Addressing Limitations of a Spatially Sensitive Large-Area Ion Chamber for Real-Time Verification of Intensity Modulated Radiation Therapy.

Transcription

1 Addressing Limitations of a Spatially Sensitive Large-Area Ion Chamber for Real-Time Verification of Intensity Modulated Radiation Therapy. by Xun Lin A thesis submitted in conformity with the requirements for the degree of Masters of Health Science in Clinical Engineering Institute of Biomaterials and Biomedical Engineering University of Toronto Copyright by Xun Lin 2015

2 Addressing Limitations of a Spatially Sensitive Large-Area Ion Chamber for Real-Time Verification of Intensity Modulated Radiation Therapy. Abstract Xun Lin Masters of Health Science in Clinical Engineering Institute of Biomaterials and Biomedical Engineering University of Toronto 2015 Lack of light transparency and overall thickness are limitations of a previously described spatially sensitive large-area ionization chamber used for real-time verification of radiation therapy beam delivery. The first limitation was addressed with investigation of a commercially available light transparent conductive glass plates as replacements for aluminum plates in the construction of the chamber. Resulting chamber produced expected spatial sensitivity, allowed the light field to be transmitted with 35% attenuation in intensity, and caused deviation of field position due to refraction up to 0.4 mm. The second limitation was investigated with novel interleaved comb patterned electrode pairs. The pattern was ablated on light transparent conductive glass plate and utilized for construction of an experimental prototype ionization chamber that was 35% thinner, light transparent, and produced spatial sensitivity comparable to original design. However, further refinement in design and manufacturing process is necessary to make a practical comb patterned ionization chamber pair. ii

3 Acknowledgments I would like to express my gratitude to my advisors Dr. Mohammad K. Islam and Dr. Robert Heaton for their patience, guidance, and support throughout the past two years. Furthermore, I would like to thank my thesis committee members Dr. David Jaffray, Dr. Catherine Coolens, and Prof. Alf Dolan for their valuable comments and guidance during the course of my research. Besides my thesis committee, I would like to acknowledge the hard working, knowledgeable, and helpful people from Princess Margaret Cancer Centre. This research would not have been possible without assistance from members of the Physics Associates, Accelerator Services, and Machine Shop staff. In particular, I would like to thank the following individuals for their contributions: Makan Farrokhkish and Jongho A. Jung for their insight and measurement data with the original IQM chamber; Bern Norrlinger for his insight and guidance with electronics and firmware design; Graham Wilson for his assistance with software development; and Ting Jun Zhang for his assistance with Blue Phantom2 measurements. Additionally, I would like to acknowledge and thank Mr. Juergen Oellig of irt Systems GmbH (Koblenz, Germany) and Mitacs Canada for providing funding for the research project. Last but not least, I would like to thank my family and friends for their support throughout my thesis. iii

4 Table of Contents ABSTRACT... II ACKNOWLEDGMENTS... III TABLE OF CONTENTS...IV LIST OF TABLES... VII LIST OF FIGURES... VIII 1 INTRODUCTION BACKGROUND INFORMATION RADIATION THERAPY Diagnosis and Treatment Planning Treatment Delivery and Linear Accelerators Complex Treatment Techniques ERRORS IN TREATMENT DELIVERY RECENT ONLINE INDEPENDENT BEAM DELIVERY MONITORING SYSTEMS THE INTEGRAL QUALITY MONITORING SYSTEM Area Integrating Fluence Monitoring Sensor Limitations LIGHT TRANSPARENT PLATES Light Transparent Conductive Layer Substrate Material Commercially Available Light Transparent Conductive Plates VIRTUAL GRADIENT IONIZATION CHAMBER Pattern Description Dose Sensitivity Spatial Sensitivity RESEARCH DETAILS RESEARCH OBJECTIVES THESIS STATEMENT METHODS AND MATERIALS EXPLORATION OF LIGHT TRANSPARENT PLATES Electrically Conductive Light Transparent Glass Plate iv

5 4.1.2 Electrical Connections Light Transparent Parallel Plate Ionization Chamber Light Transparency Evaluation Light Intensity Reduction Light Refraction Basic Overall Usability GLASS AIMS PROTOTYPE Frame Modification Gradient Measurement Short Term Reproducibility of SBRT IMRT Treatment Field Impact on Beam Intensity and Quality Beam Attenuation Beam Quality VIRTUAL GRADIENT AIMS PROTOTYPE Measurement System Glass Based Virtual Gradient Pattern Prototype (Virtual AIMS) Manufacturing Basic System Measurements Gradient Measurement Short Term Reproducibility of Sample IMRT RESULTS EXPLORATION OF LIGHT TRANSPARENT PLATES Light Transparent Parallel Plate Ionization Chamber Light Intensity Reduction Radiation Induced Discoloration Light Displacement Experiment Basic Overall Usability GLASS AIMS PROTOTYPE Gradient Measurement Short Term Reproducibility of Sample SBRT IMRT Plan Impact on Beam Intensity and Quality Beam Attenuation Beam Quality VIRTUAL GRADIENT AIMS PROTOTYPE Basic System Measurements Gradient Measurements Short Term Reproducibility of Sample SBRT IMRT Plans v

6 6 UNANTICIPATED CHALLENGES THEORETICAL CHALLENGES OF VIRTUAL GRADIENT PATTERN Signal Oscillation Pattern Crosstalk HUMIDITY AND LEAKAGE DISCUSSION LIGHT TRANSPARENT GLASS PLATE GLASS AIMS PROTOTYPE VIRTUAL GRADIENT AIMS PROTOTYPE LIMITATIONS Radiation Induced Discoloration Signal Oscillation Inherent within Virtual Gradient Pattern Inherent Risk of Crosstalk Humidity and Leakage CONCLUSIONS FUTURE WORK REFERENCES APPENDIX A CALCULATION FOR DISPLACEMENT FROM SINGLE GLASS PLATE APPENDIX B CALCULATION OF DISPLACEMENT FOR ANGLED GLASS CONFIGURATIONS Effective Angle APPLICATION Parallel Plate Symmetrical Asymmetrical vi

7 List of Tables TABLE 1. SUMMARY OF LIGHT INTENSITY TRANSMISSION MEASUREMENTS 80% LIGHT TRANSMISSION PER PLATE TABLE 2. LIGHT INTENSITY MEASUREMENT WITH RADIATION DISCOLORED GLASS PLATE TABLE 3. ANGLES OBSERVED FOR 1 MM DISPLACEMENT TABLE 4. RESULTS OF EQA MEASUREMENT ON VARIAN LINEAR ACCELERATOR WITH AND WITHOUT 2 GLASS PLATE PROTOTYPE IN LINEAR ACCELERATOR ACCESSORY TRAY TABLE 5. COMPARISON OF REPRODUCIBILITY OF A-AIMS AND G-AIMS FOR SAMPLE SBRT IMRT TREATMENT FIELD TABLE 6. RESULTS OF BEAM ATTENUATION MEASUREMENT USING NE2571A FARMER IONIZATION CHAMBER AND ADVANCED THERAPY DOSIMETER. MEASUREMENTS SHOW BEAM ATTENUATION BY GLASS AND ALUMINUM AIMS TABLE 7. LINEARITY MEASUREMENT RESULTS USING VIRTUAL AIMS AND DUAL CHANNEL IQM ELECTROMETER TO MEASURE 6 MV 10X10 CM 2 FIELDS FROM ELEKTA LINEAR ACCELERATOR TABLE 8. COMPARISON OF REPRODUCIBILITY BETWEEN A-AIMS, G-AIMS, AND V-AIMS FOR SAMPLE SBRT IMRT PLAN TABLE 9. LEAKAGE AT VARIOUS HUMIDITY LEVELS TABLE 10. CALCULATIONS FOR PARALLEL PLATE ARRANGEMENT TABLE 11. CALCULATIONS FOR SYMMETRICAL ANGLED ARRANGEMENT TABLE 12. CALCULATIONS FOR ASYMMETRICALLY ANGLED ARRANGEMENT vii

8 List of Figures FIGURE 1. SCHEMATIC DIAGRAM OF COMPONENTS WITHIN THE HEAD OF A MEDICAL LINEAR ACCELERATOR. THE HEAD STRUCTURE IS TYPICALLY MOUNTED ON A GANTRY, ALLOWING THE BEAM TO BE ROTATED ABOUT THE PATIENT FIGURE 2. PHOTO OF AN ELEKTA AGILITY MULTILEAF COLLIMATOR. GREEN LIGHT IS PROJECTED TO HELP VISUALIZE THE FIELD EDGES IN THE DARK ROOM FIGURE 3. BLOCK DIAGRAM SHOWING PLACEMENT OF SENSORS IN A REAL-TIME TREATMENT VERIFICATION SYSTEM FIGURE 4. PROCESS FLOW OF IQM SYSTEM [9] FIGURE 5. DIAGRAM OF AREA INTEGRATING FLUENCE MONITORING SENSOR [5] FIGURE 6. PHOTO OF VIRTUAL GRADIENT PATTERN PRINTED ON A PCB. PATTERN ON PCB MADE OF COPPER. TWO INTERLEAVED COLLECTING ELECTRODES LOCATED IN THE CENTRE OF PATTERN. SURROUNDING BORDER ACTS AS GUARD ELECTRODE FIGURE 7. SIMPLE VIRTUAL GRADIENT PATTERN. COMB 1 (BLUE) INCREASES IN TINE WIDTH FROM TOP TO BOTTOM WHILE COMB 2 (YELLOW) DECREASES IN TINE WIDTH FROM TOP TO BOTTOM. WIDTH OF EACH TINE PAIR REMAINS CONSTANT THROUGHOUT THE PATTERN FIGURE 8. BASIC PARALLEL PLATE IONIZATION CHAMBER PROTOTYPE CREATED WITH FTO COATED GLASS PLATES AND EXTRUDED POLYSTYRENE FOAM BLOCKS FOR SUPPORT FIGURE 9. SIMPLE SCHEMATIC DIAGRAM ILLUSTRATING HOW MEASUREMENT COMPONENTS ARE CONNECTED IN THE SIMPLE PARALLEL PLATE CONFIGURATION FIGURE 10. ILLUSTRATION SHOWING DISPLACEMENT AS A RESULT OF LIGHT RAY S MODIFIED PATH WITHIN GLASS MEDIUM. THE SHADED REGION INDICATES THE PRESENCE OF GLASS, WHILE THE GREEN LINE SHOWS THE RAY LIKE PATH OF LIGHT THROUGH THE GLASS. DASHED LINES INDICATE NORMAL TO THE INTERFACE SURFACE FIGURE 11. ILLUSTRATION OF EXPERIMENT TO CONFIRM LIGHT REFRACTION CALCULATIONS FIGURE 12. ILLUSTRATION OF LIGHT RAY PASSING THROUGH PARALLEL PLATE CONFIGURATION FIGURE 13. IMAGE OF EQA MARKERS ALONE (LEFT) AND SETUP ON A VARIAN LINEAR ACCELERATOR (RIGHT) FIGURE 14. LOCATION OF INSULATOR TO BE MODIFIED (BLUE) IN PROTOTYPE FIGURE 15. PICTURES SHOWING MLC JAW POSITIONS OF SAMPLE SBRT IMRT FIELD. EACH LEAF IN THE LINAC HAS A WIDTH OF 5 MM PROJECTED TO ISOCENTRE FIGURE 16. SETUP OF BEAM ATTENUATION MEASUREMENT FIGURE 17. PHOTO OF IBA DOSIMETRY S BLUE PHANTOM 2 SETUP FOR PERFORMING PERCENT DEPTH DOSE AND CROSSLINE BEAM PROFILE MEASUREMENTS FIGURE 18. FLOW OF SIGNAL COLLECTION INFORMATION WITH DUAL CHANNEL IQM ELECTROMETER FIGURE 19. PHOTO SHOWING FRAME TO FOR PARALLEL PLATE AND VIRTUAL AIMS PROTOTYPES FIGURE 20. PHOTO OF IONIZATION CHAMBER WITH VIRTUAL GRADIENT PATTERN IN ITS FRAME AND ELEKTA MOUNT FIGURE 21. GRAPH OF PARALLEL PLATE ION CHAMBER RESPONSE TO VARIOUS DOSES MEASURED WITH KEITHLEY MK614 SHOW HIGH DEGREE OF LINEARITY FIGURE 22. PHOTO OF GLASS AIMS AND AN ALUMINUM AIMS SIDE BY SIDE viii

9 FIGURE 23. ALUMINUM AND GLASS AIMS CHAMBER GRADIENT PROFILE MEASURING 6 MV 1X1 CM 2 RADIATION FIELD FROM ELEKTA LINEAR ACCELERATOR FIGURE 24. ALUMINUM AIMS CHAMBER GRADIENT PROFILE MEASURING 6 MV 1X1 CM 2 RADIATION FIELD FROM ELEKTA LINEAR ACCELERATOR. ONLY LINEAR REGION IS SHOWN FIGURE 25. PERCENT DEPTH DOSE MEASUREMENTS WITH AND WITHOUT ALUMINUM AIMS AT 6 MV BEAM ENERGY WITH 10X10 CM 2 FIELD FIGURE 26. PERCENT DEPTH DOSE MEASUREMENTS WITH AND WITHOUT ALUMINUM AIMS AT 6 MV BEAM ENERGY WITH 30X30 CM 2 FIELD FIGURE 27. PERCENT DEPTH DOSE MEASUREMENTS WITH AND WITHOUT GLASS AIMS AT 6 MV BEAM ENERGY WITH 10X10 CM 2 FIELD. 45 FIGURE 28. PERCENT DEPTH DOSE MEASUREMENTS WITH AND WITHOUT GLASS AIMS AT 6 MV BEAM ENERGY WITH 30X30 CM 2 FIELD. 45 FIGURE 29. DIFFERENCE BETWEEN PERCENT DEPTH DOSE MEASUREMENTS WITH AND WITHOUT ALUMINUM AIMS AT 6 MV BEAM ENERGY WITH 10X10 CM 2 FIELD FIGURE 30. DIFFERENCE BETWEEN PERCENT DEPTH DOSE MEASUREMENTS WITH AND WITHOUT GLASS AIMS AT 6 MV BEAM ENERGY WITH 10X10 CM 2 FIELD FIGURE 31. CROSSLINE BEAM PROFILE MEASURED AT 1.5 CM DEPTH BY BLUE PHANTOM WITH AND WITHOUT A-AIMS AT 6 MV ENERGY FIGURE 32. CROSSLINE BEAM PROFILE MEASURED AT 5 CM DEPTH BY BLUE PHANTOM WITH AND WITHOUT A-AIMS AT 6 MV ENERGY. 47 FIGURE 33. CROSSLINE BEAM PROFILE MEASURED AT 10 CM DEPTH BY BLUE PHANTOM WITH AND WITHOUT A-AIMS AT 6 MV ENERGY FIGURE 34. CROSSLINE BEAM PROFILE MEASURED AT 20 CM DEPTH BY BLUE PHANTOM WITH AND WITHOUT A-AIMS AT 6 MV ENERGY FIGURE 35. CROSSLINE BEAM PROFILE MEASURED AT 1.5 CM DEPTH BY BLUE PHANTOM 2 WITH AND WITHOUT G-AIMS AT 6 MV ENERGY FIGURE 36. CROSSLINE BEAM PROFILE MEASURED AT 5 CM DEPTH BY BLUE PHANTOM 2 WITH AND WITHOUT G-AIMS AT 6 MV ENERGY FIGURE 37. CROSSLINE BEAM PROFILE MEASURED AT 10 CM DEPTH BY BLUE PHANTOM 2 WITH AND WITHOUT G-AIMS AT 6 MV ENERGY FIGURE 38. CROSSLINE BEAM PROFILE MEASURED AT 20 CM DEPTH BY BLUE PHANTOM 2 WITH AND WITHOUT G-AIMS AT 6 MV ENERGY FIGURE 39. DOSE LINEARITY OF VIRTUAL AIMS WITH DUAL CHANNEL ELECTROMETER WITH REFERENCE MEASUREMENTS USING NE2571A FARMER ION CHAMBER. 10X10 CM 2 FIELD DELIVERED WITH 6 MV BEAM ENERGY. RESULTS NORMALIZED TO VALUES AT 100 MU FIGURE 40. AREA OF FLUENCE MEASUREMENT FOR VIRTUAL AIMS AND DUAL CHANNEL IQM ELECTROMETER. 100 MU DELIVERED WITH 6 MV BEAM ENERGY FIGURE 41. DOSE RATE DEPENDENCY MEASUREMENT FOR THE VIRTUAL AIMS AND DUAL IQM ELECTROMETER WITH REFERENCE MEASUREMENTS FROM NE2571A FARMER ION CHAMBER. 10X10 CM 2 FIELD DELIVERED WITH 6 MV ENERGY ix

10 FIGURE 42. NON-GRADIENT CHAMBER PROFILE OF VIRTUAL AIMS MEASURED WITH 6 MV 1X1 CM 2 RADIATION FIELD FROM AN ELEKTA LINEAR ACCELERATOR FIGURE 43. GRADIENT CHAMBER PROFILE OF VIRTUAL AIMS MEASURED WITH 6 MV 1X1 CM 2 RADIATION FIELD FROM AN ELEKTA LINEAR ACCELERATOR FIGURE 44. GRADIENT CHAMBER PROFILE OF VIRTUAL AIMS MEASURED WITH 6 MV 1X1 CM 2 RADIATION FIELD FROM AN ELEKTA LINEAR ACCELERATOR. ONLY LINEAR REGION SHOWN FIGURE 45. PERFECT RECTANGULAR FIELD SCANNING ACROSS PATTERN (LEFT). EXPECTED GRADIENT PROFILE (RIGHT). THE BLOCK STEP FUNCTION ILLUSTRATES THE GENERATION OF A UNIFORM IONIZATION DENSITY IN A PORTION OF THE CHAMBER, WHILE THE DIFFERENT COLOURS ILLUSTRATE THE PARTITIONING OF THE CHARGE BETWEEN THE COMPLEMENTARY COMBS FIGURE 46. SIMULATED GRADIENT PROFILE WHEN MEASURED WITH A SQUARE BEAM THAT CREATES A CHARGE CARRIER GENERATION REGION OF EQUAL SIZE TO THE TINE PAIR WIDTH OF A VIRTUAL GRADIENT PATTERN FIGURE 47. NON-IDEAL BEAM WITH GAUSSIAN ION SPACE CHARGE DISTRIBUTION SCANNING ACROSS PATTERN (LEFT). EXPECTED GRADIENT PROFILE (RIGHT). EACH ILLUSTRATION IN LEFT FIGURE CORRESPONDS TO A LOCAL MAXIMUM/MINIMUM IN THE CHANNELS FIGURE 48. EXPECTED SIGNAL OSCILLATION IN GRADIENT WHEN MEASURED WITH BEAM THAT CREATES A CHARGE CARRIER GENERATION REGION THAT EQUALS THE TINE PAIR WIDTH OF VIRTUAL GRADIENT PATTERN. FIGURE COURTESY OF DR. ROBERT HEATON FIGURE 49. EXPECTED SIGNAL OSCILLATION IN GRADIENT WHEN MEASURED WITH BEAM THAT CREATES A CHARGE CARRIER GENERATION REGION THAT EQUALS TWICE THE TINE PAIR WIDTH OF A VIRTUAL GRADIENT PATTERN. FIGURE COURTESY OF DR. ROBERT HEATON FIGURE 50. SCHEMATIC OF IDEAL CHARGE COLLECTION CIRCUIT FOR THE VIRTUAL GRADIENT PATTERN SYSTEM FIGURE 51. SCHEMATIC OF NON-IDEAL CHARGE COLLECTION CIRCUIT FOR THE VIRTUAL GRADIENT PATTERN SYSTEM FIGURE 52. PHOTO SHOWING HUMIDITY-LEAKAGE MEASUREMENT EXPERIMENT SETUP FIGURE 53. LINEAR CORRELATION OBSERVED BETWEEN LEAKAGE CURRENT AND HUMIDITY FOR GLASS AIMS PROTOTYPE FIGURE 54. QUADRATIC CORRELATION OBSERVED BETWEEN LEAKAGE CURRENT AND HUMIDITY FOR VIRTUAL AIMS PROTOTYPE FIGURE 55. MORE COMPLEX SITUATION FOR WHEN GLASS PLATE IS ALSO ANGLED FIGURE 56. LIGHT RAY PASSING THROUGH BASIC PARALLEL PLATE ARRANGEMENT FIGURE 57. LIGHT RAY PASSING THROUGH SENSOR WHEN BOTH PLATES ARE ANGLED WITH SAME MAGNITUDE BUT OPPOSITE DIRECTION. 83 FIGURE 58. LIGHT RAY PASSING THROUGH ASYMMETRICAL ARRANGEMENT WITH ONE ANGLED PLATE AND ANOTHER PARALLEL TO FLOOR. 84 x

11 1 Introduction Cancer is a disease that is estimated to cause a yearly death of 7.6 million, with an additional 12.7 million new cases diagnosed worldwide. Radiation therapy is one of three primary methods of cancer treatment along with chemotherapy and surgical excision and is prescribed in 50% of all cancer treatment plans [1]. The goal of radiation therapy is to deliver sufficient ionizing radiation dose to a target volume in order to destroy tumour cells while minimizing dose delivered to surrounding healthy tissue. The result of delivering sufficient ionizing radiation dose to cancer cells is the destruction of genetic information in the cells, which ultimately prevents the malignant cells from reproducing. Similarly, dose delivered to healthy tissue can result in the death of healthy cells and in addition increase the risk of developing cancer in the future [2]. Recent radiation therapy techniques have improved the effectiveness of treatment delivery at the cost of increased complexity. For example, compared to conventional methods of radiation therapy where beam forming elements remain static during treatment, modern radiation therapy techniques such as intensity modulated radiation therapy (IMRT) feature dynamic beam forming elements to optimize dose delivery [3]. The result of increased complexity is an increased risk due to an increased probability of error during treatment delivery from hardware, software, and use errors resulting in excessive dose to healthy tissue or insufficient dose to malignant cells [2]. Established quality assurance (QA) procedures such as pre-treatment patient QA and machine calibration do not sufficiently address errors that could occur during treatment delivery [3] [4]. Several research groups have recognized the need for an independent real-time monitoring system for beam fluence verification during treatment delivery. Several solutions have been proposed: the Integral Quality Monitoring (IQM) system proposed by Islam et al. utilizing a large area ion chamber to measure the dose-area-product of treatment beams, the DAVID system (manufactured by PTW-Freiburg, Germany) and an optical fibre based system proposed by Goulet et al. use an array of line-detectors to integrate radiation signals across the radiation field, and the Dolphin system manufactured by IBA Dosimetry uses a 2D array of point detectors to capture a low resolution image of the radiation field fluence [5] [6] [7] [8] [9] [10]. 1

12 Amongst the systems proposed, the IQM system is a low maintenance and easy to use system that utilizes relatively simple components in the creation of its beam fluence sensor to produce a single easy-to-interpret signal. However, the current IQM chamber design possesses some limitations. This research aims to address those limitations. 2

13 2 Background Information 2.1 Radiation Therapy Radiation therapy is performed in three general stages. These stages are diagnosis, treatment planning, and finally treatment delivery [2] [3] Diagnosis and Treatment Planning Once diagnosed and a treatment strategy adopted which includes radiation therapy, then the radiation planning process can begin. Anatomical images of the patient from imaging systems such as magnetic resonance imaging (MRI) and computed tomography (CT) are used by physicians to define a target volume and critical organs. Target volumes are defined for prescribing a dose, and critical organs are identified to allow treatment planners to create a treatment plan with a computerized treatment planning system that will deliver the prescribed target dose while minimizing the dose delivered to critical organs [3]. The treatment plan contains instructions on how to deliver the prescribed dose. These instructions are sent to a medical treatment device known as a medical linear accelerator and used to deliver the prescribed radiation [3] [11] Treatment Delivery and Linear Accelerators A medical linear accelerator (linac) is used to deliver the prescribed dosage to the target tissue. Linacs generate ionizing radiation by accelerating high energy electrons and directing the electrons to a high atomic number target such as tungsten or copper. The focal point of the beam on the metal target forms the radiation source. The high energy collision emits an x-ray beam (through bremsstrahlung interactions) while the electrons are stopped in the target. Flattening filters are applied to the original forwardly peaked beam profile to produce a uniform beam profile. A monitor chamber placed after the flattening filter monitors the quality of the beam and tracks output of the system [12]. A light source and mirror system is also included within the linear accelerators to help visualize treatment fields. A schematic diagram showing how the components are laid out in the head of a linear acceleration is shown in Figure 1. To 3

14 accommodate optimal dose delivery, the machine is able to rotate to various gantry angles around the patient. Figure 1. Schematic diagram of components within the head of a medical linear accelerator. The head structure is typically mounted on a gantry, allowing the beam to be rotated about the patient. The dose output is specified in terms of monitor units (MU) and linacs are typically tuned such that a single MU results in the absorbed dose of 1 cgy at a reference depth for a 10x10 cm 2 field at a distance of 100 cm from the radiation source. This distance coincides with the machine s isocentre, which is defined as the centre of machine s rotations [12]. Modern linear accelerators use multi-leaf collimators (MLC) to shape the x-ray beam to conform to the shape of the target volume so that as much normal tissue as possible is spared [13] [14]. MLC is a device that consists of 40 to 80 pairs of moveable leaves or strips of heavy metal capable of attenuating the radiation beam to less than 2% intensity. The leaves are typically 2 to 4

15 4 mm in width, which projects to a 5 to 10 mm width at isocentre due to beam divergence; and have a thickness of 7 to 8 cm [14] [15]. The MLC is placed in the path of an x-ray beam before the accessory tray of linear accelerators and the leaves are moved into the desired configuration to shape the radiation beam [14] [15] [5]. Figure 2 shows a photo of a multileaf collimator. The field size and MLC aperture shapes described in treatment plans are defined at the machine s isocentre (generally 100 cm from radiation source), and as a result are much smaller at the level of the MLCs. Linear accelerators project a light through the collimators aligned to the radiation beam axis that simulate the size and shape of the radiation field to be delivered. The light field is designed to follow the divergent path of the radiation field so that the edges of the radiation field falls along the light field shadow edge. A cross hair shadow is also produced in the light field to mark the centre of the radiation field. This is used to help visualize the treatment area and is one of the guides used by therapists to help align patients during patient set-up. Figure 2. Photo of an Elekta Agility Multileaf Collimator. Green light is projected to help visualize the field edges in the dark room Complex Treatment Techniques The consequence of recent improvements in radiation therapy are increased complexities and a less intuitive planning and treatment delivery processes. These complexities include plan optimization with non-uniform weighting of beamlets and delivery of beams with corresponding intensity modulation. Intensity modulation of beams is achieved with accurate synchronization 5

16 of dynamic MLC motion and radiation dose rates in corresponding accelerator gantry angle [5] [4] [16]. Intensity Modulated Radiation Therapy (IMRT) is a mode of radiation therapy that uses nonuniform radiation beam delivery in the treatment of malignant tissue [3]. The non-uniform beam is created by modulating a uniform beam with MLC position as well as sometimes employing physical modulators to create more complex dose distributions from the beam [4]. IMRT delivery is generally delivered at static gantry angles where only the beam shaping element (such as the multi-leaf collimator) move while radiation is being delivered [3]. Volumetric Modulated Arc Therapy (VMAT) on the other hand adds a further layer of complexity by adding gantry rotation and dose rate modulation during delivery of radiation [17] [18]. This adds a significant layer of abstraction to the planning process, making it more difficult to manually create or verify a treatment plan [10]. This ultimately makes the planning process less intuitive and more reliant on automation. Furthermore, the process becomes even more prone to error due to the introduction of additional variables [6]. Despite the added complexity, VMAT treatments are faster, require less beam-on time, and deliver fewer monitor units of radiation to healthy tissues in a patient when compared with conventional radiation therapy and IMRT [17] [18]. The result of the complexities is a heavier reliance on computers and automation and loss of the ability for care providers to intuitively detect errors that can potentially lead to catastrophic results in the various stages of the treatment process. 2.2 Errors in Treatment Delivery Errors in the process of treatment delivery may lead to significant risk for the patient. For example, errors in positioning of the MLC leaves or dose rates can significantly change the dose, resulting in insufficient dose to malignant tissue or excessive dose to healthy tissue ultimately resulting in inaccurate treatment or causing the patient to suffer injury or death in serious cases [4] [16]. Furthermore, sources of error such as human errors and hardware or software failures can all lead to incorrect dose delivery to patients [19] [2]. The risks of treatment delivery errors are significant and radiation therapy centres have applied substantial effort to implement risk 6

17 control processes such as machine calibration and enhanced QA of linear accelerators, and dosimetric verification of treatment plans using traditional methods and tools to reduce probability of errors during treatment; however, current risk control processes does not include any real-time independent treatment verification system, resulting in significant residual risk [5]. For example, a study has found that a total of 4407 incidents of near-miss events occurred between June 2007 and December 2010 at the Department of Radiation Oncology at John Hopkins University and the Washington University in Saint Louis-Barnes Jewish Hospital [19]. Of those 4407 incidents, 292 had the potential for severe harm to the patient [19]. Each clinic are treating approximately 170 patients per day for a total of 340 patients per day during the specified period [19]. There was 183 weeks in the period between June 2007 and December Assuming a 5 day treatment week, 155,550 treatments were delivered during the period of interest. It can then be determined that there is a risk factor of 1877 per million treatments that can result in severe harm to the patient. Similarly, a World Health Organization risk profile analysis for the period between 1992 and 2007 has found that there is a risk of approximately 1500 treatment delivery errors per million treatment courses that will result in mild to moderate injury in patients in middle and high income countries such as Australia, United Kingdom, European countries, Canada, and the United States [2]. These numbers, though lower than other risks such as adverse drug reactions (about 65,000 per million), are still significant and entail the possibility of severe consequences [2]. In an on-going effort to improve patient safety, a series of white papers was published by the American Society for Radiation Oncology s (ASTRO) Target Safely Campaign. One of the white paper, approved by the American Association of Physicists in Medicine (AAPM) and American Association of Medical Dosimetrists (AAMD), recommended to include methods to directly and independently verify/validate patient plan and treatment machine prior to, during, and after radiation delivery [20]. An independent beam delivery monitoring system capable of verifying beam delivery in real-time can fulfill this recommendation. 7

18 2.3 Recent Online Independent Beam Delivery Monitoring Systems Several research groups have recognized the importance of having an independent beam delivery monitoring system to verify treatment during delivery. A number of innovative solutions have been recently been proposed, such as Integral Quality Monitoring system developed by Islam et al. and an optical fibre based system proposed by Goulet et al. A number of vendors have also made systems commercially available such as the Dolphin system by IBA Dosimetry based on an array of ionization chambers and the DAVID device, based on a multi-wire sensor developed by PTW-Freiburg [5] [6] [7] [8] [9] [10]. All these systems have a sensor used for detection of radiation beam fluence located after the final beam shaping collimators in the linear accelerator unit. Figure 3 shows a block diagram of where the sensor is placed for real-time treatment verification. A different class of verification systems exist that utilizes a sensor placed after the patient. This type of system is not considered in the context of this research. Figure 3. Block diagram showing placement of sensors in a real-time treatment verification system. The Dolphin system utilizes a matrix of 40x40 small ionization chambers to accomplish verification of radiation beams; however, this system possesses a large up-front capital 8

19 investment and may be overly complicated in maintenance [6] [10]. The optical fiber based system by Goulet et al., which utilizes scintillating optical fibers and the photoelectric effect to estimate dose incident to the optical fibers. A limitation of the system is that it requires an errorfree reference measurement of the field to provide the most accurate readings, and has been reported that comparison with predicted values from planning software results in reduced precision, dependent on the uncertainties in dose calculation and fiber property determination [10]. The DAVID system uses thin wires to collect ions generated in the air volume between two polarizing plates and hence measures a position dependent fluence [7] [8] [9]. Due to the nature of integration along the entire wire, it is expected to be insensitive to field translational errors [10]. Furthermore, both the DAVID and optical fiber systems utilize either fibre optical wire or conductive wires that trace the collimator leaves for radiation detection [7] [8] [9] [10]. As a result, hardware modifications will be required if there is a change in the number or size of collimator leaves. 2.4 The Integral Quality Monitoring System The Integral Quality Monitoring (IQM) system is an on-line independent dose monitoring system developed by Islam et al. The system features a modified large area ionization chamber to provide a spatially sensitive dose-area-product measurement [5] [21]. Advantages of the system include ease of use and low maintenance. Unlike more complex solutions, the IQM sensor utilizes simple components and produces a single easy-to-interpret dose-area-product value that is obtained by integrating the radiation dose delivered across the ion chamber. This system has been shown to be sensitive in detecting a single leaf positional errors as small as 3 mm for 1x1 cm 2 fields and was found to be suitable for online verification of treatment fields [5] [22]. In operation, when an approved treatment plan is exported to the treatment delivery system, the plan is also automatically exported to the IQM software system, where the IQM system then calculates an expected signal. During treatment delivery, the estimated signals are compared to the measured signal to verify beam delivery and therapists can be warned when significant deviations occur [5]. Figure 4 shows the process flow of the IQM system. 9

20 Figure 4. Process flow of IQM system [9] Area Integrating Fluence Monitoring Sensor A key component of the IQM system is the ionization chamber. Ionization chambers measure radiation by collecting the charge generated through interactions of the radiation beam in the surrounding material, and gas contained in the detector [23] [24]. In the case of a parallel plate ionization chamber, a polarizing plate and collector plate are aligned in parallel with a gas volume between them. A high voltage (e.g. 500 V) is applied between the plates. When high energy radiation passes through the sensor, interactions between the radiation and material around the gas volume generate high energy electrons. Electrons passing through the chamber interact with the contained gas volume, creating ions that drift along the electric field lines to the polarizing plate or collector plate based on their respective polarity. Finally, the ions are neutralized by gaining or giving up an electron at the electrode plate and a current flows through the measurement circuit and measured by an electrometer [23] [24]. The reading is then used to estimate the amount of radiation that has passed through the detector. Many ionization chambers use air as the gas medium between the two polarizing plates and are often not air sealed, as a result, the measurements are highly dependent on atmospheric conditions such as temperature, pressure, and humidity all of which can cause significant variations in the measurements [23] [24] [25] [26]. To correct for temperature and pressure, a correction factor, ktp, is calculated. 10

21 k TP = T T 0 P 0 P where T = measured temperature P = measured pressure T 0 = reference temperature P 0 = reference pressure Application of the correction factor allows the signal to be corrected to its reference temperature and pressure condition values. Signal corrected = Signal raw k TP The area integrating fluence monitoring sensor (AIMS) is the sensor currently utilized in the IQM system. It is composed of three aluminum plates acting as electrodes, a central collector electrode and two polarizing electrodes that surround the collector electrode as shown in Figure 5. A guard electrode surrounds the edges of the collector electrode to intercept stray leakage currents between the polarizing and collecting electrodes. Figure 5. Diagram of Area Integrating Fluence Monitoring Sensor [5]. A simple method of increasing signal is to increase the chamber s volume by increasing the separation distance between the plates in order to increase the mass of gas contained within. More mass will result in more ions being created as radiation passes through the volume, increasing the signal measured. Thus, greater separation will result in a greater signal and smaller separation results in less signal [23] [24]. This principle is utilized to achieve a spatial sensitivity in the current AIMS. For the current AIMS design, a gradient of 1-10 is used which means the separation distance between a polarizing electrode varies from 1 mm to 10 mm over a 28 cm active region. 11

22 2.4.2 Limitations An important aspect of the IQM system is the ion chamber used to measure dose delivery. The current ion chamber design possesses two major limitations, namely: 1. Lack of light transparency 2. Overall chamber thickness The current ion chamber design blocks light as it utilizes opaque aluminum plates as [5]. Light transparency would be a desirable characteristic for the radiation detector as light field from the linear accelerators is utilized during QA and for patient setup before treatment to visualize radiation treatment fields [3]. By introducing light transparency, a smoother and more efficient work flow would result, as therapists would not be required to remove and re-insert the device between treatments. A second limitation of the present IQM sensor is the reliance on a physical gradient in the volume of air, resulting in its current thickness of approximately 24.5 mm, excluding frame and electronics [5]. As a result, the sensor does not have the potential to be made thinner without sacrificing spatial sensitivity. A thinner chamber is desirable to accommodate non-coplanar treatment plans and other techniques where patient or couch collisions with the linear accelerator head are more likely with thicker accessories in the linear accelerator s accessory tray [27]. The limitations of the sensor in the IQM system can potentially be rectified by modifying the design of materials to become light transparent and compact. Investigation of this modification will be the primary subject for the proposed research. 2.5 Light Transparent Plates To make the IQM chamber light transparent, it is necessary to replace the aluminum plates used in the detector with a suitable electrically conductive light transparent material. A possible method of creating an electrically conductive light transparent material is to utilize a light transparent substrate for stability and mechanical strength and coating the substrate with a thin layer of conductive material. 12

23 2.5.1 Light Transparent Conductive Layer A metallic element or alloy can be made light transparent by maintaining a low thickness. This is a method that is utilized for creating light transparent but electrically conductive electrodes in solar panels and touch screens [28] [29]. For a number of electrically conductive materials such as fluorine doped tin oxide, it has been found that a layer thickness between nm yields a good compromise between electrical resistivity and good optical transmittance [30] [31] [32]. The method of producing such a conductive layer requires a manufacturing process such as chemical deposition, spray pyrolysis, or sputtering, all of which require a substrate material to help provide structural integrity [29] Substrate Material A thin conductive layer does not possess much mechanical strength and as a result, will require a substrate material to provide stability. Furthermore, the substrate material will need to be light transparent and should not attenuate nor diffract light passing through it significantly in order to satisfy the intended purpose of creating a light transparent ionization chamber. In addition, the material should be of low atomic number to minimize its effect on the radiation beam [23]. A possible substrate material is soda-lime glass. Soda-lime glass has a mass composition of 70.52% SiO2, 13.84% Na2I, 6.98% CaO, 5.89% MgO, 2.07% Al2O3, 0.66% K2O, and 0.04% Fe2O3 [33]. The glass has an effective atomic number of about 12-13, which is close to the atomic number of aluminum, a commonly used material for parallel plate ionization chambers and the current material used in the IQM detector [5] [23] [34] Commercially Available Light Transparent Conductive Plates A readily available light transparent glass plate with conductive coating material of fluorine doped tin oxide on soda-lime glass made by Pilkington Group Limited is available [35]. The glass plates are available in different sheet resistivities from 7 Ω/sq. to 15 Ω/sq. [35]. The product meets the requirements of being light transparent and conductive, and can be used for the creation of a light transparent prototype. 13

24 2.6 Virtual Gradient Ionization Chamber Islam et al. currently utilize two thick aluminum sheets to form a large area radiation detector. The aluminum sheets are placed at an angle in order to create a physical gradient, and a thinner design would lead to a reduced gradient with the consequence of lower spatial sensitivity. This limits how thin the chamber can be made while maintaining its current functionality. It has been proposed to investigate an alternative method of spatial encoding utilizing a virtual gradient pattern. The group has created a prototype ion chamber utilizing a novel interleaved pair of complimentary comb-patterned electrodes with progressively increasing/decreasing width tines on top of a printed circuit board to create a virtual gradient. The pattern is designed to detect spatial changes without the requirement of a physical gradient in the air volume. Furthermore, the pattern can be printed on both sides of a plate with a 90 rotation to provide error detection both along and perpendicular to the direction MLC leaf motion. The group ultimately wishes to print the design on a thin transparent substrate to increase spatial sensitivity. The current prototype has been shown to be functional using a PCB prototype (collector electrode shown in Figure 6) and methods of producing this pattern on a light transparent material have been investigated here and the performance of a chamber using this pattern has been studied as the focus of this report. Figure 6. Photo of virtual gradient pattern printed on a PCB. Pattern on PCB made of copper. Two interleaved collecting electrodes located in the centre of pattern. Surrounding border acts as guard electrode. 14

25 2.6.1 Pattern Description The pattern utilizes an interleaved pair of complimentary comb-patterned electrodes with progressively increasing/decreasing width tines created on top of a square insulator. The combs consist of parallel collection channels along the opposite ends of the plate, with tines perpendicular to the collection channels, which vary in width linearly along the intended gradient detection area. The two combs are positioned so that they mirror each other with the exception that their tine variation is inversely proportional. This means as the tine width increases with position for one comb, the tine width decreases on the second. The proportional increasing and decreasing of tine widths results in a constant width for each unit pair of tines (one tine and its immediately adjacent tine from opposite comb). Along the perimeter of the plate, is a guard rail used to isolate the collectors from any stray leakage current. Refer to Figure 7 below for a simplified example of pattern. Figure 7. Simple virtual gradient pattern. Comb 1 (blue) increases in tine width from top to bottom while comb 2 (yellow) decreases in tine width from top to bottom. Width of each tine pair remains constant throughout the pattern Dose Sensitivity The pattern is dose sensitive through the same mechanism as a standard air based ionization chamber. As radiation passes through the chamber, high energy electrons are generated and as a result, air particles become ionized and are collected. Each tine collects a signal proportional to 15

26 the mass of air directly between it and the polarizing electrode. Ultimately, the combined signal of the two measurements is directly proportional to the dose Spatial Sensitivity The spatial sensitivity of the pattern is achieved from the variations in the widths of the tine. The greater the width of the tine, the greater the area that is provided for the ions be collected by the conductive surface. Amount of collected ions depends on the number of ions created in the path of the electric field formed between the conductive surface of the tine and the polarizing electrode. With more surface area to gather charge, a greater current will be induced and as a result, a greater signal will be read at the electrometer. The two signals from each set of tines provide complimentary spatial information encoding. 16

27 3 Research Details This thesis focuses on addressing the two limitations of the current IQM sensor previously described, namely the lack of light transparency and chamber thickness. 3.1 Research Objectives The overarching objectives for this thesis are to address the limitations of the current IQM sensor. Namely, these limitations are: 1. Disruption of treatment and work flow due to lack of light transparency 2. Chamber thickness limiting patient treatment geometry selection due to collision risks The limitations will be addressed specifically by: 1. Investigating commercially available soda-lime glass with electrically conductive fluorine doped tin oxide layer for suitability in designing an ion chamber 2. Comparing characteristics of aluminum based ionization chamber design when aluminum substituted with fluorine doped tin oxide coated soda-lime glass 3. Investigating virtual gradient pattern to create thinner sensor while retaining spatial sensitivity 3.2 Thesis Statement It is possible to create a light transparent ionization sensor with similar performance characteristics as the sensor currently used in the IQM system by replacing the aluminum plates with available light transparent conductive glass plates. Furthermore, the transparent conductive plate can be designed to include a virtual gradient pattern to create a thinner ionization chamber. Together, these improvements would address two limitations of the current IQM sensor design. 17

28 4 Methods and Materials Three major stages were planned for this research project: 1. Investigation into light transparent electrically conductive glass plates. 2. Create AIMS prototype using light transparent plates and compare performance with existing AIMS prototype using aluminum plates. 3. Explore virtual gradient pattern performance when using the light transparent plates under investigation. 4.1 Exploration of Light Transparent Plates To address the lack of light transparency, light transparent glass plates with a thin conductive layer was investigated as a replacement material for the aluminum plates in the sensor design Electrically Conductive Light Transparent Glass Plate Electrically conductive light transparent glass plates are commercially available from various manufacturers. One such plate from Sigma-Aldrich uses a soda-lime glass substrate with a fluorine-doped tin oxide (FTO) conductive layer was chosen for this investigation for its low cost and availability. The following specifications are provided by the manufacturer: 30 x 30 x 0.2 cm 3 Conductive layer thickness of ~5000 Angstrom 80-82% light transmittance ~7 Ω/sq. The thickness of the glass plates were measured to be 2.2 mm with a micrometer caliper Electrical Connections Electrical connections with electronics are commonly made secure with solder. This method however does not work with the electrically conductive light transparent glass plates. Alternative methods of creating a connection were explored. 18

29 One such method employed clamps in order to provide a secure wire-to-glass connection. This method however introduced limitations in how closely spaced the glass plates can be positioned as well as caused noise due to insecure connections as the prototype was moved around. The instability caused the junction resistance to vary over 3 orders of magnitude, from 5 Ω to 10 kω, creating uncertainty in the measurements in the form of noise and variations in the signal observed over successive measurements. To improve the stability of the connection, 3M 9712 conductive adhesive tape was used to secure a brass shim to the conductive layer. The brass shim provided a suitable surface for soldering wire connections to the rest of the circuit. The resulting connection incurs an additional 10 Ω at the junction compared to simple clamping method (15 Ω total), but instability at the connection and in the signal is no longer observed Light Transparent Parallel Plate Ionization Chamber A basic parallel plate ionization chamber was created utilizing two FTO coated glass plates. To maintain constant plate separation, two blocks of extruded polystyrene foam were used to create supports. Each extruded polystyrene foam block had two parallel slots 2 mm width spaced 5 mm apart along the length of the block. The channels were created on complementary sides of the extruded polystyrene foam block at equal heights relative to the base of the extruded polystyrene foam block. This created a rail that accommodates the glass plates to form a simple parallel plate chamber. The choice of extruded polystyrene foam was made to facilitate quick testing due to the low cost and excellent insulating properties. A photo of the parallel plate ionization chamber prototype is shown in Figure 8. Figure 8. Basic parallel plate ionization chamber prototype created with FTO coated glass plates and extruded polystyrene foam blocks for support. 19

30 The working principle of this prototype is identical to that of a standard parallel plate ionization chamber. An illustration of how components are connected in this configuration is shown in Figure 9. Figure 9. Simple schematic diagram illustrating how measurement components are connected in the simple parallel plate configuration. A commercially available dosimeter, the Keithley MK614, was used as the electrometer to measure the charge collected from the prototype for a 1x1 cm 2 field given at various doses of 10, 20, 50, 100, 150, 200, and 250 MU. A small field size is required as the MK614 saturates at charge collection values higher than 200 nc Light Transparency Evaluation A primary objective of this research project is to enable the use of the light fields from linear accelerators while the sensor is in place. This light field geometrically simulates the shape of the radiation field and is utilized in patient and equipment positioning. As a result, the glass plates would be deemed unsuitable if they cause significant changes in light field edge or crosshair position. Two effects the glass plates had on light fields were identified, namely light intensity reduction and light refraction. 20

31 Light Intensity Reduction The glass plates are rated by the manufacturer to have a light transmission of 80-82%. To confirm this, the intensity of light was measured in terms of illuminance (lux) with and without glass plates on a Varian linear accelerator system. The Xi multimodality x-ray measurement system by RaySafe was used to perform this measurement with its light probe accessory. Measurements were done at Unit 1 in Princess Margaret Cancer Centre with all light sources within the treatment room turned off except the light field from the accelerator head and terminal monitors. Ambient conditions were measured at isocentre height, 1 m away along the treatment couch from light field s central axis. Light field measurements were performed at isocentre Light Refraction Glass refracts light when placed in a light beam s path. This is caused by the higher index of refraction, resulting in the light s path to be altered while in the glass. As a result, glass plates are expected to create changes in the shape or the location of linac light fields when placed in the beam path. The extent of these distortions or displacements were investigated in this section Simple Calculation The glass plate can be assumed to be perfectly flat on both sides. Making this assumption, it can be said that a narrow beam of light s (i.e. laser) angle of transmittance when it leaves the glass plate will be exactly the same as the angle of incidence when the beam enters the glass regardless of the orientation of the glass itself. There will however be a displacement in the beam caused by the beam s change in trajectory within the glass. Snell s law can be used to quantify this. Refer to Figure 10 for an illustration of displacement caused by refraction. 21

32 Figure 10. Illustration showing displacement as a result of light ray s modified path within glass medium. The shaded region indicates the presence of glass, while the green line shows the ray like path of light through the glass. Dashed lines indicate normal to the interface surface. Proof from Snell s Law is derived in Appendix A along with the following equation for displacement from a single glass plate with parallel surfaces. x = thickness glass (tan θ 1 tan (sin 1 [ n 1 n 2 sinθ 1 ])) Light Displacement Experiment Experiments were conducted to evaluate the accuracy of the theoretical calculations. Glass plate was angled until a millimetre displacement was observed and the angle measured. Calculations were then done to verify that the index of refraction is similar to the expected value. Materials and equipment used for the experiment were as follows: 1. Piece of conductive glass 2. Ruler 3. Protractor 22

33 4. Laser pointers a. Red laser (650 nm wavelength) b. Green laser (532 nm wavelength) 5. Clamps The experiment was conducted as follows: 1. Laser was aligned to a point of reference on ruler and held in place with clamps. 2. Glass was placed in path of light. 3. Glass was rotated until a millimetre displacement was observed on the ruler. 4. Angle of glass rotation required to achieve millimetre displacement was recorded. 5. Corresponding index of refraction was calculated. 6. Compare with expected results. Figure 11 shows an illustration of how experiment was setup. Figure 11. Illustration of experiment to confirm light refraction calculations Displacement Calculation for Two Plate Configuration The calculations can be expanded by adding the complexity of glass plates in various configurations. The parallel plate ionization chamber configuration is the simplest and is shown in Figure 12. More complex angled configurations are considered in Appendix B. 23

34 . Figure 12. Illustration of light ray passing through parallel plate configuration. With two parallel plates, the calculation is equivalent to having a single glass plate with an equal cumulative thickness (i.e. double the thickness of one glass plate). It is useful to understand at what cumulative thickness is required to generate a 1 mm deviation in light field edge position. Through rearrangement of the equation, it is possible to trivially find the maximum thickness of glass for 1 mm or less of deviation. thickness glass = x = thickness glass (tanθ 1 tan [sin 1 [ n 1 n 2 sinθ 1 ]]) x tanθ 1 tan [sin 1 [ n 1 n 2 sinθ 1 ]] Angle of incidence and index of refraction are not currently specified. Largest clinical field available on linacs is less than 40x40 cm 2. The light field is specified at isocentre or 100 cm from the radiation source. The light source is a standard light bulb (broad spectrum) and diode, located out of the path of radiation. A mirror is placed approximately 20 cm from the radiation source before the collimators to redirect the light from the light source through the collimators towards the machine s isocentre [36] [37]. Pythagorean Theorem can then be used to estimate the approximate angle that the light would intersect with the glass plates. This angle comes out to be approximately The index of refraction in soda-lime glass is approximately

35 thickness glass = = 14.3 mm 25 1 mm tan(11.3 ) tan [sin 1 [ (1.00) (1.52) sin(11.3 )]] Thus, to keep deviation of the light field s edge at 1 mm or less, a cumulative glass material thickness below 14 mm should be maintained. The current two glass design possesses a cumulative thickness of 4.4 mm, less than half thickness required for a 1 mm deviation. x = (4.4 mm) (tan(11.3 ) tan [sin 1 [ (1.00) (1.52) sin(11.3 )]]) = 0.31 mm Even with the largest field, the estimated displacement on field edges is less than half a millimetre Basic Overall Usability It is important to evaluate the overall impact of the glass plates on the usability of the light field. To accomplish this, eqa a commercially available light field and radiation congruence validation tool by Modus Medical was utilized to quantify the effect with and without a 2 plate ionization sensor in the path of the light field. Measurements of the light field congruence were performed on a Varian TrueBeam linac both with and without a chamber in place to assess the clinical impact of the system. Setup of eqa involves preparing a large radiation field (24 x 24 cm 2 ) and positioning the electronic portal imager so that it is able to capture the entire field. Markers were aligned to the corners and centre of the light field as shown in Figure 13. An image was then acquired by the electronic portal imager. Finally, eqa was used to determine the locations of the markers in relation to the edges of the radiation field, and hence determine the light field and radiation field s congruence. A criterion to judge the results are whether the addition of the sensor causes light-radiation field displacements above the tolerances allowed by QA procedures. QA procedures at Princess Margaret Cancer Centre specify a tolerance up to 1 mm for light-radiation field displacement. Little deviation is expected as the 24x24 cm 2 light field has an incidence angle of approximately 8.5, which is less than the incidence angle required for 1 mm deviations.

36 Figure 13. Image of eqa markers alone (left) and setup on a Varian linear accelerator (right). 4.2 Glass AIMS Prototype The commercially available FTO coated glass plates can be used to create an ionization chamber with the same geometry as the original IQM chamber. The glass plates replaced aluminum plates utilized in the current sensor design for the IQM system in an attempt to produce a light transparent light IQM sensor Frame Modification To simplify and accelerate prototyping, a spare aluminum AIMS prototype was modified such that it would hold glass plates instead of aluminum plates. Further, as the glass plates are only coated with conductive material on one side, the design was also modified to use only 2 plates rather than the original 3. The insulator surrounds the central electrode, this insulator also acts as a frame to keep the central electrode level. New insulators were required as the glass plate thicknesses measured 2.2 mm while the aluminum plates measure only 1.5 mm, a 0.7 mm difference. This necessitated the machining of new insulators with a channel that is at least 2.2 mm wide to accommodate the glass plates. An extra 0.1 mm was given in order to accommodate variations along the glass surface. Furthermore, efforts were made to maintain an identical spatial gradient (1-10) and as a result, the centre of the rail needed to be shifted down by 0.7 mm. Figure 14 shows the location 26

37 of the insulator within the prototype. Polarizing electrode is held is place with spacers and pressure from frame. Figure 14. Location of insulator to be modified (blue) in prototype. A second difference in the assembly of the glass AIMS is the method used to keep the polarizing electrode in place. Aluminum can be machined such that screws can be utilized to keep the aluminum plate on a spacer. With glass, this is not trivially possible and as a result, a separate spacer with rubber insulator was made into the frame to maintain separation of the plate and apply pressure so that the glass plate would stay in place Gradient Measurement The spatial sensitivity was compared between the two glass and aluminum AIMS systems in succession following identical procedures. A 6 MV 1x1 cm 2 radiation field was prepared on an Elekta linear accelerator and the centre of the chamber under investigation was placed at a source-to-surface distance (SSD) of 75 cm on the treatment couch. The treatment couch was then moved along the gradient directions and 100 MU was delivered for each measurement at 1 cm intervals from -10 cm to 10 cm. Measurements at each location were repeated twice to check for reproducibility Short Term Reproducibility of SBRT IMRT Treatment Field Short term reproducibility of the measurements and the ability to distinguish between segments in an IMRT field were tested using a sample stereotactic body radiation therapy (SBRT) IMRT plan. SBRT plans generally feature a small number of beam segments while delivering a higher dose for each segment. The sample field was acquired from a clinical treatment plan for the purpose of testing IQM system with approval from the Research Ethics Board. Figure 15 shows a diagram of the MLC jaw positions for the sample IMRT field. The treatment field was 27

38 measured three times with each sensor in the same session using the same Elekta linear accelerator, with signals corrected for temperature and pressure. Figure 15. Pictures showing MLC jaw positions of sample SBRT IMRT field. Each leaf in the linac has a width of 5 mm projected to isocentre Impact on Beam Intensity and Quality Placing an accessory in the path of a radiation beam will cause changes to the beam that reaches the patient. It is important to evaluate whether these changes will significantly impact clinical 28

39 treatment and if so, determine what actions are necessary to account for such changes in treatment delivery Beam Attenuation The radiation intensity is expected to decrease with the presence of material such as aluminum or glass in the path. Beam attenuation measurements were done with a NE2571A Farmer ionization chamber with a brass cap and the Advanced Therapy Dosimeter by Fluke Biomedical to sample the radiation dose on the central axis of radiation fields of various sizes from an Elekta linear accelerator. The Farmer ionization chamber was aligned to isocentre and measurements were taken with and without the aluminum and glass AIMS mounted in the accessory tray. Setup of the experiment is illustrated in Figure 16. Measurements were done for 5x5, 10x10, 20x20, and 30x30 cm 2 radiation fields at both 6 and 18 MV energies. Figure 16. Setup of beam attenuation measurement Beam Quality The radiation beam quality is expected to be affected by any device intercepting the beam, which can significantly impact the target dose and coverage. As a result, it is important to measure the effect and determine its significance for clinical treatments. This was done by measuring the percent depth dose (PDD) and crossline beam profile. These measurements were performed with 29

40 IBA Dosimetry s Blue Phantom 2 water phantom at 6 MV energy. Measurements were repeated with and without the respective sensors in the path of the beam to quantify the impact of the sensor. Figure 17 shows a photo of the measurement setup. Measurements were done at a surface-to-source distance (SSD) of 100 cm. Figure 17. Photo of IBA Dosimetry s Blue Phantom 2 setup for performing percent depth dose and crossline beam profile measurements. Percent depth dose measurements were done for 10x10 cm 2 and 30x30 cm 2 field sizes with profile measurements performed for the same field sizes at a depth of 1.5 cm and 10 cm. 4.3 Virtual Gradient AIMS Prototype The second major limitation outlined for the original AIMS design is the inherent reliance on the gradient in the chamber s thickness for spatial sensitivity. A pattern based prototype also utilizes principles from the parallel plate ionization chamber, but aims to remove the air volume reliant gradient by partitioning the surface of the collector electrode so that the spatial information is encoded through the pattern rather than through the air volume gradient. Partitioning the 30

41 collector electrode involves separating the active region into two distinct interleaved comb patterns with increasing/decreasing tine widths, creating a need for modifications to the measurement system as described in Section Measurement System Due to the partitioning of the collector electrode, two separate signals are collected compared to the single signal from the original AIMS. A consequence of this is that it is not possible to directly use the existing measurement system for the virtual gradient measurement system. Instead the system was replicated in a breadboard development system utilizing the same IC chip (ACF2101) featured in the IQM system used for measuring charge. Since it is based on the same design but with an additional measurement channel, the measurement system will be referred to as the dual channel IQM electrometer. The ACF 2101 is an IC part that is used for its dual integrators and ability to switch between its two integrators with minimal noise while maintaining low charge resolution. This allows the collection of large amounts of charge by switching between the two integrators. At a high level, each integrator collects charge to a capacitor, whose terminal voltage will be proportional to the amount of charge collected. The general operation of the integrators was as follows: 1. Collect and read charge from first integrator until the threshold value is reached 2. Once threshold value reached a. Begin collecting in second integrator b. Stop collecting from first integrator, but read and add final value to total 3. Once the final value from the first integrator has been recorded: a. Begin reading charge value from second integrator b. Reset first integrator 4. Continue collecting and reading charge from second integrator until the threshold value is reached 5. Repeat 2-4 but reverse first and second integrator 31

42 Two of these chips are used to collect charge, one for each channel. Individually, the operation of the integrators in the dual channel IQM electrometer are identical to their usage in the original IQM electrometer. The electrometer is controlled by the ATmega328 microcontroller featured inside an Arduino development board. The Arduino was utilized due to its ease of use and setup. Output voltage from the electrometer is measured by the onboard analog-digital-converter (ADC) with 10-bit resolution and stored as an integer value. When polled by software, the firmware responds with the current integer value. Further automation is enabled by Elekta s icom protocol, which signals the start and end of dose delivery. Figure 18 shows the flow of signal collection from the sensor to the PC software. Collect Signal ACF2101 Dual Integrator IC (Electrometer) Current Charge[0] icom Field Start/Stop Signal Virtual AIMS Arduino Processor (Controller) Read Signal Control Signals PC Software Collect Signal ACF2101 Dual Integrator IC (Electrometer) Current Charge[1] Figure 18. Flow of signal collection information with dual channel IQM electrometer. The calibration for ADC count reading to charge conversion was done by providing a constant current with a Keithley 6221 DC and AC current source through each electrometer channel individually for a predetermined amount of time. A calibration factor is then obtained by dividing the charge accumulated from the current source by the ADC counts. 32

43 Q = A t C = Q D Where Q = charge A = current t = time D = ADC count C = charge voltage calibration factor Current values used in the test were ranged between 1 na to 5 µa, and charge was accumulated for 60 seconds. These currents were chosen as small fields have been found to produce current on the order of nano-amperes while larger fields were found to be as large as several microamperes. The known current and time values provides an expected charge value while the ADC count reading is provided by the firmware. The calibration factor is then determined from the previously listed equation. This calibration factor was used to determine the charge from the ADC count reading reported here. Q = D C Glass Based Virtual Gradient Pattern Prototype (Virtual AIMS) The PCB prototype demonstrated that the virtual gradient pattern was capable of providing spatial sensitivity. A prototype utilizing FTO coated glass plates previously explored was created and tested to overcome both major limitations outlined for the original AIMS. These limitations were the lack of light transparency and the inherent reliance on air volume for spatial sensitivity. To keep spatial sensitivity at a similar level as the original AIMS design, a gradient of 1-10 was created in the pattern (i.e. tine width varies from 0.45 mm to mm). With the use of the gradient pattern, the total space required by the virtual AIMS not including the frame is 4.4 mm for the two glass plates and 5 mm for air, for a total of 9.4 mm. This compared with the aluminum AIMS design (4.5 mm for three plates and two 10 mm air 33

44 volumes) and glass AIMS design (4.4 mm for two plates, 10 mm air separation); and the total essential space for each prototype then becomes 9.4 mm, 14.4 mm, and 24.5 mm for the virtual AIMS, glass AIMS, and aluminum AIMS respectively. This results in 35% and 60% reduction of space compared to glass and aluminum AIMS respectively Manufacturing The current prototype was created from FTO coated glass plate purchased from Sigma-Aldrich Inc. The substrate is made from soda glass and FTO is sputtered on top to create a uniform conductive layer. To create the pattern, lines in the conductive layer are ablated using a UV laser to create the described pattern. Ablation was performed by KJ Laser Micromachining. The tine gap was largely determined by the type of laser used and the number of times the ablation pattern was repeated. The manufacturer has currently identified 3 types of lasers that can be utilized to create the pattern. The laser types are UV laser, fiber laser, and CO laser that provides an ablation width of 12.7 µm, 25.4 µm, and 127 µm respectively. The current prototype was created utilizing the UV laser and as a result, the width of the ablated lines were on average approximately 12.7 µm wide. The extruded polystyrene foam frame was replaced to increase geometrical stability and to allow the prototype to be attached to a mount so that it could be placed in the linac accessory tray. To prevent point loading the glass material when it is held in place with pressure, a spacer was used to maintain plate separation while wedges with a rubber channel to distribute the pressure were used to clamp the glass to the spacer. Threaded screws were used to apply pressure to the wedges. Figure 19 shows a photo of the frame with the glass. Figure 19. Photo showing frame to for parallel plate and virtual AIMS prototypes. Finally, the mount available from the modified glass AIMS was modified so that the virtual AIMS could be attached to the mount and thus be attached to an Elekta linac. The fully assembled prototype is shown in Figure

45 Figure 20. Photo of ionization chamber with virtual gradient pattern in its frame and Elekta mount Basic System Measurements A number of measurements were made using the Virtual AIMS and dual channel IQM electrometer to ensure that the overall measurement system behaves as expected. Measurements were made on an Elekta linear accelerator with the virtual AIMS mounted in the accessory tray of the linear accelerator. A NE2571A Farmer ion chamber was set up at isocentre for reference. First, the dose linearity of the chamber and measurement system was tested. A 6 MV 10x10 cm 2 field photon beam was delivered on an Elekta linac. Beams of 10, 50, 100, 200, and 400 MU were delivered Gradient Measurement The gradients of the Virtual AIMS were measured using a similar methodology as those used for the aluminum and glass AIMS. A 6 MV 1x1 cm 2 radiation field was prepared on an Elekta linear accelerator and the centre of the chamber was placed at a surface-to-source distance (SSD) of 75 cm on the treatment couch. The treatment couch was moved along the gradient and nongradient directions and 100 MU was delivered at 1 cm intervals from -10 cm to 10 cm Short Term Reproducibility of Sample IMRT Finally, the same treatment plan described in Section was used to test the reproducibility of the virtual AIMS. 35

46 5 Results The light transparent and electrically conductive plates were investigated on their functionality as an electrode in an ionization chamber and their impact on the light field from linear accelerators. The light transparent plates were then used to create a glass AIMS prototype, which had its spatial sensitivity and reproducibility compared to the existing aluminum AIMS prototype. Furthermore, the impact on beam attenuation and quality were also measured and compared to the original AIMS chamber. Finally, a virtual gradient pattern was ablated on a light transparent plate under investigation and the resulting electrode was used to create a virtual AIMS prototype. A new set of electronics was designed and prototyped to accommodate the dual channels of the virtual AIMS, and the measurement system and sensor were evaluated for dose linearity, dose rate dependence, gradient profile measurement, and short term reproducibility of SBRT IMRT fields. 5.1 Exploration of Light Transparent Plates Light transparent glass plates were used to create a parallel plate ionization chamber and tested for basic functionality. The effect of this chamber on light field properties such as light intensity attenuation and light field edge displacement was evaluated Light Transparent Parallel Plate Ionization Chamber The resulting measurements show a linear response with regards to dose delivered as shown in Figure

47 Charge Accumulated (nc) Dose Linearity Parallel Plate Ion Chamber Measured with Keithley MK y = x R² = Dose Delivered (MU) Figure 21. Graph of parallel plate ion chamber response to various doses measured with Keithley MK614 show high degree of linearity Light Intensity Reduction Light intensity reduction measurements were done to compare the light intensity of the light field with and without glass plates. All light sources in treatment room were turned off except light field and terminal monitors. Light field measurements were performed at isocentre while ambient measurements were performed at a distance 1 m away from the light field s central axis along the treatment coach surface. The results are presented in Table 1. Table 1. Summary of light intensity transmission measurements 80% light transmission per plate. Number of Glass Plates Lux % Transmission % Transmission per Plate Ambient 0.93 Average 80.1 The results of the experiment confirm that the manufacturer s rating is accurate. In the scope of our research, the result of most interest is that a 2 plate prototype would result in light transmissions of 65.3% - in other words, a 34.6% reduction in light intensity is expected from either prototype sensor. 37

48 Radiation Induced Discoloration Exposing glass to radiation can result in a discoloration known as radiation browning. This discoloration effect is caused by ionizing radiation exciting electrons sufficiently to displace them from their normal lattice position to electron traps in the material. The area missing an electron becomes a hole centre, which can absorb some light. This discoloration is partially reversible either over time, through temperature annealing, or exposure to light [33] [38]. This phenomenon was noted to occur in the sensor on July 15, 2015 after 58,000 MU of 6 MV and 58,000 MU of 18 MV radiation was delivered on a 35x35 cm 2 field size from an Elekta linac with the virtual AIMS mounted in the accessory tray. Including the measurements completed at the time of observation, approximately 368,000 MU and 71,000 MU of 6 MV and 18 MV radiation beam respectively (439,000 MU combined) were delivered to the virtual AIMS to that point. Measurements described in Section was repeated using the same machine and a single plate exhibiting radiation browning. Results are shown in Table 2. The new light transmission values of the plates are 73.7% per plate, a loss of 6.4% compared to new plates without discoloration. Combined in a 2 plate design, light transmission of 54.3% is expected. Table 2. Light intensity measurement with radiation discolored glass plate. Ambient No Glass 1 Glass 0.94 lux 25.5 lux 18.8 lux Light Displacement Experiment To confirm the calculations, the angle required for a 1 millimetre displacement was measured. Measured angle for millimetre displacement were: Table 3. Angles observed for 1 mm displacement. Displacement (Absolute Value) 1 mm (red 650 nm wavelength) 1 mm (green 532 nm wavelength) Angle (Absolute Value) 45 degrees 46 degrees 51 degrees 55 degrees Average 45.5 degrees 53 degrees The values of the average angles along with the 1 mm shift in the previously established calculations to find the approximate index of refraction for soda lime glass which should be approximately

49 n 1 sin θ n 2 = sin (tan 1 x [tan θ ]) thickness glass = (1.00) sin θ sin (tan 1 (1.00 mm) [tan θ (2.2 mm) ]) The refractive index calculated with the values were 1.5 and 1.2 for red and green light respectively. The calculated refractive index for red light is similar to the expected value Basic Overall Usability To check basic overall usability, eqa was used to evaluate the change in deviation of light and radiation field caused by the presence of a 2 glass plate sensor. The QA results in Table 4 show a less than 1 mm difference when performed by a technician on a Varian linac with and without the sensor in the beam path. In both situations, the QA tolerance within 1 mm was met. Table 4. Results of eqa measurement on Varian linear accelerator with and without 2 glass plate prototype in linear accelerator accessory tray. Light/Radiation Displacement (cm) With Without Varian X Varian X Varian Y Varian Y

50 5.2 Glass AIMS Prototype Data is readily available within the research team for the aluminum AIMS. This data was collected and provided by Makan Farrokhkish and Jongho A. Jung. New measurements were made on the glass AIMS and compared with those from the aluminum AIMS. Figure 22. Photo of glass AIMS and an aluminum AIMS side by side Gradient Measurement Figure 23 show the gradient profile of the aluminum AIMS and glass AIMS. It can be seen that there is a drop off in the gradient at approximately +6 cm. This can be attributed to transmission through the MLC falling outside the active region of the chamber. The effect is more prominent on the positive gradient side as transmission on the thinner side would be result in a much smaller signal. A second observation is the noisier signal profile on the glass AIMS. This is expected due to the loss of the second polarizing plate in the sensor design, which effectively 40

51 Relative Reading (Normalized to Central) reduced the air volume used for measurement by half. This results in a reduction of signal and consequently, a small signal to noise ratio is expected. Direct signal magnitude comparison is made in Section Aluminum and Glass AIMS Gradient Profile 1x1 Radiation Field Aluminum AIMS Glass AIMS Location from Centre (cm) Figure 23. Aluminum and Glass AIMS chamber gradient profile measuring 6 MV 1x1 cm 2 radiation field from Elekta linear accelerator. Figure 24 show just the linear regions of the gradient profile for the aluminum and glass AIMS. Both of the linear regions can be closely matched to a linear equation with R 2 greater than However, a reduction in spatial sensitivity was observed in the glass AIMS. The aluminum AIMS has a gradient between and 1.29 over a 16 cm linear region resulting in a ratio of The glass AIMS has a gradient between and 1.26 over the same 16 cm linear region resulting in a ratio of 2.31 a 12.8% reduction in gradient. 41

52 Relative Reading (Normalized to Central) Glass AIMS Gradient Profile 1x1 Radiation Field - Linear Region Aluminum AIMS y = x R² = min: max: Aluminum AIMS Glass AIMS Linear (Aluminum AIMS) Glass AIMS 0 y = x R² = Location from Centre (cm) min: max: Linear (Glass AIMS) Figure 24. Aluminum AIMS chamber gradient profile measuring 6 MV 1x1 cm 2 radiation field from Elekta linear accelerator. Only linear region is shown Short Term Reproducibility of Sample SBRT IMRT Plan Comparison of the reproducibility between the two systems is shown in Table 5. For all field segments, the measured signal from the glass AIMS is about 60% of the signal measured from the aluminum AIMS, as expected from the ratio of chamber volumes. Table 5. Comparison of reproducibility of A-AIMS and G-AIMS for sample SBRT IMRT treatment field. A-AIMS G-AIMS Segment AVG (nc) % STDEV AVG (nc) % STDEV Average

53 5.2.3 Impact on Beam Intensity and Quality Beam attenuation and beam quality effects were measured Beam Attenuation Table 6 shows the results of the beam attenuation measurements. The average attenuation values for the glass AIMS was lower at 4.39% and 2.92% for 6 and 18 MV energies respectively compared to 5.42% and 3.75% attenuations by the aluminum AIMS for the same energy. Table 6. Results of beam attenuation measurement using NE2571A Farmer ionization chamber and Advanced Therapy Dosimeter. Measurements show beam attenuation by glass and aluminum AIMS. 6 MV Readings (nc) Transmission Attenuation Field Size (cm 2 ) Ref. G-AIMS A-AIMS Ref. G-AIMS A-AIMS Ref. G-AIMS A-AIMS 5x x x x Average MV Readings (nc) Transmission Attenuation Field Size (cm 2 ) Ref. G-AIMS A-AIMS Ref. G-AIMS A-AIMS Ref. G-AIMS A-AIMS 5x x x x Average Beam Quality Percent depth dose (PDD) results are shown in Figure 25 to Figure 28. Difference between measurements with and without sensor are shown in Figure 29 and Figure 30 for 10x10 cm 2 field. No significant difference was observed between the percent depth dose measurements for the 30x30 cm 2 field size. 43

54 Relative Dose [%] (Normalized to 15 mm) Relative Dose [%] (Normalized to 15 mm) A-AIMS PDD 6 MV, 10x10 cm 2, SSD 100 cm Without A-AIMS With A-AIMS Depth (mm) Figure 25. Percent depth dose measurements with and without aluminum AIMS at 6 MV beam energy with 10x10 cm 2 field. 120 A-AIMS PDD 6 MV, 30x30 cm 2, SSD 100 cm Without A-AIMS With A-AIMS Depth (mm) Figure 26. Percent depth dose measurements with and without aluminum AIMS at 6 MV beam energy with 30x30 cm 2 field. 44

55 Relative Dose [%] (Normalized to 15 mm) Relative Dose [%] (Normalized to 15 mm) G-AIMS PDD 6 MV, 10x10 cm 2, SSD 100 cm Without G-AIMS With G-AIMS Depth (mm) Figure 27. Percent depth dose measurements with and without glass AIMS at 6 MV beam energy with 10x10 cm 2 field. 120 G-AIMS PDD 6 MV 30x30 cm 2, SSD 100 cm Without G-AIMS With G-AIMS Depth (mm) Figure 28. Percent depth dose measurements with and without glass AIMS at 6 MV beam energy with 30x30 cm 2 field. 45

56 Relative Difference [%] (Normalized to 15 mm) Relative Difference [%] (Normalized to 15 mm) A-AIMS PDD Difference 6 MV, 10x10 cm 2, SSD 100 cm Depth (mm) Figure 29. Difference between percent depth dose measurements with and without aluminum AIMS at 6 MV beam energy with 10x10 cm 2 field. G-AIMS PDD Difference 6 MV, 10x10 cm 2, SSD 100 cm Depth (mm) Figure 30. Difference between percent depth dose measurements with and without glass AIMS at 6 MV beam energy with 10x10 cm 2 field. Crossline beam profiles measurements for the aluminum AIMS are shown in Figure 31 to Figure

57 Figure 31. Crossline beam profile measured at 1.5 cm depth by Blue Phantom with and without A-AIMS at 6 MV energy. Figure 32. Crossline beam profile measured at 5 cm depth by Blue Phantom with and without A-AIMS at 6 MV energy. 47

58 Figure 33. Crossline beam profile measured at 10 cm depth by Blue Phantom with and without A-AIMS at 6 MV energy. Figure 34. Crossline beam profile measured at 20 cm depth by Blue Phantom with and without A-AIMS at 6 MV energy. Crossline beam profiles measurements for the glass AIMS are shown in Figure 35 to Figure

59 Figure 35. Crossline beam profile measured at 1.5 cm depth by Blue Phantom 2 with and without G-AIMS at 6 MV energy. Figure 36. Crossline beam profile measured at 5 cm depth by Blue Phantom 2 with and without G-AIMS at 6 MV energy. 49

60 Figure 37. Crossline beam profile measured at 10 cm depth by Blue Phantom 2 with and without G-AIMS at 6 MV energy. Figure 38. Crossline beam profile measured at 20 cm depth by Blue Phantom 2 with and without G-AIMS at 6 MV energy. 50

61 Slight differences can be seen in the crossline profile at the horns for both aluminum (approximately 2%) and glass AIMS (approximately 1%) at 1.5 cm depths. It can however be seen that the difference caused by the aluminum AIMS is larger than the glass AIMS. 5.3 Virtual Gradient AIMS Prototype The virtual AIMS prototype was measured using the dual channel electronics system for dose linearity, spatial sensitivity, and reproducibility of a sample SBRT IMRT treatment field Basic System Measurements Linearity measurements for a fixed field size and different output settings are given in Table 7 and plotted in Figure 39. The results show linearity within the resolution of measurements with no significant deviation from linearity. Table 7. Linearity measurement results using Virtual AIMS and dual channel IQM electrometer to measure 6 MV 10x10 cm 2 fields from Elekta linear accelerator. Channel A Dose (MU) Measure 1 Measure 2 Measure 3 Average % STDEV Channel B Dose (MU) Measure 1 Measure 2 Measure 3 Average % STDEV NE2571A Dose (MU) Measure 1 Measure 2 Measure 3 Average % STDEV

62 Relative Reading (Normalized to 100MU) Dose Linearity Measurement Channel A y = x R² = 1 NE2571A Farmer y = 0.01x R² = 1 Channel B y = 0.01x R² = Dose Delivered (MU) Channel A Channel B NE2571A Farmer Linear (Channel A) Linear (Channel B) Linear (NE2571A Farmer) Figure 39. Dose linearity of Virtual AIMS with dual channel electrometer with reference measurements using NE2571A Farmer ion chamber. 10x10 cm 2 field delivered with 6 MV beam energy. Results normalized to values at 100 MU. Similarly, the system was tested for linearity when 100 MU of 6 MV was delivered from an Elekta linac at different field sizes. The results seen in Figure 40 show that the readings in both channels could be accurately predicted with a quadratic equation, which is expected as the increase in area is quadratic. The increase in signal not purely quadratic due to contributions from the beam profile details such as MLC transmission, collimator specific arrangements, and variations of beam fluence at different field sizes. 52

63 Relative Readings (Normalized to 10x10) Signal as A Function of Side of Square Field Virtual AIMS y = x x y = 0.003x x Length of Square Field (cm) Channel A Channel B Poly. (Channel A) Poly. (Channel B) Figure 40. Area of fluence measurement for Virtual AIMS and dual channel IQM electrometer. 100 MU delivered with 6 MV beam energy. Dose rate dependency was tested to ensure no significant deviations would occur as dose rates changed. Figure 41 shows the raw dose rate dependency measurements. No significant dose rate dependency was measured, minor fluctuations were observed but were consistent with reference measurements. 53

64 Figure 41. Dose rate dependency measurement for the virtual AIMS and dual IQM electrometer with reference measurements from NE2571A Farmer ion chamber. 10x10 cm 2 field delivered with 6 MV energy Gradient Measurements The non-gradient chamber profile is shown in Figure 42. It is noted that the non-gradient profile is relatively constant with a loss of signal at either end due to contributions from MLC transmission falling outside the active region of the detector. Figure 43 shows the chamber s gradient profile while Figure 44 shows only the linear region of the chamber s gradient profile. Both linear regions are shown to have a R 2 value greater than or equal to Furthermore, the gradient profile moves from values of and to 1.26 and 1.28 relative to the central measurement resulting in gradients of 2.60 and These gradients are higher than the glass AIMS and comparable to the aluminum AIMS. 54

65 Accumulated Charge (Normalized to Central) Accumulated Charge (Normalized to Central) Non-Gradient Profile for Virtual AIMS 1x1 Radiation Field Channel A Channel B Location from Centre of Chamber (cm) Figure 42. Non-gradient chamber profile of Virtual AIMS measured with 6 MV 1x1 cm 2 radiation field from an Elekta linear accelerator. Gradient Profile for Virtual AIMS 1x1 Radiation Field Channel A Channel B Location from Centre of Chamber (cm) Figure 43. Gradient chamber profile of Virtual AIMS measured with 6 MV 1x1 cm 2 radiation field from an Elekta linear accelerator. 55

66 Accumulated Charge (Normalized to Central) Virtual AIMS Gradient Profile 1x1 Radiation Field - Linear Region y = x R² = 0.99 min: (-10, ) max: (6, ) y = x R² = min: (-6, ) max: (10, ) Location from Centre of Chamber (cm) Channel A Channel B Linear (Channel A) Linear (Channel B) Figure 44. Gradient chamber profile of Virtual AIMS measured with 6 MV 1x1 cm 2 radiation field from an Elekta linear accelerator. Only linear region shown Short Term Reproducibility of Sample SBRT IMRT Plans Short term reproducibility results are shown in Table 8. The percent deviation is lower on channel B compared to channel A, the opposite is true for signal magnitude with signal magnitude of channel B being higher than channel A. Table 8. Comparison of reproducibility between A-AIMS, G-AIMS, and V-AIMS for sample SBRT IMRT plan. A-AIMS G-AIMS V-AIMS (A) V-AIMS (B) Segment AVG (nc) % STDEV AVG (nc) % STDEV AVG (nc) % STDEV AVG (nc) % STDEV Average

67 6 Unanticipated Challenges A few unanticipated challenges were identified during the course of the research project. Some of the challenges are largely theoretical, but others such as humidity proportional leakage currents have been observed and briefly investigated with experimental results. 6.1 Theoretical Challenges of Virtual Gradient Pattern A number of factors that can introduce inaccuracies in measurements with the virtual gradient pattern were identified. First is a signal oscillation that could occur along the gradient profile, and second is channel crosstalk currents that could potentially cause a loss of signal in one channel and an increase of signal in the complementary channel. These challenges have not been fully studied and is an area for further investigation Signal Oscillation The virtual gradient pattern s spatial sensitivity functions by dividing the charges resulting for a radiation beam between the two combs. The tines of the two combs varies inversely with each other. As such, when the same radiation beam is moved along the pattern, the proportion of charge collected from either electrode would change. As such, when a perfectly square field with an ideal uniform intensity distribution is moved and measured across the active measurement region, the expected gradient profile is a series of step functions as shown in Figure 45 (simplified) and Figure 46 (current prototype pattern). 57

68 Figure 45. Perfect rectangular field scanning across pattern (left). Expected gradient profile (right). The block step function illustrates the generation of a uniform ionization density in a portion of the chamber, while the different colours illustrate the partitioning of the charge between the complementary combs Rectangular Beam - Simulated Gradient Profile Charge Carrier Generation Region = Tine Pair Width Location from Centre of Chamber (cm) Channel A Channel B Figure 46. Simulated gradient profile when measured with a square beam that creates a charge carrier generation region of equal size to the tine pair width of a virtual gradient pattern. 58

69 However, due to the non-ideal distribution of charge carrier generation regions (which are proportional in to the beam size) created from the ionizing radiation beam passing through the polarizing plate, an oscillation of signal may occur when the ions are collected by the pattern. In some situations, the oscillation may be large enough that an aliasing of location occurs. This creates an issue in determining the location of a field as it is possible for the field signal to be associated with a range of locations. Figure 47 illustrates a situation where signal oscillation occurs. Note that the gradient profiles are no longer monotonic. Figure 47. Non-ideal beam with Gaussian ion space charge distribution scanning across pattern (left). Expected gradient profile (right). Each illustration in left figure corresponds to a local maximum/minimum in the channels. Simulations suggest that the amount of oscillation is related to ratio between the size of the beam and the width of a unit pair of tines. An example of a simulated gradient measurement where charge carrier generation region is equal to the tine pair width is seen in Figure

70 Relative Signal (Normalized to Central) 2 Signal Oscillation - Simulated Gradient Profile Charge Carrier Generation Region= Tine Pair Width Location from Centre of Chamber (cm) Channel A Channel B Figure 48. Expected signal oscillation in gradient when measured with beam that creates a charge carrier generation region that equals the tine pair width of virtual gradient pattern. Figure courtesy of Dr. Robert Heaton. Simulations increasing the charge carrier generation region showed that once the charge carrier generation region has been increased to twice the width of the tine pair, signal oscillations become undetectable. This suggests that there is a limitation on the maximum tine pair width that can be used without introducing uncertainties in measurements. 60

71 Relative Signal (Normalized to Central) 2 Signal Oscillation - Simulated Gradient Profile Charge Carrier Generation Region = 2 *Tine Pair Width Location from Centre of Chamer (cm) Channel A Channel B Figure 49. Expected signal oscillation in gradient when measured with beam that creates a charge carrier generation region that equals twice the tine pair width of a virtual gradient pattern. Figure courtesy of Dr. Robert Heaton Pattern Crosstalk In ideal operation, two separate combs would collect signal separately and act as two completely separate circuits. A schematic of ideal operation is shown in Figure 50. Figure 50. Schematic of ideal charge collection circuit for the virtual gradient pattern system. In reality, the two circuits are not completely separate and there is a non-infinite resistive connection between the two combs in addition to a resistance from each comb to the guard rail. 61

72 These resistances create the possibility of crosstalk current and current loss. Furthermore, each electrometer input is a virtual ground that could potentially be held at different voltage potentials, causing a potential difference across the two combs and thus crosstalk current. Figure 51 shows a schematic of the non-ideal charge collection circuit. Figure 51. Schematic of non-ideal charge collection circuit for the virtual gradient pattern system. The loss resistance (comb to ground) is very large and is has a comparatively short contact length compared to the crosstalk resistance. This is due to the pattern used by the virtual gradient ion chamber, which has two separate combs divided by a zigzagging non-conductive line that runs along the entire pattern. For the current virtual AIMS prototype, there are 52 tine pairs (104 in total) that span a 25 cm length along a 26 cm active region. length border = (number tine 1) length tine + length active = (104 1) (25 cm) + (26 cm) = 2601 cm = m Furthermore, this bordering line is required to be very small to ensure that the pattern s gradient is correct and to minimize the electric field distortion arising from non-conducting areas of the electrode. A UV laser was utilized to produce ablations that were on average approximately 12.7 µm wide. This long and thin line creates a possible issue where resistivity between the two combs are reduced to such a degree that signals will leak from one comb onto a second. In combination with water vapour in the air under conditions of high humidity, significant crosstalk current can result. 62

73 6.2 Humidity and Leakage During spring and summer months, a large amount of leakage was observed. Leakage in this case was seen as the continued accumulation of charge signal in the two measurement channels during the time the linac was not delivering radiation. This additional signal is noise and in severe cases, can mask the true signal during treatment delivery. It was that observed the leakage correlates with ambient humidity levels. It is known that humidity has an influence on the signal of ionization chambers that utilize free air [26] [39]. To test the influence of humidity on both the original AIMS and virtual gradient pattern based designs, the glass AIMS and virtual AIMS were subjected to a range of humidity levels while monitoring the leakage levels. A small room was closed off and a consumer humidifier by Sunbeam was utilized to artificially increase the humidity in the room. Once the relative humidity of the room had been sufficiently increased the humidifier was removed, and a dehumidifier by UBERHAUS (MDK-40AEN1-BA9) was used to gradually reduce the humidity. Measurements of leakage at relative humidity levels of 70%, 60%, 50%, and 40% were performed. The prototype ionization chambers were then placed in the room and the leakage was measured 45 minutes after humidity levels settled. A barometric pressure, humidity, and temperature data logger by EXTECH (SD700) was used to determine the relative humidity in the vicinity of the ionization chambers. Figure 52 shows the setup of the experiment. Note that the dehumidifier was unable to reduce the relative humidity levels of the room below 49.9% at the time of experiment. 63

74 Figure 52. Photo showing humidity-leakage measurement experiment setup. The results in Table 9, Figure 53, and Figure 54 show that a correlation between humidity levels and leakage. It can be noted that the leakage increases linearly with humidity in the glass AIMS, but the increase in the virtual AIMS is closer to a quadratic. Furthermore, leakage only occurs in a single channel while the other is close to 0. The zero value leakage is the result of the inability of the measurement system to detect negative charge values. Table 9. Leakage at various humidity levels. RH (%) V-AIMS A [na] V-AIMS B [na] V-AIMS (A+B) [na] G-AIMS [na]

75 Leakage (na) Leakage (na) Leakage vs Relative Humidity G-AIMS y = 0.036x R² = Relative Humidity Figure 53. Linear correlation observed between leakage current and humidity for glass AIMS prototype Leakage vs Relative Humidity V-AIMS y = x x R² = Relative Humidity Figure 54. Quadratic correlation observed between leakage current and humidity for virtual AIMS prototype. 65

76 7 Discussion The fluorine-doped tin oxide (FTO) coated glass has been shown to be a potential replacement for aluminum plates to achieve the objective of light transparency. However, most commercially available glass plates are only coated on one side of the glass and as a result required changing the original AIMS design from 3 plates to 2 plates. The resulting glass AIMS prototype has still shown good characteristics with regards to spatial sensitivity; however, signal to noise ratio was expectedly reduced as expected, due to a smaller collection volume. On the other hand, the virtual AIMS prototype demonstrated good spatial sensitivity with a gradient on both electrodes comparable with that of the aluminum AIMS and surpassing that of the glass AIMS. The results are encouraging as it shows the potential to separate spatial sensitivity and chamber thickness. Finally, a number of limitations were identified that affects the effectiveness of the light transparent ionization chambers. Amongst them are limitations that results in additional noise levels such as leakage, crosstalk, and inherent signal oscillations. Additionally, the discoloration caused by radiation in the glass plates also results in a reduction in light transmission and is another limitation that should be considered. 7.1 Light Transparent Glass Plate The FTO coated glass plates were found to be excellent for the purpose of introducing light transparency. The light field was not significantly displaced between from the radiation field and current light attenuation levels does not impact usability, as demonstrated by standard light field-radiation field congruence tests with eqa generating virtually identical results with and without the prototype parallel plate ionization chamber in the pathway. Finally, the FTO coated glass plates were shown to function as electrodes in a parallel plate ionization chamber as the prototype created utilizing the glass plates demonstrated expected dose linearity behaviour of a parallel plate ionization chamber. 66

77 7.2 Glass AIMS Prototype Results from glass AIMS prototypes showed that though still functional in providing spatial sensitivity, the glass AIMS prototype s performance did not achieve the same performance as the aluminum AIMS. The discrepancies in performance are hypothesized to be largely caused by the change in design from 3 plates to 2 plates, which resulted in a lower signal-to-noise ratio. The lower signal-to-noise ratio has potentially caused a number of issues such as lower reproducibility when monitoring sample treatment fields and a reduced gradient leading to a lower spatial sensitivity. Further work to verify the hypothesis can be done by creating a 3 plate glass AIMS, which would require the purchase or creation of a light transparent glass plate with conductive coating on both sides. Alternatively, the hypothesis can be investigated by increasing the separation of the 2 plate design. On the other hand, a smaller effect on the beam quality and lower beam attenuation was observed with the 2 plate design of the glass AIMS compared to the 3 plate design of the aluminum AIMS. This is an expected improvement due to the reduction in overall material thickness and slightly lower density of glass compared to aluminum. 7.3 Virtual Gradient AIMS Prototype The virtual AIMS prototype demonstrated spatial sensitivity with gradients of 2.6 and 2.8 on its two channels in the linear region. In comparison, the aluminum AIMS had a gradient of 2.65 and the glass AIMS a gradient of The comparison shows that the virtual gradient is capable of producing a spatial sensitivity that is on par or greater than the spatial sensitivity in the current AIMS design. It is encouraging to see that a light transparent prototype has been created that has spatial sensitivity separated from the chamber thickness. When tested with a sample field from SBRT IMRT treatment plan, the reproducibility of the two channels on the virtual AIMS was significantly different. While channel B had an overall reproducibility that compared favourably to the glass AIMS but was inferior to the aluminum AIMS, the reproducibility of channel A was inferior to the glass AIMS. This was sensible as the signals collected by channel A were much lower than channel B (e.g nc vs nc for Segment 67

78 1) in the fields tested, which resulted in a lower signal to noise ratio. Due to the lower signal to noise ratio, the higher deviations observed were expected. Further work on the virtual gradient pattern experiments would include optimization and finding the maximum spatial sensitivity possible with available resources (financial and technological). 7.4 Limitations A number of limitations with the prototypes were identified during the course of this research project. A few of the limitations identified resulted in a reduced signal to noise ratio due to increased noise. These limitations are humidity induced leakage currents, crosstalk currents, and signal oscillation. The latter two of which only affect the virtual AIMS prototype while humidity induced leakage currents affect all prototypes. Another limitation identified is radiation induced discoloration on the transparent glass. The discoloration results in reduced light transmission and as a result, further reduces the light intensity of light fields that pass through the light transparent prototypes Radiation Induced Discoloration Radiation induced discoloration was observed in the virtual AIMS prototype after a large amount of radiation dose was delivered (approximately 439,000 MU) over the course of 13 months. The discoloration results from electrons being excited by the additional energy and moving away from its original position. The defect left behind absorbs light and thus reduces the amount of light that passes through. This further reduction in light intensity would reduce the usability of the light field. On the other hand, the glass plates can be restored to a more suitable state by reducing the discoloration through exposing the glass plate to elevated temperatures, large amounts of light, and even to some degree by passing current through the substrate [33] [38]. However, this creates a requirement to perform routine maintenance on the device. Other glass substrates could be investigated to find one more resistant to radiation. 68

79 7.4.2 Signal Oscillation Inherent within Virtual Gradient Pattern Signal oscillations are a concern as it is possible for a beam at two different locations to generate the same signal, decreasing error detection sensitivity. Simulations have shown that for a beam size that is twice the size of the width of tine pairs within the pattern there should be no observable oscillations. As a result, a limitation exists for the maximum width tine pairs can be made and as a result. Only a preliminary investigation into whether signal oscillations can actually be observed in the virtual gradient chamber have been conducted in this study. More detailed calculations coupled with measurements are required to aid in future design work Inherent Risk of Crosstalk Connection in the current design risks the connection of two virtual ground points in the circuitry as there is a possibility for a potential difference to exist between the two virtual grounds. Issues arising from the potential difference would be noise and addition/loss of signal between the two channels. Due to the thin lines of separation, dust particle creating a short is another concern. This should be considered and the thickness of the separation line should be made thicker than dust particles. Exploring methods of increasing resistance between the two combs is an area of future study that would help reduce the noise due to crosstalk. A possible solution is to fill in the areas ablated by the laser with an insulating material, which would increase resistance between the two combs while also minimizing the chance for dirt particles to bridge the two electrodes together. However, the process would be time consuming and expensive Humidity and Leakage Humidity induced leakage was observed to be significant. In many ionization chambers, humidity is known to change the response of the chamber, but the unique designs of the prototypes under investigation makes them susceptible to not only a change in signal, but also leakage current even without radiation. In the original AIMS design, the 1 mm separation on the thin side of the chamber creates a very strong electric field that could conduct current with high humidity levels due to the increase concentration of water molecules in the air. Leakage was 69

80 observed to increase linearly with humidity levels in the aluminum and glass AIMS prototypes. Similarly, for the virtual gradient pattern high humidity levels can also cause leakage current to flow across the air volume. However, it is observed that the leakage current does not increase linearly with humidity on the virtual AIMS prototype. A possible cause is that high humidity and water molecule concentrations reduces the electrical resistance of the air in the thin border between the two combs. This directly reduces resistance between the two combs resulting in additional crosstalk current. The combination of the leakage and crosstalk currents would create the quadratic relationship with humidity levels observed from the results. A solution to prevent leakage and crosstalk caused by humidity is to create an air seal in the final prototype which would minimize water moisture from entering the chamber and would allow the sensor to function despite humidity levels. 70

81 8 Conclusions The goals of this research project were to address the two limitations of the original AIMS design utilized in the IQM system. These were: 1. Lack of light transparency 2. Overall chamber thickness The first limitation was addressed. Light transparency was introduced into the area integrating fluence monitoring sensor (AIMS) used in the Integral Quality Monitoring (IQM) system. FTO coated glass has good light transparent characteristics and can be used to create a functional ionization chamber for real-time dosimetric purposes during radiation therapy. The impact of the glass on light fields is negligible (1 mm or less deviation for 40x40 cm 2 field) up to a cumulative material thickness of 1.0 cm. Similarly, the glass AIMS utilizing the glass had no significant impact on the beam quality when placed in the path of a treatment beam aside from a 4.39% and 2.92% beam attenuation for 6 MV and 18 MV beam energies respectively. This compares favourably with the aluminum AIMS where beam attenuations of 5.42% and 3.75% were observed for 6 MV and 18 MV beam energies. This expected result came from the fact that a reduction in materials were used to create the glass AIMS. This reduction in material however also reduced the signal to noise ratio of the glass AIMS compared with the aluminum AIMS as the air volume was reduced by half. A possible consequence was the observed reduction in spatial sensitivity with the glass AIMS having a gradient of only 2.31 in the linear region, down 12.8% compared to the aluminum AIMS, which has a gradient of A future iteration of the glass AIMS prototype should aim to use a 3 plate design or increase physical separation to improve the signal to noise ratio. The second limitation was partially addressed. Spatial sensitivity can now be obtained without directly modifying the thickness of the ionization chamber. This was accomplished utilizing a novel pattern ablated from the conductive FTO layer of the glass material. The pattern is shown to be able to provide spatial sensitivity gradients of 2.79 and 2.60 for channel A and B respectively. The gradients compare favourably to the two AIMS design prototypes and suggests a similar level of spatial sensitivity was achieved as intended (all prototypes were designed with a gradient of 1-10). Furthermore, a thickness reduction of 35% was achieved as the virtual 71

82 AIMS only had an essential thickness (not including frame and electronics) of 9.4 mm while the glass AIMS requires 14.4 mm. On the other hand a number of limitations within the novel pattern needs to be further investigated and addressed to conclusively determine its viability in replacing the current sensor design. A minor objective was also accomplished: a measurement system was created to measure the dual signals from the virtual gradient pattern. This objective was accomplished by replicating the measurement system of the IQM system on breadboard but modified such that the input pathways were doubled to accommodate the dual channel nature of the virtual gradient pattern. 8.1 Future Work A limitation of soda-lime glass is the discoloration presented after large doses of radiation delivery that creates a need to either replace the electrodes overtime or increase the intensity of the light source. Finding a threshold attenuation value where a significant impact on the usability of the light field can be done in future works. The result can be utilized to predict the expected frequency that electrodes need to be replaced. Alternatively, exploration into radiation resistive light transparent materials would be of interest to mitigate this limitation. The reduced signal-to-noise ratio of the glass AIMS has been associated with a reduction in spatial sensitivity. Future work to improve the signal-to-noise ratio of the glass AIMS would involve purchasing or creating a light transparent glass plate with two conductive sides. This would allow the implementation of the original 3 plate design, doubling the air volume in the sensor and increasing the signal-to-noise ratio. A more direct comparison of materials could be made and a greater understanding of the suitability of the light transparent conductive glass materials as direct drop in replacement for aluminum. An alternative method of investigation involves doubling the air volume by simply doubling the separation of the 2 plates. Two limitations were identified in the virtual gradient pattern. These were an inherent risk of crosstalk and signal oscillations. Further exploration of signal oscillation including experimental confirmation and optimization in design could be a potential future research project. Reduction of crosstalk could be explored with possible manufacturing changes or modifications to the measurement circuit. 72

83 Finally, humidity has been identified as another limitation in the devices. With increased humidity, noise in the form of undesired leakage currents become significant and reduces accuracy of measurements. Future work can involve exploring ways to modify the chamber s frame such that an air seal is created to prevent water vapours as well as dust particles from entering the chamber. 73

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88 10 Appendix A Calculation for Displacement from Single Glass Plate Figure 10 demonstrates that if the two surfaces are parallel, the angles at the interface in the same material are the same. It is possible to show this using Snell s Law. Where n i sin θ i = n o sin θ o Snell s Law n i = index of refraction first material n o = index of refraction second material θ i = angle of entry θ o = angle of exit Rearranging Snell s Law for each surface where the light would be refracted, θ 2 = sin 1 [ n 1 n 2 sinθ 1 ] Equation 1 θ 3 = sin 1 [ n 2 n 3 sinθ 2 ] Equation 2 Substituting equation 1 into equation 2 results in: θ 3 = sin 1 [ n 2 n 3 sin (sin 1 { n 1 n 2 sinθ 1 })] = sin 1 [ n 2 n 3 n 1 n 2 sinθ 1 ] = sin 1 [ n 1 n 3 sinθ 1 ] As material before and after the glass is the same, n1 = n3 θ 3 = sin 1 [ n 1 n 1 sinθ 1 ] = θ 1 78

89 Thus, it is shown that the light ray s angle of trajectory is identical before and after the glass plate, and any alterations in the light ray s path would be due to the refraction while the light ray is still within the glass medium. Further, as the thickness of the glass plate is known, it is possible to predict the displacement of the light ray if given the incident angle as the distance the light ray travels within the glass is known through utilization of Pythagorean Theorem. x 0 = thickness glass tanθ 1 Equation 3 The displacement of light due to the glass can then be found using the angle of light within the glass, θ2. x glass = thickness glass tanθ 2 Equation 4 Finally, the displacement can then be found. x = x 0 x glass By substituting equations 3 and 4 and rearranging, the displacement is then shown to be reliant on only thickness of the glass and incident angle. x = thickness glass (tan θ 1 tan (sin 1 [ n 1 n 2 sinθ 1 ])) 11 Appendix B Calculation of Displacement for Angled Glass Configurations Once the glass is placed at an angle, complexities arise as the amount of distance that the light remains within the glass changes and as a result, the y distance with respect to the reference plane also becomes a variable. 79

90 Figure 55. More complex situation for when glass plate is also angled Effective Angle It is still possible to apply a similar approach by considering that the angle and the distance that the light travels within the glass can be found and used to find the y distance the light travelled with respect to the reference plane. The calculation starts by finding the effective angle. θ = φ + α Where θ = angle with regards to glass surface α = angle of glass rotation (known) φ = angle with regards to reference plane (known) 80

91 Along with Snell s Law, it is now possible to determine the effective angles of the light path. Distance in Glass (Hypotenuse) θ 2 = sin 1 [ n 1 n 2 sinθ 1 ] = sin 1 [ n 1 n 2 sin(φ 1 + α)] It is then possible to apply Pythagorean s Theorem by using the effective angle along with the thickness of the glass to determine not the x distance, but the distance travelled in the glass or the hypotenuse, h. Displacement h = y glass cosθ 2 The displacement caused by the glass can then be found simply: y eff = h cos φ 2 x glass = h sinφ 2 The second angle with regards to the reference plane was not calculated, so it will be substituted with the effective angle. y eff = h cos(θ 2 α) x glass = h sin(θ 2 α) Now it is possible to find the x distance the light would have travelled without the glass s interference. x 0 = y eff tanφ 1 Finally, the displacement is found with the difference of the two x distances. x = x 0 x glass 81

92 11.2 Application The application of the calculation is shown in tables for each of three different glass configurations. The glass configurations are parallel plate, 5 degree symmetrical, and 5 degree asymmetrical. On an Elekta Agility, the largest field size of 40x40 is expected to intersect with the glass at approximately As a result, 11.3 is used to find the deviation Parallel Plate The parallel plate configuration is symmetrical in all regards. As a result, the calculation only needs to be applied once and doubled. Figure 56. Light ray passing through basic parallel plate arrangement. Table 10. Calculations for parallel plate arrangement. n_1 1 n_ Glass 1 Glass 2 y_glass 2.2 mm y_glass 2.2 mm α 0 degree α 0 degree φ_ degree φ_ degree θ_ degree θ_ degree 82

93 h 2.22 mm h 2.22 mm y_eff 2.2 mm y_eff 2.2 mm x_glass mm x_glass mm x_ mm x_ mm Δx mm Δx mm Total mm Symmetrical Symmetrical applies a total of 5 degree offset on the glass between each other. With regards to the reference plane, it would be seen as a ±2.5 degree offset. Figure 57. Light ray passing through sensor when both plates are angled with same magnitude but opposite direction. Table 11. Calculations for symmetrical angled arrangement. n_1 1 n_ Left Glass 1 Left Glass 2 y_glass 2.2 mm y_glass 2.2 mm α 5 degree α 0 degree φ_ degree φ_ degree 83

94 θ_ degree θ_ degree h 2.24 mm h 2.22 mm y_eff 2.23 mm y_eff 2.20 mm x_glass mm x_glass mm x_ mm x_ mm Δx mm Δx mm Total mm Right Glass 1 Right Glass 2 y_glass 2.2 mm y_glass 2.2 mm α -5 degree α 0 degree φ_ degree φ_ degree θ_ degree θ_ degree h 2.21 mm h 2.22 mm y_eff 2.18 mm y_eff 2.2 mm x_glass mm x_glass mm x_ mm x_ mm Δx mm Δx mm Total mm Asymmetrical Finally, the asymmetrical configuration would have one plate flat, while the other is held at 5 degrees. Figure 58. Light ray passing through asymmetrical arrangement with one angled plate and another parallel to floor. Table 12. Calculations for asymmetrically angled arrangement. n_1 1 84