Introduction to Mathematical Oncology

Introduction to Mathematical Oncology provides biologically well-motivated and mathematically tractable models for cancer biology and treatment, covering medical and biological background, modeling issues, and existing methods. It introduces mathematical and programming tools, analytical and numerical studies, and new mathematical tools. It also examines multi-scale modeling efforts on prostate cancer growth and treatment dynamics, as well as mechanistically formulated models with applications to real tumors and validation using clinical data.

Format: Paperback / softback
Length: 472 pages
Publication date: 31 March 2021
Publisher: Taylor & Francis Ltd

Introduction to Mathematical Oncology provides biologically well-motivated and mathematically tractable models that facilitate both a deep understanding of cancer biology and better cancer treatment designs. It covers the medical and biological background of the diseases, modeling issues, and existing methods and their limitations. The authors introduce mathematical and programming tools, along with analytical and numerical studies of the models. They also develop new mathematical tools and look to future improvements on dynamical models.

After introducing the general theory of medicine and exploring how mathematics can be essential in its understanding, the text describes well-known, practical, and insightful mathematical models of avascular tumor growth and mathematically tractable treatment models based on ordinary differential equations. It continues the topic of avascular tumor growth in the context of partial differential equation models by incorporating the spatial structure and physiological structure, such as cell size. The book then focuses on the recent active multi-scale modeling efforts on prostate cancer growth and treatment dynamics. It also examines more mechanistically formulated models, including cell quota-based population growth models, with applications to real tumors and validation using clinical data. The remainder of the text presents abundant additional historical, biological, and medical background materials for advanced and specific treatment modeling efforts.

Extensively classroom-tested in undergraduate and graduate courses, this self-contained book allows instructors to emphasize specific topics relevant to clinical cancer biology and treatment. It can be used in a variety of ways, including a single-semester undergraduate course, a graduate-level course, or a research seminar.

The book begins with a brief overview of the history of mathematical oncology and its applications to cancer treatment. It then introduces the basic concepts of mathematical modeling, including differential equations, optimization, and simulation. The authors then discuss the medical and biological background of cancer, including the types of cancer, their causes, and their progression.

Next, the book covers the modeling issues associated with cancer. These include the development of mathematical models that can accurately represent the behavior of cancer cells, the identification of the key parameters that govern cancer growth and progression, and the development of effective treatment strategies. The authors discuss the use of mathematical models to predict the response of cancer patients to different treatments, as well as to develop new treatments.

The book also covers the existing methods and their limitations. These include the use of chemotherapy, radiation therapy, and surgery, as well as the use of targeted therapies and immunotherapies. The authors discuss the advantages and disadvantages of each method and the challenges associated with their implementation.

In addition to the mathematical models, the book also includes analytical and numerical studies of the models. These studies help to validate the models and to identify the key parameters that govern cancer growth and progression. The authors use a variety of techniques, including finite difference methods, finite element methods, and Monte Carlo methods, to solve the mathematical models.

The book also develops new mathematical tools and looks to future improvements on dynamical models. These tools include the use of machine learning and artificial intelligence to improve the accuracy of cancer predictions and to develop new treatment strategies. The authors also discuss the use of personalized medicine to tailor treatment strategies to individual patients.

Finally, the book presents abundant additional historical, biological, and medical background materials for advanced and specific treatment modeling efforts. These materials include case studies, clinical trials, and research papers. The authors provide detailed explanations of the methods used in these studies and the results obtained.

In conclusion, Introduction to Mathematical Oncology is a comprehensive and well-written book that provides biologically well-motivated and mathematically tractable models that facilitate both a deep understanding of cancer biology and better cancer treatment designs. It covers the medical and biological background of the diseases, modeling issues, and existing methods and their limitations. The authors introduce mathematical and programming tools, along with analytical and numerical studies of the models. They also develop new mathematical tools and look to future improvements on dynamical models. Extensively classroom-tested in undergraduate and graduate courses, this book allows instructors to emphasize specific topics relevant to clinical cancer biology and treatment.

Weight: 907g
Dimension: 234 x 156 (mm)
ISBN-13: 9780367783150