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

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 From published and unpublished data we construct mathematical models for fourteen ionic currents of USMCs: currents (L- and T-type), current, an hyperpolarization-activated current, three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

Mathematical models in physiology

Computational modelling of biological processes and systems has witnessed a remarkable development in recent years. The search-term (modelling OR modeling) yields over 58000 entries in PubMed, with more than 34000 since the year 2000: thus, almost two-thirds of papers appeared in the last 5–6 years, compared to only about one-third in the preceding 5–6 decades.\ud \ud The development is fuelled both by the continuously improving tools and techniques available for bio-mathematical modelling and by the increasing demand in quantitative assessment of element inter-relations in complex biological systems. This has given rise to a worldwide public domain effort to build a computational framework that provides a comprehensive theoretical representation of integrated biological function—the Physiome.\ud \ud The current and next issues of this journal are devoted to a small sub-set of this initiative and address biocomputation and modelling in physiology, illustrating the breadth and depth of experimental data-based model development in biological research from sub-cellular events to whole organ simulations

Forward Electrophysiological Modeling and Inverse Problem for Uterine Contractions during Pregnancy

Uterine contractile dysfunction during pregnancy is a significant healthcare challenge that imposes heavy medical and financial burdens on both human beings and society. In the U.S., about 12% of babies are born prematurely each year, which is a leading cause of neonatal mortality and increases the possibility of having subsequent health problems. Post-term birth, in which a baby is born after 42 weeks of gestation, can cause risks for both the newborn and the mother. Currently, there is a limited understanding of how the uterus transitions from quiescence to excitation, which hampers our ability to detect labor and treat major obstetric syndromes associated with contractile dysfunction. Therefore, it is critical to develop objective methods to investigate the underlying contractile mechanism using a non-invasive sensing technique. This dissertation focuses on the multiscale forward electromagnetic modeling of uterine contractile activities and the inverse estimation of underlying source currents from abdominal magnetic field measurements. We develop a realistic multiscale forward electromagnetic model of uterine contractions in the pregnant uterus, taking into account current electrophysiological and anatomical knowledge of the uterus. Previous models focused on generating contractile forces at the organ level or on ionic concentration changes at the cellular level. Our approach is to characterize the electromagnetic fields of uterine contractions jointly at the cellular, tissue, and organ levels. At the cellular level, focusing on both plateau-type and bursting-type action potentials, we introduce a generalized version of the FitzHugh-Nagumo equations and analyze its response behavior based on bifurcation theory. To represent the anisotropy of the myometrium, we introduce a random conductivity tensor model for the fiber orientations at the tissue level. Specifically, we divide the uterus into contiguous regions, each of which is assigned a random fiber angle. We also derive analytical expressions for the spiking frequency and propagation velocity of the bursting potential. At the organ level, we propose a realistic four-compartment volume conductor, in which the uterus is modeled based on the magnetic resonance imaging scans of a near-term woman and the abdomen is curved to match the device used to take the magnetomyography measurements. To mimic the effect of the sensing direction, we incorporate a sensor array model on the surface of abdomen. We illustrate our approach using numerical examples and compute the magnetic field using the finite element method. Our results show that fiber orientation and initiation location are the key factors affecting the magnetic field pattern, and that our multiscale forward model flexibly characterizes the limited-propagation local contractions at term. These results are potentially important as a tool for interpreting the non-invasive measurements of uterine contractions. We also consider the inverse problem of uterine contractions during pregnancy. Our aim is to estimate the myometrial source currents that generate the external magnetomyography measurements. Existing works approach this problem using synthetic electromyography data. Our approach instead proceeds in two stages: develop a linear approximation model and conduct the estimation. In the first stage, we derive a linear approximation model of the sensor-oriented magnetic field measurements with respect to source current dipoles in the myometrium, based on a lead-field matrix. In particular, this lead-field matrix is analytically computed from distributed current dipoles in the myometrium according to quasi-static Maxwell\u27s equations, using the finite element method. In the second stage, we solve a constrained least-squares problem to estimate the source currents, from which we predict the intrauterine pressure. We demonstrate our approach through numerical examples with synthetic data that are generated using our multiscale forward model. In the simulations, we assume that the excitation is located at the fundus of the uterus. We also illustrate our approach using real data sets, one of which has simultaneous contractile pressure measurements. The results show that our method well captures the short-distance propagation of uterine contractile activities during pregnancy, the change of excitation area in subsequent contractions or even in a single contraction, and the timing of uterine contractions. These findings are helpful in understanding the physiological and functional properties of the uterus, potentially enabling the diagnosis of labor and the treatment of obstetric syndromes associated with contractile dysfunction such as preterm birth and post-term birth

Characterization of uterine activity by electrohysterography

A growing number of pregnancies is complicated by miscarriage, preterm delivery, and birth defects, with consequent health problems later in life. It is therefore increasingly important to monitor the health status of mother and fetus, so as to permit timely medical intervention when acute health risks are detected. For timely recognition of complications, quantitative assessment of uterine activity can be fundamental during both pregnancy and delivery. During pregnancy, timely prediction of preterm delivery can improve the effectiveness of the required treatments. Unfortunately, the prognostic techniques employed in current obstetrical practice, namely, uterine contraction measurements using an elastic belt (external tocography), cervical change evaluation, and the use of biomarkers like fetal fibronectin, have been demonstrated to be inaccurate for the prediction of preterm delivery. In the last stage of pregnancy and during labor, contractions are routinely and constantly monitored. Especially when complications occur, e.g., when labor shows poor progress, quantitative assessment of uterine activity can guide the physician to choose a uterine contraction induction or augmentation, a cesarean section, or other therapies. Furthermore, monitoring the fetal heart response to the uterine activity (cardiotography) is widely used as a screening test for timely recognition of fetal distress (e.g. asphyxia). However, in current obstetrical practice, accurate quantitative assessment of the uterine contractions can be provided only invasively and during labor. The current golden standard for contraction monitoring, which is based on the direct internal uterine pressure (IUP) measurement by an intrauterine catheter, can be risky and its use is generally limited to very complicated deliveries. The contractile element of the uterus is the myometrium, which is composed of smooth muscle cells. Uterine contractions are caused by electrical activity in the form of action potentials (AP) that propagate through the myometrium cells. Electrohysterography is the measurement of the uterine electrical activity and can be performedby electrodes placed on the abdomen. Electrohysterographic (EHG) measurements are inexpensive and noninvasive. Moreover, it has been demonstrated that the noninvasively recorded EHG signal is representative of those APs that, by propagating from cell to cell, are the root cause of a uterine contraction. Therefore, in view of the limitation of current obstetrical practice, significant benefits could be expected from the introduction of EHG signal analysis for routine contraction monitoring. Previous studies highlighted the potential prognostic and diagnostic value of EHG signal analysis, but did not investigate the possibility of accurately estimating the IUP from noninvasive EHG recordings. Moreover, important issues like the effect of the tissues interposed between the uterus and the skin (volume conductor) on EHG recordings have not been studied. Besides, EHG signal interpretation has been typically based on single-channel measurements, while the use of multiple electrodes conveys additional information (e.g., distribution and dynamics of the electrical activation) that can possibly be predictive of delivery. In this thesis, we focus on the analysis of the EHG signal as an alternative to existing techniques for predicting preterm delivery and monitoring uterine contractions during both pregnancy and delivery. The main goal of this work is to contribute to the technical basis which is required for the introduction of electrohysterography in everyday clinical practice. A major part of this thesis investigates the possibility of using electrohysterography to replace invasive IUP measurements. A novel method for IUP estimation from EHG recordings is developed in the first part of this thesis. The estimates provided by the method are compared to the IUP invasively recorded on women during delivery and result in a root mean squared error (RMSE) with respect to the reference invasive IUP recording as low as 5 mmHg, which is comparable to the accuracy of the invasive golden standard. Another important objective of this thesis work is to contribute to the introduction of novel techniques for timely prediction of preterm delivery. As the spreading of electrical activity at the myometrium is the root cause of coordinated and effective contractions, i.e., contractions that are capable of pushing the fetus down into the birth canal ultimately leading to delivery, a multichannel analysis of the spatial propagation properties of the EHG signal could provide a fundamental contribution for predicting delivery. A thorough study of the EHG signal propagation properties is therefore carried out in this work. Parameters related to the EHG that are potentially predictive of delivery, such as the uterine area where the contraction originates (pacemaker area) or the distribution and dynamics of the EHG propagation vector, can be derived from the delay by which the signal is detected at multiple locations over the whole abdomen. To analyze the propagation of EHG signals on a large scale (cm), a method is designed for calculating the detection delay among the EHG signals recorded by by electrodes placed on the abdomen. Electrohysterographic (EHG) measurements are inexpensive and noninvasive. Moreover, it has been demonstrated that the noninvasively recorded EHG signal is representative of those APs that, by propagating from cell to cell, are the root cause of a uterine contraction. Therefore, in view of the limitation of current obstetrical practice, significant benefits could be expected from the introduction of EHG signal analysis for routine contraction monitoring. Previous studies highlighted the potential prognostic and diagnostic value of EHG signal analysis, but did not investigate the possibility of accurately estimating the IUP from noninvasive EHG recordings. Moreover, important issues like the effect of the tissues interposed between the uterus and the skin (volume conductor) on EHG recordings have not been studied. Besides, EHG signal interpretation has been typically based on single-channel measurements, while the use of multiple electrodes conveys additional information (e.g., distribution and dynamics of the electrical activation) that can possibly be predictive of delivery. In this thesis, we focus on the analysis of the EHG signal as an alternative to existing techniques for predicting preterm delivery and monitoring uterine contractions during both pregnancy and delivery. The main goal of this work is to contribute to the technical basis which is required for the introduction of electrohysterography in everyday clinical practice. A major part of this thesis investigates the possibility of using electrohysterography to replace invasive IUP measurements. A novel method for IUP estimation from EHG recordings is developed in the first part of this thesis. The estimates provided by the method are compared to the IUP invasively recorded on women during delivery and result in a root mean squared error (RMSE) with respect to the reference invasive IUP recording as low as 5 mmHg, which is comparable to the accuracy of the invasive golden standard. Another important objective of this thesis work is to contribute to the introduction of novel techniques for timely prediction of preterm delivery. As the spreading of electrical activity at the myometrium is the root cause of coordinated and effective contractions, i.e., contractions that are capable of pushing the fetus down into the birth canal ultimately leading to delivery, a multichannel analysis of the spatial propagation properties of the EHG signal could provide a fundamental contribution for predicting delivery. A thorough study of the EHG signal propagation properties is therefore carried out in this work. Parameters related to the EHG that are potentially predictive of delivery, such as the uterine area where the contraction originates (pacemaker area) or the distribution and dynamics of the EHG propagation vector, can be derived from the delay by which the signal is detected at multiple locations over the whole abdomen. To analyze the propagation of EHG signals on a large scale (cm), a method is designed for calculating the detection delay among the EHG signals recorded by multiple electrodes. Relative to existing interelectrode delay estimators, this method improves the accuracy of the delay estimates for interelectrode distances larger than 5-10 cm. The use of a large interelectrode distance aims at the assessment of the EHG propagation properties through the whole uterine muscle using a limited number of sensors. The method estimates values of velocity within the physiological range and highlights the upper part of the uterus as the most frequent (65%) pacemaker area during labor. Besides, our study suggests that more insight is needed on the effect that tissues interposed between uterus and skin (volume conductor) have on the EHG signal. With the aim of improving the current interpretation and measurement accuracy of EHG parameters with potential clinical relevance, such as the conduction velocity (CV), a volume conductor model for the EHG signal is introduced and validated. The intracellular AP at the myometrium is analytically modeled in the spatial domain by a 2-parameter exponential in the form of a Gamma variate function. The unknown atomical parameters of the volume conductor model are the thicknesses of the biological tissues interposed between the uterus and the abdominal surface. These model parameters can be measured by echography for validation. The EHG signal is recorded by an electrode matrix on women with contractions. In order to increase the spatial resolution of the EHG measurements and reduce the geometrical and electrical differences among the tissues below the recording locations, electrodes with a reduced surface and smaller interelectrode distance are needed relative to the previous studies on electrohysterography. The EHG signal is recorded, for the first time, by a 64-channel (8×8) high-density electrode grid, comprising 1 mm diameter electrodes with 4 mm interelectrode distance. The model parameters are estimated in the spatial frequency domain from the recorded EHG signal by a least mean square method. The model is validated by comparing the thickness of the biological tissues recorded by echography to the values estimated using the mathematical model. The agreement between the two measures (RMSE = 1 mm and correlation coefficient, R = 0.94) suggests the model to be representative of the underlying physiology. In the last part of this dissertation, the analysis of the EHG signal propagation focuses on the CV estimation of single APs. As on a large scale this parameter cannot be accurately derived, the propagation analysis is here carried out on a small scale (mm). Also for this analysis, the EHG signal is therefore recorded by a 3×3 cm2 high-density electrode grid containing 64 electrodes (8×8). A new method based on maximum likelihood estimation is then applied in two spatial dimensions to provide an accurate estimate of amplitude and direction of the AP CV. Simulation results prove the proposed method to be more robust to noise than the standard techniques used for other electrophysiological signals, leading to over 56% improvement of the RMS CV estimate accuracy. Furthermore, values of CV between 2 cm/s and 12 cm/s, which are in agreement with invasive and in-vitro measurements described in the literature, are obtained from real measurements on ten women in labor. In conclusion, this research provides a quantitative characterization of uterine contractions by EHG signal analysis. Based on an extensive validation, this thesis indicates that uterine contractions can be accurately monitored noninvasively by dedicated analysis of the EHG signal. Furthermore, our results open the way to new clinical studies and applications aimed at improving the understanding of the electrophysiological mechanisms leading to labor, possibly reducing the incidence of preterm delivery and improving the perinatal outcome

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

Self-organized transition to coherent activity in disordered media

Synchronized oscillations are of critical functional importance in many biological systems. We show that such oscillations can arise without centralized coordination in a disordered system of electrically coupled excitable and passive cells. Increasing the coupling strength results in waves that lead to coherent periodic activity, exhibiting cluster, local and global synchronization under different conditions. Our results may explain the self-organized transition in a pregnant uterus from transient, localized activity initially to system-wide coherent excitations just before delivery.Comment: 5 pages, 4 figure

Competing mechanisms of stress-assisted diffusivity and stretch-activated currents in cardiac electromechanics

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