Cross-bridge phosphorylation and regulation of latch state in smooth muscle

The origin of intraluminal pressure waves in gastrointestinal tract

The gastrointestinal (GI) peristalsis is an involuntary wave-like contraction of the GI wall that helps to propagate food along the tract. Many GI diseases, e.g., gastroparesis, are known to cause motility disorders in which the physiological contractile patterns of the wall get disrupted. Therefore, to understand the pathophysiology of these diseases, it is necessary to understand the mechanism of GI motility. We present a coupled electromechanical model to describe the mechanism of GI motility and the transduction pathway of cellular electrical activities into mechanical deformation and the generation of intraluminal pressure (IP) waves in the GI tract. The proposed model consolidates a smooth muscle cell (SMC) model, an actin-myosin interaction model, a hyperelastic constitutive model, and a Windkessel model to construct a coupled model that can describe the origin of peristaltic contractions in the intestine. The key input to the model is external electrical stimuli, which are converted into mechanical contractile waves in the wall. The model recreated experimental observations efficiently and was able to establish a relationship between change in luminal volume and pressure with the compliance of the GI wall and the peripheral resistance to bolus flow. The proposed model will help us understand the GI tract's function in physiological and pathophysiological conditions.

Dynamic cerebral autoregulation is governed by two time constants: Arterial transit time and feedback time constant

Dynamic cerebral autoregulation (dCA) is the mechanism that describes how the brain maintains cerebral blood flow approximately constant in response to short-term changes in arterial blood pressure. This is known to be impaired in many different pathological conditions, including ischaemic and haemorrhagic stroke, dementia and traumatic brain injury. Many different approaches have thus been used both to analyse and to quantify this mechanism in a range of healthy and diseased subjects, including data-driven models (in both the time and the frequency domain) and biophysical models. However, despite the substantial body of work on both biophysical models and data-driven models of dCA, there remains little work that links the two together. One of the reasons for this is proposed to be the discrepancies between the time constants that govern dCA in models and in experimental data. In this study, the processes that govern dCA are examined and it is proposed that the application of biophysical models remains limited due to a lack of understanding about the physical processes that are being modelled, partly due to the specific model formulation that has been most widely used (the equivalent electrical circuit). Based on the analysis presented here, it is proposed that the two most important time constants are arterial transit time and feedback time constant. It is therefore time to revisit equivalent electrical circuit models of dCA and to develop a more physiologically realistic alternative, one that can more easily be related to experimental data. KEY POINTS: Dynamic cerebral autoregulation is governed by two time constants. The first time constant is the arterial transit time, rather than the traditional 'RC' time constant widely used in previous models. This arterial transit time is approximately 1 s in the brain. The second time constant is the feedback time constant, which is less accurately known, although it is somewhat larger than the arterial transit time. The equivalent electrical circuit model of dynamic cerebral autoregulation should be replaced with a more physiologically representative model.

Multiphysics and multiscale modeling of uterine contractions: integrating electrical dynamics and soft tissue deformation with fiber orientation

The development of a comprehensive uterine model that seamlessly integrates the intricate interactions between the electrical and mechanical aspects of uterine activity could potentially facilitate the prediction and management of labor complications. Such a model has the potential to enhance our understanding of the initiation and synchronization mechanisms involved in uterine contractions, providing a more profound comprehension of the factors associated with labor complications, including preterm labor. Consequently, it has the capacity to assist in more effective preparation and intervention strategies for managing such complications. In this study, we present a computational model that effectively integrates the electrical and mechanical components of uterine contractions. By combining a state-of-the-art electrical model with the Hyperelastic Mass-Spring Model (HyperMSM), we adopt a multiphysics and multiscale approach to capture the electrical and mechanical activities within the uterus. The electrical model incorporates the generation and propagation of action potentials, while the HyperMSM simulates the mechanical behavior and deformations of the uterine tissue. Notably, our model takes into account the orientation of muscle fibers, ensuring that the simulated contractions align with their inherent directional characteristics. One noteworthy aspect of our contraction model is its novel approach to scaling the rest state of the mesh elements, as opposed to the conventional method of applying mechanical loads. By doing so, we eliminate artificial strain energy resulting from the resistance of soft tissues' elastic properties during contractions. We validated our proposed model through test simulations, demonstrating its feasibility and its ability to reproduce expected contraction patterns across different mesh resolutions and configurations. Moving forward, future research efforts should prioritize the validation of our model using robust clinical data. Additionally, it is crucial to refine the model by incorporating a more realistic uterus model derived from medical imaging. Furthermore, applying the model to simulate the entire childbirth process holds immense potential for gaining deeper insights into the intricate dynamics of labor.

Rho-Kinase Inhibition of Active Force and Passive Tension in Airway Smooth Muscle: A Strategy for Treating Airway Hyperresponsiveness in Asthma

Rho-kinase inhibitors have been identified as a class of potential drugs for treating asthma because of their ability to reduce airway inflammation and active force in airway smooth muscle (ASM). Past research has revealed that, besides the effect on the ASM's force generation, rho-kinase (ROCK) also regulates actin filament formation and filament network architecture and integrity, thus affecting ASM's cytoskeletal stiffness. The present review is not a comprehensive examination of the roles played by ROCK in regulating ASM function but is specifically focused on passive tension, which is partially determined by the cytoskeletal stiffness of ASM. Understanding the molecular basis for maintaining active force and passive tension in ASM by ROCK will allow us to determine the suitability of ROCK inhibitors and its downstream enzymes as a class of drugs in treating airway hyperresponsiveness seen in asthma. Because clinical trials using ROCK inhibitors in the treatment of asthma have yet to be conducted, the present review focuses on the in vitro effects of ROCK inhibitors on ASM's mechanical properties which include active force generation, relaxation, and passive stiffness. The review provides justification for future clinical trials in the treatment of asthma using ROCK inhibitors alone and in combination with other pharmacological and mechanical interventions.

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 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.

A life off the beaten track in biomechanics: Imperfect elasticity, cytoskeletal glassiness, and epithelial unjamming

Textbook descriptions of elasticity, viscosity, and viscoelasticity fail to account for certain mechanical behaviors that typify soft living matter. Here, we consider three examples. First, strong empirical evidence suggests that within lung parenchymal tissues, the frictional stresses expressed at the microscale are fundamentally not of viscous origin. Second, the cytoskeleton (CSK) of the airway smooth muscle cell, as well as that of all eukaryotic cells, is more solid-like than fluid-like, yet its elastic modulus is softer than the softest of soft rubbers by a factor of 104-105. Moreover, the eukaryotic CSK expresses power law rheology, innate malleability, and fluidization when sheared. For these reasons, taken together, the CSK of the living eukaryotic cell is reminiscent of the class of materials called soft glasses, thus likening it to inert materials such as clays, pastes slurries, emulsions, and foams. Third, the cellular collective comprising a confluent epithelial layer can become solid-like and jammed, fluid-like and unjammed, or something in between. Esoteric though each may seem, these discoveries are consequential insofar as they impact our understanding of bronchospasm and wound healing as well as cancer cell invasion and embryonic development. Moreover, there are reasons to suspect that certain of these phenomena first arose in the early protist as a result of evolutionary pressures exerted by the primordial microenvironment. We have hypothesized, further, that each then became passed down virtually unchanged to the present day as a conserved core process. These topics are addressed here not only because they are interesting but also because they track the journey of one laboratory along a path less traveled by.

A model of neurovascular coupling and its application to cortical spreading depolarization

Cortical spreading depolarization (CSD) is a neuropathological condition involving propagating waves of neuronal silence, and is related to multiple diseases, such as migraine aura, traumatic brain injury (TBI), stroke, and cardiac arrest, as well as poor outcome of patients. While CSDs of different severity share similar roots on the ion exchange level, they can lead to different vascular responses (namely spreading hyperemia and spreading ischemia). In this paper, we propose a mathematical model relating neuronal activities to predict vascular changes as measured with near-infrared spectroscopy (NIRS) and fMRI recordings, and apply it to the extreme case of CSD, where sustained near-complete neuronal depolarization is seen. We utilize three serially connected models (namely, ion exchange, neurovascular coupling, and hemodynamic model) which are described by differential equations. Propagating waves of ion concentrations, as well as the associated vasodynamics and hemodynamics, are simulated by solving these equations. Our proposed model predicts vasodynamics and hemodynamics that agree both qualitatively and quantitatively with experimental literature. Mathematical modeling and simulation offer a powerful tool to help understand the underlying mechanisms of CSD and help interpret the data. In addition, it helps develop novel monitoring techniques prior to data collection. Our simulated results strongly suggest that fMRI is unable to reliably distinguish between spreading hyperemia and spreading ischemia, while NIRS signals are substantially distinct in the two cases.

Membrane adhesion junctions regulate airway smooth muscle phenotype and function

The local environment surrounding airway smooth muscle (ASM) cells has profound effects on the physiological and phenotypic properties of ASM tissues. ASM is continually subjected to the mechanical forces generated during breathing and to the constituents of its surrounding extracellular milieu. The smooth muscle cells within the airways continually modulate their properties to adapt to these changing environmental influences. Smooth muscle cells connect to the extracellular cell matrix (ECM) at membrane adhesion junctions that provide mechanical coupling between smooth muscle cells within the tissue. Membrane adhesion junctions also sense local environmental signals and transduce them to cytoplasmic and nuclear signaling pathways in the ASM cell. Adhesion junctions are composed of clusters of transmembrane integrin proteins that bind to ECM proteins outside the cell and to large multiprotein complexes in the submembranous cytoplasm. Physiological conditions and stimuli from the surrounding ECM are sensed by integrin proteins and transduced by submembranous adhesion complexes to signaling pathways to the cytoskeleton and nucleus. The transmission of information between the local environment of the cells and intracellular processes enables ASM cells to rapidly adapt their physiological properties to modulating influences in their extracellular environment: mechanical and physical forces that impinge on the cell, ECM constituents, local mediators, and metabolites. The structure and molecular organization of adhesion junction complexes and the actin cytoskeleton are dynamic and constantly changing in response to environmental influences. The ability of ASM to rapidly accommodate to the ever-changing conditions and fluctuating physical forces within its local environment is essential for its normal physiological function.

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

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.

Sustained contractile force regulated by rho-kinase and protein kinase C in sheep carotid arterial smooth muscle

The time course of smooth muscle contraction can be divided into two phases, the initial phase is associated with force development, whereas the sustained phase is associated with force maintenance. Cumulative evidence suggests that the two phases are regulated by different signaling pathways and that ρ-kinase (ROCK) and protein kinase C (PKC) play an important role in regulating isometric force in sustained contractions. Since the maintenance of sustained force is critical to the function of vascular smooth muscle, unraveling the complex mechanism of force maintenance is crucial for understanding the cell biology of the muscle. The present study examined the effects of ROCK and PKC on the level of phosphorylation of the 20-kD myosin light chain (MLC20) and isometric force during a sustained contraction. We used partial activation and inhibition of ROCK and PKC to reduce the isometric force by 50% of the maximal isometric force in fully activated muscle, F_max. We then examined the level of MLC20 phosphorylation in each case. We found that in partially activated muscle the level of MLC20 phosphorylation required to maintain 50% F_max was much lower than that required in muscles where 50% reduction in F_max was achieved by partial inhibition of ROCK and PKC. The results can be explained by a model containing a contractile apparatus and a cytoskeletal scaffold where force generated by the contractile apparatus is transmitted to the extracellular domain through the cytoskeleton. The results indicate that ROCK and PKC play an important role in force transmission through the cytoskeleton.NEW & NOTEWORTHY The study supports a model that the maintenance of sustained force during a contraction of arterial smooth muscle is dependent on the intracellular transmission of force through the cytoskeleton and that ρ-kinase and protein kinase C plays an important role in the regulation of cytoskeletal integrity and its efficiency in force transmission.

Modeling and experimental approaches for elucidating multi-scale uterine smooth muscle electro- and mechano-physiology: A review

The uterus provides protection and nourishment (via its blood supply) to a developing fetus, and contracts to deliver the baby at an appropriate time, thereby having a critical contribution to the life of every human. However, despite this vital role, it is an under-investigated organ, and gaps remain in our understanding of how contractions are initiated or coordinated. The uterus is a smooth muscle organ that undergoes variations in its contractile function in response to hormonal fluctuations, the extreme instance of this being during pregnancy and labor. Researchers typically use various approaches to studying this organ, such as experiments on uterine muscle cells, tissue samples, or the intact organ, or the employment of mathematical models to simulate the electrical, mechanical and ionic activity. The complexity exhibited in the coordinated contractions of the uterus remains a challenge to understand, requiring coordinated solutions from different research fields. This review investigates differences in the underlying physiology between human and common animal models utilized in experiments, and the experimental interventions and computational models used to assess uterine function. We look to a future of hybrid experimental interventions and modeling techniques that could be employed to improve the understanding of the mechanisms enabling the healthy function of the uterus.

Characterization of the active response of a guinea pig carotid artery

This work presents a characterization of the active response of the carotid artery of guinea pig fetuses through a methodology that encompasses experiments, modeling and numerical simulation. To this end, the isometric contraction test is carried out in ring samples subjected to different levels of KCl concentrations and pre-stretching. Then, a coupled mechanochemical model, aimed at describing the smooth cell behavior and its influence on the passive and active mechanical response of the vascular tissue, is calibrated from the experimental measurements. Due to the complex stress and strain fields developed in the artery, a finite element numerical simulation of the test is performed to fit the model parameters, where those related to the phosphorylation and dephosphorylation activity along with the load-bearing capacity of the myosin cross-bridges are found to be the most predominant when sensitizing the active response. The main strengths of the model are associated with the prediction of the stationary state of the active mechanical response of the tissue through a realistic description of the mechanochemical process carried out at its cellular level.

Molecular-level evidence of force maintenance by smooth muscle myosin during LC20 dephosphorylation

Smooth muscle (SM) is found in most hollow organs of the body. Phasic SM, as found in the gut, contracts to propel content, whereas tonic SM, as found in most blood vessels, maintains tension. This force maintenance is referred to as the latch state and occurs at low levels of myosin activation (myosin light chain [LC20] phosphorylation). Molecular mechanisms have been proposed to explain the latch state but have been studied only at the whole-muscle level because of technological limitations. In the current study, an assay chamber was devised to allow injection of myosin light chain phosphatase (MLCP) during laser trap and in vitro motility assays, without creating bulk flow, to reproduce latch state conditions at the molecular level. Using the laser trap in a single-beam mode, an actin filament was brought in contact with several myosin molecules on a pedestal. Myosin pulled on the actin filament until a plateau force was reached, at which point, MLCP was injected. Force maintenance was observed during LC20 dephosphorylation, the level of which was assessed in a parallel in vitro motility assay performed in the same conditions. Force was maintained longer for myosin purified from tonic SM than from phasic SM. These data support the longstanding dogma of strong bonds caused by dephosphorylated, noncycling cross-bridges. Furthermore, MLCP injection in an in vitro motility mixture assay performed with SM and skeletal muscle myosin suggests that the maintenance of these strong bonds is possible only if no energy is provided by surrounding actively cycling myosin molecules.

Molecular Characterization and Expression Pattern of Paramyosin in Larvae and Adults of Yesso Scallop

Simple Summary

Paramyosin is an important myofibrillar protein in smooth muscle in molluscs that is not present in vertebrate muscles. This study characterized its sequence feature and expression patterns in Yesso scallop Patinopecten yessoensis and revealed the unique phosphorylation sites in scallops. The mRNA and protein expression of paramyosin was mainly found in foot and smooth adductor muscle. At late larval stages, strong paramyosin mRNA signals were detected in the symmetric positions of anterior and posterior adductor muscles. The present findings support that paramyosin may serve as the most important component of smooth muscle assembly during muscle development and catch regulation in scallops.

Abstract

Paramyosin is an important myofibrillar protein in molluscan smooth muscle. The full-length cDNA encoding paramyosin has been identified from Yesso scallop Patinopecten yessoensis. The length of paramyosin molecule has been found to be 3715 bp, which contains an open reading frame (ORF) of 2805 bp for 934 amino acid residues. Characterization of P. yessoensis paramyosin reveals the typical structural feature of coiled-coil protein, including six α-helix (α1-α6) and one coil (η) structures. Multiple phosphorylation sites have been predicted at the N-terminus of paramyosin, representing the unique phosphorylation sites in scallops. The highest levels of mRNA and protein expression of paramyosin have been found in foot and the smooth adductor muscle. According to whole-mount in situ hybridization (WISH), strong paramyosin mRNA signals were detected in the symmetric positions of anterior and posterior adductor muscles at late larval stages. These findings support that paramyosin may serve as the most important components for myogenesis and catch regulation in scallops. The present findings will not only help uncover the potential function of myofibrillar proteins in molluscs but also provide molecular evidence to infer evolutionary relationships among invertebrates.

A multiscale sliding filament model of lymphatic muscle pumping

The lymphatics maintain fluid balance by returning interstitial fluid to veins via contraction/compression of vessel segments with check valves. Disruption of lymphatic pumping can result in a condition called lymphedema with interstitial fluid accumulation. Lymphedema treatments are often ineffective, which is partially attributable to insufficient understanding of specialized lymphatic muscle lining the vessels. This muscle exhibits cardiac-like phasic contractions and smooth muscle-like tonic contractions to generate and regulate flow. To understand the relationship between this sub-cellular contractile machinery and organ-level pumping, we have developed a multiscale computational model of phasic and tonic contractions in lymphatic muscle and coupled it to a lymphangion pumping model. Our model uses the sliding filament model (Huxley in Prog Biophys Biophys Chem 7:255-318, 1957) and its adaptation for smooth muscle (Mijailovich in Biophys J 79(5):2667-2681, 2000). Multiple structural arrangements of contractile components and viscoelastic elements were trialed but only one provided physiologic results. We then coupled this model with our previous lumped parameter model of the lymphangion to relate results to experiments. We show that the model produces similar pressure, diameter, and flow tracings to experiments on rat mesenteric lymphatics. This model provides the first estimates of lymphatic muscle contraction energetics and the ability to assess the potential effects of sub-cellular level phenomena such as calcium oscillations on lymphangion outflow. The maximum efficiency value predicted (40%) is at the upper end of estimates for other muscle types. Spontaneous calcium oscillations during diastole were found to increase outflow up to approximately 50% in the range of frequencies and amplitudes tested.

Efficient computational modelling of smooth muscle orientation and function in the aorta

Understanding the mechanical effects of smooth muscle cell (SMC) contraction on the initiation and the propagation of cardiovascular diseases such as aortic dissection is critical. Framed by elastic lamellar sheets in the lamellar unit, there are SMCs in the media with a distinct radial tilt, which indicates their contribution to the radial strength. However, the mechanical effects of this type of anisotropy have not been fully discussed. Therefore, in this study, we propose a constitutive framework that models the passive and active mechanics of the aorta, taking into account the dispersed nature of the aortic constituents by applying the discrete fibre dispersion method. We suggest an isoparametric approach by evaluating various numerical integration methods and introducing a non-uniform discretization of the unit hemisphere to increase its computational efficiency. Finally, the constitutive parameters are fitted to layer-specific experimental data and initial computational results are briefly presented. The radial tilt of SMCs is also analysed, which has a noticeable influence on the mechanical behaviour of the aorta. In the absence of sufficient experimental data, the results indicate that the active contribution of SMCs has a remarkable impact on the mechanics of the healthy aorta.

A multiscale model of cerebral autoregulation

The mechanism of cerebral autoregulation ensures a continuous and sufficient blood supply to the brain to maintain normal function in the presence of changes in blood pressure. Impaired cerebral autoregulation is implicated in a range of brain diseases. We thus present here a multiscale model of cerebral autoregulation to provide a more detailed basis for a better understanding of the mechanisms behind impaired autoregulation. This model is built around a model of single arteriole, which includes a model of Nitric Oxide (NO) transport, the myogenic response, and a 4-state kinetic model coupled to a mechanical model of the vessel wall. In particular, the NO component of the model is added here to better understand the interaction mode between NO and the myogenic response, since the role of NO, the recognized effective vasodilator, is poorly understood in this context. This vessel model is then integrated within a model of the full-brain vasculature. The model is validated using a range of experimental data from the literature, both steady-state and dynamic. The model is able to predict the response of the arteriole to changes in both driving pressure and baseline pressure, indicating that the model captures well the balance between the myogenic and metabolic mechanisms. We next plan to examine the ways in which impaired autoregulation is manifested in different patient groups, potentially leading to improved therapy.

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.

Oscillating calcium signals in smooth muscle cells underlie the persistent basal tone of internal anal sphincter

A persistent basal tone in the internal anal sphincter (IAS) is essential for keeping the anal canal closed and fecal continence; its inhibition via the rectoanal inhibitory reflex (RAIR) is required for successful defecation. However, cellular signals underlying the IAS basal tone remain enigmatic. Here we report the origin and molecular mechanisms of calcium signals that control the IAS basal tone, using a combination approach including a novel IAS slice preparation that retains cell arrangement and architecture as in vivo, 2-photon imaging, and cell-specific gene-modified mice. We found that IAS smooth muscle cells generate two forms of contractions (i.e., phasic and sustained contraction) and Ca2+ signals (i.e., synchronized Ca2+ oscillations [SCaOs] and asynchronized Ca2+ oscillations [ACaOs]) that last for hours. RyRs, TMEM16A, L-type Ca2+ channels, and gap junctions are required for SCaOs, which account for phasic contraction and 75% of sustained contraction. Nevertheless, only RyRs are required for ACaOs, which contribute 25% of sustained contraction. Nitric oxide, the primary neurotransmitter mediating the RAIR, blocks both types of Ca2+ signals, leading to IAS's full relaxation. Our results show that the oscillating nature of Ca2+ signals generates and maintains the basal tone without causing cytotoxicity to IAS. Our study provides insight into fecal continence and normal defecation.

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.

A myofibre model for the study of uterine excitation-contraction dynamics

As the uterus remodels in preparation for delivery, the excitability and contractility of the uterine smooth muscle layer, the myometrium, increase drastically. But when remodelling proceeds abnormally it can contribute to preterm birth, slow progress of labour, and failure to initiate labour. Remodelling increases intercellular coupling and cellular excitability, which are the main targets of pharmaceutical treatments for uterine contraction disorders. However, the way in which electrical propagation and force development depend on intercellular coupling and cellular excitability is not fully understood. Using a computational myofibre model we study the dependency of electrical propagation and force development on intercellular coupling and cellular excitability. This model reveals that intercellular coupling determines the conduction velocity. Moreover, our model shows that intercellular coupling alone does not regulate force development. Further, cellular excitability controls whether conduction across the cells is blocked. Lastly, our model describes how cellular excitability regulates force development. Our results bridge cellular factors, targeted by drugs to regulate uterine contractions, and tissue level electromechanical properties, which are responsible for delivery. They are a step forward towards understanding uterine excitation-contraction dynamics and developing safer and more efficient pharmaceutical treatments for uterine contraction disorders.

Electrical Propagation of Vasodilatory Signals in Capillary Networks

We have developed a computational model to study electrical propagation of vasodilatory signals and arteriolar regulation of blood flow depending on the oxygen tension and agonist distribution in the capillary network. The involving key parameters of endothelial cell-to-cell electrical conductivity and plasma membrane area per unit volume were calibrated with the experimental data on an isolated endothelial tube of mouse skeletal feeding arteries. We have estimated the oxygen saturation parameters in terms of erythrocyte ATP release from the data of a left anterior descending coronary blood perfusion of dog. Regarding the acetylcholine-induced upstream conduction, our model shows that spatially uniform superfusion of acetylcholine attenuates the electrical signal propagation, and blocking calcium-activated potassium channels suppresses that attenuation. On the other hand, a local infusion of acetylcholine induces enhanced electrical propagation that corresponds to physiological relevance. Integrating the electrophysiology of endothelial tube and the electrophysiology/mechanics of a lumped arteriole, we show mechanistically that endothelial purinergic oxygen sensing of ATP released from erythrocytes and local infusion of acetylcholine are individually effective to induce vasodilatory signals to regulate blood flow in arterioles. We have recapitulated the upstream vasomotion in arterioles from the elevated oxygen tension in the downstream capillary domain. This study is a foundation for characterizing effective pharmaceutical strategies for ascending vasodilation and oxygenation.

Uterus Modeling from Cell to Organ Level: towards Better Understanding of Physiological Basis of Uterine Activity

The relatively limited understanding of the physiology of uterine activation prevents us from achieving optimal clinical outcomes for managing serious pregnancy disorders such as preterm birth or uterine dystocia. There is increasing awareness that multi-scale computational modeling of the uterus is a promising approach for providing a qualitative and quantitative description of uterine physiology. The overarching objective of such approach is to coalesce previously fragmentary information into a predictive and testable model of uterine activity that, in turn, informs the development of new diagnostic and therapeutic approaches to these pressing clinical problems. This article assesses current progress towards this goal. We summarize the electrophysiological basis of uterine activation as presently understood and review recent research approaches to uterine modeling at different scales from single cell to tissue, whole organ and organism with particular focus on transformative data in the last decade. We describe the positives and limitations of these approaches, thereby identifying key gaps in our knowledge on which to focus, in parallel, future computational and biological research efforts.

Cytoskeletal remodeling slows cross-bridge cycling and ATP hydrolysis rates in airway smooth muscle

During isometric activation of airway smooth muscle (ASM), cross-bridge cycling and ATP hydrolysis rates decline across time even though isometric force is sustained. Thus, tension cost (i.e., ATP hydrolysis rate per unit of force during activation) decreases with time. The "latch-state" hypothesis attributes the dynamic change in cross-bridge cycling and ATP hydrolysis rates to changes in phosphorylation of the regulatory myosin light chain (rMLC20 ). However, we previously showed that in ASM, the extent of rMLC20 phosphorylation remains unchanged during sustained isometric force. As an alternative, we hypothesized that cytoskeletal remodeling within ASM cells results in increased internal loading of contractile proteins that slows cross-bridge cycling and ATP hydrolysis rates. To test this hypothesis, we simultaneously measured isometric force and ATP hydrolysis rate in permeabilized porcine ASM strips activated by Ca2+ (pCa 4.0). The extent of rMLC20 phosphorylation remained unchanged during isometric activation, even though ATP hydrolysis rate (tension cost) declined with time. The effect of cytoskeletal remodeling was assessed by inhibiting actin polymerization using Cytochalasin D (Cyto-D). In Cyto-D treated ASM, isometric force was reduced while ATP hydrolysis rate increased compared to untreated ASM strips. These results indicate that external transmission of force, cross-bridge cycling and ATP hydrolysis rates are affected by internal loading of contractile proteins.

On the mechanical response of the actomyosin cortex during cell indentations

A mechanical model is presented to analyze the mechanics and dynamics of the cell cortex during indentation. We investigate the impact of active contraction on the cross-linked actin network for different probe sizes and indentation rates. The essential molecular mechanisms of filament stretching, cross-linking and motor activity, are represented by an active and viscous mechanical continuum. The filaments behave as worm-like chains linked either by passive rigid linkers or by myosin motors. In the first example, the effects of probe size and loading rate are evaluated using the model for an idealized rounded cell shape in which properties are based on the results of parallel-plate rheometry available in the literature. Extreme cases of probe size and indentation rate are taken into account. Afterward, AFM experiments were done by engaging smooth muscle cells with both sharp and spherical probes. By inverse analysis with finite element software, our simulations mimicking the experimental conditions show the model is capable of fitting the AFM data. The results provide spatiotemporal dependence on the size and rate of the mechanical stimuli. The model captures the general features of the cell response. It characterizes the actomyosin cortex as an active solid at short timescales and as a fluid at longer timescales by showing (1) higher levels of contraction in the zones of high curvature; (2) larger indentation forces as the probe size increases; and (3) increase in the apparent modulus with the indentation depth but no dependence on the rate of the mechanical stimuli. The methodology presented in this work can be used to address and predict microstructural dependence on the force generation of living cells, which can contribute to understanding the broad spectrum of results in cell experiments.

Force distribution and multi-scale mechanics in smooth muscle tissues

The mechanical role of smooth muscle tissue in many physiological processes is vital to their healthy function. In this work, we provide a deeper understanding of the underlying mechanisms that govern the smooth muscle tissue response. Specifically, we model and investigate the distribution and the transmission of passive and active forces throughout the microstructure. Broadly, smooth muscle cells contain a structural network with two types of load carrying structures: (1) contractile units made of actin and myosin filaments, which are capable of generating force, and (2) intermediate filaments. The extracellular matrix comprises elastin and collagen fibers that can sustain stress. We argue that all of the load carrying constituents in the tissue participate in the generation and the transmission of passive and active forces. We begin by modeling the response of the elements in the smooth muscle cell and defining a network of contractile units and intermediate filaments through which forces are transferred. This allows to derive an expression for the stress that develops in the cell. Next, we assume a hyperelastic behavior for the extracellular matrix and determine the stress in the tissue. With appropriate kinematic constraints and equilibrium considerations, we relate the macroscopic deformation to the stretch of the individual load carrying structures. Consequently, the stress on each element in the tissue can be computed. To validate the framework, we consider a simple microstructure of a smooth muscle tissue and fit the model parameters to experimental findings. The framework is also used to delineate experimental evidence which suggests that the suppression of intermediate filaments reduces the active and passive forces in a tissue. We show that the degradation and the reduction of the number of intermediate filaments in the cell fully explains this observation.

A Review on Microvascular Hemodynamics: The Control of Blood Flow Distribution and Tissue Oxygenation

The microcirculation is a complex network of vessels ranging from as large as 100 μm to as small as 5 μm. This complex network is responsible for the regulation of oxygen to the surrounding tissues and ensures metabolite washout. With a more complete understanding of the microcirculation's physiologic and pathologic tendencies, engineers can create new solutions to combat blood pathologies and shock-related diseases. Over the last number of decades a grown interest in the microcirculation has resulted in the development of fundamental techniques to quantify the microvasculature flow and the release of oxygen to tissues.

The effects of Cinnamaldehyde on early brain injury and cerebral vasospasm following experimental subarachnoid hemorrhage in rabbits

The neuroprotective and vasodilatory effects of cinnamaldehyde have been widely studied and documented. On the basis of these findings, we hypothesized that cinnamaldehyde exhibits therapeutic effects on subarachnoid hemorrhage-induced early brain injury and cerebral vasospasm. Thirty-two adult male New Zealand white rabbits were randomly divided into four groups of eight rabbits: control, subarachnoid hemorrhage, subarachnoid hemorrhage + vehicle, and subarachnoid hemorrhage + cinnamaldehyde. An intraperitoneal dose of 50 mg/kg cinnamaldehyde was administered 5 min following an intracisternal blood injection, followed by three further daily injections at identical doses. The animals were sacrificed 72 h after subarachnoid hemorrhage was induced. The cross-sectional areas and arterial wall thicknesses of the basilar artery were measured and hippocampal degeneration scores were evaluated. Treatment with cinnamaldehyde was effective in providing neuroprotection and attenuating cerebral vasospasm after subarachnoid hemorrhage in rabbits. It effectively increased the cross-sectional areas of the basilar artery and reduced the arterial wall thickness; in addition, hippocampal degeneration scores were lower in the cinnamaldehyde group. The findings of this study showed, for the first time to our knowledge, that cinnamaldehyde exhibits neuroprotective activity against subarachnoid hemorrhage-induced early brain injury and that it can prevent vasospasm. Potential mechanisms underlying the neuroprotection and vasodilation were discussed. Cinnamaldehyde could play a role in subarachnoid hemorrhage treatment.

Electro-Mechanical Ionic Channel Modeling for Uterine Contractions and Oxytocin Effect during Pregnancy

Uterine contractions during normal pregnancy and preterm birth are an important physiological activity. Although the cause of preterm labor is usually unknown, preterm birth creates very serious health concerns in many cases. Therefore, understanding normal birth and predicting preterm birth can help both newborn babies and their families. In our previous work, we developed a multiscale dynamic electrophysiology model of uterine contractions. In this paper, we mainly focus on the cellular level and use electromyography (EMG) and cell force generation methods to construct a new ionic channel model and a corresponding mechanical force model. Specifically, the ionic channel model takes into consideration the knowledge of individual ionic channels, which include the electrochemical and bioelectrical characteristics of individual myocytes. We develop a new sodium channel and a new potassium channel based on the experimental data from the human myometrium and the average correlations are 0.9946 and 0.9945, respectively. The model is able to generate the single spike, plateau type and bursting type of action potentials. Moreover, we incorporate the effect of oxytocin on changing the properties of the L-type and T-type calcium channels and further influencing the output action potentials. In addition, we develop a mechanical force model based on the new ionic channel model that describes the detailed ionic dynamics. Our model produces cellular mechanical force that propagates to the tissue level. We illustrate the relationship between the cellular mechanical force and the intracellular ionic dynamics and discuss the relationship between the application of oxytocin and the output mechanical force. We also propose a simplified version of the model to enable large scale simulations using sensitivity analysis method. Our results show that the model is able to reproduce the bioelectrical and electromechanical characteristics of uterine contractions during pregnancy.

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.

Global Sensitivity Analysis of High-Dimensional Neuroscience Models: An Example of Neurovascular Coupling

The complexity and size of state-of-the-art cell models have significantly increased in part due to the requirement that these models possess complex cellular functions which are thought-but not necessarily proven-to be important. Modern cell models often involve hundreds of parameters; the values of these parameters come, more often than not, from animal experiments whose relationship to the human physiology is weak with very little information on the errors in these measurements. The concomitant uncertainties in parameter values result in uncertainties in the model outputs or quantities of interest (QoIs). Global sensitivity analysis (GSA) aims at apportioning to individual parameters (or sets of parameters) their relative contribution to output uncertainty thereby introducing a measure of influence or importance of said parameters. New GSA approaches are required to deal with increased model size and complexity; a three-stage methodology consisting of screening (dimension reduction), surrogate modeling, and computing Sobol' indices, is presented. The methodology is used to analyze a physiologically validated numerical model of neurovascular coupling which possess 160 uncertain parameters. The sensitivity analysis investigates three quantities of interest, the average value of [Formula: see text] in the extracellular space, the average volumetric flow rate through the perfusing vessel, and the minimum value of the actin/myosin complex in the smooth muscle cell. GSA provides a measure of the influence of each parameter, for each of the three QoIs, giving insight into areas of possible physiological dysfunction and areas of further investigation.

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.

Biomechanical relevance of the microstructure in artery walls with a focus on passive and active components

The microstructure of arteries, consisting, in particular, of collagen, elastin, and vascular smooth muscle cells, plays a very significant role in their biomechanical response during a cardiac cycle. In this article, we highlight the microstructure and the contributions of each of its components to the overall mechanical behavior. We also describe the changes of the microstructure that occur as a result of abdominal aortic aneurysms and disease, such as atherosclerosis. We also focus on how the passive and active constituents are incorporated into a mathematical model without going into detail of the mathematical formulation. We conclude by mentioning open problems toward a better characterization of the biomechanical aspects of arteries that will be beneficial for a better understanding of cardiovascular pathophysiology.

Creatine kinase, energy reserve, and hypertension: from bench to bedside

We hypothesized that human variation in the activity of the ATP regenerating enzyme creatine kinase (CK) activity affects hypertension and cardiovascular disease risk. CK is tightly bound close to ATP-utilizing enzymes including Ca2+-ATPase, myosin ATPase, and Na+/K+-ATPase, where it rapidly regenerates ATP from ADP, H+, and phosphocreatine. Thus, relatively high CK was thought to enhance ATP-demanding processes including resistance artery contractility and sodium retention, and reduce ADP-dependent functions. In a series of studies of our group and others, CK was linked to hypertension and bleeding risk. Plasma CK after rest, used as a surrogate measure for tissue CK, was associated with high blood pressure and failure of antihypertensive therapy in case-control and population studies. Importantly, high tissue CK preceded hypertension in animal models and in humans, and human vascular tissue CK gene expression was strongly associated with clinical blood pressure. In line with this, CK inhibition substantially reduced the contractility of human resistance arteries ex vivo. We also presented evidence that plasma CK reduced ADP-dependent platelet aggregation. In subsequent intervention studies, the oral competitive CK inhibitor beta-guanidinopropionic acid (GPA) reduced blood pressure in spontaneously hypertensive rats (SHRs), and a 1-week trial of sub-therapeutic dose GPA in healthy men was uneventful. Thus, based on theoretical concepts, evidence was gathered in laboratory, case-control, and population studies that high CK is associated with hypertension and with bleeding risk, potentially leading to a new mode of cardiovascular risk reduction with CK inhibition.

A computational model of excitation and contraction in uterine myocytes from the pregnant rat

Aberrant uterine myometrial activities in humans are major health issues. However, the cellular and tissue mechanism(s) that maintain the uterine myometrium at rest during gestation, and that initiate and maintain long-lasting uterine contractions during delivery are incompletely understood. In this study we construct a computational model for describing the electrical activity (simple and complex action potentials), intracellular calcium dynamics and mechanical contractions of isolated uterine myocytes from the pregnant rat. The model reproduces variant types of action potentials - from spikes with a smooth plateau, to spikes with an oscillatory plateau, to bursts of spikes - that are seen during late gestation under different physiological conditions. The effects of the hormones oestradiol (via reductions in calcium and potassium selective channel conductance), oxytocin (via an increase in intracellular calcium release) and the tocolytic nifedipine (via a block of L-type calcium channels currents) on action potentials and contractions are also reproduced, which quantitatively match to experimental data. All of these results validated the cell model development. In conclusion, the developed model provides a computational platform for further investigations of the ionic mechanism underlying the genesis and control of electrical and mechanical activities in the rat uterine myocytes.

A Distribution-Moment Approximation for Coupled Dynamics of the Airway Wall and Airway Smooth Muscle

Asthma is fundamentally a disease of airway constriction. Due to a variety of experimental challenges, the dynamics of airways are poorly understood. Of specific interest is the narrowing of the airway due to forces produced by the airway smooth muscle wrapped around each airway. The interaction between the muscle and the airway wall is crucial for the airway constriction that occurs during an asthma attack. Although cross-bridge theory is a well-studied representation of complex smooth muscle dynamics, and these dynamics can be coupled to the airway wall, this comes at significant computational cost-even for isolated airways. Because many phenomena of interest in pulmonary physiology cannot be adequately understood by studying isolated airways, this presents a significant limitation. We present a distribution-moment approximation of this coupled system and study the validity of the approximation throughout the physiological range. We show that the distribution-moment approximation is valid in most conditions, and we explore the region of breakdown. These results show that in many situations, the distribution-moment approximation is a viable option that provides an orders-of-magnitude reduction in computational complexity; not only is this valuable for isolated airway studies, but it moreover offers the prospect that rich ASM dynamics might be incorporated into interacting airway models where previously this was precluded by computational cost.

Multi-scale and multi-physics model of the uterine smooth muscle with mechanotransduction

Preterm labor is an important public health problem. However, the efficiency of the uterine muscle during labor is complex and still poorly understood. This work is a first step towards a model of the uterine muscle, including its electrical and mechanical components, to reach a better understanding of the uterus synchronization. This model is proposed to investigate, by simulation, the possible role of mechanotransduction for the global synchronization of the uterus. The electrical diffusion indeed explains the local propagation of contractile activity, while the tissue stretching may play a role in the synchronization of distant parts of the uterine muscle. This work proposes a multi-physics (electrical, mechanical) and multi-scales (cell, tissue, whole uterus) model, which is applied to a realistic uterus 3D mesh. This model includes electrical components at different scales: generation of action potentials at the cell level, electrical diffusion at the tissue level. It then links these electrical events to the mechanical behavior, at the cellular level (via the intracellular calcium concentration), by simulating the force generated by each active cell. It thus computes an estimation of the intra uterine pressure (IUP) by integrating the forces generated by each active cell at the whole uterine level, as well as the stretching of the tissue (by using a viscoelastic law for the behavior of the tissue). It finally includes at the cellular level stretch activated channels (SACs) that permit to create a loop between the mechanical and the electrical behavior (mechanotransduction). The simulation of different activated regions of the uterus, which in this first "proof of concept" case are electrically isolated, permits the activation of inactive regions through the stretching (induced by the electrically active regions) computed at the whole organ scale. This permits us to evidence the role of the mechanotransduction in the global synchronization of the uterus. The results also permit us to evidence the effect on IUP of this enhanced synchronization induced by the presence of SACs. This proposed simplified model will be further improved in order to permit a better understanding of the global uterine synchronization occurring during efficient labor contractions.

Multiscale and Multiaxial Mechanics of Vascular Smooth Muscle

Mathematical models can facilitate an integrative understanding of the complexity underlying biological structure and function, but they must be informed and validated by empirical data. Uniaxial contraction of an arterial ring is a well-used in vitro approach for studying characteristics of smooth muscle contractility even though this experimental arrangement does not mimic the in vivo vascular geometry or loading. In contrast, biaxial contraction of an inflated and axially extended excised vessel provides broader information, both passive and active, under more realistic conditions. Few investigations have compared these two in vitro approaches directly, namely how their results overlap, how they differ, or if each provides unique complementary information. Toward this end, we present, to our knowledge, a new multiscale mathematical model of arterial contractility accounting for structural and functional constituents at molecular, cellular, and tissue levels. The artery is assumed to be a thick-walled incompressible cylinder described by an anisotropic model of the extracellular matrix and, to our knowledge, novel model of smooth muscle contractility. The latter includes a 3D structural sensitivity to deformation, including microscale muscle filament overlap and filament lattice spacing. The overall model captures uniaxial and biaxial experimental contraction data, which was not possible when accounting for filament overlap alone. The model also enables parameter sensitivity studies, which confirmed that uniaxial contraction tests are not as efficient as biaxial tests for identifying changes in vascular smooth muscle function.

Airway Bistability Is Modulated by Smooth Muscle Dynamics and Length-Tension Characteristics

Airway closure has important implications for lung disease, especially asthma; in particular, the prospect of bistability between open and closed (or effectively closed) airway states has been thought to play a prominent role in airway closure associated with the formation of clustered ventilation defects in asthma. However, many existing analyses of closure consider only static airway equilibria; here we construct, to our knowledge, a new model wherein airway narrowing and closure dynamics are modulated by coupling the airway to cross-bridge models of airway smooth muscle dynamics and force generation. Using this model, we show that important qualitative features of airway pressure-radius hysteresis loops are highly dependent on both airway smooth muscle dynamics, and the length-tension relationship. Furthermore, we show that two recent experimental results from intact bronchial segments are both expressions of the same phenomenon: that a monotonically increasing length-tension relationship, with sharply higher tension at longer lengths, is needed to drive the observed changes in low-compliance regions of the baseline pressure-radius curve. We also explore the potential implications of this finding for airway closure in coupled airway models.

Biomechanics of the human uterus

The appropriate biomechanical function of the uterus is required for the execution of human reproduction. These functions range from aiding the transport of the embryo to the implantation site, to remodeling its tissue walls to host the placenta, to protecting the fetus during gestation, to contracting forcefully for a safe parturition and postpartum, to remodeling back to its nonpregnant condition to renew the cycle of menstruation. To serve these remarkably diverse functions, the uterus is optimally geared with evolving and contractile muscle and tissue layers that are cued by chemical, hormonal, electrical, and mechanical signals. The relationship between these highly active biological signaling mechanisms and uterine biomechanical function is not completely understood for normal reproductive processes and pathological conditions such as adenomyosis, endometriosis, infertility and preterm labor. Animal studies have illuminated the rich structural function of the uterus, particularly in pregnancy. In humans, medical imaging techniques in ultrasound and magnetic resonance have been combined with computational engineering techniques to characterize the uterus in vivo, and advanced experimental techniques have explored uterine function using ex vivo tissue samples. The collective evidence presented in this review gives an overall perspective on uterine biomechanics related to both its nonpregnant and pregnant function, highlighting open research topics in the field. Additionally, uterine disease and infertility are discussed in the context of tissue injury and repair processes and the role of computational modeling in uncovering etiologies of disease. WIREs Syst Biol Med 2017, 9:e1388. doi: 10.1002/wsbm.1388 For further resources related to this article, please visit the WIREs website.

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.

An electro-mechanical multiscale model of uterine pregnancy contraction

Detecting preterm labor as early as possible is important because tocolytic drugs are much more likely to delay preterm delivery if administered early. Having good information on the real risk of premature labor also leads to fewer women who do not need aggressive treatment for premature labor threat. Currently, one of the most promising ways to diagnose preterm labor threat is the analysis of the electrohysterogram (EHG). Its characteristics have been related to preterm labor risk but they have not proven to be sufficiently accurate to use in clinical routine. One of the reasons for this is that the physiology of the pregnant uterus is insufficiently understood. Models already exist in literature that simulate either the electrical or the mechanical component of the uterine smooth muscle. Few include both components in a co-simulation of electrical and mechanical aspects. A model that can represent realistically both the electrical and the mechanical behavior of the uterine muscle could be useful for better understanding the EHG and therefore for preterm labor detection. Processing the EHG considers only the electrical component of the uterus but the electrical activity does not seem to explain by itself the synchronization of the uterine muscle that occurs during labor and not at other times. Recent studies have demonstrated that the mechanical behavior of the uterine muscle seems to play an important role in uterus synchronization during labor. The aim of the proposed study is to link three different models of the uterine smooth muscle behavior by using co-simulation. The models go from the electrical activity generated at the cellular level to the mechanical force generated by the muscle and from there to the deformation of the tissue. The results show the feasibility of combining these three models to model a whole uterus contraction on 3D realistic uterus model.

Role of catch bonds in actomyosin mechanics and cell mechanosensitivity

We propose a mechanism of adherent cell mechanosensing, based on the idea that the contractile actomyosin machinery behaves as a catch bond. For this, we construct a simplified model of the actomyosin structure that constitutes the building block of stress fibers and express the stability of cross bridges in terms of the force-dependent bonding energy of the actomyosin bond. Consistent with experimental measurements, we then consider that the energy barrier of the actomyosin bond increases for tension and show that this response is enough to explain the force-induced stabilization of a stress fiber. Further numerical simulations at the cellular level show that the catch-bond hypothesis can help in understanding and predict the sensitivity of adherent cells to substrate stiffness.

Systems-level airway models of bronchoconstriction

Understanding lung and airway behavior presents a number of challenges, both experimental and theoretical, but the potential rewards are great in terms of both potential treatments for disease and interesting biophysical phenomena. This presents an opportunity for modeling to contribute to greater understanding, and here, we focus on modeling efforts that work toward understanding the behavior of airways in vivo, with an emphasis on asthma. We look particularly at those models that address not just isolated airways but many of the important ways in which airways are coupled both with each other and with other structures. This includes both interesting phenomena involving the airways and the layer of airway smooth muscle that surrounds them, and also the emergence of spatial ventilation patterns via dynamic airway interaction. WIREs Syst Biol Med 2016, 8:459-467. doi: 10.1002/wsbm.1349 For further resources related to this article, please visit the WIREs website.