Preface
On December 23, 1971, President Richard Nixon signed into law the National Cancer Act, effectively declaring a never-ending war on cancer. Despite decades of significant investments and the relentless efforts of the medical and pharmaceutical communities, progress in efficacy of treatment for most cancers remains surprisingly limited. In 2003, the director of the National Cancer Institute issued an ambitious challenge “to eliminate the suffering and death from cancer, and to do so by 2015.” Although overly optimistic, this heroic goal was supported by the American Association for Cancer Research in 2005. Sadly, most types of cancer remain incurable and the death rate for cancers in the United States dropped only about 10 percent from 1975 to 2011.
Needless to say, new research directions and methods are desperately needed to win this ongoing war on cancer. Cancer is largely an evolving process that expresses different challenges in different patients in the same stage of disease and in the same patient at different stages. Therefore, consistent calls have been made for individualized treatment strategies, often referred to as personalized medicine. Central to any such individualization of medical intervention is the requirement for deep understanding of tumor dynamics at a variety of levels, from the whole organism to individual molecules.
Mathematical oncology is therefore emerging as a foundational discipline for modern treatment innovations. It promises to provide tools for both quantification of key parameters from patient-specific clinical data and for customizing cancer treatment using carefully formulated mathematical models. Over the past decade, mathematical oncology has grown into an exciting field evolving at a breathtaking pace. This textbook was conceived when the two of us (YK and JDN) decided to offer a graduate level course on mathematical medicine at Arizona State University (ASU) in 2007. We have since taught it many times at ASU, including a variety of mathematical models of cancer and viral infections. The book was originally set to be delivered in 2008 with the title, Dynamical Models in Medicine. However, teaching mathematical medicine the first time in earnest rapidly taught us that the book project was too broad and ambitious. After delving deep into the wonderland of mathematical medicine via research publications, we decided to limit our scope to mathematical oncology. As the years went by we continuously iterated and evolved the contents, eventually deciding to focus on biologically well motivated and mathematically tractable models that can inspire a deeper understanding of cancer biology and help design better cancer treatments. Due to these limitations, many timely and important topics of mathematical oncology are left untouched. We sincerely apologize to any colleagues who may feel slighted by such omissions, and sincerely hope that this text provides a gateway through which readers can find their way to the many excellent studies not found in these pages.
Indeed, the purpose for writing this book was primarily pedagogical. Although we hope that the book will be useful to professionals, it is intended to be used as a textbook for both graduate and upper-division undergraduate courses in mathematical oncology. It therefore contains many exercises and research projects of varying levels of difficulty.
Chapter 1 provides a brief introduction to the general theory of medicine and how mathematics can be essential in its understanding. Chapter 2 introduces the readers to some well-known, practical, and insightful mathematical models of avascular tumor growth and some 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, and 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. Chapters 7 through 12 present abundant additional historical, biological, and medical background materials for advanced and specific treatment modeling efforts.
The text may be used in a variety of ways, allowing instructors to emphasize specific topics relevant to clinical cancer biology and treatment. A sample single semester undergraduate level course may cover the first three chapters plus Chapter 5. A more ambitious graduate level course may cover the first six chapters plus selected readings from latter material and cited literature. A full year sequence on mathematical oncology may cover most of the chapters contained in this book.
A book such as this could not exist without creative input from many sources besides its authors. First and foremost, we would like to thank our students and colleagues, who in the last eight years have provided us with many helpful inputs and whose interest in mathematical medicine inspired us. We would also like to thank the School of Mathematical and Statistical Sciences at ASU for allowing us to repeatedly teach the course on mathematical medicine and for providing a first rate environment for our research efforts in mathematical medicine. We are grateful to CRC editor Sunil Nair and his team, for their unlimited patience and support during this long period of textbook development.
Last but not the least, we would like to thank our families for their constant support for this seemingly never-ending book project. In particular, YK would like to thank his wife, Aijun Zhang, for frequently reminding him that it is important to finish this book soon. YK would also like to thank his daughters Youny and Belany and son Foris for being great kids so that he can spend more time on writing this book. A special thank is due to Youny for her creative cover design for this book. JDN begs the forgiveness of his wife and daughter, Bethel and Grace, who had to share his attention with this book and endure many absences, including a months-long trip to Finland. A significant fraction of this text is a result of their patience and understanding. SEE would like to thank his co-authors for their long mentorship and perseverance in this project. He would also like to thank his family, in particular his mother and father for their unconditional support in all endeavors, his brother Keenan and sister Greta for the many friendly arguments that lead to insight, and his fiancée Lindsey, for sharing her time with this book with gentle good humor.
Yang Kuang, John D. Nagy, and Steffen E. Eikenberry
July, 20151
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