A computational framework for pharmaco-mechanical interactions in arterial walls using parallel monolithic domain decomposition methods

Journal article (2024)

Authors

Daniel Balzani Center for Interface-Dominated High Performance Materials
A. Heinlein Numerical Analysis - EEMCS , Delft Institute of Applied Mathematics
Axel Klawonn University of Cologne
Jascha Knepper University of Cologne
Sharan Nurani Ramesh Center for Interface-Dominated High Performance Materials
Oliver Rheinbach University of Technology Bergakademie Freiberg
Lea Saßmannshausen University of Cologne
Klemens Uhlmann Center for Interface-Dominated High Performance Materials
Research Group
Numerical Analysis (EEMCS) (TU Delft)
Copyright: © 2024 Daniel Balzani, A. Heinlein, Axel Klawonn, Jascha Knepper, Sharan Nurani Ramesh, Oliver Rheinbach, Lea Saßmannshausen, Klemens Uhlmann
DOI: https://doi.org/10.1002/gamm.202370002
Structural mechanics Finite element method Iterative solvers Domain decomposition methods Hypertension Overlapping Schwarz Drug transport Calcium channel blockers GDSW coarse space RGDSW coarse space Scalable preconditioners Smooth muscle cells
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Published Date

2024

Language

English

Faculty

Electrical Engineering, Mathematics and Computer Science

Department

Delft Institute of Applied Mathematics

Research Group

Numerical Analysis

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.