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.

‘This book provides a wonderfully rigorous and comprehensive treatment of the mathematics behind fractionation in radiation therapy. It consolidates a significant body of work in a consistent manner, making it a go-to reference for the expert and beginner alike. The inclusion of robust optimization and inverse optimization in the context of fractionation provides considerable depth, reinforcing the value of interdisciplinary research.'

Timothy Chan - University of Toronto

‘This text provides a unifying mathematical framework for the fractionation decision in radiotherapy. It offers a rich blend of mathematical analysis, numerical examples, codes, exercises, and bibliographic notes for an in-depth understanding and implementation of the concepts discussed. The book presents a fresh perspective to the long-standing fractionation debate in the field of radiotherapy and can inspire the design of new clinical trials to improve treatment efficacy for cancer patients.’

Ehsan Salari - Wichita State University