Angiogenesis- : understanding the mathematical challenge

Biological mathematics is based on the development of mathematical descriptions of biological systems and behaviour. We are interested in developing mathematical models of capillary sprouting, and have adopted a novel approach to our modelling, in that the mathematics is based on the biochemistry un...

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Bibliographic Details
Published in:Angiogenesis (London) 2006, Vol.9 (3), p.127-138
Main Authors: JONES, Pamela F, SLEEMAN, Brian D
Format: Article
Language:English
Subjects:
Angiopoietins - pharmacology
Animals
Biological and medical sciences
Blood and lymphatic vessels
Blood. Blood coagulation. Reticuloendothelial system
Capillaries - drug effects
Capillaries - physiology
Cardiology. Vascular system
Cardiovascular system
Diseases of the peripheral vessels. Diseases of the vena cava. Miscellaneous
Humans
Medical sciences
Models, Biological
Neovascularization, Physiologic
Pharmacology. Drug treatments
Vasodilator agents. Cerebral vasodilators
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Summary:Biological mathematics is based on the development of mathematical descriptions of biological systems and behaviour. We are interested in developing mathematical models of capillary sprouting, and have adopted a novel approach to our modelling, in that the mathematics is based on the biochemistry underpinning cell behaviour. By considering the crucial steps of the angiogenic process, and through an understanding of the biochemistry involved, we successfully developed a preliminary model of angiogenesis. More importantly, our approach is applicable to many other areas of biological research. As mathematics remains a mystery to the majority of life scientists, we have aimed to describe our mathematical modelling strategy in biological terms. The assumptions and simplifications that form the basis of the modelling are explained, pinpointing the manner in which the different biological processes are linked via the mathematics. Examples of simulations using the mathematical model are shown, highlighting the success of our approach.
ISSN:0969-6970
1573-7209
DOI:10.1007/s10456-006-9039-8