External radiotherapy dosimetry in nonstandard fields

Doctoral Thesis EXTERNAL RADIOTHERAPY DOSIMETRY IN NONSTANDARD FIELDS Mar´ıa Araceli Gago Arias Departamento de F´ısica de Part´ıculas. Universidade de Santiago de Compostela September 2013 D. Faustino G´omez Rodr´ıguez, profesor titular de universidade do Departamento de F´ısica de Part´ıculas da Universidade de Santiago de Compostela e D. Juan Pardo Montero, Investigador Miguel Servet no Instituto de Investigaci´on Sanitaria de Santiago de Compostela, INFORMAN: Que a presente memoria titulada External radiotherapy dosimetry in nonstandard fields recolle os resultados do traballo realizado por D˜na. Mar´ıa Araceli Gago Arias baixo a s´ua direcci´on e supervisi´on, e constit´ue a Tese de Doutoramento que presenta para a obtenci´on do t´ıtulo de Doutor pola Universidade de Santiago de Compostela. En Santiago de Compostela, a 17 de Setembro de 2013. Faustino G´omez Rodr´ıguez Juan Pardo Montero Agradecimientos En primer lugar me gustaría empezar mostrando mi más sincero agradecimiento a mis directores de tesis, Faustino Gómez Rodríguez y Juan Pardo Montero, por su guía, paciencia, trabajo e ideas sin los cuales este trabajo no habría sido posible. A todos los coautores de los artículos en los que he participado y a la gente con la que he trabajado directamente, que siempre han sido amables y me han dedicado su tiempo ante las innumerables dudas y preguntas que les he planteado (a algunos más que a otros, que espero, se den por aludidos). Además de la gente con la que he colaborado más directamente para la realización de esta tesis doctoral, me gustaría mostrar mi agradecimiento a todas aquellas personas con las que compartí estos años, y que espero no se molesten por no incluír sus nombres en una larga lista que voy a resumir con un: A todos mis compañeros del Grupo de Investigación en Radiofísica No puedo olvidarme de ningún modo de mi familia y amigos, que me acompañaron cuando aqueé y que siempre creyeron en mí, no estaría aquí sin vosotros. El autor también agradece la concesión de un contrato predoctoral del Plan Galego de Investigación, Innovación e Crecemento (Plan I2C) de la Xunta de Galicia en el año 2011. v Summary The dosimetry of the small and intensity modulated elds employed in radiotherapy, with high dose gradients involved, is a quite demanding task. The need for reliable measurements in these beams responds not only to quality assurance requirements, but also to the legal regulations of Radiotherapy (in Spain, Real Decreto 1566/1998 sobre Criterios de Calidad en Radioterapia, and also EURATOM 97/43). The complexity of modern radiotherapy techniques led to an extensive incorporation of thorough treatment dosimetric verication in the hospital quality assurance programs. This verication, previous to the treatment, is performed in order to check that the dose distributions delivered by the radiotherapy machine match the corresponding planned dose distributions within the required tolerances. One work performed in this thesis project consists in the study of dierent commercial detector arrays, devices widely employed for dosimetric treatment verication. The response of the detectors involved in these devices is determined in order to study the impact of the detector size, technology and layout on the measurement of intensity modulated dose distributions. The capabilities of detector arrays for the detection of uence variations is also studied, as this is one of the main objectives of treatment verication. On the other hand, also related with the quality assurance of radiotherapy, a new dosimetry protocol is studied and applied to two modern radiotherapy machines, TomoTherapy and CyberKnife, for the determination of absorbed dose to water. Until now, dosimetry protocols ensured the traceability of dose to water through the measurement of 10 cm × 10 cm radiation elds under charged particle equilibrium, following the recommendations of conventional dosimetry codes of practice, for example the TRS 398 of the International Atomic Energy Agency (IAEA). Modern radiotherapy techniques involve the use of small radiation elds and intensity modulated uencies to achieve higher conformation of the dose to the tumour volume. Additionally, there was an increase in the radiotherapy machines involving this type of radiation elds that cannot reproduce the 10 cm × 10 cm standard reference eld. This situation increases the uncertainty associated to the determination of absorbed dose to water, compromising the quality of vii treatment planning in these machines. This prompted the creation a Working Group of reference dosimetry on nonstandard elds through the collaboration of IAEA and the American Association of Physics in Medicine, which published recommendations for the development of a new dosimetry protocol: A new formalism for reference dosimetry of small and non-standard elds Medical Physics Volume 35, Issue 11, p. 5179-5186 (November 2008). The application of the new protocol to the above mentioned machines requires the denition of intermediate calibration elds and the measurement and simulation of correction factors associated to dierent ionization chambers under these radiation elds, being one of the scopes of this doctoral thesis. Finally, alanine dosimetry is a secondary standard of absorbed dose to water in the therapy dose range (1 to 20 Gy), oered by primary laboratories like the National Physical Laboratory (NPL) in UK, the National Institute of Stantards and Technology (NIST) in US, or the Physikalisch-Technische Bundesanstalt (PTB) in Germany. This dosimetry system, which is tissue equivalent and exhibits small energy dependence, involves the use of small detectors, being widely used for small elds dosimetry and the calculation of ionization chamber correction factors. Another piece of work addressed in this thesis consists on the development of an alanine dosimetry system, unique in Spain, through the quantication of the dosimeters signal by electron spin resonance and with traceability to the secondary standard of absorbed dose to water of the Radiation Physics Laboratory at the Universidade de Santiago de Compostela. viii Publications related with this work A. Gago-Arias, L. Brualla-González, D. M. González-Castaño, F. Gómez, M. Sánchez García, V. Luna Vega, J. Mosquera Sueiro, and J. PardoMontero. Evaluation of chamber response function inuence on IMRT verication using 2D commercial detector arrays. Physics in Medicine and Biology , 57(7):2005, April 2012. doi: 10.1088/0031-9155/57/7/2005 A. Gago-Arias, R. Rodríguez-Romero, P. Sánchez-Rubio, D. M. GonzálezCastaño, F. Gómez, L. Nuñez, H. Palmans, P. Sharpe, and J. PardoMontero. Correction factors for A1SL ionization chamber dosimetry in TomoTherapy: machine-specic, plan-class, and clinical elds. Medical Physics , 39(4):19641970, 2012. doi: 10.1118/1.3692181 A. Gago-Arias, E. Antolín, F. Fayos-Ferrer, R. Simón, D. M. GonzálezCastaño, H. Palmans, P. Sharpe, F. Gómez, and J. Pardo-Montero. Correction factors for ionization chamber dosimetry in CyberKnife: machinespecic, plan-class, and clinical elds. Medical Physics , 40(1):011721, 2013. doi: 10.1118/1.4773047 Other publications: D. M. González-Castaño, J. Pena, F. Gómez, A. Gago-Arias, F. J. GonzálezCastaño, D. A. Rodríguez-Silva, A. Gómez, C. Mouriño, M. Pombar, and M. Sánchez. eIMRT: a web platform for the verication and optimization of radiation treatment plans. Journal of Applied Clinical Medical Physics, 10(3), July 2009. ix List of Figures xvi 2.7 Comparison of MapCHECK2 detectors uence response functions under the incidence of pencil beam sources with dierentsizes.............................. 59 2.8 Two dimensional uence response functions of MatriXX and PTW729 ionization chambers calculated by Monte Carlo with a 0.1 mm × 0.1 mm pencil beam source. . . . . . . . . . 60 2.9 Monte Carlo calculation of the energy dependence of the uence response function of PTW729 ionization chambers. . 61 2.10 Detector dose response function for the three detectors under study. .............................. 63 2.11 Comparison of PTW729 measurements and response model for radiosurgery lateral proles of dierent eld sizes. . . . . 65 2.12 Comparison of PTW729 measurements and response model for a lateral prole of an intensity modulated beam. . . . . . 67 2.13 2D Dose distribution of a head-and-neck IMRT incidence usedinthiswork......................... 70 2.14 Scheme of the procedure followed to study the eect of the detectors response in the measurement of an IMRT incidence. 70 2.15 Gamma passing rates resulting from the comparison of the IMRT dose distribution measured with radiochromic lm and the response model of the detectors under study. . . . . 71 2.16 Comparison between the detector arrays measurement of an IMRT incidence, radiochromic lm dosimetry and the detectors response model. . . . . . . . . . . . . . . . . . . . . . . 72 2.17 Position of the uence perturbations introduced in the IMRT incidence under study. . . . . . . . . . . . . . . . . . . . . . 74 2.18 Comparison of arrays measurement for the normal and modied IMRT incidences. . . . . . . . . . . . . . . . . . . . . . 75 2.19 Change in detector response versus the magnitude of uence variation. ............................ 76 2.20 Schematic representation of the ll factor of the three detectorarrays............................. 77 2.21 Positive Predictive Values of the detector arrays to the studied uence perturbations. . . . . . . . . . . . . . . . . . . . . 78 2.22 Relative standard deviations obtained for the MapCHECK2 measurement of a linac eld. . . . . . . . . . . . . . . . . . . 79 3.1 Alanine molecular structure and radical species formed by irradiation. ........................... 86 List of Figures xvii 3.2 Alanine to water stopping power and mass absorption coef- cientsratios........................... 92 3.3 Scheme of the Zeeman energy splitting of an electron in a magneticeld........................... 98 3.4 Schematic representation of the precession of the magnetization vector under the eect of a magnetic eld. . . . . . . 102 3.5 ESR absorption and dispersion lines of a free electron. . . . 105 3.6 Alanine ESR spectrum resulting of the superposition of the ESR spectra from three radical species. . . . . . . . . . . . . 106 3.7 Schematic representation of the ESR spectrometer main components..............................107 3.8 Sketch of the magnetic and electric eld patterns in a microwave cavity and scheme of the iris screw. . . . . . . . . . 108 3.9 Representation of the eect produced by the eld modulation ontheESRsignal. .......................111 3.10 Harwell alanine pellets and irradiation holder. . . . . . . . . 113 3.11 Desiccant vessel employed for the ambient preconditioning of the alanine pellets with temperature and relative humidity monitoring. ...........................115 3.12 60 Co unit irradiation setup employed for the irradiation of thepellets.............................117 3.13 Sketch of the setup employed for the positioning of the pellets inside the ESR cavity. . . . . . . . . . . . . . . . . . . . . . 118 3.14 Picture of the ESR positioning setup attached to the spectrometerframe..........................119 3.15 Comparison of ESR signals of an irradiated alanine pellet and the background signal exhibited by the setup. . . . . . . 120 3.16 Variation of the ESR signal intensity with the position of the alanine sample in the cavity. . . . . . . . . . . . . . . . . . . 122 3.17 Impact of the spectrometer conversion time on the ESR signal to noise ratio and the signal repeatability. . . . . . . . . 124 3.18 Variations in the alanine ESR signal intensity and signal to noise ratio with the spectrometer time constant . . . . . . . 125 3.19 ESR signal intensity versus microwave power. . . . . . . . . 127 3.20 Variation of the ESR signal with the spectrometer modulationamplitude. .........................129 3.21 Variations in the ESR signal intensity of two alanine dosimeters with their orientation inside the ESR cavity. . . . . . . . 131 List of Figures xviii 3.22 Deviations in the average peak-to-peak signal intensity of two alanine pellets versus the number of pellet orientations studied. .............................132 3.23 Improvement in the alanine ESR signal to noise ratio achieved after ESR parameters optimization. . . . . . . . . . . . . . . 134 3.24 Alanine background signal. . . . . . . . . . . . . . . . . . . . 136 3.25 Comparison of the ESR signal exhibited by alanine dosimeters irradiated to 20 and 90 Gy. . . . . . . . . . . . . . . . . 137 3.26 Calibration curves constructed from the two methods for ESR signal quantication and residuals corresponding to everyt...............................146 3.27 Calibration curves constructed from the two methods for ESR signal quantication after improvements in the system and residuals corresponding to every t. . . . . . . . . . . . 153 4.1 Energy uence and lateral proles of photon beams from attened and unattened linear accelerators . . . . . . . . . 162 4.2 Diagram of the main components of a TomoTherapy unit . . 167 4.3 Diagram of the main components of a CyberKnife unit. . . . 169 4.4 Virtual Water TM phantom employed in the TomoTherapy measurement campaign . . . . . . . . . . . . . . . . . . . . . 173 4.5 TomoTherapy plan class specic reference eld dose distribution ..............................175 4.6 Dose distributions of TomoTherapy lung and head-and-neck clinical treatments. . . . . . . . . . . . . . . . . . . . . . . . 176 4.7 Exradin A1SL beam quality correction factors for intermediate calibration elds and clinical treatments in TomoTherapy 182 4.8 Summary of A1SL beam quality correction factors published to this date for TomoTherapy intermediate calibration elds. 184 4.9 Change in the output of the CyberKnife G4 linac with the delivered monitor units. . . . . . . . . . . . . . . . . . . . . 189 4.10 Spherical and anthropomorphic phantoms employed in the measurement campaign with CyberKnife . . . . . . . . . . . 190 4.11 Scheme of beam incidences and isodoses map for the CyberKnife plan class specic reference eld 1 . . . . . . . . . . 192 4.12 Scheme of beam incidences and isodoses map for the CyberKnife lung treatment . . . . . . . . . . . . . . . . . . . . 194 List of Figures xix 4.13 Scanditronix-Wellhofer CC13 and PTW31014 beam quality correction factors associated to clinical treatments in CyberKnife.............................202 4.14 Geometry of the CyberKnife unit employed for the BEAMnrc Monte Carlo simulations . . . . . . . . . . . . . . . . . . 206 4.15 Distance Between Field Edges (DBFE) and global Gamma function values obtained for dierent combinations of electron source parameters . . . . . . . . . . . . . . . . . . . . . 208 4.16 Comparison of measured and Monte Carlo calculated dose distributions of the CyberKnife unit in the Hospital Ruber International. ..........................209 4.17 Geometry of Scanditronix-Wellhofer CC13 and PTW31014 ionization chambers employed in cavity Monte Carlo simulations...............................210 4.18 Comparison of experimental and Monte Carlo calculated global beam quality correction factors for the CyberKnife elds and ionization chambers under study . . . . . . . . . . . . . . . . 212 4.19 Summary of CC13 and PTW31014 ionization chamber beam quality correction factors published to this date for CyberKnife machine specic reference elds . . . . . . . . . . . . . . . . 218 List of Tables 1.1 Reference conditions for the determination of absorbed dose to water in 60 Co and clinical high energy photon beams . . . 24 2.1 Summary of the main characteristics of MatriXX, MapCHECK2 and PTW729 detector arrays. . . . . . . . . . . . . . . . . . 51 2.2 Width of uence response functions for the detectors under study............................... 60 2.3 Comparison of uence and dose response function widths for the detectors under study. . . . . . . . . . . . . . . . . . . . 63 2.4 Information about the uence variations including position, Monitor Units and dose dierences. . . . . . . . . . . . . . . 74 3.1 ESR spectrometer parameters employed before and after optimization for alanine dosimetry applications in the therapy doserange. ...........................133 3.2 Summary of the sources of uncertainty involved in the construction of the alanine calibration curve. . . . . . . . . . . . 144 3.3 Parameters from the alanine calibration ts obtained through the two methods of ESR signal quantication. . . . . . . . . 147 3.4 Summary of the sources of uncertainty associated to the construction of an improved alanine calibration curve. . . . . . . 152 3.5 Parameters from the alanine calibration ts obtained through the two methods of ESR signal quantication after improvement of the system. . . . . . . . . . . . . . . . . . . . . . . . 152 4.1 Estimations of A1SL ionization chamber kQ,Q0 correction factor in the TomoTherapy unit under study . . . . . . . . . 178 4.2 Uncertainty budget of the TomoTherapy measurement campaign...............................179 xxi List of Tables xxii 4.3 Exradin A1SL and alanine dose measurements for the TomoTherapy elds under study and associated global beam quality correction factors . . . . . . . . . . . . . . . . . . . . 181 4.4 Exradin A1SL beam quality correction factors for intermediate calibration elds and clinical treatments in TomoTherapy 181 4.5 Estimation of PTW31014 and CC13 ionization chambers kQ,Q0 correction factors in the CyberKnife unit under study. 196 4.6 Uncertainty budget for the CyberKnife measurement campaign196 4.7 CC13, PTW31014 and alanine dose measurements for the CyberKnife elds under study. . . . . . . . . . . . . . . . . . 199 4.8 Measured beam quality correction factors associated to CC13 and PTW31013 ionization chambers for intermediate calibration elds and clinical treatments in CyberKnife . . . . . 200 4.9 Monte Carlo simulation transport parameters . . . . . . . . 204 4.10 Monte Carlo calculated beam quality correction factors associated to CC13 and PTW31013 ionization chambers for intermediate calibration elds and clinical treatments in CyberKnife.............................213 Chapter 1 Introduction 1.1 Radiation therapy By 2012, around 20% of deaths in the European Region are produced due to cancer, which constitutes the most important cause of morbidity and death in Europe after cardiovascular diseases, and involves more than 3 million new cases and 1.7 million deaths per year [1]. Among the dierent strategies currently followed to treat cancer, which include surgery, chemotherapy, hormone therapy and inmunotherapy, ionizing radiation is employed to kill or control malignant cells. This method, referred to as radiation therapy or radiotherapy, should be applied to approximately 52% of cancer diagnosed patients, as estimated by Delaney et al. [2], although the actual rate of radiotherapy treatments varies widely among dierent countries. The interaction of ionizing radiation with biological tissues produces the ionization and excitation of their constituent atoms and molecules, leading to the formation of highly reactive radicals in the intracellular material that can chemically break bonds in DNA. Although most of this damage can be repaired by the cell, unrepaired damage to the cell DNA, consisting mainly in double strand breaks, can lead the cell to lose its ability to reproduce 1 Chapter 1. Introduction 2 or die. This is due to the loss of genes with associated functions that are critical for survival, producing the death of the cell before reaching mitosis or after having undergone one or several cell cycles [3]. Quickly dividing tumor cells are generally more sensitive than other cells to ionizing radiation, being the objective of radiotherapy to deliver the amount of radiation needed to produce the desired cell killing and achieve tumor control, see Figure 1.1. Figure 1.1: Scheme of the physical, chemical and biological eects of ionizing radiation in biological tissues [4]. Radiation Therapy can be classied by the type of ionizing particles employed (photons, electrons, protons or ion beams), by the energy of these particles (low, medium or high) and by the position of the radiation source with respect to the patient (external or internal), being the objective of this thesis centered in external radiotherapy of photon beams. The amount of energy deposited in a medium by ionizing radiation per unit mass is quantied by a magnitude called absorbed dose. The eect of radiation on biological tissues is in turn related with the dose. The goal of radiotherapy will be to deliver certain amount of dose, prescribed by a Chapter 1. Introduction 3 radiation oncology doctor, to a planned target volume (PTV) surrounding the tumor region, while the dose to the healthy surrounding tissue (referred to as organs at risks, OARs) is maintained below certain levels of tolerance as to minimize side eects and preserve critical organs. For photon beams, and based on the knowledge achieved through the years about dose response and clinical error consequences, the International Commission of Radiation Units and Measurements established in 1993 a desired accuracy for the dose to the PTV lying within the range from 95% to 107% of the prescribed dose [5]. Taking into account the sources of uncertainty associated to the dierent steps that, as we will see, must be followed for the delivery of a radiotherapy treatment, the achievement of such an accuracy can result quite demanding. 1.1.1 The radiotherapy process. The radiotherapy process begins with the patient being diagnosed (site and extent of the tumor, stage, etc) and the decision of treating the disease with radiotherapy. Patient anatomical information and tissue composition are then obtained through Computed Tomography (CT), where the delineation of OARs and treatment target volumes is performed 1 . The radiation oncologist prescribes the dose to be delivered to the PTV, OARs dose constraints and the radiation modality to be employed. A team of physicists addresses then the treatment planning, which consists, for external radiotherapy, in designing a combination of beams that full the oncologist prescription [6]. For treatment planning, workstation software receiving the name of Treatment Planning Systems (TPS) is employed to optimize the beam directions, the geometrical shapes and the beam weights for the treatment. These tools use the information in the patient CT and some parameters describing the 1 The position and extent of the tumor and neighboring healthy tissue can be assessed with other imaging techniques such as magnetic resonance imaging (MRI), single-photon-emission computed tomography (SPECT) and positron emission tomography (PET). These images can be correlated to improve the accuracy of volume delineation. Chapter 1. Introduction 10 rate during treatment. Finally, developed in parallel with IMAT, TomoTherapy (Accuray Inc., Sunnyvale, CA) oers a dierent approach to the arc therapy [10]. This technique involves a compact linac, mounted on a CT ring, rotating around a patient coach that moves into the ring for an helical delivery of radiation. Conformation and modulation of a fan beam is in this case provided by a fast binary collimator. Radiosurgery Other relevant radiotherapy technique, employed to irradiate small regions with high accuracy is radiosurgery. Initially developed for the treatment of brain lesions in a single fraction delivery scheme through the use of very small eld sizes (down to 0.1 cm 2 ), radiosurgery has evolved to treat other regions, like the lung or the spinal cord, in fractionated schemes, and with intensity modulated uencies. Radiosurgery treatment units can be of dierent nature, like standard isocentric linacs equipped with special MLCs of tight mechanical tolerance (i.e. Novalis), or dedicated treatment units like GammaKnife R  (which uses 201 stationary single-point-focused cobalt 60 sources) or CyberKnife R  (a single modality linac mounted on a industrial robotic arm). Finally, most modern units do not have a attening lter in their linac head. Some of these units will be extensively studied in Chapter 4, where we will discuss the main dierences between them and standard linacs using attening lter. Chapter 1. Introduction 11 1.2 Dosimetry 1.2.1 Physical basis The term ionizing radiation is used to refer to both indirectly and directly ionizing radiation. Non-charged particles (neutrons, uncharged pions, neutrinos, etc) and short wavelength electromagnetic radiation (X rays and γ rays) are recognized as indirectly ionizing radiation as they transfer energy to materials in a two step process. In the rst one, the non charged particles, for example photons, transfer energy to charged particles through dierent processes like photoelectric eect, Compton interaction, pair production, etc. Secondly, these charged particles produce further excitation and ionization in the material. On the other hand, directly ionizing radiation, conformed by charged particles (electrons, positrons, protons, ions) impart energy directly through excitation and ionization in the material, mainly through Coulomb collisions with electrons and nuclei. Regardless the type of ionizing radiation entering a material, the total imparted energy is equal to the addition of all the energy entering the volume corresponding to the mass m minus all the energy that goes out in dierent forms (Bremsstrahlung photons, annihilation photons and electrons or incident radiation going out). This balance must include all the conversion of mass to energy and energy to mass processes such as pair production and electron positron annihilation, leading to the expression [11]: =in −out +XQ (1.1) Where in is the sum of the energies (excluding rest energies) of all the directly and indirectly ionizing particles entering the volume, out is the sum of the energies (again excluding rest energies) of all the directly and indirectly ionizing particles leaving the volume and PQ represents the net Chapter 1. Introduction 12 energy derived from rest mass (in any transformation of nuclei or elementary particles) in the volume. Dosimetry is the metrologic discipline that studies the measurement of dose, a magnitude dened as the mean energy imparted by radiation to certain amount of mass, this is: D=d dm (1.2) Where d is the mean energy imparted by ionizing radiation to a mass, dm , that should be as close a possible to a point although big enough to avoid statistical uctuations aecting the mean energy 3 . Dose is expressed in gray (Gy), by denition a joule (J) per kilogram (kg). For clinical applications (radiology and radiotherapy), reference dose is evaluated in water, as there is a precise knowledge of radiation transport in this material that allows to obtain accurate results. Additionally, the human body, consisting in 70% water and with an average density close to 1 g cm −3 , has mass radiation interaction coecients similar to those of water, being the dose to these two materials closely related. The measurement of dose is performed with a dosimeter, an apparatus in which the eect of radiation can lead to a reading M that is linked to the dose D delivered to the dosimeter active volume V . The calibration of a dosimeter consists in the determination of a coecient that converts the dosimeter reading M , which can require several corrections depending on the physical properties of the measurement system and conditions, into dose. Additionally, it may result necessary to evaluate, from the dose to the dosimeter sensitive medium, the dose to a material of interest, usually water. Under certain conditions and whenever the dosimeter does not 3 While the energy imparted  is a stochastic quantity, the dose can be considered in many situations as a non stochastic magnitude that can be described by a continuous point function in a volume of interest [12]. Chapter 1. Introduction 13 exhibit response variations with the radiation energy spectrum and irradiation conditions, dosimeter reading ratios, M1/M2 , can result equal to dose ratios, D1/D2 , being this methodology referred to as relative dosimetry. Absolute determination of dose in one of the points involved in a relative dosimetry study can serve to derive the dose in the rest of the distribution. 1.2.2 Dosimeters Physical eects arising from the interaction of radiation and matter resulting useful for the measurement of dose are quite varied, and include temperature change, luminescence, dierent chemical changes, conductivity, etc. Besides the dierent physical detection principles, dosimeters can also be classied as active or passive depending on whether they can yield real time measurements or not, see Figure 1.6. Without going into much detail, the characteristics of an ideal dosimetry system have been recognized to be: repeatability and reproducibility, accuracy and precision, sensitivity, adequate dose range, linearity with accumulated dose, independence of response as a function of energy, spatial resolution, and insensitivity to inuence quantities such as dose rate, temperature, pressure, etc. [3]. In practice all dosimeters will exhibit certain limitations, that should be always considered with respect to any specic application in order to choose the most adequate system for every measurement. Chapter 1. Introduction 14 Figure 1.6: List of dosimeter types, classied as active or passive in terms of their real time or delayed read out. The physical magnitude measured by every dosimeter type is shown in parentheses. Primary standards of dose Only three types of dosimeters are considered to be primary standards for absorbed dose, as they are widely acknowledged as having the highest metrological qualities, leading to values that are accepted without reference to other standards of the same quantity, under certain conditions and through the application of certain conversions and corrections. For a dosimetry system to be a primary standard, the measured magnitude arising from the radiation eect must be related to absorbed dose to water through a relationship involving fundamental quantities that can be known with a low uncertainty. To obtain absolute dose measurements, all other systems must be traceable to one primary standard of dose, which can be: Calorimetry This method is based on the heating eect of radiation in materials, using the temperature change of an absorber for the measurement of deposited energy. The main technical diculty of this dosimetry system lies in the Chapter 1. Introduction 15 construction of a thermally isolated segment in which to measure the temperature change. The most extended absorbers or active mediums are water and graphite, a material with radiation absorption characteristics similar to those of water, being graphite calorimetry much extended due to the diculties of working with a liquid system [13]. In water calorimetry, a direct measurement of absorbed dose to water is given by the temperature rise (after the application of some corrections related with heat defect due to water radiolysis and heat transport) and the knowledge of the specic heat capacity. Frycke dosimetry This a chemical dosimetry system where the dose is determined through the measurement of the chemical changes produced in the sensitive medium. Fricke solution can be prepared by combining 1 mmol/L ferrous ammonium sulphate with 1 mmol/L sodium chloride and 0.4 mol/L sulfuric acid in double distilled water. Irradiation of this solution will oxidize the ferrous ions Fe +2 into ferric ions Fe +3 , and concentrations of the latter will be proportional to the absorbed dose to water. Ferric ions exhibit a strong absorption in the near ultraviolet ( λ =304 nm), and thus ferric ion concentration can be determined measuring the change in absorbance of the solution by spectrometry. In this technique the chemical radiation yield has some sensitivity to the beam quality. Additionally, water to Fricke mass energy absorption ratio varies signicantly with photon energy ( ≈ 2% for 0 to 10 MeV), consequently requiring delicate correction factors for the calculation of dose to water [14]. Air lled ionization chambers Ionization chambers are the reference instrument most used in clinical routine for both absolute and relative dose measurements due to its accuracy, Chapter 1. Introduction 16 robustness, long term stability, negligible recombination losses and the deep knowledge that has been developed through the years about its response. It consists in a air lled cavity in which an electric eld is applied between two electrodes to collect the ionization charge produced in the medium. There are basically two types of ionization cavity chambers, cylindrical (also known as thimble) chambers, represented in Figure 1.7, and plane parallel chambers. For thimble type ionization chambers the geometry consists of conductive outer walls and a central collection electrode, being these two elements separated by an insulator to reduce leakage currents when a polarizing voltage is applied. A guard ring is usually included to further reduce leakage and improve the eld uniformity in the active volume of the chamber. Figure 1.7: Sketch of a Farmer thimble type air ionization chamber showing typical length and diameter, PTCFE standing for polychlorotriuoroethylene. The external electrode can be covered by a PMMA layer to make the detector waterproof. The detection mechanism involves the ionization eect of radiation: an ionizing particle crossing the active volume produces electron-ion pairs along its path. The electric eld produced through the polarization of the chamber electrodes makes these charge carriers to drift towards the electrodes, inducing a current that can be read out by an electrometer. Measurements are usually carried out with the ionization chamber placed in water and Chapter 1. Introduction 17 the collected charge can be related to dose to water. Details about this relationship are explained in Section 1.2.3.2. The Bragg-Gray cavity theory is employed to calculate dose to water from dose to air in the ionization chamber when the presence of the chamber does not perturb the uence of electrons in the measurement medium[15]. This is fullled when the range of electrons in air is considerably larger than the dimensions of the cavity, which is generally the case in megavoltage photon and electron beams for regular size air ionization chambers and large eld sizes 4 . However, actual measurements deviate from ideal Bragg-Gray conditions. Perturbations in the electron uence usually arise, and certain corrections are necessary due to: the nite size of the chamber displacing some volume of the surrounding medium (water) and modifying the attenuation of the beam at the measuring point; the non water equivalence of the chamber wall and electrode materials; the presence of the chamber stem, etc. Ionization chambers are usually vented, namely air is in contact with the exterior, which implies that temperature and pressure corrections have to be applied to account for changes in the mass of air inside the cavity arising from ambient condition changes. Given that the sensitive medium is air at atmospheric pressure, with a mass density 700 times lower than water, the signal strength will be always smaller than that of solid-state detectors. For megavoltage beam dosimetry, the size of the ionization chambers active volume generally ranges from 0.01 to 1 cm 3 , being the larger ones not suitable for small eld measurements due to averaging eects, whereas the smallest ones exhibit lower signal to noise ratios, which aect the stability of the detector. Free air and air ionization chambers are one of the primary standards for air kerma in dierent beam 4 Small cavity chambers, considered to be so with respect to the radiation eld size, are well described by the Spencer-Attix modication of the Bragg Gray theory. The eect of high energetic electrons abandoning the cavity are here considered through the use of restricted mass stopping powers. Intermediate size cavities are better described by Burlin cavity theory. In this case, a factor is introduced to take into account the electron uence generated by photon interactions occurring within the cavity [15]. Chapter 1. Introduction 18 qualities. Old dosimetry codes of practice were based on the measurement of air kerma for the ionization chamber calibration [16, 17]. However, additional uncertainties introduced for the determination of dose to water in clinical applications lead to use a new dosimetry protocol based on dose to water calibration [18, 19] within the medical physics community. For the measurement of this magnitude, diculties arising in the determination of ionization chamber volumes with the required accuracy make ionization chambers to be generally used for radiotherapy purposes with a calibration factor obtained from cross calibration with other absolute dosimetry system [3]. Other dosimetry methods Diode These solid state semiconductor detectors are p-n union type diodes. In this case, electron-hole pairs induced by radiation in the bulk of the dosimeter diuse to the depletion region, where they drift due to the intrinsic eld leading to an inverse mode current in the diode. Diodes present the advantage of exhibiting high signal to noise ratios due to the high mass density of silicon. They can be thus built with very small sizes, ≈ 10 −3 mm 3 , providing good spatial resolution. The high atomic number of silicon make diodes to exhibit energy dependence, over responding at low energies, compared to water, due to the higher photoelectric eect in silicon. They present also dependence with temperature, dose rate and radiation incidence direction. The diode sensitivity changes with integrated dose due to radiation damage, reason for which these dosimeters are more commonly used for relative dosimetry than for absolute dosimetry purposes. Chapter 1. Introduction 19 Diamond Natural high purity type IIa diamonds are a dielectric material which can be used as dosimeters, usually working similar to air ionization chambers: electrons and positive holes are produced in the diamond by radiation, moving free through the crystal and producing a current proportional to dose when a polarization voltage is applied. Dosimeters are built by sandwiching the crystal with two electrodes and polystyrene capsule. Other diamond dosimetry method consists in measuring the thermoluminescence of this material after irradiation: light emitted in the UV range when the dosimeter is heated [20]. Diamonds exhibit high signal to dose ratios, being again constructed with small dimensions for the sake of spatial resolution. They are tissue equivalent, although 3.5 times denser than water, and present low energy dependence (compared to water), and high resistance to radiation damage. However, they exhibit certain dose rate dependence, require pre-irradiation and are certainly quite expensive 5 . Alanine Alanine, CH3CH(NH2)COOH , is an amino acid with simple molecular structure. Highly stable radicals are induced in this dielectric and tissue equivalent material by ionizing radiation in a concentration that can be quantied by electron spin resonance. Alanine dosimeters are built in polycrystalline aggregate presentations including lms, rods and small pellets ( v≈ 0.05 cm 3 ), the latter resulting very useful for the measurement of small radiation elds. An alanine/ESR dosimetry system will be presented in Chapter 3. Liquid ionization chamber Ionization chambers using non-polar dielectric liquids as active medium, usually isooctane, present certain advantages. Liquid densities are closer 5 Much progress has been achieved in the development of high purity single crystal diamonds by chemical vapor deposition, and synthetic diamonds exhibit now excellent electrical properties for their use as dosimeters [21]. Chapter 1. Introduction 26 Among all the inuence quantities there is one, characteristic of every radiation eld, that is considered separately in the formalism of dosimetry protocols due to its special relevance: the beam quality, related with the uence spectral distribution of the photon beam. In order to summarize and represent the beam quality, a single quantity, referred to as beam quality index, Q , is used as beam quality descriptor, being dened and measured for every radiation beam. Dosimetry protocols include the correction factors associated to a wide range of ionization chambers as a function of the beam quality index, being employed for clinical photon beam calibration whenever the clinical beam quality diers from that employed for the detector calibration at the SDL. These correction factors, referred to as beam quality correction factors, will be presented in the following section. Beam quality correction factors Whenever an ionization chamber measurement is performed in a beam quality dierent from that in which the chamber calibration coecient was obtained, a correction factor must be added to Equation 1.3 in order to obtain the absorbed dose to water as: Dw,Q =MQ·ND,w,Q0·kQ,Q0 (1.5) where MQ is the ionization chamber reading in the beam quality Q , ND,w,Q0 is the ionization chamber calibration coecient provided by the standard laboratory for the reference beam quality Q0 , under reference conditions, and kQ,Q0 is the ionization chamber beam quality correction factor associated to the beam quality Q , dierent from the reference beam quality Q0 . In this expression, the ionization chamber reading MQ is fully corrected for any inuence quantity according to Equation 1.4. Chapter 1. Introduction 27 For high energy photon beams, the beam quality index Q dened by TRS398 is the tissue-phantom ratio, TPR 20,10 , calculated as the ratio of absorbed dose in axis, at 20 cm and 10 cm depth in a water phantom, with a constant source to chamber distance (SCD) of 100 cm and a 10 cm × 10 cm square eld dened at the chamber plane, see Figure 1.8. Figure 1.8: Geometry for measurement of TPR 20,10 under a square eld of side, AP , equal to 10 cm. (a) Geometry for the measurement of dose at point P and depth z1 = 20 cm in a water phantom; (b) Geometry for the measurement of dose at point P at depth z2 = 10 cm in a water phantom. The distance between the source and the point of measurement is SSD1 + z1 = SSD2 + z2 = 100 cm for both (a) and (b). The TPR 20,10 gives, like the beam quality descriptors chosen by other dosimetry protocols, a measurement of the eective attenuation coecient, characterizing the approximately exponential decrease of the photon depthdose curve beyond the depth of maximum dose. The TPR 20,10 has been claimed however to present certain advantages over other quality descriptors, like the %dd(10) x , due to its independence on electron contamination in the incident beam, the simplicity of the measurement, and its low sensitivity to SCD changes arising from positioning errors [18]. Chapter 1. Introduction 28 If we take into account that the ionization chamber calibration coecient at a beam quality Q can be dened as: ND,w,Q =Dw,Q/MQ (1.6) The beam quality correction factor can be expressed as the ratio of calibration coecients at the beam qualities under consideration, where Q stands again for the user beam and Q0 for the calibration or reference beam: kQ,Q0=ND,w,Q ND,w,Q0 (1.7) The Spencer-Attix formulation of the Bragg-Gray theory expresses dose to water, Dw , as the product of dose to air in the ionization chamber, Dair , and the ratio of water to air restricted mean mass collision stopping power, (L/ρ)water air , which depends on the beam quality. Under departure from ideal Bragg-Gray detector conditions, a perturbation factor that depends on beam quality and the ionization chamber model, p Q , is needed to express dose to water as a function of dose to air. This factor accounts for uence variations due to the presence of the cavity, p cav , the eect of taking the chamber eective point of measurement at the center of the cavity, p dis , the non water equivalence of the chamber wall, p wall , and the eect of the central electrode, p cel . The global perturbation factor is thus the product of all these contributions, p Q= p cav · p dis · p wall · p cel , and dose to water can be expressed as: Dw=Dair ·(L/ρ)water air ·pQ (1.8) On the other hand, the dose to air can be obtained from the mean photon energy required to create an electron-ion pair in air, Wair/e , which is considered to remain constant for energy photons up to 25 MeV [24], and the Chapter 1. Introduction 29 exposition, X , or charge produced in air per unit mass, expressed by the corrected mass normalized detector reading M/m : Dair =XWair e=M m Wair e (1.9) Equations 1.6, 1.8 and 1.9 lead to the expression of the beam quality correction factor as a function of the water to air restricted mass stopping power and perturbation factors ratios, which also vary with the beam quality: kQ,Q0=Dw,Q/MQ Dw,Q0/MQ0 =[(L/ρ)water air ·p]Q [(L/ρ)water air ·p]Q0 (1.10) Although the formalism here presented follows the methodology proposed by the TRS-398 CoP, other protocols like AAPM TG-51 follow very similar formalisms including the establishment of reference conditions and the application of beam quality correction factors. Slight dierences, arising for example from dierences in the denition of the beam quality index, are minimized through the well known relationships between them, which allows the CoPs intercomparison to test the protocols equivalence and consistency [25]. 1.2.3.3 Nonstandard eld dosimetry As we have seen, IAEA TRS-398, and also AAPM TG-51, recommend the determination of absorbed dose to water in high energy photon beams using an ionization chamber calibrated in terms of absorbed dose to water in a reference beam quality Q0 and under standard reference conditions, which are usually a 10 cm × 10 cm square eld and 100 cm source-to-surface distance (SSD) or source-to-axis distance (SAD), Table 1.1. These codes of practice established a robust path for the determination of absorbed dose to water in external radiotherapy standard beams during the decades of Chapter 1. Introduction 30 1980's and 1990's, when conformal radiotherapy, involving large radiation eld sizes compared with the range of secondary particles in water, was the predominant external radiotherapy technique employed in clinical institutions. However, the introduction in Europe and the USA of commercial multileaf collimators in 1990 [3] and the development and widespread in the clinic of IMRT by the late 1990's led to a huge increase in the use of small elds in clinical treatments. Additionally, a new generation of linear accelerators and special delivery techniques specically designed for stereotactic deliveries and IMAT has been introduced, including treatment units like: • Leksell GammaKnife R  (Elekta Instrument AB, Stockholm, Sweden), • CyberKnife R  Robotic Radiosurgery system (Accuray Inc., Sunnyvale, CA) • TomoTherapy R  Hi-Art R  (Accuray Inc., Sunnyvale, CA), • VMAT (Elekta Instrument AB, Stockholm, Sweden). The radiation delivery of these machines is mainly performed with nonstandard elds, a term used to refer either to: 1. Small elds, with transversal sizes of the same (or less) magnitude as the range of secondary electrons in the medium, which present unfavorable measurement conditions whenever there is a partial occlusion of the radiation source or if the detector employed for the measurement is large compared with the eld size. 2. Intensity modulated elds involving small elds, or extensive elds with steep dose gradients. In these elds, departure from charged particle equilibrium conditions arise and volume averaging eects can become important for many detectors due Chapter 1. Introduction 31 to the steep dose gradients and multileaf collimator penumbras, substantially increasing the uncertainty and/or error associated to the measurement of absorbed dose to water when compared with measurements in standard elds. Although reference conditions can be established in some of these modern treatment units and dosimetry protocols can still be applied, the departure from standard eld dosimetric conditions in the clinical delivery raised considerable concerns in the medical physics community [2629]. On the other hand, some new treatment units cannot fulll the standard reference conditions dened in dosimetry protocols. Determination of absorbed dose to water was initially performed in these machines following the recommendations provided by the manufacturers and through the application of certain approximations. Since the use of nonstandard elds became extensive in clinical practice in Europe and USA, a unied methodology for the measurement of absorbed dose to water under these elds was considered a necessary step for the quality assurance of the radiotherapy dosimetry chain. This situation prompted the collaboration of the International Atomic Energy Agency and the American Association of Physicists in Medicine Therapy Physics Committee for the creation of an international working group on reference dosimetry of small and nonstandard beams. A new formalism for small and composite elds reference dosimetry was proposed by Alfonso et al. [30] with the intention of complementing and extending the recommendations and methodologies contained in existing CoPs. In this section, we present the new formalism for the dosimetry of nonstandard elds. The concept of intermediate calibration eld is introduced in this formalism to dene a eld that can be delivered by the machine and stands close to the reference conditions or to the clinical delivery and the Chapter 1. Introduction 32 specic delivery technique associated to the machine. Two types of intermediate calibration elds, comprising both static and composite eld dosimetry, are dened with their associated beam quality correction factors. These intermediate calibration elds are the machine-specic-reference eld, fmsr , and the plan-class-specic-reference eld, fpcsr , that we proceed to briey present here. Intermediate calibration elds Machine specic reference eld Whenever a measurement in reference conditions is not possible due, for example, to the geometrical design of the treatment unit, a static eld, referred to as machine specic reference eld, fmsr , is dened as close as possible to the conventional reference eld. The fmsr eld size should be larger that the range of secondary electrons in the medium (water), and the measurement should be performed with a relatively small ionization chamber to ensure eective lateral charged particle equilibrium in the volume of interest. Associated to the fmsr , an ionization chamber correction factor, kfmsr,fref Qmsr,Q , is then introduced in the previously explained reference dosimetry formalism, Equation 1.5, in order to account for the dierences in geometry and beam quality between the machine specic measurement conditions and the conventional reference conditions denoted by fref . Absorbed dose to water in the machine specic reference eld is then given by: Dfmsr w,Qmsr =Mfmsr Qmsr ·ND,w,Q0·kQ,Q0·kfmsr,fref Qmsr,Q (1.11) Chapter 1. Introduction 33 Plan class specic reference eld The plan class specic intermediate calibration eld, fpcsr , is a composite eld including unit-specic delivery features, dened with the purpose of reproducing dosimetric conditions similar to those of clinical treatments. This eld would ideally deliver a homogeneous dose distribution to an extended and geometrically simple target volume, and the absorbed dose to water in this eld can be expressed as: Dfpcsr w,Qpcsr =Mfpcsr Qpcsr ·ND,w,Q0·kQ,Q0·kfpcsr,fref Qpcsr,Q (1.12) where kfpcsr,fref Qpcsr,Q is a factor to correct between the dierences between the pcsr and the conventional reference eld. This kfpcsr,fref Qpcsr,Q factor can be also expressed as the product of the machine specic reference eld correction factor and a factor correcting for the differences between the plan class specic and the machine specic reference eld: kfpcsr,fref Qpcsr,Q =kfpcsr,fmsr Qpcsr,Qmsr ·kfmsr,fref Qmsr,Q (1.13) Clinical dosimetry Once intermediate calibration elds are dened, the determination of absorbed dose to water in nonstandard beams can be addressed. The dose of a clinical eld can be obtained from the dose in either fmsr or fpcsr through the introduction of a eld factor Ω as: Dfclin w,Qclin =Dfmsr(pcsr) w,Qmsr(pcsr)·Ωfclin,fmsr(pcsr) Qclin,Qmsr(pcsr) (1.14) where, Chapter 1. Introduction 34 Figure 1.9: Scheme of the dosimetry routes introduced by the machine specic and plan class specic reference elds for the measurement of absorbed dose in nonstandard elds. Examples of possible intermediate calibration elds for machines like Tomotherapy, Cyberknife and GammaKnife. Plan class specic intermediate calibration elds are dened to deliver uniform dose distributions, in gray, with simple geometries (cylinders, spheres), to simple geometry phantoms represented by the white volumes. Ωfclin,fmsr(pcsr) Qclin,Qmsr(pcsr)=Mfclin Qclin Mfmsr(pcsr) Qmsr(pcsr) ·kfclin,fmsr(pcsr) Qclin,Qmsr(pcsr) (1.15) If the intermediate calibration elds are representative of the clinical practice, kfclin,fmsr Qclin,Qmsr and kfclin,fpcsr Qclin,Qpcsr correction factors are close to unity and the eld factors can be approximated as the ratio of chamber readings. On the other hand, in the practical case of a static eld dosimetry, these Ωfi,fj Qi,Qj Chapter 1. Introduction 35 would be equal to the standard output factors. Figure 1.9 shows a schematic representation of the paths proposed for the measurement of absorbed dose to water in nonstandard elds through static and dynamic intermediate calibration elds. Scope of the nonstandard elds new formalism The new formalism for the dosimetry of nonstandard elds was originally presented in Medical Physics [30] as a proposal for the standardization of the dosimetry procedures in the above mentioned IMRT and other special techniques. But the aim of that letter was not only to present the new dosimetry formalism but also to encourage the debate of the scientic community about the proposal. The working group on nonstandard elds also recalled that, although some static eld dosimetry data were already available for many of the modern radiotherapy techniques, a lot of research work was to be done in composite eld dosimetry in order to check the capabilities of plan class specic reference elds to study how they should be dened. Since then, several works about the dosimetry of nonstandard elds have been published [24, 31], and the topic is still subject of central attention in international medical physics conferences [32]. For the study of the new formalism, the experimental determination of ionization chamber correction factors associated to intermediate calibration elds is an important task that requires the measurement of absorbed dose to water under nonstandard conditions. Taking as an example the machine specic reference eld, it directly follows from Equation 1.11 that the kfmsr,fref Qmsr,Q correction factor can be obtained from the measurement of absorbed dose to water under the nonstandard eld, Dfmsr w,Qmsr , the fully corrected ionization chamber reading under the same eld, Mfmsr Qmsr , and the calibration coecient at the reference beam quality and reference conditions, ND,w,Q0 : Chapter 1. Introduction 42 computer based images that are processed and analysed providing a representation of the attenuation properties of the dierent structures crossed by the radiation, being of central importance the contrast, resolution and noise of the device. The use of EPID systems for treatment verication formerly included recording the integrated uence from the treatment radiation beams and extracting information about the motion and position of the MLC leaves. EPID image information can be also used to derive the dose to the EPID, which is then compared with the calculation of the TPS at the EPID plane. Methods have been also developed to translate EPID images into primary uence maps used as input in a TPS to recalculate 3D dose distributions using a phantom or patient CT data. Alternative approaches use backprojection algorithms to derive the dose to the patient from the EPID images [43]. 1.3.3.2 Film dosimetry Film dosimetry is in principle an ideal system for IMRT verication, registering two dimensional dose distributions with high spatial resolution. Films are usually placed in water equivalent phantoms at depths of interest, usually those of the PTV and OARS, see Figure 1.11. The relative dose distributions obtained can be scaled to absolute values through crosscalibration with a small ionization chamber measurement. Radiographic lm Radiographic lm consist on a radiation sensitive emulsion coated on a transparent polyester base. The emulsion contains silver halide crystals (95% silver bromide and 5% silver iodide suspended in gelatin for Kodak XTL and XV lms), which under exposure to ionizing radiation undergo certain transformations related with the ionization of silver bromide and Chapter 1. Introduction 43 the accumulation of silver ions in impurity regions leading to the darkening of the lm. Uncertainty levels with this dosimetry system depend on the irradiation conditions, the lm processing, scanning, the calibration curve and the data analysis. One drawback is the non tissue equivalence of the dosimeter materials, which introduces energy dependency with overresponse at low energy, inducing depth and eld size dependent sensitivity. Radiographic lm has been however the dosimeter most extensively employed for IMRT verication for many years, being considered an accurate system whenever appropriate procedures and careful sensitometric calibration are performed [44]. Figure 1.11: Sketch of an anthropomorphic phantom used for lm dosimetry (CIRS IMRT Thorax Phantom, CIRS Norfolk, VA, USA), where lm dosimeters are placed in the transversal planes of interest for the measurement of dose distributions. Radiochromic lm Radiochromic lms are made of several thin layers of plastic (mylar) sheet glued in sandwich with a radiosensitive gel that modies the visible light absorbance with dose. It does not need chemical developing processing and presents some advantages as higher tissue equivalence and lower energy Chapter 1. Introduction 44 dependence. First radiochromic systems exhibited uniformity and reproducibility problems that have been improved in subsequent developments, although its cost remains quite high for massive clinical applications [45]. 1.3.3.3 Detector arrays Increase in the amount of patients being treated with a complex radiotherapy technique is a common situation encountered in clinical centers once that its implantation process is successfully achieved. Speeding up treatment verication procedures allows then to respond to the clinical demand, and getting dose distributions without the need of slow processing and scanning for their latter comparison with TPS dose distributions can greatly help to attain it. In this context detector arrays can result very useful, as these devices are easy to use and they are directly connected to computers allowing not only the fast measurement of one, two or three dimensional dose distributions but also its rapid incorporation into the clinical department computing network. Figure 1.12: Two commercial detector arrays: Delta 4 detector array from Scandidos, Sweden, where diode detectors are arranged in a matrixx along two orthogonal planes to provide three dimensional dose distributions (left) and LA48 Linear Ion Chamber Array from PTW-Freiburg, Germany (right). Chapter 1. Introduction 45 Dierent commercial detector arrays appeared through the last decade responding to the clinical demands and consisting usually in a number of detectors placed at xed positions in a water equivalent phantom. The dosimetric mechanisms more extended in detection arrays are the ionization chamber and the diode, as they are robust, can be easily calibrated and can measure with low associated uncertainty. Dierent aspects related with these kind of detectors will be analyzed in detail in Chapter 2, where a study of dierent commercial solutions will be presented. Chapter 2 2D detector arrays for IMRT verication: the inuence of chamber response function In this chapter we will study the use of two dimensional detector arrays for standard radiotherapy treatment verication. A detector response model will be presented that will allow us to reproduce the measurement of the detector under the incidence of an arbitrary uence and quantify the effect introduced by such response. The performance of some of the most extended commercial solutions will be analyzed through the same methodology in order to compare their capabilities for IMRT verication and draw some conclusions about the optimal design for these kind of devices. 2.1 Introduction The verication of complex treatments with composite elds, like those of IMRT, was initially performed using radiographic lm dosimetry. The 47 Chapter 2. 2D detector arrays for IMRT verication 48 technological trend in dosimetry and medical imaging has imposed a limited availability of radiographic lm for radiotherapy departments. Other passive alternatives, such as radiochromic lm, present poor repeatability and dose uncertainty, and require time for lm processing. Accordingly, in the last ten years most manufacturers of therapy dosimetry instruments have developed detector arrays for the measurement of dose distribution in planar and cylindrical geometries. There are two main elements in the design of a detector array that determine the global performance of the device for treatment dosimetry veri- cation, namely: (a) The detection technology employed: semiconductor diode, air ionization chamber, diamond etc, together with the size of the detector. (b) The spatial distribution of detectors in the array, referred to as detector sampling frequency. Although measuring with an acceptable degree of accuracy also depends on some other factors like pre-irradiation requirements and long term stability, it is the choice of the detection technology, the design (size, shape and materials employed) and the array sampling what determines the intrinsic performance of the array, aecting: i) Sensitivity to uence variations: Depends on the signal to dose ratio exhibited by the detection technology, and the relationship between detector size and detector spacing in the array, which sets the smallest dose/uence variation that can be detected by the device. ii) Repeatability: Dened as the precision in repeated measurements performed under equal irradiation conditions. iii) Accuracy: Dened as the degree of closeness of the array dose measurements to the true value of dose at the detectors reference points. Chapter 2. 2D detector arrays for IMRT verication 49 Other important characteristics of the device are, as for any dosimetry system, the linearity in the response with dose, the dose rate and energy dependence and the anisotropy in the response to radiation from dierent directions, which can be partially corrected for but is desired to be intrinsically minimal. The electronics acquisition time can also play a role for example in the verication of the collimator leaves movement in dynamic radiotherapy modalities. Several commercial detector arrays were developed during the last years, which employ dierent combination of detection technology and spatial sampling, achieving considerable success for fast and accurate verication of complex treatments. Most of them can perform absolute dosimetry measurements through the use of a calibration coecients, generally measured for the central detector, and an array of correction factors that compensate for the inter-detector response variations through the device [46]. Most detector arrays present a two dimensional, or planar, geometry, like PTW729 (PTW-Freiburg, Germany), MapCHECK (Sun Nuclear Corporation, Melbourne FL) or StarTrack and MatriXX (IBA Dosimetry, LouvainLa-Neuve, Belgium), while three-dimensional arrays, designed with their detectors distributed in several planes, have been later released, like ArcCheck (Sun Nuclear Corporation) and Delta4 (Scandidos, Uppsala, Sweden). By the time this study was conducted, planar arrays were more extended in clinical practice and it was by far easier to have them borrowed either from the vendor or from medical institutions than the three dimensional solutions. Given that the physical principles and factors affecting the performance of both two and three dimension detector arrays are the same, we decided to focus our study on dierent designs of planar arrays. Chapter 2. 2D detector arrays for IMRT verication 50 Figure 2.1: Commercial detector arrays studied in this chapter: a) MapCHECK2, b) PTW729 and c) MatriXX. The detector arrays chosen for this study were: a) MatriXX (IBA Dosimetry): An array of 1020 cylindrical ionization chambers of 4.5 mm diameter and 5 mm height, arranged in a 32 × 32 grid with 7.62 mm center-tocenter detector distances, covering an area of 24.4 cm × 24.4 cm. The 0.3 cm thick buildup plate is made of Tecaran ABS (density 1.06 g cm −3 ), while the backscatter plate is made of RW3 (98% Polystyrol, 2% TiO 2 , density 1.045 g cm −3 ) and has a thickness of 2.2 cm. b) MapCHECK2 (Sun Nuclear Corporation): An array made of 1527 n-diode detectors with a depletion region of 0.8 mm × 0.8 mm transverse area. Detectors are distributed with a centerto-center detector distance of 1 cm in every row, with adjacent rows being laterally displaced by 0.5 cm, thus the shortest detector distance is 0.707 cm. The total area covered by the array is 36 cm × 26 cm, and Chapter 2. 2D detector arrays for IMRT verication 51 Array Field (cm × cm) Detector Type Detector size (mm) Spacing (cm) MatriXX 24.4 × 24.4 Ionization chamber 4.5 diam × 5 height 0.76 MapCHECK2 26 × 32 Diode 0.8 × 0.8 0.71 PTW729 27 × 27 Ionization chamber 5 × 5 × 5 1 Table 2.1: Summary of the main characteristics of MatriXX, MapCHECK2 and PTW729 detector arrays. the buildup and backscatter plates, of Polymethyl Methacrylate, have a mass thickness of 2 and 2.75 g cm −2 respectively. c) PTW729 (PTW-Freiburg): An array of 27 × 27 cubic ionization chambers of 5 mm side, embedded in a Polymethyl Methacrylate plate (density 1.12 g cm −3 ) with 0.5 cm ridges between them. The center-to-center detector distance is 1 cm and thus the array covers a square area of 27 cm × 27 cm side. The buildup and backscatter plates, also made of Polymethyl Methacrylate, have a thickness of 0.5 and 2 cm respectively. 2.1.1 Previous work and motivation All the commercial detector arrays just presented are widely used for treatment verication in many clinical institutions, and had been thus object of thorough characterizations before our study. Amerio et al. and Stasi et al. [47, 48] dealt with the characterization of MatriXX initial versions, specically studying the eect of the spatial resolution on the evaluation of the dose map. Spezi et al. [49] presented a characterization of PTW729, an array which was further studied by Poppe and collaborators [50, 51], showing a good performance and reliability. Jursinic and Nelms [52] presented a characterization study of the MapCHECK2 array and Banci Buonamici et al. [53] compared its performance with lm dosimetry. Chapter 2. 2D detector arrays for IMRT verication 58 Figure 2.5: a) EBT gafchromic darkening under the irradiation of the 0.5 mm × 0.5 mm pencil beam and b) lm darkening quantication proles, measured at the central x and y axis, for the determination of the collimated dose distribution. for the Monte Carlo simulation procedure. The small discrepancies found around the ionization chambers wall are thought to be due to dierences in the penumbra of the experimental and simulated radiation sources. Figure 2.6: Measured ( · ) and Monte Carlo calculated ( × ), uence spatial response functions from a 0.5 mm × 0.5 mm pencil beam with a 6 MV modality in a Siemens PRIMUS linac spectrum, MapCHECK2 (a), PTW729 (b), and MatriXX (c). Chapter 2. 2D detector arrays for IMRT verication 59 The widening eect caused when measuring Fψ with a 0.5 mm × 0.5 mm pencil beam instead of an innitesimal collimation was analyzed. Two dimensional Fψ functions were calculated with a narrower radiation source: a square pencil beam of 0.1 mm side with the same 6 MV Siemens PRIMUS linac spectrum. Figure 2.7 (a) shows the response function obtained with this collimation for MapCHECK2 diode detectors in comparison with the measured Fψ , while Figures 2.7 (b) and 2.8 (a) and (b) show the two dimensional response functions of the three detectors under study with a grid of 1 mm. The widths yielded by dierent measurements and simulations are summarized in Table 2.2, where we conrm the small but noticeable eect of the experimental 0.5 mm × 0.5 mm pencil beam in the measurement of the ionization chambers response and an important widening in the diode response. Figure 2.7: (a) Measured ( ◦ , · ) and Monte Carlo calculated ( ∗ ) MapCHECK2 Fψ response function from a 6 MV Siemens PRIMUS 0.5 mm × 0.5 mm pencil beam (pb). Monte Carlo calculated Fψ from a 0.1 mm × 0.1 mm pencil beam (  ). (b) MapCHECK2 diodes two dimensional Fψ calculated by Monte Carlo simulation with a square pencil beam source of 0.1 mm side. Finally, a full Monte Carlo study was conducted on the energy dependence of the uence response of air ionization chambers. An inverse relationship was observed between the energy of the beam and the height of the response peak associated to the ionization chamber wall, see Figure 2.9 (a). Chapter 2. 2D detector arrays for IMRT verication 60 Figure 2.8: a) PTW729 and b) MatriXX ionization chambers Fψ calculated by Monte Carlo simulation with a square pencil beam source of 0.1 mm side from a 6 MV Siemens PRIMUS linac. Fψ FWHM MapCHECK2 PTW729 MatriXX Measured (0.5 mm × 0.5 mm) 0.146 0.872 0.665 Simulated (0.5 mm × 0.5 mm) 0.140 0.821 0.648 Simulated (0.1 mm × 0.1 mm) 0.083 0.700 0.640 Table 2.2: Width, expressed as FWHM in cm, of the detectors uence response functions measured with a 0.5 mm × 0.5 mm pencil beam, and width of the response functions simulated under the incidence of a 0.5 mm × 0.5 mm and a 0.1 mm × 0.1 mm pencil beams. This behavior is understood to be a consequence of the decreased signal contribution from the secondary electrons released in the ridges between detectors (Figure 2.2) as the energy of the beam increases. We can also observe that the uence response function Fψ of an ionization chamber in a 60 Co beam and in a 6 MV linac beam are very close due to the similar average energy of these beam qualities. The relationship between the signal peak and the beam spectrum is also described in Figure 2.9 (b), where the normalized response peak is presented versus the inverse of the secondary electrons CSDA range for dierent spectra. A good linear correlation is observed between these two magnitudes. Chapter 2. 2D detector arrays for IMRT verication 61 Figure 2.9: (a) Fψ response function, normalized to central response, for a 0.5 MeV monoenergetic photon beam ( ∗ ), 60 Co (+), 6 MV Siemens PRIMUS ( ◦ ) and 1.25 MeV ( · ), 3 MeV ( × ) and 6 MeV (  ) monoenergetic photon beams. (b) The response at the detector lateral wall position plotted against the inverse of the secondary electrons CSDA range. 2.3 Detector dose response function Once the uence response functions of MapCHECK2, PTW729 and MatriXX have been studied, we proceed to analyze the impact that using these detectors has on the measurement of dose distributions. The dose deposition produced at a certain depth in a material under an incident photon energy uence ψ(x, y) can be written as the convolution/ superposition of that uence with a dose deposition kernel K(x, y, z) that Chapter 2. 2D detector arrays for IMRT verication 62 accounts for photon scatter, primary and secondary electron transport and beam broadening with depth in the material. D(x, y, z) = Z∞ −∞ Z∞ −∞ ψ(x0, y0)K(x−x0, y −y0, z)dx0dy0 (2.3) If a detector is employed to measure this dose, the signal registered by the detector can be expressed as the convolution of the dose distribution at a depth z , calculated as in Equation 2.3, with a new detector response function FD(x, y) , referred to here as `dose response function'. If we note with the symbol ⊗ the convolution integral with respect to transversal coordinates, the response S(x, y, z) of the detector is given as: S=D⊗FD=ψ⊗Fψ=ψ⊗K⊗FD (2.4) As the uence response function Fψ studied in the last section can be expressed as: Fψ=K⊗FD (2.5) The dose response function FD can be obtained through the deconvolution of Fψ with the dose deposition kernel, although it is important to observe that Equation (2.5) is only veried for realistic uence response functions and dose deposition kernels. In our work, the pencil beam dose deposition kernel was assumed to follow a single parameter Lorentz function, K(x, y, z) = λ(z) 2π[x2+y2+λ2(z)]−3 2 with λ= 1.3 mm for 6 MV photon beams at 5 cm in water [57]. FD was then obtained with an iterative algorithm deconvolving the Monte Carlo calculated Fψ functions (those obtained from the 0.1 mm × 0.1 mm pencil Chapter 2. 2D detector arrays for IMRT verication 63 MapCHECK2 PTW729 MatriXX Fψ 0.083 0.700 0.640 FD 0.077 0.630 0.500 Table 2.3: Comparison of uence and dose response functions widths, expressed as FWHM in cm. beam exhibit more realistic widths and are thus more appropriate for the calculation of FD ) and the Lorentzian dose deposition kernel. The dose response functions derived from the uence response functions of MatriXX, MapCHECK2, and PTW729 detectors are shown in Figure 2.10. The dose deposition kernel corresponding to the measurement at 5 g cm −2 mass depth causes a reduction in the width of FD compared to that of Fψ , presented in Table 2.3. Figure 2.10: Dose detector response functions, FD , obtained through the Fψ dose kernel deconvolution for MapCHECK2 ( ◦ ), MatriXX ( · ) and PTW729 ( × ) detectors. Chapter 2. 2D detector arrays for IMRT verication 64 Once the detector dose response function FD has been calculated, the signal yielded by the detector for an arbitrary dose distribution can be modeled if a reference dose distribution with high spatial resolution is available [62]. 2.3.1 Verication of the methodology The methodology above presented can be used to test the capability of the devices to measure dose distributions with steep gradients, evaluating the importance of the volume averaging eect in ionization chambers. But before proceeding with this analysis for the three arrays under study, a consistency test was performed to check the presented formalism, trying to conrm that the convolution of the dose response function, FD , of a detector with a reference dose distribution leads not only to an accurate representation of the detector signal, but also to a better result than what would be achieved through the use of Fψ . The FD model was tested both in one and two dimensions using several radiosurgery radiation elds, with 1.8 cm × 1.8 cm, 4.2 cm × 4.2 cm and 11.2 cm × 11.2 cm sizes, from a Siemens PRIMUS linac with a BrainLab MLC in 6 MV modality. Lateral proles were measured with a PTW60016 diode detector in steps of 1 mm at 5 cm depth in water. These measurements were then used as reference dose distributions and convolved with the PTW729 ionization chambers FD to obtain a model of the response of this device. The results, as well as those obtained through the convolution of the dose distribution with the Fψ of the same detector, were then compared with real measurements of the PTW729 array for the same elds. Figure 2.11 shows the results of these comparisons. The dierences found between the models involving the convolution of Fψ or FD with the reference dose distribution are small, but we can observe an overestimation of the detector averaging eect when the convolution with Fψ is performed. The accuracy achieved by the two models is quantitatively represented by Chapter 2. 2D detector arrays for IMRT verication 65 Figure 2.11: Radiosurgery lateral proles for a) 1.8 cm × 1.8 cm, b) 4.2 cm × 4.2 cm and c) 11.2 cm × 11.2 cm beam sizes. Measurements with PTW60016 diode (dashed line) are used as reference dose distribution to obtain detector response models through their convolution with FD (solid line) and Fψ ( × ), for their comparison with PTW729 detector array measurements ( ∗ ). Local relative dierences for both convolution models Fψ (+) and FD (  ) are also shown. Chapter 2. 2D detector arrays for IMRT verication 66 the local percent dose dierences between the models and the PTW729 measurements. These percent dose dierences are also shown. A higher agreement was found in all the studied cases between the FD model and the PTW729 measurements, with local relative deviations below 1%. The same test was performed for a simple intensity modulated eld made by superposition of three elds with the above mentioned eld sizes, see Figure 2.12. In these case, the dierences between the models involving the convolution of Fψ or FD with the dose distribution are smaller, probably due the positioning of the PTW729 array with respect to the radiation beam. In this measurement, the positioning of the PTW729 array caused the detectors to be placed either in at dose zones or in the middle of penumbra regions, where the detector averaging eect is low and dierences between the Fψ and FD convolutions are more dicult to detect. The discrepancies between the two models are minimal in these regions, as shown in Figure 2.11 for the single eld study. A small but noticeable improvement is nevertheless observed for the convolution with FD . The tests here presented were considered to serve as a validation for the formalism presented in Section 2.3 for ionization chamber type detectors, and thus measurements were not repeated for the MatriXX array. Regarding MapCHECK2, this methodology should not be followed because the active area of PTW60016 diode (1 mm 2 circular) is bigger than that of MapCHECK2 detectors (0.8 mm × 0.8 mm). We nevertheless rely on our methodology and use as diode FD the function obtained from the Monte Carlo calculated Fψ after deconvolution with the dose deposition kernel. Chapter 2. 2D detector arrays for IMRT verication 67 Figure 2.12: Radiosurgery IMRT beam created by the superposition of 1.8 cm × 1.8 cm, 4.2 cm × 4.2 cm and 11.2 cm × 11.2 cm elds: a) Reconstruction of the beam in two dimensions as measured with a PTW60016 diode; b) Lateral prole measured with the PTW60016 diode (dashed line), PTW729 array measurements ( ∗ ) and response models obtained through the convolution of Fψ ( × ) and FD (solid line) response functions. Relative local dierences between PTW729 measurements and Fψ (+) and FD ( · ) models are also shown. Chapter 2. 2D detector arrays for IMRT verication 74 X axis (cm) Y axis (cm) Monitor Units ∆ D max (cGy) [−2,−1.5] [9.5,10.5] 21 6.9 [−0.5,0.5] [6.5,11.5] 12 19.0 [5,5.4] [9.5,10.5] 53 18.4 [7,7.5] [5.5,6.5] 34 8.2 [−2,−1.6] [1.5,2.5] 51 15.1 [5.5,5.9] [−9.5,−10.5] 57 17.9 Table 2.4: Position in the XY plane, change in Monitor Units and maximum dose dierence registered by the treatment planning system for the uence variations introduced in the IMRT incidence. Figure 2.17: (a) MLC projection on the PTW729 surface showing a 5 mm leaf displacements in one segment, and (b) dose distribution, in gray scale, of the IMRT incidence under study: the stars positions indicate the spatial localization of the uence changes introduced for the sensitivity study. The sensitivity of the arrays to uence changes was analyzed in a detector by detector basis. The signal variation registered in every detector when the array is irradiated by these two incidences (original and manually modied) was considered to be the most appropriate quantity to study, because the detector spacing in these commercial arrays does not allow the use of the Gamma function without dose interpolation, which we preferred to avoid. Several array measurements were acquired for the normal and modied incidences, to check the repeatability achieved in the signal changes arising Chapter 2. 2D detector arrays for IMRT verication 75 from the intentional uence perturbations. Although other perturbations were studied, only those summarized in Figure 2.17(b) and Table 2.4 are presented here due to the similar results obtained in all the studied cases. The position of detectors exhibiting signal changes higher than 3% of the dose maximum are highlighted in Figure 2.18 for the three arrays. It can be observed that the uence perturbations involve signal changes in a small number of detectors, and although a higher occurrence of signal variations can be noticed in MapCHECK2, not all these variations are located in positions where uence perturbations were intentionally introduced. Figure 2.18: Comparison of arrays measurement for the normal and modied IMRT incidences. White squares show the position of the detectors exhibiting dose changes greater than 3% of the maximum dose. On the other hand, the fraction of detectors having a threshold signal over the 10% of the array maximum signal and exhibiting signal variations greater than 1.5% of the maximum signal is 1.9% for MatriXX, 1.7% for PTW729 and 17% for MapCHECK2. This general analysis would not alert about the occurrence of critical perturbations, since many verication procedures consider as acceptable dose distributions exhibiting 5% of their total points in discrepancy with the reference distribution with a tolerance Chapter 2. 2D detector arrays for IMRT verication 76 of 3% of the maximum dose [64, 65], something that would not happen in our case. The variation in the signal of the detectors was found to be Figure 2.19: Percentage of change in detector response versus the magnitude of the induced uence variations (mean value of repeated measurements) MapCHECK2 ( ∗ ), PTW729 (+) and MatriXX ( ◦ ). clearly related with the uence change, quantied by the product of the area in the segment suering variations and the monitor units variation. This is shown in Figure 2.19, where the uence perturbation is plotted against the change in array readout (the experiment was repeated twice for every device, and mean values are reported). We can see that the readout dierence increases with the uence change, although there seems to be an indication of a low sensitivity plateau for uence perturbations below 20 MU × cm 2 . A slightly higher sensitivity to the treatment uence changes was observed for the air ionization chamber arrays, which is related with the larger eective (active) area covered by these devices, see Figure 2.20. The array ll factor was here quantied as the ratio of the area covered by the FWHM of the detector spatial response function Fψ , referred to as active area in Figure 2.20, and the cell area dened by the detector grid. Fill factors amount to 55%, 44% and 8% for MatriXX, PTW729 and MapCHECK2 respectively. Chapter 2. 2D detector arrays for IMRT verication 77 Arrays with higher ll factors exhibit higher sensitivity to uence variations which are not located at the detector center positions. Figure 2.20: Schematic representation of the detectors active area and the array cell for the devices under study: a) PTW729 detectors represented by grey squares, b) MapCheck 2 detectors represented by points and c) MatriXX detectors represented by gray circles. The array cells are represented by dashed line squares and active areas are inscribed inside the solid line. The sensitivity and predictivity of the arrays to uence variations was also studied in terms of the Positive Predictive Value, PPV, a magnitude usually employed in radiology tests. The PPV is dened for a given threshold as the number of `true' positives to total positives ratio. In our case, the `true' positives stand for the number of detectors that register a signal change that is actually related with any of the intentionally introduced uence variations, and the total positives is the number of detectors exhibiting readout variation above threshold. Figure 2.21 shows the higher PPV values obtained for the ionization chamber arrays (as expected from Figure 2.18), while higher percentages of false positives were found for the diode array. It should be however noticed that for detectability thresholds above 5% of the maximum dose, the number of detectors included for MapCHECK2 PPV calculations is small: PPV values diering from unity are due to two or three detectors usually located at the beam penumbras. On the other hand, PPV values are observed to Chapter 2. 2D detector arrays for IMRT verication 78 Figure 2.21: Positive Predictive Value obtained at dierent detectability thresholds for MapCHECK2 ( ∗ ), PTW729 (+) and MatriXX ( ◦ ). decrease sharply when detectability thresholds are below 1%, 2% and 4% of the treatment maximum dose for MatriXX, PTW729 and MapCHECK2 respectively. 2.4.2.1 Sensitivity to MLC leaf displacements The dierent results obtained for the ionization and diode arrays motivated a specic investigation about the MapCHECK2 `false' positives. The hypothesis that these signal variations could due to (small) misspositionings of the multileaf collimator between measurements was investigated. The collimator employed in the treatment under study has a leaf positioning accuracy around ∼ 1 mm, which would lead to small uence variations in the segments delivered within a treatment that could be detectable by the diodes. In order to demostrate this, the MapCHECK2 array was irradiated with a 8 cm × 12 cm Siemens PRIMUS linac eld. The array was placed to have a row of diode detectors aligned with the penumbra of the beam to register the maximum signal variation arising from the MLC leaf positioning Chapter 2. 2D detector arrays for IMRT verication 79 mechanical accuracy. Two sets of 10 measurements were performed, delivering 50 MU per irradiation, the rst one maintaining the MLC leaf positions steady between measurements, and the second by moving the leaves to conform the eld before each irradiation. This repeatability study also allowed discarding drastic miss-calibrations in any of the 1527 detectors. Figure 2.22: Relative standard deviation (rsd) obtained in 10 MapCHECK2 measurements of a 8 × 12 cm 2 Siemens PRIMUS eld with 50 MU when: (a) the eld is conformed before every irradiation and (b) leaves are kept in steady positions. The set of measurements with the MLC leaves remaining steady exhibited a relative standard deviation, rsd, with respect to the maximum signal in the array for this eld, that reached a 0.5%, while the measurements involving the leaves repositioning showed rsd values up to a 3.5% for the detectors located at the beam penumbra, as shown in Figure 2.22. When sets of two measurements are compared, as it is done to obtain the signal dierence registered when the array is irradiated by the normal and modied incidence, rsd values up to 0.9% are observed for the study with no MLC movements, while variations up to 7% are observed when leaves are moved to conform the same beam between measurements. The sensitivity of MapCHECK2 diode detectors to leaf position variations of ∼ 1 mm was Chapter 2. 2D detector arrays for IMRT verication 80 thus conrmed, and the lower PPV values obtained for MapCHECK2 compared to ionization chamber arrays could be then associated with the detection of systematic small leaf displacements between segments employed in the repeated deliveries of the studied incidence. It could be then argued that the high resolution and sensitivity of the diode array can result counterproductive for treatment verication. The low ll factor of these devices can lead to important uence changes involving large signal deviations in a small number of diodes, making dicult to distinguish these perturbations from 1 mm leaf positioning errors of lower relevance. This would be the case of the second modication, see Table 2.4, where only two diodes show a discrepancy higher than 3%, see Figure 2.18. On the contrary, ionization chambers volume averaging eect minimizes the signal variations originated from MLC displacements of ∼ 1 mm. The discrepancies exhibited by the ionization chambers located in regions without important uence perturbations are thus smaller, leading to the higher PPV values observed in our study. This lower sensitivity to small leaf misplacements makes the ionization chamber arrays verication more predictive to important uence perturbations. 2.5 Conclusions In this chapter we have presented a study about detector arrays for dosimetric treatment verication, focusing on PTW729, MatriXX and MapCHECK2 commercial solutions. Energy uence detector response functions, Fψ , were measured in water for the three arrays under 6 MV linac modality and with a 0.5 mm × 0.5 mm scanning pencil beam. Monte Carlo response functions were also calculated reproducing the experimental measurements and allowing a Monte Carlo energy dependence study and the calculation of more realistic uence Chapter 2. 2D detector arrays for IMRT verication 81 response functions for narrower collimation. Dose detector response functions, FD , were then calculated as the deconvolution of Fψ and the dose deposition kernel for the depth at which the uence response function was measured. A formalism was then presented to model the response of detector arrays to arbitrary incident uences through the convolution of the corresponding reference dose distribution and the detector dose response function. This model, satisfactory validated in several radiosurgery beam measurements, was shown to avoid the overestimation of the detector effect that would result from the convolution of the dose distribution and the uence response function. Our model served to isolate and study the eect of the detectors response on the measurement of a representative IMRT dose distribution. The results show that highest accuracy is achieved with diodes, although the perturbations introduced by the ionization chambers due to volume averaging or the lateral wall response peak remain negligible for Gamma function tolerances higher than 1.5%-1.5 mm. The global performance of the devices including detector spacing was also analyzed, pointing out the impact on the Gamma test of small spatial misalignments and noise in the dose distributions under comparison. Finally, the sensitivity of the arrays to treatment uence changes was studied in a detector by detector basis. A correlation was found between uence variation and detectors response above certain threshold. The Positive Predictive Value (PPV) indicator was also calculated showing a higher predictivity to uence variations in the ionization chamber arrays for all detection thresholds. The larger sensitive area of ionization chambers would allow these devices to eectively detect uence variations located at certain distances from the detectors positions. The point-like response of diode detectors, combined with the diode arrays sampling leads to a low ll factor that does not allow the detection of some uence variations, depending on their position, which could be only avoided with a drastic decrease in the Chapter 2. 2D detector arrays for IMRT verication 82 device detector spacing, a situation that might be technically unachievable. Diodes are however more sensitive to small leaf positioning errors, as those arising from the MLC mechanical accuracy, while ionization chambers cannot detect them due to their volume averaging eect. This sensitivity to smaller uence variations lowers the predictivity of the MapCHECK2, with respect to that of ionization chamber arrays, to more important uence variations, like the 0.4 cm × 1 cm uence perturbations studied in our work. It is worth pointing out that the high sensitivity of MapCHECK2 to small uence leaf displacements would not be reected in Gamma passing rates using standard tolerances, while its lower sensitivity to large uence perturbations could have indeed consequences in Gamma passing rates for conventional tolerances. Our results show that the ideal detector array for IMRT verication would not necessarily require point-like detectors, as the averaging eect of relatively large detectors, for example air ionization chambers, enhances the sensitive area of the device compared to that of the studied diode array. Although it is clear that small detectors yield a more accurate reproduction of dose in general IMRT conditions, the task of increasing the number of detectors in an array to obtain a high ll factor presents great design and production diculties. On the contrary, the averaging eect of air ionization chambers implies that a high ll factor can be achieved in an array constructed with an aordable amount of detectors. Ionization chamber arrays can thus oer a good sensitivity to uence variations across the whole area of a detector, which is the most important requirement of any dosimetry system employed for treatment verication. The methodology followed in this work to study the arrays under the same conditions and through a common analysis allowed us to obtain comparable results to study the dierences between them. With this work we have contributed to the understanding of IMRT QA requirements, helping to focus on the improvements that can lead to optimal detector array designs. Chapter 2. 2D detector arrays for IMRT verication 83 Considering our results, a detector array involving medium size detectors, for example ionization chambers with cross section areas of v 0.25 cm 2 , and distance between detectors leading to ll factors around 50% or above would be an appropriate tool for IMRT treatment verication. Recent detection technologies, like LICs, may allow the construction of arrays with high sensitivity and ll factor. When our study was addressed, several works had been already published related with these kind of devices, rst for a LICs linear array [6668] and lately for a two dimensional LIC array covering a 100% sensitive area of 3 cm × 2 cm [69]. Linear arrays involving LICs had been developed by PTW-Freiburg for eld verication purposes [66] and by mid-2012, PTW-Freiburg also began to commercialize a 2D LIC array, the Octavius 1000 SRS R  , with Stereotactic RadioTherapy and Radiosurgery verication purposes. The latter device covers a 10 cm × 10 cm total area, with a 100% ll factor in an inner area of 5.5 cm × 5.5 cm and a ≃ 25% ll factor beyond. This device became commercially available well after this study was completed, and therefore could not be investigated here. Although only a few studies have been published to this date dealing with the characterization of this commercial solution [7072], the knowledge currently available about this detection technology and the potential capability to build LIC arrays with small detectors size (cross section areas v 0.04 cm 2 , active volumes v 0.002 cm 3 ) and full sensitive areas (100% ll factor) results very promising for the eld of radiosurgery treatment verication. Chapter 3. Alanine Dosimetry 90 ESR signal intensities involves the determination of the proportionality factor linking these two magnitudes. In practice, this factor can be calculated as the slope, CQ,T , of the linear t of dose-ESR signal intensities for a batch of alanine dosimeters that have been irradiated to dierent values of dose to water, at temperature T and under a beam quality Q . The relationship between absorbed dose to water and absorbed dose to the alanine is directly obtained taking into account Equation 3.1: Dw,Q =CQ,T ·(IESR)Q,T m=CQ,T ·K·GQ,T ·Dal,Q (3.2) It should be noted that an exponential saturation in the concentration of radicals is well known to occur at high doses [77], but signal-to-dose linearity has been observed for dose values between 0.5 Gy and 5 kGy (residuals below 1%) [83], being thus guaranteed for the therapy dose range covered in this work. 3. Small energy and dose rate dependence The response of a dosimeter can be generally dened as the ratio of the detector reading (noted by M in Chapter 1, here ESR signal intensity, IESR ), and the value of the magnitude of interest, in our case absorbed dose to water, Dw . This response usually changes with the energy of the radiation beam, represented for high energy photons by the beam quality index Q (see Chapter 1). Since the detector is always calibrated at a certain energy/beam quality Q0 , correction factors have to be applied to determine the dose at dierent energies/beam qualities. The factor to correct for the change in the energy response at dierent beam qualities, calculated for the same value of absorbed dose to water at Q0 and Q , can be expressed as: FQ,Q0=(IESR/Dw)Q (IESR/Dw)Q0 (3.3) Chapter 3. Alanine Dosimetry 91 This expression is equivalent to the rst identity of Equation 1.10, with the beam quality correction factor kQ,Q0 given by the inverse of FQ,Q0 . But we can better understand the alanine energy dependence if we consider the proportionality between the detector reading, or ESR signal intensity, and the absorbed dose to alanine, Equation 3.1, which leads to the expression: FQ,Q0=GQ GQ0 (Dal/Dw)Q (Dal/Dw)Q0 =CQ CQ0 (3.4) We can here identify two eects contributing to the energy dependence and changing the slope in the alanine calibration curve, CQ : one given by the change in the alanine radiation yield with the beam quality, and the other given by the change in the alanine to water absorbed dose ratio with the beam quality. Regarding this latter eect, and considering alanine dosimeters as medium size detectors when compared with the range of secondary electrons in that material, Burlin theory states that the deposition of energy in the detector is due to electrons generated both in the surroundings of the dosimeter and in the dosimeter itself [15]. Thus, stopping power of secondary electrons and mass absorption coecients of the incident photons need to be considered when studying the energy dependence of alanine dosimeters. The energy dependence of alanine to water ratios of these two magnitudes is shown in Figure 3.2. In practice, alanine to water dose ratios are usually calculated by Monte Carlo simulation, and the global energy dependence of the alanine is experimentally determined through the construction of calibration curves at dierent beam qualities. Variations in the alanine radiation yield with the beam quality can be thus inferred from them. For X ray beams in the kV energy range, the alanine response is lower than that at 60 Co beams, ranging from 27% to 6.5% under-response for X ray beams from 50 kV to 200 kV [81]. Monte Carlo calculations Chapter 3. Alanine Dosimetry 92 Figure 3.2: Alanine to water stopping power ratios and mass absorption coecients ratios considering only alanine, solid line, and the dosimeter material including alanine and binder, dotted line. Results for alanine pellets manufactured by Bruker (Bruker Corporation, Billerica MA, USA) [84]. show that alanine to water mass energy absorption coecients ratios cannot account for all the eect, and at least 5.7% of the underresponse at 150 kV has been found to be due to variations in the radiation yield. Recent works oer however dierent results about the contribution of the two factors involved in the energy dependence to the global variation of the alanine response [85, 86]. On the other hand, in megavoltage photon beams from 6 to 25 MV, a global under-response of approximately a 0.6% is observed in alanine with respect to that in 60 Co beams, which is mostly due to variations in the radiation yield because no signicant energy dependence is found between linac megavoltage modalities [87]. In summary, we can say that alanine can be considered to be nearly water equivalent for photons with energies above 100 keV. This energy dependence is small when compared with that of other detectors like Chapter 3. Alanine Dosimetry 93 ionization chambers, what will involve smaller uncertainties related with beam quality variations in alanine dosimetry. On the other hand, no signicant dose rate eects have been observed for alanine dosimeters irradiated to dose rates below 3 Gy/s [88]. The dose rate can be thus completely disregarded in alanine dosimetry campaigns performed in the therapy range. 4. The relatively small physical size of the dosimeter. Alanine dosimeters can be produced in many physical presentations, although manufacturers like Harwell Dosimeters Ltd., Gamma Service (Synergy Health Radeberg GmbH) and metrology institutes producing their own dosimeters like the NPL, have usually chosen cylindrical pellets of 0.5 cm diameter and 0.3 cm height. Even though smaller pellets are manufactured, this detector size, with a volume of 0.06 cm 3 , is small if compared with many of the ionization chambers usually employed for radiotherapy measurements (Farmer type chambers v≈ 0.6 cm 3 , Semiex chambers v≈ 0.3 cm 3 ). Small detector sizes are required for measurements in the steep dose gradients that can be found in small and intensity modulated radiotherapy elds, so that eld disturbance eects like volume averaging are minimized. In this context, alanine dosimeters can be appropriate detectors for measurements in new radiotherapy techniques where ionization chambers are the most operative detector for routine measurements. Alanine can provide here an alternative method for the determination of absorbed dose to water in, for example, dosimetry audits and intercomparisons. Additionally, alanine can be used for the determination of beam quality correction factors associated with ionization chambers in non standard elds, which has become a very important step of quality assurance now that many modern radiotherapy machines cannot deliver the 10 cm × 10 cm eld required for the establishment of conventional calibration reference conditions. Chapter 3. Alanine Dosimetry 94 5. Non-destructiveness of the ESR readout process. Radiation induced radicals are not altered by the signal acquisition process of ESR spectroscopy, and this implies that alanine dosimeters can be read out as many times as desired provided that the dosimeters mass is controlled so that possible signal variations associated with mass losses can be corrected for. This is an advantage compared with other methods like thermo-luminescent dosimetry, which allows the performance of alanine dosimeter cumulative studies for in vivo dosimetry of fractionated treatments, representing important savings in the amount of pellets needed for some dosimetric studies. 6. Small dependence on ambient conditions. Ambient conditions like relative humidity during the dosimeters storage aect the fading of radicals in alanine. Other factor to be taken into account is the observed increase of the radiation yield with temperature. The eect is small and can depend on both the dosimeter manufacturing process and ambient conditioning. For Lα -alanine pellet presentations 2 , the radiation yield exhibits a linear variation with a slope ranging from +0.1% ◦ C −1 to +0.2% ◦ C −1 for absorbed doses up to 50 kGy and temperature values between -10 ◦ C and 50 ◦ C [81]. The radiation yield at a temperature T can be derived from the radiation yield at an arbitrary reference temperature, T0 , and the temperature coecient cT as: GQ,T =GQ,T0·[1 + cT(T−T0)] (3.5) Where the slope, cT , takes a value of +0.11% ◦ C −1 , with an associated relative uncertainty of 2.9%, for the Harwell alanine dosimeters that are employed in this work [89]. 2 Among the two stereoisomers of alanine (Dα -alanine and Lα -alanine), Lα -alanine exhibits a temperature dependence 50% lower than Dα -alanine, being thus preferred for dosimetry [81]. Chapter 3. Alanine Dosimetry 95 In order to correct for radiation yield variations that can arise between the dierent dosimeters involved in a measurement campaign, a temperature correction factor, kT , is applied to the ESR signal. This temperature correction is needed whenever the pellets are irradiated at dierent temperatures. The correction will be simply given by the ratio of radiation yields at the dosimeter irradiation temperature T and another temperature that is taken as reference, T0 , and to which we will refer all our ESR signal intensities: kT=GQ,T0 GQ,T =1 1 + cT(T−T0)≃1−cT(T−T0) (3.6) Additionally, alanine signal quantication through ESR spectroscopy is also aected by the water content of the pellet and the temperature and humidity of the laboratory, because the spectrometer sensitivity varies with the amount of water hold by the resonator cavity. Stability in the ambient conditions during ESR signal acquisition is required in order to minimize undesired sensitivity variations, and the pellets are usually stored open in laboratory conditions for some hours before proceeding with the measurements to reduce changes in the water content of the pellet during signal acquisitions. The basic concepts just introduced are enough to identify the key factors that will condition the quality of the measurement of absorbed dose to water with an alanine/ESR system. We can classify these factors as being associated to any of the two steps that must be followed for the construction of the alanine calibration curve: a) irradiation of the alanine pellets and b) quantication of the dosimeters ESR signal. On one hand, regarding the irradiation of the pellets, variations in the alanine dosimeters radiation yield and fading must be minimized in order to ensure that the same proportionality between radical concentration and absorbed dose to alanine is maintained for all the dosimeters involved in a Chapter 3. Alanine Dosimetry 96 measurement campaign. This can be done with a systematic control in the dosimeters ambient conditions before and after irradiation and through the application of a temperature correction factor if necessary. On the other hand, a good control on the ESR spectrometer is essential to ensure both signal repeatability and the proportionality between signal intensity and radical concentration. Taking into account that there are many parameters involved in the spectrometer operation, the principles of ESR spectroscopy have to be studied to ensure a proper understanding of the spectrometer operation. 3.1.2 Basic ESR spectroscopy theory The study of the absorption and emission of radiation by matter provides information about energy dierences between nuclear, atomic, molecular or crystallographic states, and has been historically employed to investigate the structure and dynamics of matter. In Electron Spin Resonance Spectroscopy, energy states are associated with the interaction between the magnetic moments of unpaired electrons in a substance and an external magnetic eld. The pairing of electrons that occurs spontaneously in most stable molecules due to Pauli exclusion principle can be disrupted by the presence of free radicals, which are induced for example by radiation. If these radicals remain stable with time, the material becomes paramagnetic due to the interaction between the intrinsic magnetic moment of the unpaired electrons and any external magnetic eld. In the simplied case of a free electron system, the presence of a magnetic eld, B , aligns the electron intrinsic magnetic moment, µ , with the magnetic eld, and the energy associated with this interaction can be expressed as: E=µ·B (3.7) Chapter 3. Alanine Dosimetry 97 The intrinsic magnetic moment of the electron is in turn given by the product of the electron spin, S , and the electron gyromagnetic factor γe= e ge/2me , where e and me are the electric charge and mass of the electron and ge is the g-factor of the electron, also known as Landé factor: µ=γeS=gee 2me S (3.8) Due to the quantization of spin levels, the electron intrinsic angular momentum, S=~ps(s+ 1) , can only have two projections in the direction of the magnetic eld, chosen here (without loss of generality) to be aligned with the z axis, i.e. sz=~ms , with ms = ±1 2 and s=1 2 . In this way, the interaction between the external magnetic eld, B = (0,0, B0) , and the electron magnetic moment leads to two energy states, receiving this phenomenon the name of Zeeman eect: E=µ·B=µzB0=~e 2me gemsB0=±1 2geµBB0 (3.9) Where µB=~e 2me is the Bohr magneton. The object of ESR is to measure the energetic transitions between these two energy states, and for that purpose paramagnetic materials are placed in a magnetic eld under the incidence of electromagnetic radiation with the appropriate frequency, as represented in Figure 3.3. The energy dierence between the two states establishes a resonance condition for electronic transitions ∆E=hν =geµBB0 . In practice, ESR spectrometers involve the use of an electromagnetic radiation source with a frequency that is kept constant while the intensity of the magnetic eld varies until the resonance condition is fullled and there is a net absorption of microwave radiation by the sample. For most spectrometers the incident radiation is within the microwave X band region, between 9 and 10 GHz, and the external magnetic Chapter 3. Alanine Dosimetry 98 Figure 3.3: Energy splitting due to the two possible alignments of the electron magnetic moment and an external magnetic eld. The state of lowest and highest energy occur when the moment of the electron µ is aligned with and against the magnetic eld respectively. Transitions between these two states occur through the emission/absorption of microwave radiation with the appropriate frequency. ux density ranges approximately between 0.32 T and 0.37 T (3200 to 3700 gauss) to fulll the resonance condition. In order to fully understand paramagnetic spectroscopy we have to consider that an ESR sample contains many paramagnetic species and not a single electron. When a population of radicals is in thermodynamic equilibrium, the ratio of paramagnetic centers in the upper and lower energy states, nupper nlower , can be described by the Maxwell-Boltzmann equation as a function of the energy gap between the two states, ∆E , the temperature, T and the Boltzmann constant, kB , as: nupper nlower = exp −∆E kBT (3.10) For the X-band microwave frequencies employed in most ESR spectrometers ( ν≈ 9.75 GHz), hν = 40µ eV, and under standard conditions ( T = 298 K), Chapter 3. Alanine Dosimetry 99 kBT= 25.6 meV, the spins are almost equally distributed between parallel and anti-parallel with respect to the external magnetic eld, nupper/nlower ≈ 0.998 . Polarization excess can be then expressed by: P=nupper −nlower nupper +nlower =1−exp (−∆E/kBT) 1 + exp (−∆E/kBT)= tanh ∆E 2kBT (3.11) When thermal equilibrium is reached under a static magnetic eld applied in the z axis, B = (0,0, B0) , the equilibrium magnetization of the sample, M0 , calculated as the addition of all the magnetic moments per unit volume v , is expressed as a function of this polarization excess: M0=1 vX i µi=1 2~γeNPuz (3.12) Where N = nupper +nlower is the total number of unpaired electrons. Larmor theorem states that the rate of change in the magnetization, M , of the sample is equal to the torque produced by the magnetic eld: dM dt =γeM×B (3.13) Taking into account that we are considering the static magnetic eld to be parallel to the z axis, we will use Mz for the longitudinal magnetization and Mx and My for the transverse components of the magnetization. Larmor theorem indicates that the longitudinal magnetization is constant and precesses around B with a frequency ω0=γeB0 , usually referred to as Larmor frequency. If there is little interaction between the individual spins of the spin system, the phase of the precession is random and the sum of the Chapter 3. Alanine Dosimetry 106 Figure 3.6: Alanine ESR spectrum, top, consisting in the superposition of the ESR spectra for the three radicals species R1, R2 and R3 that are induced by radiation in the alanine [74]. 3.1.3 Spectrometer operation All ESR spectrometers comprise four main components, namely a microwave radiation source, a magnet, a microwave resonant cavity where the samples are placed, and a diode detector that measures the amount of radiation absorbed or emitted by the samples. Most ESR spectrometers can be classied as reection spectrometers because they measure changes in the amount of radiation that is reected back from the cavity containing the sample when the spectroscopic transitions occur. Figure 3.7 shows a schematic representation of the spectrometer, and their main components are described below. Chapter 3. Alanine Dosimetry 107 Microwave bridge: The electromagnetic radiation source and the detector are in a box called the microwave bridge. Figure 3.7: Schematic representation of the main components conforming the ESR spectrometer. At the output of the microwave source there is an attenuator that controls the ow of microwave radiation, so that the microwave power entering the cavity can be accurately tuned. Microwave radiation will then enter a circulator, which ensures that the radiation coming from the microwave attenuator is only directed to the cavity, while the radiation that is reected from the cavity is only directed to the detector. The detector is a Schottky barrier diode that converts the microwave power reected from the cavity into an electrical current. The relationship between diode current and the microwave power is known to vary from a linear proportionality to a square root dependence as the microwave power Chapter 3. Alanine Dosimetry 108 increases [91]. The optimal sensitivity required for signal intensity quantication is achieved when the diode operates in the region of square root dependence, usually achieved for incident powers higher than 1 milliwatt. The remaining component in the microwave bridge is a reference arm, which supplies the detector with an extra microwave power to ensure that the diode operates in the adequate region. Cavity: The sample to be studied by ESR spectroscopy is located inside of a microwave cavity consisting in a metal box with a rectangular shape that resonates with the microwaves, amplifying weak signals from the sample. In order to couple the microwaves into the cavity, there is a hole, called iris, with a screw that can be moved up and down to control the amount of microwaves entering the cavity, see Figure 3.8. Figure 3.8: Sketch of the magnetic and electric eld patterns in a microwave cavity, left, and scheme of the iris screw controlling the entrance of radiation in the cavity from the waveguide, right. Chapter 3. Alanine Dosimetry 109 Although we will not elaborate this in much detail, resonance in the cavity is achieved when a certain condition related with the iris aperture, and the losses in the microwave source, cavity walls and sample, is fullled. Under resonance conditions the cavity is critically coupled and microwaves remain inside the cavity conforming standing waves, being the amount of microwaves that are reected from the cavity minimized. The eciency of every cavity to store the microwave energy is expressed by its quality factor, QF , which is dened as the ratio of energy stored and dissipated in the cavity per cycle, being also related with the above mentioned parameters of iris aperture, and the cavity and microwave source impedances. When paramagnetic transitions occur, the absorption of a net microwave energy by the sample changes the eective impedance of the cavity, which will be no longer critically coupled. The microwaves are then reected back to the circulator, reaching the diode detector, which yields an electrical current conforming the ESR signal. It is worth to note that the presence of water, a microwave absorber, in the cavity lowers the QF and aects the spectrometer sensitivity. Although some amount of water inside the cavity is unavoidable due to the non zero relative humidity of the air, changes in this water content should be minimized during measurements for the sake of stability. Regarding the positioning of the samples in the cavity, it must be taken into account that most paramagnetic samples do not exhibit resonant absorption of microwaves via the electric eld, and as the electromagnetic waves have their electric and magnetic components in opposite phase, samples must be placed at a position of maximum magnetic eld. The non uniformity of the modulated magnetic eld and the distribution of standing microwaves within the cavity leads to a drastic variation of sensitivity over the intracavity space. The sensitivity usually reaches the maximum at the cavity center, decreasing for points displaced either upwards or downwards from there. Due to this, the same paramagnetic sample placed at dierent Chapter 3. Alanine Dosimetry 110 positions inside the cavity leads to signals of dierent intensities. As alanine dosimeters are not point like samples, dierent portions of the pellet are located in regions of the cavity with dierent sensitivities, contributing dierently to the total signal [83]. Signal channel, phase sensitive detector: A strategy to separate ESR signal from noise and interferences, thus improving the SNR, is usually employed in ESR spectrometers. This strategy consists in introducing a sinusoidal modulation of the magnetic eld strength that is seen by the sample. When a spectroscopic transition occurs, the eld modulation sweeps the signal and the microwaves reected from the cavity are also modulated in amplitude with the frequency of the modulated magnetic eld. The ESR signal, which would be linear over a magnetic eld interval as wide as the modulation amplitude, will instead have a sinusoidal shape with an amplitude proportional to the signal slope. A lock-in amplier (phase sensitive detector) suppresses then all the signals that do not have the frequency and phase of the magnetic eld modulation, so that both noise and electrical interference signals are eectively suppressed. Additionally, a low pass lter is coupled to the detector to remove some of the remaining high frequency noise. In Figure 3.9 we can see that the amplitude of the oscillating detected signal increases with the slope of the absorption signal in the signal channel (dierence between the absorption at the extremes of the modulated eld), being this the reason why ESR spectra are acquired as the rst derivative of the absorption signal. Among all the factors aecting the spectrometer operation, the spectrometer sensitivity is mainly determined by the resonator QF , the magnetic eld modulation amplitude and the magnetic component of the microwave eld. Chapter 3. Alanine Dosimetry 111 Figure 3.9: Schematic representation of the eect produced by the eld modulation employed for phase sensitive detection of the ESR signal. Chapter 3. Alanine Dosimetry 112 3.2 Development of an Alanine/ESR dosimetry system 3.2.1 Materials and experimental setup The construction of an alanine calibration curve for the performance of alanine dosimetry involves two main steps: the irradiation of the dosimeters and the alanine signal ESR read out. In this section we will describe the experimental setup that was employed for the performance of these two tasks. The alanine dosimeters employed in our work will be presented, including some further considerations about how to manage the inuence that ambient conditions have in the dosimeters and the spectrometer. Then, the irradiation setup will be described, and we will conclude with a description of the ESR spectrometer and a system that was specically developed for the alanine pellets positioning inside the ESR cavity. 3.2.1.1 The alanine pellets The alanine dosimeters employed in this work are the cylindrical shaped pellets manufactured by Harwell Dosimeters Ltd, see Figure 3.10, consisting in 90.9% in mass of an alanine polycrystalline aggregate and a 9.1% of high melting point paran. The diameter of the pellets is (4.83 ±0.01) mm, the height is (2.8±0.1) mm and a nominal mass of (60 ±2) mg is ensured within a production batch. One of the advantages of Harwell dosimeters is their low sensitivity to changes in the environmental conditions when compared with the alanine dosimeters from other manufacturers, which is thought to be due to the high paran content of these pellets. The low porosity of Harwell dosimeters keeps the alanine rather isolated, minimizing variations in their water content related with their exposure to ambient conditions. Additionally, Chapter 3. Alanine Dosimetry 113 Figure 3.10: Harwell alanine pellets, left, and Perspex irradiation holder, right. these pellets also further contribute to seal the quartz tube that holds the pellet inside the ESR cavity reducing the air ow through the cavity during measurements, which minimizes perturbations in cavity sensitivity due to changes in air temperature and relative humidity [92]. Another advantage of these dosimeters, shared with other manufacturers that produce alanine pellets with similar dimensions, is the relative small size of the pellets, which allows them to t in the region of uniform sensitivity of the ESR cavities. Although one Harwell alanine pellet can t inside this region, the positioning of the dosimeter in the cavity has to be accurately controlled to ensure that they are all read out in the same sensitivity region of the cavity. Besides, pellets with masses signicantly deviating from the average can produce outlying mass-normalized signals. Corrections consisting in mass normalization will only be valid in the volume of approximately uniform sensitivity that extends up to 2 mm from the cavity center in each direction [83]. The formation of radiation induced radicals in alanine is temperature dependent and this can have an eect both on the construction of the calibration curve and on subsequent determinations of absorbed dose to water with Chapter 3. Alanine Dosimetry 114 those alanine dosimeters. In order to correct the ESR signal for radiation yield variations, the temperature of the dosimeters during irradiation must be known. All the pellets involved in a measurement campaign and the pellets holder are placed at the irradiation room for temperature stabilization some hours before irradiation. The temperature of the irradiation water tank where the pellets are irradiated is then recorded in every measurement, and it is later employed to correct the radiation yield by arbitrarily choosing one of the pellets temperature as a reference. Radiation induced radicals present also a short-term evolution after irradiation that varies depending on the total dose absorbed in the pellet [93]. Variations are observed to become minimal approximately 72 hours after irradiation for most dose levels. This period of time, after which highprecision ESR measurements can be performed, is always respected in our campaigns before proceeding with the dosimeters readout. The moisture content of the pellets is another issue that needs to be controlled, as water is a substance that absorbs microwaves and aects the resonator QF . Due to this, alanine pellets with dierent moisture content will lead to dierent signal amplitudes. Variations in water content from pellet to pellet, or even changes in the relative humidity of a single pellet during ESR measurements, must be thus taken into account. The water content of a pellet depends only on the ambient humidity of the environment where it is stored, and thus all pellets included in a measurement campaign should be stored together or under identical conditions. In order to control the pellets relative humidity, a saturated aqueous solution of a particular salt is usually placed in a sealed recipient where the pellets are stored, as for certain salts the relative humidity of the ambient air in the recipient remains constant or varies slightly with temperature [94, 95]. In our work, a preconditioning was performed to the pellets employed in the measurement campaigns: a saturated solution of sodium hydrogen sulfate was placed inside a sealed desiccator where the pellets were stored for a Chapter 3. Alanine Dosimetry 115 month before irradiation, Figure 3.11. The air enclosed in the desiccator was in this way maintained under a relative humidity of 65%. Figure 3.11: (Top) Desiccant vessel containing 300 ml of a saturated solution of sodium hydrogen sulfate, the alanine pellets are held on a plastic grid. To get an airtight environment inside the desiccant, a silicon grease is applied to the cap to get the vessel properly sealed. (Bottom) Temperature and relative humidity were monitored by a data logger. Additionally, variations in the alanine moisture during ESR measurements will arise if the relative humidity of the dosimeters and the ambient humidity of the ESR room dier. As this would aect the cavity QF , pellets Chapter 3. Alanine Dosimetry 122 pellet along the vertical axis of the cavity using the motorized stage. As expected, the ESR signal intensity exhibits a maximum around the cavity center, diminishing with the square of the distance to this position, as it can be observed in Figure 3.16. Figure 3.16: ESR signal intensity versus the position of the alanine dosimeter inside the cavity. The position of the pellet is expressed by the distance to a reference position established by leveling the pellet with the outer quartz tube of the positioning setup. A parabolic t to the experimental data yielded the solution, with x in millimeters: y= 1 −0.0207 ·(x−97.34)2 (3.26) Where y is the relative peak-to-peak signal normalized to the maximum value. This t served for the determination of the position of maximum sensitivity, found at 97.34 mm from the reference position of the pellet. Measurements are performed at the position of maximum sensitivity in all experiments. Although the data used for the t exhibits certain scatter and the determination of the position with maximum sensitivity would have an associated uncertainty, it does not aect measurements providing that all Chapter 3. Alanine Dosimetry 123 the pellets involved in a campaign are measured at the same position, which only depends on the stage repeatability. The uncertainty in the determination of the maximum aect our capability to maximize the spectrometer sensitivity in our measurements. It should be noted that since the positioning setup of the alanine pellets is sometimes removed from the spectrometer for measurements related with other ESR applications, positioning recalibration is performed in every measurement campaign. 3.2.2.2 Sweep time The sweep time, or time spent by the spectrometer to acquire a spectrum, is the product of conversion time, ct , which is the diode integration time at every value of external magnetic eld intensity, and the number of magnetic eld intensities employed to acquire the spectrum. The number of points acquired by the spectrometer can be set to 512, 1024, 2048, 4096 or 8192, and recommendations are usually given to have at least 10 data points within the narrowest line of the spectrum to be resolved. In our case, for the 9.75 GHz frequency of the microwaves entering the cavity, the alanine spectrum is centered at an external magnetic eld intensity of approximately 3465 gauss, spanning for an interval of 125 gauss. As the peak-to-peak intensity is employed for signal quantication, signal peaks are placed at the center of the alanine spectrum acquisition. We must however acquire the alanine signal in a wide range of magnetic eld to correct for possible slopes in the spectrum baseline, which can distort the peak to peak intensity. Taking into account the sweep widths employed for spectrometer operation at other institutions like the PTB and the NPL, we decided to choose a sweep width of 250 gauss around the center of the alanine spectrum. For this sweep width, the number of points acquired per spectrum was set to 1024, which leads to approximately 25 data points from peak-to-peak. Chapter 3. Alanine Dosimetry 124 Regarding the conversion time, the spectrometer allows setting it to 20.48 ms, 40.96 ms, 81.92 ms, 163.84 ms, etc. The impact of the conversion time on the signal repeatability was studied by acquiring seven spectra of an alanine pellet irradiated to 50 Gy at dierent values of conversion time to calculate the relative standard deviation of the signal intensities measured at dierent ct . Figure 3.17: Improvement in the signal to noise ratio of the ESR spectrum as the conversion time increases (left) and impact of the conversion time in signal repeatability (right). We can see in Figure 3.17 that as the conversion time increases, the signal to noise ratio of the spectrum and the repeatability improve, a behavior which was rather expected. However, if the conversion time is too long, possible instabilities occurring in the spectrometer can only aect a small part of the spectrum, being dicult to detect if they arise, for example, during the acquisition of the narrow but most intense peaks of the spectrum. In a visit to the alanine dosimetry laboratory of the NPL we were recommended to avoid these kind of eects by choosing a short conversion time, and thus we decided to choose a ct of 20.48 ms. The election of both these conversion Chapter 3. Alanine Dosimetry 125 time and number of data points per spectrum determines a sweep time of 20.97 s per acquisition. 3.2.2.3 Time constant The time constant, tc , is a parameter associated to the low-pass lter that is coupled to the diode detector to suppress high frequency noise. This lter basically slows down the spectrometer response time, being the signal less aected by noise as the time constant is increased. However, if the time constant is too long with respect to the conversion time, signal distortions and shifts in the magnetic eld of resonance can arise, and closely spaced signal structures can be excessively ltered presenting apparent lower intensities. Figure 3.18: Relative ESR signal intensity (normalized at tc = 20.48 ms) versus the spectrometer time constant (left). Decrease in the noise exhibited by the ESR spectra measuerd at tc = 163.84 ms with respect to that at tc = 1.28 ms, no signal distortion is appreciated (right). The conversion time was 20.48 ms in both cases. Chapter 3. Alanine Dosimetry 126 The optimization of time constant for the alanine dosimeters readout was performed by measuring the ESR signal intensity of the pellet spectrum with a conversion time of 20.48 ms and dierent time constants ranging from 1.28 ms to 163.84 ms. Excessive ltering could be detected by the decrease the peak to peak intensity of the alanine spectrum, but as we can see in Figure 3.18, this was not the case in our measurements even for the highest time constant studied, neither we observed any shifts in the eld of resonance of the sample. Trying to nd the best methodology for the data analysis, the application an o-line noise lter to delete the high frequency components of the spectrum was studied, but changes in the frequency cut-o were observed to introduce variations of around a 0.1% in the signal repeatability. As any of the investigated time constants can be chosen without compromising the quality of our ESR measurement, we decided thus to choose a 163.84 ms tc , a rather long time constant, so we could suppress any further noise ltering from our data analysis. 3.2.2.4 Microwave power The ESR signal intensity measured by the diode increases with the microwave power. However, if the microwave power is too high, the magnetization relaxation times become longer than the time between microwave pulses and the signal saturates, being its intensity lowered and experimenting a broadening distortion. Moreover, at high microwave powers, heating eects in the resonant cavity can adversely aect the machine stability and produce changes in the moisture content of pellets during measurement. This implies that in order to measure spectral lineshapes, linewidths and intensities accurately, the spectrometer should not operate in the saturation regime. For power values below 1 mW the signal is proportional to the microwave power, while a square root dependence is observed above that Chapter 3. Alanine Dosimetry 127 value until the saturation regime is reached. A compromise to get good signal to noise ratios without signal distortion or spectrometer instabilities is ensured through the spectrometer operation in the upper part of the square root dependence region. Figure 3.19: (Left) Peak-to-peak intensity of alanine ESR spectra versus the square root of the spectrometer microwave power, the linear t performed with low values of microwave power shows the departure from the square root regime for power values above 2.53 mW, MA stands for modulation amplitude. (Right) Improvement in the signal to noise ratio of the ESR spectrum from P =0.6 mW to P =2.53 mW and distortion of the signal for P =25.26 mW. An experimental determination of the optimal microwave power was addressed by measuring the signal intensity of a pellet irradiated to 50 Gy for dierent values of microwave power. Two values of modulation amplitude, close to that employed for alanine dosimetry in the therapy dose range at the NPL laboratory, were considered in this study given the correlation between these two parameters. Figure 3.19 shows the dependence of signal intensity on microwave power as well as the improvement in the signal to noise ratio as the microwave Chapter 3. Alanine Dosimetry 128 power increases and the eventual distortion in the signal shape at very high microwave powers. As a high microwave power within the square root regime ensures a good SNR with no signal distortion, consecutive linear ts of signal intensity versus the microwave power square root were performed, progressively including higher microwave power values, in order to evaluate the departure from the linear regime in the spectrometer operation. A microwave power of 2.53 mW was considered to ensure optimal spectrometer operation avoiding saturation and was thus chosen for future measurements. 3.2.2.5 Modulation amplitude The magnetic eld modulation employed in the phase sensitive detector to lter electrical interference and noise aects also the ESR signal intensity. As the modulation amplitude ( MA ) increases so does the intensity of the ESR signal, although above a certain threshold comparable to the signal linewidth the signal broadens and becomes distorted. Undesired heating eects can also arise in the cavity at high modulation amplitudes, leading to spectrometer instabilities and the drying of the dosimeters during measurements. Modulation amplitude should be kept under the width of the narrowest ESR structure that we want to resolve, noted here as ∆B (which in the case of alanine dosimetry is the central peak-to-peak width). Taking into account that our alanine signals have ∆B≈ 8 G, spectral acquisitions were performed with modulation amplitudes below 7 G, to check whether the level of signal distortion remained acceptable. This study was underwent for two values of microwave power due to the correlated contribution of both parameters to the signal intensity. As it can be seen in Figure 3.20, substantial decrease in the noise is observed as the modulation amplitude increases, and no important distortions were Chapter 3. Alanine Dosimetry 129 Figure 3.20: (Left) Peak-to-peak intensity of alanine ESR spectra for dierent values of magnetic eld modulation amplitude. (Right) Improvement in the signal to dose ratio of the ESR spectrum from MA =2Gto MA = 7 G, no signal distortion can be appreciated. detected even for the largest value of modulation amplitude investigated here. 3.2.2.6 Signal isotropy Alanine is an orthorhombic crystal that exhibits dierent ESR spectra depending on its orientation relative to the three axes of the crystalline structure. Alanine polycrystalline powder made of randomly oriented small crystals, with low granulometry (average grain size < 200 µ m) and a suciently high number of grains, behaves as a liquid sample with stable radicals and exhibits a sinusoidal theoretical intrinsic anisotropy with period π [96]. Variations from this angular response arise however in alanine dosimeter pellets (60 mg samples). On one hand, the number of grains is not high enough and the sample does not behave as truly polycrystalline. Deviations from the periodic sinusoidal response are supposed to be also due to Chapter 3. Alanine Dosimetry 130 inhomogeneities in the alanine-binder admixture and to the instability of radicals at the surface of grains: rearrangements and transformations from one radical into another are observed, being increased when the distance between grain surfaces is decreased in the powder compacting process performed during manufacturing [97]. This implies that dierent anisotropies can be found depending on the pellet manufacturing process. The anisotropy of the alanine pellets is considered for ESR signal quantication through the acquisition of several ESR spectra at dierent orientations of the sample, by rotation of the dosimeter around the vertical axis of the cavity. The intensity corresponding to dierent orientations is then averaged. The time required to acquire several spectra at dierent orientations per pellet is however a limiting factor, as it is preferable to complete a measurement campaign, involving tens of dosimeters, in one single day to avoid eects in the measurements due to changes in ambient conditions. Two pellets respectively irradiated to 90 and 60 Gy were investigated to assess the anisotropy of our dosimeters. Several spectra were acquired at 18 dierent orientations per dosimeter (from 0 ◦ to 360 ◦ in steps of 20 ◦ ) 3 . The variation observed in the peak-to-peak signal intensity with the orientation of the pellets is shown in Figure 3.21, where type A uncertainties were calculated at each orientation from the standard deviation of ve repeated measurements. We can observe deviation from the theoretical sinusoidal shape with period π in the response of our pellets, although a certain symmetry persists in the pellet irradiated to 90 Gy, which has lower associated uncertainties. The eect of using the average intensity from the signal amplitude measured at a dierent number of pellet orientations was then analyzed considering two angular samplings, 180 ◦ or 360 ◦ . 3 We should note here that the orientations are relative to the initial positioning of the pellet, which is totally arbitrary. Chapter 3. Alanine Dosimetry 131 Figure 3.21: Signal intensity of two alanine pellets irradiated to 90 and 60 Gy, top and bottom respectively, versus their orientation inside the ESR cavity. Dierent samples of average amplitudes were calculated considering up to 9 investigated angles. From a random initial position, the angular sampling was performed considering from 2 to 9 equally spaced positions in a 180 ◦ or 360 ◦ interval. The average amplitude was then computed from the signal intensity corresponding to every sampled position through interpolation from the measured signal, taking into account the type A uncertainty of the measurements. This procedure was repeated 1000 times to calculate the standard deviation associated to the average amplitude calculated for the dierent number of orientations, Figure 3.22. We can see how the standard deviation of the mean amplitude decreases as the number of orientations increases. An overall smaller standard deviation is achieved when the sampling is performed in the 360 ◦ interval. When two pellet orientations are considered the result is however dierent, as here the 180 ◦ sampling leads to a smaller standard deviation, probably due to the persistence of certain Resumen 234 incertidumbres asociadas al sistema mediante la repetición continuada de la construcción de la curva de calibración. - En el cuarto capítulo se estudia la aplicación de la propuesta del nuevo protocolo de dosimetría para campos de radiación no estándar a dos máquinas modernas de radioterapia, TomoTherapy y CyberKnife, ambas fabricadas por Accuray Inc., Sunnyvale, CA, Estados Unidos. El objetivo de este trabajo consiste en la determinación de los factores de corrección asociados a distintas cámaras de ionización para la determinación de dosis absorbida en agua en unos campos de calibración intermedios, denidos en las máquinas con el propósito de establecer para ellas un nuevo protocolo de dosimetría. Dos tipos de campos de calibración intermedios son propuestos para cada una de las máquinas, siendo el primero de éstos un campo estático, especíco para cada máquina y lo más cercano posible al campo de referencia denido en los protocolos de dosimetría convencionales. El segundo campo de calibración intermedio es un campo compuesto, denominado campo de plan de clase, que deposita una distribución de dosis homogénea con una forma sencilla (geometría cilíndrica en el caso de TomoTherapy y esférica en el caso de CyberKnife) en un maniquí equivalente a agua de geometría adecuada (cilíndrica y esférica para TomoTherapy y CyberKnife respectivamente). El campo de calibración compuesto se introdujo en la propuesta del protocolo con el objetivo de determinar la dosis absorbida en agua en condiciones más próximas a las de los tratamientos, ya que dada la complejidad de las técnicas de radioterapia asociadas a estas máquinas, éstas podrían diferir substancialmente de las correspondientes a los campos de calibración intermedios estáticos. Los factores de corrección asociados a la medida de dosis en agua con cámara de ionización en los campos de calibración intermedios se determinó a partir de la relación entre la dosis absoluta absorbida en agua, obtenida mediante dosimetría de alanina, y el producto de la lectura corregida de la Resumen 235 cámara y el coeciente de calibración de la misma en cobalto-60. Los factores de corrección fueron también calculados mediante simulación Monte Carlo para el caso de CyberKnife. La dosimetría de alania se realizó en colaboración con el NPL de Inglaterra, ya que el sistema de dosimetría estudiado en el capítulo tres fue desarrollado de modo simultáneo a la realización de este trabajo. Distintos tratamientos clínicos reales fueron investigados, determinando los factores de corrección asociados a la medida de las cámaras de ionización para la determinación de dosis absoluta en agua en un punto de una región de dosis homogénea del volumen planicado en cada uno de tratamientos. La relación entre los factores de corrección obtenidos en los tratamientos clínicos y en los campos intermedios de calibración permitió evaluar, aunque con estadística limitada, la idoneidad de los distintos campos de calibración para la práctica clínica. En el estudio de TomoTherapy, los factores globales, kfi,fref Qi,Q0 , asociados a la cámara de ionización estudiada (Exradin A1SL de Standard Imaging) arrojaron valores por debajo de la unidad en todos los campos investigados, con desviaciónes entre un 1.6% y un 2.1%. Las incertidumbres relativas asociadas a estas medidas se situan sin embargo entorno al 2% (k=2), lo que hace que los valores sean compatibles entre sí y compatibles con la unidad, aunque la desviación sistemática resulta signicativa en un test de hipótesis involucrando la t de student. En el caso de CyberKnife no se encontraron desviaciones sistemáticas en los factores de corrección globales asociados a las cámaras estudiadas (CC13 de Scanditronix-Wellhofer y PTW31014 de PTW-Freiburg), que arrojaron valores por encima y por debajo de la unidad dependiendo del campo. Los factores de corrección para la cámara CC13 tomaron valores desviándose de la unidad entre un 0.6% y un 1.6% en las medidas experimentales, mientras que en la simulación Monte Carlo estas desviaciones variaron entre un 0.6% y un 1%. En el caso de la PTW31014, las desciaciones de la unidad medidas Resumen 236 estuvieron entre un 0.8% y un 2.3%, y entre un 0.7% y un 2.5% según las simulaciones Monte Carlo. La mayor desviación con respecto a la unidad observada en las medidas de la cámara PTW31014 son debidas a la mayor diferencia en el promediado por efecto volumen entre este detector y la alanina. Los factores obtenidos para los distintos campos son compatibles entre sí (excepto uno asociado a la medida de PTW31014 en un tratamiento clínico) dadas las incertidumbres relativas de las medidas, que rondan el 2% para la CC13 y el 2.4% para la PTW31014 (k=2), siendo ésta última ligeramente superior debido a la mayor intestabilidad de este detector. Los resultados obtenidos mediante cálculo Monte Carlo mostraron acuerdo dentro de incertidumbres con las medidas, siendo también equivalentes entre sí los factores asociados a distintos campos estudiados. A raíz de estos resultados no se encuentra evidencia para armar que los campos intermedios de calibración compuestos (planes de clase) suponen una calibración intermedia más adecuada que los campos de intermedios de calibración estáticos para la dosimetría de campos no estándar estudiados, tanto en TomoTherapy como en CyberKnife. Por otro lado, una alta uniformidad en las distribuciones de dosis de los planes de clase es requerida para la medida de factores de corrección con incertidumbres asociadas bajas, pero se ha visto que esto resulta, dependiendo de la técnica, difícil de cumplir. Este factor apoya la reivindicación de los campos intermedios de calibración estáticos como mejores candidatos para la calibiración en el marco del nuevo protocolo, ya que éstos permiten la medida de factores de corrección con incertidumbres asociadas más bajas. La consideración inicial de campos de intermedios calibración compuestos como conguraciones más cercanas a las condiciones de tratamiento clínico no ha podido ser vericada, al menos para las propuestas de distribuciones Resumen 237 de dosis cilíndricas y esféricas aquí estudiadas. La medida de las conguraciones de campo compuesto simple propuestas en los planes de clase podría resultar útil para el control de calidad de dosimetría en ciertas técnicas, al incluir éstos muchas características del suministro de tratamiento propio de cada técnica. Sin embargo, las ventajas obtenidas a meidante su uso como campos de calibración intermedios para la dosimetría clínica no ha sido demostrada. Bibliography [1] J. Ferlay, E. 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