Modification of the swirling well cell culture model to alter shear stress metrics

Effects of hemodynamic shear stress on endothelial cells have been extensively investigated using the “swirling well” method, in which cells are cultured in dishes or multiwell plates placed on an orbital shaker. A wave rotates around the well, producing complex patterns of shear. The method allows chronic exposure to flow with high throughput at low cost but has two disadvantages: a number of shear stress characteristics change in a broadly similar way from the center to the edge of the well, and cells at one location in the well may release mediators into the medium that affect the behavior of cells at other locations, exposed to different shears. These properties make it challenging to correlate cell properties with shear. The present study investigated simple alterations to ameliorate these issues. Flows were obtained by numerical simulation. Increasing the volume of fluid in the well-altered dimensional but not dimensionless shear metrics. Adding a central cylinder to the base of the well-forced fluid to flow in a square toroidal channel and reduced multidirectionality. Conversely, suspending a cylinder above the base of the well made the flow highly multidirectional. Increasing viscosity in the latter model increased the magnitude of dimensional but not dimensionless metrics. Finally, tilting the well changed the patterns of different wall shear stress metrics in different ways. Collectively, these methods allow similar flows over most of the cells cultured and/or allow the separation of different shear metrics. A combination of the methods overcomes the limitations of the baseline model.     

Computer Simulation of Two-Dimensional Continuum Flows by the Direct Simulation Monte Carlo Method

Abstract

Computer simulations using particles are an attractive method to extract microscopic information of flow phenomena [1]. The molecular dynamics (MD) method, in which Newton's equations of motions are integrated, gives the temporal development of the system. In the MD simulation of fluid flows, the computational region is limited to atomistic scales [2]. On the other hand, the direct simulation Monte Carlo (DSMC) method, in which collisions of particles are made on a probabilistic basis, has a potential of treating a realistic system with a macroscopic scale length retaining the atomistic details. The DSMC method provides an efficient way to integrate the Boltzmann equation from the rarefied gas to the near-continuum region. Bird clarified the validity of the DSMC method in the near-continuum flow region [3]. However, the DSMC method has not been applied to the continuum region and compared with the continuum hydrodynamics.     

Large Eddy Simulation and Reynolds-Averaged Navier-Stokes modeling of flow in a realistic pharyngeal airway model: an investigation of obstructive sleep apnea

Computational fluid dynamics techniques employing primarily steady Reynolds-Averaged Navier-Stokes (RANS) methodology have been recently used to characterize the transitional/turbulent flow field in human airways. The use of RANS implies that flow phenomena are averaged over time, the flow dynamics not being captured. Further, RANS uses two-equation turbulence models that are not adequate for predicting anisotropic flows, flows with high streamline curvature, or flows where separation occurs. A more accurate approach for such flow situations that occur in the human airway is Large Eddy Simulation (LES). The paper considers flow modeling in a pharyngeal airway model reconstructed from cross-sectional magnetic resonance scans of a patient with obstructive sleep apnea. The airway model is characterized by a maximum narrowing at the site of retropalatal pharynx. Two flow-modeling strategies are employed: steady RANS and the LES approach. In the RANS modeling framework both k-epsilon and k-omega turbulence models are used. The paper discusses the differences between the airflow characteristics obtained from the RANS and LES calculations. The largest discrepancies were found in the axial velocity distributions downstream of the minimum cross-sectional area. This region is characterized by flow separation and large radial velocity gradients across the developed shear layers. The largest difference in static pressure distributions on the airway walls was found between the LES and the k-epsilon data at the site of maximum narrowing in the retropalatal pharynx.     

Recent Advances in Computational Simulation of Macro-, Meso-, and Micro-Scale Biomimetics Related Fluid Flow Problems

Over the last decade, computational methods have been intensively applied to a variety of scientific researches and engineering designs. Although the computational fluid dynamics （CFD） method has played a dominant role in studying and simulating transport phenomena involving fluid flow and heat and mass transfers, in recent years, other numerical methods for the simulations at meso- and micro-scales have also been actively applied to solve the physics of complex flow and fluid-interface interactions. This paper presents a review of recent advances in multi-scale computational simulation of biomimetics related fluid flow problems. The state-of-the-art numerical techniques, such as lattice Boltzmann method （LBM）, molecular dynamics （MD）, and conventional CFD, applied to different problems such as fish flow, electro-osmosis effect of earthworm motion, and self-cleaning hydrophobic surface, and the numerical approaches are introduced. The new challenging of modelling biomimetics problems in developing the physical conditions of self-clean hydrophobic surfaces is discussed.     

An all-optical approach for probing microscopic flows in living embryos

Living systems rely on fluid dynamics from embryonic development to adulthood. To visualize biological fluid flow, devising the proper labeling method compatible with both normal biology and in vivo imaging remains a major experimental challenge. Here, we describe a simple strategy for probing microscopic fluid flows in vivo that meets this challenge. An all-optical procedure combining femtosecond laser ablation, fast confocal microscopy and 3D-particle tracking was devised to label, image and quantify the flow. This approach is illustrated by studying the flow generated within a micrometer scale ciliated vesicle located deep inside the zebrafish embryo and involved in breaking left-right embryonic symmetry. By mapping the velocity field within the vesicle and surrounding a single beating cilium, we show this method can address the dynamics of cilia-driven flows at multiple length scales, and can validate the flow features as predicted from previous simulations. This approach provides new experimental access to questions of microscopic fluid dynamics in vivo.     

Association of a fluorescent amphiphile with lipid bilayer vesicles in regions of solid-liquid-disordered phase coexistence

The effects of solid-fluid phase separations on the kinetics of association of a single-chain fluorescent amphiphile were investigated in two different systems: pure DMPC (dimyristoylphosphatidylcholine) and a 1:1 mixture of DMPC and DSPC (distearoylphosphatidylcholine). In pure DMPC vesicles, solid (s) and fluid (l(d)) phases coexist at the phase transition temperature, T(m), whereas a 1:1 mixture of DMPC and DSPC shows a stable s-l(d) phase separation over a large temperature interval. We found that in single-component bilayers, within the main phase transition, the experimental kinetics of association are clearly not single-exponential, the deviation from that function becoming maximal at the T(m). This observation can be accounted for by a rate of desorption that is slower than desorption from either fluid or solid phases, leaving the rates of insertion unchanged, but a treatment in terms of stable fluid and solid domains may not be adequate for the analysis of the association of an amphiphile with pure DMPC vesicles at the T(m). In DMPC/DSPC mixtures with solid-fluid phase coexistence, association occurs overall faster than expected based on phase composition. The observed kinetics can be described by an increase in the rate of insertion, leaving the desorption rates unchanged. The fast kinetics of insertion of the amphiphile into two-phase bilayers in two-component vesicles is attributed to a more rapid insertion into defect-rich regions, which are most likely phase boundaries between solid and fluid domains. A two-component mixture of lipids that shows a stable phase separation between l(d)-s phases over a large temperature interval thus behaves very differently from a single-component bilayer at the T(m), with respect to insertion of amphiphiles.     

Application of the synthetic jet concept to low Reynolds number biosensor microfluidic flows for enhanced mixing: a numerical study using the lattice Boltzmann method

The concept of macro scale synthetic jets has been applied to the low Reynolds number (Re=10), two-dimensional channel flows which may be found in biosensor microfluidic systems. The current numerical investigation utilizes a hybrid approach of the lattice Boltzmann (LB) method for flow field computations and a finite-difference, convection-diffusion equation for passive scalar transport. The study presents the modified main channel flow results for various wall jet geometries (derived from synthetic jets), jet inlet conditions, scaling issues and Reynolds numbers. The results indicate limited effects due to jet cavity-slot geometry, and that the forced jet imparts momentum to the channel flow thus enhancing fluid mixing.     

Secondary flow mixing due to biofilm growth in capillaries of varying dimensions

Using a magnetic resonance microscopy (MRM) technique, velocity perturbations due to biofouling in capillaries were detected in 3D velocity maps. The velocity images in each of the three square capillary sizes (2, 0.9, and 0.5 mm i.d.) tested indicate secondary flow in both the x‐ and y‐directions for the biofouled capillaries. Similar flow maps generated in a clean square capillary show only an axial component. Investigation of these secondary flows and their geometric and dynamic similarity is the focus of this study. The results showed significant secondary flows present in the 0.9 mm i.d. capillary, on the scale of 20% of the bulk fluid flow. Since this is the “standard 1 mm” size capillary used in confocal microscopy laboratory bioreactors to investigate biofilm properties, it is important to understand how these enhanced flows impact bioreactor transport. Biotechnol. Bioeng. 2009;103: 353–360. © 2009 Wiley Periodicals, Inc.     

Numerical study on flows of red blood cells with liposome-encapsulated hemoglobin at microvascular bifurcation

Flow analysis at microvascular bifurcation after partial replacement of red blood cell (RBC) with liposome-encapsulated hemoglobin (LEH) was performed using the lattice Boltzmann method. A two-dimensional symmetric Y bifurcation model with a parent vessel diameter of 20 mum and daughter branch diameters of 20 microm was considered, and the distributions of the RBC, LEH, and oxygen fluxes were calculated. When only RBCs flow into the daughter branches with unevenly distributed flows, plasma separation occurred and the RBC flow to the lower-flow branch was disproportionately decreased. On the other hand, when half of RBC are replaced by LEH, the biasing of RBC flow was enhanced whereas LEH flowed favorably into the lower-flow branch, because many LEH within the parent vessel are suspended in the plasma layer, where no RBCs exist. Consequently, the branched oxygen fluxes became nearly proportional to flows. These results indicate that LEH facilitates oxygen supply to branches that are inaccessible to RBCs.     

Breaking symmetry in non-planar bifurcations: distribution of flow and wall shear stress

Non-planarity in blood vessels is known to influence arterial flows and wall shear stress. To gain insight, computational fluid dynamics (CFD) has been used to investigate effects of curvature and out-of-plane geometry on the distribution of fluid flows and wall shear stresses in a hypothetical non-planar bifurcation. Three-dimensional Navier-Stokes equations for a steady state Newtonian fluid were solved numerically using a finite element method. Non-planarity in one of the two daughter vessels is found to deflect flow from the inner wall of the vessel to the outer wall and to cause changes in the distribution of wall shear stresses. Results from this study agree to experimental observations and CFD simulations in the literature, and support the view that non-planarity in blood vessels is a factor with important haemodynamic significance and may play a key role in vascular biology and pathophysiology.     

Stability of particle motions in a narrow channel flow

Single rows or two rows of identical circular cylinders spaced regularly in a narrow channel flow have been shown to be capable of steady flow provided the cylinders are located at equal lateral positions and with equal spacings in the flow direction. The stability of such steady flows of circular cylinders is studied for periodic perturbations of the particle positions, assuming that every other cylinder is equally perturbed in lateral position and spacing along the channel. This results in two rows which are not symmetrically placed. The suspending fluid is assumed to be an incompressible Newtonian fluid. It is assumed that no external forces or moments act on the cylinders and the effects of inertia forces on the motion of the fluid and the cylinders are negligible. The velocity field of the suspending fluid and the instantaneous velocities of the cylinders are computed by the finite element method. The translational velocities of the cylinders are obtained for a large number of particle positions, from which the trajectories of their relative motion are determined for various initial positions near the regular single-file and two-file arrangements. It is shown that when the initial arrangements of the cylinders are slightly perturbed from the regular (alternating) two-file flows, the trajectories of their relative motions become small closed loops around the regular two-file arrangements. In contrast, such small closed trajectories are not obtained when they start from the arrangements near the regular single-file flows or regular (symmetric) double-file flows, suggesting that these flows are unstable under the conditions examined.     

Mechanistic insight into the physiological relevance of helical blood flow in the human aorta: an in vivo study

The hemodynamics within the aorta of five healthy humans were investigated to gain insight into the complex helical flow patterns that arise from the existence of asymmetries in the aortic region. The adopted approach is aimed at (1) overcoming the relative paucity of quantitative data regarding helical blood flow dynamics in the human aorta and (2) identifying common characteristics in physiological aortic flow topology, in terms of its helical content. Four-dimensional phase-contrast magnetic resonance imaging (4D PC MRI) was combined with algorithms for the calculation of advanced fluid dynamics in this study. These algorithms allowed us to obtain a 4D representation of intra-aortic flow fields and to quantify the aortic helical flow. For our purposes, helicity was used as a measure of the alignment of the velocity and the vorticity. There were two key findings of our study: (1) intra-individual analysis revealed a statistically significant difference in the helical content at different phases of systole and (2) group analysis suggested that aortic helical blood flow dynamics is an emerging behavior that is common to normal individuals. Our results also suggest that helical flow might be caused by natural optimization of fluid transport processes in the cardiovascular system, aimed at obtaining efficient perfusion. The approach here applied to assess in vivo helical blood flow could be the starting point to elucidate the role played by helicity in the generation and decay of rotating flows in the thoracic aorta.     

Steady flow through a constricted cylinder by multiparticle collision dynamics

The flow characterization of blood through healthy and diseased flow geometries is of interest to researchers and clinicians alike, as it may allow for early detection, and monitoring, of cardiovascular disease. In this paper, we use a numerically efficient particle-based flow model called multiparticle collision dynamics (MPC for short) to study the effect of compressibility and slip of flow of a Newtonian fluid through a cylinder with a local constriction. We use a cumulative averaging method to compare our MPC results to the finite-element solution of the incompressible no-slip Navier-Stokes equations in the same geometry. We concentrate on low Reynolds number flows [ $Re \in (4,30)$ ] and quantify important differences observed between the MPC results and the Navier-Stokes solution in constricted geometries. In particular, our results show that upstream recirculating zones can form with the inclusion of slip and compressibility, which are not observed in the flow of an incompressible Newtonian fluid using the no-slip assumption, but have been observed experimentally for blood. Important flow features are also presented that could be used as indicators to observe compressibility and slip in experimental data where near-wall data may be difficult to obtain. Finally, we found that the cumulative averaging method used is ideal for steady particle-based flow methods, as macroscopic no-slip is readily obtained using the MPC bounce-back rule. Generally, a small spurious slip is seen using other averaging methods such as weighted spatial averages or averages over several runs, and the bounce-back rule has to be modified so as to achieve macroscopic no-slip. No modifications of the bounce-back rule were required for our simulations.     

Blood flow dynamics in saccular aneurysm models of the basilar artery

Blood flow dynamics under physiologically realistic pulsatile conditions plays an important role in the growth, rupture, and surgical treatment of intracranial aneurysms. The temporal and spatial variations of wall pressure and wall shear stress in the aneurysm are hypothesized to be correlated with its continuous expansion and eventual rupture. In addition, the assessment of the velocity field in the aneurysm dome and neck is important for the correct placement of endovascular coils. This paper describes the flow dynamics in two representative models of a terminal aneurysm of the basilar artery under Newtonian and non-Newtonian fluid assumptions, and compares their hemodynamics with that of a healthy basilar artery. Virtual aneurysm models are investigated numerically, with geometric features defined by beta = 0 deg and beta = 23.2 deg, where beta is the tilt angle of the aneurysm dome with respect to the basilar artery. The intra-aneurysmal pulsatile flow shows complex ring vortex structures for beta = 0 deg and single recirculation regions for beta = 23.2 deg during both systole and diastole. The pressure and shear stress on the aneurysm wall exhibit large temporal and spatial variations for both models. When compared to a non-Newtonian fluid, the symmetric aneurysm model (beta = 0 deg) exhibits a more unstable Newtonian flow dynamics, although with a lower peak wall shear stress than the asymmetric model (beta = 23.2 deg). The non-Newtonian fluid assumption yields more stable flows than a Newtonian fluid, for the same inlet flow rate. Both fluid modeling assumptions, however, lead to asymmetric oscillatory flows inside the aneurysm dome.     

Inflow/Outflow Boundary Conditions for Particle-Based Blood Flow Simulations: Application to Arterial Bifurcations and Trees

When blood flows through a bifurcation, red blood cells (RBCs) travel into side branches at different hematocrit levels, and it is even possible that all RBCs enter into one branch only, leading to a complete separation of plasma and RBCs. To quantify this phenomenon via particle-based mesoscopic simulations, we developed a general framework for open boundary conditions in multiphase flows that is effective even for high hematocrit levels. The inflow at the inlet is duplicated from a fully developed flow generated in a pilot simulation with periodic boundary conditions. The outflow is controlled by adaptive forces to maintain the flow rate and velocity gradient at fixed values, while the particles leaving the arteriole at the outlet are removed from the system. Upon validation of this approach, we performed systematic 3D simulations to study plasma skimming in arterioles of diameters 20 to 32 microns. For a flow rate ratio 6:1 at the branches, we observed the “all-or-nothing” phenomenon with plasma only entering the low flow rate branch. We then simulated blood-plasma separation in arteriolar bifurcations with different bifurcation angles and same diameter of the daughter branches. Our simulations predict a significant increase in RBC flux through the main daughter branch as the bifurcation angle is increased. Finally, we demonstrated the effectiveness of the new methodology in simulations of blood flow in vessels with multiple inlets and outlets, constructed using an angiogenesis model.     

A three-dimensional multiscale model for the prediction of thrombus growth under flow with single-platelet resolution

Modeling thrombus growth in pathological flows allows evaluation of risk under patient-specific pharmacological, hematological, and hemodynamical conditions. We have developed a 3D multiscale framework for the prediction of thrombus growth under flow on a spatially resolved surface presenting collagen and tissue factor (TF). The multiscale framework is composed of four coupled modules: a Neural Network (NN) that accounts for platelet signaling, a Lattice Kinetic Monte Carlo (LKMC) simulation for tracking platelet positions, a Finite Volume Method (FVM) simulator for solving convection-diffusion-reaction equations describing agonist release and transport, and a Lattice Boltzmann (LB) flow solver for computing the blood flow field over the growing thrombus. A reduced model of the coagulation cascade was embedded into the framework to account for TF-driven thrombin production. The 3D model was first tested against in vitro microfluidics experiments of whole blood perfusion with various antiplatelet agents targeting COX-1, P₂Y₁, or the IP receptor. The model was able to accurately capture the evolution and morphology of the growing thrombus. Certain problems of 2D models for thrombus growth (artifactual dendritic growth) were naturally avoided with realistic trajectories of platelets in 3D flow. The generalizability of the 3D multiscale solver enabled simulations of important clinical situations, such as cylindrical blood vessels and acute flow narrowing (stenosis). Enhanced platelet-platelet bonding at pathologically high shear rates (e.g., von Willebrand factor unfolding) was required for accurately describing thrombus growth in stenotic flows. Overall, the approach allows consideration of patient-specific platelet signaling and vascular geometry for the prediction of thrombotic episodes.     

Numerical investigation of haemodynamics in a helical-type artery bypass graft using non-Newtonian multiphase model

The classic single-phase Newtonian blood flow model ignores the motion of red blood cells (RBCs) and their interaction with plasma. To address these issues, we adopted a multiphase non-Newtonian model to carry out a comparative study between a helical artery bypass graft (ABG) and a conventional ABG in which the blood flow is composed of plasma and RBCs. The investigation focused on the mechanism of RBC buildup in an ABG but the haemodynamic parameters obtained by single-phase and multiphase models were also compared. The aggregation of RBCs along the inside wall of a conventional ABG and at the heel of its distal anastomosis was predicted while a poor aggregation was observed along the helical ABG. In addition, RBCs were observed to gradually sediment along the gravity direction. However, the computed haemodynamic parameters by multiphase model qualitatively agreed well with those by single-phase model. It was concluded that (1) the single-phase computational fluid dynamics (CFD) is reasonable to do the computation of haemodynamic parameters in ABGs; (2) secondary flow does not definitely produce buildup of RBCs in the inside curvature, its configuration played an important role in the movement of RBCs and the dominating one-way rotating flow in a helical ABG guaranteed no buildup of RBCs on its inside wall and (3) gravity direction is important for the movement of RBCs which may help to explain why doing exercise is good for human health. This study helps to shed light on the migration of RBCs in ABGs, which cannot be explored by single-phase CFD models, and provides more understanding of the underlying flow mechanism for ABG failure.     

Three-dimensional focusing of red blood cells in microchannel flows for bio-sensing applications

Three-dimensional (3D) focusing of particles in microchannels has been a long-standing issue in the design of biochemical/biomedical microdevices. Current microdevices for 3D cell or bioparticle focusing involve complex channel geometries in view of their fabrication because they require multiple layers and/or sheath flows. This paper proposes a simple method for 3D focusing of red blood cells (RBCs) in a single circular microcapillary, without any sheath flows, which is inspired from the fluid dynamics phenomenon in that a spherical particle lagging behind a Poiseuille flow migrates toward and along the channel axis. More explicitly, electrophoresis of RBCs superimposed on the pressure-driven flow is utilized to generate an RBC migration mode analogous to this phenomenon. A particle-tracking scheme with a sub-pixel resolution is implemented to spatially position red blood cells flowing through the channel, so that a probability density function (PDF) is constructed to evaluate the tightness of the cell focusing. Above a specific strength of the electric field, approximately 90% of the sheep RBCs laden in the flow are tightly focused within a beam diameter that is three times the cell dimension. Particle shape effect on the focusing is discussed by making comparisons between the RBCs and the spherical particles. The lateral migration velocity, predicted by an existing theoretical model, is in good agreement with the present experimental data. It is noteworthy that 3D focusing of non-spherical particles, such as RBCs, has been achieved in a circular microchannel, which is a significant improvement over previous focusing methodologies.     

Electroosmotic Flow in Nanoscale Parallel-plate Channels: Molecular Simulation Study and Comparison with Classical Poisson–Boltzmann Theory

Molecular dynamics simulations have been carried out for simple electrolyte systems to study the electrokinetically driven osmotic flow in parallel-plate channels of widths ～10–120?nm. The results are compared with the classical theory predictions based on the solution to the Poisson–Boltzmann equation. We find that despite some of the limitations in the Poisson–Boltzmann equation, such as assumption of the Boltzmann distribution for the ions, the classical theory captures the general trend of the variations of the osmotic flow with channel width, as characterized by the mobility of the fluid in channels between ～10 and 120?nm at moderate to low ion concentration. At moderate concentration (corresponding to relatively low surface potential), the classical theory is almost quantitative. The theory and simulation show more disagreement at low concentration, primarily caused by the high surface potential where the assumption of Boltzmann distribution becomes inaccurate. We discuss the limitations of the Poisson–Boltzmann equation as applied to the nanoscale channels.