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Nonlinear behaviors of capillary formation in a deterministic angiogenesis model. (English) Zbl 1222.92018

Summary: We consider a deterministic approach for modeling angiogenesis. The model equations form a nonlinear coupled system of partial and ordinary differential equations. We propose an efficient, accurate and locally conservative numerical method to solve the nonlinear system. Computational results indicate that the model generates the overall dendritic structure and pattern of the capillary network morphologically similar to those observed in vivo. The influence of the capillary network and the growth factor distribution on each other and their interactions are investigated using numerical simulations.

MSC:

92C15 Developmental biology, pattern formation
37N25 Dynamical systems in biology
65C20 Probabilistic models, generic numerical methods in probability and statistics
92C50 Medical applications (general)
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