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

Abstract

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.

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

“…Two distinct crosswise helically arranged fiber directions are considered, both lying in the longitudinal-circumferential plane and symmetric about the circumferential axis. The active material is modeled using the phenomenological model by Uhlmann and Balzani [63], where the models of Hai and Murphy [20] and Murtada et al [43] are extended to include the effects of stretch on the calcium-dependent and -independent contraction mechanisms.…”

“…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.…”

“…Uhlmann and Balzani [63] extended the model proposed by Murtada et al [43] to include the influence of stretch on the action of MLCP and MLCK. Here, we adopt the active response model by Uhlmann and Balzani [63] and modify it to model the impact of dihydropyridine CCBs. In a previous work [45], we already investigated the effect of CCBs on the activity of MLCK, considering constant MLCP activity.…”

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

“…where I 1 , I 2 and I 3 are the first three invariants of the right Cauchy-Green tensor, α 1 , α 2 , α 3 , α 4 > 0, α 5 > 2 and f denotes the fiber direction, which will be omitted further for brevity. Following [3], the active part Ψ a is given by…”

“…The values of the parameters in Eqs. ( 1), ( 2), ( 3), ( 4), ( 5), ( 9), (10), and (11) were taken from Uhlmann and Balzani [3]. For the coupling parameters, the values γ 1,max = 0.5024 µM, γ 3,max = 0.9 µM, p 1 = 0.6, p 3 = 0.6, c 50 = 0.5 µM were used.…”