Reduced Order Modeling for Drug Release in Arteries with Drug-Eluting Stents

  • Ranno, Anna (RWTH Aachen University)
  • Lespagnol, Fabien (Politecnico di Milano)
  • Ballarin, Francesco (Catholic University of the Sacred Heart)
  • Behr, Marek (RWTH Aachen University)
  • Zunino, Paolo (Politecnico di Milano)
  • Perotto, Simona (Politecnico di Milano)

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Reliable in silico simulations of drug release in arteries in the presence of drug eluting stents (DES) can be computationally demanding. Fully resolved 3D models have to couple blood flow, drug elution and tissue growth. In particular, stent geometries are often complex and require millions of mesh elements; in addition, hemodynamics has a characteristic time scale of seconds, unlike drug elution and tissue growth which take place over months. For all these reasons, model reduction turns out to be instrumental to reliably and efficiently simulate blood dynamics and drug elution. In this work, we model drug release through an advection-diffusion equation with steady flow. Towards this goal, we combine two model reduction techniques and validate the new approach on a benchmark case: a 2D axisymmetric artery in the presence of a ring stent segment. First, a 2D-0D topological model reduction is taken into account. Thanks to the different spatial scales between the artery diameter (about 3.6 mm) and the stent thickness (about 0.1 mm), we treat the ring stent as a small obstacle in the domain. Immersed boundary conditions and a Lagrange multiplier are adopted to impose the obstacle constraint in the advection-diffusion equation and the initial drug load. Moreover, the function space of the Lagrange multiplier is reduced to arbitrary N Fourier modes. Successively, hierarchical model reduction (HiMod) is applied to reduce the function space of the solution. HiMod reduction merges 1D finite element discretization along the blood flow direction with a modal basis expansion to include possible localized transverse dynamics (e.g., vortices, mostly occurring near the ring stent). The combination of topological and hierarchical model reduction allows us to avoid the geometrical complexity of the stent and to reduce the function space of the discrete solution. Concerning the numerical verification of the proposed method, we show that the drug concentration in the reduced model is compliant with the reference full solution.