ANALYTICAL MODEL OF LOCAL DISTRIBUTION OF CHEMICALS IN TISSUES WITH FIRST-ORDER-RATE METABOLISM KINETICS

The profile of regional distribution of chemicals in tissue is important for the development of novel locally applied therapies. Here we introduce an analytical approach for the temporal and spatial regional distribution of chemicals in living tissues. The new aspect of this model is in local chemical concentration dependence on the tissue perfusion rate, in addition to diffusion and metabolism rates. Using the Duhamel theorem we performed dimensionless and dimensional analysis for local chemical distribution and report on steady-state and transient solutions for tissues with the first-order kinetic rate of clearance by perfusion and metabolism. The predictions of our model are in good correlation with clinically observed data on percutaneous ethanol ablation of liver. Our results emphasize the importance of mathematical modeling that includes perfusion in the planning of therapies with local chemical distribution in living tissues.