In the past several decades there has been significant progress in understanding and identifying the causes of cancer and in developing effective treatment strategies. Nevertheless, a cure remains frustratingly elusive. At its most essential level, cancer involves the abnormal growth and spread of tissues within a body. Yet each cancer is unique, based on the tissue in the body where it originates and the particular person who has it. While molecular mechanisms and cell-scale dynamics governing tumor cell migration and proliferation are well studied from a biological perspective, cancer progression actually involves events that occur at multiple time and spatial scales. What occurs at the nano-scale of molecules and micro-scale of cells affects the behavior of tissue at the centimeter-scale – and vice versa. In order to better understand these multiscale linkages, mathematical modeling, analysis, and simulation have been employed to study tumor behavior. The complex shapes and invasive behavior of tumors requires a nonlinear approach, meaning that effects at various physical scales within the tissue do not necessarily influence each other additively. Hence, the combination of events may yield a response greater or less than of each component, depending whether there is synchrony. The application of such computational models in the clinical setting, however, is still in its infancy.

In this book we outline recent advances in the field of mathematical modeling and the simulation of cancer, particularly with respect to multiscale, nonlinear, computational models that integrate theory and experiment.