A continuum model for skeletal muscle contraction at homogeneous finite deformations

The contractile force in skeletal muscle models is commonly postulated to be the isometric force multiplied by a set of experimentally motivated functions which account for the muscle’s active properties. Although both flexible and simple, this approach does not automatically guarantee a thermodynamically consistent behavior. In contrast, the continuum mechanical model proposed herein is derived from fundamental principles in mechanics and guarantees a dissipative behavior. Further, the contractile force is associated with a friction clutch which provides a simple and well-defined macroscopic model for cycling cross-bridges. To show the performance of the model, it is specialized to standard experiments for rabbit tibialis anterior muscle. The results show that the model is able to capture important characteristics of skeletal muscle

Length adaptation of smooth muscle contractile filaments in response to sustained activation

Airway and bladder smooth muscles are known to undergo length adaptation under sustained contraction. This adaptation process entails a remodelling of the intracellular actin and myosin filaments which shifts the peak of the active force-length curve towards the current length. Smooth muscles are therefore able to generate the maximum force over a wide range of lengths. In contrast, length adaptation of vascular smooth muscle has attracted very little attention and only a handful of studies have been reported. Although their results are conflicting on the existence of a length adaptation process in vascular smooth muscle, it seems that, at least, peripheral arteries and arterioles undergo such adaptation. This is of interest since peripheral vessels are responsible for pressure regulation, and a length adaptation will affect the function of the cardiovascular system. It has, e.g., been suggested that the inward remodelling of resistance vessels associated with hypertension disorders may be related to smooth muscle adaptation. In this study we develop a continuum mechanical model for vascular smooth muscle length adaptation by assuming that the muscle cells remodel the actomyosin network such that the peak of the active stress-stretch curve is shifted towards the operating point. The model is specialised to hamster cheek pouch arterioles and the simulated response to stepwise length changes under contraction. The results show that the model is able to recover the salient features of length adaptation reported in the literature.Funding Agencies|Swedish Research Council [621-2009-3099]</p

A Mechanochemical 3D Continuum Model for Smooth Muscle Contraction under Finite Strains

Abstract This paper presents a modelling framework in which the mechanochemical properties of smooth muscle cells may be studied. The activation of smooth muscles is considered in a three-dimensional continuum model which is key to realistically capture the function of hollow organs such as blood vessels. On the basis of a general thermodynamical framework the mechanical and chemical phases are specialized in order to quantify the coupled mechanochemical process. A free-energy function is proposed as the sum of a mechanical energy stored in the passive tissue, a coupling between the mechanical and chemical kinetics and an energy related purely to the chemical kinetics and the calcium ion concentration. For the chemical phase it is shown that the cross-bridge model of Hai and Murphy (Am. J. Physiol. Cell Physiol., 254, C99-C106, 1988) is included in the developed evolution law as a special case. In order to show the specific features and the potential of the proposed continuum model a uniaxial extension test of a tissue strip is analysed in detail and the related kinematics and stress-stretch relations are derived. Parameter studies point to coupling phenomena; in particular the tissue response is analysed in terms of the calcium ion level. The model for smooth muscle contraction may significantly contribute to current modelling efforts of smooth muscle tissue responses

A mechanochemical 3D continuum model for smooth muscle contraction under finite strains

This paper presents a modelling framework in which the mechanochemical properties of smooth muscle cells may be studied. The activation of smooth muscles is considered in a three-dimensional continuum model which is key to realistically capture the function of hollow organs such as blood vessels. On the basis of a general thermodynamical framework the mechanical and chemical phases are specialized in order to quantify the coupled mechanochemical process. A free-energy function is proposed as the sum of a mechanical energy stored in the passive tissue, a coupling between the mechanical and chemical kinetics and an energy related purely to the chemical kinetics and the calcium ion concentration. For the chemical phase it is shown that the cross-bridge model of Hai and Murphy [1988. Am. J. Physiol. Cell Physiol. 254, C99–C106] is included in the developed evolution law as a special case. In order to show the specific features and the potential of the proposed continuum model a uniaxial extension test of a tissue strip is analysed in detail and the related kinematics and stress–stretch relations are derived. Parameter studies point to coupling phenomena; in particular the tissue response is analysed in terms of the calcium ion level. The model for smooth muscle contraction may significantly contribute to current modelling efforts of smooth muscle tissue responses

Modeling of the mechanobiological adaptation in muscular arteries

The growth and remodeling of arteries, as controlled by the local stress state and the sensory input from the endothelial cells of the artery wall, is given a novel theoretical framework incorporating the active behavior of vascular smooth muscle. We show that local sensory input maps uniquely to the ratio between a target arterial wall cross-section area corresponding to homeostatic conditions and the current arterial wall area. A growth law is formulated by taking the production rates of individual constituents of the arterial wall to be functions of this target-to-current wall area ratio. We find that a minimum active stress response of vascular smooth muscle is necessary to achieve stable adaptation of the artery wall to dynamic flow conditions. With a sufficient active stress alteration in response to stretch, stable growth toward a homeostatic state can be observed for finite step changes or ramp changes in the transmural pressure or the flow rate. (C) 2017 Elsevier Masson SAS. All rights reserved.Funding Agencies|Swedish Research Council [621-2012-3117]</p

Identification of mechanical properties of arteries with certification of global optimality

In this study, we consider identification of parameters in a non-linear continuum-mechanical model of arteries by fitting the models response to clinical data. The fitting of the model is formulated as a constrained non-linear, non-convex least-squares minimization problem. The model parameters are directly related to the underlying physiology of arteries, and correctly identified they can be of great clinical value. The non-convexity of the minimization problem implies that incorrect parameter values, corresponding to local minima or stationary points may be found, however. Therefore, we investigate the feasibility of using a branch-and-bound algorithm to identify the parameters to global optimality. The algorithm is tested on three clinical data sets, in each case using four increasingly larger regions around a candidate global solution in the parameter space. In all cases, the candidate global solution is found already in the initialization phase when solving the original non-convex minimization problem from multiple starting points, and the remaining time is spent on increasing the lower bound on the optimal value. Although the branch-and-bound algorithm is parallelized, the overall procedure is in general very time-consuming.Funding Agencies|Swedish Research CouncilSwedish Research CouncilEuropean Commission [621-2014-4165]</p

A mechanochemical 3D continuum model for smooth muscle contraction under finite strains

This paper presents a modelling framework in which the mechanochemical properties of smooth muscle cells may be studied. The activation of smooth muscles is considered in a three-dimensional continuum model which is key to realistically capture the function of hollow organs such as blood vessels. On the basis of a general thermodynamical framework the mechanical and chemical phases are specialized in order to quantify the coupled mechanochemical process. A free-energy function is proposed as the sum of a mechanical energy stored in the passive tissue, a coupling between the mechanical and chemical kinetics and an energy related purely to the chemical kinetics and the calcium ion concentration. For the chemical phase it is shown that the cross-bridge model of Hai and Murphy [1988. Am. J. Physiol. Cell Physiol. 254, C99–C106] is included in the developed evolution law as a special case. In order to show the specific features and the potential of the proposed continuum model a uniaxial extension test of a tissue strip is analysed in detail and the related kinematics and stress–stretch relations are derived. Parameter studies point to coupling phenomena; in particular the tissue response is analysed in terms of the calcium ion level. The model for smooth muscle contraction may significantly contribute to current modelling efforts of smooth muscle tissue responses

An in vivo parameter identification method for arteries : numerical validation for the human abdominal aorta

A method for identifying mechanical properties of arterial tissue in vivo is proposed in this paper and it is numerically validated for the human abdominal aorta. Supplied with pressure-radius data, the method determines six parameters representing relevant mechanical properties of an artery. In order to validate the method, 22 finite element arteries are created using published data for the human abdominal aorta. With these in silico abdominal aortas, which serve as mock experiments with exactly known material properties and boundary conditions, pressure-radius data sets are generated and the mechanical properties are identified using the proposed parameter identification method. By comparing the identified and pre-defined parameters, the method is quantitatively validated. For healthy abdominal aortas, the parameters show good agreement for the material constant associated with elastin and the radius of the stress-free state over a large range of values. Slightly larger discrepancies occur for the material constants associated with collagen, and the largest relative difference is obtained for the in situ axial prestretch. For pathological abdominal aortas incorrect parameters are identified, but the identification method reveals the presence of diseased aortas. The numerical validation indicates that the proposed parameter identification method is able to identify adequate parameters for healthy abdominal aortas and reveals pathological aortas from in vivo-like data

In vivo parameter identification in arteries considering multiple levels of smooth muscle activity

In this paper an existing in vivo parameter identification method for arteries is extended to account for smooth muscle activity. Within this method a continuum-mechanical model, whose parameters relate to the mechanical properties of the artery, is fit to clinical data by solving a minimization problem. Including smooth muscle activity in the model increases the number of parameters. This may lead to overparameterization, implying that several parameter combinations solve the minimization problem equally well and it is therefore not possible to determine which set of parameters represents the mechanical properties of the artery best. To prevent overparameterization the model is fit to clinical data measured at different levels of smooth muscle activity. Three conditions are considered for the human abdominal aorta: basal during rest; constricted, induced by lower-body negative pressure; and dilated, induced by physical exercise. By fitting the model to these three arterial conditions simultaneously a unique set of model parameters is identified and the model prediction agrees well with the clinical data.Funding Agencies|Linkoping University; Swedish Research CouncilSwedish Research CouncilEuropean Commission [621-2014-4165]</p