An estimated shape function for drift in a platelet-transport model.

Prior work has shown that concentration profiles of platelets in flowing whole blood and of platelet-sized beads in flowing blood suspensions can include near-wall excesses. A model to describe this phenomenon was built about a single-component convective diffusion equation. To incorporate redistribution to preferred sites by shear flows of red cell suspensions, the model used a drift shape function (in addition to the commonly used augmented diffusion coefficient). This paper reports experiments that provide an average concentration profile from which the shape function for that model is calculated; the experiments and shape function are for the particular conditions of 40% hematocrit, platelet-sized latex beads (2.5 microns diameter), tube ID of 217 microns, and a wall shear rate of 555 s-1. Less precise estimates of the shape function obtained from data of previous studies indicate that the shape function is similar for the hematocrit of 15%.     

Large eddy simulation of LDL surface concentration in a subject specific human aorta

The development of atherosclerosis is correlated to the accumulation of lipids in the arterial wall, which, in turn, may be caused by the build-up of low-density lipoproteins (LDL) on the arterial surface. The goal of this study was to model blood flow within a subject specific human aorta, and to study how the LDL surface concentration changed during a cardiac cycle. With measured velocity profiles as boundary conditions, a scale-resolving technique (large eddy simulation, LES) was used to compute the pulsatile blood flow that was in the transitional regime. The relationship between wall shear stress (WSS) and LDL surface concentration was investigated, and it was found that the accumulation of LDL correlated well with WSS. In general, regions of low WSS corresponded to regions of increased LDL concentration and vice versa. The instantaneous LDL values changed significantly during a cardiac cycle; during systole the surface concentration was low due to increased convective fluid transport, while in diastole there was an increased accumulation of LDL on the surface. Therefore, the near-wall velocity was investigated at four representative locations, and it was concluded that in regions with disturbed flow the LDL concentration had significant temporal changes, indicating that LDL accumulation is sensitive to not only the WSS but also near-wall flow.     

Concentration wave of a solute in an artery: the influence of curvature

Mass transport and diffusion phenomena in the arterial lumen are studied through a mathematical model. Blood flow is described by the unsteady Navier-Stokes equation and solute dynamics by an advection-diffusion equation, the convective field being provided by the fluid velocity. A linearization procedure over the steady state solution is carried out and an asymptotic analysis is used to study the effect of a small curvature with respect to the straight tube. Analytical and numerical solutions are found: the results show the characteristics of the long wave propagation and the role played by the geometry on the solute distribution and demonstrate the strong influence of curvature induced by the fluid dynamics.     

Transport processes during sterilization of vertical and 5 degree horizontal dead-legs

Experimental temperature profiles and biological kill data from dead-ended tubes of various diameters and lengths commonly used in biotechnology applications were compared to those predicted by a finite element model for steam-in-place (SIP) sterilization at 122°C. Diameter was shown experimentally and numerically to have a significant effect with larger diameter tubes exhibiting greater buoyant driven convective flow and more rapid sterilization. The overall Grashof number was shown to be the significant parameter relating magnitude of convective flow to tube diameter and varied as the diameter cubed. Analysis of air/steam mixture flow patterns showed air displacement from 0.4 cm diameter tubes to be due primarily to molecular diffusion, whereas 1.0 and 1.7 cm tubes showed a two-stage convective flow pattern. There exists a critical diameter of 0.4 cm below which SIP sterilization due to buoyancy driven flow does not occur and steam bleeders should be used.     

On transport of suspended particulates in tube flow.

Blood cells suspended in shear flows exhibit much larger dispersive motions than those predicted by the Stokes-Einstein formula for Brownian diffusion. The lateral migration and the erratic motions of the 8 microns red blood cells (RBC) is thought to be analogous to a diffusive process. It is shown that the often cited convective-diffusion theory may not be an adequate model for describing the transverse migration of suspended cells in blood flow. A comprehensive review of both the classical theory and of contemporary work in particle transport is presented, with particular emphasis on low Reynolds number tube flows. The mechanisms of Taylor dispersion, the effects of Brownian perturbations on translational and rotational motions of the suspended particles in shear fields, and the influence of integratable and chaotic advections, are individually examined. The classical experiment by Segre and Silberberg (1962) lead us to believe that particle hydrodynamics may play an important role in transverse migrations. In this light, we have further examined the hydrodynamic aspects of the so-called "tubular pinch" effect, the lateral migration of rigid spheres. We have also discussed the transverse motions of liquid drops, and the reversibility of the organization of suspensions in transport. The convective accelerations in the entrance region of a tube can produce relative velocities between fluid medium and various type of particulates if there is a difference in density. The deformable RBC, an "active-type" particle, can provide feedback to the flow from both mass and momentum considerations; the more rigid platelet, a "passive-type" particle, will experience a much smaller relative velocity as compared to the RBC. We may expect that particles of different densities are transported to different equilibrium annular positions before entering the fully developed flow region. The erratic, lateral movement of suspended particulates in steady laminar tube flow can be described by the usual Lagrangian coordinates.     

Platelet Dynamics in Three-Dimensional Simulation of Whole Blood

A high-fidelity computational model using a 3D immersed boundary method is used to study platelet dynamics in whole blood. We focus on the 3D effects of the platelet-red blood cell (RBC) interaction on platelet margination and near-wall dynamics in a shear flow. We find that the RBC distribution in whole blood becomes naturally anisotropic and creates local clusters and cavities. A platelet can enter a cavity and use it as an express lane for a fast margination toward the wall. Once near the wall, the 3D nature of the platelet-RBC interaction results in a significant platelet movement in the transverse (vorticity) direction and leads to anisotropic platelet diffusion within the RBC-depleted zone or cell-free layer (CFL). We find that the anisotropy in platelet motion further leads to the formation of platelet clusters, even in the absence of any platelet-platelet adhesion. The transverse motion, and the size and number of the platelet clusters are observed to increase with decreasing CFL thickness. The 3D nature of the platelet-RBC collision also induces fluctuations in off-shear plane orientation and, hence, a rotational diffusion of the platelets. Although most marginated platelets are observed to tumble just outside the RBC-rich zone, platelets further inside the CFL are observed to flow with an intermittent dynamics that alters between sliding and tumbling, as a result of the off-shear plane rotational diffusion, bringing them even closer to the wall. To our knowledge, these new findings are based on the fundamentally 3D nature of the platelet-RBC interaction, and they underscore the importance of using cellular-scale 3D models of whole blood to understand platelet margination and near-wall platelet dynamics.     

Platelet Dynamics in Three-Dimensional Simulation of Whole Blood

A high-fidelity computational model using a 3D immersed boundary method is used to study platelet dynamics in whole blood. We focus on the 3D effects of the platelet-red blood cell (RBC) interaction on platelet margination and near-wall dynamics in a shear flow. We find that the RBC distribution in whole blood becomes naturally anisotropic and creates local clusters and cavities. A platelet can enter a cavity and use it as an express lane for a fast margination toward the wall. Once near the wall, the 3D nature of the platelet-RBC interaction results in a significant platelet movement in the transverse (vorticity) direction and leads to anisotropic platelet diffusion within the RBC-depleted zone or cell-free layer (CFL). We find that the anisotropy in platelet motion further leads to the formation of platelet clusters, even in the absence of any platelet-platelet adhesion. The transverse motion, and the size and number of the platelet clusters are observed to increase with decreasing CFL thickness. The 3D nature of the platelet-RBC collision also induces fluctuations in off-shear plane orientation and, hence, a rotational diffusion of the platelets. Although most marginated platelets are observed to tumble just outside the RBC-rich zone, platelets further inside the CFL are observed to flow with an intermittent dynamics that alters between sliding and tumbling, as a result of the off-shear plane rotational diffusion, bringing them even closer to the wall. To our knowledge, these new findings are based on the fundamentally 3D nature of the platelet-RBC interaction, and they underscore the importance of using cellular-scale 3D models of whole blood to understand platelet margination and near-wall platelet dynamics.     

Effects of velocity jumps on blood flow in large arteries

When a human being experiences a sudden velocity change, the blood flow is disturbed. A theoretical analysis to predict the effects of sudden velocity changes on blood flow in large arteries is presented. The situations is modelled as a one-dimensional flow problem in a viscoelastic tube where the fluid viscosity convective term in the equation of motion and nonlinearity in the elastic modulus of the tube wall are neglected. The governing equations of the model are solved by Laplace transformation. The computed results show that relatively high blood pressures, capable of harming circulation, are produced even by relatively moderate velocity jumps.     

Investigation of platelet margination phenomena at elevated shear stress

Thrombosis is a common complication following the surgical implantation of blood contacting artificial organs. Platelet transport, which is an important process of thrombosis and strongly modulated by flow dynamics, has not been investigated under the shear stress level associated with these devices, which may range from tens to several hundred Pascal.The current research investigated platelet transport within blood under supra-physiological shear stress conditions through a micro flow visualization approach. Images of platelet-sized fluorescent particles in the blood flow were recorded within microchannels (2 cm x 100 microm x 100 microm). The results successfully demonstrated the occurrence of platelet-sized particle margination under shear stresses up to 193 Pa, revealing a platelet near-wall excess up to 8.7 near the wall (within 15 microm) at the highest shear stress. The concentration of red blood cells was found to influence the stream-wise development of platelet margination which was clearly observed in the 20% Ht sample but not the 40% Ht sample. Shear stress had a less dramatic effect on the margination phenomenon than did hematocrit. The results imply that cell-cell collision is an important factor for platelet transport under supra-physiologic shear stress conditions. It is anticipated that these results will contribute to the future design and optimization of artificial organs.     

Revisiting the Münch pressure-flow hypothesis for long-distance transport of carbohydrates: modelling the dynamics of solute transport inside a semipermeable tube

A mathematical model of the Münch pressure-flow hypothesis for long-distance transport of carbohydrates via sieve tubes is constructed using the Navier-Stokes equation for the motion of a viscous fluid and the van't Hoff equation for osmotic pressure. Assuming spatial dimensions that are appropriate for a sieve tube and ensuring suitable initial profiles of the solute concentration and solution velocity lets the model become mathematically tractable and concise. In the steady-state case, it is shown via an analytical expression that the solute flux is diffusion-like with the apparent diffusivity coefficient being proportional to the local solute concentration and around seven orders of magnitude greater than a diffusivity coefficient for sucrose in water. It is also shown that, in the steady-state case, the hydraulic conductivity over one metre can be calculated explicitly from the tube radius and physical constants and so can be compared with experimentally determined values. In the time-dependent case, it is shown via numerical simulations that the solute (or water) can simultaneously travel in opposite directions at different locations along the tube and, similarly, change direction of travel over time at a particular location along the tube.     

Drag-reducing polymers diminish near-wall concentration of platelets in microchannel blood flow

The accumulation of platelets near the blood vessel wall or artificial surface is an important factor in the cascade of events responsible for coagulation and/or thrombosis. In small blood vessels and flow channels this phenomenon has been attributed to the blood phase separation that creates a red blood cell (RBC)-poor layer near the wall. We hypothesized that blood soluble drag-reducing polymers (DRP), which were previously shown to lessen the near-wall RBC depletion layer in small channels, may consequently reduce the near-wall platelet excess. This study investigated the effects of DRP on the lateral distribution of platelet-sized fluorescent particles (diam. = 2 μm, 2.5 × 10?/ml) in a glass square microchannel (width and depth = 100 μm). RBC suspensions in PBS were mixed with particles and driven through the microchannel at flow rates of 6-18 ml/h with and without added DRP (10 ppm of PEO, MW = 4500 kDa). Microscopic flow visualization revealed an elevated concentration of particles in the near-wall region for the control samples at all tested flow rates (between 2.4 ± 0.8 times at 6 ml/h and 3.3 ± 0.3 times at 18 ml/h). The addition of a minute concentration of DRP virtually eliminated the near-wall particle excess, effectively resulting in their even distribution across the channel, suggesting a potentially significant role of DRP in managing and mitigating thrombosis.     

Transport Equations and Criteria for Active Transport

The relation between driving forces and the flux of solutesthat would be expected in a passive system is derived. Thisrelation is a differential equation and different solutionsare obtained which apply to different experimental conditions.Solutions are given for the cases of pure convective flow, diffusion,electrophoretic mobility, balance between diffusive and electricalforces, and transport in the presence of both concentrationand voltage differences.     

Drift and fluctuating motion of artificial platelets during the lateral transport and adhesion process near the wall

Recombinant glycoprotein Ibα latex beads (rGPIbα-LB) are a potential solution to overcoming platelet transfusion problems with artificial platelets. To understand the transport process of artificial platelets and to estimate the particle motion when adhering to the wall surface, we evaluated the lateral motion of rGPIbα-LB in terms of drift and random motion, because the lateral motion is an important factor for transport and adhesion. We observed the lateral motion of rGPIbα-LB flowing with red blood cells toward the immobilized von Willebrand factor (vWf) surface in a model arteriole at wall shear rates of 200–1000 s^?1 and 0–40% Hct. At 40% Hct, wall shear rate dependence was observed for the drift motion, i.e. the lateral velocity of rGPIbα-LB toward the wall. In the near-wall region, the drift motion of contacting particles differed substantially from that of non-contacting particles. Additionally, the trajectories of contacting particles on the vWf surface had specific motion that was not observed on the BSA surface. These results suggest that the adhesion force between rGPIbα and vWf is highly associated with the motion of particles near the wall. These features are desirable for artificial platelets, particularly for the adhesion process.     

Development of a platelet adhesion transport equation for a computational thrombosis model

Thrombosis is a significant issue for cardiovascular device development and use. While thrombosis models are available, very few are device-related and none have been thoroughly validated experimentally. Here, we introduce a surface adherent platelet transport equation into a continuum model to account for the biomaterial interface/blood interaction. Using a rotating disc system and polyurethane-urea material, we characterize steady and pulsatile flow fields using laser Doppler velocimetry. In vitro measurements of platelet adhesion are used in combination with the LDV data to provide further experimental validation. The rotating disc system is computationally studied using the device-induced thrombosis model with the surface platelet adherent transport equation. The results indicate that the flow field is in excellent agreement to the experimental LDV data and that the platelet adhesion simulations are in good agreement with the in vitro platelet data. These results provide good evidence that this transport equation can be used to express the relationship between blood and a biomaterial if the correct platelet adhesion characteristics are known for the biomaterial. Further validation is necessary with other materials.     

The use of confocal laser scanning microscopy to study the transport of biomacromolecules in a macroporous support

Large-pore materials or supports resembling polymer conduits are used as packing material in chromatographic operations. Our ongoing research has shown that, when modified with peptides or ligands, chitosan beads that are 800 microm in diameter and have 3.5% solids can be used as matrices in bioseparations. The goal of the present study is to evaluate the transport properties of biomolecules in the modified chitosan beaded matrices. Batch uptake experiments with fluorescently tagged pure human IgG, human IgA and human IgM were conducted to visualize the distribution of binding sites throughout the bead as well as to evaluate restrictions to diffusion, if any, within the support. The chromatographic performance of the macrobeads was first assessed by the classical height equivalent of a theoretical plate HETP analysis. The independence of HETP on linear flow rates studied suggests that a likely mode of solute transport within the macrobeads may be a combination of convection and diffusion-convective components. By using fluorescent-tagged immunoglobulins, the penetration of the adsorbent particle at different times and different levels of saturation was visually observed. The profiles obtained from dynamic experiments were compared to the profiles obtained from finite bath experiments. With an increase in the incubation time, the degree of penetration increased and the bead interior was saturated with FITC immunoglobulins at the end point of the finite bath experiment. In the dynamic uptake experiment, the degree of penetration was found to be a function of the linear velocity and level of breakthrough. The penetration of the bead radius, at times lower than the predicted diffusion time, suggests that the mode of transport in the chitosan beads is governed by a combination of convective and diffusive forces.