Optimal Fractionation in Radiotherapy

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.

• Presents several mathematical formulations of the fractionation problem, allowing readers to appreciate the pros and cons of these formulations
• Provides detailed mathematical derivations of solutions to all formulations, enabling a deeper understanding of the fractionation problem
• Includes Python code that executes pseudocode listings, allowing readers to run and/or modify code to solve the fractionation problem with their choice of parameters