Steady-state analysis of a mathematical model for capillary network formation in the absence of tumor source

This paper extends the work done in [S. Pamuk, Ph.D. Thesis, Iowa State University, 2000; Bull. Math. Biol. 63 (5) (2001) 801] in that we investigate the condition that is needed for the degradation of basement membrane in a mathematical model for capillary network formation. To do this, the steady-state behavior of tumor angiogenesis factor is studied under restricted assumptions, and the tumor angiogenesis factor threshold that activates the transport equations in the capillary is estimated using this steady state. Therefore, once the concentration of the tumor angiogenesis factor in the inner vessel wall reaches this threshold value, endothelial cells begin to move into the extracellular matrix for the start of angiogenesis. Furthermore, we do believe that the result we obtain in this paper provides an underlying insight into mechanisms of cell migration which are crucial for tumor angiogenesis.