A free boundary problem modeling thrombus growth

Recently, neglect of either shear stress, surface saturation, or thrombus growth in mathematical models of platelet deposition has been identified as leading cause of inability to match experimental evidence. While the consideration of shear stress is necessary to obtain at least some qualitative agreement, purely shear-dependent approaches yield notable quantitative discrepancies. In a previous paper, the author demonstrated that surface saturation significantly improves model predictions. However, discrepancies still persist when thrombus growth is neglected. Therefore, the present work develops a free boundary problem which takes this into account. Numerical simulations are performed using the level set method. The results agree well with measurements in stagnation point flow and tubular expansions, which demonstrates the coupling of flow, platelet adhesion, and aggregate growth in primary hemostasis.     

Efficiency of platelet adhesion to fibrinogen depends on both cell activation and flow

The kinetics of adhesion of platelets to fibrinogen (Fg) immobilized on polystyrene latex beads (Fg-beads) was determined in suspensions undergoing Couette flow at well-defined homogeneous shear rates. The efficiency of platelet adhesion to Fg-beads was compared for ADP-activated versus "resting" platelets. The effects of the shear rate (100-2000 s(-1)), Fg density on the beads (24-2882 Fg/microm(2)), the concentration of ADP used to activate the platelets, and the presence of soluble fibrinogen were assessed. "Resting" platelets did not specifically adhere to Fg-beads at levels detectable with our methodology. The apparent efficiency of platelet adhesion to Fg-beads readily correlated with the proportion of platelets "quantally" activated by doses of ADP, i.e., only ADP-activated platelets appeared to adhere to Fg-beads, with a maximal adhesion efficiency of 6-10% at shear rates of 100-300 s(-1), decreasing with increasing shear rates up to 2000 s(-1). The adhesion efficiency was found to decrease by only threefold when decreasing the density of Fg at the surface of the beads by 100-fold, with only moderate decreases in the presence of physiologic concentrations of soluble Fg. These adhesive interactions were also compared using activated GPIIbIIIa-coated beads. Our studies provide novel model particles for studying platelet adhesion relevant to hemostasis and thrombosis, and show how the state of activation of the platelet and the local flow conditions regulate Fg-dependent adhesion.     

In Vitro Measurement and Modeling of Platelet Adhesion on VWF-Coated Surfaces in Channel Flow

The process of platelet adhesion is initiated by glycoprotein (GP)Ib and GPIIbIIIa receptors on the platelet surface binding with von Willebrand factor on the vascular walls. This initial adhesion and detachment of a single platelet is a complex process that involves multiple bonds forming and breaking and is strongly influenced by the surrounding blood-flow environment. In addition to bond-level kinetics, external factors such as shear rate, hematocrit, and GPIb and GPIIbIIIa receptor densities have also been identified as influencing the platelet-level rate constants in separate studies, but this still leaves a gap in understanding between these two length scales. In this study, we investigate the fundamental relationship of the dynamics of platelet adhesion, including these interrelating factors, using a coherent strategy. We build a, to our knowledge, novel and computationally efficient multiscale model accounting for multibond kinetics and hydrodynamic effects due to the flow of a cellular suspension. The model predictions of platelet-level kinetics are verified by our microfluidic experiments, which systematically investigate the role of each external factor on platelet adhesion in an in vitro setting. We derive quantitative formulas describing how the rates of platelet adhesion, translocation, and detachment are defined by the molecular-level kinetic constants, the local platelet concentration near the reactive surface determined by red-blood-cell migration, the platelet effective reactive area due to its tumbling motion, and the platelet surface receptor density. Furthermore, if any of these aspects involved have abnormalities, e.g., in a disease condition, our findings also have clinical relevance in predicting the resulting change in the adhesion dynamics, which is essential to hemostasis and thrombosis.     

Glycoprotein (GP) Ib-IX-transfected cells roll on a von Willebrand factor matrix under flow. Importance of the GPib/actin-binding protein (ABP-280) interaction in maintaining adhesion under high shear

Adhesion of platelets to sites of vascular injury is critical for hemostasis and thrombosis and is dependent on the binding of the vascular adhesive protein von Willebrand factor (vWf) to the glycoprotein (GP) Ib-V-IX complex on the platelet surface. A unique but poorly defined characteristic of this receptor/ligand interaction is its ability to support platelet adhesion under conditions of high shear stress. To examine the structural domains of the GPIb-V-IX complex involved in mediating cell adhesion under flow, we have expressed partial (GPIb-IX), complete (GPIb-V-IX), and mutant (GPIbalpha cytoplasmic tail mutants) receptor complexes on the surface of Chinese hamster ovary (CHO) cells and examined their ability to adhere to a vWf matrix in flow-based adhesion assays. Our studies demonstrate that the partial receptor complex (GPIb-IX) supports CHO cell tethering and rolling on a bovine or human vWf matrix under flow. The adhesion was specifically inhibited by an anti-GPIbalpha blocking antibody (AK2) and was not observed with CHO cells expressing GPIbbeta and GPIX alone. The velocity of rolling was dependent on the level of shear stress, receptor density, and matrix concentration and was not altered by the presence of GPV. In contrast to selectins, which mediate cell rolling under conditions of low shear (20-200 s-1), GPIb-IX was able to support cell rolling at both venous (150 s-1) and arterial (1500-10,500 s-1) shear rates. Studies with a mutant GPIbalpha receptor subunit lacking the binding domain for actin-binding protein demonstrated that the association of the receptor complex with the membrane skeleton is not essential for cell tethering or rolling under low shear conditions, but is critical for maintaining adhesion at high shear rates (3000-6000 s-1). These studies demonstrate that the GPIb-IX complex is sufficient to mediate cell rolling on a vWf matrix at both venous and arterial levels of shear independent of other platelet adhesion receptors. Furthermore, our results suggest that the association between GPIbalpha and actin-binding protein plays an important role in enabling cells to remain tethered to a vWf matrix under conditions of high shear stress.     

Functional analysis of a recombinant glycoprotein Ia/IIa (Integrin alpha(2)beta(1)) I domain that inhibits platelet adhesion to collagen and endothelial matrix under flow conditions

The interaction of platelets with collagen plays an important role in primary hemostasis. Glycoprotein Ia/IIa (GPIa/IIa, integrin alpha(2)beta(1)) is a major platelet receptor for collagen. The binding site for collagen has been mapped to the I domain within the alpha(2) subunit (GPIa). In order to assess the role of the alpha(2)-I domain structure in GPIa/IIa binding to collagen, a recombinant I domain (amino acids 126-337) was expressed in Escherichia coli. The alpha(2)-I protein bound human types I and III collagen in a saturable and divalent cation-dependent manner and was blocked by the alpha(2)beta(1) function blocking antibody 6F1. The alpha(2)-I protein inhibited collagen-induced platelet aggregation (IC(50) = 600 nM). Unexpectedly, 6F1, an antibody that fails to inhibit platelet aggregation in platelet-rich plasma, blocked the inhibitory effect of the alpha(2)-I protein. The alpha(2)-I protein was able to prevent platelet adhesion to a collagen surface exposed to flowing blood under low shear stress. Interestingly, it inhibited platelet adhesion to extracellular matrix at high shear stress. These results, taken together, provide firm evidence that GPIa/IIa directly mediates the first contact of platelets with collagen under both stirring and flow conditions.     

Differential Involvement of ERK2 and p38 in platelet adhesion to collagen

We investigated the role of two MAP kinases, ERK2 and p38, in platelet adhesion and spreading over collagen matrix in static and blood flow conditions. P38 was involved in collagen-induced platelet adhesion and spreading in static adhesion conditions, whereas ERK2 was not. In blood flow conditions, with shear rates of 300 or 1500 s(-1), ERK2 and p38 displayed differential involvement in platelet adhesion, depending on the presence or absence of the von Willebrand factor (vWF). Low collagen coverage densities (0.04 microg/cm2) did not support vWF binding. During perfusions over this surface, platelet adhesion was not affected by the inhibition of ERK2 phosphorylation by PD 98059. However, abolishing p38 activation by SB 203580 treatment reduced platelet adhesion by 67 +/- 9% at 300 s(-1) and 56 +/- 2% at 1500 s(-1). In these conditions, the p38 activity required for platelet adhesion depends on the alpha2beta1 collagen receptor. At higher collagen coverage densities (0.8 microg/cm2) supporting vWF binding, the inhibition of ERK2 activity by PD 98059 decreased adhesion by 47 +/- 6% at 300 s(-1) and 72 +/- 3% at 1500 s(-1), whereas p38 inhibition had only a small effect. The ERK2 activity required for platelet adhesion was dependent on the interaction of vWF with GPIb. In conclusion, ERK2 and p38 have complementary effects in the control of platelet adhesion to collagen in a shear stress-dependent manner.     

Platelet adhesion receptors and (patho)physiological thrombus formation

In thrombus formation associated with hemostasis or thrombotic disease, blood platelets first undergo a rapid transition from a circulating state to an adherent state, followed by activation and aggregation. Under flow conditions in the bloodstream, this process potentially involves platelet-platelet, platelet-endothelium, platelet-subendothelial matrix, and platelet-leukocyte interactions. Specific adhesion receptors on platelets mediate these interactions, by engaging counter-receptors on other cells, or noncellular ligands in the plasma or matrix. The glycoprotein (GP) Ib-IX-V complex on platelets initiates adhesion at high shear stress by binding the adhesive ligand, von Willebrand Factor (vWF). GP Ib-IX-V may also mediate platelet-endothelium or platelet-leukocyte adhesion, by recognition of P-selectin or Mac-1, respectively. Other membrane glycoproteins, such as the collagen receptor GP VI, may trigger platelet activation at low shear rates. Engagement of GP Ib-IX-V or GP VI leads ultimately to platelet aggregation mediated by the integrin, alphaIIbbeta3 (GP IIb-IIIa). This review will focus on recent advances in understanding structure-activity relationships of GP Ib-IX-V, its role in initiating thrombus formation, and its emerging relationships with other vascular cell adhesion receptors.     

Characterization of liposomes carrying von Willebrand factor-binding domain of platelet glycoprotein Ibalpha: a potential substitute for platelet transfusion.

Platelet glycoprotein (GP) Ib/IX/V complex is a receptor for von Willebrand factor (vWf), which plays a crucial role in primary hemostasis by mediating platelet adhesion to injured blood vessels. We have expressed in CHO cells a fragment of GPIba that retained a vWf-binding function. The recombinant fragment (rGPIba) was incorporated into liposomes and evaluated their functions in vitro. rGPIba on the liposome surface was detectable by flow cytometric analysis. Addition of vWf and ristocetin caused specific agglutination of rGPIbalpha-liposomes, as evaluated by an aggregometer or a fluorescent microscopy. When ristocetin was added to platelet-rich plasma (PRP) pre-mixed with rhodamine-labeled rGPIbalpha-liposomes, platelets aggregated and rhodamine-fluorescence was strongly positive in the platelet thrombi, suggesting that heterologous aggregation (attachment of liposomes to platelets) occurred. Platelet aggregation in PRP at low platelet concentration (20-80 x 10(6)/ml) was enhanced by rGPIbalpha-liposomes in a dose-dependent manner. Thus, rGPIbalpha-liposomes may accumulate on vWf-exposed subendothelial tissues and enhance platelet function in vivo, supporting hemostasis in thrombocytopenic individuals.     

Platelet GP Ib/IX/V complex: physiological role

Platelets play an essential role in primary hemostasis and in thrombotic events, particularly in arterial vessels, as rheological conditions originate closer interactions between platelets and endothelium than lower shear rates. In response to vascular injury, platelets adhere to the subendothelial matrix by membrane receptors potentiating the generation of thrombin, become activated, and a series of biochemical processes induce platelet aggregation and liberation of intracellular metabolic products to the extracelular medium. Among platelet receptors, glycoprotein (GP) Ib/IX/V complex is peculiar, as it binds adhesive proteins, mainly von Willebrand factor (vWF), and thrombin, the main platelet agonist. Platelet adhesion and subsequent aggregation under conditions of high shear flow, essentially relies upon this receptor's capacity of binding to the subendothelial matrix, initiating signal transduction. Two proteins associated to GP Ib/IX/V, actin-binding protein (ABP) 280 and 14-3-3zeta, are potential mediators of signal transduction by the complex, but their specific contribution in this process is not yet fully understood. Additionally, two proteins implicated in signal transduction by immune stimuli, FcgammaRIIA and FcR gamma-chain, associate with GPIb/IX/V complex, and increasing data indicate a potential role in GPIbalpha mediated signal transduction.     

Shear-dependent 'stick-and-roll' adhesion of type 1 fimbriated Escherichia coli

It is generally assumed that bacteria are washed off surfaces as fluid flow increases because they adhere through 'slip-bonds' that weaken under mechanical force. However, we show here that the opposite is true for Escherichia coli attachment to monomannose-coated surfaces via the type 1 fimbrial adhesive subunit, FimH. Raising the shear stress (within the physiologically relevant range) increased accumulation of type 1 fimbriated bacteria on monomannose surfaces by up to two orders of magnitude, and reducing the shear stress caused them to detach. In contrast, bacterial binding to anti-FimH antibody-coated surfaces showed essentially the opposite behaviour, detaching when the shear stress was increased. These results can be explained if FimH is force-activated; that is, that FimH mediates 'catch-bonds' with mannose that are strengthened by tensile mechanical force. As a result, on monomannose-coated surfaces, bacteria displayed a complex 'stick-and-roll' adhesion in which they tended to roll over the surface at low shear but increasingly halted to stick firmly as the shear was increased. Mutations in FimH that were predicted earlier to increase or decrease force-induced conformational changes in FimH were furthermore shown here to increase or decrease the probability that bacteria exhibited the stationary versus the rolling mode of adhesion. This 'stick-and-roll' adhesion could allow type 1 fimbriated bacteria to move along mannosylated surfaces under relatively low flow conditions and to accumulate preferentially in high shear regions.     

Platelet deposition onto fibrin-coated surfaces under flow conditions

Platelet deposition on fibrin-coated surfaces and release from these adherent platelets were studied in an in vitro flow system. When a mixed suspension of washed platelets and red cells flowed through a fibrin-coated glass tube, only platelets were deposited onto the fibrin-coated surfaces. The density of adhered platelets increased with flow time and decreased with distance from the tube inlet. The adhesion rate increased with increasing shear rates from 45 s-1 to 180 s-1. This adhesion process appears to fit a diffusion-limited mathematical model. Comparing with glass and other protein-coated surfaces such as collagen, fibrinogen, or albumin coated surfaces, the number of adhered platelet per unit area decreased in the following descending order: collagen, fibrin, fibrinogen, glass, albumin. On the other hand, the degree of release reaction from these platelets decreased by another order: collagen, glass, fibrinogen, fibrin. We observed little release from platelets that were in contact with a fibrin-coated surface. Our results suggest that platelets specifically adhere to fibrin-coated surface and that this interaction does not induce platelet release.     

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.     

Quantitation of platelet adhesion to Ti and DLC-coated Ti in vitro using (125)I-labeled platelets

Measurement of platelet adhesion in vitro is a good indicator of its reactivity to implant devices in vivo. Platelets were labeled with I-125 without affecting its normal morphology and function and the labeled platelets were suspended in platelet poor plasma and exposed to Ti and diamond like carbon-coated (DLC) Ti discs, under dynamic conditions, using a parallel plate flow chamber. The test materials were washed, dried, exposed to a phosphor screen and scanned to get the images. The number of platelets that adhered to Ti was found to be higher than those that adhered to DLC coated Ti sample, irrespective of the shear stress which was varied between 2 and 16 dynes/cm(2).     

Specific adhesion of glycophorin liposomes to a lectin surface in shear flow.

The adhesion of cells to other cells or to surfaces by receptor-ligand binding in a shear field is an important aspect of many different biological processes and various cell separation techniques. The purpose of this study was to observe the adhesion of model cells with receptor molecules embedded in their surfaces to a ligand-coated surface under well-defined flow conditions in a parallel plate flow chamber. Liposomes containing glycophorin were used as the model cells to permit a variation in the adhesion parameters and then to observe the effect on adhesion. A mathematical model for cell sedimentation was created to predict the deposition time and the velocity preceding adhesion for the selection of experimental operating conditions and the methods useful for data analysis. The likelihood of cell attachment was represented by a quantity called the sticking probability which was defined as the inverse of the number of times a liposome made contact with the surface before attachment occurred. The sticking probability decreased as the cell receptor concentration was lowered from approximately 10(4) to 10(2) receptors per 4-microns diam liposome and as the shear rate increased from 5 to 22 s-1. The effect of the wall shear rate and particle diameter on detachment of liposomes from a surface was also observed.     

Influence of cell deformation on leukocyte rolling adhesion in shear flow

Blood cell interaction with vascular endothelium is important in microcirculation, where rolling adhesion of circulating leukocytes along the surface of endothelial cells is a prerequisite for leukocyte emigration under flow conditions. HL-60 cell rolling adhesion to surface-immobilized P-selectin in shear flow was investigated using a side-view flow chamber, which permitted measurements of cell deformation and cell-substrate contact length as well as cell rolling velocity. A two-dimensional model was developed based on the assumption that fluid energy input to a rolling cell was essentially distributed into two parts: cytoplasmic viscous dissipation, and energy needed to break adhesion bonds between the rolling cell and its substrate. The flow fields of extracellular fluid and intracellular cytoplasm were solved using finite element methods with a deformable cell membrane represented by an elastic ring. The adhesion energy loss was calculated based on receptor-ligand kinetics equations. It was found that, as a result of shear-flow-induced cell deformation, cell-substrate contact area under high wall shear stresses (20 dyn/cm2) could be as much as twice of that under low stresses (0.5 dyn/cm2). An increase in contact area may cause more energy dissipation to both adhesion bonds and viscous cytoplasm, whereas the fluid energy input may decrease due to the flattened cell shape. Our model predicts that leukocyte rolling velocity will reach a plateau as shear stress increases, which agrees with both in vivo and in vitro experimental observations.     

An Investigation on Platelet Transport during Thrombus Formation at Micro-Scale Stenosis

This paper reports on an investigation of mass transport of blood cells at micro-scale stenosis where local strain-rate micro-gradients trigger platelet aggregation. Using a microfluidic flow focusing platform we investigate the blood flow streams that principally contribute to platelet aggregation under shear micro-gradient conditions. We demonstrate that relatively thin surface streams located at the channel wall are the primary contributor of platelets to the developing aggregate under shear gradient conditions. Furthermore we delineate a role for red blood cell hydrodynamic lift forces in driving enhanced advection of platelets to the stenosis wall and surface of developing aggregates. We show that this novel microfluidic platform can be effectively used to study the role of mass transport phenomena driving platelet recruitment and aggregate formation and believe that this approach will lead to a greater understanding of the mechanisms underlying shear-gradient dependent discoid platelet aggregation in the context of cardiovascular diseases such as acute coronary syndromes and ischemic stroke.     

Tortuosity triggers platelet activation and thrombus formation in microvessels

Tortuous blood vessels are often seen in humans in association with thrombosis, atherosclerosis, hypertension, and aging. Vessel tortuosity can cause high fluid shear stress, likely promoting thrombosis. However, the underlying physical mechanisms and microscale processes are poorly understood. Accordingly, the objectives of this study were to develop and use a new computational approach to determine the effects of venule tortuosity and fluid velocity on thrombus initiation. The transport, collision, shear-induced activation, and receptor-ligand adhesion of individual platelets in thrombus formation were simulated using discrete element method. The shear-induced activation model assumed that a platelet became activated if it experienced a shear stress above a relative critical shear stress or if it contacted an activated platelet. Venules of various levels of tortuosity were simulated for a mean flow velocity of 0.10?cm s(-1), and a tortuous arteriole was simulated for a mean velocity of 0.47?cm s(-1). Our results showed that thrombus was initiated at inner walls in curved regions due to platelet activation in agreement with experimental studies. Increased venule tortuosity modified fluid flow to hasten thrombus initiation. Compared to the same sized venule, flow in the arteriole generated a higher amount of mural thrombi and platelet activation rate. The results suggest that the extent of tortuosity is an important factor in thrombus initiation in microvessels.     

Ristocetin-induced self-aggregation of von Willebrand factor

Von Willebrand factor (VWF) is a large multimeric adhesive glycoprotein, with complex roles in thrombosis and hemostasis, present in circulating blood and in secretory granules of endothelial cells and platelets. High shear stress triggers conformational changes responsible for both binding to the platelet receptor glycoprotein GpIb and its self-association, thus supporting the formation of platelet plug under flow. Ristocetin also promotes the interaction of VWF with GpIb and is able to induce platelet aggregation, and thus is largely used to mimic this effect in vitro. In this research paper, we followed the time course of VWF self-association in solution induced by ristocetin binding by light scattering and at the same time we collected atomic force microscopy images to clarify the nature of the assembly that is formed. In fact, this process evolves initially through the formation of fibrils that subsequently interact to form supramolecular structures whose dimensions would be capable of trapping platelets even in the absence of any degree of shear stress or interaction with external surfaces. This intrinsic property, that is the ability to self-aggregate, may be involved in some pathological settings that have been revealed in clinical practice.     

Chronic pulsatile shear stress impacts synthesis of proteoglycans by endothelial cells: effect on platelet aggregation and coagulation

Endothelial-derived proteoglycans are important regulators of the coagulation-pathway in vivo and our primary objective of this study was to determine whether chronic shear stress affected the synthesis, release, and activity of proteoglycans from bovine aortic endothelial cells (BAEC). BAEC were cultured under shear and proteoglycans were purified from BAEC conditioned media and analyzed using both anionic exchange and size exclusion chromatography. The overall amount of proteoglycans produced per cell was significantly greater for the high shear-treated samples compared to the low shear-treated samples indicating that the shear magnitude did impact cell responsiveness. While overall size and composition of the proteoglycans and glycosaminoglycan (GAG) side chains were not altered by shear, the relative proportion of the high and low molecular weight species was inversely related to shear and differed significantly from that found under static tissue culture conditions. Moreover, a unique proteoglycan peak was identified from low shear stress (5 +/- 2 dynes/cm(2)) conditioned media when compared to high shear conditions (23 +/- 8 dynes/cm(2)) via anionic exchange chromatography, suggesting that subtle changes in the GAG structures may impact activity of these molecules. In order to characterize whether these changes impacted proteoglycan function, we studied the effects of shear specific proteoglycans on the inhibition of thrombin-induced human platelet aggregation as well as on platelet-fibrin clot dynamics. Proteoglycans from high shear-treated samples were less effective inhibitors of both platelet aggregation and blood coagulation inhibition than proteoglycans from low shear-treated samples and both were less effective than proteoglycans isolated from static tissue culture samples. However, due to changes in the overall proteoglycan synthesis and release rate, the high and low shear-treated sample had essentially identical effects on these activities, suggesting that the cells were able to compensate for stress-induced proteoglycan changes. Our data suggests that shear stress, by altering proteoglycan synthesis and fine structure, may play a role in maintaining vascular hemodynamics and hemostasis.