selectable from a range of prewritten geometries. The Geant4 particle transport toolkit is ideal for use in Monte Carlo dosimetry of eye brachytherapy due to the large variety of detailed and alternative physics models it provides, and its minimised computation times. The variety of sensitive detector and physical volumes available will allow a unique and advantageous method of scoring of the absorbed dose delivered by the complex geometries of the I-125 and Ru-106 sources. Hence, in this work, a single I-125 seed and Ru-106 curved plaque were simulated using the Geant4 (4.9.3) toolkit to provide dose data over a wide range for input into developed dose planning software based on current protocol for dose optimisation. 2.7 Monte Carlo Dosimetry for Eye Plaque Brachytherapy Monte Carlo method is one of the most widely used methods of dosimtery for brachytherapy sources today (Williamson, 1991; Gleckler, Valentine & Silberstein, 1998; Granero et al., 2004, Casal et al., 2000: Ballester et al., 2001; Perez-Calatayud et al., 40

58 2002; Williamson, 2002; Rivard, 2002; Taylor & Rogers, 2008; Thompson & Rogers, 2010). The method is advantageous for the dosimetry of complex brachytherapy sources since it allows the construction of optimum experimental conditions and provides a significant reduction in uncertainty in terms of detector positioning and energy dependence. For example, the model 3500 I-Plant I-125 brachytherapy source was only recently developed in August, 2000 (Rivard, 2002) and is considerably different in design compared to the model 6711 seed. The AAPM specifically recommends both physical and Monte Carlo measurements for calculation of the TG43 dosimetric parameters for new sources before clinical implementation. Hence, Rivard (2002) obtained accurate dose distributions for the model 3500 source using Monte Carlo methods achieving close agreement with previous TLD measurements. The results of Rivard s study are a good example of the value of Monte Carlo method in dosimetry verification and quality assurance of eye brachytherapy sources. Complications in eye brachytherapy arise as a result of damage to normal surrounding tissue and structures during treatment. The intricate anatomy of the eye calls for dosimetry that specifically investigates the effect of radiation on these regions. Monte Carlo methods provide a successful means of testing these effects (Yoriyaz, Sanchez & Santos, 2005). Mourao and de Campos (2009) performed Monte Carlo simulations for dosimetry of a 15mm ROPES plaque loaded with I-125 seeds and a Ru-106 curved plaque to determine the dose delivered to the different tissues of the ocular region with the plaque attached to the sclera. CT data of the region of interest was collected and input into the simulation to model the different tissues. Two simulations were performed to investigate absorbed dose in both internal and external regions of the ocular bulb. The results were input into a TPS to generate dose distributions. The results of Mourao and de Campos (2009) showed that I-25 seeds deliver significantly higher doses to the lens compared with Ru-106, as the radiation penetrates further through the eye. The authors concluded that Ru-106 is particularly useful in treatment of 41

59 small tumours. The results of this Monte Carlo based study demonstrate the ability of Monte Carlo dosimetry for determining dose distributions in very specific anatomical regions of the eye, and its usefulness in assessing and evaluating dosimetric considerations of patient specific treatment. Monte Carlo simulation of brachytherapy sources is difficult, considering the detailed spectra, complex curved geometry, and for beta emitting plaques, the uniform distribution of radioactivity required over the surface of the plaque. A number of inaccuracies in dosimetry of such sources have been reported (Cross et al., 2001) due to the difficulty in achieving source uniformity in the simulation. For example, Rivard et al. (2009), published a significant dose overestimate in regions of clinical interest using Monte Carlo method due to a lack of consideration of source heterogeneity for a number of plaque sources. The authors obtained dose distributions for Pd-103, I-125 and Cs-131 seeds using Monte Carlo methods and compared them with a conventional treatment planning system. Over 50% of dose points obtained for each source were in disagreement with the conventional TPS results based on the superposition method of dose calculation. The steep dose gradients close to the source were reported to be an important factor in this result. Monte Carlo dosimetry for complex sources can therefore be considered unreliable in comparison with some experimental methods due to variations in dose close to the source, as well as variations in source specifications in the literature (Cross et al., 2001). The multiple types of sensitive volumes available in Monte Carlo toolkits such as Geant4 can, however, make source modelling less problematic. For example, Sanchez-Reyes et al. (1998) accurately calculated 3D dose distributions for CCA and CCB BEBIG Ru-106 plaques immersed in a 6cm radius water sphere concentric with each plaque using Monte Carlo method. The results agreed with data supplied by the manufacturer within 10% for a number of distances from both plaque types. In recent times, Mowlavi and Yazdani (2008) published on a successful model of the eye in Monte Carlo code, achieving dose distributions in both tumour and normal tissue from 42

60 CCA and CCB Ru-106 plaques. The results were in close agreement with the manufacturer, with uncertainty within 1%. This result further illustrates the potential of Monte Carlo methods for accurately predicting dose within small gradients and close to normal tissue, which is of great importance to the ultimate successful treatment planning of eye brachytherapy patients. Monte Carlo based dosimetric calculations have been used previously to optimize current TPS, which are limited by the uncertainty in measurements and calculations of the TG43 protocol (Thompson, Taylor & Rogers, 2008; Thompson & Rogers, 2010; Dolan et al., 2006). Granero et al. (2004) performed Monte Carlo simulations of the 15mm ROPES plaque to obtain accurate dose distributions to be compared with and incorporated into current TPS. The study accurately simulated the model 6711 seed in multiple configurations in the plaque and demonstrated the steep dose gradients along the eye and a significantly reduced dose rate external to the eye. The effects of backscattered photons and the attenuation by the backing were investigated at small and large distances from the source, showing a significant dose reduction near the edge of the eye, and a 4% reduction in dose due to the plaque steel cover. These results ultimately lead to the conclusion that the TPS dose calculation is inaccurate around the border of the eye. The results highlight the consequence of the simplified algorithm used in TPS for eye brachytherapy on the accurate prediction of dose rate distributions in specific regions of the eye. This result has been further exemplified for a number of brachytherapy sources recently in the work of Rivard et al. (2009). Monte Carlo method of I-125 brachytherapy dosimetry has been well covered in the literature (Dolan et al., 2006; Yoriyaz et al., 2005; Mourao & de Campos, 2009; Rivard, 2002; Thompson & Rogers, 2010; Thompson et al., 2008; Williamson, 1988; Rivard et al., 2009). Furthermore, literature shows that Monte Carlo methods can handle the tissue inhomogeneities and the complex geometry of the convex applicators that require an even distribution of radioactivity from the source (Astrahan, 2003). Currently, the research concentrates on dosimetry of mainly the CCA and CCB type Ru-106 curved plaques and there is a lack of work surrounding other plaque dimensions and designs despite the 43

61 considerable differences in dose distributions they each produce. The methods used to score dose from the CCD Ru-106 plaque in this work will be acceptable for dosimetry of a number of plaque types. The aim of this research, not dissimilar to those described, is to achieve accurate dosimetric results for eye brachytherapy sources using Monte Carlo simulations for input into developed dose planning software based on dose calculations defined in current protocols. Not only will the dose planning software provide a comparison between Monte Carlo derived and TG43 dose distributions, but will include output in the form of a 2D dose pixel map for direct correlation with the Medipix2 experimental results. The results are hoped to reflect the conclusions of other similar studies and improve on the published methods of Monte Carlo dosimetry for I-125 and Ru-106 sources for eye brachytherapy. 44

62 Chapter Three Dose Planning Software Currently, dose planning software for eye plaque brachytherapy sources lack the ability to accurately describe the dose delivered to the eye at known small distances from the source due to the limitations in experimental methods of dosimetry, and hence the published dose protocol. In order to test the accuracy of the published dose data for brachytherapy sources, it is necessary to measure and calculate the dosimetric parameters of the protocol. This effectively involves replicating the dose calculation algorithm and generating dose parameters in a program that may be configured to the user s preference. Of particular interest are the tabulated dose parameters of the TG43 protocol for brachytherapy sources, such as I-125, where in the case of brachytherapy for the treatment of ocular melanoma, the radial distances published are not sufficiently comprehensive to guarantee a reliable dose calibration for the applicable treatment distances. In the same way, the Ru-106 plaque designs are complex in structure and spectrum and the accepted standard values require further testing. A treatment planning software package was developed at the CMRP to predict the dose delivered to the eye during a typical eye plaque brachytherapy treatment based on TG43 dose data. The program is capable of providing dose maps and depth-dose in multiple planes of the eye for multiple seed configurations. Being based on the TG43 protocol method of dose calculation, it is envisioned that dose arrays with reduced uncertainty and increased accuracy at points close to the plaque surface, obtained through Monte Carlo methods of dosimetry, will be input directly into such a program for dose optimisation. 45

63 3.1 Software Development The dose planning software, Eyecan, was designed and developed using the QT programming package. The program was designed to specifically model the 15mm ROPES plaque loaded with Amersham Health Model 6711 I-125 seeds (see Fig. 14). Not only is this plaque the most commonly used plaque in I-125 eye brachytherapy, but it was also used in experimental dosimetry methods recently performed at CMRP using the Medipix2 silicon pixelated counting device. This detector provides high spatial resolution dosimetry imaging of the dose distribution in the medium with a fast read-out. The Eyecan software therefore was designed such that the results of the physical measurements could be verified quickly with the TG43 protocol. A 256 x 256 pixel array of dose distribution was incorporated into the software generating pixel maps comparable to those produced by the Medipix2. The Medipix2 output is shown in Figure 15. This capability is useful in dose planning as it allows an instant visual depiction of the dose distribution over a large number of points in the medium. Figure 14. Photographic image of the 15mm ROPES plaque and acrylic insert fully loaded with ten 6711 model I-125 brachytherapy seeds 46

64 Figure 15. Medipix 256 x 256 pixel map output Ultimately, the program allows for individual seed configuration and activity selection, and determines the dose deposited within the eye and surrounding volumes, as well as providing the maximum dose and location. A variety of output and capabilities useful in dose planning will be available. The success of the software relies heavily, however, on the seed geometry and the accuracy of the dose calculation at each point in the medium Plaque Geometry The 15mm ROPES plaque has ten seed positions available in the acrylic insert for a variety of seed configurations. The dose delivered to a point of interest will be a superposition of the dose contribution from each individual seed in the desired configuration. Hence, the position of each seed assumed by the software must accurately reflect the true plaque. The seed positions relative to the centre of the acrylic insert were measured in the physical plaque. With the centre of the inner surface of the plaque assumed to be the origin (see Fig. 16), the coordinates of each seed were input into the code based on physical measurements of the acrylic insert, as well as the manufacturer s data sheet. 47

65 Figure 16. Plaque coordinate system assumed in code. The seeds were numbered from one to 10 and each given a coordinate and relative angle vector based on their position in the plaque. A schematic of the seed configuration is shown in Figure 17. Seeds one, two and three are positioned in a higher plane relative to the origin than the outer seeds, positioned at z = -0.01cm. Seeds four to ten were positioned in the same plane at z = 0.025cm. The (x,y) coordinates of each seed centre numbered from one to 10 are shown in Table 6. The program records the direction for each seed for later use in the dose calculation. When the coordinate of a point of interest is identified, the code calls the coordinate and angle vector of each selected seed in the configuration and inputs them into the dose calculation. Table 6. Seed coordinates and direction vectors. Coordinate Direction Vector Seed No. x (cm) y (cm) z (cm) u v w

66 Figure 17. Seed configuration in 15mm ROPES plaque showing the respective positions of seed numbers The geometry of any plaque type may be specified in the code to provide dose calculation unique to a number of sources. This extends to the implementation of complex geometry, such as the Ru-106 plaque, which is spherical in shape and has a uniform distribution of radioactivity over the inner surface. The interface is being further developed to include a plaque selection menu for improved eye brachytherapy treatment planning Dose Calculation The software aims to provide dose calculations at any points of interest in the treatment volume of the eye and its surrounding structures. This volume extends 25mm from the centre of the plaque. The program therefore was designed to consider a point in any plane of the eye and calculate dose from this point calling on TG43 tabulated dose data for the Model 6711 seed. This calculation must take into consideration seed geometry of the chosen configuration previously described. 49

67 Figure 18. Coordinate system for dose calculation. Note that the seed is in the x-y plane. At every point of consideration in the treatment medium, the dose contribution from each seed at that point is calculated individually and then superimposed. For each individual calculation, the relative angle of the point of interest to the seed of interest is calculated using the seed coordinate and relative angle vector listed in Table 6. This involves transforming the coordinate system of the seed (Fig. 18) using the dot product of its angle vector. Figure 19. Relative point of measurement, R(x, y, z) at relative angle θ and distance r from the point of measurement to the centre of the seed The position of the point of measurement must first be considered relative to the centre of the seed, such that, 50

68 x x, y y z z R( x, y, z), (3.1) p s p s p s To determine the distance, r from the point R(x,y,z) (Fig. 19) to the centre of the seed, the software calculates the magnitude of the vectors, r x x y y z z (3.2) The inverse cosine of the dot product of two unit vectors gives the angle between the vectors. This is used to calculate the angle, θ, giving x,y,z cos 1 r u,v,w u 2 v 2 w 2 (3.3) And hence, u x v y w z 1 cos (3.4) r u v w The point of measurement may now be considered only in terms of r and θ and the dose contribution from this point is then generated via a linear interpolation of the dose points available from the TG43 tabulated data. 3.2 Output The output and design of the user interface is simple in layout, user friendly and offers advanced analysis options. Five main windows are available to the user, one for seed and activity selection and four others generating dose data in a variety of forms each accompanied by a visual component from a unique viewing point (see Fig. 20). 51

69 Figure 20. Eyecan user interface and output Plaque Configuration The program allows for the selection of any number or arrangement of seeds with variable input activity in either units of U, mci, or MBq. Regardless of the chosen unit, the program converts all input activity to units of air kerma strength, U (where 1U = 1cGycm 2 h -1 ), and then calculates dose. The diameter of the eye may also be specified or varied in this window Medipix Output This window displays the 256 x 256 pixel (55 x 55µm pixels) map of dose distribution in the specified plane of interest along the central axis (z-axis) of the plaque, where z = 0mm corresponds to the plane of the plaque inner surface (see Fig.16). The difference in dose is demonstrated by the change in intensity of the colour scale with 52

70 bright spots indicating regions of higher dose and dark spots indicating areas of lower dose (see Fig. 21). The colour scale may also be calibrated to match the Medipix2 colour scale using the available slide scale. There is an option for both the image and the array to be saved as individual files for further analysis or input into other software. a) b) Figure 21. a) Eyecan five seed pixel map, 12mm from plaque on central axis; b) Eyecan ten seed pixel map, 0mm on plaque central axis displaying the accuracy of seed geometry assumed by the software Cross Section A cross sectional view of the dose distribution can be generated showing the dose gradient on the y-axis using a similar colour scale as in the Medipix2 output (see Fig. 22). The y-coordinate may be specified depending on the position of interest. Again, both the image and the data array may be exported separately. 53

71 Figure 22. Cross sectional view in treatment volume at y = 0mm, through the centre of the eye, showing regions of high dose at the apex Depth Dose Distribution The depth dose on the plaque central axis is generated based on a specified treatment time where zero is considered to be infinite time by the program. The dose is calculated in increments of 0.1mm from the centre of the plaque and can be exported into data analysis software for further graphing and formatting options. The depth dose output (see Fig. 23) is of particular significance in treatment verification being used for calibration to ensure the source is behaving in accordance with the protocol. 54

72 Dose Rate (mgy/hr) Depth (mm) Figure 23. Depth dose curve on the central axis of the 15mm ROPES plaque loaded with ten I-125 seeds with activity of 0.4Ci per seed Isodose Further to depth dose, isodose curves indicating high and low regions of equal dose may be generated (see Fig. 24). This feature is also of great importance to the quality assurance of dosimetry and treatment used in identifying hot and cold spots, particularly at small distances from the seed. 55

73 Figure 24. Isodose curves on the central axis of the 15mm ROPES plaque loaded with ten I-125 seeds of 0.4Ci activity per seed where blue represents dose points of 5Gy (±1%), green represents dose points of 50Gy (± 1.4%) and red represents dose points of 200Gy (± 2%). Discussion The Eyecan treatment planning software for eye plaque brachytherapy is consistent with the TG43 protocol for dose calculation about the model 6711 I-125 brachytherapy source. Drawing on tabulated dose data from the TG43 protocol, Eyecan calculates the dose at a point of interest by superimposing the dose contribution from each seed at that point and generating a variety of outputs for dose verification. The software calculates the dose calculation based on the geometry of the 15mm ROPES plaque and offers dose distributions from any number of seed configurations from one to 10 seeds. Eyecan is novel in its design, generating a pixel map analogous to the output of the Medipix2 detector. This unique capability offers instant visual insight into the dose distribution over a 256 x 256 (55 x 55um pixel size) field. The Eyecan software accurately calculates the dose distributions based on the superposition method of dose calculation employed in current TPS with capabilities that suffice to allow fundamental analysis and calibration of eye plaque brachytherapy sources. 56

74 The measurements performed with the Medipix2 detector obtained dose data for radial distances from 0.1mm to 25mm every 1mm from the 15mm ROPES plaque loaded with five and 10 seed configurations. The data obtained were compared with the TG43 protocol generated by the Eyecan dose planning software (see Fig. 25). The results were in close agreement, however, inaccuracy arises due to the lack of tabulated data points at the desired depths of comparison. This limitation calls for Monte Carlo methods of dosimetry to provide depth dose and anisotropy data for very small distances from the source. Figure 25. Depth dose Central axis depth dose (z = 0mm to z = 25mm) measured by Medipix2 compared with tabulated data from the TG43 protocol. A number of studies have used Monte Carlo methods to provide increased accuracy dose distributions as input data into novel treatment planning systems for eye brachytherapy (Granero et al., 2004, Rivard et al., 2009). Not only is the Eyecan software user friendly, fast and reliable but it creates an ideal opportunity for Monte Carlo data with increased accuracy to be input into the code with ease for dose optimisation. The TG43 protocol is 57

75 inaccurate for close distances to the seed. Current commercially available TPS for use in I-125 eye brachytherapy are based on the TG43 protocol for measurement and are therefore unable to accurately describe the dose distribution in the eye at every point of interest about the source. Furthermore, TPS for beta-emitting plaques such as the BEBIG designed Plaque Simulator are based on an 11 point protocol of measurement, leaving distances falling outside this range unaccounted for, and are based on measurements with finite sized detectors. The advanced Monte Carlo techniques used in this thesis for I-125 and Ru-106 eye brachytherapy sources will provide a method of more accurately describing dose distributions at every point in the treatment medium and in very close proximity to the source. This data will be suitable for incorporation into Eyecan for dose optimisation and comparison with current protocols. Eyecan provides a well established and secure foundation for dose calculation in eye brachytherapy, such that a variety of sources and plaque designs could be modelled in the future. 58

76 Chapter Four Iodine-125 based eye plaque dosimetry The TG43 protocol and TPS based on this formalism for I-125 brachytherapy, such as Eyecan, are inaccurate due to the limited data in tabulated dosimetric parameters within the TG43 protocol. Geometry functions are particularly limited between distances 0.025cm and 1cm on the central axis and anisotropy functions are not available for radial distances less than 0.5cm from the source. When considering eye plaque brachytherapy, where dose gradients are steep, the distances very close to the plaque are of extreme importance to the successful treatment of the tumour and the remaining quality of vision of the patient. Furthermore, the physical volume of the eye itself creates a far smaller margin for error anatomically than most other brachytherapy procedures. The purpose of this chapter is to provide, using advanced Monte Carlo methods, an array of I-125 doserate data accurate over a large range of radial distances to be incorporated into Eyecan for dose optimisation. It is important to note that the dosimetric parameters of the TG43 protocol were determined and evaluated using a combination of experimental and Monte Carlo methods. The experimental measurements were taken with TLDs and have a published uncertainty of 8.7% and the Monte Carlo measurements have an uncertainty of 2.5% at radial distance 1cm and 5% at r = 5cm (Gearheart et al., 2000, Nath & Yue, 2000; Rivard et al., 2004). The aim of this chapter is to improve the uncertainty of calculated TG43 dosimetric parameters using advanced Monte Carlo methods as well as provide a greater number of reference points. TLDs have inherent limitations, including poor spatial resolution. It has been described that the Medipix2 device can provide high spatial resolution dosimetry, with the potential for 3D dosimetric imaging. A combination of Medipix2, TG43 measurements and the Monte Carlo methods of this thesis could be developed to ultimately offer an advanced, high accuracy dosimetry model based on three 59

77 complimentary approaches. This model can be built into the Eyecan software for dose optimisation. 4.1 Monte Carlo Simulation of I-125 Source Monte Carlo simulation techniques were used to model a single Amersham Health model 6711 I-125 seed in water using the Geant4.9.3 Monte Carlo toolkit to obtain TG43 parameters at increments of five degrees and radial distances ranging from 0.1cm to 2.5cm in increments of 0.1cm. This will allow for the more accurate dose calculation within the geometrical ranges necessary for eye plaque brachytherapy, providing a more concise set of function data arrays Simulation Geometry I-125 loaded plaques are the preferred source in eye plaque brachytherapy (Chan et al., 2001). The Amersham Health model 6711 I-125 seed is the most widely used interstitial brachytherapy source used today (Rivard et al., 2004) and hence was chosen for this simulation. I-125 Seed Geometry The seed construction assumed by the photon transport code is shown below, differing slightly from that described in Chapter Two in that it is solely cylindrical in geometry having flattened endcaps as opposed to curved. This geometry was based on the model provided by Williamson (1998) to provide simplicity in coding. In this model, the seed is defined as a set of concentric cylinders with an inner silver rod 0.5mm diameter onto which I-125 is uniformly distributed over the cylindrical surface. The source is encapsulated within a titanium shell 0.8mm in diameter and 0.06mm in thickness and endcaps with average thickness of 0.5mm. Schematic drawings of the seed geometry are shown in figure 26 and figure

78 Figure 26. Longitudinal view of seed geometry assumed by Monte Carlo simulation as per Williamson (1988) Figure 27. Transverse view of seed geometry assumed by Monte Carlo simulation as per Williamson (1988) Scoring Geometry The scoring volumes defined in the simulation must be designed such that they provide an accurate representation of the dose deposited in the medium. The ultimate goal is to reduce the uncertainty with which the dose is measured and to provide accurate radial dose measurements consistent with the TG43 protocol. The physical volume of the eye must be considered as well as the dose drop-off that will occur with distance from the source. The diameter of the eye is assumed to be 24mm and hence the scoring was defined over radial distances ranging from 1mm 25mm from the centre of the source. 61

79 The scoring volumes in the simulation consisted of a set of 25 concentric toroids of tube radius 0.1mm and torus radius ranging from 1mm 25mm. The scoring toroids were therefore positioned every 1mm at an angle,, from the centre of the source (assuming radial symmetry). The scoring toroids were positioned such that every point through the circumference of the toroid is at the same radial distance, r from the centre of the seed and subtends the same angle, (see Fig. 28). This ensures an equal measure of dose at every point on the circumference of the ring and hence why dose may be summed over the total toroid volume, increasing the scoring statistics. Figure 28. Toroid position relative to the centre of the source with every point of measurement the same distance, r and angle, from the source A second set of toroids was mirror imaged through the transverse plane of the seed, providing a total of 50 scoring volumes for improved statistics and increased data collection efficiency (see Fig. 29). 62

80 Figure 29. Geant4 visualisation of Monte Carlo simulation of model 6711 seed showing inner silver core (magenta), air gap (blue) and titanium shell (silver), and set of 50 concentric scoring toroids (red) positioned 1mm apart. Since I-125 seeds are a cylindrically symmetric linear source, the anisotropy function can assume four-quadrant symmetry and therefore need only be defined over a 90 degree range. Hence, the simulation was run for two billion particles a total of 18 times corresponding to one simulation every 5 degrees from the central axis from 90 to 5 degrees about the source. For 90 degrees, the toroids were not mirrored, as the volumes would be the same. To measure at zero degrees however, the scoring toroids were replaced with solid cylinders of varying radius and thickness to accurately score the dose 63

81 over the 25mm range, with larger radius cylinders used for 1cm and greater distances (see Fig. 30). Figure 30. Geant4 visualisation of Monte Carlo simulation of single 6711 seed with scoring tubes (red) positioned every 1mm on the source central axis. Each simulation determined the average absorbed dose per primary in each scoring volume by converting the total energy deposition in each volume from MeV to joules, then dividing by mass of the individual scoring volumes and the total number of primary particles simulated. The average absorbed dose per primary was then halved to account for the mirrored volumes (excluding at 90 degrees). The error estimate was determined using standard deviation and standard error with 95% confidence limits of the average dose deposition per event, d, the average dose squared per deposition, d 2 and the total number of events, N. The standard deviation (SD) in the average dose for total number of events, N is determined by the average dose squared, minus the square of the average dose, 2 2 d d SD (4.1) N From this, the standard error, with 95% confidence limits, was determined by multiplying the standard deviation by two. Finally, the error estimate was determined as a fraction of the total average energy and converted to a percentage. The output was obtained in terms of depth (mm), dose (Gy) and percentage error. The results were collated and used to obtain tabulated dose-rate and anisotropy data to be compared with those provided by the TG43 protocol. 64

82 4.1.2 Physics Considerations The source consists of three materials; dry air, silver and titanium, and was positioned in water as it is assumed to be tissue equivalent. The photon transport processes considered by the simulation were low energy photoelectric effect and scattering (Compton and coherent). The electron processes included were low energy ionisation, low energy Bremsstrahlung and multiple scattering, the cross sections for which were obtained from the G4EMLOW.6.9 low-energy data set (Geant4 Collaboration, 2002). A range cut-off value of 1 micron was set for all particles in the simulation, corresponding to an energy of 990eV for photons in all materials and 990eV for electrons in water and air. This value is the lower energy limit to the physics library in Geant4. Electron energy cuts in titanium and silver were 2.77keV and 7.57keV respectively. Any particle histories falling below these cut-off energies will deposit their energy immediately within the region of the particle and that energy included in the calculation. Secondary particles, such as scattered electrons, were also tracked Particle Generation The simulated seed must not only accurately reflect the true model in construction, but in the way it emits radiation. The generation of photons from the surface of the source is a completely random process. That is, the particle will have a random energy based on the source spectrum, random generation coordinate on the surface of the cylinder and a random direction. These random generation processes are naturally dependent on the source geometry, and will be described in detail in the following sections. Random Energy I-125 is a low energy photon emitter, which decays via electron capture and has a halflife of 59.4 days (Rivard et al., 2004). In the simulation, a random number generator was used to select the energy of the primary photon based on the probability of emission. The 65

83 photon spectrum consists of five main energies, which are listed with their probabilities in Table 7 below (Attix, 2004). Table 7. I-125 source spectra. Photon energy (kev) Photons per disintegration Random Coordinate Primary photons are emitted from the surface of the silver rod at the core of the source. A photon may be generated from any point on the cylindrical surface of the rod and hence, the simulation must randomly select a coordinate representing this location. This location may be a coordinate on the side of the cylinder or on one of the two endcaps and therefore random coordinate selection was based on the areas of these two respective surfaces. Figure 31. Surface generation geometry. 66

84 Considering the geometry shown in figure 31, the simulation was programmed to generate a random number between zero and 2A E + A S. If the random number was less than A E, the particle was generated from the bottom endcap. If the random number was between A E and 2A E, the particle was generated from the top endcap, and if the random number was greater than 2A E, the particle was generated from the side. If a particle was generated from one of the endcaps of the silver rod, a random x and random y coordinate were generated between r and +r, Figure 32. Endcap coordinates. A test was performed to check whether the (x,y) coordinate was located within a circle of radius r (x 2 + y 2 r 2 ). If this condition was not met, the generation of the (x,y) coordinate was repeated. The z coordinate of generation was set to L/2 for the bottom endcap and +L/2 for the top endcap, where L is the length of the silver rod. In order to generate a particle from the side of the cylindrical surface of the rod, a random number was generated between L/2 and +L/2, representing the z coordinate of generation. To generate a random x and y coordinate around the circumference of the cylinder, a random angle was generated between zero and 2π. 67

85 Figure 33. Endcap coordinate generation. Thus, the y coordinate was defined by rcosθ and the x coordinate by rsinθ. Random Direction To ensure the generated particle is emitted in a random direction from the surface of the silver rod (see Fig. 34) as would occur with the true source, a random a, b, c, coordinate was generated representing the directions (x,y,z). These random coordinates were converted into a random vector, n and then into a unit vector,?n using the unit vector equation,?n n n (4.2) Where n = a 2 +b 2 +c 2 (4.3) And n n 2 (4.4) A condition of n = a 2 + b 2 + c 2 1 was set to ensure the random point of particle generation reflects a point within a sphere, ensuring all angles have equal probability of generation. 68

86 Figure 34. Geant4 visualisation of Monte Carlo simulation of model 6711 seed showing the inner silver core (magenta), air gap (blue) and titanium shell (silver). Photon emission, represented in green, demonstrates the generation from the surface of the silver core, and electrons, in red (shown in the zoom window) demonstrate the generation of secondary particles in the physics model. 4.2 Derivation of geometry function The geometry function assumes an approximation of the spatial distribution of radioactivity within the seed and provides a correction to be applied to each discrete point of measurement (Rivard et al., 2004). For a point source, this correction is an inverse square relationship, G P 1 (4.5) r r, 2 69

87 For a finite line source, the geometry function is defined by, if 0 G L r, Lr sin (4.6) r L / 4 if 0 Where β defines the angle subtended by the lines from the endpoints of the source of length, L to the point of measurement, P(r, θ) in radians (figure 35). While the TG43 protocol provides tabulated data for the geometry function of a 3mm line source, there are significant gaps in the data for values within the range of 0cm and 2.5cm. Moreover, as previously described, the anisotropy function is not provided by the formalism for values of r < 0.5cm. Therefore, for the purpose of this work, the geometry function for a single Amersham 6711 I-125 seed was calculated using equation 4.6 derived as a function of r, θ and L. Figure 35. Coordinate system of seed showing the angle Beta relative to the centre of the seed. Consider a point, P(r, θ) at a distance r from the centre or midpoint, M of a cylindrical source of length, L of 3mm (see Fig. 35). The hypothetical lines drawn from the 70

88 endpoints, (-L/2, 0) and (L/2, 0) of the source to the point P(r, θ), form the line vectors, V1 and V 2. V V V rx1 rx2 ry1,2 r cos L / 2 r cos L / 2 r sin (4.7) The line vectors V1 and V2 therefore are, V1 V 2 r cos L / 2, r sin r cos L / 2, r sin (4.8) The magnitude of these vectors is defined by, V1 V 2 V1 V1 V 2 V 2 (4.9) The dot product of the vectors, V1 and V2 is then given by, V1 V2 V1V2cos (4.10) and therefore, V1 V 2 cos 1 (4.11) V1 V 2 The unit vectors, V ˆ 1 and V ˆ 2 can then be defined by, 71

89 Vˆ1 V1 V1 V 2 Vˆ2 V 2 (4.12) Therefore, by definition, the angle, β, between the two vectors V1 and V2, is the inverse cosine of the dot product of the unit vectors, cos 1 Vˆ1 Vˆ 2 (4.13) The geometry function, G L, can now be written as a function of r, L and θ, and simplifies to (King, Anderson & Mills, 2001) 1 tan r sin / r cos 2 r sin r cos L L r sin sin / 2 1 sin L L 2 / 2 G r, L (4.14) From this, tabulated values for the geometry function of the Amersham 6711 seed with length, L, of 3mm can be obtained for any value of r or θ. 4.3 Results The dose per primary source particle was obtained from the Monte Carlo simulation of the I-125 source for radial distances of 1mm to 25mm incremented every 1mm for polar angles of zero to 90 degrees every 5 degrees about the source. The simulation data can be found in the format of a dose array in Appendix A. The geometry function for each point was determined using the described derivation and TG43 dosimetric parameters calculated. The results are listed in Table 8 and Table 9 and are compared with corresponding tabulated data provided by the TG43 protocol. The radial dose function was calculated every 0.1cm for values of 0.1cm r 2.5cm. Values of r < 0.9cm were within 2% uncertainty and less than 3% for values of r < 72

90 2.5cm. Figure 36 shows the Monte Carlo and the TG43 radial dose distribution on the central axis of the source. The two dose distributions are in very good agreement. The Monte Carlo code predicts a slightly larger dose for values of r < 1cm by as much as 2.8% and slightly lower values for r > 1cm by about 1.2%. Both distributions show a slight upturn in dose up to r = 0.3cm. Table 8. Comparatively tabulated radial dose function values, g(r), obtained from Monte Carlo (MC) simulation and TG43 data. r (cm) MC Error (%) TG43 Discrepancy (%)

91 g(r) MC TG r/cm Figure 36. Radial dose function demonstrating the Depth-dose delivered on the central axis compared with TG43 data. The anisotropy function takes into account variations in dose due to the attenuation by the encapsulating shell. The anisotropy function data calculated from the Monte Carlo distribution is listed in Table 9 with corresponding TG43 tabulated values for polar angles from zero to 80 degrees and radial distances ranging from 0.5cm to 2cm. There is a slight dip in dose evident at 80 degrees a distance r = 0.5cm from the centre of the source. The Monte Carlo results show a significantly lower dose for polar angles < 10 at r = 0.5cm. More specifically, at this value of r, the Monte Carlo derived anisotropy shows an almost 50% reduction in anisotropy compared with the TG43 result at zero degrees. All values are within 5% error, with significantly reduced uncertainty for larger values of theta, being less than 1% at r = 0.5cm. This reduced uncertainty at small values of r highlights the potential for this technique in quality assurance for eye brachytherapy. The increased error at small values of theta is due to decreased statistics as the volume of the scoring toroids is reduced. 74

92 Polar angle, θ (degrees) Table 9. Monte Carlo (MC) derived anisotropy functions, F(r,θ), comparison with TG43 tabulated data. r MC Error (%) TG43 MC Error (%) TG43 MC Error (%) TG Figure 37 displays the anisotropy distributions obtained by the Monte Carlo code and the TG43 protocol. Polynomials have been fitted to the Monte Carlo derived points for ease of comparison. This plot shows agreement between the two distributions at larger values of θ and demonstrates the under dose at smaller values obtained in the Monte Carlo method. 75

93 Anisotropy Function r = 0.5 (TG43) r = 1cm (TG43) r = 2cm (TG43) Poly. (r = 0.5cm (MC)) Poly. (r = 1cm (MC)) Poly. (r = 2cm (MC)) Polar Angle (deg) Figure 37. Monte Carlo anisotropy functions compared with tabulated data provided by the TG43 protocol. Discussion The Monte Carlo simulations performed using the Geant4 Monte Carlo toolkit provide accurate dosimetry of the model 6711 seed with decreased uncertainty, especially for small values of r. The dose-rate distributions obtained by the Monte Carlo code were compared with the tabulated dose-rate parameters provided in the TG43 protocol. The radial dose distributions were in good agreement and the anisotropy functions showed close agreement for large values of r and angle, theta about the seed. This result verifies the suitability of Monte Carlo based dosimetry methods for I-125 eye brachytherapy and highlights its potential for dose optimization. An upturn in dose was evident from 90 to 70 degrees about the source for small values of r. It is assumed that this upturn is most likely due to attenuation and geometry effects of the source. It is also likely that the significantly lower anisotropy functions at small 76

94 values of theta are a direct result of attenuation and geometry effects of the endcaps of the seed (Dolan, Li & Williamson, 2006). The seed geometry assumed by the Monte Carlo code did not have curved endcaps nor did it consider generating from beneath the silver surface of the inner rod. Both the Monte Carlo derived and TG43 data show an upturn in dose for small radial distances (0cm < r < 0.25cm). The origin of this characteristic in dose distributions has been hypothesised and tested by a number of recent studies. For example, Taylor and Rogers (2008) showed using Monte Carlo techniques, that the upturn in radial dose function at small distances from the source is a result of the contribution of low energy x- rays emitted by the titanium shell of the I-125 seeds. The authors also concluded, as others have (Furhang & Anderson, 1999; Furhang & Wallace, 2000; Rivard, 2002), that the upturn is in part due to the breakdown of the line-source geometry function at small values of r. The results of this research are consistent with the radial distributions obtained by its contemporaries. The source model and scoring techniques used in this chapter provide a good base for improving these results, possibly reducing the upturn at small distances from the source. A point source check was performed confirming this justification of variations in dose close to the linear source. Recently, a Monte Carlo simulation was performed by a member of CMRP using an I-125 point source with spherical detectors, every 1mm from the point source to verify the dip in dose occurring at 90 degrees in the original line source simulation presented in this work, was due to the seed geometry. Also, this simulation was performed to test the random direction vector was in fact, random. The results demonstrate and prove that the dip is simply a result of variations in the geometry of the seed and attenuation due to seed materials very close to the source. These new simulations using the refined and advanced geometry have been developed further by CMRP since this work and are currently providing a direct output in the form of the TG43 formalism (i.e. the simulation automatically calculates and outputs the TG43 dosimetric parameters for each value of r and θ). 77

95 Future work should also be directed into using the described Monte Carlo scoring techniques to measure absorbed dose from the 15mm ROPES plaque itself loaded with the model 6711 seed. Recent studies have explored the effect of the acrylic insert and steel backing of the plaque on the absorbed dose in the medium using Monte Carlo methods (Granero et al., 2004; Thompson et al., 2008) and this work holds great potential in improving on such results. Monte Carlo methods have also been used to test the effect of different types of tissue on the dose distribution in and near the eye (Thompson et al., 2008). These tests could be performed using the Monte Carlo scoring techniques developed in this work. In this work, a Monte Carlo method of obtaining accurate dose-rate distributions within very close proximity to a single I-125 brachytherapy seed has been designed using the Geant4 toolkit. The results from the single seed can be incorporated into the Eyecan software for dose calculation based on multiple seed configurations within the 15mm ROPES plaque. This software is designed to accurately calculate the dose at any point based on the superposition of dose from each individual seed positioned at one of any ten different coordinates in the plaque. Essentially, the results of this chapter are most useful in treatment verification and dose optimisation as they are suitable for input into TPS such as Eyecan for quality assurance in a clinical setting. 78

96 Chapter Five Ruthenium-106 based eye plaque dosimetry Ru-106 plaques for use in eye brachytherapy are unique in that they cannot be modelled as either a point or line source, rather they are uniformly coated with radioactivity over their curved surface. Dosimetry, therefore, for Ru-106 plaques, proves to be particularly challenging because of their geometry. Furthermore, being a beta emitter, the emitted radiation has a short range, making dose gradients steep, with high dose rates close to the inner surface of the plaque enhancing the difficulty of measurement. This chapter aims to overcome these challenges by using novel Monte Carlo methods with unique and advanced scoring geometry to model the plaques. The dose distributions obtained in the described simulations will be compared with the current Protocol of Measurements and it is hoped the dose rate data obtained will be adopted in Ru-106 based treatment planning systems, not dissimilar to that described in Chapter 3 for I Monte Carlo Simulation of Ru-106 Source There are currently 16 BEBIG Ruthernium-106 plaque designs available for use in a variety of applications (Eckert & Ziegler BEBIG GmbH, 2008). The BEBIG CCD type plaque, used in the treatment of uveal and choroidal melanoma, was the plaque of choice for this simulation to allow for comparison with recent physical measurements performed at the CMRP. The BEBIG CCD Ru-106 plaque was modelled using the Geant4.9.3 toolkit to calculate the dose delivered to the eye in a typical Ru-106 brachytherapy treatment and to verify current values provided by the manufacturer Simulation Geometry Two Monte Carlo simulations were performed for the Ru-106 plaque, one providing depth dose data on the central axis for calibration, and the second providing a dose rate array spanning the entire volume of the eye for future input into treatment 79

97 planning software. Two different scoring methods were used for each simulation for overall reduced uncertainty, the geometry for which is described in the following section. Source Geometry The BEBIG Ru-106 CCD plaque has a rim diameter of 17.9mm, height of 4.3mm and a radius of curvature of 12mm as specified by the manufacturer. It also has two eyelets for surgical attachment purposes protruding from the outer circumference of the plaque (see Fig. 38). The source model included in the simulation did not include the two eyelets for simplified geometry. Figure 38. BEBIG Ru-106 CCD plaque. The source construction assumed by the code was a silver spherical cap of 12mm radius, 1mm thickness and a height of 4.3mm (Eckert & Ziegler BEBIG GmbH, 2008) shown in figure 39 and figure 40. The surface of the plaque was uniformly coated with Ru-106 and a silver foil radiation window was constructed on the inner surface of the plaque of 0.1mm thickness (see Fig. 39) (Eckert & Ziegler BEBIG GmbH, 2008). Figure 39. Ru-106 CCD plaque geometry assumed by the Monte Carlo code. 80

98 Figure 40. Cross section of Ru-106 CCD plaque geometry assumed by Monte Carlo code. Figure 41. Geant4 visualisation of Monte Carlo simulation of Ru-106 plaque showing silver curved surface (silver). Photon emission, represented in green, demonstrate the generation from the inner surface of the plaque. Generated electrons are absorbed in the silver window but secondary electrons, in red, are visible. 81

99 Scoring Geometry Measuring dose in the medium of the eye demands scoring volumes capable of detection over a small range of depth and angle. The measurements obtained must accurately reflect the dose distribution that would occur in the eye during a routine treatment. In order to provide dose rate data consistent with current treatment planning software in Ru- 106 eye brachytherapy, knowledge of the central axis depth dose is necessary for comparison with the protocol of measurements provided by the manufacturer. In addition to this, off-axis dose rate and relative dose distribution close to the source are important for dose optimisation. In this work, two types of Monte Carlo simulations were performed to achieve these goals, with two individual scoring techniques employed. To measure the central axis depth dose, a calibration simulation was performed using a series of scoring cylinders (G4Tubs) 0.5mm thick and 0.2mm in radius. The scoring cylinders were positioned at 90 degrees, 1mm from the centre of the plaque. A total of 25 cylinders were used (shown in figure 42), 1mm apart along the central axis from the plaque, to provide comparison data with the BEBIG Protocol of Measurements. 82

100 Figure 42. Geant4 visualisation of the Monte Carlo simulated Ru-106 plaque (silver) with scoring tubes (red) positioned 1mm apart from the inner surface of the plaque on the plaque central axis through the volume of the eye (blue). The second simulation incorporated concentric scoring rings, similar to the concentric toroid method utilised in chapter 4, to provide dose distribution data over the total volume of the eye. In this simulation, sets of 25 concentric scoring rings (G4Tubs) were positioned at a variable distance along the central axis of the plaque (see Fig. 43). The rings were 0.2mm thick and of radius ranging from 1mm 25mm. A simulation was performed every 1mm from the centre of the plaque, simply moving the position of the set of rings each time up to and including a distance of 25mm from the plaque. By simply shifting the position of the set of rings along the central axis of the plaque, dose data was obtained over a large volume of the medium. A total of 25 simulations were performed every 1mm from 1mm 25mm from the centre of the plaque essentially providing a total 83

101 of 625 scoring rings over which to sample. When combined with the central axis calibration data, a total of 650 sampled regions encompassed the eye. The energy deposited in each scoring tube and ring was converted to absorbed dose with respective error estimates. Results were output in terms of depth (mm), dose (Gy) and percentage error for each detector and compared with the standard accepted Protocol of Measurements and current TPS. Figure 43. Geant4 visualisation of the Monte Carlo simulated Ru-106 plaque (silver) with scoring toroids (red) positioned 1mm apart on the plaque central axis (z = 12mm) through the volume of the eye (blue). 84

102 5.1.2 Physics Considerations The materials included in the simulation were; air, silver, titanium and placed in a water phantom for tissue equivalence. The transport processes considered by the code for photons were low energy photoelectric absorption and scattering (Compton and coherent). Low energy ionisation, low energy Bremsstrahlung and multiple scattering were considered for electrons. The cross sections used for these low energy Geant4 models are from the G4EMLOW.6.9 data set. Range cuts for particles in the simulation were matched to those used in previous simulations Particle Generation As with I-125 based Monte Carlo dosimetry, the particle generation from the surface of the spherical Ru-106 plaque must accurately represent the true source. The CCD plaque geometry and construction reflects a curved surface in the shape of a spherical cap, which is uniformly coated with Ru-106 and hence, particles may be emitted from any point on its surface. The process of generation therefore relies on random energy selection based on the source spectrum, random coordinate on the surface of the source, and random direction. The surface geometry and spectrum of Ru-106 is more complex and involved than that of the model 6711 I-125 seed and had to be considered carefully so to ensure an accurate model of the true source was simulated. Random Energy Ruthenium-106 decays by beta emission via Rhodium-106 with a maximum energy of 39.4keV. Rhodium-106 has a short half life of only 30 seconds thus it is assumed that it emits energy at the same rate as Ruthenium-106. The main electron contribution to the spectrum is from the decay of Rhodium-106 and, hence, the decay spectrum is of great significance to the Monte Carlo code. Rhodium-106 has a maximum beta energy emission of 3.54MeV and an average energy emission of 1.41MeV. The Ru-106 spectra had to be considered carefully in preparation to ensure all contributions to dose from different emissions were accounted for in the simulation. Decay data for Ru-106 from the National Nuclear Data Center (2001) was obtained from Appendix A of the ICRU Report 85

103 72 (2004) (see Tables 4 & 5). This data provides photon contamination emission probabilities 0.1% per disintegration. Photon contamination contribution from Rh-106 is significant being 33.3%, which can be broken down into seven different emission energies, all of which were considered in the simulation (see Table 4). It was crucial, therefore, to the accuracy of the calculation that the complete, though complex, beta decay spectra be included in the simulation. All energies in the simulation were selected based on the probability from the calculated beta-ray spectrum provided by the ICRU Report 72 (2004) (see Table 5). Due to their short range, approximately 95% of the low energy electrons from the Ru-106 nuclide were expected to be absorbed by the thin silver foil window (Eckert & Ziegler BEBIG GmbH, 2008). The beta-ray spectrum included assumed by the code consisted of 41 sampled energies up to a maximum of 3.54MeV and is listed below. Random Coordinate The Ru-106 plaque was defined in the code as a spherical cap shaped source with inner height, h, of 4.3mm and inner radius, R, of 12.1mm. The inner radius, R, was set to be 0.1mm greater than the plaque radius of curvature to account for the 100µm silver foil (figure 44) lining the inner surface of the plaque. The source should be evenly distributed over the area of the inner surface of the plaque. By definition of the area of a segment circle (Weisstein, 1999), Surface Area 2 rh (5.1) Since the surface area is proportional to h of any part of the segment, a linear distribution of h will provide a linear distribution of area, hence it will suffice to provide an even distribution of the source. 86

104 Figure 44. Plaque surface geometry for particle generation. A particle may originate from any point on the inner surface of the spherical plaque of height, h and radius, R. A random coordinate must be generated representing the location of this point on the spherical surface. This coordinate may be at any height within the plaque. To determine a random height on the inner plaque surface, generate a random number was generated between zero and h, denoted by z since h is linear in the z direction (see Fig. 45). It is necessary therefore to consider the plaque a series of slices or rings located at any point, z, from zero to h. At the point z, there exists a ring of possible (x,y) coordinates at which the particle may be generated, the location of which is dependent on the circumference of the ring at that particular height. To determine the radius, r, of the ring at height z, the following definition was considered (Weisstein, 1999), r z 2 R z (5.2) 87

105 Figure 45. Ring geometry. To determine the locations of the (x,y) coordinate of the particle generated on the surface of the ring, a random x and y coordinate were generated around the circumference of the ring by selecting a random angle between zero and 2π. Figure 46. Coordinate generation. Thus, from figure 46, the y coordinate was rcosθ and the x coordinate was rsinθ. The z coordinate of generation is represented by the random height, z, less 0.1mm to account for the offset from the origin since the origin is defined as the inner surface of the plaque beneath the thickness of the silver foil lining. 88

106 Random Direction To ensure the generated particle is emitted in a random direction from the surface of the plaque as would occur with the true source, a random a, b, c, coordinate was generated between zero and 1, representing the directions (x,y,z). These random coordinates were converted into a random vector, n and then into a unit vector, nˆ by way of the unit vector equation, n nˆ (5.3) n Where, n a b c (5.4) And, 2 n n (5.5) A condition of n a 2 b 2 c 2 1 was set to ensure the random point of particle generation reflects a point within a sphere, allowing all angles to have equal probability of generation. 5.2 Results A dose array was obtained from the Monte Carlo simulations, consisting of depth dose from 1mm to 25mm through the central axis calibration simulation, and 1mm-25mm through the off axis simulations. This amounts to a total measured 650 dose points throughout the volume of the eye. The dose array can be found in full in Appendix A. The simulation produced a null result for particular radial distances and angles from the source where the scoring toroid crossed through the plaque itself. Since these points were not desired, no dose was recorded. The Monte Carlo derived central axis depth dose was compared with the depth dose generated by the BEBIG Plaque Simulator. The results are 89

107 found in Table 10 and a plot in Figure 47. The uncertainty in the Monte Carlo results was good for all radial angles and distances from the centre of the source, being less than 10%, however, the uncertainty on the central axis increased significantly with distance from the source. This is due to the reduction in interactions with distance from the source. Table 10. Monte Caro and TPS derived depth dose on plaque central axis. Depth (mm) MC Error Plaque (%) Simulator Both sets of data have been normalised to unity at 1cm for comparison in Figure 47. The Monte Carlo results were considerably different to the TPS generated depth dose data revealing the difficulty in accurately scoring dose from the curved surface of the plaque. The most deviation from the predicted dose distributions occurs at very close distances to the plaque surface. 90

108 Reletive Dose MC Bebig Depth (mm) Figure 47. Monte Carlo derived Ru-106 CCD plaque central axis depth dose compared with central axis dose generated from the Plaque Simulator. Discussion A Monte Carlo simulation was performed to predict the dose deposited in a medium from a Ru-106 CCD plaque. An array of scoring toroids were modelled a number of distances from the centre of the source to score throughout the true volume of the eye. The detailed methods of particle generation and scoring for the Monte Carlo simulations performed in this chapter highlight the complexity of dosimetry for Ru-106 plaques. The geometry is intricate and the criterion of uniform radioactive distribution across the surface of the source further increases the potential for error in measurement, despite novel Monte Carlo scoring techniques employed. Furthermore, replicating the complicated energy spectrum of Ru-106 is a challenging task and has significant impact on the accuracy of results. A significantly higher dose was delivered to the medium at small distances (r 1cm) from the plaque in comparison with the TPS results. This is most likely a product of the thickness of the source and the depth of particle generation modelled in the simulation. This method was based on plaque construction outlined in the Ru-106 Plaque Fact sheet 91

109 (Eckert & Ziegler BEBIG GmbH, 2008) where the Monte Carlo simulation generated particles from the surface of an infinitesimally thin layer of silver 0.1mm beneath the plaque surface. Astrahan (2003) determined that the radioactivity of the plaque is a distribution through 0.2mm of the silver. Figure 48 is a detailed schematic of the Ru-106 plaque geometry provided by Eye Physics, LLC (Los Alamitos, CA, USA). The image also indicates a mm thick gap between where the radioactive part begins and the edge of the plaque itself. These geometric variations between the physical plaque and the simulated plaque are evident in the considerable discrepancies between measured and predicted dose data. The initial slope of Monte Carlo obtained dose distribution is mainly due to electrons and lower energy photons. However, as depth increases, a harder spectrum is produced due to absorbed low energy photons leading to a decrease in dose gradient. This effect should be considered in an updated Monte Carlo simulation, where the source will be generated as a 0.2mm thick distribution rather than a linear distribution. Figure 48. BEBIG Ru-106 plaque applicator schematic showing detailed geometric source specifications (Eye Physics, LLC, Los Alamitos, CA, USA see While the results of this simulation do not agree with the commercial system, they do raise a lot of questions regarding the consistency of the source specifications in the literature. The accuracy of the Monte Carlo dosimetry for eye plaque brachytherapy performed in this thesis has been demonstrated by the results of Chapter 4. The results of 92