Emergent behaviors in a deterministic model of the human uterus

Forces Involved with Labor and Delivery-A Biomechanical Perspective

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

Estimating uterine source current during contractions using magnetomyography measurements

Understanding the uterine source of the electrophysiological activity of contractions during pregnancy is of scientific interest and potential clinical applications. In this work, we propose a method to estimate uterine source currents from magnetomyography (MMG) temporal course measurements on the abdominal surface. In particular, we develop a linear forward model, based on the quasistatic Maxwell’s equations and a realistic four-compartment volume conductor, relating the magnetic fields to the source currents on the uterine surface through a lead-field matrix. To compute the lead-field matrix, we use a finite element method that considers the anisotropic property of the myometrium. We estimate the source currents by minimizing a constrained least-squares problem to solve the non-uniqueness issue of the inverse problem. Because we lack the ground truth of the source current, we propose to predict the intrauterine pressure from our estimated source currents by using an absolute-value-based method and compare the result with real abdominal deflection recorded during contractile activity. We test the feasibility of the lead-field matrix by displaying the lead fields that are generated by putative source currents at different locations in the myometrium: cervix and fundus, left and right, front and back. We then illustrate our method by using three synthetic MMG data sets, which are generated using our previously developed multiscale model of uterine contractions, and three real MMG data sets, one of which has simultaneous real abdominal deflection measurements. The numerical results demonstrate the ability of our method to capture the local contractile activity of human uterus during pregnancy. Moreover, the predicted intrauterine pressure is in fair agreement with the real abdominal deflection with respect to the timing of uterine contractions.

The uterine pacemaker of labor

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

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.

Mechanotransduction mechanisms for coordinating uterine contractions in human labor

This review presents evolving concepts of how the human uterus contracts in pregnancy, with emphasis on the mechanisms of long-distance signaling. Action potential propagation has historically been assumed to be the sole mechanism for signaling and tissue recruitment over both short and long distances. However, data in animals and humans indicate that a single action potential does not travel distances greater than a few centimeters. To address this enigma, a long-distance signaling mechanism based on hydraulic signaling and mechanotransduction is developed. By combining this mechanism for long-distance signaling with the action potential propagation mechanism for signaling over short distances, a comprehensive dual mechanism model (or 'dual model') of uterine function is formulated. Mechanotransduction is an accepted phenomenon of myometrium, but the dual model identifies mechanotransduction as relevant to normal labor. For hydraulic signaling, a local contraction slightly increases intrauterine pressure, which globally increases wall tension. Increased wall tension then mechanically induces additional local contractions that further raise pressure. This leads to robust, positive feedback recruitment that explains the emergence of consistently strong contractions of human labor. Three key components of the dual model - rapid long-distance signaling, mechanical triggering, and electrical activity - converge with the concept of mechanically sensitive electrogenic pacemakers distributed throughout the wall. The dual model retains excitation-contraction coupling and action potential propagation for signaling over short distances (<10cm) and hence is an extension of the action potential model rather than a replacement.

Linking myometrial physiology to intrauterine pressure; how tissue-level contractions create uterine contractions of labor

The mechanisms used to coordinate uterine contractions are not known. We develop a new model based on the proposal that there is a maximum distance to which action potentials can propagate in the uterine wall. This establishes "regions", where one action potential burst can rapidly recruit all the tissue. Regions are recruited into an organ-level contraction via a stretch-initiated contraction mechanism (myometrial myogenic response). Each uterine contraction begins with a regional contraction, which slightly increases intrauterine pressure. Higher pressure raises tension throughout the uterine wall, which initiates contractions of more regions and further increases pressure. The positive feedback synchronizes regional contractions into an organ-level contraction. Cellular automaton (CA) simulations are performed with Mathematica. Each "cell" is a region that is assigned an action potential threshold. An anatomy sensitivity factor converts intrauterine pressure to regional tension through the Law of Laplace. A regional contraction occurs when regional tension exceeds regional threshold. Other input variables are: starting and minimum pressure, burst and refractory period durations, enhanced contractile activity during an electrical burst, and reduced activity during the refractory period. Complex patterns of pressure development are seen that mimic the contraction patterns observed in laboring women. Emergent behavior is observed, including global synchronization, multiple pace making regions, and system memory of prior conditions. The complex effects of nifedipine and oxytocin exposure are simulated. The force produced can vary as a nonlinear function of the number of regions. The simulation directly links tissue-level physiology to human labor. The concept of a uterine pacemaker is re-evaluated because pace making activity may occur well before expression of a contraction. We propose a new classification system for biological CAs that parallels the 4-class system of Wolfram. However, instead of classifying the rules, biological CAs should classify the set of input values for the rules that describe the relevant biology.

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.

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).