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20 Mathematical modelling of angiogenesis and vascular adaptation

Elsevier Science & Technology
DOI: 10.1016/s1571-0831(06)80024-9
  • Medicine


Publisher Summary This chapter discusses the properties of the vascular system. Blood flow is necessary to develop realistic models of angiogenesis. Most of the models in the literature concentrate on endothelial cell migration in response to the chemotactic stimulus of the vascular endothelial growth factor (VEGF) and neglect most issues such as blood flow and hematocrit heterogeneity, coupling among metabolic needs of tissue, and vascular structural adaptation. However, these phenomena must be taken into account when coupling models of angiogenesis to models of solid-tumor growth. The usual assumption is that the local concentration of oxygen or other nutrients is proportional to the local concentration of endothelial cells. This assumption may be overly simplistic because of blood-flow heterogeneity. When the nutrient concentration is proportional to the local endothelial cell concentration, the growth of the colony is markedly different from that for which blood-flow heterogeneity is taken into account. A similar situation arises at the time of modeling chemotherapy. If it is assumed that the blood-borne concentration of a drug is proportional to the local concentration of endothelial cells, it might overestimate the concentration of the drug reaching regions in which blood flow is poor and underestimate the concentration in regions where blood flow is high. As a result, the intrinsic nonuniformity in the spatial structure of many solid tumors may be an important factor in predicting the efficacy of chemotherapy protocols.

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