Computer Simulation of Platelet Adhesion around Stent Struts in the Presence and Absence of Tissue Defects around Them

Aim To predict platelet accumulation around stent struts in the presence or absence of tissue defects around them. Methods Computer simulations were performed using virtual platelets implementing the function of the three membrane proteins: glycoprotein (GP) Ibα, GPIIb/IIIa, and GPVI. These platelets were perfused around the stent struts implanted into the vessel wall in the presence or absence of tissue defects around them using within the simulation platform. The number of platelets that adhered around stent struts was calculated by solving the blood flow using Navier–Stokes equation along with the adhesion of membrane protein modeled within the platform. Results Platelet accumulation around stent struts occurred mostly at the downstream region of the stent strut array. The majority of platelets adhered at the downstream of the first bend regardless of the tissue defect status. Platelet adhesion around stent struts occurred more rapidly in the presence of tissue defects. Conclusion Computer simulation using virtual platelets suggested a higher rate of platelet adhesion in the presence of tissue defects around stent struts.


Introduction
Coronary stent implantation is a common procedure for treating patients with acute and chronic coronary artery diseases [1][2][3]. Indeed, stent implantation is effective for preventing acute phase coronary occlusion by restoration of normal anatomy [4]. Stent thrombosis occurring in the subacute phase is managed well with appropriate antiplatelet therapy [5]. Antiplatelet therapy helps to maintain the arterial lumen, and thus, it also facilitates maintenance/restoration of normal anatomy. Recently, drug-eluting stents (DES) using sirolimus [6,7], paclitaxel [8,9], or zotarolimus [10] have been shown to prevent restenosis by inhibiting smooth muscle growth [11]. Drug-eluting stents were proven to be effective in reducing the need for target vessel revascularization in patients at high risk for restenosis without a significant increase in the risk of myocardial infarction or death [12].
Due to the reduced risk of thrombotic complication with recent stents, the more recent recommended length for strong antiplatelet therapy using the combination of aspirin and P2Y 12 inhibitors has been shortened [13][14][15]. In general, the risk of thrombotic events is no longer higher than the risk of serious bleeding complication caused by dual antiplatelet therapy several months after DES implantation [16]. Stent thrombosis in late term is rare but is an event that can lead to severe, negative patient outcomes including death [17,18]. However, it is suggested that risk stratification based on various conditions can be helpful to identify patients who require extended antiplatelet therapy [19]. Risk stratification demonstrates that there is a higher risk of late phase stent thrombosis in patients with malapposition of stents [20][21][22][23][24].
us, it may be reasonable to consider longer DAPT duration for patients with stent malapposition. However, extending DAPT duration is associated with a higher risk of serious bleeding complication [25,26]. us, further studies are needed to develop safer treatment strategies that specifically target patients with stent malapposition. e mechanism of an increased risk of stent thrombosis in patients with stent malapposition is not understood [23,27].
is lack of understanding creates a barrier for developing new treatment protocols. In patients with drugeluting stents, stent malapposition was associated with tissue defects around stent struts due to delayed tissue repair [28].
is has been suggested to be the result of drugs inhibiting cell proliferation [26] and could be contributing to high thrombosis rate [22]. From these findings, the present hypothesis was that tissue defects around stents caused by malapposition are contributing to the high rate of thrombosis by increasing the rate of platelet adhesion to the vessel wall.
Recent advances in the calculation power of computer and information technology facilitates in silico analysis by constructing various complicated biological phenomena such as thrombus formation by solving basic physical/ chemical equations [27,29,30]. Using this technology, computer simulation models of platelets adhesion under various blood flow conditions were developed [29]. In this study, these computer simulations are applied to examine the contribution of tissue defects around the stent struts on the rate of platelet adhesion.

Virtual Platelet.
Virtual platelets implementing the function of adhesion at site of endothelial injury, activation, and aggregation were used in this study. e details of virtual platelets have been published previously [29]. e function of three major platelet membrane proteins, namely, glycoprotein (GP) Ibα, GPIIb/IIIa, and GPVI, was integrated into the virtual platelet, computer simulation as in the Kelvin-Voigt model [29]. Virtual platelets adhere at the region of virtual endothelial injury mimicking the function of GPIbα interacting with the von Willebrand factor (VWF) and collagen fibrils exposed to the blood stream [29]. e outside-in signaling caused by stimulations of GPVI (by collagen) [31], GPIbα (by VWF) [31], and other chemical receptors on platelets (by various soluble agents such as adenosine 5'-diphosphate (ADP) [32], epinephrine [33], and thrombin [34]) were modeled by the activation of virtual platelet upon adhesion to the vessel wall. To model the firm adhesion caused by platelet activation, the binding constant was increased upon platelet adhesion on VWF/collagen as published previously [29]. e validity of the abovementioned virtual platelet model was confirmed by extended computer simulation implementing the local activation of coagulant cascade on activated platelets [30]. Biological validity of the virtual platelets used in this study was confirmed by experiments using human blood specimens and parallel plate flow chambers [31][32][33][34][35][36].

Solving Blood Flow around Stent
Struts. Blood flow around stent struts were calculated by solving the discretized Navier-Stokes equation [27,29,30]. Briefly, the diameter of the target vessel was set to 3 mm. Blood flow was simulated as pulsatile flow with a linear change in blood flow from 0 to 22.5 mm/sec. e initial density of platelets in blood was set to 300 × 10 6 /ml and distributed uniformly. e Δt for calculation was defined as 0.01 second. e stents are implanted as shown in Figure 1(a). Stent struts were implanted into the vessel wall as shown in Figure 1(b). e stent strut has a round shape with a diameter of 0.09144 mm. Half of the diameter of stent struts was buried in the vessel wall, but the other half was exposed to the blood stream. e initial direction of blood flow was set to be parallel to y-direction (x-and z-axis components were 0).

Tissue Defect around Stent Strut.
Tissue defects are organized around the stent struts as illustrated in Figure 2. e sizes of tissue defects were equal to the diameter of stent struts ( Figure 2(c)).

Conditions for the Simulation.
Virtual blood with the density of 1,000 kg/m 3 and dynamic kinematic viscosity coefficient of 0.001004 m 2 /s was perfused for 30 seconds in the virtual vessel with the diameter of 3 mm and in the presence of stent struts with or without tissue defects. e number of virtual platelets adhering around stent struts was calculated with a high-performance computer equipped with an Intel ® Xeon Phi TM 7210 processor (Intel Corporation, Santa Clara, CA, USA). e distribution of platelet adhesion at 1-, 3-, and 10-second perfusion of virtual blood is shown in both conditions in the presence and absence of tissue defect around stents. Time-dependent changes in the number of platelets adhering to the area around stent struts were calculated. Calculated results are also shown as supplemental movies.

Blood Flow toward the Vessel Wall Was Observed
Downstream of Stent Strut. Although the initial z-axis component of blood flow velocity was 0, flow in the z-axis direction was observed when the blood flow reached the stent struts. e distributions of z-axis components of blood flow around stents at maximum velocity (mm/sec) in the absence and presence of tissue defect are shown in Figures 3(a) and 3(b), respectively. Z-axis direction velocity toward the vessel wall was higher downstream than upstream of stent strut.

Platelet Adhesion Was Pronounced around the First Stent
Struts Compared to the Second Strut. Figure 4 shows the snapshots of three-dimensional (3D) projection view delineating platelet adhesion around stents in the presence and absence of tissue defects. Almost no platelets adhered around the stents at 1 second both in the presence and absence of tissue defect. Adhered platelets increased in a time-dependent manner from 3 to 10 seconds. Despite similarly higher velocity of z-axis blood flow toward the vessel wall in the downstream of stent struts (Figure 3), more platelet adhesions were observed at downstream of the first stent strut as compared to the second at 3 seconds. e difference was larger in the absence of tissue defects (Figure 4(a)) as compared to the condition with tissue defects ( Figure 4(b)). At 10 seconds, more platelet adhesion was observed in the presence of tissue defects compared with no tissue defects. Although the platelet adhesion was increased with tissue defects in downstream of both the first and second stent struts, the difference was larger around the second stent strut than the first. Full movie demonstrating the time-dependent changes in the number of platelets adhered around stent strut in the presence and absence of tissue defect is provided as supplementary materials (Movies A and B).

Platelet Adhesion Was Increased with the Presence of
Tissue Defect. Figure 5 shows the time-dependent increase in the number of platelets adhered in the simulation area shown as XY plane in Figure 3 from 0 to 30 seconds. Indeed, the number of adhered platelets was higher in the presence of tissue defects than that in their absence. At 30 seconds, it reached to 490/mm 2 in the absence of tissue defects and reached 3420/mm 2 in its presence.

Discussion
Supporting initial hypothesis, the computer simulation suggested higher rate of platelet adhesion around stent struts implanted into the vessel wall in the presence of tissue defects around them as compared to absence tissue defects. is difference is likely due to the changes in the distribution of z-axis component of platelet motions induced by the presence of stent struts because the z-axis direction velocity of blood flow toward the vessel wall was apparently higher downstream than upstream of stent struts. is was further supported by the finding that the z-axis direction velocity at downstream of stent strut in the presence of tissue defects was higher as compared to that without defects. e results of the present research suggest that actual platelet adhesion is not fully determined by the z-axis velocity of blood flow. Indeed, apparently, more platelet adhesion was observed downstream of the first stent strut than the second strut at 3 and 10 seconds of blood perfusion regardless of the presence of tissue defects. e reason for this difference is not fully understood. Reduced platelet density around the second stent strut caused by the consumption of platelet by adhesion around the first stent strut is one potential explanation. However, platelet adhesion was increased with tissue defects regardless of the locations and thus supports the conclusion that tissue defects may be an important contributor for higher rate of stent thrombosis in patients with late malapposition.
Potential factors influencing the risk of late stent thrombosis are summarized in Table 1 [37][38][39]. General factors such as thrombogenicities exerted by platelet reactivity are managed by the appropriate use of dual antiplatelet therapy [40]. Local factors such as the thrombogenicity of the stent struts were also improved by using less thrombogenic materials and shapes [36]. A critical issue, especially for the late stent thrombosis with the use of drug-eluting stents, is the malapposition [20]. Stent malapposition or incomplete stent apposition is a morphological description defined by the lack of contact between at least one stent strut and the underlying intimal surface of the arterial wall in a segment not overlying a side branch. Clinical observations suggest a higher prevalence of tissue defects around stents causing late stent malapposition in patients experiencing late stent thrombosis [23,24,26,41,42]. However, it is important to note that the prevalence of stent malapposition differs substantially with the use of different diagnostic devices and studies. Even with the use of intravascular ultrasound (IVUS), the prevalence of late stent-malposition ranges significantly between studies from the lowest of 0% at 8 months [43] to 25% at 9 months [44]. Other studies using optical coherence tomography (OCT) report high prevalence of acute stent malapposition in 62% of the lesions treated, and 31% of them remained as malappositions at 6 months [42]. New onset of late acquired malapposition was observed in 15% of the lesions [42]. ese reports suggest that imaging devices cannot completely eliminate stent malappositions.
In general, late stent malapposition is recognized as a risk factor for stent thrombosis. But, a recent report by Im et al. also demonstrated that none of the 351 patients experienced clinical stent thrombosis within 8.6 ± 10.3 months of follow-up. Meta-analysis showed higher risk of late malapposition as compared to the bare metal stent with an odds ratio of 2.49 (CI 95% 1.15-5.35) [26].
us, stent malapposition is one of the risk factors for stent thrombosis, but the majority of late acquired stent malapposition remains asymptomatic. e results of the present investigation show a higher rate of platelet adhesion around stent struts in the presence of tissue defects in comparison with its absence. ese results do not contradict clinical findings because the accumulation of platelets is one of the triggers for thrombus formation, but contributions from other factors such as local   activation of coagulant factor is necessary to cause symptomatic coronary thrombosis [45]. Higher rate of platelet accumulation downstream of stent struts has been previously documented with human blood and flow chamber experiments [36]. is computer simulation finding is in good agreement with these previous biological, experimental findings. Detailed clinical observations with the use of OCT in patients with very late stent thrombosis revealed the presence of in-stent neointimal rupture in approximately 70% of patients [46]. e rate of neointimal rupture was higher than the prevalence of stent malapposition of 42% [46]. e contributing role of platelets in neointimal plaque formation remains to be elucidated [47,48]. e higher rate of platelet accumulation shown here may suggest a contributing role of accumulated platelets for neointimal formation and future rupture.

Limitations.
is study has several limitations as listed below.
(i) Predictive calculation in this simulation was conducted only for 30 seconds. It is likely that longer times are required for the process of stent thrombosis to be complete. us, the present results should be interpreted as predictive of only the initial part of the clinical phenomena, which might not necessarily result in clinically significant events such as stent thrombosis. (ii) e clinical thrombosis often appears as sudden cardiac death or ST-elevation myocardial infarction, which is likely to be caused by arterial occlusive thrombi including both platelet and fibrin [3,49]. is simulation only predicted early platelet accumulation but did not include the process of coagulation cascade leading to fibrin formation. (iii) is simulation only included tissue defect around stent struts as a parameter but not others such as old age and renal dysfunction. Personalized prediction inclusive of these factors on the influence of stent thrombosis achieved may be understood by future studies. (iv) e interaction between platelets and erythrocytes should play a role for determining the motion of platelets. is factor was not included in the current analysis. Future studies examining this aspect are now being designed in this laboratory.

Fundamental Strengths of Simulation Calculation Are the
Following. e numbers of platelets accumulated around stent could be quantitatively calculated from the basic physical principals.

Conclusion
In conclusion, higher rate of platelet adhesion around stent struts in the presence of tissue defects as compared with its absence is shown in this computer simulation study. is study results support the notion that higher rate of platelet adhesion in the presence of tissue defects is a risk factor for stent thrombosis. Computer simulation provides insight into the higher risk of stent thrombosis in patients with stent malapposition. Data Availability e results of this study are generated by simulation calculation.

Conflicts of Interest
Shinya Goto acknowledge a grant-in-aid from MEXT/JSPS KAKENHI (19H03661), AMED (A368TS), Bristol-Myers Squibb for independent research support project (33999603) and a grant from Nakatani Foundation for Advancement of Measuring Technologies in Biomedical Engineering and Vehicle Racing Commemorative Foundation. Shinya Goto also discloses grant support from Sanofi, Pfizer, and Bristol Myer Squibb and Ono Pharma.

Supplementary Materials
Movies demonstrating the platelet adhesion in the presence and absence of tissue defect. Movie A and movie B demonstrate the platelet adhesion in the absence and presence of tissue defect around stent struts, respectively. e size and direction of each image is the same as