A continuum model for excitation-contraction of smooth muscle under finite deformations

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.

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.

A Chemomechanobiological Model of the Long-Term Healing Response of Arterial Tissue to a Clamping Injury

Vascular clamping often causes injury to arterial tissue, leading to a cascade of cellular and extracellular events. A reliable in silico prediction of these processes following vascular injury could help us to increase our understanding thereof, and eventually optimize surgical techniques or drug delivery to minimize the amount of long-term damage. However, the complexity and interdependency of these events make translation into constitutive laws and their numerical implementation particularly challenging. We introduce a finite element simulation of arterial clamping taking into account acute endothelial denudation, damage to extracellular matrix, and smooth muscle cell loss. The model captures how this causes tissue inflammation and deviation from mechanical homeostasis, both triggering vascular remodeling. A number of cellular processes are modeled, aiming at restoring this homeostasis, i.e., smooth muscle cell phenotype switching, proliferation, migration, and the production of extracellular matrix. We calibrated these damage and remodeling laws by comparing our numerical results to in vivo experimental data of clamping and healing experiments. In these same experiments, the functional integrity of the tissue was assessed through myograph tests, which were also reproduced in the present study through a novel model for vasodilator and -constrictor dependent smooth muscle contraction. The simulation results show a good agreement with the in vivo experiments. The computational model was then also used to simulate healing beyond the duration of the experiments in order to exploit the benefits of computational model predictions. These results showed a significant sensitivity to model parameters related to smooth muscle cell phenotypes, highlighting the pressing need to further elucidate the biological processes of smooth muscle cell phenotypic switching in the future.

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.

Biomechanics of the human uterus

The appropriate biomechanical function of the uterus is required for the execution of human reproduction. These functions range from aiding the transport of the embryo to the implantation site, to remodeling its tissue walls to host the placenta, to protecting the fetus during gestation, to contracting forcefully for a safe parturition and postpartum, to remodeling back to its nonpregnant condition to renew the cycle of menstruation. To serve these remarkably diverse functions, the uterus is optimally geared with evolving and contractile muscle and tissue layers that are cued by chemical, hormonal, electrical, and mechanical signals. The relationship between these highly active biological signaling mechanisms and uterine biomechanical function is not completely understood for normal reproductive processes and pathological conditions such as adenomyosis, endometriosis, infertility and preterm labor. Animal studies have illuminated the rich structural function of the uterus, particularly in pregnancy. In humans, medical imaging techniques in ultrasound and magnetic resonance have been combined with computational engineering techniques to characterize the uterus in vivo, and advanced experimental techniques have explored uterine function using ex vivo tissue samples. The collective evidence presented in this review gives an overall perspective on uterine biomechanics related to both its nonpregnant and pregnant function, highlighting open research topics in the field. Additionally, uterine disease and infertility are discussed in the context of tissue injury and repair processes and the role of computational modeling in uncovering etiologies of disease. WIREs Syst Biol Med 2017, 9:e1388. doi: 10.1002/wsbm.1388 For further resources related to this article, please visit the WIREs website.

Identification of the mechanical parameters for the human uterus in vivo using intrauterine pressure measurements

There are limited experimental data to characterize the mechanical response of human myometrium. A method is presented in this work to identify mechanical parameters describing the active response of human myometrium from the in vivo intrauterine pressure measurements. The human uterine contraction during labor is simulated by implementing a coupled model in a finite element scheme, and the intrauterine pressure is evaluated as the outcome. A meta-model is developed to approximate the finite element simulation response with a lower computational cost and used to identify model parameters through fitting its prediction to the in vivo measurements. Copyright © 2016 John Wiley & Sons, Ltd.

Length adaptation of smooth muscle contractile filaments in response to sustained activation

Airway and bladder smooth muscles are known to undergo length adaptation under sustained contraction. This adaptation process entails a remodelling of the intracellular actin and myosin filaments which shifts the peak of the active force-length curve towards the current length. Smooth muscles are therefore able to generate the maximum force over a wide range of lengths. In contrast, length adaptation of vascular smooth muscle has attracted very little attention and only a handful of studies have been reported. Although their results are conflicting on the existence of a length adaptation process in vascular smooth muscle, it seems that, at least, peripheral arteries and arterioles undergo such adaptation. This is of interest since peripheral vessels are responsible for pressure regulation, and a length adaptation will affect the function of the cardiovascular system. It has, e.g., been suggested that the inward remodelling of resistance vessels associated with hypertension disorders may be related to smooth muscle adaptation. In this study we develop a continuum mechanical model for vascular smooth muscle length adaptation by assuming that the muscle cells remodel the actomyosin network such that the peak of the active stress-stretch curve is shifted towards the operating point. The model is specialised to hamster cheek pouch arterioles and the simulated response to stepwise length changes under contraction. The results show that the model is able to recover the salient features of length adaptation reported in the literature.

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

Contractions of uterine smooth muscle cells consist of a chain of physiological processes. These contractions provide the required force to expel the fetus from the uterus. The inclusion of these physiological processes is, therefore, imperative when studying uterine contractions. In this study, an electro-chemo-mechanical model to replicate the excitation, activation, and contraction of uterine smooth muscle cells is developed. The presented modeling strategy enables efficient integration of knowledge about physiological processes at the cellular level to the organ level. The model is implemented in a three-dimensional finite element setting to simulate uterus contraction during labor in response to electrical discharges generated by pacemaker cells and propagated within the myometrium via gap junctions. Important clinical factors, such as uterine electrical activity and intrauterine pressure, are predicted using this simulation. The predictions are in agreement with clinically measured data reported in the literature. A parameter study is also carried out to investigate the impact of physiologically related parameters on the uterine contractility.

Bio-Chemo-Mechanical Models of Vascular Mechanics

Models of vascular mechanics are necessary to predict the response of an artery under a variety of loads, for complex geometries, and in pathological adaptation. Classic constitutive models for arteries are phenomenological and the fitted parameters are not associated with physical components of the wall. Recently, microstructurally-linked models have been developed that associate structural information about the wall components with tissue-level mechanics. Microstructurally-linked models are useful for correlating changes in specific components with pathological outcomes, so that targeted treatments may be developed to prevent or reverse the physical changes. However, most treatments, and many causes, of vascular disease have chemical components. Chemical signaling within cells, between cells, and between cells and matrix constituents affects the biology and mechanics of the arterial wall in the short- and long-term. Hence, bio-chemo-mechanical models that include chemical signaling are critical for robust models of vascular mechanics. This review summarizes bio-mechanical and bio-chemo-mechanical models with a focus on large elastic arteries. We provide applications of these models and challenges for future work.