Experimental approach for testing the uncoupling between cardiovascular variability series

Surrogate data approaches to assess the significance of directed coherence: application to EEG activity propagation

This paper addresses the topic of evaluating the significance of frequency domain measures of causal coupling in multivariate time series through generation of surrogate data. The considered approaches are the traditional Fourier Transform (FT) algorithm and a new causal FT (CFT) algorithm for surrogate data generation. Both algorithms preserve the FT modulus of the original series; differences are in the phase relationships, that are completely destroyed for FT surrogates and imposed after switching off the link over the considered causal direction for CFT surrogates. The ability of the algorithms to assess causality in the frequency domain was tested using the directed coherence as discriminating parameter. Evaluation on simulated multivariate linear processes and application over multichannel EEG recordings showed that the utilization of CFT surrogates improves specificity of the test for nonzero spectral causality, as FT surrogates may attribute to a direct coupling the presence of indirect connectivity patterns.

Interactions between TGF-dependent and myogenic oscillations in tubular pressure and whole kidney blood flow in both SDR and SHR

We previously showed that nonlinear interactions between the two renal autoregulatory mechanics (tubuloglomerular feedback and the myogenic mechanism) were observed in the stop flow pressure (SFP) and whole kidney blood flow data from Sprague-Dawley rats (SDR) using time-invariant bispectrum analysis ( 3 , 4 ). No such nonlinear interactions were observed in either SFP or whole kidney blood flow data obtained from spontaneously hypertensive rats (SHR). We speculated that the failure to detect nonlinear interactions in the SHR data may be related to our observation that these interactions were not continuous and therefore had time-varying characteristics. Thus the absence of such nonlinear interactions may be due to an inappropriate time-invariant method being applied to data that are especially time varying in nature. We examine this possibility in this paper by using a time-varying bispectrum approach, which we developed for this purpose. Indeed, we found significant nonlinear interactions in SHR ( n = 18 for SFP; n = 12 for whole kidney blood flow). Moreover, the duration of nonlinear coupling is found statistically to be longer ( P = 0.001) in SFP data from either SDR or SHR than it is in whole kidney data from either type of rat. We conclude that nonlinear coupling is present at both the single nephron as well as the whole kidney level for SDR and SHR. In addition, SHR data at the whole kidney level exhibit the most transient nonlinear coupling phenomena.

Surrogate Data Analysis for Assessing the Significance of the Coherence Function

In cardiovascular variability analysis, the significance of the coupling between two time series is commonly assessed by setting a threshold level in the coherence function. While traditionally used statistical tests consider only the parameters of the adopted estimator, the required zero-coherence level may be affected by some features of the observed series. In this study, three procedures, based on the generation of surrogate series sharing given properties with the original but being structurally uncoupled, were considered: independent identically distributed (IID), Fourier transform (FT), and autoregressive (AR). IID surrogates maintained the distribution of the original series, while FT and AR surrogates preserved the power spectrum. The ability of the three methods to define the threshold for zero coherence was validated and compared by computer simulations reproducing typical cardiovascular interactions. While the IID threshold depended only on record length and design parameters of the coherence estimator, FT and AR thresholds were frequency-dependent with peaks corresponding to the local maxima of the estimated coherence. FT and AR surrogates were able to compensate spurious coherence peaks due to equal-frequency but independent oscillations in the two series. The benefit of frequency-dependent thresholds was evident for short series with narrow-band oscillations. Thus, surrogates preserving the power spectrum of the original series are recommended to avoid false coupling detections in the presence of oscillations occurring at nearby frequencies but produced by different mechanisms, as may frequently happen in cardiovascular and cardiorespiratory regulation.

Causal transfer function analysis to describe closed loop interactions between cardiovascular and cardiorespiratory variability signals

Although the concept of transfer function is intrinsically related to an input-output relationship, the traditional and widely used estimation method merges both feedback and feedforward interactions between the two analyzed signals. This limitation may endanger the reliability of transfer function analysis in biological systems characterized by closed loop interactions. In this study, a method for estimating the transfer function between closed loop interacting signals was proposed and validated in the field of cardiovascular and cardiorespiratory variability. The two analyzed signals x and y were described by a bivariate autoregressive model, and the causal transfer function from x to y was estimated after imposing causality by setting to zero the model coefficients representative of the reverse effects from y to x. The method was tested in simulations reproducing linear open and closed loop interactions, showing a better adherence of the causal transfer function to the theoretical curves with respect to the traditional approach in presence of non-negligible reverse effects. It was then applied in ten healthy young subjects to characterize the transfer functions from respiration to heart period (RR interval) and to systolic arterial pressure (SAP), and from SAP to RR interval. In the first two cases, the causal and non-causal transfer function estimates were comparable, indicating that respiration, acting as exogenous signal, sets an open loop relationship upon SAP and RR interval. On the contrary, causal and traditional transfer functions from SAP to RR were significantly different, suggesting the presence of a considerable influence on the opposite causal direction. Thus, the proposed causal approach seems to be appropriate for the estimation of parameters, like the gain and the phase lag from SAP to RR interval, which have a large clinical and physiological relevance.