A structure-sensitive continuum model of arterial drug deposition

The successful function of drug-eluting devices used in the treatment of atherosclerosis relies on the concentration and retention of the drug in the vessel wall. While drug deposition necessarily depends on the underlying tissue structure, conventional models do not account for the intrinsic structural complexity of arterial tissue and its impact on deposition. By employing only average bulk material properties, the capability to predict the potential for local toxicity or therapeutic failure is limited. To address these limitations, we have developed a model that accounts explicitly for variations in the tissue structure. The approach uses a laminate approximation of the underlying microscopic structure to specify an expression for the continuous spatial dependence of the effective macroscopic material properties. Based on this continuum description, we derive an analytic expression for drug uptake into arterial tissue under typical ex vivo experimental conditions. This expression is used to extract relevant material properties for paclitaxel in bovine arteries based on available literature data. The best fit parameters are then used as the basis for numerical simulations of long-term deposition behavior from a stent with a pure paclitaxel coating. The results of these simulations are quantitatively consistent with previously reported in vivo observations. We also demonstrate that significant errors can arise in both the interpretation of experimental data and the prediction of drug deposition when structural heterogeneities are ignored. Establishing a robust deposition model can ultimately reduce empiricism in the design of drug-eluting devices, providing a facile means to guide the development and refinement of these technologies.