Spatial heterogeneity and microvascular fluid exchange: a simple macroscopic equation

The effect of the spatial distribution of capillary membrane "pores" on the estimate for the hydraulic conductivity (Lp) and the reflection coefficient (sigma s) in the presence of an axial gradient in the hydrostatic pressure difference (delta P) is examined. The differential fluid balance is integrated along the length of the capillary and a simple analytic solution is obtained for a capillary membrane of arbitrary structure. The effective hydrostatic pressure difference, (delta P)eff, is not simply the average of the arterial [(delta P)a] and venous [(delta P)v] pressure differences but is instead found to be (delta P)eff identical to [(delta P)a + (delta P)v]/2 + kappa [(delta P)a - (delta P)v]/2, where kappa identical to 1 - 2 (Lp1/Lp). The two macroscopic coefficients, Lp and Lp1, are related to integrals of the pore density along the length of the capillary. Failure to account for spatial heterogeneity may lead to an incorrect interpretation of the experimental data, e.g., the estimate for sigma s could be greater than 1 or less than 0 depending on the pore distribution and pressure gradient along the capillary. The single capillary hydraulic conductivity measurements of Gore [1982), Amer. J. Physiol. 242, H268-H287) and data on the microvascular pressure distributions (Bohlen and Gore (1977), Microvasc. Res. 14, 251-264) are used to estimate the magnitude of these effects.