University of New Mexico UNM Digital Repository Physics & Astronomy ETDs Electronic Theses and Dissertations Fall 11-10-2017 Proposed Method for Measuring the LET of Radiotherapeutic Particle Beams Stephen D. Bello University of New Mexico - Main Campus Follow this and additional works at: https://digitalrepository.unm.edu/phyc_etds Part of the Astrophysics and Astronomy Commons, Health and Medical Physics Commons, Other Medical Sciences Commons, and the Other Physics Commons Recommended Citation Bello, Stephen D.. "Proposed Method for Measuring the LET of Radiotherapeutic Particle Beams." (2017). https://digitalrepository.unm.edu/phyc_etds/167 This Dissertation is brought to you for free and open access by the Electronic Theses and Dissertations at UNM Digital Repository. It has been accepted for inclusion in Physics & Astronomy ETDs by an authorized administrator of UNM Digital Repository. For more information, please contact [email protected]. Dedication To my father, who started my interest in physics, and my mother, who encouraged me to expand my mind. iii Acknowledgments I’d like to thank my advisor, Dr. Michael Holzscheiter, for his endless support, as well as putting up with my relentless grammatical errors concerning the focus of our research. And Dr. Shuang Luan for his feedback and criticism. iv Proposed Method for Measuring the LET of Radiotherapeutic Particle Beams by Stephen Donald Bello B.S., Physics & Astronomy, Ohio State University, 2012 M.S., Physics, University of New Mexico, 2017 Ph.D, Physics, University of New Mexico, 2017 Abstract The Bragg peak geometry of the depth dose distributions for hadrons allows for precise and e↵ective dose delivery to tumors while sparing neighboring healthy tis- sue. Further, compared against other forms of radiotherapeutic treatments, such as electron beam therapy (EBT) or photons (x and γ-rays), hadrons create denser ion- ization events along the particle track, which induces irreparable damage to DNA, and thus are more e↵ective at inactivating cancerous cells. The measurement of radi- ation’s ability to inactivate cellular reproduction is the relative biological e↵ectiveness (RBE). A quality related to the RBE that is a measurable physical property is the linear energy transfer (LET), a measurement of the deposited energy over the par- ticle track. The purpose of this work was to develop a method of measuring LET of radiotherapeutic beams using an air-filled ionization chamber (IC) and liquid-filled ionization chamber (LIC). Through analysis of the IC and LIC signals, we deter- mined a correlation between the recombination index (IC/LIC) and dose-averaged LET. v Contents Abstract iv 1 Introduction 1 2 Radiotherapy 5 2.1 Fluence .................................. 7 2.2 AbsorbedDose .............................. 7 2.3 Radiation and Matter Interactions . 8 2.3.1 Charged-Particle Interactions . 9 2.4 Stopping Power . 10 2.4.1 The Bethe-Bloch Equation . 12 2.4.2 Continuous Slowing Down Approximation . 14 2.4.3 Multiple Coulomb Scattering . 15 2.5 Relative Biological E↵ectiveness (RBE) . 17 2.5.1 RBE Dependencies . 20 2.6 Linear Energy Transfer (LET) . 23 3Dosimetry 27 3.1 Ionization Chambers . 28 3.2 Initial Recombination . 30 3.2.1 Geminate Recombination - Onsager’s Theory . 31 vi Contents 3.2.2 Columnar Recombination - Ja↵e’sTheory ........... 33 3.3 General Recombination . 35 4DeterminationofLET 40 4.1 The Experimental Setup . 41 4.1.1 The Heidelberg Ion-Beam Therapy Center . 44 4.1.2 Characteristics of the Beam . 46 4.1.3 Gaussian Distribution of the Beam . 47 4.2 Instrumentation.............................. 49 4.2.1 The IC: PTW Roos . 49 4.2.2 The LIC: MicroLion . 51 4.3 FLUKAandLET............................. 52 4.3.1 LETAverages........................... 53 4.4 Experimental Results . 58 4.4.1 Beam Spread Corrections on the IC . 64 4.4.2 Beam Spot Size Corrections . 67 4.4.3 Proton Calibration Curves . 76 4.4.4 Carbon Calibration Curves . 77 4.4.5 Oxygen Calibration Curves . 78 4.4.6 Combined Calibration Curves . 80 Summary and Conclusions 84 Discussion and Outlook 87 References 89 vii Chapter 1 Introduction The geometric profile of energy deposited by radiotherapeutic hadron beams is ad- vantageous for treating deep-seated tumors compared to other forms of radiation, such as electron beam therapy (EBT) and photons (x-rays and γ-rays). The steep increase and subsequent exponential decay in the depth dose distribution near the end of the particle track (i.e. the Bragg peak), allows for accurate three-dimensional painting of tumors while sparing healthy tissue located along the entrance plateau and distal tail of the depth dose distribution from the majority of damaging radia- tion. The nuclear charge of hadrons also allows radial steering of the beam, enabling true 3-D mapping of tumorous masses. For hadrons, heavier charged particles have several advantages over lighter charged particles. Radial scattering, where the beam spreads due to multiple Coulomb scattering, has dependency on the atomic mass, which makes heavier charged particles superior (i.e. He instead of H). Also, due to their greater atomic mass and nuclear charge, carbon and oxygen ions have higher ionization event densities along the particle track compared to protons. This higher ionization event density induces numerous forms of damage to DNA molecules, rang- ing from base loss and base change, H2-bond breakage, pyrimidine dimers, DNA cross-linkage, single-strand breaks (SSB) and double-strand breaks (DSB). These ef- 1 Chapter 1. Introduction fects are prominent around the Bragg peak, where the energy deposited along the particle track is several times that of the distal tail and entrance plateau, leading to the increased biological e↵ectiveness of hadrons compared to other forms of radiation in the target region. For hadrons and other types of ionizing radiation, the percentage of cells within the tumor that survive and reproduce is related to a biological quality known as the relative biological e↵ectiveness (RBE). The RBE is the ratio between the absorbed dose required by ionizing radiation and x-rays (220 keV photons) to induce identical damage to DNA molecules and biological tissues. However, calculating RBE is dif- ficult due to its dependency on multiple biological and physical variables - type of ionizing particle, dose, dose rate, type of tissue, oxygenation level of the tissue and the selected biological endpoint (i.e. the expected survival fraction). Therefore, it’s advantageous to work with a physical property of the beam related to the RBE - the linear energy transfer (LET), which is a measurement of the energy deposited along the particle track. LET can be calculated using Monte Carlo codes (Fluka, Shield-HIT12A) [Ferrari 2005, Bassler 2017], which simulate conditions for both tis- sues and experimental setups. But so far, no method for directly measuring LET, which would make such calculations unnecessary, has been reported. A correlation between RBE and LET has been reported [Sorensen 2011], which sug- gests LET is an acceptable physical surrogate for the purposes of treatment planning. The ability to directly measure LET in-situ would be advantageous for keeping the high RBE region on the target volume and away from healthy tissues. To perform LET measurements of radiation, two ionization chambers were utilized. The first was an air-filled ionization chamber (IC) and the second was a liquid-filled ioniza- tion chamber (LIC), which was filled with isooctane. Although ICs have higher resolution than LICs in beam direction, LICs are preferable for dose distributions with narrow beam profiles and sharp penumbras. Due to the higher density of liquids 2 Chapter 1. Introduction compared to gases, LICs can be constructed several times smaller than ICs. How- ever, while LICs are advantageous due to their small diameter, the high density of liquids leads to recombination e↵ects within the sensitive volume, which suppresses the detected signal (i.e. quenching). On the other hand, ICs, due to the low density of air, experiences little recombination. All, or nearly all, of the electron-ion pairs created in ICs are captured by the collecting electrode while an appreciable fraction of electron-ion pairs in LICs recombine. There are two forms of recombination. The first is Initial Recombination (IR), which involves electron-ion pairs produced by a single particle track recombining before detection by the ionization chamber. Initial Recombination consists of two com- ponents. Geminate recombination (described by Onsager’s Theory) [Onsager 1938] involves an electron recombining with the original ion while columnar recombination (Ja↵e’s Theory) [Acciarri 2013] involves an electron recombining with a di↵erent ion produced along the track of the same charged particle. The second is General Re- combination (GR), which involves electrons and ions produced along the tracks from di↵erent charged particles recombining into a neutral atom. General Recombination is inversely proportional to the voltage applied across the sensitive volume. Thus, at the voltages used in the experiment, GR was e↵ectively negligible in the LIC. Initial Recombination on the other hand, is dependent upon the LET, with higher LET particles producing more ionization events per unit length along their track, creating more electron-ion pairs. Our work involved developing a method capable of relating LET to the ratio be- tween the IC and LIC signals. In the water phantom at the Heidelberg Ion-Beam Therapy Center (HIT), the ionization chambers were held flush to each other, the IC (PTW Roos) in front and LIC (MicroLion) in the rear. The ionization chambers were attached to a mobile apparatus capable of precise movements, ranging from centime- ter to sub-millimeter steps. This allowed for accurate measurement of di↵erent ion 3 Chapter 1. Introduction species, one after the other, at identical depths within the water phantom for the IC and LIC, the latter of which experienced quenching due to IR (GR was minimized by the applied voltage).