| A Mathematical Model of the First Steps of Turnour-Related Angiogenesis' Capillary Sprout Formation and Secondary (2008) | |||||||||||||
Abstract | |||||||||||||
| The growth of a solid turnour is dependent on an adequate supply of nutrients. A turnout can establish a blood supply by inducing neighbouring blood vessels to sprout and grow towards it, a process known as anglogenesis. The turnout cells may secrete a number of diffusible chemicals which stimulate endothelial cells (EC) to proliferate and to rearrange themselves into capillary tubes or sprouts. In this paper we focus firstly upon the early stage of angiogenesis wherein the EC group together in the parent vessel to form the initial capillary sprout buds. A mathematical model for the formation of the capillary buds is presented which focuses on the potential role that haptotaxis may play. In the second part of the paper we turn attention to the EC within the growing and developing capillary sprouts as they migrate towards the turnout cells. Once again the potential role of haptotaxis is focussed upon. | |||||||||||||
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