Large-amplitude, short-wave peristalsis and its implications for transport

Mixed uncertainty analysis on pumping by peristaltic hearts using Dempster-Shafer theory

In this paper, we introduce the numerical strategy for mixed uncertainty propagation based on probability and Dempster-Shafer theories, and apply it to the computational model of peristalsis in a heart-pumping system. Specifically, the stochastic uncertainty in the system is represented with random variables while epistemic uncertainty is represented using non-probabilistic uncertain variables with belief functions. The mixed uncertainty is propagated through the system, resulting in the uncertainty in the chosen quantities of interest (QoI, such as flow volume, cost of transport and work). With the introduced numerical method, the uncertainty in the statistics of QoIs will be represented using belief functions. With three representative probability distributions consistent with the belief structure, global sensitivity analysis has also been implemented to identify important uncertain factors and the results have been compared between different peristalsis models. To reduce the computational cost, physics constrained generalized polynomial chaos method is adopted to construct cheaper surrogates as approximations for the full simulation.

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.

Valveless pumping behavior of the simulated embryonic heart tube as a function of contractile patterns and myocardial stiffness

During development, the heart begins pumping as a valveless multilayered tube capable of driving blood flow throughout the embryonic vasculature. The mechanical properties and how they interface with pumping function are not well-defined at this stage. Here, we evaluate pumping patterns using a fluid-structure interaction computational model, combined with experimental data and an energetic analysis to investigate myocardial mechanical properties. Through this work, we propose that a myocardium modeled as a Neo-Hookean material with a material constant on the order of 10 kPa is necessary for the heart tube to function with an optimal pressure and cardiac output.

Frequency-specific, valveless flow control in insect-mimetic microfluidic devices

Inexpensive, portable lab-on-a-chip devices would revolutionize fields like environmental monitoring and global health, but current microfluidic chips are tethered to extensive off-chip hardware. Insects, however, are self-contained and expertly manipulate fluids at the microscale using largely unexplored methods. We fabricated a series of microfluidic devices that mimic key features of insect respiratory kinematics observed by synchrotron-radiation imaging, including the collapse of portions of multiple respiratory tracts in response to a single fluctuating pressure signal. In one single-channel device, the flow rate and direction could be controlled by the actuation frequency alone, without the use of internal valves. Additionally, we fabricated multichannel chips whose individual channels responded selectively (on with a variable, frequency-dependent flow rate, or off) to a single, global actuation frequency. Our results demonstrate that insect-mimetic designs have the potential to drastically reduce the actuation overhead for microfluidic chips, and that insect respiratory systems may share features with impedance-mismatch pumps.

MHD peristaltic flow of nanofluid in a vertical channel with multiple slip features: an application to chyme movement

The mathematical modelling of biological fluids is of utmost importance due to its applications in various fields of medicine. The peristaltic mechanism plays a crucial role in understanding numerous biological flows. The current paper emphasizes on the MHD peristalsis of Jeffrey nanofluid flowing through a vertical channel when subjected to the combined heat/mass transportation. The equations for the current flow scenario are developed with relevant assumptions for which the perturbation technique is followed to simulate the solution. The expressions of velocity, temperature and concentration are obtained, and the solutions of skin-friction coefficient, Nusselt number and Sherwood number at the wall are acquired. Further, the influence of relevant parameters on various physical quantities for both non-Newtonian Jeffery and viscous fluid is graphically analyzed. The outcomes are deliberated in detail Further, it is renowned that the current study has many biomechanical applications such as the movement of chyme motion in the gastrointestinal tract and during the surgery to take control of the flow of blood by adjusting the magnetic field intensity.

A semi-automated finite difference mesh creation method for use with immersed boundary software IB2d and IBAMR

Numerous fluid-structure interaction problems in biology have been investigated using the immersed boundary method. The advantage of this method is that complex geometries, e.g., internal or external morphology, can easily be handled without the need to generate matching grids for both the fluid and the structure. Consequently, the difficulty of modeling the structure lies often in discretizing the boundary of the complex geometry (morphology). Both commercial and open source mesh generators for finite element methods have long been established; however, the traditional immersed boundary method is based on a finite difference discretization of the structure. Here we present a software library for obtaining finite difference discretizations of boundaries for direct use in the 2D immersed boundary method. This library provides tools for extracting such boundaries as discrete mesh points from digital images. We give several examples of how the method can be applied that include passing flow through the veins of insect wings, within lymphatic capillaries, and around starfish using open-source immersed boundary software.

Uncertainty quantification reveals the physical constraints on pumping by peristaltic hearts

Most biological functional systems are complex, and this complexity is a fundamental driver of diversity. Because input parameters interact in complex ways, a holistic understanding of functional systems is key to understanding how natural selection produces diversity. We present uncertainty quantification (UQ) as a quantitative analysis tool on computational models to study the interplay of complex systems and diversity. We investigate peristaltic pumping in a racetrack circulatory system using a computational model and analyse the impact of three input parameters (Womersley number, compression frequency, compression ratio) on flow and the energetic costs of circulation. We employed two models of peristalsis (one that allows elastic interactions between the heart tube and fluid and one that does not), to investigate the role of elastic interactions on model output. A computationally cheaper surrogate of the input parameter space was created with generalized polynomial chaos expansion to save computational resources. Sobol indices were then calculated based on the generalized polynomial chaos expansion and model output. We found that all flow metrics were highly sensitive to changes in compression ratio and insensitive to Womersley number and compression frequency, consistent across models of peristalsis. Elastic interactions changed the patterns of parameter sensitivity for energetic costs between the two models, revealing that elastic interactions are probably a key physical metric of peristalsis. The UQ analysis created two hypotheses regarding diversity: favouring high flow rates (where compression ratio is large and highly conserved) and minimizing energetic costs (which avoids combinations of high compression ratios, high frequencies and low Womersley numbers).

An Immersed Interface Method for Discrete Surfaces

Fluid-structure systems occur in a range of scientific and engineering applications. The immersed boundary (IB) method is a widely recognized and effective modeling paradigm for simulating fluid-structure interaction (FSI) in such systems, but a difficulty of the IB formulation of these problems is that the pressure and viscous stress are generally discontinuous at fluid-solid interfaces. The conventional IB method regularizes these discontinuities, which typically yields low-order accuracy at these interfaces. The immersed interface method (IIM) is an IB-like approach to FSI that sharply imposes stress jump conditions, enabling higher-order accuracy, but prior applications of the IIM have been largely restricted to numerical methods that rely on smooth representations of the interface geometry. This paper introduces an immersed interface formulation that uses only a C 0 representation of the immersed interface, such as those provided by standard nodal Lagrangian finite element methods. Verification examples for models with prescribed interface motion demonstrate that the method sharply resolves stress discontinuities along immersed boundaries while avoiding the need for analytic information about the interface geometry. Our results also demonstrate that only the lowest-order jump conditions for the pressure and velocity gradient are required to realize global second-order accuracy. Specifically, we demonstrate second-order global convergence rates along with nearly second-order local convergence in the Eulerian velocity field, and between first- and second-order global convergence rates along with approximately first-order local convergence for the Eulerian pressure field. We also demonstrate approximately second-order local convergence in the interfacial displacement and velocity along with first-order local convergence in the fluid traction along the interface. As a demonstration of the method's ability to tackle more complex geometries, the present approach is also used to simulate flow in a patient-averaged anatomical model of the inferior vena cava, which is the large vein that carries deoxygenated blood from the lower extremities back to the heart. Comparisons of the general hemodynamics and wall shear stress obtained by the present IIM and a body-fitted discretization approach show that the present method yields results that are in good agreement with those obtained by the body-fitted approach.

Kinking and Torsion Can Significantly Improve the Efficiency of Valveless Pumping in Periodically Compressed Tubular Conduits. Implications for Understanding of the Form-Function Relationship of Embryonic Heart Tubes

Valveless pumping phenomena (peristalsis, Liebau-effect) can generate unidirectional fluid flow in periodically compressed tubular conduits. Early embryonic hearts are tubular conduits acting as valveless pumps. It is unclear whether such hearts work as peristaltic or Liebau-effect pumps. During the initial phase of its pumping activity, the originally straight embryonic heart is subjected to deforming forces that produce bending, twisting, kinking, and coiling. This deformation process is called cardiac looping. Its function is traditionally seen as generating a configuration needed for establishment of correct alignments of pulmonary and systemic flow pathways in the mature heart of lung-breathing vertebrates. This idea conflicts with the fact that cardiac looping occurs in all vertebrates, including gill-breathing fishes. We speculate that looping morphogenesis may improve the efficiency of valveless pumping. To test the physical plausibility of this hypothesis, we analyzed the pumping performance of a Liebau-effect pump in straight and looped (kinked) configurations. Compared to the straight configuration, the looped configuration significantly improved the pumping performance of our pump. This shows that looping can improve the efficiency of valveless pumping driven by the Liebau-effect. Further studies are needed to clarify whether this finding may have implications for understanding of the form-function relationship of embryonic hearts.