The goal in radiotherapy for cancer is to maximize tumor-kill while limiting toxic effects on nearby healthy anatomies. This is attempted via spatial localization of radiation dose, temporal dispersion of radiation dose, and radiation modality selection. The spatial component involves prescribing a high dose to the tumor and putting upper limits on the dose delivered to the healthy anatomies. The radiation intensity profile is then optimized to meet this treatment protocol as closely as possible. This is called fluence-map optimization. The temporal component of the problem involves breaking the total planned dose into several treatment sessions called fractions, which are administered over multiple weeks. This gives the healthy tissue some time to recover between sessions, as it possesses better damage-repair capabilities than the tumor. The key challenge on this temporal side is to choose an optimal number of fractions and the corresponding dosing schedule. This is called the optimal fractionation problem, and has been studied clinically for over a hundred years. Radiotherapy can be administered using different modalities such as photons, protons, and carbon ions. The choice of a modality depends on its physical characteristics and its radiobiological power to damage cells. This tutorial provides a detailed account of mathematical models that utilize the ubiquitous linear-quadratic (LQ) dose-response framework to guide decisions in the fractionation and modality selection problems. The tutorial emphasizes efficient exact solution methods developed in the last five years, and touches upon diverse methodological techniques from linear, nonlinear, convex, inverse, robust, and stochastic dynamic optimization. A brief overview of work that integrates the spatial and temporal components of the problem, and also of mathematical methodology designed to adapt doses to the tumor’s observed biological condition, is included. Potential directions for future research are outlined. Since treatment decisions in this tutorial are driven by a dose-response model, it fits within a paradigm called response-guided dosing, interpreted in a broad sense.
Author: Archis Ghate