Rheophoresis-A broader concept of platelet dispersivity (original) (raw)
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Physics of Fluids
The radial distribution of cells in blood flow inside vessels is highly non-homogeneous. This leads to numerous important properties of blood, yet the mechanisms shaping these distributions are not fully understood. The motion of cells is governed by a variety of hydrodynamic interactions and cell-deformation mechanics. Properties, such as the effective cell diffusivity, are therefore difficult to investigate in flows other than pure shear flows. In this work, several single-cell, cell-pair, and large-scale many-cell simulations are performed using a validated numerical model. Apart from the single-cell mechanical validations, the arising flow profile, cell free layer widths, and cell drift velocities are compared to previous experimental findings. The motion of the cells at various radial positions and under different flow conditions is extracted, and evaluated through a statistical approach. An extended diffusive flux-type model is introduced which describes the cell diffusivities under a wide range of flow conditions and incorporates the effects of cell deformability through a shear dependent description of the cell collision cross sections. This model is applicable for both red blood cells and platelets. Further evaluation of particle trajectories shows that the margination of platelets cannot be the net result of gradients in diffusivity. However, the margination mechanism is strongly linked to the gradient of the hematocrit level. Finally, it shows that platelets marginate only until the edge of the red blood cell distribution and they do not fill the cell free layer.
Fluid shear as a possible mechanism for platelet diffusivity in flowing blood
Journal of Biomechanics, 1986
Platelet transport theory is based on convection diffusion and describes adequately the influence of wail shear rate, platelet concentration and axial (down stream) position. Until now, the influence of the predominant factors affecting platelet adherence, the hematocrit and the red cell size, was not included in this theory. Their role remained hidden in the platelet diffusivity (Dv), which was assumed to be related to the shear rate (7) expressed in s-' by a power law function D, = m;", in which m and n were thought to be constants.
Microvascular Research, 1987
Methods involving microscopy were used to obtain concentration profiles of plateletsized beads during flow through glass channels. Suspensions of fluorescent latex beads (2.38 pm diam) and washed red blood cells were made from an isotonic albumin-dextrose solution. A syringe pump regulated the suspension flow through glass channels, which were either 50 or 100 pm wide; most experiments used a wall shear rate of 1630 set-'. Via stroboscopic epifluorescence microscopy, photographs were collected on image planes parallel to the channel wall. Profiles of the bead concentration in the narrow channel direction were made by assembling counts of the focused bead images in the photographs. The results showed that a near-wall excess of the beads occurred when the suspension contained a significant fraction of red cells (over 7%). For hematocrits of 15 to 45% (the highest studied), the excess was above five times the concentration in the central region. Experiments with channels of both widths showed the region of excess beads was 5 to 8 pm thick. A series of experiments with SO-pm channels, with a suspension hematocrit of 15%, and with wall shear rates from 50 to 3180 sect' showed that near-wall excesses were large only for wall shear rates of 430 set-' and above. This work demonstrated the effects of wall shear rate (flow rate) and hematocrit on the number of platelet-sized beads near a surface and hence illustrated physical (rheological) factors that act in blood-surface interaction. 0
Finite platelet size could be responsible for platelet margination effect
Biophysical journal, 2011
Blood flows through vessels as a segregated suspension. Erythrocytes distribute closer to the vessel axis, whereas platelets accumulate near vessel walls. Directed platelet migration to the vessel walls promotes their hemostatic function. The mechanisms underlying this migration remain poorly understood, although various hypotheses have been proposed to explain this phenomenon (e.g., the available volume model and the drift-flux model). To study this issue, we constructed a mathematical model that predicts the platelet distribution profile across the flow in the presence of erythrocytes. This model considers platelet and erythrocyte dimensions and assumes an even platelet distribution between erythrocytes. The model predictions agree with available experimental data for near-wall layer margination using platelets and platelet-modeling particles and the lateral migration rate for these particles. Our analysis shows that the strong expulsion of the platelets from the core to the periphery of the blood vessel may mainly arise from the finite size of the platelets, which impedes their positioning in between the densely packed erythrocytes in the core. This result provides what we believe is a new insight into the rheological control of platelet hemostasis by erythrocytes.
Near-wall excess of platelets induced by lateral migration of erythrocytes in flowing blood
The American journal of physiology, 1993
In this study we present experimental data on the inhomogeneous distribution of platelets in polyethylene tubes (200 microns diam) based on the inverse Fåhraeus effect for platelets. It is shown that platelets are expelled toward the red blood cell-depleted marginal layer near the tube wall by mutual interaction with erythrocytes. By means of a straightforward model, the near-wall concentration of platelets could be estimated from measurements on the average tubular platelet concentration. The marginal layer originates from the hydrodynamic interaction of the deformable erythrocytes with the tube wall. If the tube diameter is large compared with the size of the erythrocytes, the lateral migration effects can effectively be scaled on the absolute distance between the erythrocytes and the tube wall. This results in the main conclusion that the near-wall concentration of platelets is significantly enhanced up to about seven times the average concentration, practically irrespective of t...
Influence of erythrocyte shape on platelet scattering towards vessel wall
International Journal of Biomedical Engineering and Technology, 2016
Red Blood Cell (RBC) geometry forms unique distinguished shape. This shape is thought to have a major influence on both the function and the dynamics of the moving erythrocyte. The shape of the RBC is hypothesised to cause platelet scattering and diffusion towards vessel wall. The current study is built to provide a detailed review of the previous theories that discuss the influence of RBC shape on its functionality and dynamics, a detailed focus on the influence of RBC dynamics on platelet migration towards the vessel wall is presented. Afterwards, computational results representing the influence of RBC shape on platelet migration to the vessel wall are listed. The results involve comparison between circular and elliptical RBCs using low Reynolds number channel flow regime. It is shown that this migration process is primarily affected by the diameter of the RBC and not by its shape.
Computational model of whole blood exhibiting lateral platelet motion induced by red blood cells
International Journal for Numerical Methods in Biomedical Engineering, 2010
An Immersed Boundary method is developed in which the fluid's motion is calculated using the lattice Boltzmann method. The method is applied to explore the experimentally-observed lateral redistribution of platelets and platelet-sized particles in concentrated suspensions of red blood cells undergoing channel flow. Simulations capture red-blood-cell-induced lateral platelet motion and the consequent development of a platelet concentration profile that includes an enhanced concentration within a few microns of the channel walls. In the simulations, the near-wall enhanced concentration develops within approximately 400 msec starting from a random distribution of red blood cells and a uniform distribution of platelet-sized particles.
Grow with the flow: a spatial-temporal model of platelet deposition and blood coagulation under flow
Mathematical Medicine and Biology, 2010
The body's response to vascular injury involves two intertwined processes: platelet aggregation and coagulation. Platelet aggregation is a predominantly physical process, whereby platelets clump together, and coagulation is a cascade of biochemical enzyme reactions. Thrombin, the major product of coagulation, directly couples the biochemical system to platelet aggregation by activating platelets and by cleaving fibrinogen into fibrin monomers that polymerize to form a mesh that stabilizes platelet aggregates. Together, the fibrin mesh and the platelet aggregates comprise a thrombus that can grow to occlusive diameters. Transport of coagulation proteins and platelets to and from an injury is controlled largely by the dynamics of the blood flow. To explore how blood flow affects the growth of thrombi and how the growing masses, in turn, feed back and affect the flow, we have developed the first spatial-temporal mathematical model of platelet aggregation and blood coagulation under flow that includes detailed descriptions of coagulation biochemistry, chemical activation and deposition of blood platelets, as well as the two-way interaction between the fluid dynamics and the growing platelet mass. We present this model and use it to explain what underlies the threshold behaviour of the coagulation system's production of thrombin and to show how wall shear rate and near-wall enhanced platelet concentrations affect the development of growing thrombi. By accounting for the porous nature of the thrombus, we also demonstrate how advective and diffusive transport to and within the thrombus affects its growth at different stages and spatial locations.
Model of platelet transport in flowing blood with drift and diffusion terms
Biophysical Journal, 1991
A drift term is added to the convective diffusion equation for platelet transport so that situations with near-wall excesses of platelets can be described. The mathematical relationship between the drift and the fully developed, steady-state platelet concentration profile is shown and a functional form of the drift that leads to concentration profiles similar to experimentally determined profiles is provided. The transport equation is numerically integrated to determine concentration profiles in the developing region of a tube flow. With the approximate drift function and typical values of augmented diffusion constant, the calculated concentration profiles have near-wall excesses that mimic experimental results, thus implying the extended equation is a valid description of rheological events. Stochastic differential equations that are equivalent to the convective diffusion transport equation are shown, and simulations with them are used to illustrate the impact of the drift term on platelet concentration profiles during deposition in a tube flow.
Platelet Motion near a Vessel Wall or Thrombus Surface in Two-Dimensional Whole Blood Simulations
Biophysical Journal, 2013
Computational simulations using a two-dimensional lattice-Boltzmann immersed boundary method were conducted to investigate the motion of platelets near a vessel wall and close to an intravascular thrombus. Physiological volume fractions of deformable red blood cells and rigid platelet-size elliptic particles were studied under arteriolar flow conditions. Tumbling of platelets in the red-blood-cell depleted zone near the vessel walls was strongly influenced by nearby red blood cells. The thickness of the red-blood-cell depleted zone was greatly reduced near a thrombus, and platelets in this zone were pushed close to the surface of the thrombus to distances that would facilitate their cohesion to it. The distance, nature, and duration of close platelet-thrombus encounters were influenced by the porosity of the thrombus. The strong influence on platelet-thrombus encounters of red-blood-cell motion and thrombus porosity must be taken into account to understand the dynamics of platelet attachment to a growing thrombus.