Model of platelet transport in flowing blood with drift and diffusion terms (original) (raw)
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An estimated shape function for drift in a platelet-transport model
Biophysical Journal, 1994
Pnor work has shown that concentraton profiles of platelets in flowing whole blood and of platelet-sized beads in fowing blood suspensxios can include near-wall excesses. A moder to describe this phernoenon was built about a singlecomponent convective diffusion equation. To irporate redistribui to peferred sites by shear flows of red cell suspensions, the model used a drift shape furton (in addition to the commonly used augmented difusion coefficnt). This paper reports experiments that provide an average concentration profile from which the shape function for that model is calculated; the experiments and shape funcion are for the parublar codtons of 40% hematocrit, platelet-sized latex beads (2.5 pm diameter), tube ID of 217 pm, 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 furtion is similar for the hematocrit of 15%.
Вестник ТОГУ (Bullet), 2014
For numerical modeling of the platelet transport in the shear flow the diffusion tensor estimation is of great importance. Shear-induced diffusion plays a key role in the particle transport. A numerical method for solution of equations of a platelet transport model using a full diffusion tensor is modified. The calculation results for the platelet thrombus formation model for various Reynolds numbers are given.
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.
Transient lateral transport of platelet-sized particles in flowing blood suspensions
Biophysical Journal, 1994
Concentration profiles of 2.5 pm latex beads were measured to demonstrate lateral transport of platelet-sized objects in flows of blood suspensions; the flows had equivalent Poiseuille wall shear rates (WSRs) from 250 to 1220 s-1. Each experimental trial began with a steady flow of suspension without beads in a thin-walled capillary tube (219 pm ID; 10.2 pm SD). The tube entrance was then switched to a reservoir containing suspension of equal hematocrit, but with beads, for a short interval of flow at the same WSR. This process established a paraboloidal tongue of labeled suspension with a transient concentration gradient at its surface. The tube and contents were rapidly frozen to fix the suspended particles in flow-determined locations. Segments of frozen tube were collected at distances from the entrance corresponding to 13%, 39%, and 65% of the axial extent of the ideal paraboloidal tongue. Concentration profiles were estimated from distances measured on fluorescence microscope images of cross-cut tube segments. Experiments used tubes either 40 or 50 cm long, suspension hematocrits of 0, 15, or 40%, and bead concentrations in the range of 1.5-2.2 x 1 05/mm3. Profiles for 0% hematocrit suspension, a dilute, single-component suspension, had features expected in normal diffusive mixing in a flow. Distinctly different profiles and more lateral transport occurred when the suspensions contained red cells; then, all profiles for 13% extent had regions of excess bead concentration near the wall. Suspension flows with 40% hematocrit exhibited the largest amount of lateral transport. A case is made that, to a first approximation, the rate of lateral transport grew linearly with WSR; however, statistical analysis showed that for 40% hematocrit, less lateral transport occurred when the WSR was 250 s-1 or 1220 s-1 than 560 s-1, thus indicating that the rate behavior is more complex.
Calculation of platelet clot growth based on advection-diffusion equations
Mathematical Models and Computer Simulation, 2015
A numerical method for solving equations of a model for platelet transport in blood plasma flow and platelet clot formation is modified. The full matrix for shear-induced diffusion of the platelets is used. A comparison of a blood clot’s shapes corresponding to various lengths of vessel wall damage is given.
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.
Numerical simulation of blood flows with non-uniform distribution of erythrocytes and platelets
Russian Journal of Numerical Analysis and Mathematical Modelling, 2000
Blood cell interactions present an important mechanism in many processes occurring in blood. Due to different blood cell properties, cells of different types behave differently in the flow. One of observed behaviours is segregation of erythrocytes, which group near the flow axis, and platelets, which migrate towards the blood vessel wall. In this work, a three dimensional model based on Dissipative Particle Dynamics method is used to study the interaction of erythrocytes and platelets in a flow inside a cylindrical channel. The erythrocytes are modelled as elastic highly deformable membranes, while platelets are modelled as elastic spherical membranes which tend to preserve their spherical shape. As the result of modelling, the separation of erythrocytes and platelets in a cylindrical vessel flow is shown for vessels of different diameters. Erythrocyte and platelet distribution profiles in vessel cross-section are in good agreement with existing experimental results. The described 3-D model can be used for further modelling of blood flow-related problems.
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.
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...
Rheophoresis-A broader concept of platelet dispersivity
Biorheology, 1982
Interactions among red cells and platelets in flowing blood result in significant dispersive motions of the platelets, which are commonly modelled by an effective diffusion coefficient. This paper examines an additional platelet flux, termed rheophoresis, to model platelet motions due to the gradient of hematocrit. Rheophoretic effects occur near walls because geometric exclusion and fluid mechanical repulsion of red cells create a hematocrit gradient there. Models using rheophoretic flux show that platelet concentration near walls is elevated; such models provide a consistent interpretation of available experimental data. Estimates show the coefficients for traditional effective diffusivity and the rheophoretic diffusivity have similar magnitudes. The effects of rheophoresis on axial development of platelet concentration profiles and on surface deposition are discussed.