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.
Copyright Owner
Springer-Verlag
Copyright Date
2001
Language
en
File Format
application/pdf
Recommended Citation
Levine, Howard; Sleeman, Brian D.; and Nilsen-Hamilton, Marit, "Mathematical modeling of the onset of capillary formation initiating angiogenesis" (2001). Mathematics Publications. 160.
https://lib.dr.iastate.edu/math_pubs/160
Included in
Biochemistry, Biophysics, and Structural Biology Commons, Cell Biology Commons, Dynamical Systems Commons
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.