In this paper, we discuss a technique for weakly enforcing flow rate conditions in computational hemodynamics. In particular, we study the effectiveness of cutting lateral branches from the computational domain and replacing them with non-perturbing boundary conditions to simplify the geometrical reconstruction and the numerical simulation. All these features are investigated both in the case of rigid and compliant walls. Several numerical results are presented to discuss the reliability of the proposed method.

Medicated cardiovascular stents, also called drug eluting stents (DES) represent a relevant application of controlled drug release mechanisms. Modeling of drug release from DES also represents a challenging problem for theoretical and computational analysis. In particular, the study of drug release may require to address models with singular behavior, arising for instance in the analysis of drug release in the small diffusion regime. Moreover, the application to realistic stent configurations requires to account for complex designs of the device. To efficiently obtain satisfactory simulations of DES we rely on a multiscale strategy, involving lumped parameter models (0D) to account for drug release, one dimensional models (1D) to efficiently handle complex stent patterns and fully three-dimensional models (3D) for drug transfer in the artery, including the lumen and the arterial wall. The application of these advanced mathematical models makes it possible to perform a computational analysis of the fluid dynamics and drug release for a medicated stent implanted into a coronary bifurcation, a treatment where clinical complications still have to be fully understood.

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