A mass transfer model of temporal drug deposition in artery walls

A new mass transfer model has been formulated and implemented for predicting the penetration of liquid medication into an arterial wall. The model takes separate account of the transport of medication in the tissue and in the liquid stream. The transport equations take into consideration both diffusion and advection. An original lateral transport mechanism relating the drug concentrations in the tissue and in the advecting liquid stream is postulated and calibrated with experimental data from the literature. The special features of the mechanism are its non-Fickian nature and the accounting of the affinity (binding) of the drug to the tissue. Once established, the model was applied by means of numerical simulation to the in-artery distribution of Paclitaxel, a drug whose function is to minimize restenosis of the artery wall. The application encompassed parametric values of the duration of the drug therapy, the viscosity of the advecting fluid, and the pressure used to drive the drug into the tissue. It was found that the drug concentration at a clinically relevant depth in the artery wall varied linearly with the duration of the therapy, increased with increasing values of the driving pressure, and decreased for higher viscosities of the advecting fluid. In addition to its capabilities for predicting drug concentrations during the therapy duration period, the simulations also were able to follow the temporal variations of the drug distribution after the cessation of the therapy.