Toward a multiscale model of the uterine electrical activity

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.

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.

Uterine slow wave: directionality and changes with imminent delivery

OBJECTIVE

The slow wave (SW) of the electrohysterogram (EHG) may contain relevant information on the electrophysiological condition of the uterus throughout pregnancy and labor. Our aim was to assess differences in the SW as regards the imminence of labor and the directionality of uterine myoelectrical activity.

APPROACH

The SW of the EHG was extracted from the signals of the Icelandic 16-electrode EHG database in the bandwidth [5, 30] mHz and its power, spectral content, complexity and synchronization between the horizontal (X) and vertical (Y) directions were characterized by the root mean square (RMS), dominant frequency (domF), sample entropy (SampEn) and maximum cross-correlation (CCmax) of the signals, respectively. Significant differences between parameters at time-to-delivery (TTD) ≤7 vs. >7 days and between the horizontal vs. vertical directions were assessed.

MAIN RESULTS

The SW power significantly increased in both directions as labor approached (TTD≤7d vs. >7d (mean±SD): x= 0.12±0.10 vs. 0.08±0.06mV; y= 0.12±0.09 vs. 0.08±0.05mV), as well as the dominant frequency in the horizontal direction (= 9.1±1.3 vs. 8.5±1.2mHz) and the synchronization between both directions (= 0.44±0.16 vs. 0.36±0.14). Furthermore, its complexity decreased in the vertical direction (= 6.13·10-2±8.7·10-3 vs. 6.50·10-2±8.3·10-3), suggesting a higher cell-to-cell electrical coupling. Whereas there were no differences between the SW features in both directions in the general population, statistically significant differences were obtained between them in individuals in many cases.

SIGNIFICANCE

Our results suggest that the SW of the EHG is related to bioelectrical events in the uterus and could provide objective information to clinicians in challenging obstetric scenarios.

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.

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.

Dedicated Entropy Measures for Early Assessment of Pregnancy Progression From Single-Channel Electrohysterography

OBJECTIVE

Preterm birth is a large-scale clinical problem involving over 10% of infants. Diagnostic means for timely risk assessment are lacking and the underlying physiological mechanisms unclear. To improve the evaluation of pregnancy before term, we introduce dedicated entropy measures derived from a single-channel electrohysterogram (EHG).

METHODS

The estimation of approximate entropy (ApEn) and sample entropy (SampEn) is adjusted to monitor variations in the regularity of single-channel EHG recordings, reflecting myoelectrical changes due to pregnancy progression. In particular, modifications in the tolerance metrics are introduced for improving robustness to EHG amplitude fluctuations. An extensive database of 58 EHG recordings with 4 monopolar channels in women presenting with preterm contractions was manually annotated and used for validation. The methods were tested for their ability to recognize the onset of labor and the risk of preterm birth. Comparison with the best single-channel methods according to the literature was performed.

RESULTS

The reference methods were outperformed. SampEn and ApEn produced the best prediction of delivery, although only one channel showed a significant difference () between labor and nonlabor. The modified ApEn produced the best prediction of preterm delivery, showing statistical significance () in three channels. These results were also confirmed by the area under the receiver operating characteristic curve and fivefold cross validation.

CONCLUSION

The use of dedicated entropy estimators improves the diagnostic value of EHG analysis earlier in pregnancy.

SIGNIFICANCE

Our results suggest that changes in the EHG might manifest early in pregnancy, providing relevant prognostic opportunities for pregnancy monitoring by a practical single-channel solution.

Mathematical modeling of the female reproductive system: from oocyte to delivery

From ovulation to delivery, and through the menstrual cycle, the female reproductive system undergoes many dynamic changes to provide an optimal environment for the embryo to implant, and to develop successfully. It is difficult ethically and practically to observe the system over the timescales involved in growth and development (often hours to days). Even in carefully monitored conditions clinicians and biologists can only see snapshots of the development process. Mathematical models are emerging as a key means to supplement our knowledge of the reproductive process, and to tease apart complexity in the reproductive system. These models have been used successfully to test existing hypotheses regarding the mechanisms of female infertility and pathological fetal development, and also to provide new experimentally testable hypotheses regarding the process of development. This new knowledge has allowed for improvements in assisted reproductive technologies and is moving toward translation to clinical practice via multiscale assessments of the dynamics of ovulation, development in pregnancy, and the timing and mechanics of delivery. WIREs Syst Biol Med 2017, 9:e1353. doi: 10.1002/wsbm.1353 For further resources related to this article, please visit the WIREs website.

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.

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.

Reprint of 'A nonlinear parameterization of multivariate electrohysterographical signals'

Electrohysterography is a technique which measures a bioelectrical activity of a uterus. This paper presents an application of a nonlinear parameterization of multivariate electrohysterographical signals for a uterine activity assessment to improve unsatisfactory a labor prediction accuracy by methods published in literature. A multivariate sample entropy used for differentiated 4-channel electrohysterographical signals, general Spearman's correlation and a combined index being the sum of them, were tested. These nonlinear measures use joint information contained in a multivariate signal. The results confirm that the combined index provides the best assessment of uterine contractions: 87% sensitivity and 50% specificity of labor prediction in the studied data. These results should be verified in a prospective study.

Improved Prediction of Preterm Delivery Using Empirical Mode Decomposition Analysis of Uterine Electromyography Signals

Preterm delivery increases the risk of infant mortality and morbidity, and therefore developing reliable methods for predicting its likelihood are of great importance. Previous work using uterine electromyography (EMG) recordings has shown that they may provide a promising and objective way for predicting risk of preterm delivery. However, to date attempts at utilizing computational approaches to achieve sufficient predictive confidence, in terms of area under the curve (AUC) values, have not achieved the high discrimination accuracy that a clinical application requires. In our study, we propose a new analytical approach for assessing the risk of preterm delivery using EMG recordings which firstly employs Empirical Mode Decomposition (EMD) to obtain their Intrinsic Mode Functions (IMF). Next, the entropy values of both instantaneous amplitude and instantaneous frequency of the first ten IMF components are computed in order to derive ratios of these two distinct components as features. Discrimination accuracy of this approach compared to those proposed previously was then calculated using six differently representative classifiers. Finally, three different electrode positions were analyzed for their prediction accuracy of preterm delivery in order to establish which uterine EMG recording location was optimal signal data. Overall, our results show a clear improvement in prediction accuracy of preterm delivery risk compared with previous approaches, achieving an impressive maximum AUC value of 0.986 when using signals from an electrode positioned below the navel. In sum, this provides a promising new method for analyzing uterine EMG signals to permit accurate clinical assessment of preterm delivery risk.

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.

Automated conduction velocity analysis in the electrohysterogram for prediction of imminent delivery: a preliminary study

Background. Analysis of the electrohysterogram (EHG) is a promising diagnostic tool for preterm delivery. For the introduction in the clinical practice, analysis of the EHG should be reliable and automated to guarantee reproducibility. Study Goal. Investigating the feasibility of automated analysis of the EHG conduction velocity (CV) for detecting imminent delivery. Materials and Methods. Twenty-two patients presenting with uterine contractions (7 preterm) were included. An EHG was obtained noninvasively using a 64-channel high-density electrode grid. Contractions were selected based on the estimated intrauterine pressure derived from the EHG, the tocodynamometer, and maternal perception. Within the selected contractions, the CV vector was identified in two dimensions. Results. Nine patients delivered within 24 hours and were classified as a labor group. 64 contractions were analyzed; the average amplitude of the CV vector was significantly higher for the labor group, 8.65 cm/s ± 1.90, compared to the nonlabor group, 5.30 cm/s ± 1.47 (P < 0.01). Conclusion. The amplitude of the CV is a promising parameter for predicting imminent (preterm) delivery. Automated estimation of this parameter from the EHG signal is feasible and should be regarded as an important prerequisite for future clinical studies and applications.

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.

Automatic evaluation of progression angle and fetal head station through intrapartum echographic monitoring

Labor progression is routinely assessed through transvaginal digital inspections, meaning that the clinical decisions taken during the most delicate phase of pregnancy are subjective and scarcely supported by technological devices. In response to such inadequacies, we combined intrapartum echographic acquisitions with advanced tracking algorithms in a new method for noninvasive, quantitative, and automatic monitoring of labor. Aim of this work is the preliminary clinical validation and accuracy evaluation of our automatic algorithm in assessing progression angle (PA) and fetal head station (FHS). A cohort of 10 parturients underwent conventional labor management, with additional translabial echographic examinations after each uterine contraction. PA and FHS were evaluated by our automatic algorithm on the acquired images. Additionally, an experienced clinical sonographer, blinded regarding the algorithm results, quantified on the same acquisitions of the two parameters through manual contouring, which were considered as the standard reference in the evaluation of automatic algorithm and routine method accuracies. The automatic algorithm (mean error ± 2SD) provided a global accuracy of 0.9 ± 4.0 mm for FHS and 4° ± 9° for PA, which is far above the diagnostic ability shown by the routine method, and therefore it resulted in a reliable method for earlier identification of abnormal labor patterns in support of clinical decisions.

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.

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.