Experimental approach for testing the uncoupling between cardiovascular variability series

In cardiovascular variability analysis, the significance of the coupling between two series is commonly assessed by defining a zero level on the magnitude-squared coherence (MSC). Although the use of the conventional value of 0.5 does not consider the dependence of MSC estimates on the analysis parameters, a theoretical threshold T-t is available only for the weighted covariance (WC) estimator. In this study, an experimental threshold for zero coherence T-e was derived by a statistical test from the sampling distribution of MSC estimated on completely uncoupled time series. MSC was estimated by the WC method (Parzen window, spectral bandwidth B=0.015, 0.02, 0.025, 0.03 Hz) and by the parametric autoregressive (AR) method (model order M=4, 8, 12, 16), on time series with length L=180, 300, 420, 540s. T-e decreased with increasing 8 and L and with decreasing M (range: 0.11-0.54 for WC estimator, 0.06-0.46 for AR estimator). Values for the typical parameter settings of WC and AR estimation (B = 0.025 Hz; M = 8; L = 300 s) were, respectively, 0.24 and 0.17. Moreover, T-t was always higher (range: 0.12-0.65) and the results were less dependable than those for T-e in defining the zero level of MSC. Thus, with the proposed method, the hypothesis of uncoupling is rejected by accounting for the parameters that affect the confidence of spectral and cross-spectral estimates. The broad applicability of this approach should favour its introduction for assessing the significance of the coupling between cardiovascular variability series.