Transient solutions of equations for countercurrent capillary exchange

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Abstract
A model for passive countercurrent capillary exchange is presented, and solutions for transient responses are obtained. The model is applied to an analysis of hydrogen gas exchange in the renal medulla. Estimates of medullary flow per gram tissue are in reasonable agreement with estimates obtained with vascular tracers and similar to the values for whole kidney. Semilog plots of tissue washout curves appear nearly linear but will overestimate flow if the countercurrent process is inefficient and will underestimate flow if the countercurrent exchange is efficient. Analysis of the countercurrent process also provides some insights into the importance of tracer exchange between capillaries in vascular beds not arranged in orderly countercurrent networks. Capillaries in other vascular beds that are close enough together to permit considerable exchange of inert gas tracers may simulate countercurrent effects if some of the adjacent capillaries are in countercurrent or staggered cocurrent arrangements.