Animal-to-human extrapolation using compartmental models

We have been studying how to use compartmental models to reliably extrapolate toxicological experimental results from one animal species to another with the ultimate goal of useful extrapolation to man. We have taken, as the fundamental core of our analysis, the physically necessary equations describing mass balance. These equations are the classical Fickian equations of the form VdC/dt = Q(a - v). These equations are not a complete set since they are insufficient to provide estimation of venous, arterial, or tissue concentrations with time. Therefore, the mass balance equations must be augmented with additional phenomenological relations to permit the desired calculations. Many investigators use the venous exist condition. While it is clear how to extrapolate the mass balance equations from one sized animal to another or from one species to another, it is not clear how to extrapolate the venous exit condition. In this research we have evaluated the venous exit condition by comparing it with approximate analyses of perfusion and substance diffusion in the tissue.