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.

Effect of constitutive law on the erythrocyte membrane response to large strains.

Three constitutive laws, that is the Skalak, neo-Hookean and Yeoh laws, commonly employed for describing the erythrocyte membrane mechanics are theoretically analyzed and numerically investigated to assess their accuracy for capturing erythrocyte deformation characteristics and morphology. Particular emphasis is given to the nonlinear deformation regime, where it is known that the discrepancies between constitutive laws are most prominent. Hence, the experiments of optical tweezers and micropipette aspiration are considered here, for which relationships between the individual shear elastic moduli of the constitutive laws can also be established through analysis of the tension-deformation relationship. All constitutive laws were found to adequately predict the axial and transverse deformations of a red blood cell subjected to stretching with optical tweezers for a constant shear elastic modulus value. As opposed to Skalak law, the neo-Hookean and Yeoh laws replicated the erythrocyte membrane folding, that has been experimentally observed, with the trade-off of sustaining significant area variations. For the micropipette aspiration, the suction pressure-aspiration length relationship could be excellently predicted for a fixed shear elastic modulus value only when Yeoh law was considered. Importantly, the neo-Hookean and Yeoh laws reproduced the membrane wrinkling at suction pressures close to those experimentally measured. None of the constitutive laws suffered from membrane area compressibility in the micropipette aspiration case.

An Explicit-Correction-Force Scheme of IB-LBM Based on Interpolated Particle Distribution Function.

In order to obtain a better numerical simulation method for fluid-structure interaction (FSI), the IB-LBM combining the lattice Boltzmann method (LBM) and immersed boundary method (IBM) has been studied more than a decade. For this purpose, an explicit correction force scheme of IB-LBM was proposed in this paper. Different from the current IB-LBMs, this paper introduced the particle distribution function to the interpolation process from the fluid grids to the immersed boundary at the mesoscopic level and directly applied the LBM force models to obtain the interface force with a simple form and explicit process. Then, in order to ensure the mass conservation in the local area of the interface, this paper corrected the obtained interface force with the correction matrix, forming the total explicit-correction-force (ECP) scheme of IB-LBM. The results of four numerical tests were used to verify the order of accuracy and effectiveness of the present method. The streamline penetration is limited and the numerical simulation with certain application significance is successful for complex boundary conditions such as the movable rigid bodies (free oscillation of the flapping foil) and flexible deformable bodies (free deformation of cylinders). In summary, we obtained a simple and alternative simulation method that can achieve good simulation results for engineering reference models with complex boundary problems.

A Simplified Linearized Lattice Boltzmann Method for Acoustic Propagation Simulation.

A simplified linearized lattice Boltzmann method (SLLBM) suitable for the simulation of acoustic waves propagation in fluids was proposed herein. Through Chapman-Enskog expansion analysis, the linearized lattice Boltzmann equation (LLBE) was first recovered to linearized macroscopic equations. Then, using the fractional-step calculation technique, the solution of these linearized equations was divided into two steps: a predictor step and corrector step. Next, the evolution of the perturbation distribution function was transformed into the evolution of the perturbation equilibrium distribution function using second-order interpolation approximation of the latter at other positions and times to represent the nonequilibrium part of the former; additionally, the calculation formulas of SLLBM were deduced. SLLBM inherits the advantages of the linearized lattice Boltzmann method (LLBM), calculating acoustic disturbance and the mean flow separately so that macroscopic variables of the mean flow do not affect the calculation of acoustic disturbance. At the same time, it has other advantages: the calculation process is simpler, and the cost of computing memory is reduced. In addition, to simulate the acoustic scattering problem caused by the acoustic waves encountering objects, the immersed boundary method (IBM) and SLLBM were further combined so that the method can simulate the influence of complex geometries. Several cases were used to validate the feasibility of SLLBM for simulation of acoustic wave propagation under the mean flow.

Thermal Lattice Boltzmann Flux Solver for Natural Convection of Nanofluid in a Square Enclosure.

In the present study, mathematical modeling was performed to simulate natural convection of a nanofluid in a square enclosure using the thermal lattice Boltzmann flux solver (TLBFS). Firstly, natural convection in a square enclosure, filled with pure fluid (air and water), was investigated to validate the accuracy and performance of the method. Then, influences of the Rayleigh number, of nanoparticle volume fraction on streamlines, isotherms and average Nusselt number were studied. The numerical results illustrated that heat transfer was enhanced with the augmentation of Rayleigh number and nanoparticle volume fraction. There was a linear relationship between the average Nusselt number and solid volume fraction. and there was an exponential relationship between the average Nusselt number and Ra. In view of the Cartesian grid used by the immersed boundary method and lattice model, the immersed boundary method was chosen to treat the no-slip boundary condition of the flow field, and the Dirichlet boundary condition of the temperature field, to facilitate natural convection around a bluff body in a square enclosure. The presented numerical algorithm and code implementation were validated by means of numerical examples of natural convection between a concentric circular cylinder and a square enclosure at different aspect ratios. Numerical simulations were conducted for natural convection around a cylinder and square in an enclosure. The results illustrated that nanoparticles enhance heat transfer in higher Rayleigh number, and the heat transfer of the inner cylinder is stronger than that of the square at the same perimeter.

Hydrodynamic Behavior of Self-Propelled Particles in a Simple Shear Flow.

The hydrodynamic properties of a squirmer type of self-propelled particle in a simple shear flow are investigated using the immersed boundary-lattice Boltzmann method in the range of swimming Reynolds number 0.05 ≤ Res ≤ 2.0, flow Reynolds number 40 ≤ Rep ≤ 160, blocking rate 0.2 ≤ κ ≤ 0.5. Some results are validated by comparing with available other results. The effects of Res, Rep and κ on the hydrodynamic properties of squirmer are discussed. The results show that there exist four distinct motion modes for the squirmer, i.e., horizontal mode, attractive oscillation mode, oscillation mode, and chaotic mode. Increasing Res causes the motion mode of the squirmer to change from a constant tumbling near the centerline to a stable horizontal mode, even an oscillatory or appealing oscillatory mode near the wall. Increasing the swimming intensity of squirmer under the definite Res will induce the squirmer to make periodic and stable motion at a specific distance from the wall. Increasing Rep will cause the squirmer to change from a stable swimming state to a spiral motion or continuous rotation. Increasing κ will strengthen the wall's attraction to the squirmer. Increasing swimming intensity of squirmer will modify the strength and direction of the wall's attraction to the squirmer if κ remains constant.

Digital transformation of droplet/aerosol infection risk assessment realized on "Fugaku" for the fight against COVID-19.

The fastest supercomputer in 2020, Fugaku, has not only achieved digital transformation of epidemiology in allowing end-to-end, detailed quantitative modeling of COVID-19 transmissions for the first time but also transformed the behavior of the entire Japanese public through its detailed analysis of transmission risks in multitudes of societal situations entailing heavy risks. A novel aerosol simulation methodology was synthesized out of a combination of a new CFD methods meeting industrial demands in the solver, CUBE (Jansson et al., 2019), which not only allowed the simulations to scale massively with high resolution required for micrometer virus-containing aerosol particles but also enabled extremely rapid time-to-solution due to its ability to generate the digital twins representing multitudes of societal situations in a matter of minutes, attaining true overall application high performance; such simulations have been running for the past 1.5°years on Fugaku, cumulatively consuming top supercomputer-class resources and the communicated by the media as well as becoming the basis for official public policies.

Lattice Boltzmann simulations on the tumbling to tank-treading transition: effects of membrane viscosity.

The tumbling to tank-treading (TB-TT) transition for red blood cells (RBCs) has been widely investigated, with a main focus on the effects of the viscosity ratio [Formula: see text] (i.e., the ratio between the viscosities of the fluids inside and outside the membrane) and the shear rate [Formula: see text] applied to the RBC. However, the membrane viscosity [Formula: see text] plays a major role in a realistic description of RBC dynamics, and only a few works have systematically focused on its effects on the TB-TT transition. In this work, we provide a parametric investigation on the effect of membrane viscosity [Formula: see text] on the TB-TT transition for a single RBC. It is found that, at fixed viscosity ratios [Formula: see text], larger values of [Formula: see text] lead to an increased range of values of capillary number at which the TB-TT transition occurs; moreover, we found that increasing [Formula: see text] or increasing [Formula: see text] results in a qualitatively but not quantitatively similar behaviour. All results are obtained by means of mesoscale numerical simulations based on the lattice Boltzmann models. This article is part of the theme issue 'Progress in mesoscale methods for fluid dynamics simulation'.

Electrodiffusion with Calcium-Activated Potassium Channels in Dendritic Spine.

We investigate calcium signaling feedback through calcium-activated potassium channels of a dendritic spine by applying the immersed boundary method with electrodiffusion. We simulate the stochastic gating of such ion channels and the resulting spatial distribution of concentration, current, and membrane voltage within the dendritic spine. In this simulation, the permeability to ionic flow across the membrane is regulated by the amplitude of chemical potential barriers. With spatially localized ion channels, chemical potential barriers are locally and stochastically regulated. This regulation represents the ion channel gating with multiple subunits, the open and closed states governed by a continuous-time Markov process. The model simulation recapitulates an inhibitory action on voltage-sensitive calcium channels by the calcium-activated potassium channels in a stochastic manner as a non-local feedback loop. The model predicts amplified calcium influx with more closely placed channel complexes, proposing a potential mechanism of differential calcium handling by channel distributions. This work provides a foundation for future computer simulation studies of dendritic spine motility and structural plasticity.

Exploring the sensitivity in jellyfish locomotion under variations in scale, frequency, and duty cycle.

Jellyfish have been called one of the most energy-efficient animals in the world due to the ease in which they move through their fluid environment, by product of their bell kinematics coupled with their morphological, muscular, material properties. We investigated jellyfish locomotion by conducting in silico comparative studies and explored swimming performance across different fluid scales (i.e., Reynolds Number), bell contraction frequencies, and contraction phase kinematics (duty cycle) for a jellyfish with a fineness ratio of 1 (ratio of bell height to bell diameter). To study these relationships, an open source implementation of the immersed boundary method was used (IB2d) to solve the fully coupled fluid-structure interaction problem of a flexible jellyfish bell in a viscous fluid. Thorough 2D parameter subspace explorations illustrated optimal parameter combinations in which give rise to enhanced swimming performance. All performance metrics indicated a higher sensitivity to bell actuation frequency than fluid scale or duty cycle, via Sobol sensitivity analysis, on a higher performance parameter subspace. Moreover, Pareto-like fronts were identified in the overall performance space involving the cost of transport and forward swimming speed. Patterns emerged within these performance spaces when highlighting different parameter regions, which complemented the global sensitivity results. Lastly, an open source computational model for jellyfish locomotion is offered to the science community that can be used as a starting place for future numerical experimentation.

Pumping Patterns and Work Done During Peristalsis in Finite-Length Elastic Tubes.

Balloon dilation catheters are often used to quantify the physiological state of peristaltic activity in tubular organs and comment on their ability to propel fluid which is important for healthy human function. To fully understand this system's behavior, we analyzed the effect of a solitary peristaltic wave on a fluid-filled elastic tube with closed ends. A reduced order model that predicts the resulting tube wall deformations, flow velocities, and pressure variations is presented. This simplified model is compared with detailed fluid-structure three-dimensional (3D) immersed boundary (IB) simulations of peristaltic pumping in tube walls made of hyperelastic material. The major dynamics observed in the 3D simulations were also displayed by our one-dimensional (1D) model under laminar flow conditions. Using the 1D model, several pumping regimes were investigated and presented in the form of a regime map that summarizes the system's response for a range of physiological conditions. Finally, the amount of work done during a peristaltic event in this configuration was defined and quantified. The variation of elastic energy and work done during pumping was found to have a unique signature for each regime. An extension of the 1D model is applied to enhance patient data collected by the device and find the work done for a typical esophageal peristaltic wave. This detailed characterization of the system's behavior aids in better interpreting the clinical data obtained from dilation catheters. Additionally, the pumping capacity of the esophagus can be quantified for comparative studies between disease groups.

Vascular journey and adhesion mechanics of micro-sized carriers in narrow capillaries.

In this work a Lattice Boltzmann-Immersed Boundary method is used for predicting the dynamics of rigid and deformable adhesive micro-carriers (1 µm) navigating a capillary by the size of 10 µm with 20% hematocrit. Red cells and particles are modeled as a collection of mass-spring elements responding to a bending potential, an elastic potential and total enclosed area conservation constraint. Furthermore, particle surfaces are uniformly decorated with adhesive molecules (ligands) interacting with receptors disposed on the walls. Particle adhesion is modeled as a short-range ligad-receptor interaction and in term of formation and destruction probability functions that discriminate whether a chemical bond can be formed or destroyed. If a bond is established an attractive elastic force is activated. Particle transport and adhesion are characterized in terms of their ability to reach the capillary peripheries (margination rate) and firmly adhere the vasculature. This analysis is carried out systematically by varying particles' and cells' releasing positions and stiffness (Ca = 0 and 10-2). Moreover, three rigid and soft representative particles are transported on a finer mesh (Δx = 15 nm) and the chemical strength of their adhesive coating is varied (σ = 0.5, 1.0, and 2.0) to precisely analyze the resulting adhesion mechanics. Stiffness is found to weakly influence the margination rate while significantly affect the ability of such constructs to efficiently interact with the endothelium by forming stable chemical bonds.

Collective Pulsing in Xeniid Corals: Part II-Using Computational Fluid Dynamics to Determine if There are Benefits to Coordinated Pulsing.

Coordinated movements have been shown to enhance the speed or efficiency of swimming, flying, and pumping in many organisms. Coordinated pulsing has not been observed in many cnidarians (jellyfish, anemones, corals), as is the case for the xeniid corals considered in our corresponding paper. This observation opens the question as to whether xeniid corals, and cnidarians in general, do not coordinate their pulsing behavior for lack of a hydrodynamic advantage or for other reasons. For example, a diffuse nervous system with lack of substantial sensory input may not be capable of such coordination. Similarly, grouping may serve a defensive role rather than a fluid dynamic role. In this paper, the immersed boundary method is used to quantify the volumetric flux of fluid generated by an individual xeniid coral polyp in comparison with a pair of polyps. Both the distances between the polyps and the phase difference between each polyp are considered. More specifically, the fully coupled fluid-structure interaction problem of a coral polyp driving fluid flow is solved using a hybrid version of the immersed boundary method where the Navier-Stokes equations are solved using a finite differences and the elasticity equations describing the coral are solved using finite elements. We explore three possible hypotheses: (1) pulsing in pairs increases upward flow above the polyps and is thus beneficial, (2) these benefits vary with the polyps' pulsing phase difference, and (3) these benefits vary with the distance between the polyps. We find that there is no substantial hydrodynamic advantage to pulsing in a pair for any phase difference. The volumetric flux of fluid generated by each coral also decreases as the distance between polyps is decreased. This surprising result is consistent with measurements taken from another cnidarian with similar behavior, the upside down jellyfish, in which each medusa drives less flow when in a group.

Stabilization approaches for the hyperelastic immersed boundary method for problems of large-deformation incompressible elasticity.

The immersed boundary method is a mathematical framework for modeling fluid-structure interaction. This formulation describes the momentum, viscosity, and incompressibility of the fluid-structure system in Eulerian form, and it uses Lagrangian coordinates to describe the structural deformations, stresses, and resultant forces. Integral transforms with Dirac delta function kernels connect the Eulerian and Lagrangian frames. The fluid and the structure are both typically treated as incompressible materials. Upon discretization, however, the incompressibility of the structure is only maintained approximately. To obtain an immersed method for incompressible hyperelastic structures that is robust under large structural deformations, we introduce a volumetric energy in the solid region that stabilizes the formulation and improves the accuracy of the numerical scheme. This formulation augments the discrete Lagrange multiplier for the incompressibility constraint, thereby improving the original method's accuracy. This volumetric energy is incorporated by decomposing the strain energy into isochoric and dilatational components, as in standard solid mechanics formulations of nearly incompressible elasticity. We study the performance of the stabilized method using several quasi-static solid mechanics benchmarks, a dynamic fluid-structure interaction benchmark, and a detailed three-dimensional model of esophageal transport. The accuracy achieved by the stabilized immersed formulation is comparable to that of a stabilized finite element method for incompressible elasticity using similar numbers of structural degrees of freedom.

Electrophoretic transport and dynamic deformation of bio-vesicles.

Study of the deformation dynamics of cells and other sub-micron vesicles, such as virus and neurotransmitter vesicles are necessary to understand their functional properties. This mechanical characterization can be done by submerging the vesicle in a fluid medium and deforming it with a controlled electric field, which is known as electrodeformation. Electrodeformation of biological and artificial lipid vesicles is directly influenced by the vesicle and surrounding media properties and geometric factors. The problem is compounded when the vesicle is naturally charged, which creates electrophoretic forcing on the vesicle membrane. We studied the electrodeformation and transport of charged vesicles immersed in a fluid media under the influence of a DC electric field. The electric field and fluid-solid interactions are modeled using a hybrid immersed interface-immersed boundary technique. Model results are verified with experimental observations for electric field driven translocation of a virus through a nanopore sensor. Our modeling results show interesting changes in deformation behavior with changing electrical properties of the vesicle and the surrounding media. Vesicle movement due to electrophoresis can also be characterized by the change in local conductivity, which can serve as a potential sensing mechanism for electrodeformation experiments in solid-state nanopore setups.

Computational analysis of nitric oxide biotransport in a microvessel influenced by red blood cells.

It is pivotal that endothelium-dependent Nitric Oxide (NO) consumed by hemoglobin (Hb) inside red blood cells (RBCs) membrane, regulates the vascular tone. The whole processes of NO transport in vessel containing flowing RBCs is still not clear, such as NO production in endothelium, diffusion in plasma and consumption inside RBCs. In this work, the motion of RBCs in a microvessel is investigated by using immersed boundary lattice Boltzmann method (IB-LBM) first and the deformability of RBCs is expressed by using spring network model which is based on the minimum energy principle. Furthermore, the interaction between RBCs is considered. Based on the wall shear stress (WSS), NO production rate originated from endothelium was obtained by using a hyperbolic model. NO distribution inside the microvessel with multiple RBCs was computed by using immersed boundary finite difference method (IB-FDM). The result shows that a large (small) WSS exists at locations with a relatively wide(narrow) gap between the wall and cell. In terms of mass transfer, an increase of RBC membrane permeability leads to a decrease of NO concentration in the vessel and the surrounding endothelium significantly. In addition, with the increasing of hematocrit (Hct) value, NO concentration distribution in the whole vessel decreases both in the lumen and vascular wall. Finally, the thickness of RBCs-depleted layer gradually decreases with the weakened deformability of RBCs membrane, and the change degree of cell free layer (CFL) thickness decreases as the bending stiffness is relatively higher. Thus, when bending stiffness is higher, the NO concentration in vascular wall is reduced resulting from the thinner CFL.

Lift and Drag Acting on the Shell of the American Horseshoe Crab (Limulus polyphemus).

The intertidal zone is a turbulent landscape where organisms face numerous mechanical challenges from powerful waves. A model for understanding the solutions to these physical problems, the American horseshoe crab (Limulus polyphemus), is a marine arthropod that mates in the intertidal zone, where it must contend with strong ambient flows to maintain its orientation during locomotion and reproduction. Possible strategies to maintain position include either negative lift generation or the minimization of positive lift in flow. To quantify flow over the shell and the forces generated, we laser-scanned the 3D shape of a horseshoe crab, and the resulting digital reconstruction was used to 3D-print a physical model. We then recorded the movement of tracking particles around the shell model with high-speed video and analyzed the time-lapse series using particle image velocimetry (PIV). The velocity vector fields from PIV were used to validate numerical simulations performed with the immersed boundary (IB) method. IB simulations allowed us to resolve the forces acting on the shell, as well as the local three-dimensional flow velocities and pressures. Both IB simulations and PIV analysis of vorticity and velocity at a flow speed of 13 cm/s show negative lift for negative and zero angles of attack, and positive lift for positive angles of attack in a free-stream environment. In shear flow simulations, we found near-zero lift for all orientations tested. Because horseshoe crabs are likely to be found primarily at near-zero angles of attack, we suggest that this negative lift helps maintain the orientation of the crab during locomotion and mating. This study provides a preliminary foundation for assessing the relationship between documented morphological variation and potential environmental variation for distinct populations of horseshoe crabs along the Atlantic Coast. It also motivates future studies which could consider the stability of the horseshoe crab in unsteady, oscillating flows.

Numerical modeling of fluid and oxygen exchanges through microcirculation for the assessment of microcirculation alterations caused by type 2 diabetes.

Type 2 diabetes mellitus (DM2) is frequently accompanied by microcirculation complications, including structural and functional alterations, which may have serious effects on substance exchanges between blood and interstitial tissue and the health of organs. In this paper, we aim to study the influence of microcirculation alterations in DM2 patients on fluid and oxygen exchanges through a model analysis. A fluid flow and oxygen transport model were developed by considering the interplay between blood in capillary network and interstitial tissue. The two regions were separately represented by 1D network model and 3D volume model, and the immersed boundary method (IBM) was adopted to solve fluid and mass transfer between these two regions. By using the model, the steady flow field and the distributions of oxygen in capillary network and surrounding tissue were firstly simulated. In the interstitial volume, fluid pressure and oxygen tension decreased with the increase of distance from the network; in the network, oxygen tension in blood plasma dropped from 100 mm Hg at the entrance to about 40 mm Hg at the exit. We further tested several structural and functional disorders related to diabetic pathological conditions. Simulated results show that the impaired connectivity of the network could result in poor robustness in maintaining blood flow and perfused surface; under high fluid permeability conditions of capillary walls, the pressure gradient was much larger around the capillary bed, and this alteration led to a saturation level of the interstitial pressure when lymphatic flow drainage can't work effectively; the variations in network connectivity and permeability of capillary wall also had unfavorable influence on oxygen distributions in interstitial tissue. In addition, when the oxygen releasing capacity of hemoglobin was confined by glycosylated hemoglobin (HbA1) in the case of diabetes, the plasma could not be complemented with adequate oxygen and thus the hypoxic tissue range will be extended. This study illustrates that when microcirculation disturbances, including the structure of capillary network, the wall osmosis property and the capacity of blood binding oxygen occur in DM2, some negative impacts are raised on microvascular hemodynamics and metabolism circumstance of interstitial tissue.

Mathematical Model of Contractile Ring-Driven Cytokinesis in a Three-Dimensional Domain.

In this paper, a mathematical model of contractile ring-driven cytokinesis is presented by using both phase-field and immersed-boundary methods in a three-dimensional domain. It is one of the powerful hypotheses that cytokinesis happens driven by the contractile ring; however, there are only few mathematical models following the hypothesis, to the author's knowledge. I consider a hybrid method to model the phenomenon. First, a cell membrane is represented by a zero-contour of a phase-field implicitly because of its topological change. Otherwise, immersed-boundary particles represent a contractile ring explicitly based on the author's previous work. Here, the multi-component (or vector-valued) phase-field equation is considered to avoid the emerging of each cell membrane right after their divisions. Using a convex splitting scheme, the governing equation of the phase-field method has unique solvability. The numerical convergence of contractile ring to cell membrane is proved. Several numerical simulations are performed to validate the proposed model.

Cell Damage Index as Computational Indicator for Blood Cell Activation and Damage.

Shear-induced hemolysis is a major concern in the design and optimization of blood-contacting devices. Even with a small amount of mechanical stress, inflammatory reactions can be triggered in the cells. Blood damage is typically estimated using continuum fluid dynamics simulations. In this study, we report a novel cell damage index (CDI) obtained by simulations on the single-cell level in a lattice Boltzmann fluid flow. The change of the cell surface area gives important information on mechanical stress of individual cells as well as for whole blood. We are using predefined basic channel designs to analyze and compare the newly developed CDI to the conventional blood damage calculations in very weak shear stress scenarios. The CDI can incorporate both volume fraction and channel geometry information into a single quantitative value for the characterization of flow in artificial chambers.