ADAPTIVE RADIATION THERAPY for HEAD AND NECK CANCER and the DIGITAL TWIN

This book was written to fill a specific gap. Three research communities—mathematical biology, radiation oncology, and data science—have converged around a single idea: the digital twin of a cancer patient. Yet, no textbook I am aware of presents the full stack, from the biology of squamous cell carcinoma to the weak formulation of a reaction–diffusion equation, from the linear-quadratic survival curve to the adjoint of a 4D-variational assimilation scheme. Students and clinicians who want to understand adaptive radiation therapy (ART) for head and neck cancer (HNC) are forced to assemble their knowledge from scattered papers. This volume attempts to provide that knowledge in one coherent treatise. Scope. We focus on head and neck cancer because it is the paradigmatic site for ART: tumors shrink dramatically during treatment, organs-at-risk sit millimeters away, and the consequences of miscalculation—xerostomia, dysphagia, osteoradionecrosis—are lifelong. The mathematical and computational machinery developed here, however, generalizes to prostate, lung, brain, pancreas, and beyond. A reader who masters this volume can follow the contemporary digital-twin literature in any solid tumor. Audience. The book is self-contained for the reader with a background equivalent to a first-year graduate program in applied mathematics, physics, engineering, or biomedical sciences. We assume familiarity with multivariable calculus, linear algebra, and basic probability. Everything else—the biology, the radiation physics, the numerical analysis, the deep learning—is developed from first principles. Chapters are layered: the opening sections of each chapter are accessible to any motivated graduate student; the later sections contain the full mathematical machinery for specialists.