Bimodal Distribution of Angiographic Measures of Restenosis Six Months After Coronary Stent Placement
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Abstract
Background Restenosis has been perceived as the tail end of a normal distribution of the response of the vessel to the intervention. However, recent studies have described a bimodal distribution for de novo lesions after percutaneous transluminal coronary angioplasty. This finding suggests that some lesions may be more susceptible for restenosis. Whether this holds true for a wider spectrum of lesions undergoing stent placement is not yet known. The present study analyzes the frequency distribution of angiographic indexes of restenosis 6 months after coronary stent implantation.
Methods and Results Quantitative angiographic evaluation was performed in 1084 lesions of 1084 patients before, immediately after, and 6 months after successful PalmazSchatz stent placement; this represented 80.4% of patients eligible for followup angiography. Principal end points of the analysis were angiographic indexes of restenosis at 6 months. Twentytwo lesions that became totally occluded at followup were excluded from most parts of the analysis. Diameter stenosis, minimal luminal diameter (MLD), and lumen loss at 6 months did not follow a normal pattern; the bimodal pattern was demonstrated through deconvolution that yielded two separate normal components delineating two lesion populations, which developed distinctively different degrees of lumen renarrowing. The first and larger subgroup of lesions, which was less prone to restenosis, was centered around a mean value of 27% for diameter stenosis and 2.19 mm for MLD, whereas the second subgroup, with a greater tendency for restenosis, was situated around a mean value of 68% for diameter stenosis and 0.76 mm for MLD. The intersection point between the two theoretical normal distribution components was 53.5% for diameter stenosis and 1.09 mm for MLD at followup.
Conclusions Frequencydistribution curves of angiographic indexes of restenosis after coronary stent placement have a bimodal pattern, suggesting the existence of two distinct populations with different propensity to restenosis. These findings may encourage future efforts for the timely identification of the subset with a higher risk as the target of specific antirestenotic strategies.
Restenosis has often been conceived as an ubiquitous healing process involving more or less all lesions as the inevitable response to the injury caused by balloon dilatation.^{1} In support of this concept, various groups of authors have found that angiographic measures of lumen narrowing after balloon angioplasty follow a normal, gaussian distribution curve,^{2,3} concluding that restenosis is a continuous process occurring not in an unusual or selected subset of patients but randomly in all patients. This view has questioned the validity of the categorical definitions of restenosis, including that most commonly used of a ≥50% diameter stenosis at followup. Nevertheless, various investigators have continued in their attempts to identify clinical, lesional, and procedural factors to characterize a subgroup of patients at higher risk for restenosis.^{4–10} The continuous view of restenosis has been challenged by a study that demonstrated a bimodal distribution of diameter stenosis at late followup and suggested that restenosis may be a distinct pathophysiological process that occurs in some lesions but not in others.^{11} Subsequently, it was recognized that bimodal distribution of quantitative angiographic measures of restenosis could be present but difficult to discern due to the imprecision of the quantitative systems and the relatively low frequency of restenosis.^{12} These findings were recently confirmed with a detailed analysis of the angiographic followup outcome in >3500 de novo lesions after conventional angioplasty.^{13} Although the distribution curves did not appear to be bimodal at first glance, curve deconvolution identified two distinct groups of lesions: one with and one without overall late luminal renarrowing.^{13} The generalization of this model to a broader spectrum of lesions and to other coronary interventional devices may provide new insights into the process of restenosis and may help in better defining the target of future efforts for the reduction of restenosis.
The aim of this study was to assess the distribution features of angiographic restenosis indexes at 6 months after coronary stent implantation.
Methods
Patients
All patients in whom the placement of one or more stents was attempted in the 4year period from May 1992 through April 1996 were considered possible candidates for the study. Indications for stenting were extensive coronary artery dissections or suboptimal results (residual stenosis of >30%) after PTCA and lesions in venous bypass grafts. Of the total of 1494 candidates, the following criteria led to the exclusion of 145 patients: stent implantation in the presence of cardiogenic shock complicating acute myocardial infarction (37 patients, 2.5%); unsuccessful stent placement, if it was impossible to place the stent at the desired site or achieve a satisfactory angiographic result (residual stenosis <30%) (41 patients, 2.7%); stenting primarily intended as a bridge to CABG (11 patients, 0.7%); and any cardiac event during the first 30 days after the procedure, such as death, myocardial infarction, CABG, repeat PTCA, or stent vessel occlusion (56 patients, 3.7%). The 1349 eligible patients (with 1753 lesions) were asked to undergo control angiography at 6 months or earlier in the case of symptoms or objective signs of ischemia. Any precocious control angiography (within a period of <4 months from the procedure) was deemed as qualifying for this study if resulting in a reintervention at the target lesion or definite restenosis; otherwise, the patients were encouraged to be reinvestigated. Followup angiography at a median of 188 days (interquartile range, 173 to 203 days) was carried out in 1084 patients (80.4%), who had 1399 lesions treated with stent placement.
Stent Placement and Poststenting Treatment
The stent implantation technique has been described previously.^{14} All patients received 15 000 U heparin and 500 mg aspirin IV before PTCA. Short 7mm or articulated 15mm PalmazSchatz stents (Johnson & Johnson) were delivered under fluoroscopic guidance after having been handcrimped on conventional angioplasty balloons. Balloon size and pressure were left to the operator’s discretion. Multiple stents (more than one standard or two short stents) were deployed if necessary to cover the full extent of the target lesion or of the dissection if it was incurred. The short stent (7 mm) was used as a unit of analysis (one standard, articulated 15mm stent was counted as 2 stent units). Adequacy of the final result was based solely on the angiographic assessment.
After sheath removal and pressure bandage application, heparin infusion was started in all patients and continued for 12 hours. All patients were administered 100 mg aspirin PO BID throughout the study. In the first half of the study period, patients were treated with an anticoagulation regimen consisting of heparin for 5 to 10 days and phenprocoumon (Marcumar; HoffmanLa Roche) for 4 to 6 weeks (397 patients), whereas most of the patients within the last 2 years were treated with combined antiplatelet therapy with 250 mg ticlopidine BID in addition to aspirin (687 patients).
Coronary Angiographic Evaluation
Qualitative angiographic assessment was done by the operator during or immediately after the procedure. The angiogram was assessed for the presence of vessel occlusion before PTCA or stenting and dissections^{15} immediately before stent placement. The vessel was considered occluded in the presence of TIMI flow grade 0 or 1. An occlusion was considered recent in the setting of acute myocardial infarction or if it occurred as a complication of the PTCA procedure preceding stent implantation; otherwise, it was considered chronic.
Quantitative angiographic analysis was made by operators not involved in the intervention with the use of the automated edgedetection system CMS (Medis Medical Imaging Systems). The contrastfilled nontapered catheter tip was used for calibration. MLD, RD, percent diameter stenosis, and diameter of the maximally inflated balloon were obtained with this analysis system. The measurements were done for the angiogram before and immediately after stenting and for that recorded at followup. Care was taken to choose identical projections of the target lesion for all assessed angiograms. Balloontovessel ratio was calculated as diameter of the inflated balloon divided by the coronary RD. Late loss was computed as the difference between the final poststenting MLD and the MLD at followup angiography. We recently demonstrated for this system an accuracy of −0.006 mm and a precision of 0.075 mm,^{16} which are very similar to the values of Reiber et al.^{17}
Data Analysis
The issue of handling multiple lesions in the same patient is very complex. Although there are data supporting the lesiontolesion independence of restenosis,^{18} this assumption is not yet fully proven. Therefore, the analyses were made on a perpatient basis, with selection at random of only one lesion in the patients with multilesion interventions. To validate this approach, the same analyses were done including solely singlelesion patients, and the differences were negligible.
Data are expressed as percentages for discrete variables and as mean±SD for continuous variables. The frequency distribution of the angiographic variables was described through parameters such as mean, median, mode, skewness, and kurtosis and tested for normality by means of the KolmogorovSmirnov goodnessoffit test. For graphical presentation histograms, hanging histobars and frequencydistribution curves are used. For distribution curves with bimodal appearance and a marked deviation from the theoretical normal curve, deconvolution in two bestfitted normally distributed curves was performed with the EM algorithm^{19} with the SPlus statistical package (SPlus Version 3.3, StaSci Division, MathSoft). The stability of the findings presented was ensured through the use of bootstrapping with 1000 replications of the original data and performance of the deconvolution with the mean values obtained from the 1000 random samplings for each parameter in study.^{20} As a result, the mean, SD, and proportion of the population belonging to each of the estimated component normal distributions were obtained and used to construct the combined mixture distribution. The mixture distribution was tested for equality against the respective observed frequency distribution by means of the KolmogorovSmirnov test. The bootstrapping technique also allowed the calculation of the intersection point between the two component normal distribution curves, together with its nonparametric CI. Statistical significance was accepted for all values of P<.05.
Results
The Table⇓ describes the clinical characteristics of the patients included in this study, together with the angiographic and procedural data. A relevant proportion of the patients presented with highrisk features such as acute myocardial infarction (16.8%), unstable angina pectoris (34.6%), and multivessel disease (74.6%). Most of the lesions were located in the left anterior descending coronary artery. The intervention reduced diameter stenosis from 76.6±15.1% before stenting to 5.4±10.5% immediately after stenting. This was achieved with a mean balloontovessel ratio of 1.07±0.14 and deployment of 2.56±1.50 stent units (ie, 7mm stent segments). At 6month followup, the population presented with a diameter stenosis of 37.7±23.2% and a restenosis rate (diameter stenosis of ≥50%) of 25.6%. Fig 1⇓ presents the histograms for diameter stenosis and MLD both immediately after the intervention and at followup for all 1084 lesions. Although both diameter stenosis and MLD immediately after stenting approximated a normal distribution (Fig 1A⇓ and 1B⇓), a different shape is present in the histograms of diameter stenosis and MLD at followup (Fig 1C⇓ and 1D⇓). Visual assessment of the latter histograms identifies three peaks. For diameter stenosis at followup (Fig 1C⇓), the first peak is centered around a 30% value, the second is centered around a 70% value, and the last peak corresponds exclusively to the 22 totally occluded lesions at control angiography. For MLD at followup (Fig 1D⇓), the histogram reveals the reciprocal pattern of that for diameter stenosis. The small group of total occlusions at followup was analyzed separately: 41% of these lesions had been occluded before the intervention as well, increasing the likelihood that reocclusion may have occurred early and asymptomatically. Because thrombosis, a quite different mechanism than restenosis, cannot be ruled out with certainty as the cause of these occlusions and given the small number of these lesions (2% of the total population), we decided to exclude them from further analysis. The following analyses were based on all the lesions without total occlusions at followup (ie, 1062 lesions). The distributions for MLD and diameter stenosis before the intervention were significantly skewed due to the high proportion of total occlusions. This is easily deducible from a mode of 0 mm for MLD and 100% for diameter stenosis. These distributions returned to normal, however, after logarithmic transformation for MLD and exponential transformation for diameter stenosis. The analysis was then concentrated on the angiographic parameters at followup. The distribution of RD showed a unimodal shape, which was not significantly different from the normal distribution (Fig 2⇓). A bimodal pattern is evident from the frequencydistribution curves of both diameter stenosis (Fig 3A⇓) and MLD (Fig 4A⇓) at followup, with a significant deviation from the hypothetical normal distribution as demonstrated by the hanging histobars on Figs 3B⇓ and 4B⇓, respectively. The density estimate for diameter stenosis is also shown in Fig 3C⇓, with the twocomponent normal distributions obtained as a result of its deconvolution. The EM algorithm identified two normally distributed curves as components of the observed distribution curve for diameter stenosis at followup. The first component corresponds to a larger subgroup representing 78% (CI, 63% to 84%) of all lesions and including lesions with a diameter stenosis centered around a mean value of 27±13.5%. The second component corresponds to a smaller subgroup, 22% (CI, 16% to 37%) of all lesions, centered around a mean diameter stenosis of 68±13%. As indicated by Fig 3C⇓, the two components intersect at the value of 53.5%, defining a cutoff value for the division of the two lesion populations. The two normal distribution curves were then combined to form a single distribution (Fig 3C⇓) representing the theoretical frequency distribution for the entire population as estimated with the EM algorithm. Apart from the striking visual resemblance of this curve to the observed frequencydistribution curve, the KolmogorovSmirnov goodnessoffit test demonstrated that the two distributions were not statistically different (P=.20). The stability of the obtained intersection point of 53.5% for diameter stenosis was assessed by calculating its 95% CI through the use of 1000 Monte Carlo bootstrap replications of the data. The 95% CI was found to be between 42.5% and 60.5% (Fig 3C⇓). Fig 3D⇓ depicts the distribution of the replicated intersection points and the estimated CI.
A similar pattern was verified for MLD at followup angiography. The density estimate is shown on Fig 4C⇑ with the twocomponent normal distributions obtained as a result of its deconvolution by means of the EM algorithm. Fifteen percent (CI, 11% to 19%) of the lesions formed the first subgroup with a mean MLD of 0.76±0.30 mm. In the second and larger subgroup, 85% (CI, 81% to 89%) of the population was composed of lesions with a mean MLD of 2.19±0.63 mm. As illustrated in Fig 4C⇑, the intersection point of these two curves corresponds to an MLD of 1.09 mm, which was considered the cutoff value dividing the two lesion populations. The mixture distribution produced by the combination of the two normal distribution components and the smoothed observed distribution fit well for a wide range of values, with no statistical difference between them (P=.19, KolmogorovSmirnov test). Again, Fig 4C⇑ and 4D⇑ presents the results of 1000 bootstrap replications for the assessment of the stability of the intersection point of 1.09 mm for MLD. The 95% CI provided by this analysis lays between 0.97 and 1.20 mm (Fig 4C⇑), and the distribution of intersection points is displayed in Fig 4D⇑.
The analysis of frequencydistribution curves for diameter stenosis and MLD at followup identified two distinct subsets of lesions. We analyzed the interrelation of the subgroups identified by these two parameters. An MLD of ≥1.09 mm was associated with a diameter stenosis of ≤53.5% in 94.1% of the cases, whereas an MLD of <1.09 mm was followed by a diameter stenosis of >53.5% in 97.1% of the cases, resulting in an overall accuracy of 94.5%.
The same type of analysis was performed on the frequencydensity curve of late lumen loss (Fig 5A⇓). It showed a markedly nonnormal distribution pattern as demonstrated by the hanging histobars on Fig 5B⇓, even after logarithmic transformation (P=.002, KolmogorovSmirnov test for normality). After deconvolution, twocomponent normal distributions were obtained with centers around 0.51±0.32 and 1.47±0.66 mm, respectively (Fig 5C⇓), with 55% (CI, 42% to 64%) of the lesions belonging to the first component. The mean intersection point of the twocomponent normal distributions as estimated with the bootstrap replications was situated at the value of 0.93 mm, with a CI between 0.76 and 1.18 mm (Fig 5D⇓). The mixture distribution obtained from the addition of the twocomponent normal distributions demonstrated no statistically significant difference from the observed distribution of the late loss parameter (P=.09, KolmogorovSmirnov test).
Additional analyses were made to exclude the possibility that the bimodal pattern described above may have been the effect of the distortion produced by certain characteristics of this study population. Frequencydistribution curves for diameter stenosis and MLD at followup were reconstructed after removal of the lesions that were occluded at the time of the intervention and the same bimodal pattern as before was reproduced.
Discussion
This study provides strong evidence for the existence of a bimodal frequency distribution of 6month angiographic indexes of restenosis. In particular, this pattern was present in the distribution curves of both diameter stenosis and MLD. The bimodal pattern of the distribution curves for diameter stenosis and MLD can be identified visually and was statistically proven with curve deconvolution technique followed by goodnessoffit tests. There is a striking similarity in the bimodal pattern between the frequencydistribution curve for diameter stenosis in our study and that of King et al.^{11} The similarity is more subtle with the curve described for the same parameter by Lehman et al.^{13} All three studies coincide with the finding that the two peaks of the distribution curve for diameter stenosis at followup correspond to similar centers around 30% and 70%, respectively. The second subgroup includes approximately one third of the population in the PTCA studies^{11,13} and ∼20% in our study. This corresponds well with the known difference in restenosis rates in favor of stenting.^{21,22}
The major finding of this study derived from the bimodal shape of the distribution curves for diameter stenosis, MLD, and lumen loss at 6month followup after stenting is the suggestion of the existence of two different lesion populations—one that is less prone to restenosis and one with a high likelihood of restenosis. Our study provides an important extension of similar findings after PTCA, due to at least two advantages. First, patients were not excluded due to patient and lesion risk profiles. Baseline patient and lesion characteristics indicate that stenting was often carried out in a highrisk setting (Table⇑). Second, previous intravascular ultrasound imaging have suggested that neointimal hyperplasia plays an exclusive role in the restenosis after stenting^{23}; therefore, our bimodal pattern of the distribution curve may in fact reflect two subgroup of lesions with different propensities to hyperplasia. In combining the previous results for PTCA^{11,13} with our results, the bimodal pattern of frequencydistribution curves for restenosis indexes may actually be generalized for all the lesions most commonly treated and for the coronary interventions most commonly used, such as PTCA and stenting.
An important finding of this study is that the observed distribution curves for all three measures of restenosis (ie, diameter stenosis, MLD, and late loss at 6month followup) did not follow a normal pattern (Figs 3 through 5⇑⇑⇑). The deconvolution in twocomponent normal distributions was possible for all three curves. A finding that deserves comment is that deconvolution of the frequencydistribution curve for late lumen loss estimated that the proportion of lesions belonging to the curve component with more pronounced lumen renarrowing was almost the double that estimated for diameter stenosis. The discrepancy between the incidence of restenosis as assessed by diameter stenosis– and late lumen loss–derived indexes has been accentuated after stenting.^{24} Because of the major acute gain achieved with stenting, more lumen loss can be accommodated afterward without leading to a significant increase in diameter stenosis.
The bimodal pattern in the distribution of diameter stenosis may also renew the interest in the frequently criticized categorical approach for the assessment of restenosis. There has been much debate on the optimal binary definition of restenosis.^{12,25} The most commonly used criterion, that of a ≥50% diameter stenosis at followup, has more of a historical than physiological basis.^{26} We found that the intersection point of the estimated distribution curves for the two populations of lesions corresponds to a value of 53.5% diameter stenosis. This cutoff value was well validated through the bootstrapping technique and is very close to the traditional restenosis criterion of 50%. This may provide the most frequently used criterion of restenosis with a theoretical basis.
Bootstrapping was used throughout the analysis. It is a new technique for the assessment of the stability of statistical estimators and the construction of nonparametric CIs. We used 1000 replications of the original data of our end points of analysis (ie, diameter stenosis, MLD, and late lumen loss) to then draw at random a large number of bootstrap samples, each the same size as the original. The main advantage of such a procedure is that the sampling distribution is not mathematically estimated but empirically reconstructed based on all the original characteristics of the data. These advantages strengthen the validity of the results of the present study. Additional analyses were made to exclude possible sources of bias. More than 10% of the lesions analyzed in this report were chronic occlusions or acute occlusions as the cause of acute myocardial infarction. This factor may have conveyed a particular risk for restenosis and may have distorted the distribution curve of restenosis indexes. This possibility was excluded because the curve shape was maintained even after confinement of the analysis to lesions that were initially patent. The quantitative angiographic system may represent another source of bias due to a systematic imprecision. However, we used a well validated system,^{16,17} and it is highly unlikely for it to be responsible for the introduction of an artificial second peak in the curve. A systematic error, as such, would distort all serial measurements, which did not occur in our analysis. Neither before nor immediately after the intervention did the distribution curves of diameter stenosis and MLD have a bimodal pattern. Moreover, the RD at followup was normally distributed.
Conclusions
This study demonstrates that angiographic indexes of restenosis at 6month followup after coronary stent placement present frequency distributions with a bimodal pattern suggesting the existence of two distinct populations with different propensities to restenosis. These findings, which parallel those recently reported with PTCA, contradict the longstanding view that restenosis is a continuous process that may affect at random all patients after coronary interventions. The findings may provide a new basis for future efforts aimed at identifying the subset at higher risk, which will become the target of specific antirestenotic strategies.
Selected Abbreviations and Acronyms
CABG  =  coronary artery bypass graft surgery 
CI  =  confidence interval 
EM  =  expectation maximization 
MLD  =  minimal luminal diameter 
PTCA  =  percutaneous transluminal coronary angioplasty 
RD  =  reference diameter 
Footnotes

Reprint requests to Prof Dr A. Schömig, Deutsches Herzzentrum München, Lazarettstr 36, 80636 München, Germany.
 Received May 21, 1997.
 Revision received August 14, 1997.
 Accepted August 22, 1997.
 Copyright © 1997 by American Heart Association
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 Bimodal Distribution of Angiographic Measures of Restenosis Six Months After Coronary Stent PlacementAlbert Schömig, Adnan Kastrati, Shpend Elezi, Helmut Schühlen, Josef Dirschinger, Felix Dannegger, Manfred Wilhelm and Kurt UlmCirculation. 1997;96:38803887, published online before print December 2, 1997http://dx.doi.org/10.1161/01.CIR.96.11.3880
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 Bimodal Distribution of Angiographic Measures of Restenosis Six Months After Coronary Stent PlacementAlbert Schömig, Adnan Kastrati, Shpend Elezi, Helmut Schühlen, Josef Dirschinger, Felix Dannegger, Manfred Wilhelm and Kurt UlmCirculation. 1997;96:38803887, published online before print December 2, 1997http://dx.doi.org/10.1161/01.CIR.96.11.3880
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