A model of Stokesian peristalsis and vesicle transport in a three-dimensional closed cavity

Tissue hydraulics in reproduction

The development of functional eggs and sperm are critical processes in mammalian development as they ensure successful reproduction and species propagation. While past studies have identified important genes that regulate these processes, the roles of luminal flow and fluid stress in reproductive biology remain less well understood. Here, we discuss recent evidence that support the diverse functions of luminal fluid in oogenesis, spermatogenesis and embryogenesis. We also review emerging techniques that allow for precise quantification and perturbation of tissue hydraulics in female and male reproductive systems, and propose new questions and approaches in this field. We hope this review will provide a useful resource to inspire future research in tissue hydraulics in reproductive biology and diseases.

Rapid Prototypable Biomimetic Peristalsis Bioreactor Capable of Concurrent Shear and Multi-Axial Strain

Peristalsis is a nuanced mechanical stimulus comprised of multi-axial strain (radial and axial strain) and shear stress. Forces associated with peristalsis regulate diverse biological functions including digestion, reproductive function, and urine dynamics. Given the central role peristalsis plays in physiology and pathophysiology, we were motivated to design a bioreactor capable of holistically mimicking peristalsis. We engineered a novel rotating screw-drive based design combined with a peristaltic pump, in order to deliver multi-axial strain and concurrent shear stress to a biocompatible polydimethylsiloxane (PDMS) membrane "wall." Radial indentation and rotation of the screw drive against the wall demonstrated multi-axial strain evaluated via finite element modeling. Experimental measurements of strain using piezoelectric strain resistors were in close alignment with model-predicted values (15.9 ± 4.2% vs. 15.2% predicted). Modeling of shear stress on the "wall" indicated a uniform velocity profile and a moderate shear stress of 0.4 Pa. Human mesenchymal stem cells (hMSCs) seeded on the PDMS "wall" and stimulated with peristalsis demonstrated dramatic changes in actin filament alignment, proliferation, and nuclear morphology compared to static controls, perfusion, or strain, indicating that hMSCs sensed and responded to peristalsis uniquely. Lastly, significant differences were observed in gene expression patterns of calponin, caldesmon, smooth muscle actin, and transgelin, corroborating the propensity of hMSCs toward myogenic differentiation in response to peristalsis. Collectively, our data suggest that the peristalsis bioreactor is capable of generating concurrent multi-axial strain and shear stress on a "wall." hMSCs experience peristalsis differently than perfusion or strain, resulting in changes in proliferation, actin fiber organization, smooth muscle actin expression, and genetic markers of differentiation. The peristalsis bioreactor device has broad utility in the study of development and disease in several organ systems.

Driving a Microswimmer with Wall-Induced Flow

Active walls such as cilia and bacteria carpets generate background flows that can influence the trajectories of microswimmers moving nearby. Recent advances in artificial magnetic cilia carpets offer the potentiality to use a similar wall-generated background flow to steer bio-hybrid microrobots. In this paper, we provide some ground theoretical and numerical work assessing the viability of this novel means of swimmer guidance by setting up a simple model of a spherical swimmer in an oscillatory flow and analysing it from the control theory viewpoint. We show a property of local controllability around the reference free trajectories and investigate the bang-bang structure of the control for time-optimal trajectories, with an estimation of the minimal time for suitable objectives. By direct simulation, we have demonstrated that the wall actuation can improve the wall-following transport by nearly 50%, which can be interpreted by synchronous flow structure. Although an open-loop control with a periodic bang-bang actuation loses some robustness and effectiveness, a feedback control is found to improve its robustness and effective transport, even with hydrodynamic wall-swimmer interactions. The results shed light on the potentialities of flow control and open the way to future experiments on swimmer guidance.

Biomechanics of Early Life in the Female Reproductive Tract

Early human life that starts at the onset of fertilization and ends with implantation of the embryo in the uterine wall is the foundation for a successful pregnancy. The different stages during this period require biomechanical mechanisms, which are mostly unknown due to difficulties to conduct in vivo studies in humans.

Electro-Osmosis Modulated Viscoelastic Embryo Transport in Uterine Hydrodynamics: Mathematical Modeling

Embryological transport features a very interesting and complex application of peristaltic fluid dynamics. Electro-osmotic phenomena are also known to arise in embryo transfer location. The fluid dynamic environment in embryological systems is also known to be non-Newtonian and exhibits strong viscoelastic properties. Motivated by these applications, the present article develops a new mathematical model for simulating two-dimensional peristaltic transport of a viscoelastic fluid in a tapered channel under the influence of electro-osmosis induced by asymmetric zeta potentials at the channel walls. The robust Jeffrey viscoelastic model is utilized. The finite Debye layer electro-kinetic approximation is deployed. The moving boundary problem is transformed to a steady boundary problem in the wave frame. The current study carries significant physiological relevance to an ever-increasing desire to study intrauterine fluid flow motion in an artificial uterus. The consequences of this model may introduce a new mechanical factor for embryo transport to a successful implantation site. Hydrodynamic characteristics are shown to be markedly influenced by the electro-osmosis, the channel taper angle, and the phase shift between the channel walls. Furthermore, it is demonstrated that volumetric flow rates and axial flow are both enhanced when the electro-osmotic force aids the axial flow for specific values of zeta potential ratio. Strong trapping of the bolus (representative of the embryo) is identified in the vicinity of the channel central line when the electro-osmosis opposes axial flow. The magnitude of the trapped bolus is observed to be significantly reduced with increasing tapered channel length whereas embryo axial motility is assisted with aligned electro-osmotic force.

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.

Interaction of toroidal swimmers in Stokes flow

A doughnut-shaped object supporting surface rotations was a hypothetical construct proposed by both Taylor and Purcell as a swimmer that would be able to propel itself in a Stokesian fluid because of the irreversibility of its stroke. Here we numerically examine the hydrodynamic interaction of pairs and trios of these free toroidal swimmers. First, we study the axisymmetric case of two toroidal swimmers placed in tandem, and show that a single torus of a corotating pair is more efficient than when it swims alone, but less efficient when paired with a counterrotating partner. Using a regularized Stokeslet framework, we study the nonaxisymmetric case of toroidal swimmers whose axes are initially parallel, but not collinear. These perturbed in tandem swimmers can exhibit qualitatively different trajectories that may, for instance, repel the swimmers or have them settle into a periodic state. We also illustrate interesting dynamics that occur for different initial configurations of three tori.

Morphogenetic implications of peristaltic fluid-tissue dynamics in the embryonic lung

Peristalsis begins in the lung as soon as the smooth muscle forms, and persists until birth. Since the prenatal lung is liquid-filled, smooth muscle action can deform tissues and transport fluid far from the immediately adjacent tissues. Stretching of embryonic tissues and sensation of internal fluid flows have been shown to have potent morphogenetic effects. We hypothesize that these effects are at work in lung morphogenesis. To place that hypothesis in a quantitative framework, we analyze a model of the fluid-structure interactions between embryonic tissues and lumen fluid resulting from peristaltic waves that partially occlude the airway. We find that if the airway is closed, deformations are synchronized; by contrast, if the trachea is open, maximal occlusion precedes maximal pressure. We perform a parametric analysis of how occlusion, stretch, and flow depend on tissue stiffnesses, smooth muscle force, tissue shape and size, and fluid viscosity. We find that most of these relationships are governed by simple ratios.