Simulation of Arterial Walls: Growth, Fiber Reorientation, and Active Response

Uhlmann, Klemens; Zahn, Anna; Balzani, Daniel

doi:10.1007/978-3-030-92339-6_8

Cited by 3 publications

(1 citation statement)

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“…Since antihypertensive drugs primarily work by interacting with SMC activation, it is important to have an SMC model that allows for a meaningful description of drug-tissue interaction. There are several models that describe the active response of arteries [9,43,44,54,63,64,68,69]. The well-accepted cross-bridge phosphorylation model by Hai and Murphy [20] describes the influence of MLCK and MLCP on contraction.…”

Section: Introductionmentioning

confidence: 99%

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

Balzani,

Heinlein,

Klawonn

et al. 2024

GAMM-Mitteilungen

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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.

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Section: Introductionmentioning

confidence: 99%

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

Balzani,

Heinlein,

Klawonn

et al. 2024

GAMM-Mitteilungen

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First steps towards modeling the interaction of cardiovascular agents and smooth muscle activation in arterial walls

Ramesh

Uhlmann

Lea

et al. 2023

Proc Appl Math and Mech

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Numerical simulation of the response of healthy and pathological arteries to cardiovascular agents can provide valuable information to the physician in the treatment of diseases such as hypertension, atherosclerosis, and the Marfan syndrome. Here, we provide a first step towards a computational framework to model the effects of antihypertensive agents on the mechanical response of arterial walls. A material model is developed by extending an existing formulation for wall tissue to incorporate the effects of calcium‐ion channel blockers. The resulting coupled deformation‐diffusion problem is then solved using the finite element method. Simulation results with drug activity show that, indeed, an increased lumen diameter due to reduced contraction is obtained. Additionally, a decrease in the rate of arterial contraction is observed, which is also consistent with expected behavior. Finally, we compare results for an implicit or explicit treatment of the the deformation‐diffusion coupling, and we observe that both coupling schemes yield comparable results for a wide range of time step sizes.

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Chemo-mechanical modeling of smooth muscle cell activation for the simulation of arterial walls under changing blood pressure

Uhlmann

Balzani

2023

Biomech Model Mechanobiol

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In this paper, a novel chemo-mechanical model is proposed for the description of the stretch-dependent chemical processes known as Bayliss effect and their impact on the active contraction in vascular smooth muscle. These processes are responsible for the adaptive reaction of arterial walls to changing blood pressure by which the blood vessels actively support the heart in providing sufficient blood supply for varying demands in the supplied tissues. The model is designed to describe two different stretch-dependent mechanisms observed in smooth muscle cells (SMCs): a calcium-dependent and a calcium-independent contraction. For the first one, stretch of the SMCs leads to an inlet of calcium ions which activates the myosin light chain kinase (MLCK). The increased activity of MLCK triggers the contractile units of the cells resulting in the contraction on a comparatively short time scale. For the calcium-independent contraction mechanism, stretch-dependent receptors of the cell membrane stimulate an intracellular reaction leading to an inhibition of the antagonist of MLCK, the myosin light chain phosphatase resulting in a contraction on a comparatively long time scale. An algorithmic framework for the implementation of the model in finite element programs is derived. Based thereon, it is shown that the proposed approach agrees well with experimental data. Furthermore, the individual aspects of the model are analyzed in numerical simulations of idealized arteries subject to internal pressure waves with changing intensities. The simulations show that the proposed model is able to describe the experimentally observed contraction of the artery as a reaction to increased internal pressure, which can be considered a crucial aspect of the regulatory mechanism of muscular arteries.

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Simulation of Arterial Walls: Growth, Fiber Reorientation, and Active Response

Cited by 3 publications

References 50 publications

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

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

First steps towards modeling the interaction of cardiovascular agents and smooth muscle activation in arterial walls

Chemo-mechanical modeling of smooth muscle cell activation for the simulation of arterial walls under changing blood pressure

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