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

A new model for evaluating pressure-induced vascular tone in small cerebral arteries

The capacity of small cerebral arteries (SCAs) to adapt to pressure fluctuations has a fundamental physiological role and appears to be relevant in different pathological conditions. Here, we present a new computational model for quantifying the link, and its contributors, between luminal pressure and vascular tone generation in SCAs. This is assembled by combining a chemical sub-model, representing pressure-induced smooth muscle cell (SMC) signalling, with a mechanical sub-model for the tone generation and its transduction at tissue level. The devised model can accurately reproduce the impact of luminal pressure on different cytoplasmic components involved in myogenic signalling, both in the control case and when combined with some specific pharmacological interventions. Furthermore, the model is also able to capture and predict experimentally recorded pressure-outer diameter relationships obtained for vessels under control conditions, both in a Ca2 + -free bath and under drug inhibition. The modularity of the proposed framework allows the integration of new components for the study of a broad range of processes involved in the vascular function.

Modeling Reactive Hyperemia to Better Understand and Assess Microvascular Function: A Review of Techniques

Reactive hyperemia is a well-established technique for the non-invasive evaluation of the peripheral microcirculatory function, measured as the magnitude of limb re-perfusion after a brief period of ischemia. Despite widespread adoption by researchers and clinicians alike, many uncertainties remain surrounding interpretation, compounded by patient-specific confounding factors (such as blood pressure or the metabolic rate of the ischemic limb). Mathematical modeling can accelerate our understanding of the physiology underlying the reactive hyperemia response and guide in the estimation of quantities which are difficult to measure experimentally. In this work, we aim to provide a comprehensive guide for mathematical modeling techniques that can be used for describing the key phenomena involved in the reactive hyperemia response, alongside their limitations and advantages. The reported methodologies can be used for investigating specific reactive hyperemia aspects alone, or can be combined into a computational framework to be used in (pre-)clinical settings.

Shear stress and intravascular pressure effects on vascular dynamics: two-phase blood flow in elastic microvessels accounting for the passive stresses

We study the steady hemodynamics in physiological elastic microvessels proposing an advanced fluid-structure interaction model. The arteriolar tissue is modeled as a two-layer fiber-reinforced hyperelastic material representing its Media and Adventitia layers. The constitutive model employed (Holzapfel et al. in J Elast 61:1-48, 2000) is parametrized via available data on stress-strain experiments for arterioles. The model is completed by simulating the blood/plasma flow in the lumen, using the thixotropic elasto-viscoplastic model in its core, and the linear Phan-Thien and Tanner viscoelastic model in its annular part. The Cell-Free Layer (CFL) and the Fåhraeus and Fåhraeus-Lindqvist effects are considered via analytical expressions based on experimental data (Giannokostas et al. in Materials (Basel) 14:367, 2021b). The coupling between tissue deformation and blood flow is achieved through the experimentally verified pressure-shear hypothesis (Pries et al. Circ Res 77:1017-1023, 1995). Our calculations confirm that the increase in the reference inner radius produces larger expansion. Also, by increasing the intraluminal pressure, the thinning of the walls is more pronounced and it may reach 40% of the initial thickness. Comparing our predictions with those in rigid-wall microtubes, we conclude that apart from the vital importance of vasodilation, there is an up to 25% reduction in wall shear stress. The passive vasodilation contributes to the decrease in the tissue stress fields and affects the hemodynamic features such as the CFL thickness, reducing the plasma layer when blood flows in vessels with elastic walls, in quantitative agreement with previous experiments. Our calculations verify the correctness of the pressure-shear hypothesis but not that of the Laplace law.

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.

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.

A microscopically motivated model for the remodeling of cardiomyocytes

We present a thermodynamically based model that captures the remodeling effects in cardiac muscle cells. This work begins with the formulation of the kinematics of a cardiomyocyte resulting from a prescribed macroscopic deformation and the reorganization of the internal structure. Specifically, relations between the macroscopic deformation and the number of sarcomeres, the sarcomere stretch, and the number of myofibrils in the cell are determined. The remodeling process is split into two separate phases-(1) elongation/shortening of the existing myofibrils by addition/detachment of sarcomeres and (2) formation of new myofibrils. The remodeling associated with each phase is modeled through a dissipation postulate. We show that remodeling is based on a competition between the internal energy, the entropy, the energy supplied to the system by ATP and other sources to drive the remodeling process, and dissipation mechanisms. While the variations in entropy associated with phase (1) are neglected, the substantial entropy loss associated with the formation of new myofibrils is determined. To illustrate the merit of the proposed framework, we compute the response of cardiomyocytes subjected to isometric axial stretch that are either free to deform or fixed in the transverse direction. We also examine the predictions of this model for cardiomyocytes subjected to various cyclic loadings. The proposed framework is capable of capturing a wide range of remodeling effects and agrees with experimental observations.

Simulation of the uterine contractions and foetus expulsion using a chemo-mechanical constitutive model

During vaginal delivery women sustain stretching of their pelvic floor, risking tissue injury and adverse outcomes. Since studies in pregnant women are limited with ethical constraints, computational models have become an interesting alternative to elucidate the pregnancy mechanisms. This research investigates the uterine contractions during foetus expulsion without an imposed trajectory. Such physical process is captured by means of a chemo-mechanical constitutive model, where the uterine contractions are triggered by chemical stimuli. The foetus descent, which includes both pushing and resting stages, has a descent rate within the physiological range. Moreover, the behaviour of the foetus and the uterus stretch agree well with clinical data presented in the literature. The follow-up of this study will be to obtain a complete childbirth simulation, considering also the pelvic floor muscles and its supporting structures. The simulation of a realistic rate of descent, including the pushing and resting stages, is of significant importance to study the pelvic floor muscles due to their viscoelastic nature.

Mechanical Characterization and Material Modeling of Diabetic Aortas in a Rabbit Model

Diabetes has been recognized as a major risk factor to cause macrovascular diseases and plays a key role in aortic wall remodeling. However, the effects of diabetes on elastic properties of aortas remain largely unknown and quantitative mechanical data are lacking. Thirty adult rabbits (1.6-2.2 kg) were collected and the type 1 diabetic rabbit model was induced by injection of alloxan. A total of 15 control and 15 diabetic rabbit (abdominal) aortas were harvested. Uniaxial and biaxial tensile tests were performed to measure ultimate tensile strength and to characterize biaxial mechanical behaviors of the aortas. A material model was fitted to the biaxial experimental data to obtain constitutive parameters. Histological and mass fraction analyses were performed to investigate the underlying microstructure and dry weight percentages of elastin and collagen in the control and the diabetic aortas. No statistically significant difference was found in ultimate tensile strength between the control and the diabetic aortas. Regarding biaxial mechanical responses, the diabetic aortas exhibited significantly lower extensibility and significantly higher tissue stiffness than the control aortas. Notably, tissue stiffening occurred in both circumferential and axial directions for the diabetic aortas; however, mechanical anisotropy does not change significantly. The material model was able to fit biaxial experimental data very well. Histology showed that a number of isolated foam cells were embedded in the diabetic aortas and hyperplasia of collagen was identified. The dry weight percentages of collagen within the diabetic aortas increased significantly as compared to the control aortas, whereas no significant change was found for that of elastin. Our data suggest that the diabetes impairs elastic properties and alters microstructure of the aortas and consequently, these changes may further contribute to complex aortic wall remodeling.

Identification of the mechanical parameters for the human uterus in vivo using intrauterine pressure measurements

There are limited experimental data to characterize the mechanical response of human myometrium. A method is presented in this work to identify mechanical parameters describing the active response of human myometrium from the in vivo intrauterine pressure measurements. The human uterine contraction during labor is simulated by implementing a coupled model in a finite element scheme, and the intrauterine pressure is evaluated as the outcome. A meta-model is developed to approximate the finite element simulation response with a lower computational cost and used to identify model parameters through fitting its prediction to the in vivo measurements. Copyright © 2016 John Wiley & Sons, Ltd.

Adaptation of active tone in the mouse descending thoracic aorta under acute changes in loading

Arteries can adapt to sustained changes in blood pressure and flow, and it is thought that these adaptive processes often begin with an altered smooth muscle cell activity that precedes any detectable changes in the passive wall components. Yet, due to the intrinsic coupling between the active and passive properties of the arterial wall, it has been difficult to delineate the adaptive contributions of active smooth muscle. To address this need, we used a novel experimental-computational approach to quantify adaptive functions of active smooth muscle in arterial rings excised from the proximal descending thoracic aorta of mice and subjected to short-term sustained circumferential stretches while stimulated with various agonists. A new mathematical model of the adaptive processes was derived and fit to data to describe and predict the effects of active tone adaptation. It was found that active tone was maintained when the artery was adapted close to the optimal stretch for maximal active force production, but it was reduced when adapted below the optimal stretch; there was no significant change in passive behavior in either case. Such active adaptations occurred only upon smooth muscle stimulation with phenylephrine, however, not stimulation with KCl or angiotensin II. Numerical simulations using the proposed model suggested further that active tone adaptation in vascular smooth muscle could play a stabilizing role for wall stress in large elastic arteries.

Simulating uterine contraction by using an electro-chemo-mechanical model

Contractions of uterine smooth muscle cells consist of a chain of physiological processes. These contractions provide the required force to expel the fetus from the uterus. The inclusion of these physiological processes is, therefore, imperative when studying uterine contractions. In this study, an electro-chemo-mechanical model to replicate the excitation, activation, and contraction of uterine smooth muscle cells is developed. The presented modeling strategy enables efficient integration of knowledge about physiological processes at the cellular level to the organ level. The model is implemented in a three-dimensional finite element setting to simulate uterus contraction during labor in response to electrical discharges generated by pacemaker cells and propagated within the myometrium via gap junctions. Important clinical factors, such as uterine electrical activity and intrauterine pressure, are predicted using this simulation. The predictions are in agreement with clinically measured data reported in the literature. A parameter study is also carried out to investigate the impact of physiologically related parameters on the uterine contractility.

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.

Human thoracic and abdominal aortic aneurysmal tissues: Damage experiments, statistical analysis and constitutive modeling

Development of aortic aneurysms includes significant morphological changes within the tissue: collagen content increases, elastin content reduces and smooth muscle cells degenerate. We seek to quantify the impact of these changes on the passive mechanical response of aneurysms in the supra-physiological loading range via mechanical testing and constitutive modeling. We perform uniaxial extension tests on circumferentially and axially oriented strips from five thoracic (65.6 years ± 13.4, mean ± SD) and eight abdominal (63.9 years ± 11.4) aortic fusiform aneurysms to investigate both continuous and discontinuous softening during supra-physiological loading. We determine the significance of the differences between the fitted model parameters: diseased thoracic versus abdominal tissues, and healthy (Weisbecker et al., J. Mech. Behav. Biomed. Mater. 12, 93-106, 2012) versus diseased tissues. We also test correlations among these parameters and age, Body Mass Index (BMI) and preoperative aneurysm diameter, and investigate histological cuts. Tissue response is anisotropic for all tests and the anisotropic pseudo-elastic damage model fits the data well for both primary loading and discontinuous softening which we interpret as damage. We found statistically relevant differences between model parameters fitted to diseased thoracic versus abdominal tissues, as well as between those fitted to healthy versus diseased tissues. Only BMI correlated with fitted model parameters in abdominal aortic aneurysmal tissues.