A Modified Hai–Murphy Model of Uterine Smooth Muscle Contraction

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.

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.

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.

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.

Selenoprotein N Was Required for the Regulation of Selenium on the Uterine Smooth Muscle Contraction in Mice

Selenium (Se) is an essential micronutrient affecting various aspects of health. The balance of the Se concentration has an important protective and promoter effect on physiological function in inducing muscular disorders in smooth muscle. Selenoprotein N (SelN) is closely related to Ca²⁺ release. The present study aimed to determine the effects and mechanism of action of dietary Se on uterine smooth muscle contraction via SelN using a mouse model. Quantitative polymerase chain reaction (qPCR) analysis was performed to detect mRNA levels. Western blotting was performed to detect protein levels. The results of the immunohistochemical analysis showed that Se had an effect on the uterine smooth muscle. The Se-supplement increased the release of Ca²⁺, Ca²⁺-calmodulin (CaM) expression, myosin light chain kinase (MLCK) expression, and myosin light chain (MLC) phosphorylation but did not affect ROCK and RhoA in uterine smooth muscle. Furthermore, the lack of Se showed an opposite impact. The effects of Se regulation were closely related to SelN. The interference of mouse SelN was performed on the uterine smooth muscle cell. Additionally, the results displayed the regulation of Se on the release of Ca²⁺, CaM expression, MLCK expression, and MLC phosphorylation were significant inhibited, and there was no effect on ROCK and RhoA. In conclusion, Se played an important role in regulating the process of contraction in uterine smooth muscle with SelN.

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.

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.

Biomathematical pattern of EMG signal propagation in smooth muscle of the non-pregnant porcine uterus

Uterine contractions are generated by myometrial smooth muscle cells (SMCs) that comprise most of the myometrial layer of the uterine wall. Aberrant uterine motility (i.e., hypo- or hyper-contractility or asynchronous contractions) has been implicated in the pathogenesis of infertility due to the failure of implantation, endometriosis and abnormal estrous cycles. The mechanism whereby the non-pregnant uterus initiates spontaneous contractions remains poorly understood. The aim of the present study was to employ linear synchronization measures for analyzing the pattern of EMG signal propagation (direction and speed) in smooth muscles of the non-pregnant porcine uterus in vivo using telemetry recording system. It has been revealed that the EMG signal conduction in the uterine wall of the non-pregnant sow does not occur at random but it rather exhibits specific directions and speed. All detectable EMG signals moved along the uterine horn in both cervico-tubal and tubo-cervical directions. The signal migration speed could be divided into the three main types or categories: i. slow basic migration rhythm (SBMR); ii. rapid basic migration rhythm (RBMR); and iii. rapid accessory migration rhythm (RAMR). In conclusion, the EMG signal propagation in smooth muscles of the porcine uterus in vivo can be assessed using a linear synchronization model. Physiological pattern of the uterine contractile activity determined in this study provides a basis for future investigations of normal and pathologicall myogenic function of the uterus.

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.

The role of cellular coupling in the spontaneous generation of electrical activity in uterine tissue

The spontaneous emergence of contraction-inducing electrical activity in the uterus at the beginning of labor remains poorly understood, partly due to the seemingly contradictory observation that isolated uterine cells are not spontaneously active. It is known, however, that the expression of gap junctions increases dramatically in the approach to parturition, by more than one order of magnitude, which results in a significant increase in inter-cellular electrical coupling. In this paper, we build upon previous studies of the activity of electrically excitable smooth muscle cells (myocytes) and investigate the mechanism through which the coupling of these cells to electrically passive cells results in the generation of spontaneous activity in the uterus. Using a recently developed, realistic model of uterine muscle cell dynamics, we investigate a system consisting of a myocyte coupled to passive cells. We then extend our analysis to a simple two-dimensional lattice model of the tissue, with each myocyte being coupled to its neighbors, as well as to a random number of passive cells. We observe that different dynamical regimes can be observed over a range of gap junction conductances: at low coupling strength, corresponding to values measured long before delivery, the activity is confined to cell clusters, while the activity for high coupling, compatible with values measured shortly before delivery, may spread across the entire tissue. Additionally, we find that the system supports the spontaneous generation of spiral wave activity. Our results are both qualitatively and quantitatively consistent with observations from in vitro experiments. In particular, we demonstrate that the increase in inter-cellular electrical coupling observed experimentally strongly facilitates the appearance of spontaneous action potentials that may eventually lead to parturition.

A constitutive model for cytoskeletal contractility of smooth muscle cells

The constitutive model presented in this article aims to describe the main bio-chemo-mechanical features involved in the contractile response of smooth muscle cells, in which the biochemical response is modelled by extending the four-state Hai–Murphy model to isotonic contraction of the cells and the mechanical response is mainly modelled based on the phosphorylation-dependent hyperbolic relation between isotonic shortening strain rate and tension. The one-dimensional version of the model is used to simulate shortening-induced deactivation with good agreement with selected experimental measurements. The results suggest that the Hai–Murphy biochemical model neglects the strain rate effect on the kinetics of cross-bridge interactions with actin filaments in the isotonic contractions. The two-dimensional version and three-dimensional versions of the model are developed using the homogenization method under finite strain continuum mechanics framework. The two-dimensional constitutive model is used to simulate swine carotid media strips under electrical field stimulation, experimentally investigated by Singer and Murphy, and contraction of a hollow airway and a hollow arteriole buried in a soft matrix subjected to multiple calcium ion stimulations. It is found that the transverse deformation may have significant influence on the response of the swine carotid medium. In both cases, the orientation of the maximal value of attached myosin is aligned with the orientation of maximum principal stress.