Mathematical model of the filtration in the vascular network of the ophidian glomerulus

The present work is a mathematical model of the fluid filtration in the glomerular network occurring in snakes. The model is based on the differential form of Starling's hypothesis and takes into account the angioarchitecture of the network and the behaviour on the microrheology of blood with nucleated red cells. The model predicts the hemodynamics and the transvascular fluxes in each vascular segment within the network. The model is applied to a vascular network of the glomerulus of the garter snake. A value of 0.593 microns/(s.mmHg) was determined for the hydraulic conductivity of the glomerular capillaries using the geometrical data of the network together with experimental data for the pressures and the blood flow rate reported in the literature. The analysis shows that the local filtration rates cover a wide range. In some of the vascular segments, the filtration leads to such a high increase in colloid-osmotic pressure that the level of the transvascular hydrostatic pressure difference is reached. Mathematical simulations of the variation of the glomerular blood flow rate due to vasoactivity of preglomerular arterioles show the effect on the filtration rate and the hemorheologic parameters.