Journal
COMPUTATIONAL MECHANICS
Volume 53, Issue 3, Pages 449-464Publisher
SPRINGER
DOI: 10.1007/s00466-013-0958-0
Keywords
Tumor angiogenesis; Isogeometric analysis; Numerical simulations; Random walk; Capillary growth
Funding
- European Research Council through the FP7 Ideas Starting Grant program [307201]
- Conselleria de Educacion e Ordenacion Universitaria de la Xunta de Galicia
- Conselleria de Educacion e Ordenacion Universitaria de la Xunta de Galicia [CN2011/002]
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The growth of new vascular networks from pre-existing capillaries (angiogenesis) plays a pivotal role in tumor development. Mathematical modeling of tumor-induced angiogenesis may help understand the underlying biology of the process and provide new hypotheses for experimentation. Here, we couple an existing deterministic continuum theory with a discrete random walk, proposing a new model that accounts for chemotactic and haptotactic cellular migration. We propose an efficient numerical method to approximate the solution of the model. The accuracy, stability and effectiveness of our algorithms permitted us to perform large-scale three-dimensional simulations which, in contrast to two-dimensional calculations, show a topological complexity similar to that found in experiments. Finally, we use our model and simulations to investigate the role of haptotaxis and chemotaxis in the mobility of tip endothelial cells and its influence in the final vascular patterns.
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