A mathematical model of tumour angiogenesis incorporating cellular traction and viscoelastic effects

Angiogenesis is defined as the outgrowth and formation of new vessels from a pre-existing vascular network (Rakusan, In: Cardiac Growth and Regenerati on. Annals of the New York Academy of Sciences, 1995), and is of fundamenta l importance in understanding the processes by which a tumour achieves vasc ularization. Diffusible substances, collectively called tumour angiogenesis factors are released from the tumour to elicit a variety of responses from the surrounding tissues, most importantly the migration of endothelial cel ls (lining neighbouring vessels) towards the tumour. To facilitate locomoti on, the cells exert appreciable traction forces upon the interstitial extra cellular matrix which, in turn, influences the resulting direction of their migration. In this paper, we examine the role played by cellular traction during cell migration and the corresponding viscoelastic effects of the ext racellular matrix. (C) 2000 Academic Press.