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

A computationally efficient anisotropic electrophysiological multiscale uterus model: From cell to organ and myometrium to abdominal surface

BACKGROUND AND OBJECTIVE

Preterm labor is a global problem affecting the health of newborns. Despite numerous studies reporting electrophysiological changes throughout pregnancy, the underlying mechanism that triggers labor remains unclear. Electrophysiological modeling can provide additional information to better understand the physiological transition from pregnancy to labor. Previous uterine electrophysiological models do not consider either the tissue thickness or fiber structure, which have both been shown to significantly impact propagation patterns.

METHODS

This paper presents a parallel computational model of the uterus using the bioengineering modeling environment OpenCMISS. This model is a multiscale anisotropic model that spans different levels from cell to organ. At the cellular level, the model utilizes a mathematical representation of uterine myocytes based on multiple ion channels. In the 3D uterine model, fiber structures are added, ranging from horizontal rings in the inner layer to vertically downward fibers in the outer layer, to more accurately depict the electrophysiological activities of the uterus. Additionally, we have developed a multilayer volume conduction model based on the boundary element method to describe the propagation of electrical signals from the myometrium to the abdominal surface.

RESULTS

Our model can not only reproduce faithfully both local non-propagated and global propagated electrical activity, but also simulate the fast wave low and fast wave high components of the electrohysterogram (EHG) on the abdominal surface. The model results support the hypothesis that the fast wave high of the EHG signal is related to uterine excitability and fast wave low is related to signal propagation. The amplitude of the simulated signal on the abdominal surface falls in the ranges of real EHG data, which is inversely proportional to the abdominal subcutaneous fat thickness, and the signal waveform highly depends on electrode position and the relative distance to the pacemaker. In addition, the propagation velocity is highly dependent on the uterus geometry and falls in the real-world data range CONCLUSIONS: Our models facilitate a better understanding of the electrophysiological changes of the uterus during pregnancy and labor, and allow for an investigation of drug effects and/or structural or anatomical abnormalities.

An update on pacemaking in the myometrium

Timely and efficient contractions of the smooth muscle of the uterus - the myometrium - are crucial to a successful pregnancy outcome. These episodic contractions are regulated by spontaneous action potentials changing cell and tissue electrical excitability. In this short review we will document and discuss current knowledge of these processes. Those seeking a conclusive account of myometrial pacemaking mechanisms, or indeed a definitive description of the anatomical site of uterine pacemaking, may be disappointed. Rather, after almost a century of investigation, and in spite of promising studies in the last decade or so, there remain many gaps in our knowledge. We review the progress that has been made using recent technologies including in vivo and ex vivo imaging and electrophysiology and computational modelling, taking evidence from studies of animal and human myometrium, with particular emphasis on what may occur in the latter. We have prioritized physiological studies that bring us closer to understanding function. From our analyses we suggest that in human myometrium there is no fixed pacemaking site, but rather mobile, initiation sites produce the connectivity for synchronizing electrical and contractile activity. We call for more studies and funding, as physiological understanding of pacemaking gives hope to being better able to treat clinical conditions such as preterm and dysfunctional labours.

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.

Feasibility of continuous intra-uterine pressure measurements during amnioreduction in twin-to-twin transfusion syndrome therapy

INTRODUCTION

This work explores the feasibility of simultaneous and continuous intra-abdominal, intra-uterine, and arterial blood pressure measurements to examine the hemodynamic perturbation expected during therapeutic amnioreduction and to better understand the protective role of the placenta during that treatment.

METHODS

Patients with twin-to-twin transfusion syndrome were treated with fetoscopic laser ablation followed by amnioreduction. Intra-abdominal, intra-uterine, and mean arterial pressures were simultaneously recorded during amnioreduction performed in steps of 200 mL. Placental thickness and uterine dimensions were measured before and after amnioreduction by ultrasonography.

RESULTS

Useful pressure recordings were obtained between volume reduction steps and short hands-off periods in four studies. Median amnioreduction volume was 1400 mL corresponding to a median uterine volume reduction of 1121 mL. Mean intra-uterine pressure significantly fell from 24.8 to 13.6 mmHg (p = 0.011) and intra-abdominal pressure significantly decreased from 13.4 to 9.2 mmHg after amnioreduction (p = 0.015). Uterine pressure recordings revealed transient contractions (A, in mmHg) following individual amnioreduction steps, which increased with fractional amnioreduction (F, no dimension) (A = 17.23*F + 11.81; r = 0.50, p = 0.001).

DISCUSSION

Simultaneous and continuous measurement of intra-abdominal, intra-uterine, and arterial blood pressures during amnioreduction is feasible. The dynamics reveal transient uterine contractions reaching levels comparable to those seen during childbirth which seem to oppose impending maternal hypovolemia by placental steal at the expense of temporarily reducing placental perfusion pressure and underline the importance of uterine and placental interaction.

Steady-state approximations for Hodgkin-Huxley cell models: Reduction of order for uterine smooth muscle cell model

Multi-scale mathematical bioelectrical models of organs such as the uterus, stomach or heart present challenges both for accuracy and computational tractability. These multi-scale models are typically founded on models of biological cells derived from the classic Hodkgin-Huxley (HH) formalism. Ion channel behaviour is tracked with dynamical variables representing activation or inactivation of currents that relax to steady-state dependencies on cellular membrane voltage. Timescales for relaxation may be orders of magnitude faster than companion ion channel variables or phenomena of physiological interest for the entire cell (such as bursting sequences of action potentials) or the entire organ (such as electromechanical coordination). Exploiting these time scales with steady-state approximations for relatively fast-acting systems is a well-known but often overlooked approach as evidenced by recent published models. We thus investigate feasibility of an extensive reduction of order for an HH-type cell model with steady-state approximations to the full dynamical activation and inactivation ion channel variables. Our effort utilises a published comprehensive uterine smooth muscle cell model that encompasses 19 ordinary differential equations and 105 formulations overall. The numerous ion channel submodels in the published model exhibit relaxation times ranging from order 10-1 to 105 milliseconds. Substitution of the faster dynamic variables with steady-state formulations demonstrates both an accurate reproduction of the full model and substantial improvements in time-to-solve, for test cases performed. Our demonstration here of an effective and relatively straightforward reduction method underlines the particular importance of considering time scales for model simplification before embarking on large-scale computations or parameter sweeps. As a preliminary complement to more intensive reduction of order methods such as parameter sensitivity and bifurcation analysis, this approach can rapidly and accurately improve computational tractability for challenging multi-scale organ modelling efforts.

Monitoring uterine contractions during labor: current challenges and future directions

Organ-level models are used to describe how cellular and tissue-level contractions coalesce into clinically observable uterine contractions. More importantly, these models provide a framework for evaluating the many different contraction patterns observed in laboring patients, ideally offering insight into the pitfalls of currently available recording modalities and suggesting new directions for improving recording and interpretation of uterine contractions. Early models proposed wave-like propagation of bioelectrical activity as the sole mechanism for recruiting the myometrium to participate in the contraction and increase contraction strength. However, as these models were tested, the results consistently revealed that sequentially propagating waves do not travel long distances and do not encompass the gravid uterus. To resolve this discrepancy, a model using 2 mechanisms, or a "dual model," for organ-level signaling has been proposed. In the dual model, the myometrium is recruited by action potentials that propagate wave-like as far as 10 cm. At longer distances, the myometrium is recruited by a mechanotransduction mechanism that is triggered by rising intrauterine pressure. In this review, we present the influential models of uterine function, highlighting their main features and inconsistencies, and detail the role of intrauterine pressure in signaling and cervical dilation. Clinical correlations demonstrate the application of organ-level models. The potential to improve the recording and clinical interpretation of uterine contractions when evaluating labor is discussed, with emphasis on uterine electromyography. Finally, 7 questions are posed to help guide future investigations on organ-level signaling mechanisms.

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.

Statistical shape analysis of gravid uteri throughout pregnancy by a ray description technique

In order to study the anatomical variability of the uterus induced by pregnancy, a parametrization of gravid uterine geometry based on principal component analysis (PCA) is proposed. Corresponding meshes used for PCA are created by a ray description technique applied to a reference mesh. A smoothed voxel-based methodology is applied to determine the reference mesh from a database of 11 real shapes produced by the FEMONUM project. The ray-based correspondence technique is compared to two existing methods (He, Giessen) as well as a proposed mixed method. Principal component analysis results are based on a database of 11 existing shapes. Results of the parametrization show that 90% of the total variance of the database can be represented with four new shape parameters and that a wide spectrum of shapes can be generated. Graphical Abstract Proposed correspondence technique compared to existing methods.

Forces Involved with Labor and Delivery-A Biomechanical Perspective

Childbirth is a primarily biomechanical process of physiology, and one that engineers have recently begun to address in a broader fashion. Computational models are being developed to address the biomechanical effects of parturition on both maternal and fetal tissues. Experimental research is being conducted to understand how maternal tissues adapt to intrauterine forces near the onset of labor. All of this research requires an understanding of the forces that are developed through maternal efforts-both uterine contractions and semi-voluntary pushing-and that can be applied by the clinician to assist with the delivery. This work reviews the current state of knowledge regarding forces of labor and delivery, with a focus on macro-level biomechanics.

Review and Study of Uterine Bioelectrical Waveforms and Vector Analysis to Identify Electrical and Mechanosensitive Transduction Control Mechanisms During Labor in Pregnant Patients

The bioelectrical signals that produce uterine contractions during parturition are not completely understood. The objectives are as follows: (1) to review the literature and information concerning uterine biopotential waveforms generated by the uterus, known to produce contractions, and evaluate mechanotransduction in pregnant patients using electromyographic (EMG) recording methods and (2) to study a new approach, uterine vector analysis, commonly used for the heart: vectorcardiography analysis. The patients used in this study were as follows: (1) patients at term not in labor (n = 3); (2) patients during the 1st stage of labor at cervical dilations from 2 to 10 cm (n = 30); and (3) patients in the 2nd stage of labor and during delivery (n = 3). We used DC-coupled electrodes and PowerLab hardware (model no. PL2604, ADInstruments, Castle Hill, Australia), with software (LabChart, ADInstruments) for storage and analysis of biopotentials. Uterine and abdominal EMG recordings were made from the surface of each patient using 3 electrode pairs with 1 pair (+ and -, with a 31-cm spacing distance) placed in the right/left position (X position) and with 1 pair placed in an up/down position (Y position, also 31 cm apart) and with the third pair at the front/back (Z position). Using signals from the three X, Y, and Z electrodes, slow (0.03 to 0.1 Hz, high amplitude) and fast wave (0.3 to 1 Hz, low amplitude) biopotentials were recorded. The amplitudes of the slow waves and fast waves were significantly higher during the 2nd stage of labor compared to the 1st stage (respectively, p = 9.54 × e^-3 and p = 3.94 × e^-7). When 2 channels were used, for example, the X vs. Y, for 2-D vector analysis or 3 channels, X vs. Y vs. Z, for 3-D analysis, are plotted against each other on their axes, this produces a vector electromyometriogram (EMMG) that shows no directionality for fast waves and a downward direction for slow waves. Similarly, during the 2nd stage of labor during abdominal contractions ("pushing"), the slow and fast waves were enlarged. Manual applied pressure was used to evoke bioelectrical activity to examine the mechanosensitivity of the uterus. Conclusions: (1) Phasic contractility of the uterus is a product of slow waves and groups of fast waves (bursts of spikes) to produce myometrial contractile responses. (2) 2-D and 3-D uterine vector analyses (uterine vector electromyometriogram) demonstrate no directionality of small fast waves while the larger slow waves represent the downward direction of biopotentials towards the cervical opening. (3) Myometrial cell action event excitability and subsequent contractility likely amplify slow wave activity input and uterine muscle contractility via mechanotransduction systems. (4) Models illustrate the possible relationships of slow to fast waves and the association of a mechanotransduction system and pacemaker activity as observed for slow waves and pacemakers in gastrointestinal muscle. (5) The interaction of these systems is thought to regulate uterine contractility. (6) This study suggests a potential indicator of delivery time. Such vector approaches might help us predict the progress of gestation and better estimate the timing of delivery, gestational pathologies reflected in bioelectric events, and perhaps the potential for premature delivery drug and mechanical interventions.

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.

Accuracy of electromyometrial imaging of uterine contractions in clinical environment

Clinically, uterine contractions are monitored with tocodynamometers or intrauterine pressure catheters. In the research setting, electromyography (EMG), which detects electrical activity of the uterus from a few electrodes on the abdomen, is feasible, can provide more accurate data than these other methods, and may be useful for predicting preterm birth. However, EMG lacks sufficient spatial resolution and coverage to reveal where uterine contractions originate, how they propagate, and whether preterm contractions differ between women who do and do not progress to preterm delivery. To address those limitations, electromyometrial imaging (EMMI) was recently developed and validated to non-invasively assess three-dimensional (3D) electrical activation patterns on the entire uterine surface in pregnant sheep. EMMI uses magnetic resonance imaging to obtain subject-specific body-uterus geometry and collects uterine EMG data from up to 256 electrodes on the body surface. EMMI software then solves an ill-posed inverse computation to combine the two datasets and generate maps of electrical activity on the entire 3D uterine surface. Here, we assessed the feasibility to clinically translate EMMI by evaluating EMMI's accuracy under the unavoidable geometrical alterations and electrical noise contamination in a clinical environment. We developed a hybrid experimental-simulation platform to model the effects of fetal kicks, contractions, fetal/maternal movements, and noise contamination caused by maternal respiration and environmental electrical activity. Our data indicate that EMMI can accurately image uterine electrical activity in the presence of geometrical deformations and electrical noise, suggesting that EMMI can be reliably translated to non-invasively image 3D uterine electrical activation in pregnant women.

Competing Mechanisms of Stress-Assisted Diffusivity and Stretch-Activated Currents in Cardiac Electromechanics

We numerically investigate the role of mechanical stress in modifying the conductivity properties of cardiac tissue, and also assess the impact of these effects in the solutions generated by computational models for cardiac electromechanics. We follow the recent theoretical framework from Cherubini et al. (2017), proposed in the context of general reaction-diffusion-mechanics systems emerging from multiphysics continuum mechanics and finite elasticity. In the present study, the adapted models are compared against preliminary experimental data of pig right ventricle fluorescence optical mapping. These data contribute to the characterization of the observed inhomogeneity and anisotropy properties that result from mechanical deformation. Our novel approach simultaneously incorporates two mechanisms for mechano-electric feedback (MEF): stretch-activated currents (SAC) and stress-assisted diffusion (SAD); and we also identify their influence into the nonlinear spatiotemporal dynamics. It is found that (i) only specific combinations of the two MEF effects allow proper conduction velocity measurement; (ii) expected heterogeneities and anisotropies are obtained via the novel stress-assisted diffusion mechanisms; (iii) spiral wave meandering and drifting is highly mediated by the applied mechanical loading. We provide an analysis of the intrinsic structure of the nonlinear coupling mechanisms using computational tests conducted with finite element methods. In particular, we compare static and dynamic deformation regimes in the onset of cardiac arrhythmias and address other potential biomedical applications.