On a phenomenological model for active smooth muscle contraction

Unraveling the complexity of vascular tone regulation: a multiscale computational approach to integrating chemo-mechano-biological pathways with cardiovascular biomechanics

Vascular tone regulation is a crucial aspect of cardiovascular physiology, with significant implications for overall cardiovascular health. However, the precise physiological mechanisms governing smooth muscle cell contraction and relaxation remain uncertain. The complexity of vascular tone regulation stems from its multiscale and multifactorial nature, involving global hemodynamics, local flow conditions, tissue mechanics, and biochemical pathways. Bridging this knowledge gap and translating it into clinical practice presents a challenge. In this paper, a computational model is presented to integrate chemo-mechano-biological pathways with cardiovascular biomechanics, aiming to unravel the intricacies of vascular tone regulation. The computational framework combines an algebraic description of global hemodynamics with detailed finite element analyses at the scale of vascular segments for describing their passive and active mechanical response, as well as the molecular transport problem linked with chemo-biological pathways triggered by wall shear stresses. Their coupling is accounted for by considering a two-way interaction. Specifically, the focus is on the role of nitric oxide-related molecular pathways, which play a critical role in modulating smooth muscle contraction and relaxation to maintain vascular tone. The computational framework is employed to examine the interplay between localized alterations in the biomechanical response of a specific vessel segment-such as those induced by calcifications or endothelial dysfunction-and the broader global hemodynamic conditions-both under basal and altered states. The proposed approach aims to advance our understanding of vascular tone regulation and its impact on cardiovascular health. By incorporating chemo-mechano-biological mechanisms into in silico models, this study allows us to investigate cardiovascular responses to multifactorial stimuli and incorporate the role of adaptive homeostasis in computational biomechanics frameworks.

A new look at an old problem: 3D modeling of accommodation reveals how age-related biomechanical changes contribute to dysfunction in presbyopia

Presbyopia is an age-related ocular disorder where accommodative ability declines so that an individual's focusing range is insufficient to provide visual clarity for near and distance vision tasks without corrective measures. With age, the eye exhibits changes in biomechanical properties of many components involved in accommodation, including the lens, sclera, and ciliary muscle. Changes occur at different rates, affecting accommodative biomechanics differently, but individual contributions to presbyopia are unknown. We used a finite element model (FEM) of the accommodative mechanism to simulate age-related changes in lens stiffness, scleral stiffness, and ciliary contraction to predict differences in accommodative function. The FEM predicts how ciliary muscle action leads to lens displacement by initializing a tensioned unaccommodated lens (Phase 0) then simulating ciliary muscle contraction in accommodation (Phase 1). Model inputs were calibrated to replicate experimentally measured lens and ciliary muscle in 30-year-old eyes. Predictions of accommodative lens deformation were verified with additional imaging studies. Model variations were created with altered lens component stiffnesses, scleral stiffness, or ciliary muscle section activations, representing fifteen-year incremental age-related changes. Model variations predict significant changes in accommodative function with age-related biomechanical property changes. Lens changes only significantly altered lens thickening with advanced age (46% decrease at 75 years old) while sclera changes produced progressive dysfunction with increasing age (23%, 36%, 49% decrease at 45, 60, and 75 years old). Ciliary muscle changes effected lens position modulation. Model predictions identified potential mechanisms of presbyopia that likely work in combination to reduce accommodative function and could indicate effectiveness of treatment strategies and their dependency on patient age or relative ocular mechanical properties.

A literature review on large intestinal hyperelastic constitutive modeling

Impacts, traumas and strokes are spontaneously life-threatening, but chronic symptoms strangle patient every day. Colorectal tissue mechanics in such chronic situations not only regulates the physio-psychological well-being of the patient, but also confirms the level of comfort and post-operative clinical outcomes. Numerous uniaxial and multiaxial tensile experiments on healthy and affected samples have evidenced significant differences in tissue mechanical behavior and strong colorectal anisotropy across each layer in thickness direction and along the length. Furthermore, this study reviewed various forms of passive constitutive models for the highly fibrous colorectal tissue ranging from the simplest linearly elastic and the conventional isotropic hyperelastic to the most sophisticated second harmonic generation image based anisotropic mathematical formulation. Under large deformation, the isotropic description of tissue mechanics is unequivocally ineffective which demands a microstructural based tissue definition. Therefore, the information collected in this review paper would present the current state-of-the-art in colorectal biomechanics and profoundly serve as updated computational resources to develop a sophisticated characterization of colorectal tissues.

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.

A Chemomechanobiological Model of the Long-Term Healing Response of Arterial Tissue to a Clamping Injury

Vascular clamping often causes injury to arterial tissue, leading to a cascade of cellular and extracellular events. A reliable in silico prediction of these processes following vascular injury could help us to increase our understanding thereof, and eventually optimize surgical techniques or drug delivery to minimize the amount of long-term damage. However, the complexity and interdependency of these events make translation into constitutive laws and their numerical implementation particularly challenging. We introduce a finite element simulation of arterial clamping taking into account acute endothelial denudation, damage to extracellular matrix, and smooth muscle cell loss. The model captures how this causes tissue inflammation and deviation from mechanical homeostasis, both triggering vascular remodeling. A number of cellular processes are modeled, aiming at restoring this homeostasis, i.e., smooth muscle cell phenotype switching, proliferation, migration, and the production of extracellular matrix. We calibrated these damage and remodeling laws by comparing our numerical results to in vivo experimental data of clamping and healing experiments. In these same experiments, the functional integrity of the tissue was assessed through myograph tests, which were also reproduced in the present study through a novel model for vasodilator and -constrictor dependent smooth muscle contraction. The simulation results show a good agreement with the in vivo experiments. The computational model was then also used to simulate healing beyond the duration of the experiments in order to exploit the benefits of computational model predictions. These results showed a significant sensitivity to model parameters related to smooth muscle cell phenotypes, highlighting the pressing need to further elucidate the biological processes of smooth muscle cell phenotypic switching in the future.

The action of ciliary muscle contraction on accommodation of the lens explored with a 3D model

The eye's accommodative mechanism changes optical power for near vision. In accommodation, ciliary muscle excursion relieves lens tension, allowing it to return to its more convex shape. Lens deformation alters its refractive properties, but the mechanics of ciliary muscle actions are difficult to intuit due to the complex architecture of the tissues involved. The muscle itself comprises three sections of dissimilarly oriented cells. These cells contract, transmitting forces through the zonule fibers and extralenticular structures. This study aims to create a finite element model (FEM) to predict how the action of the ciliary muscle sections leads to lens displacement. The FEM incorporates initialization of the disaccommodated lens state and ciliary muscle contraction, with three muscle sections capable of independent activation, to drive accommodative movement. Model inputs were calibrated to replicate experimentally measured disaccommodated lens and accommodated ciliary muscle shape changes. Additional imaging studies were used to validate model predictions of accommodative lens deformation. Models were analyzed to quantify mechanical actions of ciliary muscle sections in lens deformation and position modulation. Analyses revealed that ciliary muscle sections act synergistically: the circular section contributes most to increasing lens thickness, while longitudinal and radial sections can oppose this action. Conversely, longitudinal and radial sections act to translate the lens anteriorly with opposition from the circular section. This FEM demonstrates the complex interplay of the three sections of ciliary muscle in deforming and translating the lens during accommodation, providing a useful framework for future investigations of accommodative dysfunction that occurs with age in presbyopia.

Computational Study of Growth and Remodeling in Ascending Thoracic Aortic Aneurysms Considering Variations of Smooth Muscle Cell Basal Tone

In this paper, we investigate the progression of Ascending Thoracic Aortic Aneurysms (ATAA) using a computational model of Growth and Remodeling (G&R) taking into account the composite (elastin, four collagen fiber families and Smooth Muscle Cells—SMCs) and multi-layered (media and adventitia) nature of the aorta. The G&R model, which is based on the homogenized Constrained Mixture theory, is implemented as a UMAT in the Abaqus finite-element package. Each component of the mixture is assigned a strain energy density function: nearly-incompressible neo-Hookean for elastin and Fung-type for collagen and SMCs. Active SMCs tension is additionally considered, through a length-tension relationship having a classic inverted parabola shape, in order to investigate its effects on the progression of ATAA in a patient-specific model. A sensitivity analysis is performed to evaluate the potential impact of variations in the parameters of the length-tension relationships. These variations reflect in variations of SMCs normal tone during ATAA progression, with active stress contributions ranging between 30% (best case scenario) and 0% (worst case scenario) of the total wall circumferential stress. Low SMCs active stress in the worst case scenarios, in fact, affect the rates of collagen deposition by which the elastin loss is gradually compensated by collagen deposition in the simulated ATAA progression, resulting eventually in larger aneurysm diameters. The types of length-tension relationships leading to a drop of SMCs active stress in our simulations reveal a critical condition which could also result in SMCs apoptosis.

On a coupled electro-chemomechanical model of gastric smooth muscle contraction

The stomach is a central organ in the gastrointestinal tract that performs a variety of functions, in which the spatio-temporal organisation of active smooth muscle contraction in the stomach wall (SW) is highly regulated. In the present study, a three-dimensional model of the gastric smooth muscle contraction is presented, including the mechanical contribution of the mucosal and muscular layer of the SW. Layer-specific and direction-dependent model parameters for the active and passive stress-stretch characteristics of the SW were determined experimentally using porcine smooth muscle strips. The electrical activation of the smooth muscle cells (SMC) due to the pacemaker activity of the interstitial cells of Cajal (ICC) is modelled by using FitzHugh-Nagumo-type equations, which simulate the typical ICC and SMC slow wave behaviour. The calcium dynamic in the SMC depends on the SMC membrane potential via a gaussian function, while the chemo-mechanical coupling in the SMC is modelled via an extended Hai-Murphy model. This cascade is coupled with an additional mechano-electrical feedback-mechanism, taking into account the mechanical response of the ICC and SMC due to stretch of the SW. In this way the relaxation responses of the fundus to accommodate incoming food, as well as the typical peristaltic contraction waves in the antrum for mixing and transport of the chyme, have been well replicated in simulations performed at the whole organ level. STATEMENT OF SIGNIFICANCE: In this article, a novel three-dimensional electro-chemomechanical model of the gastric smooth muscle contraction is presented. The propagating waves of electrical membrane potential in the network ofinterstitial cells of Cajal (ICC) and smooth muscle cells (SMC) lead to a global pattern of change in the calciumdynamics inside the SMC. Taking additionally into account the mechanical response of the ICC and SMC due to stretch of the stomach wall, also referred to as mechanical feedback-mechanism, the result is a complex spatio-temporal regulation of the active contraction and relaxation of the gastric smooth muscle tissue. Being a firstapproach, in future view such a three-dimensional model can give an insight into the complexload transferring system of the stomach wall, as well as into the electro-chemomechanicalcoupling process underlying smooth muscle contraction in health and disease.

A multiscale active structural model of the arterial wall accounting for smooth muscle dynamics

Arterial wall dynamics arise from the synergy of passive mechano-elastic properties of the vascular tissue and the active contractile behaviour of smooth muscle cells (SMCs) that form the media layer of vessels. We have developed a computational framework that incorporates both these components to account for vascular responses to mechanical and pharmacological stimuli. To validate the proposed framework and demonstrate its potential for testing hypotheses on the pathogenesis of vascular disease, we have employed a number of pharmacological probes that modulate the arterial wall contractile machinery by selectively inhibiting a range of intracellular signalling pathways. Experimental probes used on ring segments from the rabbit central ear artery are: phenylephrine, a selective α1-adrenergic receptor agonist that induces vasoconstriction; cyclopiazonic acid (CPA), a specific inhibitor of sarcoplasmic/endoplasmic reticulum Ca²⁺-ATPase; and ryanodine, a diterpenoid that modulates Ca²⁺ release from the sarcoplasmic reticulum. These interventions were able to delineate the role of membrane versus intracellular signalling, previously identified as main factors in smooth muscle contraction and the generation of vessel tone. Each SMC was modelled by a system of nonlinear differential equations that account for intracellular ionic signalling, and in particular Ca²⁺ dynamics. Cytosolic Ca²⁺ concentrations formed the catalytic input to a cross-bridge kinetics model. Contractile output from these cellular components forms the input to the finite-element model of the arterial rings under isometric conditions that reproduces the experimental conditions. The model does not account for the role of the endothelium, as the nitric oxide production was suppressed by the action of L-NAME, and also due to the absence of shear stress on the arterial ring, as the experimental set-up did not involve flow. Simulations generated by the integrated model closely matched experimental observations qualitatively, as well as quantitatively within a range of physiological parametric values. The model also illustrated how increased intercellular coupling led to smooth muscle coordination and the genesis of vascular tone.

Microstructure-based constitutive model of coronary artery with active smooth muscle contraction

Currently, there is no full three-dimensional (3D) microstructural mechanical model of coronary artery based on measured microstructure including elastin, collagen and smooth muscle cells. Many structural models employ mean values of vessel microstructure, rather than continuous distributions of microstructure, to predict the mechanical properties of blood vessels. Although some models show good agreements on macroscopic vessel responses, they result in a lower elastin stiffness and earlier collagen recruitment. Hence, a full microstructural constitutive model is required for better understanding vascular biomechanics in health and disease. Here, a 3D microstructural model that accounts for all constituent microstructure is proposed to predict macroscopic and microscopic responses of coronary arteries. Coronary artery microstructural parameters were determined based on previous statistical measurements while mechanical testing of arteries (n = 5) were performed in this study to validate the computational predictions. The proposed model not only provides predictions of active and passive stress distributions of vessel wall, but also enables reliable estimations of material parameters of individual fibers and cells and thus predicts microstructural stresses. The validated microstructural model of coronary artery sheds light on vascular biomechanics and can be extend to diseased vessels for better understanding of initiation, progression and clinical treatment of vascular disease.

The Esophagiome: concept, status, and future perspectives

The term "Esophagiome" is meant to imply a holistic, multiscale treatment of esophageal function from cellular and muscle physiology to the mechanical responses that transport and mix fluid contents. The development and application of multiscale mathematical models of esophageal function are central to the Esophagiome concept. These model elements underlie the development of a "virtual esophagus" modeling framework to characterize and analyze function and disease by quantitatively contrasting normal and pathophysiological function. Functional models incorporate anatomical details with sensory-motor properties and functional responses, especially related to biomechanical functions, such as bolus transport and gastrointestinal fluid mixing. This brief review provides insight into Esophagiome research. Future advanced models can provide predictive evaluations of the therapeutic consequences of surgical and endoscopic treatments and will aim to facilitate clinical diagnostics and treatment.

Bio-Chemo-Mechanical Models of Vascular Mechanics

Models of vascular mechanics are necessary to predict the response of an artery under a variety of loads, for complex geometries, and in pathological adaptation. Classic constitutive models for arteries are phenomenological and the fitted parameters are not associated with physical components of the wall. Recently, microstructurally-linked models have been developed that associate structural information about the wall components with tissue-level mechanics. Microstructurally-linked models are useful for correlating changes in specific components with pathological outcomes, so that targeted treatments may be developed to prevent or reverse the physical changes. However, most treatments, and many causes, of vascular disease have chemical components. Chemical signaling within cells, between cells, and between cells and matrix constituents affects the biology and mechanics of the arterial wall in the short- and long-term. Hence, bio-chemo-mechanical models that include chemical signaling are critical for robust models of vascular mechanics. This review summarizes bio-mechanical and bio-chemo-mechanical models with a focus on large elastic arteries. We provide applications of these models and challenges for future work.

Investigating the role of smooth muscle cells in large elastic arteries: a finite element analysis

Physiological loading in large elastic arteries is considered to be mainly carried by the passive components of the media but it is not known how much the contraction of the smooth muscle cells is actually involved in the load carrying. Smooth muscle contraction is considered to occur in a relatively slow time domain but the contraction is able to produce significant tension. In the present work the role of smooth muscle contraction in large elastic arteries is investigated by analyzing how changes in the intracellular calcium, and thereby the active tone of smooth muscle cells, influence the deformation and stress behavior; different intracellular calcium functions and medial wall thicknesses with cycling internal pressure are studied. In particular, a recently proposed mechanochemical model (Murtada et al., 2012. J. Theor. Biol. 297, 176-186), which links intracellular calcium with mechanical contraction and an anisotropic model representing the elastin/collagen composite, was implemented into a 3D finite element framework. Details of the implementation procedure are described and a verification of the model implementation is provided by means of the isometric contraction/relaxation analysis of a medial strip at optimal muscle length. In addition, numerically obtained pressure-radius relationships of arterial rings modeled with one and two layers are analyzed with different geometries and at different calcium levels; a comparison with the Laplace equation is provided. Finally, a two-layer arterial ring is loaded with a realistic pressure wave and with various intracellular calcium functions (different amplitudes and mean values) and medial wall thicknesses; residual stresses are considered. The finite element results show that changes in the calcium amplitudes hardly have an influence on the current inner ring radius and the circumferential stress. However, an increase in the mean intracellular calcium value and the medial wall thickness leads to a clear influence on the deformation and the stress behavior.

A continuum model for excitation-contraction of smooth muscle under finite deformations

The main focus in most of the continuum based muscle models is the mechanics of muscle contraction while other physiological processes governing muscle contraction, e.g., cell membrane excitation and activation, are ignored. These latter processes are essential to initiate contraction and to determine the amount of generated force, and by excluding them, the developed model cannot replicate the true behavior of the muscle in question. The aim of this study is to establish a thermodynamically and physiologically consistent framework which allows us to model smooth muscle contraction by including cell membrane excitability and kinetics of myosin phosphorylation, along with dynamics of smooth muscle contraction. The model accounts for these processes through a set of coupled dissipative constitutive equations derived by applying first principles. To show the performance of the derived model, it is evaluated for two different cases: a chemo-mechanical study of pig taenia coli cells where the excitation process is excluded, and an electro-chemo-mechanical study of rat myometrium. The results show that the model is able to replicate important aspects of the smooth muscle excitation-contraction process.

Microstructural constitutive model of active coronary media

Although vascular smooth muscle cells (VSMCs) are pivotal in physiology and pathology, there is a lack of detailed morphological data on these cells. The objective of this study was to determine dimensions (width and length) and orientation of swine coronary VSMCs and to develop a microstructural constitutive model of active media. The dimensions, spatial aspect ratio and orientation angle of VSMCs measured at zero-stress state were found to follow continuous normal (or bimodal normal) distributions. The VSMCs aligned off circumferential direction of blood vessels with symmetrical polar angles 18.7° ± 10.9°, and the local VSMC deformation was affine with tissue-level deformation. A microstructure-based active constitutive model was developed to predict the biaxial vasoactivity of coronary media, based on experimental measurements of geometrical and deformation features of VSMCs. The results revealed that the axial active response of blood vessels is associated with multi-axial contraction as well as oblique VSMC arrangement. The present morphological database is essential for developing accurate structural models and is seminal for understanding the biomechanics of muscular vessels.

A three-dimensional chemo-mechanical continuum model for smooth muscle contraction

Based on two fields, namely the placement and the calcium concentration, a chemo-mechanically coupled three-dimensional model, describing the contractile behaviour of smooth muscles, is presented by means of a strain energy function. The strain energy function (Schmitz and Böl, 2011) is additively decomposed into a passive part, relating to elastin and collagen, and an active calcium-driven part related to the chemical contraction of the smooth muscle cells. For the description of the calcium phase the four state cross-bridge model of Hai and Murphy (Hai and Murphy, 1988) has been implemented into the finite element method. Beside three-dimensional illustrative boundary-value problems demonstrating the features of the presented modelling concept, simulations on an idealised artery document the applicability of the model to more realistic geometries.