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.     

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%.     

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.     

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.     

Blood clot formation under flow: the importance of factor XI depends strongly on platelet count

A previously validated mathematical model of intravascular platelet deposition and tissue factor (TF)-initiated coagulation under flow is extended and used to assess the influence on thrombin production of the activation of factor XI (fXI) by thrombin and of the activation of factor IX (fIX) by fXIa. It is found that the importance of the thrombin-fXIa-fIXa feedback loop to robust thrombin production depends on the concentration of platelets in the blood near the injury. At a near-wall platelet concentration of ~250,000/μL, typical in vessels in which the shear rate is <200 s(-1), thrombin activation of fXI makes a significant difference only at low densities of exposed TF. If the near-wall platelet concentration is significantly higher than this, either because of a higher systemic platelet count or because of the redistribution of platelets toward the vessel walls at high shear rates, then thrombin activation of fXI makes a major difference even for relatively high densities of exposed TF. The model predicts that the effect of a severe fXI deficiency depends on the platelet count, and that fXI becomes more important at high platelet counts.     

Activation and extinction models for platelet adhesion

Adherent platelets are an important part of both thrombus formation and in certain stages of atherogenesis. Platelets can be activated by potent chemicals released from adherent platelets and adhere far more readily than unactivated ones. An analytical and numerical model is presented utilising high Peclet number for the activation and adhesion of platelets in shear flows. The model uses a similarity transformation, which characterises the relationship between convective, diffusive transport and the bulk platelet activating reaction mechanism. A first order surface reaction mechanism is used to model platelet adhesion at the wall (cell) surface. The reduced Damk?hler number, M, characterises the importance of the bulk reaction and includes both convective and diffusive terms. For a high rate of blood flow (M-->0) the activation of platelets can effectively be terminated. In contrast, for (M-->infinity) an inner layer of activated platelets exists with an infinitesimally thin reaction sheet separating activated and non-activated platelets. This characterisation by the Damk?hler number highlights results found clinically, in that thrombus forms in areas of low shear (high M) and in some cases an increased blood flow (low M) can inhibit the activation of platelets completely. The model shows the critical balance that exists between convection, diffusion and reaction.     

Margination and adhesion dynamics of tumor cells in a real microvascular network

In tumor metastasis, the margination and adhesion of tumor cells are two critical and closely related steps, which may determine the destination where the tumor cells extravasate to. We performed a direct three-dimensional simulation on the behaviors of the tumor cells in a real microvascular network, by a hybrid method of the smoothed dissipative particle dynamics and immersed boundary method (SDPD-IBM). The tumor cells are found to adhere at the microvascular bifurcations more frequently, and there is a positive correlation between the adhesion of the tumor cells and the wall-directed force from the surrounding red blood cells (RBCs). The larger the wall-directed force is, the closer the tumor cells are marginated towards the wall, and the higher the probability of adhesion behavior happen is. A relatively low or high hematocrit can help to prevent the adhesion of tumor cells, and similarly, increasing the shear rate of blood flow can serve the same purpose. These results suggest that the tumor cells may be more likely to extravasate at the microvascular bifurcations if the blood flow is slow and the hematocrit is moderate.     

Influence of erythrocyte aggregation on radial migration of platelet-sized spherical particles in shear flow

Blood platelets when activated are involved in the mechanisms of hemostasis and thrombosis, and their migration toward injured vascular endothelium necessitates interaction with red blood cells (RBCs). Rheology co-factors such as a high hematocrit and a high shear rate are known to promote platelet mass transport toward the vessel wall. Hemodynamic conditions promoting RBC aggregation may also favor platelet migration, particularly in the venous system at low shear rates. The aim of this study was to confirm experimentally the impact of RBC aggregation on platelet-sized micro particle migration in a Couette flow apparatus. Biotin coated micro particles were mixed with saline or blood with different aggregation tendencies, at two shear rates of 2 and 10 s⁻¹ and three hematocrits ranging from 20 to 60%. Streptavidin membranes were respectively positioned on the Couette static and rotating cylinders upon which the number of adhered fluorescent particles was quantified. The platelet-sized particle adhesion on both walls was progressively enhanced by increasing the hematocrit (p < 0.001), reducing the shear rate (p < 0.001), and rising the aggregation of RBCs (p < 0.001). Particle count was minimum on the stationary cylinder when suspended in saline at 2 s⁻¹ (57 ± 33), and maximum on the rotating cylinder at 60% hematocrit, 2 s⁻¹ and the maximum dextran-induced RBC aggregation (2840 ± 152). This fundamental study is confirming recent hypotheses on the role of RBC aggregation on venous thrombosis, and may guide molecular imaging protocols requiring injecting active labeled micro particles in the venous flow system to probe human diseases.     

Rheological properties of the blood influencing selectin-mediated adhesion of flowing leukocytes

We studied how the rheological properties of blood influenced capture and rolling adhesion of leukocytes as well as their margination in the bloodstream. When citrated, fluorescently labeled blood was perfused through glass capillaries coated with P-selectin, leukocytes formed numerous rolling attachments. The number of attached leukocytes increased as the hematocrit was increased between 10% and 30% and was essentially constant from 30% to 50%. In EDTA-treated blood, adhesion was absent, and the flux of marginated cells varied little with increasing hematocrit. However, the velocity of marginated leukocytes increased monotonically, whereas the volumetric flow rate was constant, implying that the flow velocity profile became blunted and wall shear rate increased. Thus increasing hematocrit promoted attachment for a given total flow rate, without increasing margination, even though wall shear rate and blood viscosity increased. Blood was diluted to 20% hematocrit with plasma, 40-kDa dextran (to reduce red blood cell aggregation), or 500-kDa dextran (to enhance aggregation). Increasing aggregation correlated with increasing leukocyte adhesion and with more slow-flowing leukocytes near the wall. Thus flowing erythrocytes promote leukocyte adhesion, either by causing margination of leukocytes or by initiating and stabilizing attachments that follow.     

Platelet adhesive dynamics. Part I: characterization of platelet hydrodynamic collisions and wall effects

Abnormally high shear stresses encountered in vivo induce spontaneous activation of blood platelets and formation of aggregates, even in the absence of vascular injury. A three-dimensional multiscale computational model—platelet adhesive dynamics—is developed and applied in Part I and Part II articles to elucidate key biophysical aspects of GPIbα-von-Willebrand-factor-mediated interplatelet binding that characterizes the onset of shear-induced platelet aggregation. In this article, the hydrodynamic effects of the oblate spheroidal shape of platelets and proximity of a plane wall on the nature of cell-cell collisions are systematically investigated. Physical quantities characterizing the adhesion probabilities between colliding platelet surfaces for the entire range of near-wall encounters between two platelets are obtained for application in platelet adhesive dynamics simulations of platelet aggregation explored in a companion article. The technique for matching simulation predictions of interplatelet binding efficiency to experimentally determined efficiencies is also described. Platelet collision behavior is found to be strikingly different from that of spheres, both close to and far from a bounding wall. Our results convey the significant effects that particle shape and presence of a bounding wall have on the particle trajectories and collision mechanisms, collision characteristics such as collision time and contact area, and collision frequency.     

Pulsatile flow in a coronary artery using multiphase kinetic theory

Pulsatile flow in a model of a right coronary artery (RCA) was previously modeled as a single-phase fluid and as a two-phase fluid using experimental rheological data for blood as a function of hematocrit and shear rate. Here we present a multiphase kinetic theory model which has been shown to compute correctly the viscosity of red blood cells (RBCs) and their migration away from vessel walls: the Fahraeus–Lindqvist effect. The computed RBC viscosity decreases with shear rate and vessel size, consistent with measurements. The pulsatile computations were performed using a typical cardiac waveform until a limit cycle was well established. The RBC volume fractions, shear stresses, shear stress gradients, granular temperatures, viscosities, and phase velocities varied with time and position during each cardiac cycle. Steady-state computations were also performed and were found to compare well with time-averaged transient results. The wall shear stress and wall shear stress gradients (both spatial and temporal) were found to be highest on the inside area of maximum curvature. Potential atherosclerosis sites are identified using these computational results.     

Comparison of blood particle deposition models for non-parallel flow domains

Adhesions of monocytes and platelets to a vascular surface, particularly in regions of flow stagnation, recirculation, and reattachment, are a significant initial event in a broad spectrum of particle-wall interactions that significantly influence the formation of stenotic lesions and mural thrombi. A number of approximations are available for the simulation of both monocyte and platelet interactions with the vascular surface. For the simulation of blood particle adhesion, this study hypothesizes that: (a) the discrete element approach, which accounts for finite particle size and inertia, is advantageous in the context of non-parallel flow domains including stagnation, recirculation, and reattachment; and (b) the likelihood for particle deposition may be effectively approximated as being non-linearly proportional to local particle concentration, residence time, and wall proximity. Models such as wall shear stress correlations, the multicomponent mixture approach, and Lagrangian particle tracking with and without hydrodynamic particle-wall interactions were evaluated. Quantitative performance of the selected models was established by comparisons to available experimental data sets for non-parallel axisymmetric suspension flows of monocytes and platelets. Factors including the convective-diffusive transport of particles, finite particle size and inertia, as well as near-wall hydrodynamic interactions were found to significantly influence blood particle deposition. Of the models studied, the near-wall residence time approach was found to be a particularly effective indicator for the deposition of monocytes (r2=0.74) and platelets (r2=0.57), given that nano-scale physical and biochemical effects must be greatly approximated in computational simulations involving relatively large-scale geometries and complex flow fields.     

Finite platelet size could be responsible for platelet margination effect

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.     

Computational investigation of blood cell transport in retinal microaneurysms

Microaneurysms (MAs) are one of the earliest clinically visible signs of diabetic retinopathy (DR). MA leakage or rupture may precipitate local pathology in the surrounding neural retina that impacts visual function. Thrombosis in MAs may affect their turnover time, an indicator associated with visual and anatomic outcomes in the diabetic eyes. In this work, we perform computational modeling of blood flow in microchannels containing various MAs to investigate the pathologies of MAs in DR. The particle-based model employed in this study can explicitly represent red blood cells (RBCs) and platelets as well as their interaction in the blood flow, a process that is very difficult to observe in vivo. Our simulations illustrate that while the main blood flow from the parent vessels can perfuse the entire lumen of MAs with small body-to-neck ratio (BNR), it can only perfuse part of the lumen in MAs with large BNR, particularly at a low hematocrit level, leading to possible hypoxic conditions inside MAs. We also quantify the impacts of the size of MAs, blood flow velocity, hematocrit and RBC stiffness and adhesion on the likelihood of platelets entering MAs as well as their residence time inside, two factors that are thought to be associated with thrombus formation in MAs. Our results show that enlarged MA size, increased blood velocity and hematocrit in the parent vessel of MAs as well as the RBC-RBC adhesion promote the migration of platelets into MAs and also prolong their residence time, thereby increasing the propensity of thrombosis within MAs. Overall, our work suggests that computational simulations using particle-based models can help to understand the microvascular pathology pertaining to MAs in DR and provide insights to stimulate and steer new experimental and computational studies in this area.     

Role of erythrocytes in leukocyte-endothelial interactions: mathematical model and experimental validation.

The binding of circulating cells to the vascular wall is a central process in inflammation, metastasis, and therapeutic cell delivery. Previous in vitro studies have identified the adhesion molecules on various circulating cells and the endothelium that govern the process under static conditions. Other studies have attempted to simulate in vivo conditions by subjecting adherent cells to shear stress as they interact with the endothelial cells in vitro. These experiments are generally performed with the cells suspended in Newtonian solutions. However, in vivo conditions are more complex because of the non-Newtonian flow of blood, which is a suspension consisting of 20-40% erythrocytes by volume. The forces imparted by the erythrocytes in the flow can contribute to the process of cell adhesion. A number of experimental and theoretical studies have suggested that the rheology of blood can influence the binding of circulating leukocytes by increasing the normal and axial forces on leukocytes or the frequency of their collision with the vessel wall, but there have been no systematic investigations of these phenomena to date. The present study quantifies the contribution of red blood cells (RBCs) in cell capture and adhesion to endothelial monolayers using a combination of mathematical modeling and in vitro studies. Mathematical modeling of the flow experiments suggested a physical mechanism involving RBC-induced leukocyte dispersion and/or increased normal adhesive contact. Flow chamber studies performed with and without RBCs in the suspending medium showed increases in wall collision and binding frequencies, and a decrease in rolling velocity in the presence of erythrocytes. Increased fluid viscosity alone did not influence the binding frequency, and the differences could not be attributed to large near-wall excesses of the lymphocytes. The results indicate that RBCs aid in the transport and initial engagement of lymphocytes to the vascular wall, modifying the existing paradigm for immune cell surveillance of the vascular endothelium by adding the erythrocyte as an essential contributor to this process.     

Platelet adhesion onto the wall of a flow chamber with an obstacle

In the present study, the data of the initial adhesion of platelets onto the wall of a flow chamber with an obstacle in steady human blood flows were obtained. The flowfields and the distribution of stress-related factors were simulated numerically by a finite volume method and the fluid dynamic effect on the platelet adhesion is discussed. In addition to the wall shear effect, the normal stress effect was also taken into account. A parameter Vn/¦Vt¦ was devised to assess the combined effect of both shear and normal forces in platelet adhesion. It was found that the peak adhesion occurred next to, but not on, the impingement point on the obstacle where the value of Vn/¦Vt¦ was negative. In these regions, direct impact played a major role in platelet adhesion. On the other hand, near the separation point before the obstacle where Vn/¦Vt¦ was insignificant, the mechanism was believed to be different from that in the direct impact region. Denser adhesion there might be caused by the accumulation and frequent collision of particles due to flow retardation and/or detour of the flow path. Interestingly, relatively low adhesion was found inside the recirculation regions. These results show that the normal stress effect (impingement) should be considered in platelet adhesion in addition to the shear effect.     

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.     

Platelet thrombi produced on cultured endothelial cells by the dye/light method.

Platelet adhesion and aggregation were induced on cultured endothelial cells using the fluorescent dye/light method. A cone-and-plate apparatus was newly developed to observe interactions between platelets and cultured endothelial cells under a shear flow condition. The platelet deposition grew on the light-irradiated area of the cells. Degree of endothelial cell injury induced by the dye/light reaction seemed to depend on the dye concentration. Application of either aspirin or indomethacin significantly inhibited the growth of platelet aggregation, but was not effective for the platelet adhesion to endothelial cells. The platelet thrombi were formed on endothelial cells without their denudation. It was found by transmission electron microscopy that platelets directly adhered to endothelial cells which were not seriously damaged. This thrombus model is expected to be applicable to some physiological and pharmacological studies investigating platelet-endothelial cell interaction and mechanism of platelet thrombus formation in blood vessels.     

Simulation of particle-hemodynamics in a partially occluded artery segment with implications to the initiation of microemboli and secondary stenoses.

Computational results of laminar incompressible blood-particle flow analyses in an axisymmetric artery segment with a smooth local area constriction of 75 percent have been presented. The flow input waveform was sinusoidal with a nonzero average. The non-Newtonian behavior of blood was simulated with a modified Quemada model, platelet concentrations were calculated with a drift-flux model, and monocyte trajectories were described and compared for both Newtonian and Quemada rheologies. Indicators of "disturbed flow" included the time-averaged wall shear stress (WSS), the oscillatory shear index (OSI), and the wall shear stress gradient (WSSG). Implications of the vortical flow patterns behind the primary stenosis to the formation of microemboli and downstream stenoses are as follows. Elevated platelet concentrations due to accumulation in recirculation zones mixed with thrombin and ADP complexes assumed to be released upstream in high wall shear stress regions, could form microemboli, which are convected downstream. Distinct near-wall vortices causing a local increase in the WSSG and OSI as well as blood-particle entrainment with possible wall deposition, indicate sites susceptible to the onset of an additional stenosis proximal to the initial geometric disturbance.