Annals of Biomedical Engineering

, Volume 38, Issue 7, pp 2263–2273

Computational Investigation of the Delamination of Polymer Coatings During Stent Deployment

Authors

  • C. G. Hopkins
    • Department of Mechanical and Biomedical Engineering and National Centre for Biomedical Engineering ScienceNational University of Ireland
  • P. E. McHugh
    • Department of Mechanical and Biomedical Engineering and National Centre for Biomedical Engineering ScienceNational University of Ireland
    • Department of Mechanical and Biomedical Engineering and National Centre for Biomedical Engineering ScienceNational University of Ireland
Article

DOI: 10.1007/s10439-010-9972-y

Cite this article as:
Hopkins, C.G., McHugh, P.E. & McGarry, J.P. Ann Biomed Eng (2010) 38: 2263. doi:10.1007/s10439-010-9972-y

Abstract

Recent advances in angioplasty have involved the application of polymer coatings to stent surfaces for purposes of drug delivery. Given the high levels of deformation developed in the plastic hinge of a stent during deployment, the achievement of an intact bond between the coating and the stent presents a significant mechanical challenge. Problems with coating delamination have been reported in recent experimental studies. In this paper, a cohesive zone model of the stent–coating interface is implemented in order to investigate coating debonding during stent deployment. Simulations reveal that coatings debond from the stent surface in tensile regions of the plastic hinge during deployment. The critical parameters governing the initiation of delamination include the coating thickness and stiffness, the interface strength between the coating and stent surface, and the curvature of the plastic hinge. The coating is also computed to debond from the stent surface in compressive regions of the plastic hinge by a buckling mechanism. Computed patterns of coating delamination correlate very closely with experimental images. This study provides insight into the critical factors governing coating delamination during stent deployment and offers a predictive framework that can be used to improve the design of coated stents.

Keywords

Polymer coatingStent deploymentDelaminationCohesive zoneFinite element

Introduction

Vascular stents are commonly used to treat atherosclerosis, a condition associated with heart disease which involves the deposition of fatty lipids or plaque in an artery. To regain adequate blood flow through the vessel, the metallic stent is expanded, undergoing large strains to remain as a permanent scaffold. Due to the trauma of this implantation, there is ~30% chance that the proliferation of smooth muscle cells (restenosis), will re-occlude the vessel,10 requiring further treatment. Stent coatings function to increase device biocompatibility and primarily to deliver anti-proliferative drugs.26 The coating must also have suitable mechanical properties such that occurrences of delamination and fracture during stent crimping and implantation are eliminated.6,12,25 Delamination of polymer coatings on commercial stents has been reported14,20,21,24 using SEM analysis (see Fig. 1). Coating damage in vivo has also been reported in studies involving diamond-like carbon and porous aluminum oxide-coated stents.7,11,13,15
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FIGURE 1

Delamination of stents coatings after stent deployment (a) stent hinge region24 (reprint with permission from Oxford University Press) (b) Cypher® stent14 (reprint with permission from Wiley Periodicals Inc.)

Stent coating failure in vivo could lead to several negative clinical complications. Damage to a coating may increase the risk of thrombosis. The dosage of a drug contained in the coating could be reduced or the delivery misguided.14 The breakdown of the coating barrier may allow the release of irritant or toxic ions from the metallic stent, leading to an inflammatory response. Debris from the coating caught in the blood stream could also create micro-embolisms.9,13

The complex geometry of a balloon-deployed stent gives rise to localized regions of high plastic strain which correlate to areas where delamination is predominant as shown in Fig. 1. In order to adequately design coatings to withstand large deformation, knowledge of the mechanisms attributing to delamination is essential.

In this study, a finite-element model is developed whereby a cohesive zone law is applied at the interface of the stent and coating to simulate delamination during the stents crimping and deployment stages. Cohesive zone laws have been established as a means to simulate the decohesion of surfaces.2,17,27,30 A cohesive zone model has been applied in previous work where Abdul-Baqi and Van der Giessen1, 2 simulated the nanoindentation of a coating. Also using this approach, McGarry et al.17 and McGarry and McHugh16 simulated the detachment of cells from an underlying substrate. The delamination of a coating undergoing cyclic heat loads was simulated by Hattiangadi and Siegmund8 using an adapted Xu Needleman cohesive zone model.

In this study, it is hypothesized that debonding of polymer coatings from highly strained regions of the stent surface during deployment can be accurately modeled using a cohesive zone framework at the stent–coating interface. The first objective of this computational study is to investigate the mechanisms of debonding of biomedical stent coatings during stent deployment using a mixed mode cohesive zone model. Secondly, the design parameters which govern the initiation of coating debonding during deployment are analyzed. Finally, a case study is presented in which our modeling framework is applied to two commercially adapted stent designs and three relevant biomedical grade polymer coatings. It is demonstrated that our computational framework is capable of predicting patterns of coating debonding reported in previous experimental studies.

Methods

Cohesive Zone Formulation

The mathematical characterization of the interaction between the coating and the stent surface is determined by the exponential cohesive zone model described by Xu and Needleman.28 The cohesive interface is described in terms of a constitutive law relating relative displacements of two interacting surfaces in the normal and tangential directions (Δn and Δt, respectively) to the corresponding tractional forces between them (Tn and Tt). These tractional components are determined from an interface potential function ϕ(Δn, Δt) whereby;
$$ T_{\text{n}} = {\frac{\partial \phi }{{\partial \Updelta_{\text{n}} }}};\quad T_{\text{t}} = {\frac{\partial \phi }{{\partial \Updelta_{\rm t} }}} $$
(1)
where ϕ is the work of separation, given as:
$$ \phi (\Updelta_{\rm n} ,\Updelta_{\rm t} ) = \phi_{\rm n} + \phi_{\rm n} \exp \left( { - {\frac{{\Updelta_{\rm n} }}{{\delta_{\rm n} }}}} \right)\left\{ {\left[ {1 - r + {\frac{{\Updelta_{\rm n} }}{{\delta_{\rm n} }}}} \right]{\frac{{1 - {q}}}{{{r} - 1}}} - \left[ {q + \left( {{\frac{{{r} - {q}}}{{{r} - 1}}}} \right){\frac{{\Updelta_{\rm n} }}{{\delta_{\rm n} }}}} \right]\exp \left( { - {\frac{{\Updelta_{\rm t}^{2} }}{{\delta_{\rm t}^{2} }}}} \right)} \right\} $$
(2)
This leads to the following expressions relating traction to interface separation28;
$$ T_{\text{n}} = - \left( {{\frac{{\phi_{\text{n}} }}{{\delta_{\text{n}} }}}} \right)\exp \left( { - {\frac{{\Updelta_{\text{n}} }}{{\delta_{\text{n}} }}}} \right)\left\{ {\left( {{\frac{{\Updelta_{\text{n}} }}{{\delta_{\text{n}} }}}} \right)\exp \left(- {{\frac{{\Updelta_{\text{t}}^{2} }}{{\delta_{\text{t}}^{2} }}}} \right) + \left[ {\left( {{\frac{1 - q}{r - 1}}} \right)} \right]\left[ {1 - \exp \left( { - {\frac{{\Updelta_{\text{t}}^{2} }}{{\delta_{\text{t}}^{2} }}}} \right)} \right]\left[ {r - {\frac{{\Updelta_{\text{n}} }}{{\delta_{\text{n}} }}}} \right]} \right\} $$
(3)
$$ T_{\text{t}} = - \left( {{\frac{{\phi_{\text{n}} }}{{\delta_{\text{n}} }}}} \right)\left( {{\frac{{2\delta_{\text{n}} }}{{\delta_{\text{t}} }}}} \right)\left( {{\frac{{\Updelta_{\text{t}} }}{{\delta_{\text{t}} }}}} \right)\left\{ {q + \left( {{\frac{r - q}{r - 1}}} \right)\left( {{\frac{{\Updelta_{\text{n}} }}{{\delta_{\text{n}} }}}} \right)} \right\}\exp \left( { - {\frac{{\Updelta_{\text{n}} }}{{\delta_{\text{n}} }}}} \right)\exp \left( { - {\frac{{\Updelta_{\text{t}}^{2} }}{{\delta_{\text{t}}^{2} }}}} \right) $$
(4)
where q = ϕtn, δn, and δt are the critical normal and tangential characteristic lengths, respectively, and r = Δn*/δnn* is the value of normal displacement following complete tangential separation with Tn = 0). The works of normal and tangential separation are related in Eqs. (5) and (6) to the normal and tangential interfacial adhesion strengths σmax and τmax, respectively;
$$ \phi_{\text{t}} = \sqrt {{\frac{e}{2}}}\tau_{\max } \delta_{\text{t}} $$
(5)
$$ \phi_{\text{n}} = \sigma_{\max } e\delta_{\text{n}} $$
(6)
where e = exp(1).
The normalized traction–separation profiles for pure tangential (Δn = 0) and pure normal (Δt = 0) displacement are displayed in Fig. 2. In a finite-element model after a node has been critically displaced, the tractional forces at that node reduce to zero.
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FIGURE 2

Xu and Needleman28 cohesive zone model. Plots of normalized tractional forces for (a) normal reaction for Δt = 0, (b) tangential reaction for Δn = 0

Finite-Element Model

The cohesive zone model is incorporated into ABAQUS™ Standard (V.6.7-1, ABAQUS Inc., RI, USA) via a user-defined interface subroutine (UINTER). This interface model is applied along the contacting stent and coating surfaces.

Due care is required when selecting the input parameters to the cohesive zone model. The interface bond strength in the normal and tangential directions is assumed equal so τmax = σmax. The normal and tangential characteristic length scales δn and δt are also set equal and given a value of 0.5 μm. This results in the coupling energy parameter are q ≈ 0.43.

A generic ‘U-shaped’ plastic hinge geometry (see Fig. 3) is used to investigate the mechanisms of coating delamination. Two different stent geometries were created based on the Cypher® (Cordis, Johnson & Johnson, USA) and Taxus® (Boston Scientific Inc., USA) designs, referred to as Designs 1 and 2, respectively (see Fig. 4). The stent geometries are represented as 2D units (indicated by the dashed lines in Fig. 4), which for the purposes of finite-element modeling give an adequate prediction of the stents deformation processes.5,18 Additionally, several experimental studies14,21,24 have shown that delamination occurs primarily from the stent surfaces normal to the circumferential direction. This allows for the simulation of a 2D stent-coating system in order to investigate the primary mechanisms of coating delamination. Stents and coatings are meshed using 2D plane strain elements.
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FIGURE 3

Schematic of generic stent unit geometry and boundary conditions where t and rn is the thickness and radius of the neutral axis of the coating, respectively, and L is half the strut length. The curvature of the geometry is specified as κ = 1/rn

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FIGURE 4

Stent geometries; (a) Design 1 adapted from the Cypher® stent and (b) Design 2 adapted from the Taxus® stent geometry. Dashed lines indicate unit cell designs. Deployment of stent is in the circumferential direction indicated. do is the original displacement of the hinge at the strut half length L. L = 0.4 mm for Design 1 and 0.28 mm for Design 2

After being coated, a stent is crimped onto a balloon and later expanded to a set deployment radius once inside the stenosed artery. To simulate these mechanical processes, boundary conditions on the unit cells are applied primarily in the circumferential direction to insure periodic deformation of the unit. Large deformation kinematics is assumed for all simulations in this study. Preliminary studies were performed using the generic ‘U-shaped’ hinge model to determine appropriate mesh density for the simulations.

The 316L stainless steel stent is modeled assuming rate-independent elastic–plastic material behavior with a von Mises yield criterion, where its Young’s Modulus is 200 GPa and its yield strength is 264 MPa.19 The polymer coatings used in this study are chosen for their commercial relevance to drug eluting stents; a biomedical grade polyurethane Chronoflex® AR (AdvanSource Biomaterials Corporation, MA, USA), poly-styrene-b-isobutyl-b-styrene (SIBS), and polyurethane-glyco-phosphorylcholine (PU-GPC). The SIBS is a rubbery polymer used on some Taxus® generation stents. PU-GPC is a polymer blend consisting of 20 wt% PC which is a popular biomaterial sought after for its hydrophilic exterior that is ‘biomimicing’ when in vivo. Blends of PC are used on Medtronic and Abbott Vascular stent systems. Hyperelastic materials’ behavior with properties being based on published stress–strain test data is assumed for Chronoflex,3 SIBS,4 and PU-GPC.31 Strain rate-dependent data have not been published for these materials and are therefore not considered in this study. Preliminary simulations were performed to give an appreciation of the relative elastic stiffness of the materials in the range of strain experienced by the coatings. Within the 0–40% strain range, the Chronoflex and SIBS exhibit a relatively linear stress strain response with a Young’s moduli of ~23 and ~2 MPa, respectively. In this range, the PU-GPC exhibits primarily bi-modal behavior that approaches bi-linear format with a transition point at ~10% strain, with approximate Young’s modulus of ~240 MPa in the first phase (before transition) and ~7 MPa in the second phase (after transition) (Fig. 5).
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FIGURE 5

Uniaxial test data of polymer coatings Chronoflex, SIBS, and PU GPC3,4,31

Results

Analysis of the tractional forces generated during coating delamination of the ‘U-shaped’ generic stent (Fig. 3) reveals the occurrence of mixed mode delamination. Figures 6a and 6b show tractional forces at 90° to the stent surface where debonding initiation occurs, indicating Mode I fracture or normal delamination. The peak normal tractional force, indicated by the red dot in Fig. 6a, corresponds to the normal interface strength term σmax. Mixed mode delamination is then displayed as the coating begins to ‘peel’ from the remainder of the stent. Upon increased deployment, delamination progresses as shown in Fig. 6d give a mix of both normal and tangential tractional forces (Fig. 6c) along the stent strut. The direction of debonding is predominately tangential, with the peak tangential traction being very close to τmax (as indicated by the red dot in Fig. 6c).
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FIGURE 6

Modes of delamination. (a) Normal and tangential tractional forces at the interface point where debonding initiation starts, reaching the maximum normal traction indicated by the red dot. This location of initiation is at the center of curvature indicated in (b). (c) Plot of the normal and tangential tractional forces at the region indicated by the arrow in (d). Delamination initiates due to peeling of the coating and results in a predominantly tangential tractional force with the peak indicated as a red dot in (c)

As stent deformation is governed by deformation of the plastic hinge and consequent rotation of the connecting struts, it is useful to define the circumferential strain per unit strut length as:
$$ {\frac{{\varepsilon_{\text{c}} }}{L}} = {\frac{{d_{\text{f}} - d_{\text{o}} }}{{d_{\text{o}} L}}} $$
(7)
where df and do are the original and final stent circumferences and L is the half-length of a strut. For complex stent unit-cell designs which consist of more than one plastic hinge, the contribution of each hinge to the total circumferential strain will differ, so Eq. (7) should be computed based on the deformation and strut length of each individual hinge.
Using the ‘U-shaped’ stent model, simulations are performed for the three aforementioned polymer coatings for coating thicknesses of 5, 10, and 15 μm. Such coating thicknesses lie within the range of coating thickness for commercially available stents. For each coating thickness, an interface strength, σmax, is determined so that coating delamination does not initiate until a deployment corresponding to εc = 3 is achieved. From Fig. 7, a near linear relationship is computed between coating thickness and interface strength. It is also clear that a higher interface strength is required to prevent delamination of stiffer coatings before the desired level of stent deployment is achieved. Regarding mesh sensitivity, a decrease in element length from 2.5 to 1.25 μm at the stent–coating interface resulted in a change in σmax of less than 1%. A further decrease in element length to 0.5 μm produced no change in σmax. Therefore, elements of length 1.25 μm are used at the stent–coating interface for all subsequent simulations.
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FIGURE 7

Maximum normal interface strength required at debonding initiation for a circumferential strain εc = 3 plotted for varying thicknesses of the polymer coatings

In a further series of simulations, the ‘U-shaped’ stent model is utilized in a parameter study to explore the relationship among coating geometry, elasticity, stent deployment radius, and interface bond strength. For this analysis, the hyperelastic properties utilized are those of the three polymer materials in addition to generic coating materials with Young’s moduli ranging from 10 to 70 MPa. Results show that Mode I debonding initiation can be predicted by the dimensionless interface strength \( (\bar{S}) \) term given in Eq. (8). This term relates the coating curvature (κ), thickness (t), and Young’s modulus (E) to the normal interface strength (σmax)
$$ \bar{S} = {\frac{{\sigma_{\max } }}{Et\kappa }} $$
(8)
The dimensionless interface strength term in Eq. (8) is plotted against εc/L in Fig. 8, showing a non-linear relationship. This plot functions as a ‘design curve,’ where knowledge of the dimensionless interface strength for a given tensile hinge can be translated to predict the maximum expansion of the hinge before coating delamination occurs. It is noted that the SIBS and Chronoflex coatings at the initiation of delamination experience strains in the region 20–40%, where their stress strain behavior is still relatively linear and so a corresponding Young’s modulus can be determined. However, this is not the case for the PU-GPC coating, with an increased stiffness only remains linear to ~10% strain (Fig. 5) and so the design curve cannot be used to predict delamination for such non-linear material behavior.
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FIGURE 8

Design curve relating the dimensionless interface strength to the radial strain per unit length (εc/L) experienced by the U-shaped stent unit. A polynomial curve fit to the data is plotted as a green line

Case Study

The unit stent geometries investigated in this case study, shown in Figs. 10a and 10b, are based on the commercially available Cypher and Taxus stents, referred to as Designs 1 and 2, respectively. Coating thicknesses consistent with those of their commercially available versions are assumed (12.5 μm for Design 1 and 16 μm for Design 2). A relevant σmax value for a thin hyperelastic polymer coating on an elastic–plastic substrate is not available in literature. An estimate for σmax is determined in this study using a published SEM image of coating delamination.21 Figure 9a shows coating delamination at the hinge section of a Cypher® stent. The unknown parameters from the published delamination image are the coating Young’s modulus (E) and the interface strength (σmax), with coating thickness (t) and curvature (κ) being known. Based on the dimensionless interface strength established above (Eq. 8), we must simply determine the correct ratio of (σmax/E) in order to simulate the coating delamination shown in Fig. 9a. Simulations reveal that (σmax/E) = 2.14 × 10−3 yields the correct pattern and magnitude of coating delamination, as shown in Fig. 9b. It should once again be stressed that, while material properties of the Cypher® stent coating are not known to the authors, the establishment of the dimensionless interface strength (Eq. 8) allows us to determine the correct (σmax/E) ratio based on the measured geometric parameters and debonding patterns. As an illustration, if the coating material shown in Fig. 9a is assumed to be Chronoflex then an interface strength of σmax = 0.05 MPa would yield the correct amount of delamination. It is important to note that if we assumed a different coating material, identical amounts of delamination could be computed by choosing an appropriate value of σmax based on Eq. (8).
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FIGURE 9

(a) Cypher stent delamination at hinge region21 (reprint with permission from HMP Communications). (b) Finite-element model used to ascertain suitable σmax estimate

In order to access the performance of the design curve established in Fig. 8, the εc/L value at which delamination initiation occurs at a tensile surface of the plastic hinge (Figs. 10a and 10b) for a specific coating is plotted on the graph in Fig. 10c. Simulations are performed for two coating materials, with σmax = 0.05 and 0.2 MPa for the Chronoflex coatings and σmax = 0.05 and 0.009 MPa for the SIBS coatings. This represents four different ratios of (σmax/E), including a ratio of 2.14 × 10−3 as calibrated from Fig. 9a (Chronoflex with σmax = 0.05 MPa). Results for the PU-GPC coating are not shown in Fig. 10c due to its non-compliance with Eq. (8) as a result of its highly non-linear material properties, as discussed previously.
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FIGURE 10

(a) Design 1 indicating tensile hinge A. (b) Design 2 with tensile hinges B, C, and D indicated. (c) Plot of the dimensionless interface strength against the circumferential strain per unit strut length (εc/L). Results determined from finite element simulations for each hinge are superimposed on the design curve. Asterisk (*) denotes a hinge which did not delaminate following stent over-deployment. Symbol † denotes Mode II initiation

Overall, results show close compliance with the predictions of the design curve established in Fig. 8. The dimensionless interface strength values for the SIBS coating on Hinge A of Design 1 and Hinges C and D of Design 2 lie above the design curve; therefore, debonding of the coating is not predicted to occur, even for large εc/L values. From Fig. 12a, the coating remains fully attached to Hinges C and D even when the stent is over-deployed. This can be attributed to the large radius of curvature of these hinges, which leads to an increased dimensionless interface strength, as dictated by Eq. (8).

Although debonding initiation is shown to be primarily Mode I at the tensile region of the plastic hinge, mixed mode delamination is observed upon further deployment in both stent designs. In fact for hinge C, which has a very large radius of curvature, Mode II debonding initiation is computed for dimensionless interface strengths (σmax/Etκ) of 0.085 and 0.045, as indicated in Fig. 10c. Additionally, buckling of the coating is computed in compressive regions of plastic hinges for both designs, as shown in Figs. 11 and 12.
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FIGURE 11

Finite-element simulation of Chronoflex coating delamination on Design 1 stent deployed to εc = 1.8 with an interface strength of 0.05 MPa

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FIGURE 12

(a) Result of finite element simulation for the SIBS coating on Design 2 with an interface strength of 0.05 MPa and deployed to εc = 1.8. (b) Image of a stent with a similar hinge geometry and patterns of delamination to Design 2, highlighted by blue arrow (tensile region) and black arrow (compressive region)24

Figure 11 shows delamination of the coating that occurs on stent Design 1 at a circumferential strain of εc = 1.8. Parameters have been chosen based on delamination observed experimentally (Fig. 9a). As shown in Fig. 10c, tensile delamination initiates at εc/L = 0.4 mm−1c = 0.16). However, from Fig. 11, further deployment results in buckling of the coating from the stent surface in compressive regions of the plastic hinge. This phenomenon first occurs at εc = 0.636 in the vicinity of a geometric discontinuity where a connector strut intersects the plastic hinge. At εc = 1.1, a second occurrence of compressive buckling initiates in a region of high compressive stress on the plastic hinge. From Fig. 11, significant amounts of the coating are predicted to detach from the stent surface following deployment to εc = 1.8.

Figure 12a illustrates the predicted pattern of coating debonding at εc = 1.8 for stent Design 2 with a SIBS coating and an interface strength of σmax = 0.05 MPa. As shown in Fig. 10c, tensile delamination only occurs at hinge B (initiating at εc/L = 4.18, or εc = 1.17), with the coating remaining fully attached to the stent at hinges C and D. Debonding of the coating by buckling on the compressive side of Hinge B is computed to initiate at εc = 1.57 and, as can be seen from Fig. 12a, significant removal of the coating on the compressive side of the hinge is predicted at εc = 1.8. An identical pattern of debonding on the tensile and compressive side of a similar plastic hinge has been reported experimentally by Regar et al.,24 as shown in Fig. 12b.

Discussion

For the first time a computational modeling framework has been developed to simulate stent coating delamination. We have demonstrated that cohesive zone modeling of a stent–coating interface results in the simulation of debonding patterns of polymer coatings during stent deployment that correlate closely with debonding patterns reported in experimental studies. Furthermore, our simulations have allowed for the identification of critical parameters that govern delamination of stent coatings during deployment.

Simulations of coating delamination on stent geometries reveal that debonding occurs mainly in the high strain plastic hinge regions. This result is supported by previous experimental studies of stent coatings using SEM analysis.14,20,21,24 This study reveals that the initiation of coating debonding in the tensile region of the plastic hinge is dependent on the coating thickness, the coating material, and the curvature of the hinge. Stiff, thick coatings on plastic hinges of high curvature are shown to debond at lower levels of stent deployment. Clearly an increase in interface strength between the stent surface and the coating will delay the on-set of coating debonding. A dimensionless grouping of the critical parameters that govern debonding initiation in tensile regions has been identified. For a required level of stent deployment for any stent design, a critical dimensionless interface strength can be identified, above which tensile delamination will not occur. This should allow for safe design of coating thickness, stiffness, and bond-strength and should provide a significant step toward elimination of coating delamination.

Results demonstrate that debonding initiation at the tensile surface of the plastic hinge of a polymer-coated stent is predominantly Mode I. However, when further stent deployment occurs following debonding initiation, the coating peels away from the curved surface introducing mixed mode fracture which becomes predominantly Mode II along the flat stent strut. Furthermore, Mode II debonding initiation is computed for a hinge with a large radius of curvature in our case study. The conditions that lead to the development of Mode II initiation in a symmetric hinge are currently being investigated in a parallel study. Additionally, mixed mode delamination is also computed in compressive regions of the stent surface, leading to buckling of the coating. Compressive buckling is computed to initiate at a higher deployment level than that that computed for tensile delamination. This may be related to the fact that during stent deployment compressive surfaces of the plastic hinge have a lower curvature (κ) than tensile surfaces, and consequently a higher dimensionless interface strength. However, initiation of buckling does not appear to be governed by our ‘design curve’ for initiation of tensile delamination. The mechanism of compressive delamination is quite different to that computed in tensile regions and further investigation of coating buckling in compressive regions of the plastic hinge is ongoing. The experimental study of Regar et al.24 demonstrates identical patterns of coating buckling in compressive regions as computed by our simulations.

Patterns of coating delamination in the tensile region of the plastic hinge computed in this study are very similar to observed SEM images of coating debonding in the studies of Levy et al.,14 Ormiston et al.,20 Otsuka et al.,14,20,21,24 and Regar et al.24 In this study, an SEM image of tensile delamination in a Cypher stent from Otsuka et al.21 was used to determine the ratio of interface strength to coating stiffness (σmax/E) for this commercially available drug eluting stent. The model was calibrated using reported values of coating thickness,22 and deployment and delamination magnitudes estimated from the SEM image.21 It should be noted that, while no information was available on the coating material or interface strength for this stent design, our methodology allows for the computation of the required (σmax/E), assuming that the coating material exhibits linear behavior in the range of deformation experienced during deployment.

Based on our calibration of the (σmax/E) for reported coating delamination in a Cypher® stent,21 an interface strength in the range ~0.005–0.05 MPa should be expected if coating stiffness lies between that of SIBS (~2 MPa) and Chronoflex (~23 MPa). This range of interface strengths is very similar to a range of ~0.007–0.07 MPa estimated from the investigation of polymer peel tests by Rahulkumar et al.23 The full range of interface strengths used in our parametric studies (0.009–1 MPa) also complies closely with a range between 0.14 and 0.4 MPa estimated from the work of Yan et al.29 for a polymer peel test on a steel substrate. It can therefore be concluded that all results in this study are computed for realistic ranges of interface strengths and for commercially relevant polymer coating materials.3,4,31 We are currently performing a series of mixed mode experimental tests to determine interface properties for polymer coatings on stainless steel substrates, allowing for the precise measurement of τmax and σmax.

One shortcoming of our calibration of coating delamination in stent Design 1 is that we have not included pre-stress in the coating. The experimental image of Otsuka et al.21 would suggest that the coating may contain some pre-stress, as the debonded material appears to be stretched across the plastic hinge. The inclusion of such pre-stress would only serve to accelerate debonding in our models, thus strengthening the motivation for analysis of coating delamination during stent deployment. The effect of pre-stress will be investigated in future simulations.

Results for the multiple hinge Taxus stent geometry (Design 2) reveal very similar patterns of tensile delamination to those computed for a Cypher stent geometry (Design 1). Both designs exhibit a close compliance to our ‘design curve’ with similar debonding initiation being computed for both designs for a given coating material and interface strength. The smallest hinge (B) in Design 2 exhibits the earliest tensile debonding during deployment, whereas the largest hinge (C) exhibits the highest deployment at the onset of tensile debonding, followed closely by hinge A in Cypher stent (Design 1). These results are not unexpected when one considers the non-dimensional geometric parameter (tκ) for each hinge in the two designs. Results suggest that the use of a compliant SIBS coating will result in least debonding for a given interface strength. Regarding the buckling of coatings in compressive regions of the plastic hinge, the earliest buckling is computed in the vicinity of a geometric discontinuity of the Cypher stent. It might therefore be reasonable to suggest that application of a coating to regions of high curvature or geometric discontinuities should be avoided.

It should be noted by the reader that this case study should not be treated as a direct comparison of two commercially available drug eluting stents, as precise information regarding the coating and interface properties are unavailable for both designs. The purpose of our case study is to demonstrate the ability of our modeling framework to predict locations of coating debonding and deployment conditions required to produce debonding for commercially available stent geometries.

Conclusion

In conclusion, our modeling framework allows for the prediction of coating delamination in tensile regions of plastic hinges during stent deployment. Delamination initiation is governed by coating thickness and stiffness, interface strength, and hinge curvature. Simulations also predict coating buckling in compressive regions of the plastic hinge. Such patterns of coating debonding have been reported in experimental studies of commercially available polymer-coated stents, thus providing strong motivation for the predictive modeling framework presented in this study.

Acknowledgment

C.H. was supported by an Irish Research Council for Science, Engineering and Technology Postgraduate Scholarship.

Copyright information

© Biomedical Engineering Society 2010