Tutorials in Radiotherapy Physics

Advanced Topics with Problems and Solutions

Patrick N. McDermott

• Publisher: CRC Press
• Year: 2016
• Print ISBN: 9781138445680
• eBook ISBN: 9781498755559
• Edition: 1
• Topic: Medicine
• Subtopic: Biotechnology in Medicine

The Topics Every Medical Physicist Should Know

Tutorials in Radiotherapy Physics: Advanced Topics with Problems and Solutions covers selected advanced topics that are not thoroughly discussed in any of the standard medical physics texts. The book brings together material from a large variety of sources, avoiding the need for you to search through and digest the vast research literature. The topics are mathematically developed from first principles using consistent notation.

Clear Derivations and In-Depth Explanations

The book offers insight into the physics of electron acceleration in linear accelerators and presents an introduction to the study of proton therapy. It then describes the predominant method of clinical photon dose computation: convolution and superposition dose calculation algorithms. It also discusses the Boltzmann transport equation, a potentially fast and accurate method of dose calculation that is an alternative to the Monte Carlo method. This discussion considers Fermi–Eyges theory, which is widely used for electron dose calculations. The book concludes with a step-by-step mathematical development of tumor control and normal tissue complication probability models. Each chapter includes problems with solutions given in the back of the book.

Prepares You to Explore Cutting-Edge Research

This guide provides you with the foundation to read review articles on the topics. It can be used for self-study, in graduate medical physics and physics residency programs, or in vendor training for linacs and treatment planning systems.

1

THE PHYSICS OF ELECTRON ACCELERATION IN MEDICAL LINACS

1.1 INTRODUCTION

Let us estimate the sort of energy and beam current necessary to achieve a desirable penetration depth and dose rate. We first consider the beam energy. The deepest target in the human body is in the pelvis. Let us suppose that we need to reach a depth of 30 cm with no more than 50% beam attenuation. In this case, we need photons with energy such that the half-value layer thickness equals 30 cm in water. This corresponds to photons with an energy of approximately 5 MeV. The average energy in a bremsstrahlung spectrum is about one-third of the maximum energy. Therefore, the electron beam energy needs to be about 15 MeV. We would not want to use beam energies much larger than this because this would waste photons that would pass right through the patient and because we want the beam to be attenuated beyond the target to reduce the dose to normal tissues.

As the reader may already know, linac beams are pulsed (see Section 1.9). The beam currents quoted in this section are time averages over a timescale long compared to the individual pulses. Calculation of the necessary average beam current is most easily done for electron treatments. For photon treatments, we have the question of the efficiency of bremsstrahlung photon production in the target and the transmission of the flattening filter. Modern medical linear accelerators have a dose rate on the order of 600 cGy/min. The dose rate due to electrons is

$\stackrel{·}{D}[\text{Gy}\text{}{\text{s}}^{-1}]=1.6\times {10}^{-10}\stackrel{·}{\Phi }[{\text{cm}}^{-2}{\text{s}}^{-1}]{\left(\frac{dT}{\text{ρ}dx}\right)}_c[{\text{MeV/cm}}^{-2}{\text{g}}^{-1}],$

(1.1)

where $\stackrel{.}{\text{Φ}}$ is the fluence rate in cm⁻² s⁻¹ and the mass collision stopping power is given in units of MeV cm² g⁻¹ (Attix, 1986). For 10 MeV electrons, the mass collision stopping power is 2.0 MeV cm² g⁻¹ in water. To obtain the desired dose rate, the fluence rate must be 3.2 × 10⁸ cm⁻² s⁻¹. Let us suppose that the beam is 10 cm × 10 cm in cross-sectional area. In this case, we can calculate the necessary average beam current to be approximately 5 nA. In reality, the average beam current is actually considerably higher than this for the following reasons. To reduce the variation in the energy of the accelerated electrons, the beam passes through an energy slit in the bending magnet. According to Karzmark et al. (1993, p. 190), this energy slit may pass as little as 5% of the beam. This raises the necessary raw beam current for electron mode to approximately 0.1 μA. In addition, the electron gun current needs to be even higher than the beam current because only some fraction of the electrons are captured and accelerated.

For a photon treatment, the beam current needs to be between 100 and 1000 times greater than for an electron treatment. The required average beam current is up to 100 μA. Photon beam current requirements are complicated by the efficiency of x-ray production in th...

Table of contents

• Cover
• Half Title
• Title Page
• Copyright
• Dedication
• Contents
• Preface
• Acknowledgments
• Author
• 1 The Physics of Electron Acceleration in Medical Linacs
• 2 Proton Therapy Physics: Protons for Pedestrians
• 3 Convolution/Superposition Dose Computation Algorithms
• 4 Deterministic Radiation Transport: A Rival to Monte Carlo Methods
• 5 Tumor Control and Normal Tissue Complication Probability Models in Radiation Therapy
• Appendix: Problem Solutions
• Index