Simulating uterine contraction by using an electro-chemo-mechanical model

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.

Fetus descent simulation with the active uterine contraction during the vaginal delivery: MRI-based evaluation and uncertainty quantification

Finite element models ranging from single to multiscale models have been widely used to gain valuable insights into the physiological delivery process and associated complication scenarios. However, the fetus descent simulation with the active uterine contraction is still challenging for validation and uncertainty quantification issues. The present study performed a fetus descent simulation using the active uterine contraction. Then, simulation outcomes were evaluated using theoretical and in vivo MRI childbirth data. Moreover, parameter uncertainty and propagation were also performed. A maternal pelvis model was developed. The active uterine contraction was modeled using a transversely isotropic Mooney-Rivlin material. Displacement trajectories were compared between simulation, theoretical and in vivo MRI childbirth data. Monte Carlo (M.C) and Polynomial Chaos Expansion (PCE) methods were applied to quantify uncertain parameters and their propagations. Obtained results showed that fetal descent behavior is consistent with the MRI-based observation as well as the theoretical trajectory (curve of Carus). The head downward vertical displacement ranges from 0 to approximately 47 mm. A reduction of 50% in uterine size was observed during the simulation. Three high-sensitive parameters (C 1 , C 2 , Ca 0 ) were also identified. Our study suggested that the use of the active uterine contraction is essential for simulating vaginal delivery but the global parameter sensitivity, parameter uncertainty, and outcome evaluation should be carefully performed. As a perspective, the developed approach could be extrapolated for patient-specific modeling and associated delivery complication simulations to identify risks and potential therapeutic solutions.

Modeling of the biomechanical behavior and growth of the human uterus during pregnancy

Premature birth poses a challenge to public health, with one in ten babies being born prematurely worldwide. The pathological distension of the uterus can create tension in the uterine wall, triggering contractions that may lead to birth, including premature birth. While there has been an increase in the use of computational models to study pregnancy in recent years, ethical challenges have limited research on the mechanical properties of the uterus during gestation. This study proposes a biomechanical model based on a stretch-driven growth mechanism to describe uterine evolution during the second half of the gestational period. The constitutive model employed is anisotropic, reflecting the presence of fibers in uterine tissue, and it is also considered incompressible. The geometric model representing the uterine body was derived from truncated ellipsoids, subject to intrauterine pressure as loading. Simulation results indicate that the proposed model is effective in reproducing growth patterns documented in the literature, such as simultaneous increases in intrauterine volume and uterine tissue volume, accompanied by a reduction in uterine wall thickness within limits reported in experimental data.

On the uncertainty quantification of the active uterine contraction during the second stage of labor simulation

Uterine contractions in the myometrium occur at multiple scales, spanning both organ and cellular levels. This complex biological process plays an essential role in the fetus delivery during the second stage of labor. Several finite element models of active uterine contractions have already been developed to simulate the descent of the fetus through the birth canal. However, the developed models suffer severe reliability issues due to the uncertain parameters. In this context, the present study aimed to perform the uncertainty quantification (UQ) of the active uterine contraction simulation to advance our understanding of pregnancy mechanisms with more reliable indicators. A uterus model with and without fetus was developed integrating a transversely isotropic Mooney-Rivlin material with two distinct fiber orientation architectures. Different contraction patterns with complex boundary conditions were designed and applied. A global sensitivity study was performed to select the most valuable parameters for the uncertainty quantification (UQ) process using a copula-based Monte Carlo method. As results, four critical material parameters (C 1 , C 2 , K , Ca 0 ) of the active uterine contraction model were identified and used for the UQ process. The stress distribution on the uterus during the fetus descent, considering first and second fiber orientation families, ranged from 0.144 to 1.234 MPa and 0.044 to 1.619 MPa, respectively. The simulation outcomes revealed also the segment-specific contraction pattern of the uterus tissue. The present study quantified, for the first time, the effect of uncertain parameters of the complex constitutive model of the active uterine contraction on the fetus descent process. As perspectives, a full maternal pelvis model will be coupled with reinforcement learning to automatically identify the delivery mechanism behind the cardinal movements of the fetus during the active expulsion process.

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.

Golgi Reassembly Stacking Protein 2 Modulates Myometrial Contractility during Labor by Affecting ATP Production

The mechanism of maintaining myometrial contractions during labor remains unclear. Autophagy has been reported to be activated in laboring myometrium, along with the high expression of Golgi reassembly stacking protein 2 (GORASP2), a protein capable of regulating autophagy activation. This study aimed to investigate the role and mechanism of GORASP2 in uterine contractions during labor. Western blot confirmed the increased expression of GORASP2 in laboring myometrium. Furthermore, the knockdown of GORASP2 in primary human myometrial smooth muscle cells (hMSMCs) using siRNA resulted in reduced cell contractility. This phenomenon was independent of the contraction-associated protein and autophagy. Differential mRNAs were analyzed using RNA sequencing. Subsequently, KEGG pathway analysis identified that GORASP2 knockdown suppressed several energy metabolism pathways. Furthermore, reduced ATP levels and aerobic respiration impairment were observed in measuring the oxygen consumption rate (OCR). These findings suggest that GORASP2 is up-regulated in the myometrium during labor and modulates myometrial contractility mainly by maintaining ATP production.

Chemo-mechanical modeling of smooth muscle cell activation for the simulation of arterial walls under changing blood pressure

In this paper, a novel chemo-mechanical model is proposed for the description of the stretch-dependent chemical processes known as Bayliss effect and their impact on the active contraction in vascular smooth muscle. These processes are responsible for the adaptive reaction of arterial walls to changing blood pressure by which the blood vessels actively support the heart in providing sufficient blood supply for varying demands in the supplied tissues. The model is designed to describe two different stretch-dependent mechanisms observed in smooth muscle cells (SMCs): a calcium-dependent and a calcium-independent contraction. For the first one, stretch of the SMCs leads to an inlet of calcium ions which activates the myosin light chain kinase (MLCK). The increased activity of MLCK triggers the contractile units of the cells resulting in the contraction on a comparatively short time scale. For the calcium-independent contraction mechanism, stretch-dependent receptors of the cell membrane stimulate an intracellular reaction leading to an inhibition of the antagonist of MLCK, the myosin light chain phosphatase resulting in a contraction on a comparatively long time scale. An algorithmic framework for the implementation of the model in finite element programs is derived. Based thereon, it is shown that the proposed approach agrees well with experimental data. Furthermore, the individual aspects of the model are analyzed in numerical simulations of idealized arteries subject to internal pressure waves with changing intensities. The simulations show that the proposed model is able to describe the experimentally observed contraction of the artery as a reaction to increased internal pressure, which can be considered a crucial aspect of the regulatory mechanism of muscular arteries.

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.

On the management of maternal pushing during the second stage of labor: a biomechanical study considering passive tissue fatigue damage accumulation

BACKGROUND

During the second stage of labor, the maternal pelvic floor muscles undergo repetitive stretch loading as uterine contractions and strenuous maternal pushes combined to expel the fetus, and it is not uncommon that these muscles sustain a partial or complete rupture. It has recently been demonstrated that soft tissues, including the anterior cruciate ligament and connective tissue in sheep pelvic floor muscle, can accumulate damage under repetitive physiological (submaximal) loads. It is well known to material scientists that this damage accumulation can not only decrease tissue resistance to stretch but also result in a partial or complete structural failure. Thus, we wondered whether certain maternal pushing patterns (in terms of frequency and duration of each push) could increase the risk of excessive damage accumulation in the pelvic floor tissue, thereby inadvertently contributing to the development of pelvic floor muscle injury.

OBJECTIVE

This study aimed to determine which labor management practices (spontaneous vs directed pushing) are less prone to accumulate damage in the pelvic floor muscles during the second stage of labor and find the optimum approach in terms of minimizing the risk of pelvic floor muscle injury.

STUDY DESIGN

We developed a biomechanical model for the expulsive phase of the second stage of labor that includes the ability to measure the damage accumulation because of repetitive physiological submaximal loads. We performed 4 simulations of the second stage of labor, reflecting a directed pushing technique and 3 alternatives for spontaneous pushing.

RESULTS

The finite element model predicted that the origin of the pubovisceral muscle accumulates the most damage and so it is the most likely place for a tear to develop. This result was independent of the pushing pattern. Performing 3 maternal pushes per contraction, with each push lasting 5 seconds, caused less damage and seemed the best approach. The directed pushing technique (3 pushes per contraction, with each push lasting 10 seconds) did not reduce the duration of the second stage of labor and caused higher damage accumulation.

CONCLUSION

The frequency and duration of the maternal pushes influenced the damage accumulation in the passive tissues of the pelvic floor muscles, indicating that it can influence the prevalence of pelvic floor muscle injuries. Our results suggested that the maternal pushes should not last longer than 5 seconds and that the duration of active pushing is a better measurement than the total duration of the second stage of labor. Hopefully, this research will help to shed new light on the best practices needed to improve the experience of labor for women.

Mechanical Effects of a Maylard Scar During a Vaginal Birth After a Previous Caesarean

Caesarean section is one of the most common surgeries worldwide, even though there is no evidence supporting maternal and perinatal long-term benefits. Furthermore, the mechanical behavior of a caesarean scar during a vaginal birth after caesarean (VBAC) is not well understood since there are several questions regarding the uterine wound healing process. The aim of this study is to investigate the biomechanical Maylard fiber reorientation and stiffness influence during a VBAC through computational methods. A biomechanical model comprising a fetus and a uterus was developed, and a chemical-mechanical constitutive model that triggers uterine contractions was used, where some of the parameters were adjusted to account for the matrix and fiber stiffness increase in the caesarean scar. Several mechanical simulations were performed to analyze different scar fibers arrangements, considering different values for the respective matrix and fibers stiffness. The results revealed that a random fiber arrangement in the Maylard scar has a much higher impact on its mechanical behavior during a VBAC than the common fibers arrangement present in the uninjured uterine tissue. An increase of the matrix scar stiffness exhibits a lower impact, while an increase of the fiber's stiffness has no significant influence.

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.

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.

Simulation of the uterine contractions and foetus expulsion using a chemo-mechanical constitutive model

During vaginal delivery women sustain stretching of their pelvic floor, risking tissue injury and adverse outcomes. Since studies in pregnant women are limited with ethical constraints, computational models have become an interesting alternative to elucidate the pregnancy mechanisms. This research investigates the uterine contractions during foetus expulsion without an imposed trajectory. Such physical process is captured by means of a chemo-mechanical constitutive model, where the uterine contractions are triggered by chemical stimuli. The foetus descent, which includes both pushing and resting stages, has a descent rate within the physiological range. Moreover, the behaviour of the foetus and the uterus stretch agree well with clinical data presented in the literature. The follow-up of this study will be to obtain a complete childbirth simulation, considering also the pelvic floor muscles and its supporting structures. The simulation of a realistic rate of descent, including the pushing and resting stages, is of significant importance to study the pelvic floor muscles due to their viscoelastic nature.

Biomathematical pattern of EMG signal propagation in smooth muscle of the non-pregnant porcine uterus

Uterine contractions are generated by myometrial smooth muscle cells (SMCs) that comprise most of the myometrial layer of the uterine wall. Aberrant uterine motility (i.e., hypo- or hyper-contractility or asynchronous contractions) has been implicated in the pathogenesis of infertility due to the failure of implantation, endometriosis and abnormal estrous cycles. The mechanism whereby the non-pregnant uterus initiates spontaneous contractions remains poorly understood. The aim of the present study was to employ linear synchronization measures for analyzing the pattern of EMG signal propagation (direction and speed) in smooth muscles of the non-pregnant porcine uterus in vivo using telemetry recording system. It has been revealed that the EMG signal conduction in the uterine wall of the non-pregnant sow does not occur at random but it rather exhibits specific directions and speed. All detectable EMG signals moved along the uterine horn in both cervico-tubal and tubo-cervical directions. The signal migration speed could be divided into the three main types or categories: i. slow basic migration rhythm (SBMR); ii. rapid basic migration rhythm (RBMR); and iii. rapid accessory migration rhythm (RAMR). In conclusion, the EMG signal propagation in smooth muscles of the porcine uterus in vivo can be assessed using a linear synchronization model. Physiological pattern of the uterine contractile activity determined in this study provides a basis for future investigations of normal and pathologicall myogenic function of the uterus.