The Mathematical Institute, University of Oxford, Eprints Archive

A Review of Mathematical Models for the Formation of
Vascular Networks

Scianna, M. and Bell, C. G. and Preziosi, L. (2012) A Review of Mathematical Models for the Formation of
Vascular Networks.
Annals of Biomedical Engineering . (Submitted)

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Abstract

Mainly two mechanisms are involved in the formation of blood vasculature: vasculogenesis and angiogenesis. The former consists of the formation of a capillary-like network from either a dispersed or a monolayered population of endothelial cells, reproducible also in vitro by specific experimental assays. The latter consists of the sprouting of new vessels from an existing capillary or post-capillary venule. Similar phenomena are also involved in the formation of the lymphatic system through a process generally called lymphangiogenesis.

A number of mathematical approaches have analysed these phenomena. This paper reviews the different modelling procedures, with a special emphasis on their ability to reproduce the biological system and to predict measured quantities which describe the overall processes. A comparison between the different methods is also made, highlighting their specific features.

Item Type:Article
Subjects:D - G > General
Research Groups:Oxford Centre for Collaborative Applied Mathematics
ID Code:1628
Deposited By:Peter Hudston
Deposited On:24 Nov 2012 08:58
Last Modified:24 Nov 2012 08:58

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