The fetal membranes are an important biological structure for pregnancy that surrounds and protects the fetus. They are layered structures, comprising the amnion, the chorion, and part of the maternal layer decidua. During gestation, they undergo complex microstructural changes, such as the weakening of the tissue in preparation for delivery. Little is known about the influence of the collagen fibers organization within the amnion in the rupture process of the fetal membranes. Non-crystalline X-ray diffraction (XRD) has been applied to study the collagen organization in some soft tissues, such as the cornea, breast, bone, cartilage, and, more recently, amnion. Some studies have suggested that the loss of the regular structure of the collagen fibers in the amnion may represent a contributing factor to PPROM. This work aims to analyze the biomechanics of fetal membranes under different off-plane collagen fibers within it through the potential of numerical analysis to understand whether it has a potential impact on preterm pre-labor rupture of the fetal membrane (PPROM).

A multilayer model of the fetal membrane was developed based on a robust inflation mechanical test dataset. In terms of constitutive models, the amnion was characterized by the modified version of the Buerzle-Mazza constitutive model (μo=2.4MPa, q=2.96, m5=0.463, m2=0.00228, m3=41.12, m4=1.27, N=32). The chorion (E=1MPa, υ=0.41) and the decidua (E=1MPa, υ=0.49) were characterized by elastic linear properties.

The evolution of the maximum principal stress curves with pressure in the amnion when the off-plane angle is set to 0° or 10° is different from the cases where the same parameter is set to 20° or 30°: for the first two values, the curves always increase throughout the entire simulation; for the 20° and 30° angles, the stress is 0 for smaller pressures and a rapid increase in stress is verified for higher pressures. The maximum principal stress is larger when the angle is changed from 0° to 10°, and from 30° to 20°. In the chorion layer, the maximum principal stress at the apex of the membrane increases with the off-plane angle.

Different off-plane fiber angles had a strong impact in terms of maximum principal stress in both layers, especially in the mechanical dominant layer amnion. In terms of PPROM, it is very likely that certain off-plane collagen fibers that lead to higher maximum principal stresses potentiate the rupture of the membrane. These results highlight the potential of our model to characterize the biomechanics of fetal membranes under different physiological conditions.

Pelvic floor disorders, including uterine prolapse and urinary incontinence, have a significant impact on women’s quality of life and well-being, affecting between one-third and one-half of all women [1]. For uterine prolapse, risk factors include advancing age, obesity, physical inactivity, and parity. The disease is caused by a weakening of pelvic floor musculature and other supporting anatomical structures, such as the uterine ligaments. Currently, tissue changes leading to the development and progression of uterine prolapse through mechanical and molecular alterations are understudied. Since aging and hormonal changes may affect components of the extracellular matrix, including collagen fibrils and their nanostructure (d-spacing) [2], it is crucial to investigate changes in the collagen backbone of the uterine support structures to gain a deeper understanding of the development and progression of uterine prolapse. As part of the uterine support structures, the broad ligament connects the uterus to the lateral pelvic walls and is often described as a double layer of peritoneum. Consequently, our aim was to investigate the characteristics and nanoscale behavior under loading of collagen in the broad ligament.

Broad ligament samples were obtained according to local ethics regulations from women of different ages (66 ± 22 years) post mortem. Quadratic samples (15 × 15 mm²) were subjected to biaxial stretching with simultaneous microfocussed ultra-small-angle X-ray scattering (USAXS) to determine changes in collagen fiber orientation and d-spacing with deformation (MiNaXS beamline P03/PETRA III, DESY) [3]. Deformation was increased in a stepwise manner (0%, 5%, 10%, 15%, 20%). For each step, a map of 1 × 1mm² with 25 individual USAXS measurements was created. In addition, samples adjacent to the USAXS-samples were prepared for histological assessment of collagen orientation, elastin and proteoglycan content, and cellular properties. Slices were cut in frontal, sagittal, and horizontal orientation to allow collagen fiber assessment from different directions.

Radial integration of scattering data indicated the presence of two main orthogonal collagen fibril orientations. With increasing tissue strain, collagen d-spacing (an indicator of fibril strain) and fibril alignment increased while fibril thickness decreased (all p<0.05). Preliminary histological evaluation from slides with orthogonally oriented cuts confirmed the presence of multiple main collagen fiber orientations. Collagen fibers exhibited crimping. Further, the broad ligament samples were cell rich and included small vessels.

Histological evaluation confirmed the presence of multiple predominant fiber orientations as indicated by USAXS. This is in agreement with descriptions of fiber distribution in peritoneum [4]. Compared to reported fibril strains in tendons [5], the observed fibril strain in the broad ligament was smaller. This could be explained by the much higher alignment of collagen fibers to a unidirectional loading axis in tendons. The presented findings provide a more detailed understanding of collagen characteristics of the broad ligament and may contribute to the development of biomechanical models of the uterine support system.

References:

[1] MacLennan et al., 2000, DOI: 10.1111/j.1471-0528.2000.tb11669.x.

[2] Fang et al., 2012, DOI: 10.1038/jid.2012.47.

[3] Euchler et al., 2022, DOI: 10.1088/1742-6596/2380/1/012109.

[4] Liu et al., 2017, DOI: 10.1016/j.biomaterials.2016.11.041.

[5] Barreto et al., 2023, DOI: 10.1016/j.matbio.2022.11.006.

Childbirth trauma during the second stage of labor is a prevalent concern, affecting millions of women worldwide. Levator ani muscle (LAM) trauma, which can impact 6-40% of women undergoing vaginal delivery, particularly nulliparous individuals, is a prevalent injury arising from childbirth. LAM trauma can lead to persistent morbidity and the necessity of future surgical intervention for 10-20% of patients. However, predicting and diagnosing pelvic floor lesions can be challenging. To address this issue, biomechanical simulations have been used as a helpful tool to evaluate pelvic floor muscle (PFM) injuries. However, using the finite element method (FEM) for these simulations can be a time-consuming process. Thus, it is important to explore alternative techniques for applying these methods in a clinical setting. One promising approach is to use machine learning (ML) algorithms, which can leverage simulation data to offer faster results. The present study aims to develop a ML framework to predict stresses on the PFM during childbirth by training ML algorithms on FEM simulation data.

To generate the data, 2744 childbirth simulations were performed in Abaqus software, in which the material parameters of the constitutive model used to characterize the PFM were changed. The constitutive parameters varied between ranges of values ​​according to the literature, thus allowing to characterize the pelvic floor of most women. A total of 1715 simulations were successfully completed.

A dataset was created in which each observation corresponds to a node of the pelvic floor in one simulation. Specifically, 46 nodes located in the inferior portion of the PFM were selected, which is the region that undergoes the most stretching during childbirth. Features such as node number and position, initial coordinates, and material parameters were used for training. Four ML models, namely Random Forest (RF), Extreme Gradient Boosting (XGBT), Support Vector Regression (SVR), and Artificial Neural Networks (ANN), were chosen for the study. A training and test set were created with a 90/10 split, recurring to a stratification method to guarantee the same feature distribution in both sets. Subsequently, hyperparameter optimization with cross-validation was performed. The models' performance was measured by the mean squared error (MSE) and the mean absolute error (MAE).

The stress values were measured at the moment of maximum stretch, and ranged from 0 to 30 MPa. The results for predicting the maximum principal stresses showed that the ANN produced the best outcomes, with a MSE of 0.112 and a MAE of 0.191. Conversely, the SVR model had the highest error, with a MSE of 0.444 and a MAE of 0.356. Both tree-based algorithms performed reasonably well and were closer to the outcomes achieved by the ANN. The ANN is capable of making predictions in approximately 120 milliseconds, indicating its potential for real-time applications.

The current work represents an advance in the field of childbirth computational simulations using artificial intelligence tools. The ability to predict the stresses suffered by the woman on the pelvic floor immediately before or during childbirth could aid in medical decision-making and in the identification of non-visible injuries.

Tissue development in normal and pathological conditions is driven by a set of biological phenomena. Growth is characterized by a change of mass which might be positive (tissue growth) by cell division, cell enlargement, and extracellular matrix secretion, or negative (tissue atrophy) by cell death, cell shrinkage or resorption [1]. Cancer is a malignant pathology characterized by accelerated and uncontrolled cellular growth and proliferation [2]. In 2020, it was estimated 19.3 million newly diagnosed cases and almost 10.0 million cancer deaths, worldwide [3]. The development of solid tumors is a multi-factor biological process, as it is influenced by molecular and genetic factors, cell-cell and cell-extracellular interactions, and vascularization (in particular oxygen and nutrients supply) [4].

Several experimental and theoretical efforts have been taken to unravel the mechanisms of tumor growth. Constitutive mechanics models are one of these approaches as they can help describe mass changes and stress development during the events of tumor progression [4]. From a biomechanical perspective, solid tumors are hyperelastic, compressible, anisotropic materials with a mechanical behavior both space and time-dependent, whose mass varies over time [5]. In this work, the goal is to establish a computational framework to model tissue growth to be latter applied for solid tumors.

Initially, a constitutive model to describe the anisotropic growth of a solid mass is implemented [6] considering the multiplicative decomposition of the deformation gradient into an elastic and a growth contribution [7]. In this first attempt, anisotropic growth is considered a strain-driven process with a privileged direction for growth due to the presence of a micro-structure [8]. To ease the use of this model in more complex scenarios, the constitutive model is implemented into the finite element software Abaqus® using a user-defined subroutine (UMAT). To validate the UMAT subroutine, the numerical solution for a single unitary hexahedral finite element is computed for a set of deformation cases in the software ABAQUS® and compared to the analytical solution [6].

Finally, the UMAT is implemented in an in-silico model of a solid tumor surrounded by the extracellular matrix (simplified by a parallelepiped) and cyclic uniaxial and biaxial stretch scenarios are applied. The Cauchy stresses are recorded in the direction of the applied displacements as function of the stretch. At the unload final state, the embedded tumor presents a positive volume change as the tumor grows irreversibly in an anisotropic manner. Future steps include the incorporation of a tumor growth law derived by experimental evidence and the implementation of a stress-driven anisotropic growth evolution.

References

[1] Ambrosi D, Guana F. Stress-Modulated Growth. Mathematics and Mechanics of Solids 2007;12:319–42. https://doi.org/10.1177/1081286505059739.

[2] Ambrosi D, Amar M Ben, Cyron CJ, DeSimone A, Goriely A, Humphrey JD, et al. Growth and remodelling of living tissues: Perspectives, challenges and opportunities. J R Soc Interface 2019;16. https://doi.org/10.1098/rsif.2019.0233.

[3] Sung H, Ferlay J, Siegel RL, Laversanne M, Soerjomataram I, Jemal A, et al. Global Cancer Statistics 2020: GLOBOCAN Estimates of Incidence and Mortality Worldwide for 36 Cancers in 185 Countries. CA Cancer J Clin 2021;71:209–49. https://doi.org/https://doi.org/10.3322/caac.21660.

[4] Xue S-L, Li B, Feng X-Q, Gao H. Biochemomechanical poroelastic theory of avascular tumor growth. J Mech Phys Solids 2016;94:409–32. https://doi.org/10.1016/j.jmps.2016.05.011.

[5] Ramírez-Torres A, Rodríguez-Ramos R, Merodio J, Penta R, Bravo-Castillero J, Guinovart-Díaz R, et al. The influence of anisotropic growth and geometry on the stress of solid tumors. Int J Eng Sci 2017;119:40–9. https://doi.org/10.1016/j.ijengsci.2017.06.011.

[6] Vila Pouca MCP, Areias P, Göktepe S, Ashton-Miller JA, Natal Jorge RM, Parente MPL. Modeling permanent deformation during low-cycle fatigue: Application to the pelvic floor muscles during labor. J Mech Phys Solids 2022;164:104908. https://doi.org/10.1016/j.jmps.2022.104908.

[7] Rodriguez EK, Hoger A, McCulloch AD. Stress-dependent finite growth in soft elastic tissues. J Biomech 1994;27:455–67. https://doi.org/10.1016/0021-9290(94)90021-3.

[8] Soleimani M, Muthyala N, Marino M, Wriggers P. A novel stress-induced anisotropic growth model driven by nutrient diffusion: Theory, FEM implementation and applications in bio-mechanical problems. J Mech Phys Solids 2020;144:104097. https://doi.org/10.1016/j.jmps.2020.104097.

Acknowledgements: The authors gratefully acknowledge the support from the Portuguese Foundation of Science under the grant SFRH/BD/09480/2022 and the funding of the research project PTDC/EME-APL/1342/2020.

The Finite Element Method (FEM) is a powerful tool that enables the simulation of many complex engineering problems. In complex analysis, such as in the modelling of biological and biomechanical phenomena, it is necessary to specify the constitutive equations that describe the biomechanical behaviour of such materials.

Soft tissues and other biological materials subjected to large deformations present an extremely nonlinear behaviour, which makes the constitutive modelling of such materials a complex task and expensive in terms of time and computational resources. Alternatively, it is possible to use surrogate models, which consist of models that replace the traditional and expensive main models to overcome some computational limitations.

Such surrogates can learn the behaviour of the soft tissue when trained on previously acquired data and then replace the expensive numerical models. To develop the surrogates, Artificial Neural Networks (ANNs) will be trained from a large dataset with the deformations (inputs) and the corresponding stresses (outputs). Then, the weights and biases of the trained model will be used to write the forward pass equations in Fortran to implement a general user material subroutine (UMAT) for the Finite Element software ABAQUS. The surrogate models will be tested under homogeneous deformation cases and under more complex examples, where it is shown the values of the maximum principal stress obtained with a conventional UMAT and with the ANN. In the future, this data driven approach is going to be applied to soft tissues, such as the pelvic floor muscles.

The female pelvic cavity is a very complex anatomical region. Pelvic dysfunction, especially pelvic organ prolapse (POP) and urinary incontinence (UI), have a negative impact on women's lives, and it happens when the support mechanisms of the pelvic cavity become fragile. UI has a prevalence of a up to 28%, with stress urinary incontinence (SUI) being the most common form [1,2], characterized by involuntary urinary leakage during physical strain, coughing or an increase in intra-abdominal pressure (IAP). Existing treatments for these disorders are divided into conservative and invasive. The last ones consist of surgical interventions and should be used in patients in whom the first treatments did not work, or when the severity of the dysfunction is high.

SUI occurs when the intravesical pressure exceeds urethral resistance at which the urethra has the ability to remain closed [2]. Furthermore, it comes to a point when neither the pubourethral ligaments (PULs) [3] and the arcus tendineous fasciae pelvis (ATFP) [4] can stabilize the bladder neck (BN) [5]. Assessment of BN mobility in patients with SUI is essentially clinical, however, the imaging techniques such as ultrasound (US) and magnetic resonance imaging (MRI) are used as a method for evaluating this characteristic. The outcomes of radiographic images have been crucial and used as input for numerical methods.

The aim of the present study was to establish the IAP values and the in vivo biomechanical properties of the bladder tissue for two distinct groups (continent women and women with SUI). The numerical simulations of Valsalva maneuver were performed, applying the Ogden hyperelastic constitutive model to the bladder and also the inverse finite element analysis (FEA).

This study focuses on adapting an inverse FEA to estimate the in vivo properties of the bladder, using a constitutive model of the female pelvic cavity and MR images acquired at rest and during the Valsalva maneuver, for two distinct groups (continent and incontinent women). The bladder neck’s displacements were compared between computational simulation and MR images.

The results of the FEA showed that the bladder tissue of incontinent women have the highest stiffness approximately 47% higher when compared to continent women.

References

1. Jansson MH, et al. Stress and urgency urinary incontinence one year after a first birth—prevalence and risk factors. A prospective cohort study. Acta Obstetricia et Gynecologica Scandinavica 2021; 100(12):2193–2201.

2. Falah-Hassani K, et al. The pathophysiology of stress urinary incontinence: a systematic review and meta-analysis. International Urogynecology Journal 2021; 32(3):501–552.

3. Kefer JC, et al. Pubo-urethral ligament transection causes stress urinary incontinence in the female rat: A novel animal model of stress urinary incontinence. Journal of Urology 2008; 179(2):775–778.

4. Iyer J, et al. Introduction and Epidemiology of Pelvic Floor Dysfunction. In: Rane A, Rane A, Durrant J, Tamilselvi A, Sandhya G, eds. Ambulatory Urology and Urogynaecology. Wiley Online Library; 2021.

5. Occelli B, et al. Anatomic study of arcus tendineus fasciae pelvis. European Journal of Obstetrics and Gynecology and Reproductive Biology 2001; 97(2):213–219.