The use of mathematical models to describe various aspects of tumor growth has a history that spans the last five decades. However, the recent surge in the understanding of the processes that act at multiple scales to drive the advancement of cancer is allowing novel mathematical models of tumorigenesis to be developed. Cancer modeling is capturing the interest of clinical and experimental cancer researchers as they are becoming increasingly aware of the value of quantitative approaches and the impact that interdisciplinary research can have on the field.

The potential for progress is exciting for all; as an example, NATURE recently published an article entitled Mathematical Oncology: Caner Summed Up where the authors stated, "understanding the complex, non-linear systems in cancer biology will require ongoing interdisciplinary, interactive research in which mathematical models, informed by extant data and continuously revised by new information, guide experimental design and interpretation." As new experimental data becomes available and computational methods become more accessible, the future of cancer modeling is, without doubt, the formulation of a complete multi-scale, mathematical framework that possibly combines continuous and discrete approaches to model tumor initiation (including mutation acquisition, cancer stems cells, and tumor heterogeneity), resulting in an avascular tumor that undergoes the angiogenic switch and becomes vascular invasive. The existence of such a virtual tumor model has the potential to greatly impact the way cancer is studied and treated.

Here at the University of Michigan, new collaborations are being forged in order to combine mathematical modeling, numerical simulation and in vivo experiment to gain deeper understanding of the cellular and sub-cellular processes associated with tumor growth.

Research Groups at the University of Michigan

Trachette Jackson (Mathematics)

Sean Morrison (Life Science Institute, Cell & Developmental Biology)

Jacques Nor (Dentistry and Biomedical Engineering)

Len Sander (Physics)

Max Wicha (Comprehensive Cancer Center, Dept of Internal Medicine)