Important Physical Regulatory Roles of Erythrocytes on Platelet Adhesion Under Blood Flow Conditions.


 Aim: Functional roles of erythrocytes on platelet adhesion to vessel wall under blood flow condition is still to be elucidated. Methods: Blood specimens containing native, biochemically fixed, or artificial erythrocytes, at various hematocrits were perfused on immobilized von Willebrand factor (VWF) at a shear rate of 1,500 s− 1. Number of platelets adhered on VWF within the region of interest (ROI: 5x103 µm2) was serially measured for 2 minutes using the fluorescent microscopy system. Regression analyses were conducted to evaluate the relationship between the rates of platelet adhesion and the hematocrit values. Computer simulation of platelet adhesion on the wall of von Willebrand factor (VWF) at a shear rate of 1,500 s− 1 was conducted by solving governing equations with a finite-difference method on K-computer. Calculations were conducted at various hematocrits conditions in the computational domain of 100 µm (x-axis) x 400 µm (y-axis) x 100 µm (z-axis). Results: Biological experiments demonstrated the positive correlations between the rates of platelet adhesion and hematocrit values in native, fixed, and artificial erythrocytes. (r = 0.992, 0.934, and 0.825, p < 0.05 for all) The number of platelets adhered after 2 minutes blood perfusion at 24% hematocrit of 221.7 ± 22.6/5x103 µm2 (fixed erythrocytes) and 208.0 ± 26.5/5x103 µm2(artificial ones), respectively, were comparable to that with native ones of 195.9 ± 28.3/5x103 µm2. The simulation results demonstrated the hematocrit dependent increase in platelet adhesion rates (94.3/sec at 10%, 185.2/sec at 20%, and 327.9/sec at 30%, respectively) suggesting the importance of augmented z-axis fluctuation of flowing platelet by erythrocytes as the cause of platelet adhesion. Conclusions: Our experimental results indicate the importance of the physical roles of erythrocytes inducing wall-normal fluctuations of flowing platelets on their vessel adhesion under blood flow conditions.


Introduction
Platelets adhere on damaged vessel wall through their glycoprotein (GP)Iba binding with von Willebrand factor (VWF) under blood ow conditions. 1, 2 3, 4 VWF mediated shear-induced platelet aggregation occurs even in the absence of erythrocytes. 5, 6 7 However, platelet adhesion on injured vessel wall is known to be in uenced by the presence of erythrocytes. [8][9][10] Indeed, the risk of thrombotic diseases caused by mural thrombi such as myocardial infarction 11 12 is in uenced by hematocrit level. 13,14 Many biological studies dissecting the mechanism of platelet adhesion under blood ow conditions were conducted in the presence of erythrocytes. [1][2][3][15][16][17] Some reports suggested the importance of biochemical roles of erythrocytes, [18][19][20][21][22][23][24] but others supported biophysical roles. 8,20,24,25 Previously published simple model of blood ow suggested the potential importance of near-wall rebounding collisions of platelet in the presence of erythrocytes. 25 However, precise functional roles of erythrocytes for the platelet adhesion and thrombus formation are still to be elucidated.
Here we investigate the mechanism underlining the in uence of erythrocytes on the rates of platelet adhesion using a medical-engineering cooperation approach combining large-scale computer simulation with biological experiments.

Biological Experiments 1) Preparation of Blood Specimens
Venous blood specimens were collected from adult volunteers. Our study protocol for drawing blood from human volunteers was approved by the Internal Review Board (IRB) of Tokai University School of Medicine (17R17). Written informed consents were obtained from all participants. All the study subjects were instructed to abstain from drugs known to interfere with platelet function (such as aspirin or P2Y 12 inhibitors) at least a month preceding the study. The blood samples were immediately transferred into plastic tubes containing 1/10 volume of the speci c thrombin inhibitor Argatroban (Mitsubishi Tanabe Pharma Corporation, Osaka Japan) at a concentration of 100 µmol/L. Both erythrocytes and platelets were separated from the blood samples and stored as previously reported. 7,26 Biochemically xed erythrocytes ( xed erythrocytes) were prepared by exposing separated native erythrocytes to paraformaldehyde solution (2%) for 10 minutes. Then, residual paraformaldehyde was washed three times by 10 mM Hepes buffer (0.14 mM NaCl and 10 mM Hepes). Particles of polystyrenecopolymer were prepared as arti cial erythrocytes (density 1.05 g/cm 3 , diameter 8 µm (Thermo Fisher scienti c, MA, USA). For each experiment, concentrations of native, xed, and arti cial erythrocytes are adjusted with hematocrit values.

2) Measurements of the Number of Platelet Adhered on VWF
A method to calculate the number of platelets adhered on VWF under various blood ow condition in the presence of erythrocytes was established previously. 3,16 According to previous publication, all the experiments were conducted at blood ow condition achieving the wall shear rate of 1,500 s -1 . 16,27 To clarify whether erythrocytes in uence platelet adhesion by their bio-chemical or physical functions, the rates of platelet adhesion on VWF at initial 2 minutes in the presence of native (erythrocytes), chemically xed ( xed erythrocytes), and arti cial erythrocyte (arti cial erythrocytes) at various hematocrits were measured.
Reconstitute blood specimens containing native, xed, and arti cial erythrocyte at various hematocrits were prepared in the presence of 200,000/µl of platelets rendered uorescent by addition of FITCconjugated antibody against glycoprotein (GP) IIb/IIIa of abciximab. (gifted from Dr. Nakada in Centcore Co., USA)

3) Calculation of the Platelet Adhesion Rate
To calculate platelet adhesion rate, regression analyses, settling the intercept for both x-and y-axis as 0, were conducted between perfusion time and the number of platelets adhered on VWF in the presence of native, xed, and arti cial erythrocytes at various hematocrits. The slope of regression lines in each analysis was interpreted as the rate of platelet adhesion on the VWF wall (number of platelet bound/5x10 3 µm 2 /second).

4) Statistical Analysis for Biological Experiments
All numerical data are expressed as mean ± SD unless otherwise speci ed.
For comparison of number of platelets adhered on VWF wall after 2 minutes blood perfusion under different conditions, one-way analysis of variance (ANOVA) was conducted. The differences among groups of data were assessed by Newman-Keuls post-hoc test when ANOVA suggested statistical difference. A two-sided p value of 0.05 was considered to denote statistical signi cance.

1) Simulation System
Numerical simulations of blood ow in the presence of platelet and erythrocytes were conducted using the method we developed previously . 28 29 Brie y, the system is consisted of Newtonian uid and the vesicles are constructed with hyper-elastic membrane. The uid was considered incompressible. The cell membranes were assumed to have no thickness, but the elastic tension was considered. The governing equations for incompressible Navier-Stokes equations coupling with uid-structure interaction were solved by means of a nite-difference method. The erythrocytes and the platelets were treated as vesicles coupled with uid-structure interaction. Platelet adhesion process to the vessel wall was analyzed by multiscale modeling of coupling continuum scale nite difference method with the molecular scale Monte Carlo method. 30 The adhesion of platelets to the vessel wall is caused by the protein-protein bindings (GP1ba proteins on the platelet binding with VWF proteins on the vessel wall.). This proteinprotein binding process is modeled using the concept of transition state theory and evaluated by Monte Carlo simulation, solving the equations for the stochastic process of each biding. 30 Biochemical characteristics, such as release of ADP are not included in this simulation system.
Computational domain was set to the region with 100 mm (x-axis) x 400 mm (y-axis) x 100 mm (z-axis). VWF modelled to bind with platelet GPIba was settled at z wall of the computational domain to mimic the biological experiments. As the initial condition, 8,632 platelets were settled in the computational domain (2.158 x 10 3 / L). Periodical boundary condition was imposed and pressure gradient was added to realize wall shear stress of 1,500 s -1 for the uid viscosity of 1.2e -3 Pa.s in the blood ows in x-direction. This pressure gradient was set as a constant value throughout the various hematocrit conditions

2) Deformability of Erythrocytes
A spherical vesicle in this system was prepared to subject to an unbounded shear ow. Material property of erythrocytes was given as previously reported. 28 Fluid mechanical dimensionless numbers in our system were Reynolds (Re = ργ ḋ2/(4μ)) and the capillary (Ca = μγ ḋ/(2Es)) numbers, where ρ denote density, d denotes the vesicle diameter, γ ̇ the shear rate, μ represent viscosity, and Es is the surface elastic modulus. In the present study, the Reynolds number was xed at Re = 0.01, while the capillary number was variable. Both mean velocity (cm/s) and apparent relative viscosity of the uids were calculated under various hematocrit conditions.

3) Evaluation of the Number of Platelets Adhering on the Vessel Wall
The number of platelets adhered on the vessel wall were counted using simulation results in the region of 400 µm × 100 µm for each second. Total number of adhered platelets after 2 minutes perfusion was calculated for comparison with biological experiments. All the simulations were conducted on K computer. (RIKEN, Kobe, Japan)

Biological Experiments
Platelet adhesion increased with high hematocrit level regardless of the types of erythrocytes (Native, Fixed, and Arti cial Erythrocyte) To distinguish the biochemical and biophysical effect of erythrocytes on initial platelet adhesion, we carried out a series of experiments by perfusing blood on xed VWF wall in the presence of various types of erythrocytes (native, chemically xed, or arti cial) at various hematocrit values. As shown in Fig. 1, number of platelets bound within the ROI (5 x 10 3 /µm 2 ) increased linearly with perfusion time in the presence of native erythrocytes at various hematocrit levels. Similar relationships were shown in the presence of xed and arti cial erythrocytes ( Fig. 2 and Fig. 3). The rates of platelet adhesion were constantly greater at higher hematocrit conditions regardless of the type of erythrocytes used (native, chemically xed, or arti cial) ( Table 1).

Numerical Simulation
Numerical simulation of platelet adhesion to the vessel wall in the presence of erythrocytes at various hematocrits shows importance of z-axis uctuation.
Next, to gain theoretical insight on our nding, we performed a computer simulation. Fig 6 and corresponding movie shows the distribution of erythrocytes (red vesicles) and platelet (yellow vesicles) in the simulation domain (x axis: 100 mm, y axis: 400 mm, and z-axis: 100 mm) with hematocrits of 20%. As an initial condition (Fig 6A), erythrocytes and platelets were distributed randomly and uniformly. When blood starts owing, erythrocytes become deformed to the discoid shape in the ow direction (Fig 6B, 6C, and 6D). Erythrocytes move toward the center region of the channel due to Fåhraeus-Lindqvist effect. 31 . The mean velocity of erythrocytes and platelets decreased in higher hematocrits in the xed pressure gradient (Table 2). Platelets, of which volume is relatively smaller than an erythrocyte, move along interspaces of erythrocytes. When the distance between a platelet and -z wall becomes close, the bond between VWF and GPIba is formed and the platelet adheres to the wall as shown as blue dots in panel B, C, and D in Fig. 6. Number of platelet adhered on the vessel wall at 2 minutes perfusion in the presence of erythrocytes at 10, 20, 30% hematocrit were calculated as 8343, 22304, and 44088/per 400 µm × 100 µm ROI, respectively. It is of notes that we did not implement any chemical interactions in this simulator. Thus, the results further support the importance of physical roles of erythrocytes.

Combined Analysis
Direct comparison between biological experiments and computer simulation shows similarity.

Discussion
Here, we show in both, biological experiments and computer simulation, that platelet adhesion on VWF under a blood ow condition increase depending on hematocrit levels. Our experimental results suggest that in uences of erythrocytes on platelet adhesion are not depend on their bio-chemical function, but on physical presence. Computer simulation solving Navier-Stokes equations coupled with uid-structure interaction provided similar hematocrit-dependent increase in the rate of platelet adhesion gave theoretical support on our biological experimental ndings. It suggests the importance of the near-wall access of platelets by central migration of erythrocytes in owing blood which was established by Fahraeus R in early 20 th century. 32,33 The most important biological role of erythrocytes is to transport oxygen from lung to peripheral organ.
Erythrocytes themselves have active metabolic activities. 34 The cellular energy metabolisms are mediated by substances known to in uence platelet activation such as adenosin 5'-tri and di phosphate.
(ATP and ADP). [35][36][37] ADP is known as strong activator for platelets. 38,39 There are several previous publications demonstrating the regulatory role of erythrocytes for platelet activation. 19,24 However, our results suggest that bio-chemical role of erythrocytes on platelet adhesion rate under blood ow condition is limited as compared to their bio-physical roles.
Our results assessing the effect of erythrocytes on platelet adhesion here is focusing only for platelet adhesion under shear rate of 1,500 s -1 . Previous publication demonstrated that the binding between activated GPIIb/IIIa and brinogen/VWF occurred only under wall shear rate lower than 750 s -1 . Platelet may still be activated by ADP released from erythrocytes, 35 but the rate of platelet adhesion was not in uenced in this experimental condition. Our results can be interpreted as focusing only on the initial phase of platelet adhesion occurring within 2 minutes of blood perfusion. Thus, our present results are not con icting with the previous publication indicating the important role of ADP for stabilization of platelet adhesion and thrombi because the previous ones focus more about later phase of blood perfusion. 4 17 In the parallel plate ow chamber, blood ow between 2-glass plates is assumed to follow Hagen-Poiseuille equation. 40,41 The fact of axial accumulation of erythrocytes in the ow chamber were previously demonstrated. 42 Yet, the relationship between axial accumulation of erythrocytes and the rate of platelet adhesion at the wall has yet to be clari ed. Here computer simulation with the use of full Eulerian Fluid-Structure Inter-action (FSI) solver 43 44 showed increased wall-normal uctuations of owing platelets induced by axially accumulated erythrocytes as the cause of platelet adhesion to the wall. All the basic equations to solve the structure and position of erythrocytes and platelet under blood ow condition was simulated by nite difference volume-of-uid scheme with fractional step algorithm by high performance computer K. Indeed, both uid-structure and uid-membrane interaction were handled with Eulerian numerical approach. 44 44 Biological validity of this model was con rmed by shape changes in owing erythrocytes in capillary circulation in mice. 45 As con rmed by simulation results shown in this paper, higher platelet adhesion rates in the presence of erythrocytes at higher hematocrits should re ect increased grade of z-axis uctuation of platelet present close to the VWF wall.
There are a few methodological limitations on this study. First, biological experiments were conducted only at one wall shear rate condition of 1,500 s -1 . The impact of the presence of erythrocytes on the rates of platelet adhesion at the wall may differ at other wall shear rate conditions. Second, the number of platelets were counted manually, but not automatically. We might have missed some platelet that once bound on VWF but did not stay for a long period. However, these limitations do not in uence our main results of higher rate of platelet adhesion in the presence of higher concentration of erythrocytes.
In conclusion, we show here the importance of the physical effect of erythrocyte for platelet adhesion rates on the wall under blood ow condition. The increased platelet adhesion rates with higher hematocrits could be explained by axial accumulation of erythrocytes and increased z-axis uctuation of platelet close to vessel wall.