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A mechanochemical model of angiogenesis and vasculogenesis

Published online by Cambridge University Press:  15 November 2003

Daphne Manoussaki
Daphne Manoussaki*
Affiliation:
Department of Applied Mathematics, University of Crete, 71409 Heraklion, Greece. [email protected].
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Abstract

Vasculogenesis and angiogenesis are two different mechanisms for bloodvessel formation. Angiogenesis occurs when new vessels sprout from pre-existing vasculature in response to external chemical stimuli. Vasculogenesis occurs via the reorganization of randomly distributed cells into a blood vessel network. Experimental modelsof vasculogenesis have suggested that the cells exert traction forcesonto the extracellular matrix and that these forces may playan important role in the network forming process.In order to study the role of the mechanical and chemical forcesin both of these stages of blood vessel formation, we present amathematical model which assumes that (i) cells exert traction forcesonto the extracellular matrix, (ii) the matrix behaves as a linearviscoelastic material, (iii) the cells move along gradients ofexogenously supplied chemical stimuli (chemotaxis) and (iv) these stimuli diffuse or are uptaken by the cells.We study the equations numerically, present an appropriate finite difference scheme and simulate the formation of vascular networks in a plane. Our results compare very well with experimental observations and suggest that spontaneous formation of networks can be explained via a purely mechanical interaction betweencells and the extracellular matrix. We find that chemotaxis alone is not a sufficient force to stimulate formation of pattern. Moreover, duringvessel sprouting, we find that mechanical forces can help in the formationof well defined vascular structures.

Keywords

Angiogenesisvasculogenesischemotaxisextracellular matrixtheoretical modelsnumerical solution.
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 37 , Issue 4: Special issue on Biological and Biomedical Applications , July 2003 , pp. 581 - 599
Copyright
© EDP Sciences, SMAI, 2003

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