A mathematical analysis of a model for capillary network formation in the absence of endothelial cell proliferation

B. D. Sleeman; A. R. A. Anderson; M. A. J. Chaplain

doi:10.1016/S0893-9659(99)00132-9

A mathematical analysis of a model for capillary network formation in the absence of endothelial cell proliferation

B. D. Sleeman, A. R. A. Anderson, M. A. J. Chaplain

Applied Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

An analysis of a parabolic partial differential equation modelling capillary network formation is presented. The model includes terms representing cell random motility, chemotaxis, and haptotaxis due to the presence of chemical stimuli: tumour angiogenic factors and fibronectin. The analysis provides an underlying insight into mechanisms of cell migration which are crucial for tumour angiogenesis. Specific 1 and 2D examples are discussed in detail.

Original language	English
Pages (from-to)	121-127
Number of pages	7
Journal	Applied Mathematics Letters
Volume	12
Issue number	8
DOIs	https://doi.org/10.1016/S0893-9659(99)00132-9
Publication status	Published - 1999

Keywords

Angiogenesis
Chemotaxis
Haptotaxis

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10.1016/S0893-9659(99)00132-9

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title = "A mathematical analysis of a model for capillary network formation in the absence of endothelial cell proliferation",

abstract = "An analysis of a parabolic partial differential equation modelling capillary network formation is presented. The model includes terms representing cell random motility, chemotaxis, and haptotaxis due to the presence of chemical stimuli: tumour angiogenic factors and fibronectin. The analysis provides an underlying insight into mechanisms of cell migration which are crucial for tumour angiogenesis. Specific 1 and 2D examples are discussed in detail.",

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AU - Sleeman, B. D.

AU - Anderson, A. R. A.

AU - Chaplain, M. A. J.

PY - 1999

Y1 - 1999

N2 - An analysis of a parabolic partial differential equation modelling capillary network formation is presented. The model includes terms representing cell random motility, chemotaxis, and haptotaxis due to the presence of chemical stimuli: tumour angiogenic factors and fibronectin. The analysis provides an underlying insight into mechanisms of cell migration which are crucial for tumour angiogenesis. Specific 1 and 2D examples are discussed in detail.

AB - An analysis of a parabolic partial differential equation modelling capillary network formation is presented. The model includes terms representing cell random motility, chemotaxis, and haptotaxis due to the presence of chemical stimuli: tumour angiogenic factors and fibronectin. The analysis provides an underlying insight into mechanisms of cell migration which are crucial for tumour angiogenesis. Specific 1 and 2D examples are discussed in detail.

KW - Angiogenesis

KW - Chemotaxis

KW - Haptotaxis

U2 - 10.1016/S0893-9659(99)00132-9

DO - 10.1016/S0893-9659(99)00132-9

M3 - Article

SN - 0893-9659

VL - 12

SP - 121

EP - 127

JO - Applied Mathematics Letters

JF - Applied Mathematics Letters

IS - 8

ER -

A mathematical analysis of a model for capillary network formation in the absence of endothelial cell proliferation

Abstract

Keywords

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