An effective time-constant algorithm for drug transport to capillaries and surrounding tissues

Expressions for a single time constant were developed in Maple (Waterloo Maple, Inc.) to calculate the rate at which a drug reaches steady-state levels in the blood capillaries and neighboring tissues. The solute concentration in the capillary region was represented by a one-dimensional convection-diffusion model. In a first case study, the plasma and the tissue reached equilibrium very quickly. Within the dynamic regime, the amount of drugs collected in both compartments increased with the Peclet number while the relaxation time to a steady-state value decreased. A similar conclusion was drawn, in a second case study, when axial and radial diffusive transports were considered important in the lungs or the skin. Also, as the mass transfer Biot number decreased, a larger amount of medication was delivered to the tissue at a given time during the transient period. Additional applications of the approach included the analysis of oxygen transport in peripheral nerves and the design of hollow fibre bioreactors.