(Circulation. 1996;93:1123-1132.)
© 1996 American Heart Association, Inc.
Articles |
Contributions of Frequency Distribution Analysis to the Understanding of Coronary Restenosis
A Reappraisal of the Gaussian Curve
From the Thoraxcenter (P.W.S.) and Cardialysis (R.M.), Erasmus University, Rotterdam, Netherlands, and the University of Washington School of Medicine (K.G.L.), Seattle, Wash.
Correspondence to Kenneth G. Lehmann, MD, Section of Cardiology (111C), Seattle Veterans Affairs Medical Center, 1660 S Columbian Way, Seattle, WA 98108.
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.
Methods and 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 
2 statistic and Kolmogorov-Smirnov test),
even after the exclusion of the 236 stenoses that displayed
total occlusions at follow-up angiography. Examination of
deviations 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.
Key Words: angioplasty • coronary disease • restenosis
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