Mathematical Biology Seminar

Amy Bauer, University of Michigan
Wednesday Feb 7, 2007
2:55pm in LCB 219
A Cell-Based Model Exhibiting Branching and Anastomosis During Tumor-Induced Angiogenesis


In this talk I will describe a new cell-based model of tumor-induced angiogenesis. Tumor-induced angiogenesis is the formation of new blood vessels from existing vasculature in response to chemical signals from a tumor. This process marks the pivotal transition from avascular to vascular tumor growth, a progressive stage of cancer beyond which cancer becomes extremely difficult to treat and survival rates decrease.

The model is structured in terms of the dynamics occurring at different time and length scales, that is at the extracellular and intercellular levels. At the extracellular level, the model describes diffusion, uptake, and decay of tumor-secreted pro-angiogenic factor (VEGF). At the cellular level, the model uses a discrete lattice Monte Carlo algorithm based on system-energy reduction to describe cell migration, growth, division, cellular adhesion, and the evolving structure of the tissue. This model provides a quantitative framework to test hypotheses on the biochemical and biomechanical mechanisms that cause tumor-induced angiogenesis.

Results from numerical simulations will be presented that demonstrate the model's ability to capture realistic vascular structures and more complex events such as branching (vessel bifurcation) and anastomosis (vessels fusing). Our studies show that different VEGF gradient profiles dramatically affect vessel morphology and that cell proliferation further from the tip of the new vessel yielded faster average rates of vessel extension. Results also suggest that heterogeneities in the tissue may be important mechanisms leading to vessel branching.