Campus Units

Mathematics, Biochemistry, Biophysics and Molecular Biology, Roy J. Carver Department of

Document Type

Article

Publication Version

Accepted Manuscript

Publication Date

3-2001

Journal or Book Title

Journal of Mathematical Biology

Volume

42

First Page

195

Last Page

238

DOI

10.1007/s002850000037

Abstract

It is well accepted that neo-vascular formation can be divided into three main stages (which may be overlapping): (1) changes within the existing vessel, (2) formation of a new channel, (3) maturation of the new vessel.

In this paper we present a new approach to angiogenesis, based on the theory of reinforced random walks, coupled with a Michaelis-Menten type mechanism which views the endothelial cell receptors as the catalyst for transforming angiogenic factor into proteolytic enzyme in order to model the first stage. In this model, a single layer of endothelial cells is separated by a vascular wall from an extracellular tissue matrix. A coupled system of ordinary and partial differential equations is derived which, in the presence of an angiogenic agent, predicts the aggregation of the endothelial cells and the collapse of the vascular lamina, opening a passage into the extracellular matrix. We refer to this as the onset of vascular sprouting. Some biological evidence for the correctness of our model is indicated by the formation of teats in utero. Further evidence for the correctness of the model is given by its prediction that endothelial cells will line the nascent capillary at the onset of capillary angiogenesis.

Comments

The final publication is available at Springer via https://doi.org/10.1007/s002850000037. Levine, Howard A., Brian D. Sleeman, and Marit Nilsen-Hamilton. "Mathematical modeling of the onset of capillary formation initiating angiogenesis." Journal of Mathematical Biology 42, no. 3 (2001): 195-238. Posted with permission.

Copyright Owner

Springer-Verlag

Language

en

File Format

application/pdf

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