A computer-based simulation of childbirth using the partial Dirichlet-Neumann contact method with total Lagrangian explicit dynamics on the GPU

Novel hybrid rigid-deformable fetal modeling for simulating the vaginal delivery within the second stage of labor

BACKGROUND AND OBJECTIVE

The fetal representation as a 3D articulated body plays an essential role to describe a realistic vaginal delivery simulation. However, the current computational solutions have been oversimplified. The objective of the present work was to develop and evaluate a novel hybrid rigid-deformable modeling approach for the fetal body and then simulate its interaction with surrounding fetal soft tissues and with other maternal pelvis soft tissues during the second stage of labor.

METHODS

CT scan data was used for 3D fetal skeleton reconstruction. Then, a novel hybrid rigid-deformable model of the fetal body was developed. This model was integrated into a maternal 3D pelvis model to simulate the vaginal delivery. Soft tissue deformation was simulated using our novel HyperMSM formulation. Magnetic resonance imaging during the second stage of labor was used to impose the trajectory of the fetus during the delivery.

RESULTS

Our hybrid rigid-deformable fetal model showed a potential capacity for simulating the movements of the fetus along with the deformation of the fetal soft tissues during the vaginal delivery. The deformation energy density observed in the simulation for the fetal head fell within the strain range of 3 % to 5 %, which is in good agreement with the literature data.

CONCLUSIONS

This study developed, for the first time, a hybrid rigid-deformation modeling of the fetal body and then performed a vaginal delivery simulation using MRI-driven kinematic data. This opens new avenues for describing more realistic behavior of the fetal body kinematics and deformation during the second stage of labor. As perspectives, the integration of the full skeleton body, especially the upper and lower limbs will be investigated. Then, the completed model will be integrated into our developed next-generation childbirth training simulator for vaginal delivery simulation and associated complication scenarios.

Fast soft-tissue deformations coupled with mixed reality toward the next-generation childbirth training simulator

High-quality gynecologist and midwife training is particularly relevant to limit medical complications and reduce maternal and fetal morbimortalities. Physical and virtual training simulators have been developed. However, physical simulators offer a simplified model and limited visualization of the childbirth process, while virtual simulators still lack a realistic interactive system and are generally limited to imposed predefined gestures. Objective performance assessment based on the simulation numerical outcomes is still not at hand. In the present work, we developed a virtual childbirth simulator based on the Mixed-Reality (MR) technology coupled with HyperMSM (Hyperelastic Mass-Spring Model) formulation for real-time soft-tissue deformations, providing intuitive user interaction with the virtual physical model and a quantitative assessment to enhance the trainee's gestures. Microsoft HoloLens 2 was used and the MR simulator was developed including a complete holographic obstetric model. A maternal pelvis system model of a pregnant woman (including the pelvis bone, the pelvic floor muscles, the birth canal, the uterus, and the fetus) was generated, and HyperMSM formulation was applied to simulate the soft tissue deformations. To induce realistic reactions to free gestures, the virtual replicas of the user's detected hands were introduced into the physical simulation and were associated with a contact model between the hands and the HyperMSM models. The gesture of pulling any part of the virtual models with two hands was also implemented. Two labor scenarios were implemented within the MR childbirth simulator: physiological labor and forceps-assisted labor. A scoring system for the performance assessment was included based on real-time biofeedback. As results, our developed MR simulation application was developed in real-time with a refresh rate of 30-50 FPS on the HoloLens device. HyperMSM model was validated using FE outcomes: high correlation coefficients of [0.97-0.99] and weighted root mean square relative errors of 9.8% and 8.3% were obtained for the soft tissue displacement and energy density respectively. Experimental tests showed that the implemented free-user interaction system allows to apply the correct maneuvers (in particular the "Viennese" maneuvers) during the labor process, and is capable to induce a truthful reaction of the model. Obtained results confirm also the possibility of using our simulation's outcomes to objectively evaluate the trainee's performance with a reduction of 39% for the perineal strain energy density and 5.6 mm for the vertical vaginal diameter when the "Viennese" technique is applied. This present study provides, for the first time, an interactive childbirth simulator with an MR immersive experience with direct free-hand interaction, real-time soft-tissue deformation feedback, and an objective performance assessment based on numerical outcomes. This offers a new perspective for enhancing next-generation training-based obstetric teaching. The used models of the maternal pelvic system and the fetus will be enhanced, and more delivery scenarios (e.g. instrumental delivery, breech delivery, shoulder dystocia) will be designed and integrated. The third stage of labor will be also investigated to include the delivery of the placenta, and the clamping and cutting of the umbilical cord.

Can maternal hormones play a significant role in delivery mode?

The aim of this study was primarily to evaluate the levels of progesterone, oestradiol and relaxin during different delivery modes and secondarily to assess specific traits and changes in maternal pelvic dimensions during pregnancy and childbirth, in correlation with foetal size and maternal hormonal profile. Nulliparous women (n = 448) were evaluated at three different stages, during first trimester, at the time of admission for childbirth and finally just before childbirth. Each examination included clinical internal pelvimetry, blood sample collection for defining the hormones levels in peripheral maternal circulation and ultrasonographic measurements of specific variables of the pubic symphysis and the foetus. We included 304 nulliparous women divided in three groups. According to our results, there was statistically significant difference at the mean progesterone, oestradiol and relaxin range during different modes of childbirth (p-value < .01). We also found significant correlation between the newborn's weight and the changes in pubic symphysis dimensions. However, no significant association was noted between maternal hormones studied and the changes in pelvic dimensions.IMPACT STATEMENTWhat is already known on this subject? Mode of childbirth can be affected by various aspects, like maternal pelvic anatomy, foetal size and hormonal status at the time of labour. Hormonal fluctuations along with mechanical forces caused by the foetus are believed to lead to morphological alterations to promote natural vaginal childbirth.What do the results of this study add? Our results clearly showed that successful vaginal delivery is characterised by the prevalence of a hyperoestrogenic environment with higher values of intrapartum oestradiol range and significant increase in maternal serum relaxin levels. We also proved that progesterone levels do not decrease during vaginal childbirth, and we concluded that foetal size seems to be the most crucial factor causing alterations in maternal pelvis during parturition.What are the implications of these findings for clinical practice and further research? Our findings could form part of a set of key factors included in future algorithms or computerised biomechanical models for predicting potential childbirth mode. Larger multicenter studies should confirm our results and evaluate their clinical significance in the decision making to ensure safe childbirth and optimal maternal and perinatal outcomes.

A Computational Procedure to Derive the Curve of Carus for Childbirth Computational Modeling

Computational modeling serves an important role in childbirth-related research. Prescribed fetal descent trajectory is a key characteristic in childbirth simulations. Two major types of fully prescribed fetal descent trajectory can be identified in the literature: straight descent trajectories and curve of Carus. The straight descent trajectory has the advantage of being simpler and could serve as a reasonable approximation for relatively small fetal movements during labor, but it cannot be used to simulate the entire childbirth process. Curve of Carus is the well-recognized fetal descent trajectory with physiological significance. However, no mathematical description of the curve of Carus can be found in the existing computational studies. This status of curve of Carus simulation in the literature hinders the direct comparison of results across different studies and the advancement of computational techniques built upon previous research. The goals of this study are: (1) propose a universal approach to achieve the curve of Carus for the second stage of labor, from the point when the fetal head engages the pelvis to the point when the fetal head is fully delivered. (2) demonstrate its utility when considering various fetal head sizes. The current study provides a detailed formulation of the curve of Carus, considering geometries of both the mother and the fetus. The maternal geometries were obtained from MRI data, and the fetal head geometries were based on laser scanning of a replica of a real fetal head.

Recurrent neural network to predict hyperelastic constitutive behaviors of the skeletal muscle

Hyperelastic constitutive laws have been commonly used to model the passive behavior of the human skeletal muscle. Despite many efforts, the use of accurate finite element formulations of hyperelastic constitutive laws is still time-consuming for a real-time medical simulation system. The objective of the present study was to develop a deep learning model to predict the hyperelastic constitutive behaviors of the skeletal muscle toward a fast estimation of the muscle tissue stress.A finite element (FE) model of the right psoas muscle was developed. Neo-Hookean and Mooney-Rivlin laws were used. A tensile test was performed with an applied body force. A learning database was built from this model using an automatic probabilistic generation process. A long-short term memory (LSTM) neural network was implemented to predict the stress evolution of the skeletal muscle tissue. A hyperparameter tuning process was conducted. Root mean square error (RMSE) and associated relative error was quantified to evaluate the precision of the predictive capacity of the developed deep learning model. Pearson correlation coefficients (R) was also computed.The nodal displacements and the maximal stresses range from 70 to 227 mm and from 2.79 to 5.61 MPa for Neo-Hookean and Monney-Rivlin laws, respectively. Regarding the LSTM predictions, the RMSE ranges from 224.3 ± 3.9 Pa (8%) to 227.5 [Formula: see text] 5.7 Pa (4%) for Neo-Hookean and Monney-Rivlin laws, respectively. Pearson correlation coefficients (R) of 0.78 [Formula: see text] 0.02 and 0.77 [Formula: see text] 0.02 were obtained for Neo-Hookean and Monney-Rivlin laws, respectively.The present study showed that, for the first time, the use of a deep learning model can reproduce the time-series behaviors of the complex FE formulations for skeletal muscle modeling. In particular, the use of a LSTM neural network leads to a fast and accurate surrogate model for the in silico prediction of the hyperelastic constitutive behaviors of the skeletal muscle. As perspectives, the developed deep learning model will be integrated into a real-time medical simulation of the skeletal muscle for prosthetic socket design and childbirth simulator.

HyperMSM: A new MSM variant for efficient simulation of dynamic soft-tissue deformations

BACKGROUND AND OBJECTIVE

Fast, accurate, and stable simulation of soft tissue deformation is a challenging task. Mass-Spring Model (MSM) is one of the popular methods used for this purpose for its simple implementation and potential to provide fast dynamic simulations. However, accurately simulating a non-linear material within the mass-spring framework is still challenging. The objective of the present study is to develop and evaluate a new efficient hyperelastic Mass-Spring Model formulation to simulate the Neo-Hookean deformable material, called HyperMSM.

METHODS

Our novel HyperMSM formulation is applicable for both tetrahedral and hexahedral mesh configurations and is compatible with the original projective dynamics solver. In particular, the proposed MSM variant includes springs with variable rest-lengths and a volume conservation constraint. Two applications (transtibial residual limb and the skeletal muscle) were conducted.

RESULTS

Compared to finite element simulations, obtained results show RMSE ranges of [2.8%-5.2%] and [0.46%-5.4%] for stress-strain and volumetric responses respectively for strains ranging from -50% to +100%. The displacement error range in our transtibial residual limb simulation is around [0.01mm-0.7 mm]. The RMSE range of relative nodal displacements for the skeletal psoas muscle model is [0.4%-1.7%].

CONCLUSIONS

Our novel HyperMSM formulation allows hyperelastic behavior of soft tissues to be described accurately and efficiently within the mass-spring framework. As perspectives, our formulation will be enhanced with electric behavior toward a multi-physical soft tissue mass-spring modeling framework. Then, the coupling with an augmented reality environment will be performed.

Childbirth Computational Models: Characteristics and Applications

The biomechanical process of childbirth is necessary to usher in new lives-but it can also result in trauma. This physically intense process can put both the mother and the child at risk of injuries and complications that have life-long impact. Computational models, as a powerful tool to simulate and explore complex phenomena, have been used to improve our understanding of childbirth processes and related injuries since the 1990s. The goal of this paper is to review and summarize the breadth and current state of the computational models of childbirth in the literature-focusing on those that investigate the mechanical process and effects. We first summarize the state of critical characteristics that have been included in computational models of childbirth (i.e., maternal anatomy, fetal anatomy, cardinal movements, and maternal soft tissue mechanical behavior). We then delve into the findings of the past studies of birth processes and mechanical injuries in an effort to bridge the gap between the theoretical, numerical assessment and the empirical, clinical observations and practices. These findings are from applications of childbirth computational models in four areas: (1) the process of childbirth itself, (2) maternal injuries, (3) fetal injuries, and (4) protective measures employed by clinicians during delivery. Finally, we identify some of the challenges that computational models still face and suggest future directions through which more biofidelic simulations of childbirth might be achieved, with the goal that advancing models may provide more efficient and accurate, patient-specific assessment to support future clinical decision-making.