Strut Position, Blood Flow, and Drug Deposition
http://www.100md.com
《循环学杂志》
the Harvard–MIT Division of Health Sciences and Technology, Massachusetts Institute of Technology, Cambridge (B.B., A.R.T., P.S., A.G., C.R., E.R.E.)
Department of Medicine, Harvard Medical School, Cardiovascular Division, Brigham and Women’s Hospital, Boston, Mass (C.R., E.R.E.).
Abstract
Background— The intricacies of stent design, local pharmacology, tissue biology, and rheology preclude an intuitive understanding of drug distribution and deposition from drug-eluting stents (DES).
Methods and Results— A coupled computational fluid dynamics and mass transfer model was applied to predict drug deposition for single and overlapping DES. Drug deposition appeared not only beneath regions of arterial contact with the strut but surprisingly also beneath standing drug pools created by strut disruption of flow. These regions correlated with areas of drug-induced fibrin deposition surrounding DES struts in porcine coronary arteries. Fibrin deposition immediately distal to individual isolated drug-eluting struts was twice as great as in the proximal area and for the stent as a whole was greater in distal segments than proximal segments. Adjacent and overlapping stent struts increased computed arterial drug deposition by far less than the sum of their combined drug load. In addition, drug eluted from the abluminal stent strut surface accounted for only 11% of total deposition, whereas, remarkably, drug eluted from the adluminal surface accounted for 43% of total deposition. Thus, local blood flow alterations and location of drug elution on the strut were far more important in determining arterial wall drug deposition and distribution than were drug load or arterial wall contact with coated strut surfaces.
Conclusions— Simulations that coupled strut configurations with flow dynamics correlated with in vivo effects and revealed that drug deposition occurs less via contact between drug coating and the arterial wall than via flow-mediated deposition of blood-solubilized drug.
Key Words: drugs ; hemodynamics ; restenosis ; stents
Introduction
Drug penetration into the tissue is critical for drug efficacy,1 yet drug-eluting stents (DES) "lose" a good portion of their load into the flowing blood stream. Thus, in previous analyses, drug deposition was envisioned as localized to regions beneath the struts contacting the arterial wall, and blood flow was modeled as a perfect sink for luminal drug.2,3 However, luminally protruding struts alter flow, thereby creating areas of separation, recirculation, and stagnation4,5 where drug can pool with minimal dilution from flow,6 and substantial drug deposition could occur from these pools of blood-solubilized drug. The impact of flow alterations around struts may vary as the number and/or spacing of struts and stents change.4–7 Sophisticated stent designs contact the wall asymmetrically and establish a variable circumferential drug load,8 with complex, nonuniform flow alterations along the wall.6 Furthermore, multiple adjacent or overlapping DES add to the amount of local drug, degree of strut protrusion into the lumen, depth of strut penetration into the artery, area of contact with the arterial wall, and alterations in flow. When these effects are coupled with the complexity of drug delivery8 and tissue binding,9 an intuitive understanding of drug-tissue interactions becomes impossible.
To assess the importance of fluid dynamics on drug deposition, we applied a coupled computational fluid dynamics and mass transfer model to variable stent designs and overlapping regions of DES. The computational methods allowed us to study the effects of flow on arterial drug delivery while varying strut position, shape, and coating under rigorous conditions that cannot be controlled in vivo even when the most refined methods are used for animal tissue analysis. Mathematical modeling of this and similar problems is indispensable precisely because clinical and animal studies increasingly define areas of concern but are not able to fully characterize them. In this study, the spatial distribution of fibrin accumulation as a footprint of drug that was rapidly eluted off a paclitaxel DES into the tissue matched predictions and validated this approach. The results of this study have important implications for the clinical approach to DES use and provide a new paradigm by which to consider the design and to evaluate future generations of stents.
Methods
Mathematical Model
The computational domain comprised a long axial arterial section idealized as a rectangle, nondimensionalized relative to strut dimensions (Figure 1). Struts were assumed to be square. The arterial wall thickness was 10 times the strut thicknesses, and lumen was 30-fold wide. Luminal drug distribution was modeled by coupling the steady-state convection-diffusion equation (Figure 2, Eq 6) with the steady-state Navier-Stokes (Figure 2, Eqs 2 and 3) and continuity equations (Figure 2, Eq 1). Drug concentration was set to zero at the luminal inlet (Eq 8), and an open boundary condition was applied at the distal boundary (Figure 2, Eq 9). The Navier-Stokes equation was solved using no-slip boundary conditions at the blood-tissue and blood-stent strut interfaces. A Poiseuille parabolic profile was applied at the luminal inlet (Figure 2, Eq 4). A zero pressure boundary condition was applied at the outlet (Figure 2, Eq 5). Drug transport within the tissue was modeled as a simple diffusion process (Figure 2, Eq 7), with an impermeable boundary condition at the perivascular wall (Figure 2, Eq 10), continuity of flux at the tissue-blood interface (Figure 2, Eq 11), and symmetry boundary conditions on the proximal and distal walls (Figure 2, Eq 12). Stent drug release was simulated as a Dirichlet boundary condition, with a drug concentration of unity at strut surfaces (Figure 2, Eqs 13 and 14). Drug-transport parameters, tissue, blood, and flow properties were based on standard values.10
Numerical Solution
Computational fluid dynamics software (CFDRC) was modified to solve Eqs 1 through 14 in Figure 2 in a coupled manner. A finite-volume scheme generated a steady-state solution for blood velocity and blood- and tissue-phase drug concentration profiles. The geometry was meshed with 44 472 voxels. A tolerance of 1x10–4 guaranteed that overall error for any variable was 4 orders of magnitude less than the bulk, systemic variable values. Discretization of the diffusion term in the mass balance equation was handled in standard fashion.11 Potential instabilities at high Peclet numbers required special handling of the discretization of the convective term. A second-order limiter spatial differencing scheme with a blending factor of 0.1 was applied to the convective term. This scheme set drug concentration at the boundary of voxels to the concentration at the center of the upwind voxel plus 90% of half the difference between the center concentration of the upwind voxel and the voxel upwind to that. The limiter restricts the voxel boundary value to the range of surrounding voxel center values. A first-order upwind spatial differencing scheme was applied to the velocity variable, setting the velocity at each voxel boundary to the center velocity of the nearest proximal voxel. The spatially discretized velocity and drug concentration variables were solved iteratively using a conjugate gradient-squared algorithm with a preconditioning linear equation solver. All simulations were executed using a Peclet number of 105 to ensure stability and to coincide with expected values. Sensitivity analysis confirmed that the average drug tissue concentration was stable and changed by <1% when the mesh density was doubled.
In Vivo Stent Implantation
Coronary arteries of farm swine (35.8±4.6 kg, Animal Biotech Industries, Inc) were stented with two bare metal stents (BMSs) (8x3 mm, ML-Penta, Guidant Corp) or with 2 stents coated on the abluminal and side faces with paclitaxel (8x3 mm, Achieve, Guidant Corp) with an intended 3-mm overlap length and 10% oversizing compared with the baseline vessel diameter (ratio of stent to artery, 1.1:1) using methods previously described.12 Injury scores were correspondingly low, in the range of 0 to 0.3. Although the Achieve stent did not demonstrate marked clinical efficacy in human clinical trials,13 its rapid drug elution and coating coverage made it an ideal tool in preclinical and pilot clinical studies.14–18 The rapid early delivery of a drug (paclitaxel) provides a histopathological early marker of drug presence, namely fibrin; for this reason rather than clinical use, this device was chosen for validation of the mathematical model inferences. Because other standard techniques for spatial drug mapping within the arterial wall such as radiolabeling and fluorescence labeling of the drug do not allow sufficiently high-spatial-resolution drug detection or differentiation between drug on the strut and drug within the tissue, fibrin was used as a biological marker for drug deposition. Animal care and procedures were in accordance with the guidelines of the American Association for the Accreditation of Laboratory Animal Care and the National Institutes of Health.
Arteries were harvested 28 days after implantation, fixed in 10% neutral buffered formalin, embedded in methacrylate resin, sawed and microtome sectioned, radiographed in 2 orthogonal planes, and then sawed and microtome sectioned. A total of 10 pairs of stents were evaluated in each group. Five BMS pairs and 5 DES pairs were cross sectioned proximal to, distal to, and at the overlap of the 2 stents. The remaining 5 stent pairs were sectioned in a longitudinal plane, and individual struts were examined. Fibrin content detected with Carstair’s fibrin stain (Figure 3) was used as a marker for drug effect within the arterial wall19,20 and quantified by color segmentation with Adobe Photoshop, version 5.0. Fibrin content in cross sections was determined as a percent of the total vessel wall area and in longitudinal sections as the linear extent proximally or distally from the stent strut normalized to strut width. Data were evaluated with a 2-tailed paired Student t test.
Results
Single Isolated Stent Struts
Simulations predicted that 2 distinct recirculation regions form proximal and distal to single struts; the latter is significantly larger than the former (Figure 4A). These zones create pockets of stagnant drug-laden blood that allow drug accumulation at the luminal-arterial wall interface and subsequent entry into the arterial wall. Drug deposition is highest when all strut surfaces elute drug, surprisingly is lowest when only the bottom, or abluminal, contacting surface is drug eluting, and is reduced by only 11% when the drug coating is removed from the contacting surface. Unexpectedly, the noncontacting top and distal strut surfaces individually account for 30% and 43% of total drug deposition, respectively. Even when the strut is unapposed to the arterial wall, residing 1 strut height above the arterial wall, drug deposition drops by only 19% compared with an apposed strut. The location of drug coating also determines the concentration profile. When only the contacting strut surface is drug coated, drug concentration peaks directly beneath the strut; when only the contacting surface is drug free, the peak drug concentration occurs distal to the strut and is of greater magnitude (Figure 4B).
Multiple Struts
The concentration profile for multiple struts depends on interstrut spacing. A single peak profile was noted when multiple struts were placed consecutively 1 strut width apart (Figure 5). The profile width was as follows: (d+1)n, where d is the interstrut distance measured in strut lengths and n is the number of evenly spaced consecutive stent struts. As the interstrut distance increases, the peak concentration falls, and discrete peaks form over each strut (Figure 5). Increasing separation results in lower peak drug concentrations (Figure 5) but higher average arterial drug concentrations (not shown). When the interstrut distance is 7 strut widths, typical for clinical stents, the proximal peak magnitude is 7% greater than that from a single isolated strut, whereas the distal peak magnitude is 40% greater than that from a single isolated strut (Figure 5). In all cases, tissue segments beneath distal struts have greater peak magnitudes than those beneath proximal struts.
Overlapping DES increase local drug load, alter blood flow, and potentially increase the direct contact between strut and tissue. The resultant effects on drug deposition depend on relative strut configurations. The flow fields associated with side-by-side and stacked configurations are equivalent to those of single struts that are twice the width or height, respectively. When stacked struts are staggered relative to each other, a third region of stagnant flow is formed that is bordered by the bottom surface of the topmost strut and a side surface of the bottom (Figure 6). Peak concentrations resulting from different overlapping strut configurations rise by 22% to 34% compared with the single-strut case (Figure 7A). If drug is removed from 1 of 2 overlapping struts, the counterintuitive and dominant role of flow is even more evident. If the DES strut remains in contact with the arterial wall but is covered on the luminal aspect by a BMS strut, total deposition is reduced >50% (Figure 8B). When the configuration is reversed, with the DES superior to the BMS and without arterial wall contact, the peak concentration is displaced distally 4 strut lengths (Figure 7B), but remarkably, drug deposition is reduced by only 16% (Figure 8B).
In practice, stent placement invariably leads to some degree of strut embedding in the arterial wall. In our simulations, embedding struts into the arterial wall increased the peak drug concentrations with increased local arterial wall contact but reduced the distal deposition because less strut surface area is exposed to blood and less flow disruption and subsequent flow-mediated drug delivery ensue (not shown). These effects were most pronounced when, in an overlapping 2-strut case, the bottom strut was entirely embedded within the wall of the artery and the top strut was flush against the arterial wall. The peak concentration increased by 45% but total arterial drug deposition decreased by 6.8% compared with the case in which the bottom strut was flush against the wall.
In Vivo Stent Implantation
The peristrut deposition of fibrin in paclitaxel-eluting Achieve stents 28 days after implantation was used as a marker for drug effect19,20 and model predictions of flow-mediated drug delivery. In cross sections, the zone of the arterial wall rich in fibrin was quantified as a percent of total arterial wall area and was 20-fold higher for DES (18±3% of the area) than BMSs (0.9±0.3%; P<0.0002). Sections with overlapping DES (14±2%) had 2.8-fold more fibrin than single-stent distal sections of the same arteries (5±1%); in turn, distal sections had 6-fold more fibrin than single-stent proximal sections (0.8±0.3%; P<0.05) of the same arteries. In longitudinal sections, fibrin extended twice as far distally from isolated struts (1.27±0.2 strut lengths) than proximally from the same struts (0.73±0.2 strut lengths; Figure 3; P=0.02).
Discussion
Intuition dictates that drug released from stents enters an artery in meaningful amounts only if present at the DES-arterial interface. Conventional wisdom has therefore held that flowing blood is detrimental to drug delivery, siphoning drug off stents and diluting it in the blood stream before arterial entry. Hence, thinner struts ought to be more effective than thicker struts carrying the same drug payload, and only abluminal coatings are required on DES. On the contrary, our mathematical model that couples computational fluid dynamics and mass transfer in an idealized stented artery and in vivo spatial mapping of drug-effect after coronary arterial implantation of a DES (Figure 3) demonstrated that the role of flow is complex and even counterintuitive. Flow elevates arterial drug deposition beyond levels achieved exclusively via arterial wall contact. Drug deposition is determined by a complex interplay between strut-arterial wall contact, amount and location of drug release, and flow profiles, which depend on strut size and position. These findings explain the emerging and expanding information on the limitations and challenges of DES and potentially will affect the clinical use and evaluation of this technology.
Single Struts
If only contacting surfaces deposited drug, one might optimize DES design for delivery by broadening struts, inducing deeper stent penetration where the sides, not simply the abluminal face, contact the wall, or coating only the abluminal surface of each strut. Yet, simulations predict that direct strut contact accounts for only 38% of peak (Figure 4B) and 11% of total arterial drug, suggesting that another process actually dominates. The complex role of flow in stent-based drug delivery becomes apparent when we examine cases in which drug load and/or flow profiles are altered. For instance, doubling the DES strut thickness increased the drug supply and flow disruption and consequently increased total arterial drug deposition by 20%. In contrast, doubling the strut thickness without increasing the drug load resulted in the same flow disruption, but because less drug was eluted into the recirculation zones, drug deposition decreased by >30% (Figure 8A and 8B). Strut protrusion disrupts blood flow and creates stagnation zones that, when fed drug from noncontacting strut surfaces, establish standing drug pools along the vessel surface. Flow profiles around struts, dictated by strut shape, and the location of the drug-eluting surfaces determine whether drug solubilized within the blood is convectively washed away or instead is trapped in stagnant zones for subsequent deposition.
The fraction of drug convectively delivered to the arterial wall is responsible for elevating both local peak and nonlocal distal arterial drug concentrations (Figure 4B). The overall tissue uptake is therefore determined by both partitioning from drug sources in direct contact with the tissue and flow-mediated convective transport of drug pools into the arterial wall. Indeed, the deposition profile established by struts with all surfaces coated is the algebraic sum of the profiles obtained from struts with drug only on the abluminal surface and struts with every other strut face coated (Figure 4B). Noncontacting strut surfaces can contribute up to 90% of arterial drug deposition, and the top (adluminal) surface provides half of this amount. Thus, even nonapposed struts removed a full strut thickness from the wall can deliver the greatest bulk of drug to the vessel wall, perhaps explaining the remarkably predictable and uniform efficacy of clinical use of DES. Intravascular ultrasound reveals that many struts remain incompletely apposed to the vessel even after high-pressure deployment.21 If only apposed struts could deliver drug, one would expect more frequent focal restenotic failure and restenosis rates that correlated with stent length, as is the case with BMSs.22 On the contrary, however, even arteries with malapposed struts have no substantial neointimal growth,21,23 and there is minimal correlation of stent length with restenosis.24,25
Multiple Struts
Struts do not reside in isolation. They surround the lumen in a ring and extend along the length of the blood vessel. The concern for nonuniform drug deposition with the variable strut spacing of modern stent designs8,26 was seen to be justified when struts were spaced >2 strut distances apart (Figure 5). Strut spacing is critical to drug deposition. A section underlying a fixed number of closely adjacent struts is effectively exposed to a wider single strut (equal to the width of the struts and their intervening space), whereas the remainder of the artery is without exposure. Because struts are spaced farther apart, total drug deposition rises, as does the variability of interstrut drug concentration. Peaks and troughs are evident, and an ascending distribution is observed proximally to distally (Figure 5). Indeed, our in vivo experiment showed that fibrin deposition was twice as large on the distal as on the proximal aspect of DES struts and significantly higher in distal than proximal sections of stented arteries. This flow-dependent spatial distribution may explain in part why some DES reduce late lumen loss at their distal edges.27
When stents overlap, one must consider strut positioning in 2 dimensions. A second stent presents twice as much drug but also alters flow around struts. As a result, peak arterial drug concentrations vary with extent of flow alterations and only increase significantly compared with the single-stent case when positioning of struts is optimized (Figures 7A and 8A). Flow disruption created by the close proximity of struts in any overlapping strut configuration diminishes the ability of the additional drug-eluting struts to contribute to drug deposition, increasing the fractional drug washout. Although total deposition depends nonlinearly on drug load, when stents overlap, the arterial surface area receiving high doses of drug is greater, extending beyond the strut contact area into drug-laden stagnation regions. Because delayed vascular healing follows high drug dosages,20 overlap regions may alter vascular healing by increasing drug not only under or adjacent to struts but also in distal tissue segments or in interstrut zones. These issues, coupled with the temporal development of intimal hyperplasia, increase the complexity of drug deposition and amplify the dependence of tissue deposition on strut position and flow.
The role of flow disruption is further validated by examining the case in which DES and BMSs are used together. When only one device has drug, deposition is always less than with 2 DES and never higher than with a single DES (Figure 8B). Moreover, when the BMS is expanded into an artery that contains a previously implanted DES, drug delivery suffers. If, however, the DES is expanded into an artery where a previously implanted BMS resides and is in contact with flowing blood, the added flow disruption from increased strut height, combined with drug availability on the innermost strut, extends the flow stagnation zones and area to which drug could be delivered (Figures 7B and 8B). Of more clinical relevance is the extension of these observations to anticipated drug delivery from overlapping DES delivering different drugs. Even if the transport parameters of both drugs are equal, one would anticipate differential deposition, with the innermost DES contributing far more drug to the wall than the outer, more abluminally apposed DES. In every case, strut positioning has a complex effect. Strut spacing determines flow disruptions, drug load, and degree of injury imposed on the artery. Situations that increase peak concentrations may actually reduce total drug deposition and vice versa.
Embedded Struts
Minimizing vascular injury often conflicts with minimizing luminal flow disruption: the more superficial the strut, the greater the impact on flow; the deeper the strut, the greater the vascular injury. Closely apposed stent struts or overlapping stents create the worst of both situations and significantly change drug delivery. The outermost struts are driven deeper, and the innermost struts protrude more. Deeper penetration increases direct contact and drug delivery but increases injury and reduces the surface area of stent that can deliver drug distally. Increased flow disruption increases the standing zones and resultant drug delivery. Consequently, the deeper the struts are, the more localized the drug deposition is. Peak drug concentrations rise, but total deposition falls (Figures I and II in online-only Data Supplement). The impact of embedding and the role of protrusion on formation of stagnation zones suggest that stent designs with thinner struts may actually deliver less drug in a nonuniform distribution than thicker struts.
Strut Geometry
Stent struts are not often square; most are trapezoidal, and some are rounded. To test how strut geometry alters our findings for square struts, we conducted an additional series of simulations. By placing a range of differently shaped noneluting BMP tops atop the square DES, we maintained constant drug load while the effect of different flow profiles on arterial drug deposition was studied. These simulations illustrate that strut geometry affects the extent of drug spread only slightly (Figure III in the Data Supplement) and has minimal effect on the maximum degree of drug deposition. Strut protrusion into the flow field and aspects of the strut coated with drug are more important than overall shape. Strut shape extends the area of the artery exposed to low levels of drug only downstream of the strut. Shape has no impact on the amount of drug residing in the recirculation zone proximal to the stent strut. Similarly, the site of maximum concentration is nearly the same for all the tested shapes, but square struts result in a smaller area of total distribution (Figure III in the Data Supplement). As an example, the total deposition was 17% higher for the triangular top strut than the square strut alone, although the concentration profiles do not show significant changes in the peak profile.
Moreover, the single strut simulations show that blood flow can carry drug downstream to be deposited well beyond the stent strut and that the degree of this extension of distribution is a function of strut shape. When a stent of many struts is examined in this model, there is a small degree of superposition of drug effect from serial struts, and distribution increases downstream (Figure IV in the Data Supplement). Here, strut shape has an effect, albeit subtle. When multiple struts were modeled, we observed a 10% increase in total drug deposition with only a slight increase in peak concentration for the triangular top strut compared with the square top strut.
Clinical Implications
This article uses computational and animal models to address important clinical issues at the interface of stent design, tissue pharmacology, and vascular biology. The findings raise a number of immediate clinical issues. The most timely concerns for DES systems are those that force changes in our perception of drug distribution after elution, the impact of strut overlap, and the importance of stent design. The idea that drug can be delivered to the vessel wall only if stent struts are in contact with the wall is incorrect. Hence, for example, malapposition of struts is not by necessity counterproductive to drug delivery. Even stents not directly apposed to the vessel wall can deliver drug. Similarly, the increasing use of multiple stents in an intervention will mean that struts abut other struts, not just the wall. Conventional wisdom holds that 2 struts over 1 arterial segment provide "double the dose" of delivered drug, raising the possibility of double the effect or double the toxicity. Our data show that the addition of a second DES abutting or overlapping a first only modestly increases the dose delivered and actually detracts from the dose if one is a BMS (Figure 8A and 8B). If overlapping stents provide increased toxicity, it is not from heightened dose alone. Rather, the safety of overlap is determined by the extent of additional mechanical injury induced by insertion of multiple proximate stents and the spatial extension of drug over the exacerbated injury. The mass of added and overlapping stents creates flow disturbances that deliver drug farther beyond where a single strut covers an artery. These data are critical at a time when the approach to overlapping stents is unclear, when clinicians must choose between long stents and overlapping stents, and when DES occasionally are used with BMSs.
Finally, our article shows that central precepts that drive current DES development must now be called into question. It has been assumed that abluminal coating alone can ensure optimal delivery of drug to the wall while minimizing loss of drug into the bloodstream and that thinner struts are better than thicker struts for reasons of enhanced deliverability. We show that abluminally coated drug accounts for <50% of the drug that ends up in the arterial wall. The addition of drug on one other face significantly increases the amount of drug that can be delivered to segments of a stented artery. Addition of drug to nonapposed strut faces greatly enhances drug delivery in areas adjacent to, but not underneath, the struts. This finding, coupled with the impact of stent design on flow-mediated stagnant pools and the demonstration that less drug is delivered to the vessel wall with thin stents, emphasizes the idea that, in addition to its recognized importance for mechanical injury and procedural success,8,28 stent design is also of paramount importance in dictating drug therapy.
Study Limitations and Future Directions
Mathematical modeling is indispensable precisely when clinical and animal studies increasingly define areas of concern but cannot fully characterize them. The predictions of these models are becoming increasingly important as our experience with DES emerges in increasingly challenging clinical environments. Computational methods are valuable in isolating and understanding mechanisms for drug delivery, yet idealized models do not account for all possible clinical variables. In our mathematical model, we made some simplifications such as neglecting drug metabolism and binding, assuming homogeneous, healthy tissue composition, assuming negligible arterial drug transport via vasa vasorum, and considering only 2D flow. Substantial work remains to include drug-specific pharmacokinetics,9,29 unique vascular ultrastructure such as vessel disease30 and topographies,31 and even the impact of intimal hyperplasia and thrombosis on DES function. The results of this study motivate further study of the relationship between the complex 3D flow generated over the stent mesh and total arterial drug deposition. We would hypothesize that the longitudinal patterns we describe here will also provide the dominant effects in more complex settings.
Further limitations exist in analyzing in vivo data because of the paucity of high-resolution techniques for detecting drug deposited within the tissue and differentiating it from drug adherent to the strut. Thus, fibrin was used in this study for its ability to differentiate between tissue-deposited drug and drug adhering to the strut surface. The mathematical model does not include drug-specific properties so as to focus the study on the effects of blood flow on arterial deposition of a generic drug, although the in vivo validation was confined to a specific drug. The properties of rapamycin that increase its tissue retention include its specific binding to a complex of proteins and general binding to plasma and tissue proteins.32 Thus, broad generalization beyond drugs like rapamycin that do not share similar physicochemical properties would be unwarranted.
The coupling of fluid dynamics with stent design and pharmacology of local delivery creates a powerful tool by which to evaluate DES. Using a combined approach that mixes mathematical and animal-based modeling, we now show that direct contact of DES struts with target tissue is important but not essential because drug deposition does not necessarily scale linearly with drug load or stent-artery contact area. The relative positioning of struts and flow over the stent determine tissue concentration. As we define the kinetics of drug release and tissue uptake, computational models may suggest even more creative and efficient means of delivering drugs for a range of vascular indications and patients.
Acknowledgments
This study was supported in part by grants from the National Institutes of Health to Dr Edelman (HL-49309, HL-60407, and HL-62457) and a Philip Morris External Research Program Postdoctoral Fellowship to Dr Tzafriri. We thank Dr Kartik Shah of CFDRC and Dr Chao-Wei Hwang.
Footnotes
The first 2 authors contributed equally to this article.
The online-only Data Supplement can be found with this article at http://circ.ahajournals.org/cgi/content/full/CIRCULATIONAHA.104.512475/DC1.
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Holmes DR Jr, Leon MB, Moses JW, Popma JJ, Cutlip D, Fitzgerald PJ, Brown C, Fischell T, Wong SC, Midei M, Snead D, Kuntz RE. Analysis of 1-year clinical outcomes in the SIRIUS trial: a randomized trial of a sirolimus-eluting stent versus a standard stent in patients at high risk for coronary restenosis. Circulation. 2004; 109: 634–640.
Degertekin M, Arampatzis CA, Lemos PA, Saia F, Hoye A, Daemen J, Tanabe K, Lee CH, Hofma SJ, Sianos G, McFadden E, van der Giessen W, Smits PC, de Feyter PJ, van Domburg RT, Serruys PW. Very long sirolimus-eluting stent implantation for de novo coronary lesions. Am J Cardiol. 2004; 93: 826–829.
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Serruys PW, Degertekin M, Tanabe K, Russell ME, Guagliumi G, Webb J, Hamburger J, Rutsch W, Kaiser C, Whitbourn R, Camenzind E, Meredith I, Reeves F, Nienaber C, Benit E, Disco C, Koglin J, Colombo A. Vascular responses at proximal and distal edges of paclitaxel-eluting stents: serial intravascular ultrasound analysis from the TAXUS II trial. Circulation. 2004; 109: 627–633.
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Lovich MA, Creel C, Hong K, Hwang CW, Edelman ER. Carrier proteins determine local pharmacokinetics and arterial distribution of paclitaxel. J Pharm Sci. 2001; 90: 1324–1335.
Hwang CW, Edelman ER. Arterial ultrastructure influences transport of locally delivered drugs. Circ Res. 2002; 90: 826–832.
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Levin AD, Vukmirovic N, Hwang CW, Edelman ER. Specific binding to intracellular proteins determines arterial transport properties for rapamycin and paclitaxel. Proc Natl Acad Sci U S A. 2004; 101: 9463–9467.(Brinda Balakrishnan, SB; )
Department of Medicine, Harvard Medical School, Cardiovascular Division, Brigham and Women’s Hospital, Boston, Mass (C.R., E.R.E.).
Abstract
Background— The intricacies of stent design, local pharmacology, tissue biology, and rheology preclude an intuitive understanding of drug distribution and deposition from drug-eluting stents (DES).
Methods and Results— A coupled computational fluid dynamics and mass transfer model was applied to predict drug deposition for single and overlapping DES. Drug deposition appeared not only beneath regions of arterial contact with the strut but surprisingly also beneath standing drug pools created by strut disruption of flow. These regions correlated with areas of drug-induced fibrin deposition surrounding DES struts in porcine coronary arteries. Fibrin deposition immediately distal to individual isolated drug-eluting struts was twice as great as in the proximal area and for the stent as a whole was greater in distal segments than proximal segments. Adjacent and overlapping stent struts increased computed arterial drug deposition by far less than the sum of their combined drug load. In addition, drug eluted from the abluminal stent strut surface accounted for only 11% of total deposition, whereas, remarkably, drug eluted from the adluminal surface accounted for 43% of total deposition. Thus, local blood flow alterations and location of drug elution on the strut were far more important in determining arterial wall drug deposition and distribution than were drug load or arterial wall contact with coated strut surfaces.
Conclusions— Simulations that coupled strut configurations with flow dynamics correlated with in vivo effects and revealed that drug deposition occurs less via contact between drug coating and the arterial wall than via flow-mediated deposition of blood-solubilized drug.
Key Words: drugs ; hemodynamics ; restenosis ; stents
Introduction
Drug penetration into the tissue is critical for drug efficacy,1 yet drug-eluting stents (DES) "lose" a good portion of their load into the flowing blood stream. Thus, in previous analyses, drug deposition was envisioned as localized to regions beneath the struts contacting the arterial wall, and blood flow was modeled as a perfect sink for luminal drug.2,3 However, luminally protruding struts alter flow, thereby creating areas of separation, recirculation, and stagnation4,5 where drug can pool with minimal dilution from flow,6 and substantial drug deposition could occur from these pools of blood-solubilized drug. The impact of flow alterations around struts may vary as the number and/or spacing of struts and stents change.4–7 Sophisticated stent designs contact the wall asymmetrically and establish a variable circumferential drug load,8 with complex, nonuniform flow alterations along the wall.6 Furthermore, multiple adjacent or overlapping DES add to the amount of local drug, degree of strut protrusion into the lumen, depth of strut penetration into the artery, area of contact with the arterial wall, and alterations in flow. When these effects are coupled with the complexity of drug delivery8 and tissue binding,9 an intuitive understanding of drug-tissue interactions becomes impossible.
To assess the importance of fluid dynamics on drug deposition, we applied a coupled computational fluid dynamics and mass transfer model to variable stent designs and overlapping regions of DES. The computational methods allowed us to study the effects of flow on arterial drug delivery while varying strut position, shape, and coating under rigorous conditions that cannot be controlled in vivo even when the most refined methods are used for animal tissue analysis. Mathematical modeling of this and similar problems is indispensable precisely because clinical and animal studies increasingly define areas of concern but are not able to fully characterize them. In this study, the spatial distribution of fibrin accumulation as a footprint of drug that was rapidly eluted off a paclitaxel DES into the tissue matched predictions and validated this approach. The results of this study have important implications for the clinical approach to DES use and provide a new paradigm by which to consider the design and to evaluate future generations of stents.
Methods
Mathematical Model
The computational domain comprised a long axial arterial section idealized as a rectangle, nondimensionalized relative to strut dimensions (Figure 1). Struts were assumed to be square. The arterial wall thickness was 10 times the strut thicknesses, and lumen was 30-fold wide. Luminal drug distribution was modeled by coupling the steady-state convection-diffusion equation (Figure 2, Eq 6) with the steady-state Navier-Stokes (Figure 2, Eqs 2 and 3) and continuity equations (Figure 2, Eq 1). Drug concentration was set to zero at the luminal inlet (Eq 8), and an open boundary condition was applied at the distal boundary (Figure 2, Eq 9). The Navier-Stokes equation was solved using no-slip boundary conditions at the blood-tissue and blood-stent strut interfaces. A Poiseuille parabolic profile was applied at the luminal inlet (Figure 2, Eq 4). A zero pressure boundary condition was applied at the outlet (Figure 2, Eq 5). Drug transport within the tissue was modeled as a simple diffusion process (Figure 2, Eq 7), with an impermeable boundary condition at the perivascular wall (Figure 2, Eq 10), continuity of flux at the tissue-blood interface (Figure 2, Eq 11), and symmetry boundary conditions on the proximal and distal walls (Figure 2, Eq 12). Stent drug release was simulated as a Dirichlet boundary condition, with a drug concentration of unity at strut surfaces (Figure 2, Eqs 13 and 14). Drug-transport parameters, tissue, blood, and flow properties were based on standard values.10
Numerical Solution
Computational fluid dynamics software (CFDRC) was modified to solve Eqs 1 through 14 in Figure 2 in a coupled manner. A finite-volume scheme generated a steady-state solution for blood velocity and blood- and tissue-phase drug concentration profiles. The geometry was meshed with 44 472 voxels. A tolerance of 1x10–4 guaranteed that overall error for any variable was 4 orders of magnitude less than the bulk, systemic variable values. Discretization of the diffusion term in the mass balance equation was handled in standard fashion.11 Potential instabilities at high Peclet numbers required special handling of the discretization of the convective term. A second-order limiter spatial differencing scheme with a blending factor of 0.1 was applied to the convective term. This scheme set drug concentration at the boundary of voxels to the concentration at the center of the upwind voxel plus 90% of half the difference between the center concentration of the upwind voxel and the voxel upwind to that. The limiter restricts the voxel boundary value to the range of surrounding voxel center values. A first-order upwind spatial differencing scheme was applied to the velocity variable, setting the velocity at each voxel boundary to the center velocity of the nearest proximal voxel. The spatially discretized velocity and drug concentration variables were solved iteratively using a conjugate gradient-squared algorithm with a preconditioning linear equation solver. All simulations were executed using a Peclet number of 105 to ensure stability and to coincide with expected values. Sensitivity analysis confirmed that the average drug tissue concentration was stable and changed by <1% when the mesh density was doubled.
In Vivo Stent Implantation
Coronary arteries of farm swine (35.8±4.6 kg, Animal Biotech Industries, Inc) were stented with two bare metal stents (BMSs) (8x3 mm, ML-Penta, Guidant Corp) or with 2 stents coated on the abluminal and side faces with paclitaxel (8x3 mm, Achieve, Guidant Corp) with an intended 3-mm overlap length and 10% oversizing compared with the baseline vessel diameter (ratio of stent to artery, 1.1:1) using methods previously described.12 Injury scores were correspondingly low, in the range of 0 to 0.3. Although the Achieve stent did not demonstrate marked clinical efficacy in human clinical trials,13 its rapid drug elution and coating coverage made it an ideal tool in preclinical and pilot clinical studies.14–18 The rapid early delivery of a drug (paclitaxel) provides a histopathological early marker of drug presence, namely fibrin; for this reason rather than clinical use, this device was chosen for validation of the mathematical model inferences. Because other standard techniques for spatial drug mapping within the arterial wall such as radiolabeling and fluorescence labeling of the drug do not allow sufficiently high-spatial-resolution drug detection or differentiation between drug on the strut and drug within the tissue, fibrin was used as a biological marker for drug deposition. Animal care and procedures were in accordance with the guidelines of the American Association for the Accreditation of Laboratory Animal Care and the National Institutes of Health.
Arteries were harvested 28 days after implantation, fixed in 10% neutral buffered formalin, embedded in methacrylate resin, sawed and microtome sectioned, radiographed in 2 orthogonal planes, and then sawed and microtome sectioned. A total of 10 pairs of stents were evaluated in each group. Five BMS pairs and 5 DES pairs were cross sectioned proximal to, distal to, and at the overlap of the 2 stents. The remaining 5 stent pairs were sectioned in a longitudinal plane, and individual struts were examined. Fibrin content detected with Carstair’s fibrin stain (Figure 3) was used as a marker for drug effect within the arterial wall19,20 and quantified by color segmentation with Adobe Photoshop, version 5.0. Fibrin content in cross sections was determined as a percent of the total vessel wall area and in longitudinal sections as the linear extent proximally or distally from the stent strut normalized to strut width. Data were evaluated with a 2-tailed paired Student t test.
Results
Single Isolated Stent Struts
Simulations predicted that 2 distinct recirculation regions form proximal and distal to single struts; the latter is significantly larger than the former (Figure 4A). These zones create pockets of stagnant drug-laden blood that allow drug accumulation at the luminal-arterial wall interface and subsequent entry into the arterial wall. Drug deposition is highest when all strut surfaces elute drug, surprisingly is lowest when only the bottom, or abluminal, contacting surface is drug eluting, and is reduced by only 11% when the drug coating is removed from the contacting surface. Unexpectedly, the noncontacting top and distal strut surfaces individually account for 30% and 43% of total drug deposition, respectively. Even when the strut is unapposed to the arterial wall, residing 1 strut height above the arterial wall, drug deposition drops by only 19% compared with an apposed strut. The location of drug coating also determines the concentration profile. When only the contacting strut surface is drug coated, drug concentration peaks directly beneath the strut; when only the contacting surface is drug free, the peak drug concentration occurs distal to the strut and is of greater magnitude (Figure 4B).
Multiple Struts
The concentration profile for multiple struts depends on interstrut spacing. A single peak profile was noted when multiple struts were placed consecutively 1 strut width apart (Figure 5). The profile width was as follows: (d+1)n, where d is the interstrut distance measured in strut lengths and n is the number of evenly spaced consecutive stent struts. As the interstrut distance increases, the peak concentration falls, and discrete peaks form over each strut (Figure 5). Increasing separation results in lower peak drug concentrations (Figure 5) but higher average arterial drug concentrations (not shown). When the interstrut distance is 7 strut widths, typical for clinical stents, the proximal peak magnitude is 7% greater than that from a single isolated strut, whereas the distal peak magnitude is 40% greater than that from a single isolated strut (Figure 5). In all cases, tissue segments beneath distal struts have greater peak magnitudes than those beneath proximal struts.
Overlapping DES increase local drug load, alter blood flow, and potentially increase the direct contact between strut and tissue. The resultant effects on drug deposition depend on relative strut configurations. The flow fields associated with side-by-side and stacked configurations are equivalent to those of single struts that are twice the width or height, respectively. When stacked struts are staggered relative to each other, a third region of stagnant flow is formed that is bordered by the bottom surface of the topmost strut and a side surface of the bottom (Figure 6). Peak concentrations resulting from different overlapping strut configurations rise by 22% to 34% compared with the single-strut case (Figure 7A). If drug is removed from 1 of 2 overlapping struts, the counterintuitive and dominant role of flow is even more evident. If the DES strut remains in contact with the arterial wall but is covered on the luminal aspect by a BMS strut, total deposition is reduced >50% (Figure 8B). When the configuration is reversed, with the DES superior to the BMS and without arterial wall contact, the peak concentration is displaced distally 4 strut lengths (Figure 7B), but remarkably, drug deposition is reduced by only 16% (Figure 8B).
In practice, stent placement invariably leads to some degree of strut embedding in the arterial wall. In our simulations, embedding struts into the arterial wall increased the peak drug concentrations with increased local arterial wall contact but reduced the distal deposition because less strut surface area is exposed to blood and less flow disruption and subsequent flow-mediated drug delivery ensue (not shown). These effects were most pronounced when, in an overlapping 2-strut case, the bottom strut was entirely embedded within the wall of the artery and the top strut was flush against the arterial wall. The peak concentration increased by 45% but total arterial drug deposition decreased by 6.8% compared with the case in which the bottom strut was flush against the wall.
In Vivo Stent Implantation
The peristrut deposition of fibrin in paclitaxel-eluting Achieve stents 28 days after implantation was used as a marker for drug effect19,20 and model predictions of flow-mediated drug delivery. In cross sections, the zone of the arterial wall rich in fibrin was quantified as a percent of total arterial wall area and was 20-fold higher for DES (18±3% of the area) than BMSs (0.9±0.3%; P<0.0002). Sections with overlapping DES (14±2%) had 2.8-fold more fibrin than single-stent distal sections of the same arteries (5±1%); in turn, distal sections had 6-fold more fibrin than single-stent proximal sections (0.8±0.3%; P<0.05) of the same arteries. In longitudinal sections, fibrin extended twice as far distally from isolated struts (1.27±0.2 strut lengths) than proximally from the same struts (0.73±0.2 strut lengths; Figure 3; P=0.02).
Discussion
Intuition dictates that drug released from stents enters an artery in meaningful amounts only if present at the DES-arterial interface. Conventional wisdom has therefore held that flowing blood is detrimental to drug delivery, siphoning drug off stents and diluting it in the blood stream before arterial entry. Hence, thinner struts ought to be more effective than thicker struts carrying the same drug payload, and only abluminal coatings are required on DES. On the contrary, our mathematical model that couples computational fluid dynamics and mass transfer in an idealized stented artery and in vivo spatial mapping of drug-effect after coronary arterial implantation of a DES (Figure 3) demonstrated that the role of flow is complex and even counterintuitive. Flow elevates arterial drug deposition beyond levels achieved exclusively via arterial wall contact. Drug deposition is determined by a complex interplay between strut-arterial wall contact, amount and location of drug release, and flow profiles, which depend on strut size and position. These findings explain the emerging and expanding information on the limitations and challenges of DES and potentially will affect the clinical use and evaluation of this technology.
Single Struts
If only contacting surfaces deposited drug, one might optimize DES design for delivery by broadening struts, inducing deeper stent penetration where the sides, not simply the abluminal face, contact the wall, or coating only the abluminal surface of each strut. Yet, simulations predict that direct strut contact accounts for only 38% of peak (Figure 4B) and 11% of total arterial drug, suggesting that another process actually dominates. The complex role of flow in stent-based drug delivery becomes apparent when we examine cases in which drug load and/or flow profiles are altered. For instance, doubling the DES strut thickness increased the drug supply and flow disruption and consequently increased total arterial drug deposition by 20%. In contrast, doubling the strut thickness without increasing the drug load resulted in the same flow disruption, but because less drug was eluted into the recirculation zones, drug deposition decreased by >30% (Figure 8A and 8B). Strut protrusion disrupts blood flow and creates stagnation zones that, when fed drug from noncontacting strut surfaces, establish standing drug pools along the vessel surface. Flow profiles around struts, dictated by strut shape, and the location of the drug-eluting surfaces determine whether drug solubilized within the blood is convectively washed away or instead is trapped in stagnant zones for subsequent deposition.
The fraction of drug convectively delivered to the arterial wall is responsible for elevating both local peak and nonlocal distal arterial drug concentrations (Figure 4B). The overall tissue uptake is therefore determined by both partitioning from drug sources in direct contact with the tissue and flow-mediated convective transport of drug pools into the arterial wall. Indeed, the deposition profile established by struts with all surfaces coated is the algebraic sum of the profiles obtained from struts with drug only on the abluminal surface and struts with every other strut face coated (Figure 4B). Noncontacting strut surfaces can contribute up to 90% of arterial drug deposition, and the top (adluminal) surface provides half of this amount. Thus, even nonapposed struts removed a full strut thickness from the wall can deliver the greatest bulk of drug to the vessel wall, perhaps explaining the remarkably predictable and uniform efficacy of clinical use of DES. Intravascular ultrasound reveals that many struts remain incompletely apposed to the vessel even after high-pressure deployment.21 If only apposed struts could deliver drug, one would expect more frequent focal restenotic failure and restenosis rates that correlated with stent length, as is the case with BMSs.22 On the contrary, however, even arteries with malapposed struts have no substantial neointimal growth,21,23 and there is minimal correlation of stent length with restenosis.24,25
Multiple Struts
Struts do not reside in isolation. They surround the lumen in a ring and extend along the length of the blood vessel. The concern for nonuniform drug deposition with the variable strut spacing of modern stent designs8,26 was seen to be justified when struts were spaced >2 strut distances apart (Figure 5). Strut spacing is critical to drug deposition. A section underlying a fixed number of closely adjacent struts is effectively exposed to a wider single strut (equal to the width of the struts and their intervening space), whereas the remainder of the artery is without exposure. Because struts are spaced farther apart, total drug deposition rises, as does the variability of interstrut drug concentration. Peaks and troughs are evident, and an ascending distribution is observed proximally to distally (Figure 5). Indeed, our in vivo experiment showed that fibrin deposition was twice as large on the distal as on the proximal aspect of DES struts and significantly higher in distal than proximal sections of stented arteries. This flow-dependent spatial distribution may explain in part why some DES reduce late lumen loss at their distal edges.27
When stents overlap, one must consider strut positioning in 2 dimensions. A second stent presents twice as much drug but also alters flow around struts. As a result, peak arterial drug concentrations vary with extent of flow alterations and only increase significantly compared with the single-stent case when positioning of struts is optimized (Figures 7A and 8A). Flow disruption created by the close proximity of struts in any overlapping strut configuration diminishes the ability of the additional drug-eluting struts to contribute to drug deposition, increasing the fractional drug washout. Although total deposition depends nonlinearly on drug load, when stents overlap, the arterial surface area receiving high doses of drug is greater, extending beyond the strut contact area into drug-laden stagnation regions. Because delayed vascular healing follows high drug dosages,20 overlap regions may alter vascular healing by increasing drug not only under or adjacent to struts but also in distal tissue segments or in interstrut zones. These issues, coupled with the temporal development of intimal hyperplasia, increase the complexity of drug deposition and amplify the dependence of tissue deposition on strut position and flow.
The role of flow disruption is further validated by examining the case in which DES and BMSs are used together. When only one device has drug, deposition is always less than with 2 DES and never higher than with a single DES (Figure 8B). Moreover, when the BMS is expanded into an artery that contains a previously implanted DES, drug delivery suffers. If, however, the DES is expanded into an artery where a previously implanted BMS resides and is in contact with flowing blood, the added flow disruption from increased strut height, combined with drug availability on the innermost strut, extends the flow stagnation zones and area to which drug could be delivered (Figures 7B and 8B). Of more clinical relevance is the extension of these observations to anticipated drug delivery from overlapping DES delivering different drugs. Even if the transport parameters of both drugs are equal, one would anticipate differential deposition, with the innermost DES contributing far more drug to the wall than the outer, more abluminally apposed DES. In every case, strut positioning has a complex effect. Strut spacing determines flow disruptions, drug load, and degree of injury imposed on the artery. Situations that increase peak concentrations may actually reduce total drug deposition and vice versa.
Embedded Struts
Minimizing vascular injury often conflicts with minimizing luminal flow disruption: the more superficial the strut, the greater the impact on flow; the deeper the strut, the greater the vascular injury. Closely apposed stent struts or overlapping stents create the worst of both situations and significantly change drug delivery. The outermost struts are driven deeper, and the innermost struts protrude more. Deeper penetration increases direct contact and drug delivery but increases injury and reduces the surface area of stent that can deliver drug distally. Increased flow disruption increases the standing zones and resultant drug delivery. Consequently, the deeper the struts are, the more localized the drug deposition is. Peak drug concentrations rise, but total deposition falls (Figures I and II in online-only Data Supplement). The impact of embedding and the role of protrusion on formation of stagnation zones suggest that stent designs with thinner struts may actually deliver less drug in a nonuniform distribution than thicker struts.
Strut Geometry
Stent struts are not often square; most are trapezoidal, and some are rounded. To test how strut geometry alters our findings for square struts, we conducted an additional series of simulations. By placing a range of differently shaped noneluting BMP tops atop the square DES, we maintained constant drug load while the effect of different flow profiles on arterial drug deposition was studied. These simulations illustrate that strut geometry affects the extent of drug spread only slightly (Figure III in the Data Supplement) and has minimal effect on the maximum degree of drug deposition. Strut protrusion into the flow field and aspects of the strut coated with drug are more important than overall shape. Strut shape extends the area of the artery exposed to low levels of drug only downstream of the strut. Shape has no impact on the amount of drug residing in the recirculation zone proximal to the stent strut. Similarly, the site of maximum concentration is nearly the same for all the tested shapes, but square struts result in a smaller area of total distribution (Figure III in the Data Supplement). As an example, the total deposition was 17% higher for the triangular top strut than the square strut alone, although the concentration profiles do not show significant changes in the peak profile.
Moreover, the single strut simulations show that blood flow can carry drug downstream to be deposited well beyond the stent strut and that the degree of this extension of distribution is a function of strut shape. When a stent of many struts is examined in this model, there is a small degree of superposition of drug effect from serial struts, and distribution increases downstream (Figure IV in the Data Supplement). Here, strut shape has an effect, albeit subtle. When multiple struts were modeled, we observed a 10% increase in total drug deposition with only a slight increase in peak concentration for the triangular top strut compared with the square top strut.
Clinical Implications
This article uses computational and animal models to address important clinical issues at the interface of stent design, tissue pharmacology, and vascular biology. The findings raise a number of immediate clinical issues. The most timely concerns for DES systems are those that force changes in our perception of drug distribution after elution, the impact of strut overlap, and the importance of stent design. The idea that drug can be delivered to the vessel wall only if stent struts are in contact with the wall is incorrect. Hence, for example, malapposition of struts is not by necessity counterproductive to drug delivery. Even stents not directly apposed to the vessel wall can deliver drug. Similarly, the increasing use of multiple stents in an intervention will mean that struts abut other struts, not just the wall. Conventional wisdom holds that 2 struts over 1 arterial segment provide "double the dose" of delivered drug, raising the possibility of double the effect or double the toxicity. Our data show that the addition of a second DES abutting or overlapping a first only modestly increases the dose delivered and actually detracts from the dose if one is a BMS (Figure 8A and 8B). If overlapping stents provide increased toxicity, it is not from heightened dose alone. Rather, the safety of overlap is determined by the extent of additional mechanical injury induced by insertion of multiple proximate stents and the spatial extension of drug over the exacerbated injury. The mass of added and overlapping stents creates flow disturbances that deliver drug farther beyond where a single strut covers an artery. These data are critical at a time when the approach to overlapping stents is unclear, when clinicians must choose between long stents and overlapping stents, and when DES occasionally are used with BMSs.
Finally, our article shows that central precepts that drive current DES development must now be called into question. It has been assumed that abluminal coating alone can ensure optimal delivery of drug to the wall while minimizing loss of drug into the bloodstream and that thinner struts are better than thicker struts for reasons of enhanced deliverability. We show that abluminally coated drug accounts for <50% of the drug that ends up in the arterial wall. The addition of drug on one other face significantly increases the amount of drug that can be delivered to segments of a stented artery. Addition of drug to nonapposed strut faces greatly enhances drug delivery in areas adjacent to, but not underneath, the struts. This finding, coupled with the impact of stent design on flow-mediated stagnant pools and the demonstration that less drug is delivered to the vessel wall with thin stents, emphasizes the idea that, in addition to its recognized importance for mechanical injury and procedural success,8,28 stent design is also of paramount importance in dictating drug therapy.
Study Limitations and Future Directions
Mathematical modeling is indispensable precisely when clinical and animal studies increasingly define areas of concern but cannot fully characterize them. The predictions of these models are becoming increasingly important as our experience with DES emerges in increasingly challenging clinical environments. Computational methods are valuable in isolating and understanding mechanisms for drug delivery, yet idealized models do not account for all possible clinical variables. In our mathematical model, we made some simplifications such as neglecting drug metabolism and binding, assuming homogeneous, healthy tissue composition, assuming negligible arterial drug transport via vasa vasorum, and considering only 2D flow. Substantial work remains to include drug-specific pharmacokinetics,9,29 unique vascular ultrastructure such as vessel disease30 and topographies,31 and even the impact of intimal hyperplasia and thrombosis on DES function. The results of this study motivate further study of the relationship between the complex 3D flow generated over the stent mesh and total arterial drug deposition. We would hypothesize that the longitudinal patterns we describe here will also provide the dominant effects in more complex settings.
Further limitations exist in analyzing in vivo data because of the paucity of high-resolution techniques for detecting drug deposited within the tissue and differentiating it from drug adherent to the strut. Thus, fibrin was used in this study for its ability to differentiate between tissue-deposited drug and drug adhering to the strut surface. The mathematical model does not include drug-specific properties so as to focus the study on the effects of blood flow on arterial deposition of a generic drug, although the in vivo validation was confined to a specific drug. The properties of rapamycin that increase its tissue retention include its specific binding to a complex of proteins and general binding to plasma and tissue proteins.32 Thus, broad generalization beyond drugs like rapamycin that do not share similar physicochemical properties would be unwarranted.
The coupling of fluid dynamics with stent design and pharmacology of local delivery creates a powerful tool by which to evaluate DES. Using a combined approach that mixes mathematical and animal-based modeling, we now show that direct contact of DES struts with target tissue is important but not essential because drug deposition does not necessarily scale linearly with drug load or stent-artery contact area. The relative positioning of struts and flow over the stent determine tissue concentration. As we define the kinetics of drug release and tissue uptake, computational models may suggest even more creative and efficient means of delivering drugs for a range of vascular indications and patients.
Acknowledgments
This study was supported in part by grants from the National Institutes of Health to Dr Edelman (HL-49309, HL-60407, and HL-62457) and a Philip Morris External Research Program Postdoctoral Fellowship to Dr Tzafriri. We thank Dr Kartik Shah of CFDRC and Dr Chao-Wei Hwang.
Footnotes
The first 2 authors contributed equally to this article.
The online-only Data Supplement can be found with this article at http://circ.ahajournals.org/cgi/content/full/CIRCULATIONAHA.104.512475/DC1.
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