Demonstration of Circadian Rhythm in Heart Rate Turbulence using Novel   Application of Correlator Functions
  Background: It has been difficult to demonstrate circadian rhythm in the two parameters of heart rate turbulence, turbulence onset (TO) and turbulence slope (TS).   Objective: To devise a new method for detecting circadian rhythm in noisy data, and apply it to selected Holter recordings from two post-myocardial infarction databases, Cardiac Arrhythmia Suppression Trial (CAST, n=684) and Innovative Stratification of Arrhythmic Risk (ISAR, n=327).   Methods: For each patient, TS and TO were calculated for each hour with >4 VPCs. An autocorrelation function Corr(Delta t) = <TS(t) TS(t+Delta t)> was then calculated, and averaged over all patients. Positive Corr(Delta t) indicates that TS at a given hour and Delta t hours later are similar. TO was treated likewise. Simulations and mathematical analysis showed that circadian rhythm required Corr(Delta t) to have a U-shape consisting of positive values near Delta t=0 and 23, and negative values for intermediate Delta t. Significant deviation of Corr(Delta t) from the correlator function of pure noise was evaluated as a chi-squared value.   Results: Circadian patterns were not apparent in hourly averages of TS and TO plotted against clock time, which had large error bars. Their correlator functions, however, produced chi-squared values of ~10 in CAST (both p<0.0001) and ~3 in ISAR (both p<0.0001), indicating presence of circadian rhythmicity.   Conclusion: Correlator functions may be a powerful tool for detecting presence of circadian rhythms in noisy data, even with recordings limited to 24 hours. 
Mari Watanabe, Mark Alford, Raphael Schneider, Axel Bauer, Petra   Barthel, Phyllis Stein, Georg Schmidt