  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.
