Numeric processing of Lorenz plots of R-R intervals from long-term ECGs: Comparison with time-domain measures of heart rate variability for risk stratification after myocardial infarction

Abstract

The so-called “Lorenz plots” are scatterplots that show the R-R interval as a function of the preceding R-R intervals. Repeatedly, it has been proposed that these plots might be used for visualizing the variability of the heart rate and that the assessment of heart rate variability (HRV) from these plots might be superior to conventional measures of HRV. However, a precise numeric evaluation of the images of Lorenz plots has never been suggested. To classify the images of Lorenz plots, a computer package that measures their density was developed. For each rectangular area of the plot, the relative number of R1/R2 samples in that area is established and a function is created that assigns the maximum relative number of samples (ie, the maximum density) to each size of an area of the plot. Plots that are very compact result in a sharply falling density function, while plots that are more diffuse lead to a flat density function. The distinction between such types of density function may be expressed as a logarithmic integral of the density function to express the “compactness” of the plot numerically. As the computational demands of this approach are intensive, an approximate method that restricts the measurement of the density to the area around the peak of the plot was also developed. The results of this approximate method correlate strongly with the full results ( r = .98), and approximate measurement of one plot requires less than 1 minute of computer time. The approximate method has been applied to a set of 24-hour Holter records obtained from 637 survivors of acute myocardial infarction. For each record, the SDNN and SDANN values were also calculated as conventional measures of HRV. Both the density of the Lorenz plots and the conventional measures of HRV were used to investigate the differences among 48 patients who suffered an arrhythmic event (sudden death or sustained symptomatic ventricular tachycardia) during a 2-year follow-up period and the remaining 589 patients without arrhythmic postinfarction complications. At a sensitivity of 30%, the Lorenz plot density distinguished the patients with events with a positive predictive accuracy of 58%, while the SDNN and SDANN led to a positive predictive accuracy of only 23 and 18%, respectively. Thus, a detailed analysis of Lorenz plots is feasible and more clinically useful than the conventional measures of HRV.