Optimal Fractionation in Radiotherapy

Archis Ghate

• Publisher: Cambridge University Press
• Year: 2023
• Topic: Mathematics
• eBook ISBN:
  9781009341141
• Subtopic: Mathematics General
• Index: Mathematics

This monograph provides a mathematically rigorous overview of optimal fractionation in cancer radiotherapy, which seeks to address the fundamental tradeoff of maximizing tumor-kill while protecting nearby healthy tissue from toxic effects. Most mathematical research on exact solutions to this problem is scattered across journals in applied mathematics, operations research, radiobiology, medicine, and medical physics. These works rarely include rigorous proofs or detailed derivations of their methodologies. Moreover, computer programs utilized for conducting numerical experiments seldom accompany these publications, thereby jeopardizing reproducibility. This monograph aims to provide a comprehensive pedagogical reference that brings researchers up to speed on optimal fractionation, utilizing and illustrating analytical techniques from linear algebra, calculus, linear programming, quadratic and nonlinear programming, robust optimization, and inverse optimization. Its purpose is to help readers understand the mathematics behind the optimal fractionation problem, empowering them to contribute original work to this field.

Table of contents

• Cover
• Half-title
• Endorsements
• Title page
• Copyright information
• Dedication
• Contents
• Preface
• 1 Introduction
• 2 Fractionation with a Single Organ-at-Risk
• 3 Fractionation with Multiple Organs-at-Risk
• 4 Robust Fractionation
• 5 Inverse Fractionation
• 6 Spatiotemporally Integrated Fractionation
• 7 Robust Spatiotemporally Integrated Fractionation
• 8 Fractionation with Two Modalities
• 9 Robust Fractionation with Two Modalities
• 10 Directions for Future Work
• Appendix Background on Optimization
• References
• Index