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

Daniel Balzani, Alexander Heinlein, Axel Klawonn*, Jascha Knepper, Sharan Nurani Ramesh, Oliver Rheinbach, Lea Saßmannshausen, Klemens Uhlmann

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

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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.

Original languageEnglish
Article numbere202370002
Number of pages26
JournalGAMM Mitteilungen
Issue number1
Publication statusPublished - 2024


Financial funding from the Deutsche Forschungsgemeinschaft (DFG) through the Priority Program 2311 “Robust coupling of continuum‐biomechanical in silico models to establish active biological system models for later use in clinical applications—Co‐design of modeling, numerics and usability,” project ID 465228106, is greatly appreciated. The authors gratefully acknowledge the scientific support and HPC resources provided by the Erlangen National High Performance Computing Center (NHR@FAU) of the Friedrich‐Alexander‐Universität Erlangen‐Nürnberg (FAU) under the NHR project k105be. NHR funding is provided by federal and Bavarian state authorities. NHR@FAU hardware is partially funded by the German Research Foundation (DFG)—440719683. Open Access funding enabled and organized by Projekt DEAL.


  • calcium channel blockers
  • domain decomposition methods
  • drug transport
  • finite element method
  • GDSW coarse space
  • hypertension
  • iterative solvers
  • overlapping Schwarz
  • RGDSW coarse space
  • scalable preconditioners
  • smooth muscle cells
  • structural mechanics


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