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A Cell-Based Model Exhibiting Branching and Anastomosis during Tumor-Induced Angiogenesis

Amy L. Bauer ^*, Trachette L. Jackson ^* and Yi Jiang 

^* Department of Mathematics, University of Michigan, Ann Arbor, Michigan; and Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico

Correspondence: Address reprint requests to Y. Jiang, Tel.: 505-665-5745; E-mail: jiang{at}lan1.gov.

This work describes the first cell-based model of tumor-induced angiogenesis. At the extracellular level, the model describes diffusion, uptake, and decay of tumor-secreted pro-angiogenic factor. At the cellular level, the model uses the cellular Potts model based on system-energy reduction to describe endothelial cell migration, growth, division, cellular adhesion, and the evolving structure of the stroma. Numerical simulations show: 1), different tumor-secreted pro-angiogenic factor gradient profiles dramatically affect capillary sprout morphology; 2), average sprout extension speeds depend on the proximity of the proliferating region to the sprout tip, and the coordination of cellular functions; and 3), inhomogeneities in the extravascular tissue lead to sprout branching and anastomosis, phenomena that emerge without any prescribed rules. This model provides a quantitative framework to test hypotheses on the biochemical and biomechanical mechanisms that control tumor-induced angiogenesis.

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