Publication: Two dimensional soliton in tumor induced angiogenesis
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2020-08-05
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IOP Science
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Abstract
Ensemble averages of a stochastic model show that, after a formation stage, the tips of active blood vessels in an angiogenic network form a moving two dimensional stable diffusive soliton, which advances toward sources of growth factor. Here we use methods of multiple scales to find the diffusive soliton as a solution of a deterministic equation for the mean density of active endothelial cells tips. We characterize the diffusive soliton shape in a general geometry, and find that its vector velocity and the trajectory of its center of mass along curvilinear coordinates solve appropriate collective coordinate equations. The vessel tip density predicted by the soliton compares well with that obtained by ensemble averages of simulations of the stochastic model.
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Noise models, Nonlinear dynamics, Pattern formation, Systems biology
Bibliographic citation
Bonilla, L.L., Carretero, M. y Terragni, F. (2020). Two dimensional soliton in tumor induced angiogenesis. Journal of Statistical Mechanics: Theory and Experiment.