CONTRIBUTIONS OF FREQUENCY-DISTRIBUTION ANALYSIS TO THE UNDERSTANDINGOF CORONARY RESTENOSIS - A REAPPRAISAL OF THE GAUSSIAN CURVE

Background Clinical restenosis after balloon angioplasty can be catego rized by use of dichotomous terms based on the presence or absence of recurrent myocardial ischemia. In contrast, recent investigations have concluded that late luminal renarrowing, documented through angiograp hic imaging, occurs to a variable extent in nearly all stenoses. This process has been characterized by a guassian or normal frequency distr ibution, with restenosis simply representing an extreme form of this d elayed remodeling. In the current study, frequency distribution analys is was used to examine the process of coronary restenosis in a large c ohort of patients at risk. Methods and Results Quantitative coronary a ngiographic analysis was applied to 9279 cineangiograms obtained in 30 93 patients before and immediately after angioplasty and after 6-month follow-up. Late loss, defined as the change in minimum lumen diameter of the target stenosis from postdilation to follow-up, did not statis tically conform to a normal distribution (P<.0001 by both chi(2) stati stic and Kolmogorov-Smirov test), even after the exclusion of the 236 stenoses that displayed total occlusions at follow-up angiography. Exa mination of deviations from a normal curve revealed an excessively hig h frequency of stenoses that experienced either little change (0.0+/-0 .3 mm) or marked changed (1.0 to 2.0 mm) in late loss, with a low freq uency of stenoses with intermediate values (0.3 to 1.0 mm). Similarly, although the distribution of percent diameter stenosis of the target lesion was statistically normal immediately after dilation, this gauss ian distribution disappeared during the follow-up period. Other angiog raphic indexes of restenosis also failed to approximate a normal curve . In an attempt to improve the goodness of fit, a probabilistic model of late loss was created on the basis of deconvolution of the observed data distribution. Two theoretical, discrete populations of stenoses were identified, one with and one without overall late luminal narrowi ng. Unlike the gaussian distribution, this model provided a good repre sentation of the observed data (P=NS for lack of fit). Conclusions The frequency distributions of angiographic indexes of restenosis often s uperficially resemble a gaussian curve, an appearance that is artifact ually enhanced by the measurement imprecision of current quantitative techniques. Nevertheless, standard indexes of coronary restenosis fail to conform statistically to a normal distribution. The pattern of dev iations observed supports the possible existence of discrete subpopula tions of lesions, each with a different propensity toward the developm ent of restenosis after coronary intervention.