A Convection-Diffusion Model of Indicator Transport through an Organ

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Abstract
A model for interpretation of extravascular indicator dilution experiments is proposed, in which the indicator is assumed to enter the blood-tissue exchange region through vascular sources, to equilibrate instantaneously and locally between blood and tissue at the capillary-cell level, and, while maintaining this local equilibration, to be transported to vascular sinks by simultaneous diffusion and convection at a more macroscopic distance level. The model has the mathematical form of the time-dependent Fick diffusion equation to which a convection term was added. The model contains as opposite limiting cases the washout-type models and a recently proposed delayed wave model of the indicator dilution process. The various features of the extravascular indicator outflow pattern-appearance time, modal time, semi-log downslope, and dispersion about the mean-are described in terms of two parameters: (1) a diffusion parameter, square of source-to-sink distance divided by diffusion coefficient of the indicator in the tissue; (2) a convection parameter, the blood flow divided by steady-state solubility volume of distribution of the indicator in the tissue. In contrast to the preceding opposite limiting cases, the present model accounts plausibly for extravascular indicator experiments in dog kidney.