Numerical Study on Effects of Drug-coating Position of Drug-eluting Stents on Drug Concentration

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1 Journal of Medical and Biological Engineering, 34(5): Numerical Study on Effects of Drug-coating Position of Drug-eluting Stents on Drug Concentration Yu Chen 1 Fei Yan 1 Wen-Tao Jiang 1,* Qing-Yuan Wang 1 Yu-Bo Fan 2 1 Laboratory of Biomechanical Engineering, Department of Applied Mechanics, Sichuan University, Chengdu , China 2 School of Biological Science and Medical Engineering, Beihang University, Beijing , China Received 22 May 2013; Accepted 26 Sep 2013; doi: /jmbe.1570 Abstract As consequences of the implantation of drug-eluting stents (DESs), hemodynamic changes and drug diffusion have significant effects on in-stent restenosis. In particular, the drug-coating position on DESs can affect drug concentration distribution in blood and the vascular wall. Therefore, investigating the effects of the drug-coating position on drug distribution is important for the optimal design of DESs, in terms of both geometry and drug coatings. In this paper, three-dimensional virtual stent models with different drug-coating positions were built to numerically investigate the drug concentration distribution. The results were compared with those from two-dimensional simulation models. It was demonstrated that an increase of the contacting surface increases drug concentration in the vascular wall, and constrains the increase of the low wall shear stress (WSS) region (which normally increases with the height of DESs). The results show that the drug coated on the contacting surface effectively enters the vascular wall without interference from blood flow. Increasing the drug on the contacting surface and decreasing the height of a DES are optimal for reducing the risk of restenosis. Keywords: Drug-eluting stent (DES), Drug concentration, Drug-coating position, Hemodynamics, Contacting surface 1. Introduction Coronary arteries are the most susceptible arteries to atherosclerosis, which is a common occurrence with cardiovascular disease. Drug-eluting stent (DES) therapy is considered as a milestone in the evolution of percutaneous coronary intervention therapy [1]. However, studies have found that DESs can increase the risks of cardiac death and myocardial infarction, which are caused by coronary thrombosis in non-cardiac death [2]. Many researchers have investigated the effects of geometry, drug-coating/loading scheme, and drug release patterns of stents. A previous study [3] analyzed the influence of Reynolds number and the width/ height ratio of the stent on drug concentration distribution; they found that coronary DESs should be considered where luminal flow, strut design and pulsatility have direct effects on tissue drug uptake after local delivery. Researchers [4] studied the contribution of the drug released into the blood flow with respect to the efficacy of drug deposition and penetration into the arterial walls using three-dimensional (3D) models. Other schemes [5] simulated the concentration distribution of heparin and taxol in blood. An experimental approach [6] confirmed * Corresponding author: Wen-Tao Jiang Tel: ; Fax: scubme@aliyun.com that drug-coating position significantly affects drug distribution. Balakrishnan [7,8] and Dong [9] applied numerical methods to investigate the effects of drug-coating position on drug distribution. Balakrishnan studied two-dimensional (2D) straight artery stents and found that increasing the stent height alone increases drug concentration. Dong studied 2D curved artery stents and found that the drug-coating position and stent spacing have significant effects on drug deposition in a curved artery. The present study uses 3D models to further study the influence of drug-coating position in DESs on the drug distribution in blood and the vascular wall. Computational fluid dynamics (CFD) is used to investigate the effects of drug-coating position on the drug concentration in 3D straight/curved DESs. The relationships between drug-coating position, drug concentration, and in-stent restenosis are studied. The results provide theoretical guidance for the optimization of DES design. 2. Methods 2.1 Models To compare the effects of drug-coating position on drug concentration, two stents with different configurations were built and respectively implanted into a straight vessel and a curved vessel. Below, the stent in the straight vessel is referred to as the straight stent and that in the curved vessel is referred

2 488 J. Med. Biol. Eng., Vol. 34 No to as the curved stent. The configuration of the straight stent, with four stent struts, is shown in Fig. 1. The coronary artery diameter is 3 mm [10], the arterial wall thickness is 0.5 mm [11], and the stent diameter and length are 3 and 9 mm, respectively [7]. The cross-section of a stent strut is a 0.1 mm 0.1 mm square. The configuration of the curved stent, with six stent struts, is shown in Fig. 1. The coronary artery diameter is 3 mm, the arterial wall thickness is 0.5 mm, and the stent diameter and length are 3 and 15 mm, respectively. The curvature radius is 10 mm. The cross-section of a stent strut is a 0.1 mm 0.1 mm square. For both stent configurations, the stent struts and links are identical in size, thickness, and surface area. The stent surface was assumed to perfectly fit with the vascular wall. grid independence, which was achieved at 3,000,000 cells for all models. 2.2 Boundary conditions Blood was assumed to be a steady, isotropic, and incompressible Newtonian fluid with constant density and viscosity. The vessel walls were assumed to be impermeable and rigid; although to some extent this assumption is not accurate, the elasticity of the walls is less important than the gross features of the flow. Previous studies have shown that the effect of non-newtonian fluid behavior is negligible [12,13]. Consequently, the governing equations can be written as: u j 0 x j u jui P u u i j ( ) x j xi x j x j xi ( i, j 1,2,3) ( 1 ) where and are the density and dynamic viscosity of blood, respectively. = 1055 kg/m 3 and = kg/m s [14]. u i is the velocity vector of blood and P is the pressure. The parabolic profile with a centerline velocity of 0.46 m/s [7] was applied at the inlet: Figure 1. 3D drug-eluting stent models in straight and curved arteries. According to different drug-coating positions on the stents, there are four models for each stent configuration (straight and curved): Model A: all-coated stents, i.e., drug coating on all surfaces (I, II, III, and IV), as shown in Fig. 2; Model B: drug coating on the contacting surface (I); Model C: drug coating on the non-contacting proximal and distal surfaces (II and III); Model D: drug coating on the non-contacting top surface (IV). V z inlet 2 2 x y 0.46 (1 ) 2 r V 0 r inlet where V z and V r are the blood velocities in the axial and radial directions, respectively, with radius r = m. A zero-pressure boundary condition was applied at the outlet: P 0 (3) outlet Luminal drug transport was described by the steady-state convection-diffusion equation and drug transport through the vascular wall was modeled by the steady-state diffusion equation: (2) f ( uif kf ) 0 xi xi t ( kt ) 0 xi xi ( i 1, 2,3) (4) where f and t are the drug concentrations in the blood and vascular wall, respectively. The diffusion coefficients of the drug in blood ( kf ) and tissue ( kt ) are 10-7 and m 2 /s, respectively [7]. Figure 2. Coating positions of drug-coated section. Gambit (version 2.3, ANSYS, Inc., USA) software was used to mesh these models. Unstructured meshes were selected for all eight models. Grids were refined at the stents and the vascular surfaces to improve computational accuracy. The size-function in Gambit and the grid adaptation in Fluent (version 6.3, ANSYS, Inc.) were applied to refine the meshes, particularly in the areas near the stents. The refinement on the meshes was stopped when the computational results reached f inlet t r f kf r f 0, 0 z perivascular wall blood outlet 0 t kt r tissue (5) (6) (Tissue-blood interface) (7) t 0 (Upstream/downstream boundaries of the tissue) (8) z

3 Numerical Analysis of Drug Coating of DES 489 1(1 indicates the stent surfaces assigned for drug-coatin)(9) The drug transport in tissues was modeled as a simple diffusion process, with an impermeable boundary condition on the perivascular wall (shown in Eq. 6). The continuity of flux at the tissue-blood interface is shown in Eq. 7. The boundary conditions of the upstream and downstream boundaries of the tissue (shown in Eq. 8) allowed drug transport to distal tissue segments. As shown in Eq. 9, the drug release of the stents was simulated with a Dirichlet boundary condition. For the drug coated, unit 1 was defined as 100% full drug coated and 0 means no drug on the stent surface, thus, the drug concentration values of the drug-coated surfaces in Models A, B, C and D were set as 1. All the values of drug concentration mentioned in this paper, which represent the range of the drug concentration from 0 to 1, are relative value, and the maximum value (near 1) indicates relatively high drug concentration. The computations were conducted by using the commercial CFD package, FLUENT 6.3(ANSUS Inc.), in which a finite volume method was used to discretize the governing equations. A 3D single-precision format and a segregated solver were used, and the SIMPLEC algorithm was applied for the velocity-pressure correction. The standard format was chosen for the pressure discretization and a second-order upwind format was selected for the momentum equations. The convergence threshold of residual error was set as Results To clearly observe the hemodynamic behavior and drug concentration for the two stent configurations, three segments and four lines were chosen for the investigation (as shown in Fig. 3). The stented arteries in the models were divided into proximal, middle, and distal segments. Line A is the reference line in blood with 1.25-mm offset from the centre line of blood vessel, and line B, C and D are the reference lines with a 1.45-mm, 1.55-mm and 1.75 mm offset from the centre line of blood vessel, respectively. Figure 3. Illustrations of reference lines and segments. The drug concentration curves of lines A and B (reference lines in blood) are shown in Figs. 4 and 4, respectively. It can be seen that the drug concentration on line A in Model C is lower than that in Model D, and that recirculation zones formed near the stents, causing drug deposition and thus a high drug concentration. As shown in the circle in Fig. 4, the drug concentration on line B in Model C is much higher than that in Model D. This indicates the effect of the stents on drug deposition near the vascular wall: the closer to the vascular wall, the higher is the level of deposition [15]. There was nearly no drug released into the blood in Model B. Figure 4. Drug concentration curves in straight blood vessel. Lines A and B. The drug concentration curves on lines C and D (in the vascular wall) are shown in Figs. 5 and 5, respectively. The drug concentration peak on line C appears on the stent struts and links in the four models. Because the drug in Model B directly entered the vascular wall, the peak value reached 70% that in Model A. In Models C and D, recirculation zones were formed by the stent struts and links in blood, which caused drug accumulation and high-drug-concentration regions, eventually increasing the amount of drug entering the vascular wall. In contrast, the drug concentration of the regions without stent struts and links is very low, as shown in Model B, because the drug entry into the vascular wall in Model B is different from those in Models C and D. The drug concentration curves in Models C and D are similar for a given flow field, and the drug concentration in the distal region is higher than that in the proximal region. Because the drug diffused in both the circumferential and radial directions, all drug concentration curves are flat on line D. Due to the diffusion effect on the regions without stent struts and links, the drug concentrations in Models B and C also show a significant increase. As the near-stent drug concentration in Model D is relatively low, the effect of the drug spread from the stent struts and links to the regions far from the stent struts and links is not obvious. The above analysis demonstrates that: (1) as the drug diffused along the radial direction into the vascular wall, the drug concentration in Model B increased and became uniform; (2) the drug concentration in Model A was the sum of those in Models B, C, and D; (3) there was no interaction between the different drug-coated surfaces in the vascular walls.

4 490 J. Med. Biol. Eng., Vol. 34. No Figure 5. Drug concentration curves on straight vascular wall. Lines C and D. To better observe the drug diffusion in the circumferential direction in the vascular walls, a cross section was selected in the middle of the stented blood vessel. In the cross section, the drug concentration at the mid-wall position of the vascular walls (as shown in Fig. 6) was unfolded in the circumferential direction. The drug concentration curves are shown in Fig. 6. It can be clearly seen that the drug concentration peak near the stent struts and links appeared in Models A, B, and C, but not in Model D. The peak-trough difference is 0.2 in Model A, 0.12 in Model B, and 0.09 in Model C. This implies that the increase of drug concentration near the stent struts and links was mostly caused by the drug coating on the contacting surface and the non-contacting proximal/distal surfaces, with the drug coating on the noncontacting top surface having little effect. Figure 6. Drug distribution in circumferential direction in vascular wall. Reference location and drug concentration curves. The drug concentration curves of inner/outer bends along line A in the curved vessel are shown in Figs. 7 and 7, respectively. The drug concentration trends in Models C and D are similar, showing high drug concentrations near the stent struts and links. Due to blood flow, the drug concentration is near zero in the proximal region. There is a ten-fold difference in the drug concentration between the inner and outer bends of the stents. Blood flow greatly influences the drug concentration at the outer bend of the stents, and the curve shows significant fluctuation. On line A, the drug concentration in Model D is higher than that in Model C, and the drug concentration in Model B is nearly zero. The drug concentration curves on line B of the inner/outer bends of the curved stents are shown in Figs. 7(c) and 7(d), respectively. It can be seen that the drug concentration difference between the inner and outer bends is reduced; the drug concentration of the inner bend is 3 to 4 times greater than that of the outer bend; the drug concentration peaks of the inner and outer bends are nearly the same, but the drug concentration differences in regions far from the stent struts and links are obvious. For the drug concentration at the inner bend, the first stent struts are consistent, but the remaining stent struts showed the proximal high and distal low phenomena, that is high concentrations at proximal segments and low concentrations at distal segments. The drug concentration curves of the inner/outer bends of the curved vascular wall on line C are shown in Figs. 8 and, respectively. There are still drug concentration differences between the inner and outer bends, but the differences have gotten smaller. Even though the drug in Model B is free from blood flow and theoretically the drug concentration of the inner and outer bends should be consistent, in reality there are differences. This is because under bending deformation, the outer bend is stretched and the inner bend is compressed. It means that if the same amount of drug enters the different volumes, drug concentration in the inner bend and outer bend of the vascular wall will be different. With the influence of blood flow and stent bends, in the regions far from the stent struts and links, the drug concentration of the inner bend is higher than that of the outer bend. The drug concentration curves of the inner and outer bends of the curved vessel on line D are shown in Figs. 8(c) and (d), respectively. There are still drug concentration differences for the inner bend and outer bend, especially in Models C and D, for which the drug concentration of the inner bend is nearly twice as much as that of the outer bend. In Model B, the peak value of drug concentration near the struts and links in the vascular wall decreased from around 75% to around 50%; however, the drug concentration between the struts and links significantly increased. This implies that in high-drug-concentration regions, the drug diffused in the radial and circumferential directions, and the drug concentration gradually became uniform. The biggest difference between the drug concentrations of the inner bend and the outer bend is the significant decrease between the stent struts and the links. In particular, Models C and D show significant decline of the outer-bend drug concentration between the second and third struts; the drug concentration in the distal region was smaller than that in the proximal region.

5 Numerical Analysis of Drug Coating of DES 491 (c) (c) (d) Figure 7. Drug concentration curves in Lines A and B in the blood. Inner and outer bends of Line A and (c) inner and (d) outer bends of Line B. This implies that for the curved stents, the effects of blood flow and stent bend on the drug concentration should be taken into account. In Models C and D, the drug concentrations in the middle and proximal regions were half that of the inner bend stents. The comparisons of mean values of the drug concentrations in the proximal, middle, and distal regions of the stents are shown in Fig. 9. For Model B, the drug concentration had few changes in the proximal, middle, and distal regions. Due to blood flow, Models C and D show gradual increases of drug concentration. In particular, for Model D, the drug concentration in the proximal region was half that in the distal region. In Model B, the drug directly entered the vascular wall with little influence from blood flow; therefore, the drug concentrations are nearly same in the proximal, middle, and distal regions of stents in the straight vessel. The drug concentrations in Models C and D show the same trend, namely (d) Figure 8. Drug concentration curves in Lines C and D on vascular wall. Inner and outer bends of Line C and (c) inner and (d) outer bends of Line D. increasing distribution curves for both straight and curved vessels. Because the non-contacting top surface is closer to blood, the drug concentration in Model D shows an obvious phenomenon- proximal low and distal high, that is low concentrations at proximal segments and high concentrations at distal segments, especially in the curved vessel. Based on the above analysis, the different drug concentrations in the proximal and distal regions are caused by the drug coating on the non-contacting surfaces of the stents. The drug concentration in the curved vessel does not only show the phenomena of proximal low and distal high, which is caused by blood flow, but also show the phenomena of inner high and outer low, that is high concentrations in inner bend and low concentrations in outer bend, which is caused by different curves (as shown in Fig. 10). In terms of the overall drug concentration, the drug concentration of the outer bend in the curved vessel is 70.4% that of the inner bend; more precisely, it is 86%, 67.5%, and 64% those for the proximal,

6 492 J. Med. Biol. Eng., Vol. 34 No Figure 9. Comparison of drug concentration for the models in proximal, middle, and distal regions of stents in straight and curved vessels. Figure 11. Comparison of percentages of Model B, C, and D for allcoated Model A in 2D and 3D models. 4. Discussion Figure 10. Comparison of drug concentration at inner and outer bends in curved artery. middle, and distal regions, respectively. This implies that the differences in drug concentration between the proximal and distal regions, as well as between the inner and outer bends, are caused by blood flow and vessel curve. The volume-weighted average concentrations in the straight and curved models were calculated. The results are shown in Fig. 11. In the straight vessel, the drug amounts from the contacting surface and the non-contacting top surface respectively account for 27% and 27% of the total drug deposition, compared to 11% and 30% in 2D models [7]. In the curved vessel, the drug amounts from contacting surface and the non-contacting top surface respectively account for 25.4% and 27.2% of the total drug deposition, compared to 12% and 27% in 2D models [9]. The percentages of Model B, C and D are the proportion of drug concentration in the vascular wall for all-coated surfaces Model A (Model A is 100% in this situation), so the sum of Model B, C, and D is 100%. In numerical simulations, the vascular wall is commonly simplified as a rigid wall [16]. Studies have demonstrated that this assumption has little impact on the calculation results [17]. Even though the conditions do not perfectly reflect reality, the surface elasticity of the wall is not very critical under the flow conditions considered here [12]. Moreover, the arterial elasticity is gradually reduced during the development of atherosclerosis, and after stents are implanted, the arterial rigidity gets strengthened [13]. Therefore, all in all, the assumption of rigid wall in the models is reasonable. For large and medium arteries, it is appropriate to simplify the blood as an incompressible Newtonian fluid with constant density and viscosity. Because red blood cells are smaller than the blood vessel diameter in large and medium arteries, blood can be considered a continuous fluid. Because the diameter of blood vessels is larger than 0.5 mm, the blood flow shear rate is very high in the vessel, and consequently blood viscosity becomes a constant and has no relationship with the shear rate [18]. Finally, calculation error should be less than 2% [19]. Therefore for blood in large and medium arteries, it is appropriate to simplify the blood as an incompressible Newtonian fluid of constant density and viscosity. From the drug concentration curves in the blood and vascular wall, it can be seen that the drug concentration in the vascular wall consists of two parts. Some of the drug entered the vascular wall directly from the contacting surface and some entered the blood from the non-contacting surfaces, and finally the vascular wall. The total drug quantity is the sum of these two parts.

7 Numerical Analysis of Drug Coating of DES 493 Intuitively, if the drug entered the vascular wall directly from the contacting surface, the advantages are no influence of blood flow and less drug loss, and the disadvantage are uneven drug distribution in the vascular wall (the drug concentration near the stents could be much higher than that of regions far from the stents). In contrast, if the drug entered the blood from the non-contacting surfaces, the drug concentration in the vascular wall is more even, but the influence of blood flow is large, and thus the drug concentration in the distal region is much higher than that in the proximal region and the drug loss is large. Based on the above analysis, the following can be concluded: (1) Along with the diffusion of the drug in the radial direction of the vascular wall, the drug concentration curves tended to be flat because the drug in the circumferential direction can spread to the region far from the stents, and consequently the drug concentration in this region increased gradually. (2) The drug deposition from both the contacting and non-contacting proximal/distal surfaces can cause uneven distribution. Therefore, increasing the amount of drug on the contacting surfaces cannot always make the uniformity of drug distribution worse. (3) For the stents in a curved artery, as shown in Fig. 10, the drug concentration in the distal region is higher than that in the proximal region and that of the inner bend is higher than that of the outer bend. Blood flow in the curved artery thus leads to uneven drug concentration at inner/outer bends. (4) When the stents are bent, the outer bend links get stretched and the spaces between the outer bends of the struts become bigger, whereas the inner bend links get squeezed and the spaces between the inner bends of struts become smaller. This leads to different drug concentrations on the inner and outer bends. (5) Regarding drug deposition from the various surfaces, the trends from 2D models are consistent with those from 3D models, but the values are different. The results of 2D simulation may be completely different from those of 3D simulation. Therefore, even though a considerable amount of the drug in the vascular wall comes from the drug on the non-contacting top and proximal/distal surfaces, when all stent surfaces were drug-coated, the phenomenon- proximal low and distal high of drug distribution can appear in the blood and vascular walls. These uneven distributions are mainly caused by blood flow. In order to improve the uniformity of distribution, the drug coating on the surface of the stents should be optimized, such as using uneven drug coating (a heavier coating in the proximal region than that in the distal region). The previous analysis showed that because the drug coating on the non-contacting surface is affected by blood flow, which can affect the drug release into the vascular wall, an optimized drug coating for one blood flow state may not be suitable for another. However, optimizing the drug distribution for various states of blood flow is quite complicated and impractical. Drug coating on the contacting surface can provide effective drug release into the vascular wall that is unaffected by blood flow. The uniformity of drug distribution in the vascular wall can thus be improved by optimizing the drug loading on the contacting surface. Using 2D simulation to simplify the model analysis can reduce computation time and resources at the cost of some inaccuracy. When accuracy is important, 3D analysis should be used. As shown in Section 3, the amounts of the drug from the contacting surface calculated by the 3D method (27%, 25.4%) are much bigger than those obtained from 2D simulation (11%, 12%). The contribution of the contacting surface to the drug concentration in the vascular wall was underestimated in the 2D numerical simulation. This is due to the following reasons: (1) in 2D models, the non-contacting proximal/distal surfaces of stents are perpendicular to the direction of blood flow, and the drug is prone to gather in the recirculation region, whereas in 3D models, the blood flow vector and most of the proximal/ distal surfaces are at acute angles (in the same direction at some positions). (2) In 2D models, the drug only diffuses in the axial and radial directions in the vascular wall, whereas in 3D simulation models, the drug diffuses in the axial, radial, and circumferential directions, which is consistent with reality. Due to the limitations of 2D models, Balakrishnan [7] found that an increase of the stents height was the only factor that improved the drug concentration in the vascular wall. However, based on the results of 3D simulation, the contacting surfaces enhance drug release and absorption; therefore, increasing the area of the contacting surface improves the drug concentration in the vascular wall and avoids the increase of the low WSS region caused by an increase in DES height. Studies on the drug release and absorption of DES should thus be conducted using 3D models. 5. Conclusion In this paper, the effects of drug-coating position on the drug concentration were analyzed using 3D DES models. It was found that: In traditional 2D models, the blood flow directions are perpendicular to most of the non-contacting proximal/distal surfaces, but in 3D models, in most situations, the blood flow directions are not perpendicular to most of the non-contacting proximal/distal surfaces and the nonperpendicular cannot effectively block the blood flow and caused drug accumulation. Therefore, it is very necessary to study DES drug release and absorption using 3D models. Increasing the area of the contacting surface increases the drug concentration in the vascular wall and avoids the possible increase of the low WSS region caused by an increased DES height. Drug coating on the contacting surface can provide effective drug release in the vascular wall without interference from blood flow. Therefore, it is possible to improve the uniformity of drug concentration in the vascular wall by optimizing drug loading on the contacting surface. DES design can be optimized 1) by increasing the drug on the contacting surface (to improve drug concentration in the vascular wall) and 2) by reducing the stent height (to reduce the low WSS distribution). Such a design can make the distribution of drug concentration more uniform and inhibit restenosis.

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