The effects of tumor angiogenesis factor (TAF) and tumor inhibitor factors (TIFs) on tumor vascularization: A mathematical model

A mathematical model, which examines the effects of Tumor Angiogenesis Factor (TAF) and Tumor Inhibitor Factors (TIFs) on tumor angiogenesis and predicts the onset of vascularization, is presented. The TAF and TIFs are produced within the tumor, while in the prevascular stage, by a layer of viable proliferating cancer cells on the tumor boundary. When the concentrations of TAF and TIFs have reached a critical level, they are released into the surrounding tissue. If TAF and TIFs have penetrated the tissue to the extent that they can reach the tips of the neighboring capillaries, then regulation of the formation of new blood vessels begins. The present model describes this process in three stages, and the appropriate diffusion equations for the production and secretion of TAF and TIFs are solved in spherical geometry. The concentrations of these chemical substances are monitored and the rate of growth of the capillary boundary, which moves towards the tumor surface marking the onset of vascularization, is determined.