Mathematical models of tumor response in advanced radiotherapy techniques

Abstract

Radiotherapy is a cancer treatment that consists of irradiating tumors to eliminate tumor cells while maintaining the dose on neighbor organs/tissues within tolerance levels. Mathematical models predict the efficacy and toxicity of radiotherapy, assisting in designing more effective and less toxic treatments. This thesis aims to design mathematical models of tumor response to advanced radiotherapies by using ordinary (ODEs), partial (PDEs), delay (DDEs), and impulsive differential equations (IDEs). The focus is on radioimmunotherapy and FLASH radiotherapy, which involve biological mechanisms that require the development of novel mathematical models, as the existing ones for conventional radiotherapy are not directly applicable.