Mathematical modeling of electrical activity of uterine muscle cells

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.

In Silico Electrophysiological Investigation of Transient Receptor Potential Melastatin-4 Ion Channel Biophysics to Study Detrusor Overactivity

Enhanced electrical activity in detrusor smooth muscle (DSM) cells is a key factor in detrusor overactivity which causes overactive bladder pathological disorders. Transient receptor potential melastatin-4 (TRPM4) channels, which are calcium-activated cation channels, play a role in regulating DSM electrical activities. These channels likely contribute to depolarizing the DSM cell membrane, leading to bladder overactivity. Our research focuses on understanding TRPM4 channel function in the DSM cells of mice, using computational modeling. We aimed to create a detailed computational model of the TRPM4 channel based on existing electrophysiological data. We employed a modified Hodgkin-Huxley model with an incorporated TRP-like current to simulate action potential firing in response to current and synaptic stimulus inputs. Validation against experimental data showed close agreement with our simulations. Our model is the first to analyze the TRPM4 channel's role in DSM electrical activity, potentially revealing insights into bladder overactivity. In conclusion, TRPM4 channels are pivotal in regulating human DSM function, and TRPM4 channel inhibitors could be promising targets for treating overactive bladder.

Pregnancy state before the onset of labor: a holistic mechanical perspective

Successful pregnancy highly depends on the complex interaction between the uterine body, cervix, and fetal membrane. This interaction is synchronized, usually following a specific sequence in normal vaginal deliveries: (1) cervical ripening, (2) uterine contractions, and (3) rupture of fetal membrane. The complex interaction between the cervix, fetal membrane, and uterine contractions before the onset of labor is investigated using a complete third-trimester gravid model of the uterus, cervix, fetal membrane, and abdomen. Through a series of numerical simulations, we investigate the mechanical impact of (i) initial cervical shape, (ii) cervical stiffness, (iii) cervical contractions, and (iv) intrauterine pressure. The findings of this work reveal several key observations: (i) maximum principal stress values in the cervix decrease in more dilated, shorter, and softer cervices; (ii) reduced cervical stiffness produces increased cervical dilation, larger cervical opening, and decreased cervical length; (iii) the initial cervical shape impacts final cervical dimensions; (iv) cervical contractions increase the maximum principal stress values and change the stress distributions; (v) cervical contractions potentiate cervical shortening and dilation; (vi) larger intrauterine pressure (IUP) causes considerably larger stress values and cervical opening, larger dilation, and smaller cervical length; and (vii) the biaxial strength of the fetal membrane is only surpassed in the cases of the (1) shortest and most dilated initial cervical geometry and (2) larger IUP.

Biophysical Mechanisms of Vaginal Smooth Muscle Contraction: The Role of the Membrane Potential and Ion Channels

The vagina is an essential component of the female reproductive system and is responsible for providing female sexual satisfaction. Vaginal smooth muscle contraction plays a crucial role in various physiological processes, including sexual arousal, childbirth, and urinary continence. In pathophysiological conditions, such as pelvic floor disorders, aberrations in vaginal smooth muscle function can lead to urinary incontinence and pelvic organ prolapse. A set of cellular and sub-cellular physiological mechanisms regulates the contractile properties of the vaginal smooth muscle cells. Calcium influx is a crucial determinant of smooth muscle contraction, facilitated through voltage-dependent calcium channels and calcium release from intracellular stores. Comprehensive reviews on smooth muscle biophysics are relatively scarce within the scientific literature, likely due to the complexity and specialized nature of the topic. The objective of this review is to provide a comprehensive description of alterations in the cellular physiology of vaginal smooth muscle contraction. The benefit associated with this particular approach is that conducting a comprehensive examination of the cellular mechanisms underlying contractile activation will enable the creation of more targeted therapeutic agents to control vaginal contraction disorders.

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.

Oxytocin augmentation and neurotransmitters in prolonged delivery: An experimental appraisal

The uterus is a highly innervated organ, and during labor, this innervation is at its highest level. Oxytocinergic fibers play an important role in labor and delivery and, in particular, the Lower Uterine Segment, cervix, and fundus are all controlled by motor neurofibers. Oxytocin is a neurohormone that acts on receptors located on the membrane of the smooth cells of the myometrium. During the stages of labor and delivery, its binding causes myofibers to contract, which enables the fundus of the uterus to act as a mediator. The aim of this study was to investigate the presence of oxytocinergic fibers in prolonged and non-prolonged dystocic delivery in a cohort of 90 patients, evaluated during the first and second stages of labor. Myometrial tissue samples were collected and evaluated by electron microscopy, in order to quantify differences in neurofibers concentrations between the investigated and control cohorts of patients. The authors of this experiment showed that the concentration of oxytocinergic fibers differs between non-prolonged and prolonged dystocic delivery. In particular, in prolonged dystocic delivery, compared to non-prolonged dystocic delivery, there is a lower amount of oxytocin fiber. The increase in oxytocin appeared to be ineffective in patients who experienced prolonged dystocic delivery, since the dystocic labor ended as a result of the altered presence of oxytocinergic fibers detected in this group of patients.

Predictions from a mathematical approach to model ionic signaling for rapid responses of Sertoli cells exhibit similarities to pharmacological approaches

Sertoli cells are essential for the male reproduction system as they provide morphological support and nutrients for germ cells to guarantee ongoing spermatogenesis. The aim of this work was to predict the electrical properties at the plasma membrane that trigger Sertoli cell rapid responses by involving ionic channels. The rapid responses of Sertoli cells in culture were monitored using patch clamp electrical measurement and compared to data obtained using pharmacological tools (from intact seminiferous tubules). A mathematical model was used to define the roles of potassium channels and the ATP-dependent Na+/K+pump in these responses. Mathematical data verification was also performed to determine the resting and hormonal stimulated membrane potentials of Sertoli cells in the intact seminiferous tubules and of Sertoli cells in culture (patch clamp measurements). The prediction of these data based on mathematical modeling demonstrated, for the first time, the involvement of potassium channels and the activation of Na+/K+pump in the hyperpolarization of Sertoli cells and their consequent rapid responses. Moreover, the mathematical analysis showing the involvement of ionic balance in the rapid responses of these cells to hormones, such as follicle-stimulating hormone, is consistent with previous reports obtained using pharmacological techniques in Sertoli cells. Thus, the validation of such data is reliable and represents a first step in the proposition for a mathematical model to predict rapid responses of Sertoli cells to hormonal stimuli.

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.

On the prediction of premature births in Hispanic labour patients using uterine contractions, heart beat signals and prediction machines

Preterm birth is a global epidemic affecting millions of mothers across different ethnicities. The cause of the condition remains unknown but has recognised health-based implications, in addition to financial and economic ones. Machine Learning methods have enabled researchers to combine datasets using uterine contraction signals with various forms of prediction machines to improve awareness of the likelihood of premature births. This work investigates the feasibility of enhancing these prediction methods using physiological signals including uterine contractions, and foetal and maternal heart rate signals, for a population of south American women in active labour. As part of this work, the use of the Linear Series Decomposition Learner (LSDL) was seen to lead to an improvement in the prediction accuracies of all models, which included supervised and unsupervised learning models. The results from the supervised learning models showed high prediction metrics upon the physiological signals being pre-processed by the LSDL for all variations of the physiological signals. The unsupervised learning models showed good metrics for the partitioning of Preterm/Term labour patients from their uterine contraction signals but produced a comparatively lower set of results for the various kinds of heart rate signals investigated.

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.

Pattern Formation in a Spatially Extended Model of Pacemaker Dynamics in Smooth Muscle Cells

Spatiotemporal patterns are common in biological systems. For electrically coupled cells, previous studies of pattern formation have mainly used applied current as the primary bifurcation parameter. The purpose of this paper is to show that applied current is not needed to generate spatiotemporal patterns for smooth muscle cells. The patterns can be generated solely by external mechanical stimulation (transmural pressure). To do this we study a reaction-diffusion system involving the Morris-Lecar equations and observe a wide range of spatiotemporal patterns for different values of the model parameters. Some aspects of these patterns are explained via a bifurcation analysis of the system without coupling - in particular Type I and Type II excitability both occur. We show the patterns are not due to a Turing instability and that the spatially extended model exhibits spatiotemporal chaos. We also use travelling wave coordinates to analyse travelling waves.

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.

A biophysically constrained computational model of the action potential of mouse urinary bladder smooth muscle

Urinary incontinence is associated with enhanced spontaneous phasic contractions of the detrusor smooth muscle (DSM). Although a complete understanding of the etiology of these spontaneous contractions is not yet established, it is suggested that the spontaneously evoked action potentials (sAPs) in DSM cells initiate and modulate the contractions. In order to further our understanding of the ionic mechanisms underlying sAP generation, we present here a biophysically detailed computational model of a single DSM cell. First, we constructed mathematical models for nine ion channels found in DSM cells based on published experimental data: two voltage gated Ca2+ ion channels, an hyperpolarization-activated ion channel, two voltage-gated K+ ion channels, three Ca2+-activated K+ ion channels and a non-specific background leak ion channel. The ion channels' kinetics were characterized in terms of maximal conductances and differential equations based on voltage or calcium-dependent activation and inactivation. All ion channel models were validated by comparing the simulated currents and current-voltage relations with those reported in experimental work. Incorporating these channels, our DSM model is capable of reproducing experimentally recorded spike-type sAPs of varying configurations, ranging from sAPs displaying after-hyperpolarizations to sAPs displaying after-depolarizations. The contributions of the principal ion channels to spike generation and configuration were also investigated as a means of mimicking the effects of selected pharmacological agents on DSM cell excitability. Additionally, the features of propagation of an AP along a length of electrically continuous smooth muscle tissue were investigated. To date, a biophysically detailed computational model does not exist for DSM cells. Our model, constrained heavily by physiological data, provides a powerful tool to investigate the ionic mechanisms underlying the genesis of DSM electrical activity, which can further shed light on certain aspects of urinary bladder function and dysfunction.

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.

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.

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.

Reconstruction of Cell Surface Densities of Ion Pumps, Exchangers, and Channels from mRNA Expression, Conductance Kinetics, Whole-Cell Calcium, and Current-Clamp Voltage Recordings, with an Application to Human Uterine Smooth Muscle Cells

Uterine smooth muscle cells remain quiescent throughout most of gestation, only generating spontaneous action potentials immediately prior to, and during, labor. This study presents a method that combines transcriptomics with biophysical recordings to characterise the conductance repertoire of these cells, the ‘conductance repertoire’ being the total complement of ion channels and transporters expressed by an electrically active cell. Transcriptomic analysis provides a set of potential electrogenic entities, of which the conductance repertoire is a subset. Each entity within the conductance repertoire was modeled independently and its gating parameter values were fixed using the available biophysical data. The only remaining free parameters were the surface densities for each entity. We characterise the space of combinations of surface densities (density vectors) consistent with experimentally observed membrane potential and calcium waveforms. This yields insights on the functional redundancy of the system as well as its behavioral versatility. Our approach couples high-throughput transcriptomic data with physiological behaviors in health and disease, and provides a formal method to link genotype to phenotype in excitable systems. We accurately predict current densities and chart functional redundancy. For example, we find that to evoke the observed voltage waveform, the BK channel is functionally redundant whereas hERG is essential. Furthermore, our analysis suggests that activation of calcium-activated chloride conductances by intracellular calcium release is the key factor underlying spontaneous depolarisations.

A well-known problem in electrophysiologal modeling is that the parameters of the gating kinetics of the ion channels cannot be uniquely determined from observed behavior at the cellular level. One solution is to employ simplified “macroscopic” currents that mimic the behavior of aggregates of distinct entities at the protein level. The gating parameters of each channel or pump can be determined by studying it in isolation, leaving the general problem of finding the densities at which the channels occur in the plasma membrane. We propose an approach, which we apply to uterine smooth muscle cells, whereby we constrain the list of possible entities by means of transcriptomics and chart the indeterminacy of the problem in terms of the kernel of the corresponding linear transformation. A graphical representation of this kernel visualises the functional redundancy of the system. We show that the role of certain conductances can be fulfilled, or compensated for, by suitable combinations of other conductances; this is not always the case, and such “non-substitutable” conductances can be regarded as functionally non-redundant. Electrogenic entities belonging to the latter category are suitable putative clinical targets.

Modeling Magnetomyograms of Uterine Contractions during Pregnancy Using a Multiscale Forward Electromagnetic Approach

Understanding the mechanisms of uterine contractions during pregnancy is especially important in predicting the onset of labor and thus in forecasting preterm deliveries. Preterm birth can cause serious health problems in newborns, as well as large financial burdens to society. Various techniques such as electromyography (EMG) and magnetomyography (MMG) have been developed to quantify uterine contractions. However, no widely accepted method to predict labor based on electromagnetic measurement is available. Therefore, developing a biophysical model of EMG and MMG could help better understand uterine contractions, interpret real measurements, and detect labor. In this work, we propose a multiscale realistic model of uterine contractions during pregnancy. At the cellular level, building on bifurcation theory, we apply generalized FitzHugh-Nagumo (FHN) equations that produces both plateau-type and bursting-type action potentials. At the tissue level, we introduce a random fiber orientation model applicable to an arbitrary uterine shape. We also develop an analytical expression for the propagation speed of transmembrane potential. At the organ level, a realistic volume conductor geometry model is provided based on magnetic resonance images of a pregnant woman. To simulate the measurements from the SQUID Array for Reproductive Assessment (SARA) device, we propose a sensor array model. Our model is able to reproduce the characteristics of action potentials. Additionally, we investigate the sensitivity of MMG to model configuration aspects such as volume geometry, fiber orientation, and pacemaker location. Our numerical results show that fiber orientation and pacemaker location are the key aspects that greatly affect the MMG as measured by the SARA device. We conclude that sphere is appropriate as an approximation of the volume geometry. The initial step towards validating the model against real MMG measurement is also presented. Our results show that the model is flexible to mimic the limited-propagation magnetic signature during the emergence and decay of a uterine contraction.

A novel LabVIEW-based multi-channel non-invasive abdominal maternal-fetal electrocardiogram signal generator

This paper describes the design, construction, and testing of a multi-channel fetal electrocardiogram (fECG) signal generator based on LabVIEW. Special attention is paid to the fetal heart development in relation to the fetus' anatomy, physiology, and pathology. The non-invasive signal generator enables many parameters to be set, including fetal heart rate (FHR), maternal heart rate (MHR), gestational age (GA), fECG interferences (biological and technical artifacts), as well as other fECG signal characteristics. Furthermore, based on the change in the FHR and in the T wave-to-QRS complex ratio (T/QRS), the generator enables manifestations of hypoxic states (hypoxemia, hypoxia, and asphyxia) to be monitored while complying with clinical recommendations for classifications in cardiotocography (CTG) and fECG ST segment analysis (STAN). The generator can also produce synthetic signals with defined properties for 6 input leads (4 abdominal and 2 thoracic). Such signals are well suited to the testing of new and existing methods of fECG processing and are effective in suppressing maternal ECG while non-invasively monitoring abdominal fECG. They may also contribute to the development of a new diagnostic method, which may be referred to as non-invasive trans-abdominal CTG +  STAN. The functional prototype is based on virtual instrumentation using the LabVIEW developmental environment and its associated data acquisition measurement cards (DAQmx). The generator also makes it possible to create synthetic signals and measure actual fetal and maternal ECGs by means of bioelectrodes.

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.

Propagation of electrical activity in uterine muscle during pregnancy: a review

The uterine muscle (the myometrium) plays its most evident role during pregnancy, when quiescence is required for adequate nourishment and development of the foetus, and during labour, when forceful contractions are needed to expel the foetus and the other products of conception. The myometrium is composed of smooth muscle cells. Contraction is initiated by the spontaneous generation of electrical activity at the cell level in the form of action potentials. The mechanisms underlying uterine quiescence during pregnancy and electrical activation during labour remain largely unknown; as a consequence, the clinical management of preterm contractions during pregnancy and inefficient uterine contractility during labour remains suboptimal. In an effort to improve clinical management of uterine contractions, research has focused on understanding the propagation properties of the electrical activity of the uterus. Different perspectives have been undertaken, from animal and in vitro experiments up to clinical studies and dedicated methods for non-invasive parameter estimation. A comparison of the results is not straightforward due to the wide range of different approaches reported in the literature. However, previous studies unanimously reveal a unique complexity as compared to other organs in the pattern of uterine electrical activity propagation, which necessarily needs to be taken into consideration for future studies to be conclusive. The aim of this review is to structure current variegated knowledge on the properties of the uterus in terms of pacemaker position, pattern, direction and speed of the electrical activity during pregnancy and labour.

Computational modeling of spike generation in serotonergic neurons of the dorsal raphe nucleus

Serotonergic neurons of the dorsal raphe nucleus, with their extensive innervation of limbic and higher brain regions and interactions with the endocrine system have important modulatory or regulatory effects on many cognitive, emotional and physiological processes. They have been strongly implicated in responses to stress and in the occurrence of major depressive disorder and other psychiatric disorders. In order to quantify some of these effects, detailed mathematical models of the activity of such cells are required which describe their complex neurochemistry and neurophysiology. We consider here a single-compartment model of these neurons which is capable of describing many of the known features of spike generation, particularly the slow rhythmic pacemaking activity often observed in these cells in a variety of species. Included in the model are 11 kinds of ion channels: a fast sodium current INa, a delayed rectifier potassium current IKDR, a transient potassium current IA, a slow non-inactivating potassium current IM, a low-threshold calcium current IT, two high threshold calcium currents IL and IN, small and large conductance potassium currents ISK and IBK, a hyperpolarization-activated cation current IH and a leak current ILeak. In Sections 3-8, each current type is considered in detail and parameters estimated from voltage clamp data where possible. Three kinds of model are considered for the BK current and two for the leak current. Intracellular calcium ion concentration Cai is an additional component and calcium dynamics along with buffering and pumping is discussed in Section 9. The remainder of the article contains descriptions of computed solutions which reveal both spontaneous and driven spiking with several parameter sets. Attention is focused on the properties usually associated with these neurons, particularly long duration of action potential, steep upslope on the leading edge of spikes, pacemaker-like spiking, long-lasting afterhyperpolarization and the ramp-like return to threshold after a spike. In some cases the membrane potential trajectories display doublets or have humps or notches as have been reported in some experimental studies. The computed time courses of IA and IT during the interspike interval support the generally held view of a competition between them in influencing the frequency of spiking. Spontaneous activity was facilitated by the presence of IH which has been found in these neurons by some investigators. For reasonable sets of parameters spike frequencies between about 0.6Hz and 1.2Hz are obtained, but frequencies as high as 6Hz could be obtained with special parameter choices. Topics investigated and compared with experiment include shoulders, notches, anodal break phenomena, the effects of noradrenergic input, frequency versus current curves, depolarization block, effects of cell size and the effects of IM. The inhibitory effects of activating 5-HT1A autoreceptors are also investigated. There is a considerable discussion of in vitro versus in vivo firing behavior, with focus on the roles of noradrenergic input, corticotropin-releasing factor and orexinergic inputs. Location of cells within the nucleus is probably a major factor, along with the state of the animal.

A continuum model for excitation-contraction of smooth muscle under finite deformations

The main focus in most of the continuum based muscle models is the mechanics of muscle contraction while other physiological processes governing muscle contraction, e.g., cell membrane excitation and activation, are ignored. These latter processes are essential to initiate contraction and to determine the amount of generated force, and by excluding them, the developed model cannot replicate the true behavior of the muscle in question. The aim of this study is to establish a thermodynamically and physiologically consistent framework which allows us to model smooth muscle contraction by including cell membrane excitability and kinetics of myosin phosphorylation, along with dynamics of smooth muscle contraction. The model accounts for these processes through a set of coupled dissipative constitutive equations derived by applying first principles. To show the performance of the derived model, it is evaluated for two different cases: a chemo-mechanical study of pig taenia coli cells where the excitation process is excluded, and an electro-chemo-mechanical study of rat myometrium. The results show that the model is able to replicate important aspects of the smooth muscle excitation-contraction process.

Preliminary global sensitivity analysis of a uterine electrical activity model

A comprehensive multiscale model of the uterine muscle electrical activity would permit understanding the important link between the genesis and evolution of the action potential at the cell level and the process leading to labor. Understanding this link can open the way to more effective tools for the prediction of labor and prevention of preterm delivery.

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

The muscular layer of the uterus (myometrium) undergoes profound changes in global excitability prior to parturition. Here, a mathematical model of the myocyte network is developed to investigate the hypothesis that spatial heterogeneity is essential to the transition from local to global excitation which the myometrium undergoes just prior to birth. Each myometrial smooth muscle cell is represented by an element with FitzHugh-Nagumo dynamics. The cells are coupled through resistors that represent gap junctions. Spatial heterogeneity is introduced by means of stochastic variation in coupling strengths, with parameters derived from physiological data. Numerical simulations indicate that even modest increases in the heterogeneity of the system can amplify the ability of locally applied stimuli to elicit global excitation. Moreover, in networks driven by a pacemaker cell, global oscillations of excitation are impeded in fully connected and strongly coupled networks. The ability of a locally stimulated cell or pacemaker cell to excite the network is shown to be strongly dependent on the local spatial correlation structure of the couplings. In summary, spatial heterogeneity is a key factor in enhancing and modulating global excitability.

Computer models to study uterine activation at labour

Improving our understanding of the initiation of labour is a major aim of modern obstetric research, in order to better diagnose and treat pregnant women in which the process occurs abnormally. In particular, increased knowledge will help us identify the mechanisms responsible for preterm labour, the single biggest cause of neonatal morbidity and mortality. Attempts to improve our understanding of the initiation of labour have been restricted by the inaccessibility of gestational tissues to study during pregnancy and at labour, and by the lack of fully informative animal models. However, computer modelling provides an exciting new approach to overcome these restrictions and offers new insights into uterine activation during term and preterm labour. Such models could be used to test hypotheses about drugs to treat or prevent preterm labour. With further development, an effective computer model could be used by healthcare practitioners to develop personalized medicine for patients on a pregnancy-by-pregnancy basis. Very promising work is already underway to build computer models of the physiology of uterine activation and contraction. These models aim to predict changes and patterns in uterine electrical excitation during term labour. There have been far fewer attempts to build computer models of the molecular pathways driving uterine activation and there is certainly scope for further work in this area. The integration of computer models of the physiological and molecular mechanisms that initiate labour will be particularly useful.

Cross-correlation analysis of multichannel uterine EMG signals

The prevention of preterm labor remains one of the primary goals of obstetric research. One way to achieve this goal effectively is to understand the mechanisms regulating the uterine contractility. Herein, we evaluate the correlation between uterine electrical activities recorded from spatially-distributed regions by calculating the nonlinear regression coefficient. Results have shown that, during pregnancy, the degree of interdependence between signals is very high whereas, at labor, the correlation between the signals decreases remarkably. We conclude that pregnancy is characterized by the presence of few local potential sources dominating the other sources while at the onset of labor, the number of these sources increases remarkably which affects therefore the correlation between the signals.

Ultrasound analysis of the uterine wall movement for improved electrohysterographic measurement and modeling

During pregnancy, analysis of the electrohysterogram (EHG), which measures the uterine electrical activity, can provide a fundamental contribution for the assessment of uterine contractions and the diagnosis of preterm labor. However, several aspects concerning uterine physiology and its link with EHG measurements are still unclear. As a consequence, the EHG is not yet part of the clinical practice. There is general consensus that modeling and analysis of the EHG can be improved only by understanding and integrating the main properties of the uterine physiology at different levels, e:g:, cellular, tissue, and organ, and of different nature, e:g:, electrical, mechanical, and structural. In this study, we use transabdominal ultrasound (US) measurements to investigate the mechanical changes that the uterus undergoes during pregnancy under the effect of contractions. We refer to this measurement as mechanohysterogram. Analysis of the mechanohysterogram highlights, for the first time, two phenomena that can influence EHG signal interpretation, namely, changes in uterine wall thickness during contractions and respiration-induced uterine wall movements. Our results suggest that these phenomena can affect the interpretation of the EHG and should therefore be taken into account for accurate modeling and assessment of the uterine electrical activity.

A multiscale model of the electrohysterogram the BioModUE_PTL project

The electrohysterogram (EHG) is a promising means of monitoring pregnancy and of detecting a risk of preterm labor. To improve our understanding of the EHG as well as its relationship with the physiologic phenomena involved in uterine contractility, we plan to model these phenomena in terms of generation and propagation of uterine electrical activity. This activity can be realistically modeled by representing the principal ionic dynamics at the cell level, the propagation of electrical activity at the tissue level and then the way it is reflected on the skin surface through the intervening tissue. We present in this paper the different steps leading to the development and validation of a biophysics based multiscale model of the EHG, going from the cell to the electrical signal measured on the abdomen.

Better pregnancy monitoring using nonlinear correlation analysis of external uterine electromyography

The objective of this paper is to evaluate the novel method for analyzing the nonlinear correlation of the uterine electromyography (EMG). The application of this method may improve monitoring in pregnancy, labor detection, and preterm labor detection. Uterine EMG signals recorded from a 4 × 4 matrix of electrodes on the subjects' abdomen are used here. The propagation was analyzed using the nonlinear correlation coefficient h(2). Signals from 49 women (36 during pregnancy and 13 in labor) at different gestational age were used. ROC curves were computed to evaluate the potential of three methods to differentiate between 174 contractions recorded during pregnancy and 115 contractions recorded during labor. The results indicate considerably better performance of the nonlinear correlation analysis (area under curve = 0.85) when compared to classical frequency parameters (area under curve = 0.76 and 0.66) in distinguishing labor contractions from normal pregnancy contractions. We conclude that the analysis of the propagation of the uterine electrical activity using the nonlinear correlation coefficient h(2) is a promising way of improving the usefulness of uterine EMG signals for clinical purposes, such as monitoring in pregnancy, labor detection, and prediction of preterm labor.

Multiscale forward electromagnetic model of uterine contractions during pregnancy

BACKGROUND

Analyzing and monitoring uterine contractions during pregnancy is relevant to the field of reproductive health assessment. Its clinical importance is grounded in the need to reliably predict the onset of labor at term and pre-term. Preterm births can cause health problems or even be fatal for the fetus. Currently, there are no objective methods for consistently predicting the onset of labor based on sensing of the mechanical or electrophysiological aspects of uterine contractions. Therefore, modeling uterine contractions could help to better interpret such measurements and to develop more accurate methods for predicting labor. In this work, we develop a multiscale forward electromagnetic model of myometrial contractions during pregnancy. In particular, we introduce a model of myometrial current source densities and compute its magnetic field and action potential at the abdominal surface, using Maxwell's equations and a four-compartment volume conductor geometry. To model the current source density at the myometrium we use a bidomain approach. We consider a modified version of the Fitzhugh-Nagumo (FHN) equation for modeling ionic currents in each myocyte, assuming a plateau-type transmembrane potential, and we incorporate the anisotropic nature of the uterus by designing conductivity-tensor fields.

RESULTS

We illustrate our modeling approach considering a spherical uterus and one pacemaker located in the fundus. We obtained a travelling transmembrane potential depolarizing from -56 mV to -16 mV and an average potential in the plateau area of -25 mV with a duration, before hyperpolarization, of 35 s, which is a good approximation with respect to the average recorded transmembrane potentials at term reported in the technical literature. Similarly, the percentage of myometrial cells contracting as a function of time had the same symmetric properties and duration as the intrauterine pressure waveforms of a pregnant human myometrium at term.

CONCLUSIONS

We introduced a multiscale modeling approach of uterine contractions which allows for incorporating electrophysiological and anatomical knowledge of the myometrium jointly. Our results are in good agreement with the values reported in the experimental technical literature, and these are potentially important as a tool for helping in the characterization of contractions and for predicting labor using magnetomyography (MMG) and electromyography (EMG).

The electrical activities of the uterus during pregnancy

In contrast to the current state of knowledge of cardiac and of gastrointestinal electrophysiology, our current knowledge of the physiology of the uterus during pregnancy is still very rudimentary. Despite seminal work performed in the past decades, there are still significant areas that we know little about. In this review, some of these areas are explored. For example, although many studies have tried to find the site of the uterus pacemaker, such a site has not yet been found and its mechanism and location remain, to date, a mystery. Similarly, there is much confusion as to the mechanism of propagation of the electrical impulse. Although the existence of gap junctions, connecting neighboring myometrial cells to each other, have been known since 1977, alternative or additional mechanisms are being suggested such as the potential existence of a network of interstitial cells, similar to the one that is functioning in the gut, or the involvement of stretch receptors to synchronize activity and contraction. In recent years, high-resolution studies have been introduced enabling detailed analysis of the location and spatial patterns of propagation. This work is being developed at the in-vitro level in isolated tissues, in the whole organ and in several animal species. Most recently, a surge in new technology enabling high fidelity and high resolution recording from the human uterus through the abdominal wall are being explored which could ultimately lead to new diagnostic tools and a clearer understanding of the physiology of pregnancies and (premature) labor.

Toward a multiscale model of the uterine electrical activity

A comprehensive multiscale model of the uterine muscle electrical activity would permit understanding the important link between the genesis and evolution of the action potential at the cell level and the process leading to labor. Understanding this link can open the way to more effective tools for the prediction of labor and prevention of preterm delivery. A first step toward the realization of such a model is presented here. By using as starting point a previously published model of the generation of the uterine muscle action potential at the cell level, a significant reduction of the model complexity is here achieved in order to simulate 2-D propagation of the cellular activity at the uterine tissue level, for tissue strips of arbitrary dimension. From the obtained dynamic behavior of the electrical activity simulated at the tissue level, the use of a previously validated volume conductor model at the organ level permits us to simulate the electrohysterogram as recorded on the abdominal surface by an electrode array. Qualitative evaluation of the model at the cell level and at the organ level confirms the potential of the proposed multiscale approach for further refinement and extension aiming at clinical application.

A computational model of the ionic currents, Ca2+ dynamics and action potentials underlying contraction of isolated uterine smooth muscle

Uterine contractions during labor are discretely regulated by rhythmic action potentials (AP) of varying duration and form that serve to determine calcium-dependent force production. We have employed a computational biology approach to develop a fuller understanding of the complexity of excitation-contraction (E-C) coupling of uterine smooth muscle cells (USMC). Our overall aim is to establish a mathematical platform of sufficient biophysical detail to quantitatively describe known uterine E-C coupling parameters and thereby inform future empirical investigations of physiological and pathophysiological mechanisms governing normal and dysfunctional labors. From published and unpublished data we construct mathematical models for fourteen ionic currents of USMCs: currents (L- and T-type), current, an hyperpolarization-activated current, three voltage-gated currents, two -activated current, -activated current, non-specific cation current, - exchanger, - pump and background current. The magnitudes and kinetics of each current system in a spindle shaped single cell with a specified surface area∶volume ratio is described by differential equations, in terms of maximal conductances, electrochemical gradient, voltage-dependent activation/inactivation gating variables and temporal changes in intracellular computed from known fluxes. These quantifications are validated by the reconstruction of the individual experimental ionic currents obtained under voltage-clamp. Phasic contraction is modeled in relation to the time constant of changing . This integrated model is validated by its reconstruction of the different USMC AP configurations (spikes, plateau and bursts of spikes), the change from bursting to plateau type AP produced by estradiol and of simultaneous experimental recordings of spontaneous AP, and phasic force. In summary, our advanced mathematical model provides a powerful tool to investigate the physiological ionic mechanisms underlying the genesis of uterine electrical E-C coupling of labor and parturition. This will furnish the evolution of descriptive and predictive quantitative models of myometrial electrogenesis at the whole cell and tissue levels.

Development and application of human virtual excitable tissues and organs: from premature birth to sudden cardiac death

The electrical activity of cardiac and uterine tissues has been reconstructed by detailed computer models in the form of virtual tissues. Virtual tissues are biophysically and anatomically detailed, and represent quantitatively predictive models of the physiological and pathophysiological behaviours of tissue within an isolated organ. The cell excitation properties are quantitatively reproduced by equations that describe the kinetics of a few dozen proteins. These equations are derived from experimental measurements of membrane potentials, ionic currents, fluxes, and concentrations. Some of the measurements were taken from human cells and human ion channel proteins expressed in non-human cells, but they were mostly taken from cells of other animal species. Data on tissue geometry and architecture are obtained from the diffusion tensor magnetic resonance imaging of ex vivo or post mortem tissue, and are used to compute the spread of current in the tissue. Cardiac virtual tissues are well established and reproduce normal and pathological patterns of cardiac excitation within the atria or ventricles of the human heart. They have been applied to increase the understanding of normal cardiac electrophysiology, to evaluate the candidate mechanisms for re-entrant arrhythmias that lead to sudden cardiac death, and to predict the tissue level effects of mutant or pharmacologically-modified ion channels. The human full-term virtual uterus is still in development. This virtual tissue reproduces the in vitro behaviour of uterine tissue biopsies, and provides possible mechanisms for premature labour.