The kinetics of solute clearance by a single tissue capillary of limited permeability: explicit solutions of two models and their bounds

Capillary net and injection modeling

A former work proved that the physiological Krogh model is valid and can be used as a tool by physicians and biologists in order to simulate drug injections. Here, after a short critical review, a more complete model describing the capillary net is established. A numerical method which can be used to solve the associate mathematical model is explained. Then, the results are discussed and used to explain why the Krogh model is valid despite its simplifying hypotheses. Diffusion and permeability coefficients are also estimated.

Evolution of the concentration field of an antibiotic during an injection

A complete mathematical model is presented which describes a substrate injection into a capillary and its diffusion in tissues. Numerical methods are implemented and compared, simplification is discussed and the results' behaviour is studied. A new experimental technique yields curves which are compared to the numerical solutions of the model and used for estimating diffusion and permeability coefficients. Furthermore it is proved that the physiological Krogh model is valid and can be used as a tool by physicians and biologists.

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.