In this book we describe recent efforts to model tumor growth and invasion using an interdisciplinary approach that integrates mathematical and computational models of cancer with laboratory experiments and clinical data. The aim of these efforts has been to provide insight into the root causes of solid tumor invasion and metastasis, to aid in the understanding of experimental and clinical observations, and to help design new, targeted, experiments and treatment strategies. The ultimate goal is for modeling and simulation to aid in the development of individualized therapy protocols that minimize patient suffering while maximizing treatment effectiveness. In order to achieve this objective, mathematical and computational models are needed that quantify the links of three dimensional tumor-tissue architecture with the growth, invasion, and underlying microscale cellular and environmental characteristics. This approach requires a multiscale modeling framework that is capable of linking the molecular and cell scales directly to the patient data.

There are many ways to evaluate the progression of these efforts. Here we follow the major stages that progressively incorporate the complexity of the tumor environment: (i) modeling of avascular tumors in vitro and in silico to assess stages of tumor growth; (ii) interactions between a tumor and its in vivo microenvironment; (iii) modeling of vascularized tumors in silico to assess angiogenesis and vascular growth; (iv) modeling of vascularized tumors in vivo and in silico to assess tumor progression in the body.