title: Angiogenesis - understanding the mathematical challenge.
abstract: 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.
authors.affiliation: Leeds Institute of Molecular Medicine, University of Leeds, JIF Building, St. James's University Hospital, Leeds LS9 7TF, UK. p.jones@leeds.ac.uk
authors.forename: Pamela F
authors.initials: PF
authors.lastname: Jones
authors.forename: Brian D
authors.initials: BD
authors.lastname: Sleeman
mesh_terms: D042682:Angiopoietins / Q000494:pharmacology; D000818:Animals; D002196:Capillaries / Q000187:drug effects / Q000502:physiology; D006801:Humans; D008954:Models, Biological; D018919:Neovascularization, Physiologic
chemical_list: D042682:Angiopoietins