Investigating the level of significance of the coherence function in cardiovascular variability analysis

Although the presence of significant coupling between cardiovascular variability series is usually verified according to the threshold value of 0.5 in the coherence function (CF), spectral estimator parameters should also be considered. In this study, the surrogate data technique was introduced to define the level of significance of the CF. The proposed method determined a frequency-dependent threshold over which the hypothesis of zero coherence was rejected. The weighted covariance method and the autoregressive method were used to estimate the CF on simulated series with different degrees of linear coupling and on real cardiovascular data. The threshold was dependent on the type and parameters of the adopted coherence estimator and on the record length, demonstrating the applicability of the method for all types of spectral estimators. This should favour its introduction for assessing the reliability of transfer function estimates in cardiovascular variability analysis.