title: Contributions of frequency distribution analysis to the understanding of coronary restenosis. A reappraisal of the gaussian curve.
abstract: BACKGROUND
  Clinical restenosis after balloon angioplasty can be categorized 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 angiographic imaging, occurs to a variable extent in nearly all stenoses. This process has been characterized by a gaussian or normal frequency distribution, with restenosis simply representing an extreme form of this delayed remodeling. In the current study, frequency distribution analysis was used to examine the process of coronary restenosis in a large cohort of patients at risk.
  
  
  RESULTS
  Quantitative coronary angiographic analysis was applied to 9279 cineangiograms obtained in 3093 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 statistically conform to a normal distribution (P<.0001 by both chi2 statistic and Kolmogorov-Smirnov test), even after the exclusion of the 236 stenoses that displayed total occlusions at follow-up angiography. Examination of deviation from a normal curve revealed an excessively high frequency of stenoses that experienced either little change (0.0+/-0.3 mm) or marked change (1.0 to 2.0 mm) in late loss, with a low frequency 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 gaussian distribution disappeared during the follow-up period. Other angiographic 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 narrowing. Unlike the gaussian distribution, this model provided a good representation of the observed data (P=NS for lack of fit).
  
  
  CONCLUSIONS
  The frequency distributions of angiographic indexes of restenosis often superficially resemble a gaussian curve, an appearance that is artifactually 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 deviations observed supports the possible existence of discrete subpopulations of lesions, each with a different propensity toward the development of restenosis after coronary intervention.
authors.affiliation: University of Washington School of Medicine, Seattle, WA, USA.
authors.forename: K G
authors.initials: KG
authors.lastname: Lehmann
authors.forename: R
authors.initials: R
authors.lastname: Melkert
authors.forename: P W
authors.initials: PW
authors.lastname: Serruys
mesh_terms: D000328:Adult; D000368:Aged; D015906:Angioplasty, Balloon, Coronary / Q000009:adverse effects*; D017023:Coronary Angiography; D003327:Coronary Disease / Q000209:etiology*; D005260:Female; D006801:Humans; D008297:Male; D008875:Middle Aged; D012008:Recurrence