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

doi:10.1002/gamm.202370002

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 journal › Article › Scientific › peer-review

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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.

Original language	English
Article number	e202370002
Number of pages	26
Journal	GAMM Mitteilungen
Volume	47
Issue number	1
DOIs	https://doi.org/10.1002/gamm.202370002
Publication status	Published - 2024

Funding

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.

Keywords

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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10.1002/gamm.202370002

GAMM-Mitteilungen - 2024 - Balzani - A computational framework for pharmaco‐mechanical interactions in arterial walls usingFinal published version, 3.36 MBLicence: CC BY-NC-ND

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

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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AU - Nurani Ramesh, Sharan

AU - Rheinbach, Oliver

AU - Saßmannshausen, Lea

AU - Uhlmann, Klemens

PY - 2024

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N2 - 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.

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

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