Mathematical modeling, analysis and simulation are set to play crucial roles in explaining tumor behavior, and the uncontrolled growth of cancer cells over multiple time and spatial scales. This book, the first to integrate state-of-the-art numerical techniques with experimental data, provides an in-depth assessment of tumor cell modeling at multiple scales. The first part of the text presents a detailed biological background with an examination of single-phase and multi-phase continuum tumor modeling, discrete cell modeling, and hybrid continuum-discrete modeling. In the final two chapters, the authors guide the reader through problem-based illustrations and case studies of brain and breast cancer, to demonstrate the future potential of modeling in cancer research. This book has wide interdisciplinary appeal and is a valuable resource for mathematical biologists, biomedical engineers and clinical cancer research communities wishing to understand this emerging field.
Vittorio Cristini is Professor of Health Information Sciences and Biomedical Engineering at the University of Texas, and of Systems Biology at the M. D. Anderson Cancer Center, Houston. He is also Honorary Professor of Mathematics at the University of Dundee, Scotland. Professor Cristini is a leading researcher in the fields of mathematical and computational biology, complex fluids, materials science and mathematical oncology. He has published several chapters in books and over 60 journal articles. John Lowengrub is a Professor of Mathematics, Materials Science, and Biomedical and Chemical Engineering at the University of California, Irvine. He has published over 80 journal articles along with several book chapters. Professor Lowengrub is a leading researcher in the fields of mathematical and computational biology, mathematical oncology, complex fluids, and materials science. His research has been supported by various institutions including the National Science Foundation, the National Institutes of Health, and the State of California.
Part I. Theory: 1. Introduction; 2. Biological background; 3. Continuum tumor modeling: single phase; 4. Analysis and calibration of single-phase continuum tumor models; 5. Continuum tumor modeling: multiphase; 6. Discrete cell modeling; 7. Hybrid continuum-discrete models; 8. Numerical schemes; Part II. Applications: 9. Continuum tumor modeling: a multidisciplinary approach; 10. Agent-based cell modeling: application to breast cancer.