Dynamical Models in Medicine

This self-contained book focuses on mathematical models related to cancer growth and treatment. It presents the medical and biological background of the diseases, specific issues to be modeled, and existing methods and their limitations. The book introduces mathematical and programming tools, along with analytical and numerical studies of the models. The authors also develop new mathematical tools and look to future improvements on dynamical models. The text provides many classroom-tested exercises and projects at the end of most chapters. Chapter 1 provides a brief introduction to the general theory of medicine and how mathematics can be essential in its understanding. Chapter 2 introduces readers to some well-known, practical, and insightful mathematical models of avascular tumor growth and mathematically tractable treatment models based on ordinary differential equations. Chapter 3 continues the topic of avascular tumor growth in the context of partial differential equation (PDE) models by incorporating the spatial structure while Chapter 4 expands the topic of avascular tumor growth in a PDE context by incorporating physiological structure, such as cell size. Chapter 5 focuses on the recent active multi-scale modeling efforts on prostate cancer growth and treatment dynamics. Chapter 6 exposes readers to more mechanistically formulated models, including cell quota-based population growth models with applications to real tumors and validation using clinical data. The remaining chapters present abundant additional historical, biological, and medical background materials for advanced and specific treatment modeling efforts. Although this book is useful to professionals in various fields, it is designed as a textbook for both graduate and upper-division undergraduate courses in mathematical oncology. The text can be used in a variety of ways, allowing instructors to emphasize specific topics relevant to clinical cancer biology and treatment. A sample single semester