A mathematical model of fluid transport in the kidney

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Abstract
A mathematical model of the rat kidney is developed from glomerular and tubular submodels. It is assumed that all nephrons are identical, that the hydraulic pressure in the tubules obeys Hagen-Poiseuille''s law, that the rate of fluid reabsorption depends on the flow rate of tubular fluid and that the tubules are distensible. The independent variables of the model are selected to comply with experimental measurements in the hydropenic rat. The model is used to evaluate the mechanism of glomerulotubular balance: changing the mean ultrafiltration pressure in the glomerular capillaries has a substantial influence on glomerular filtration rate (GFR). A change in the rate of fluid reabsorption in the proximal tubules has a strong influence on GFR notwithstanding that the change in GFR is smaller than that in the rate of fluid reabsorption. The calculated values for the hydraulic pressure profile in the tubular system and the interstitial pressure during ureteral obstruction are in close agreement with experimental measurements. Increasing the arterial hematocrit above normal causes a substantial decrease in GFR, while reducing it below normal has only a small effect on GFR.