Theoretical modeling of endovascular drug delivery into a multilayer arterial wall from a drug-coated balloon

Drug-coated balloons (DCBs) are used commonly for delivering drug into diseased arteries. When applied on the inner surface of an artery, drug is transported from the balloon into the multilayer arterial wall through diffusion and advection, where it is ultimately absorbed through binding reactions. Mathematical modeling of these mass transport processes has the potential to help understand and optimize balloon-based drug delivery, thereby ensuring both safety and efficacy. The present work derives a closed-form solution for the multilayer cylindrical convection-diffusion-reaction (CDR) transport problem that occurs in balloon-based endovascular drug delivery. The model is presented for an arbitrary number of layers, and accounts for various transport processes in terms of relevant non-dimensional numbers. Quasi-orthogonality for this multilayer problem is derived. Closed-form expressions for the amounts of drug delivered by the balloon, bound in each arterial layer and lost from the external surfaces are derived. It is shown that only a small fraction of drug from the balloon is actually delivered into the artery during the short exposure time, which is influenced strongly by the diffusion coefficient of the inner-most layer. Further, binding of the drug is found to depend strongly on the reaction coefficient, expressed in terms of the Damköhler number. It is shown that boundary conditions on the inner and outer surfaces, expressed in terms of Sherwood numbers, play a role in drug uptake over a longer time period. The model is general enough to be applicable for a wide variety of scenarios and operational conditions, including an arbitrary number of layers. Results from this work provide fundamental insights into drug transport and uptake processes. In addition, these results may help improve the safety and efficacy of balloon-based drug delivery.