Spatial heterogeneity enhances and modulates excitability in a mathematical model of the myometrium

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.

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.

Pacemaking function of two simplified cell models

Simplified nonlinear models of biological cells are widely used in computational electrophysiology. The models reproduce qualitatively many of the characteristics of various organs, such as the heart, brain, and intestine. In contrast to complex cellular ion-channel models, the simplified models usually contain a small number of variables and parameters, which facilitates nonlinear analysis and reduces computational load. In this paper, we consider pacemaking variants of the Aliev-Panfilov and Corrado two-variable excitable cell models. We conducted a numerical simulation study of these models and investigated the main nonlinear dynamic features of both isolated cells and 1D coupled pacemaker-excitable systems. Simulations of the 2D sinoatrial node and 3D intestine tissue as application examples of combined pacemaker-excitable systems demonstrated results similar to obtained previously. The uniform formulation for the conventional excitable cell models and proposed pacemaker models allows a convenient and easy implementation for the construction of personalized physiological models, inverse tissue modeling, and development of real-time simulation systems for various organs that contain both pacemaker and excitable cells.

Connexins: Key Players in the Control of Vascular Plasticity and Function

Of the 21 members of the connexin family, 4 (Cx37, Cx40, Cx43, and Cx45) are expressed in the endothelium and/or smooth muscle of intact blood vessels to a variable and dynamically regulated degree. Full-length connexins oligomerize and form channel structures connecting the cytosol of adjacent cells (gap junctions) or the cytosol with the extracellular space (hemichannels). The different connexins vary mainly with regard to length and sequence of their cytosolic COOH-terminal tails. These COOH-terminal parts, which in the case of Cx43 are also translated as independent short isoforms, are involved in various cellular signaling cascades and regulate cell functions. This review focuses on channel-dependent and -independent effects of connexins in vascular cells. Channels play an essential role in coordinating and synchronizing endothelial and smooth muscle activity and in their interplay, in the control of vasomotor actions of blood vessels including endothelial cell reactivity to agonist stimulation, nitric oxide-dependent dilation, and endothelial-derived hyperpolarizing factor-type responses. Further channel-dependent and -independent roles of connexins in blood vessel function range from basic processes of vascular remodeling and angiogenesis to vascular permeability and interactions with leukocytes with the vessel wall. Together, these connexin functions constitute an often underestimated basis for the enormous plasticity of vascular morphology and function enabling the required dynamic adaptation of the vascular system to varying tissue demands.

Computational physiology of uterine smooth muscle

Pregnancy can be accompanied by serious health risks to mother and child, such as pre-eclampsia, premature birth and postpartum haemorrhage. Understanding of the normal physiology of uterine function is essential to an improved management of such risks. Here we focus on the physiology of the smooth muscle fibres which make up the bulk of the uterine wall and which generate the forceful contractions that accompany parturition. We survey computational methods that integrate mathematical modelling with data analysis and thereby aid the discovery of new therapeutic targets that, according to clinical needs, can be manipulated to either stop contractions or cause the uterine wall muscle to become active.

The uterine pacemaker of labor

The laboring uterus is generally thought to initiate contractions much similar to the heart, with a single, dedicated pacemaker. Research on human and animal models over decades has failed to identify such pacemaker. On the contrary, data indicate that instead of being fixed at a site similar to the sinoatrial node of the heart, the initiation site for each uterine contraction changes during time, often with each contraction. The enigmatic uterine "pacemaker" does not seem to fit the standard definition of what a pacemaker should be. The uterine pacemaker must also mesh with the primary physiological function of the uterus - to generate intrauterine pressure. This requires that most areas of the uterine wall contract in a coordinated, or synchronized, manner for each contraction of labor. It is not clear whether the primary mechanism of the uterine pacemaker is a slow-wave generator or an impulse generator. Slow waves in the gut initiate localized smooth muscle contractions. Because the uterus and the gut have somewhat similar cellular and tissue structure, it is reasonable to consider if uterine contractions are paced by a similar mechanism. Unfortunately, there is no convincing experimental verification of uterine slow waves. Similarly, there is no convincing evidence of a cellular mechanism for impulse generation. The uterus appears to have multiple widely dispersed mechanically sensitive functional pacemakers. It is possible that the coordination of organ-level function occurs through intrauterine pressure, thus creating wall stress followed by activation of many mechanosensitive electrogenic pacemakers.

A computational method for three-dimensional reconstruction of the microarchitecture of myometrial smooth muscle from histological sections

Background

The fibrous structure of the myometrium has previously been characterised at high resolutions in small tissue samples (< 100 mm³) and at low resolutions (∼500 μm per voxel edge) in whole-organ reconstructions. However, no high-resolution visualisation of the myometrium at the organ level has previously been attained.

Methods and results

We have developed a technique to reconstruct the whole myometrium from serial histological slides, at a resolution of approximately 50 μm per voxel edge. Reconstructions of samples taken from human and rat uteri are presented here, along with histological verification of the reconstructions and detailed investigation of the fibrous structure of these uteri, using a range of tools specifically developed for this analysis. These reconstruction techniques enable the high-resolution rendering of global structure previously observed at lower resolution. Moreover, structures observed previously in small portions of the myometrium can be observed in the context of the whole organ. The reconstructions are in direct correspondence with the original histological slides, which allows the inspection of the anatomical context of any features identified in the three-dimensional reconstructions.

Conclusions and significance

The methods presented here have been used to generate a faithful representation of myometrial smooth muscle at a resolution of ∼50 μm per voxel edge. Characterisation of the smooth muscle structure of the myometrium by means of this technique revealed a detailed view of previously identified global structures in addition to a global view of the microarchitecture. A suite of visualisation tools allows researchers to interrogate the histological microarchitecture. These methods will be applicable to other smooth muscle tissues to analyse fibrous microarchitecture.

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.

Characterizing the Propagation of Uterine Electrophysiological Signals Recorded with a Multi-Sensor Abdominal Array in Term Pregnancies

The objective of this study was to quantify the number of segments that have contractile activity and determine the propagation speed from uterine electrophysiological signals recorded over the abdomen. The uterine magnetomyographic (MMG) signals were recorded with a 151 channel SARA (SQUID Array for Reproductive Assessment) system from 36 pregnant women between 37 and 40 weeks of gestational age. The MMG signals were scored and segments were classified based on presence of uterine contractile burst activity. The sensor space was then split into four quadrants and in each quadrant signal strength at each sample was calculated using center-of-gravity (COG). To this end, the cross-correlation analysis of the COG was performed to calculate the delay between pairwise combinations of quadrants. The relationship in propagation across the quadrants was quantified and propagation speeds were calculated from the delays. MMG recordings were successfully processed from 25 subjects and the average values of propagation speeds ranged from 1.3-9.5 cm/s, which was within the physiological range. The propagation was observed between both vertical and horizontal quadrants confirming multidirectional propagation. After the multiple pairwise test (99% CI), significant differences in speeds can be observed between certain vertical or horizontal combinations and the crossed pair combinations. The number of segments containing contractile activity in any given quadrant pair with a detectable delay was significantly higher in the lower abdominal pairwise combination as compared to all others. The quadrant-based approach using MMG signals provided us with high spatial-temporal information of the uterine contractile activity and will help us in the future to optimize abdominal electromyographic (EMG) recordings that are practical in a clinical setting.

Alterations in gap junction connexin43/connexin45 ratio mediate a transition from quiescence to excitation in a mathematical model of the myometrium

The smooth muscle cells of the uterus contract in unison during delivery. These cells achieve coordinated activity via electrical connections called gap junctions which consist of aggregated connexin proteins such as connexin43 and connexin45. The density of gap junctions governs the excitability of the myometrium (among other factors). An increase in gap junction density occurs immediately prior to parturition. We extend a mathematical model of the myometrium by incorporating the voltage-dependence of gap junctions that has been demonstrated in the experimental literature. Two functional subtypes exist, corresponding to systems with predominantly connexin43 and predominantly connexin45, respectively. Our simulation results indicate that the gap junction protein connexin45 acts as a negative modulator of uterine excitability, and hence, activity. A network with a higher proportion of connexin45 relative to connexin43 is unable to excite every cell. Connexin45 has much more rapid gating kinetics than connexin43 which we show limits the maximum duration of a local burst of activity. We propose that this effect regulates the degree of synchronous excitation attained during a contraction. Our results support the hypothesis that as labour approaches, connexin45 is downregulated to allow action potentials to spread more readily through the myometrium.

The location of pacemakers in the uteri of pregnant guinea pigs and rats

The pregnant uterus is a smooth muscle organ whose pattern of contraction is dictated by the propagation of electrical impulses. Such electrical activity may originate from one or more pacemakers, but the location of these sites has not yet been determined. To detect the location of the pacemaker in the gravid uterus, two approaches were used: 1) determine the site from where the contraction started using isolated uteri from the pregnant guinea pig, and videotape their contractions; and 2) record, in isolated uteri from pregnant term rats, with 240 extracellular electrodes simultaneously, and determine where the electrical bursts started. In both the contractile and electrophysiological experiments, there was not a single, specific pacemaker area. However, most contractions (guinea pig 87%) and bursts (rat 76%) started close to the mesometrial border (mean 2.7 ± 4.0 mm SD in guinea pigs and 1.3 ± 1.4 mm in rats). In addition, in the rat, most sites of initiations were located closer to the ovarial end of the horn (mean distance from the ovarial end 6.0 ± 6.2 mm SD), whereas such an orientation was not seen in the guinea pig. In both guinea pig and rat uteri at term, there is not one specific pacemaker area. Rather, contractile and electrical activity may arise from any site, with the majority starting close to the mesometrial border. Furthermore, in the rat, most activities started at the ovarial end of the horn. This may suggest a slightly different pattern of contraction in both species.

Progress in understanding electro-mechanical signalling in the myometrium

In this review, we give a state-of-the-art account of uterine contractility, focussing on excitation-contraction (electro-mechanical) coupling (ECC). This will show how electrophysiological data and intracellular calcium measurements can be related to more modern techniques such as confocal microscopy and molecular biology, to advance our understanding of mechanical output and its modulation in the smooth muscle of the uterus, the myometrium. This new knowledge and understanding, for example concerning the role of the sarcoplasmic reticulum (SR), or stretch-activated K channels, when linked to biochemical and molecular pathways, provides a clearer and better informed basis for the development of new drugs and targets. These are urgently needed to combat dysfunctions in excitation-contraction coupling that are clinically challenging, such as preterm labour, slow to progress labours and post-partum haemorrhage. It remains the case that scientific progress still needs to be made in areas such as pacemaking and understanding interactions between the uterine environment and ion channel activity.

Functional and morphological development of the womb throughout life

The uterus undergoes changes throughout a woman's life, beginning with her own embryonic development when she is still in the womb, commencing a monthly cycle at the onset of adulthood, and undergoing dramatic changes during pregnancy and parturition. The impact of preterm labour and other perinatal health problems is significant, both in human and financial terms; therefore the study of the physiological and regulatory changes which the uterus undergoes can be of enormous potential benefit. Here we briefly review the current state of knowledge, with an emphasis on the importance of changes in connectivity in the uterine smooth muscle cell network and on recent mathematical modelling work aimed at elucidating the role of spatial heterogeneity in this connected network.