Spectral decomposition in multichannel recordings based on multivariate parametric identification
01 Nov 1997-IEEE Transactions on Biomedical Engineering (Institute of Electrical and Electronics Engineers)-Vol. 44, Iss: 11, pp 1092-1101
TL;DR: A method of spectral decomposition in multichannel recordings is proposed, which represents the results of multivariate (MV) parametric identification in terms of classification and quantification of different oscillating mechanisms.
Abstract: A method of spectral decomposition in multichannel recordings is proposed, which represents the results of multivariate (MV) parametric identification in terms of classification and quantification of different oscillating mechanisms. For this purpose, a class of MV dynamic adjustment (MDA) models in which a MV autoregressive (MAR) network of causal interactions is fed by uncorrelated autoregressive (AR) processes is defined. Poles relevant to the MAR network closed-loop interactions (cl-poles) and poles relevant to each AR input are disentangled and accordingly classified. The autospectrum of each channel can be divided into partial spectra each relevant to an input. Each partial spectrum is affected by the cl-poles and by the poles of the corresponding input; consequently, it is decomposed into the relevant components by means of the residual method. Therefore, different oscillating mechanisms, even at similar frequencies, are classified by different poles and quantified by the corresponding components. The structure of MDA models is quite flexible and can be adapted to various sets of available signals and a priori hypotheses about the existing interactions; a graphical layout is proposed that emphasizes the oscillation sources and the corresponding closed-loop interactions. Application examples relevant to cardiovascular variability are briefly illustrated.
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TL;DR: A comprehensive review of the analysis, understanding and applications of coupling functions can be found in this paper, where a variety of methods have been developed for detecting and reconstructing coupling functions from measured data.
Abstract: The dynamical systems found in Nature are rarely isolated. Instead they interact and influence each other. The coupling functions that connect them contain detailed information about the functional mechanisms underlying the interactions and prescribe the physical rule specifying how an interaction occurs. Here, we aim to present a coherent and comprehensive review encompassing the rapid progress made recently in the analysis, understanding and applications of coupling functions. The basic concepts and characteristics of coupling functions are presented through demonstrative examples of different domains, revealing the mechanisms and emphasizing their multivariate nature. The theory of coupling functions is discussed through gradually increasing complexity from strong and weak interactions to globally-coupled systems and networks. A variety of methods that have been developed for the detection and reconstruction of coupling functions from measured data is described. These methods are based on different statistical techniques for dynamical inference. Stemming from physics, such methods are being applied in diverse areas of science and technology, including chemistry, biology, physiology, neuroscience, social sciences, mechanics and secure communications. This breadth of application illustrates the universality of coupling functions for studying the interaction mechanisms of coupled dynamical systems.
234 citations
Cites methods from "Spectral decomposition in multichan..."
...Multivariate interactions have been the subject of much attention recently, especially in developing methods for detecting the couplings (Baselli et al., 1997; Duggento et al., 2012; Faes et al., 2011; Frenzel and Pompe, 2007; Kralemann et al., 2011; Nawrath et al., 2010; Paluš and Vejmelka, 2007)....
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TL;DR: Alpha(XXAR) is comparable to or significantly smaller than the baroreflex gains derived from sequence, power spectrum, and cross-spectrum analyses and from less complex causal parametric models, thus demonstrating that simpler estimates may be biased by the contemporaneous presence of regulatory mechanisms other than barore Flex mechanisms.
Abstract: A double exogenous autoregressive (XXAR) causal parametric model was used to estimate the baroreflex gain (αXXAR) from spontaneous R-R interval and systolic arterial pressure (SAP) variabilities in...
185 citations
Cites background or methods from "Spectral decomposition in multichan..."
...aPS~LF! 5 Î Prr~LF! Psap~LF! aPS~HF! 5 Î Prr~HF! Psap~HF! (8)...
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...2 and 6) are identified via a least-squares procedure (8, 15)....
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...The model order is fixed at 10, and the coefficients of the bivariate AR model are identified via least-squares methods (8, 15)....
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...5 and 4) are identified using a generalized least-squares approach (8, 24)....
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TL;DR: It is shown that frequency modulation of low‐beta and high‐beta rhythms significantly contributes to the involvement of the human STN in movement preparation, execution and recovery, and that the FM patterns are regulated by the dopamine levels in the system.
Abstract: Event-related changes of brain electrical rhythms are typically analysed as amplitude modulations of local field potential (LFP) oscillations, like radio amplitude modulation broadcasting. In telecommunications, frequency modulation (FM) is less susceptible to interference than amplitude modulation (AM) and is therefore preferred for high-fidelity transmissions. Here we hypothesized that LFP rhythms detected from deep brain stimulation (DBS) electrodes implanted in the subthalamic nucleus (STN) in patients with Parkinson's disease could represent movement-related activity not only in AM but also in FM. By combining adaptive autoregressive identification with spectral power decomposition, we were able to show that FM of low-beta (13-20 Hz) and high-beta (20-35 Hz) rhythms significantly contributes to the involvement of the human STN in movement preparation, execution and recovery, and that the FM patterns are regulated by the dopamine levels in the system. Movement-related FM of beta oscillatory activity in the human subthalamic nucleus therefore provides a novel informational domain for rhythm-based pathophysiological models of cortico-basal ganglia processing.
176 citations
Cites methods from "Spectral decomposition in multichan..."
...The time-varying power spectrum of the average movement-related AAR model 〈θ(t)〉 was divided into components relevant to real poles or to pairs of complex conjugate poles in the z-domain using the residual method (Baselli et al. 1997; see Foffani et al. 2004a for details)....
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TL;DR: A method based on a bivariate autoregressive model to derive the strength of the causal coupling on both arms of a closed loop is proposed, which correctly detects a significant coupling only on the pathway from the RR interval to the SAP.
Abstract: The coherence function measures the amount of correlation between two signals x and y as a function of the frequency, independently of their causal relationships. Therefore, the coherence function is not useful in deciding whether an open-loop relationship between x and y is set (x acts on y, but the reverse relationship is prevented) or x and y interact in a closed loop (x affects y, and vice versa). This study proposes a method based on a bivariate autoregressive model to derive the strength of the causal coupling on both arms of a closed loop. The method exploits the definition of causal coherence. After the closed-loop identification of the model coefficients, the causal coherence is calculated by switching off separately the feedback or the feedforward path, thus opening the closed loop and fixing causality. The method was tested in simulations and applied to evaluate the degree of the causal coupling between two variables known to interact in a closed loop mainly at a low frequency (LF, around 0.1 Hz) and at a high frequency (HF, at the respiratory rate): the heart period (RR interval) and systolic arterial pressure (SAP). In dogs at control, the RR interval and the SAP are highly correlated at HF. This coupling occurs in the causal direction from the RR interval to the SAP (the mechanical path), while the coupling on the reverse causal direction (the baroreflex path) is not significant, thus pointing out the importance of the direct effects of respiration on the RR interval. Total baroreceptive denervation, by opening the closed loop at the level of the influences of SAP on RR interval, does not change these results. In elderly healthy men at rest, the RR interval and SAP are highly correlated at the LF and the HF. At the HF, a significant coupling in both causal directions is found, even though closed-loop interactions are detected in few cases. At the LF, the link on the baroreflex pathway is negligible with respect to that on the reverse mechanical one. In heart transplant recipients, in which SAP variations do not cause RR interval changes as a result of the cardiac denervation, the method correctly detects a significant coupling only on the pathway from the RR interval to the SAP.
158 citations
TL;DR: In this article, the authors investigated the effect of cardiovascular rehabilitation and exercise training on autonomic regulation, such as HRV and baroreflex gain, in 40 patients with ischemic heart disease after major IHD events.
146 citations
References
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TL;DR: In this article, a new estimate minimum information theoretical criterion estimate (MAICE) is introduced for the purpose of statistical identification, which is free from the ambiguities inherent in the application of conventional hypothesis testing procedure.
Abstract: The history of the development of statistical hypothesis testing in time series analysis is reviewed briefly and it is pointed out that the hypothesis testing procedure is not adequately defined as the procedure for statistical model identification. The classical maximum likelihood estimation procedure is reviewed and a new estimate minimum information theoretical criterion (AIC) estimate (MAICE) which is designed for the purpose of statistical identification is introduced. When there are several competing models the MAICE is defined by the model and the maximum likelihood estimates of the parameters which give the minimum of AIC defined by AIC = (-2)log-(maximum likelihood) + 2(number of independently adjusted parameters within the model). MAICE provides a versatile procedure for statistical model identification which is free from the ambiguities inherent in the application of conventional hypothesis testing procedure. The practical utility of MAICE in time series analysis is demonstrated with some numerical examples.
47,133 citations
"Spectral decomposition in multichan..." refers background in this paper
...Usually, the model order is determined after successive increments until the hypotheses are fulfilled and a minimum of Akaike’s figure of merit is reached [22]....
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Book•
01 Jan 1987
TL;DR: Das Buch behandelt die Systemidentifizierung in dem theoretischen Bereich, der direkte Auswirkungen auf Verstaendnis and praktische Anwendung der verschiedenen Verfahren zur IdentifIZierung hat.
Abstract: Das Buch behandelt die Systemidentifizierung in dem theoretischen Bereich, der direkte Auswirkungen auf Verstaendnis und praktische Anwendung der verschiedenen Verfahren zur Identifizierung hat. Da ...
20,436 citations
"Spectral decomposition in multichan..." refers background in this paper
...Parametric spectral analysis [5], [6] permits only the recognition and quantification of the oscillatory components in the single signals [7]; on the contrary, multivariate (MV) parametric identification [8]–[11] provides further information about the causal interactions among the signals [12], [13] and about cross-spectral patterns [14]–[16], but it is difficult to use it for a better comprehension of the rhythmogenetic mechanisms....
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Book•
19 Aug 2009
TL;DR: In this article, the mean and autocovariance functions of ARIMA models are estimated for multivariate time series and state-space models, and the spectral representation of the spectrum of a Stationary Process is inferred.
Abstract: 1 Stationary Time Series.- 2 Hilbert Spaces.- 3 Stationary ARMA Processes.- 4 The Spectral Representation of a Stationary Process.- 5 Prediction of Stationary Processes.- 6* Asymptotic Theory.- 7 Estimation of the Mean and the Autocovariance Function.- 8 Estimation for ARMA Models.- 9 Model Building and Forecasting with ARIMA Processes.- 10 Inference for the Spectrum of a Stationary Process.- 11 Multivariate Time Series.- 12 State-Space Models and the Kalman Recursions.- 13 Further Topics.- Appendix: Data Sets.
5,260 citations
Book•
01 Jan 1987
TL;DR: This new book provides a broad perspective of spectral estimation techniques and their implementation concerned with spectral estimation of discretespace sequences derived by sampling continuousspace signals.
2,731 citations