Substrate concentrations in tissue surrounding single capillaries

A mathematical model for the laser treatment of heart disease

“…The permeability coefficient of capillaries is b à B2250  10 À6 m s À1 (Salathe and Wang, 1980), so that the value of k; the ratio of the timescales of uptake and diffusion, based on this value is estimated to lie between Oð10 À1 Þ and Oð1Þ: However, it is possible that the walls of the laser-created channels are more permeable than capillaries so that the vale of k is smaller still. Alternatively, there is evidence that, after a period of about a month, the tunnels become lined with a layer of fibrin thrombus which might act to reduce the wall permeability (Horvath et al, 1995).…”

“…Thus we consider both limits of small and large wall permeability. The tissue is assumed to consume oxygen at a rate Q Ã C Ã 0 y; where Q Ã B2 Â 10 À3 s À1 (Salathe and Wang, 1980), which gives l; the ratio of diffusion to uptake timescales, as lB0:2: However, this parameter may be significantly smaller, depending on the degree of tissue ischemia.…”