A PHYSICOMATHEMATICAL CONCEPT OF CONTINUOUS DISTRIBUTION OF SPECIFIC BLOOD FLOW THROUGH THE ORGANS

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Abstract
The distribution of specific blood flow throughout the vascular bed of an organ has been treated analytically. Appropriate integral transforms have been derived for the actual determination of the distribution function when the tracer indicator remains confined to the lumen of the vessels. The integral equations derived are of the Volterra type, and the distribution function of specific blood flow is one reducible to the Euler beta function. It is expected that, under certain transformations, the distribution function of specific blood flow for a given organ, like the structure and shape of the latter, would not vary to any significant extent under different physiological conditions. Such transformations render the whole process practically an invariant one. It will be shown subsequently, with actual experimental data, that this is so for the kidney. The distribution functions dealt with thus far are those in a single variable. This obviously constitutes a preliminary step in the study of distribution. From the physiological point of view it is more important to determine the simultaneous distribution of 2 variables in the same unit (ventilation and flow per unit air volume in the lung, blood flow and filtration rate per unit blood volume in the kidney). The question of compound distribution for 2 or more physiological quantities is now under study.

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