Model of platelet transport in flowing blood with drift and diffusion terms

Eckstein, Eugene C.; Belgacem, Fethi Bin Muhammad

doi:10.1016/s0006-3495(91)82030-6

Cited by 115 publications

(115 citation statements)

References 26 publications

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“…The impact of this assumption is believed to be small because the Smoluchovski number, ratio of shear gradient encounter rate to random-walk collision rate, for platelets in the flow considered here is quite high, and an augmentation of platelet diffusivity would not have a significant effect. We focus on the onset of the aggregation and consider small aggregates of size Ϸ100 m. For aggregates of this size the increase of platelet near-wall concentration caused by the presence of the red blood cells should have minor effects on the results obtained here (24). The few other cells typical of whole blood such as the leukocytes are omitted from the model as being too low in number density to have a significant dynamic effect.…”

Section: Simulation Methodologymentioning

confidence: 99%

Blood flow velocity effects and role of activation delay time on growth and form of platelet thrombi

Pivkin

Richardson

Karniadakis

2006

Proc. Natl. Acad. Sci. U.S.A.

148

120

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Mural thrombi are composed dominantly of platelets and develop under a blood flow. Portions can break off and are carried in the blood flow as emboli. Thrombus growth rates are affected by the velocity of the blood flow, but they do not simply increase with it, they exhibit a maximum, with subsequent decrease. Whereas this variation indicates an interaction of biochemical and physical processes, studies have concentrated widely on understanding only the biochemical processes. Here we show results of simulation of thrombus formation in 3D flows by accounting for the movements of individual platelets. Each platelet follows prescribed rules for interactions while the local flow around the thrombus continuously adjusts to the growing structure of the thrombus, also when embolization occurs. With an activation delay time assigned to each platelet we demonstrate the dependence of thrombus growth rate on blood velocity as found experimentally by Begent and Born [Begent N, Born GV (1970) Nature 227:926 -930]. With activated platelets having mutual tensile action sustainable up to a prescribed distance we achieve thrombus growth faster than with shorter maximum distances that make a thrombus less porous; when the prescribed maximum distance is large enough the thrombus shape is not like a ''hill'' but like a ''carpet.'' We find that thrombus growth rate is enhanced by modest pulsatility but less so when pulsations are amplified in part because of more embolization.direct numerical simulations ͉ platelet aggregation ͉ in vivo comparison ͉ stochastic modeling A cute thrombogenesis in a flowing bloodstream can occur on damaged tissues in normal circulation (1). It has also been observed in blood flow over vascular prostheses (2) and in artificial internal organs, such as prosthetic heart valves (3). The thrombi are composed predominantly of platelets, and they can develop even in the presence of systemic anticoagulants such as heparin (4).Blood flow velocity effects were investigated systematically in vivo by Begent and Born (1), who obtained quantitative data on thrombus growth rates for a range of blood flow rates. Their study remains the clearest time-resolved in vivo study of the effect of blood flow rates on thrombus formation. Richardson (5) subsequently proposed that Begent and Born's observations were consistent with a shear-flow aggregation process (6, 7) in which an activation delay time of the platelets is allowed for, a delay time between each platelet's close encounter with the thrombus and its development of ability to adhere to the thrombus, and which was estimated then to be the order of 0.1-0.2 s. A predicted consequence of this finding was that the height-to-length ratio for thrombi would be lower in blood flows, where a significant fraction of the activated platelets escaped the primary thrombus before their activation delay time had elapsed; this was demonstrated later by Born and Richardson (8). More recent experiments by Petrishchev and Mikhailova (9) in vivo and van Gestel et al. (10) in vitro produc...

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Section: Simulation Methodologymentioning

confidence: 99%

Blood flow velocity effects and role of activation delay time on growth and form of platelet thrombi

Pivkin

Richardson

Karniadakis

2006

Proc. Natl. Acad. Sci. U.S.A.

148

120

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“…3,4 Similarly, platelet dysfunction or antiplatelet therapy can be associated with bleeding risks. [5][6][7] Furthermore, the function of blood is highly dependent on hemodynamic forces; examples include shear-induced platelet activation at Ͼ 5000/s shear rate, 8,9 requirement of VWF in arterial thrombosis, [10][11][12] shear effects on VWF structure/function and GPIb-VWF A1 domain-bonding dynamics, [13][14][15][16][17] RBC-dependent platelet migration toward the wall, 18,19 and convection-enhanced mass transfer to and from local zones of clotting or bleeding. 20,21 Defining, quantifying, and linking a patient's unique platelet phenotype or coagulation phenotype under hemodynamic conditions to clinical risk remains a diagnostic challenge.…”

Section: Introductionmentioning

confidence: 99%

Multiscale prediction of patient-specific platelet function under flow

Flamm¹,

Colace²,

Chatterjee³

et al. 2012

Blood

107

121

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During thrombotic or hemostatic episodes, platelets bind collagen and release ADP and thromboxane A 2 , recruiting additional platelets to a growing deposit that distorts the flow field. Prediction of clotting function under hemodynamic conditions for a patient's platelet phenotype remains a challenge. A platelet signaling phenotype was obtained for 3 healthy donors using pairwise agonist scanning, in which calcium dye-loaded platelets were exposed to pairwise combinations of ADP, U46619, and convulxin to activate the P2Y 1 /P2Y 12 , TP, and GPVI receptors, respectively, with and without the prostacyclin receptor agonist iloprost. A neural network model was trained on each donor's pairwise agonist scanning experiment and then embedded into a multiscale Monte Carlo simulation of donor-specific platelet deposition under flow. The simulations were compared directly with microfluidic experiments of whole blood flowing over collagen at 200 and 1000/s wall shear rate. The simulations predicted the ranked order of drug sensitivity for indomethacin, aspirin, MRS-2179 (a P2Y 1 inhibitor), and iloprost. Consistent with measurement and simulation, one donor displayed larger clots and another presented with indomethacin resistance (revealing a novel heterozygote TP-V241G mutation). In silico representations of a subject's platelet phenotype allowed prediction of blood function under flow, essential for identifying patientspecific risks, drug responses, and novel genotypes. IntroductionDuring a clotting event, platelets respond to combinatorial stimuli, including collagen, adenosine diphosphate (ADP), thromboxane A 2 (TXA 2 ), thrombin, epinephrine, and serotonin, as well as endothelialderived inhibitors such as nitric oxide and prostacyclin (PGI 2 ). Excessive platelet buildup at the site of cardiovascular disease and plaque rupture causes more than 1 million heart attacks and strokes in the United States each year. Excessive thrombus formation after plaque rupture remains difficult to predict and can be linked to hyperactive platelet function. 1,2 Therefore, low-dose aspirin to inhibit platelet cyclooxygenase-1 (COX-1) and clopidogrel to inhibit platelet P2Y 12 signaling are used widely in patients with cardiovascular risks, although patient response to these drugs can vary.Interindividual variations in platelet reactivity, even in the healthy population, have been associated with several factors, including female sex, fibrinogen level, ethnicity, inherited variations, and polymorphisms. 3,4 Similarly, platelet dysfunction or antiplatelet therapy can be associated with bleeding risks. [5][6][7] Furthermore, the function of blood is highly dependent on hemodynamic forces; examples include shear-induced platelet activation at Ͼ 5000/s shear rate, 8,9 requirement of VWF in arterial thrombosis, 10-12 shear effects on VWF structure/function and GPIb-VWF A1 domain-bonding dynamics, 13-17 RBC-dependent platelet migration toward the wall, 18,19 and convection-enhanced mass transfer to and from local zones of clotting or bleeding....

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“…Eckstein & Belgacem [20] proposed an additional drift term to mimic RBC enhanced motion, whereas more sophisticated approaches involving the explicit dependence of the diffusion coefficient on the local haematocrit and shear rate have also been proposed [21,22]. The dependence on these quantities has already been recognized in early experimental work [4,23].…”

Section: Introductionmentioning

confidence: 99%

Where do the platelets go? A simulation study of fully resolved blood flow through aneurysmal vessels

2013

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One contribution of 25 to a Theme Issue 'The virtual physiological human: integrative approaches to computational biomedicine'. Despite the importance of platelets in the formation of a thrombus, their transport in complex flows has not yet been studied in detail. In this paper we simulated red blood cells and platelets to explore their transport behaviour in aneurysmal geometries. We considered two aneurysms with different aspect ratios (AR ¼ 1.0, 2.0) in the presence of fast and slow blood flows (Re ¼ 10, 100), and examined the distributions of the cells. Low velocities in the parent vessel resulted in a large stagnation zone inside the cavity, leaving the initial distribution almost unchanged. In fast flows, an influx of platelets into the aneurysm was observed, leading to an elevated concentration. The connection of the platelet-rich cellfree layer (CFL) with the outer regions of the recirculation zones leads to their increased platelet concentration. These platelet-enhanced recirculation zones produced a diverse distribution of cells inside the aneurysm, for the different aspect ratios. A thin red blood CFL that was occupied by platelets was observed on the top of the wide-necked aneurysm, whereas a high-haematocrit region very close to the vessel wall was present in the narrow-necked case. The simulations revealed that non-trivial distributions of red blood cells and platelets are possible inside aneurysmal geometries, giving rise to several hypotheses on the formation of a thrombus, as well as to the wall weakening and the possible rupture of an aneurysm.

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Model of platelet transport in flowing blood with drift and diffusion terms

Cited by 115 publications

References 26 publications

Blood flow velocity effects and role of activation delay time on growth and form of platelet thrombi

Blood flow velocity effects and role of activation delay time on growth and form of platelet thrombi

Multiscale prediction of patient-specific platelet function under flow

Where do the platelets go? A simulation study of fully resolved blood flow through aneurysmal vessels

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