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 Regeneration. Annals of the New York Academy of Sciences, 1995), and is of fundamental importance in understanding the processes by which a tumour achieves vascularization. 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 cells (lining neighbouring vessels) towards the tumour. To facilitate locomotion, the cells exert appreciable traction forces upon the interstitial extracellular 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 extracellular matrix.