A computational framework for pharmaco-mechanical interactions in arterial walls using parallel monolithic domain decomposition methods
Daniel Balzani (Center for Interface-Dominated High Performance Materials)
Alexander Heinlein (TU Delft - Electrical Engineering, Mathematics and Computer Science, TU Delft - Electrical Engineering, Mathematics and Computer Science)
Axel Klawonn (Universität zu Köln)
Jascha Knepper (Universität zu Köln)
Sharan Nurani Ramesh (Center for Interface-Dominated High Performance Materials)
Oliver Rheinbach (University of Technology Bergakademie Freiberg)
Lea Saßmannshausen (Universität zu Köln)
Klemens Uhlmann (Center for Interface-Dominated High Performance Materials)
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Abstract
A computational framework is presented to numerically simulate the effects of antihypertensive drugs, in particular calcium channel blockers, on the mechanical response of arterial walls. A stretch-dependent smooth muscle model by Uhlmann and Balzani is modified to describe the interaction of pharmacological drugs and the inhibition of smooth muscle activation. The coupled deformation-diffusion problem is then solved using the finite element software FEDDLib and overlapping Schwarz preconditioners from the Trilinos package FROSch. These preconditioners include highly scalable parallel GDSW (generalized Dryja–Smith–Widlund) and RGDSW (reduced GDSW) preconditioners. Simulation results show the expected increase in the lumen diameter of an idealized artery due to the drug-induced reduction of smooth muscle contraction, as well as a decrease in the rate of arterial contraction in the presence of calcium channel blockers. Strong and weak parallel scalability of the resulting computational implementation are also analyzed.
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