Abstract
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 Tt is available only for the weighted covariance (WC) estimator. In this study, an experimental threshold for zero coherence Te 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. Te decreased with increasing B and L and with decreasing M (range: 3.11–0.54 for WC estimator, 0.06–0.46 for AR estimator). Values for the typical parameter settings of WC and AR estimation (B=0.025Hz; M=8; L=300s) were, respectively, 0.24 and 0.17. Moreover, Tt was always higher (range: 0.12–0.65) and the results were less dependable than those for Te 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.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Baselli, G., Cerutti, S., Civardi, S., Liberati, D., Lombardi, F., Malliani, A., andPagani, M. (1986): ‘Spectral and cross-spectral analysis of heart rate and arterial blood pressure variability signals’,Comput. Biomed. Res.,19, pp. 520–534
Benignus, V. A. (1969): ‘Estimation of the coherence spectrum and its confidence interval using the Fast Fourier Transform’,IEEE Trans. Audio Electroacoust 17, pp. 145–150
Blackman, R. B., andTukey, J. W. (1959): ‘The measurement of power spectra from the point of view of communications engineering’, (Dover, New York, 1959)
Cadzow, J. A., andSolomon, O. M. (1987): ‘Linear modeling and the coherence function’,IEEE Trans. Acoust, Speech, Signal Process.,35, pp. 19–28
Cevese, A., Gulli, G., Polati, E., Gottin, L., andGrasso, R. (2001): ‘Baroreflex and oscillation of heart period at 0.1 Hz studied by alpha-blockade and cross-spectral analysis in healthy humans’,J. Physiol.,531, pp. 235–244
Challis, R. E., andKitney, R. I. (1991): ‘Biomedical signal processing (in four parts). Part 3. The power spectrum and coherence function’,Med. Biol. Eng. Comput.,29, pp. 225–241
De Boer, R. W., Karemaker, J. M., andStrackee, J. (1985): ‘Relationships between short-term blood-pressure fluctuations and heart-rate variability in resting subjects: a spectral analysis approach’,Med. Biol. Eng. Comput.,23, pp. 352–358
Di Rienzo, M., Castiglioni, P., Parati, G., Mancia, G., andPedotti, A. (1996): ‘Effects of sino-aortic denervation on spectral characteristics of blood pressure and pulse interval variability: a wide-band approach’,Med. Biol. Eng. Comput.,34, pp. 133–141
Fisher, L. D., andVan Belle, G. (1993): ‘Biostatistics. A methodology for health sciences’ (John Wiley & Sons, New York, 1993)
Furlan, R., Porta, A., Costa, F., Tank, J., Baker, L., Schiavi, R., Robertson, D., Malliani, A., andMosqueda-Garcia, R. (2000): ‘Oscillatory patterns in sympathetic neural discharge and cardiovascular variables during orthostatic stimulus’,Circulation,101, pp. 886–892
Jenkins, G. M., andWatts, D. G. (1968): ‘Spectral analysis and its applications’ (Holden-Day, San Francisco, 1968)
Kay, S. M. (1988): ‘Modern spectral estimation. Theory & application’ (Prentice Hall, Englewood Cliffs, New Jersey, 1988)
Koopmans, L. H. (1974): ‘The spectral analysis of time series’ (Academic Press, New York, 1974)
Maestri, R., Pinna, G. D., Robbi, E., Gnemmi, M., andLa, Rovere, M. T. (2001): ‘Prognostic value of noninvasive baroreflex sensitivity in chronic heart failure patients’,Comput. in Cardiol.,28, pp. 597–600
Mancia, G., Parati, G., Castiglioni, P., andDi Rienzo, M. (1999): ‘Effect of sinoaortic denervation on frequency-domain estimates of baroreflex sensitivity in conscious cats’,Am. J. Physiol.,276, pp. H1987-H1993
More, M., Vieira, A., Lee, D. T. L., andKailath, T. (1978): ‘Recursive multichannel maximum entropy spectral estimation’,IEEE Trans. Geosci.,16, pp. 85–94
Munakata, M., Imai, Y., Sekino, H., andAbe, K. (1993): ‘Rhythmic oscillations of blood pressure and R-R interval in patients with chronic renal failure’,Med. Biol. Eng. Comput.,31, pp. S115-S122
Nollo, G., Porta, A., Faes, L., Del Greco, M., Disertori, M., andRavelli, F. (2001): ‘Causal linear parametric model for baroreflex gain assessment in patients with recent myocardial infarction’,Am. J. Physiol. Heart Circ. Physiol.,280, pp. H1830-H1839
Pagani, M., Lombardi, F., Guzzetti, S., Rimoldi, O., Furlan, R., Pizzinelli, P., Sandrone, G., Malfattq, G., Dell'Orto, S., Piccaluga, E., Turiel, M., Baselli, G., Cerutti, S., andMalliani, A. (1986): ‘Power spectral analysis of heart rate and arterial pressure variabilities as a marker of sympatho-vagal interaction in man and conscious dog’,Circ. Res.,59, pp. 178–193
Pinna, G. D., andMaestri, R. (2001): ‘Reliability of transfer function estimates in cardiovascular variability analysis’,Med. Biol. Eng. Comput.,39, pp. 338–347
Pitzalis, M. V., Mastropasqua, F., Massari, F., Passantino, A., Colombo, R., Mannarini, A., Forleo, C., andRizzon, P. (1998): ‘Effect of respiratory rate on the relationships between RR interval and systolic blood pressure fluctuations: a frequency-dependent phenomenon’,Cardiovasc. Res.,38, pp. 332–339
Porta, A., Furlan, R., Rimoldi, O., Pagani, M., Malliani, A., andVan De Borne, P. (2002): ‘Quantifying the strength of the linear causal coupling in closed loop interacting cardiovascular variability signals’,Biol. Cybern.,86, pp. 241–251
Priestley, M. B. (1981): ‘Spectral analysis and time series’ (Academic Press, London, 1981)
Robbe, H. W. J., Mulder, L. J. M., Ruddel, H., Langewitz, W. A., Veldman, J. B. P., andMulder, G. (1987). ‘Assessment of baroreceptor reflex sensitivity by means of spectral analysis’,Hypertension,10, pp. 538–543
Saul, J. P., Berger, R. D., Albrecht, P., Stein, S. P., Hui Chen, M., andCohen, R. J. (1991): ‘Transfer function analysis of the circulation: unique insights into cardiovascular regulation’,Am. J. Physiol.,261, pp. H1231-H1245
Task Force European Society of Cardiology andNorth American Society of Pacing Electrophysiology (1996): ‘Heart rate variability. Standards of measurement, physiological interpretation, and clinical use’,Eur. Heart. J.,17, pp. 354–381
Taylor, J. A., Carr, D. L., Myers, C. W., andEckberg, D. L. (1998): ‘Mechanisms underlying very-low-frequency RR-interval oscillations in humans’,Circulation,98, pp. 547–555
Taylor, J. A., andEckberg, D. L. (1996): ‘Fundamental relations between short-term RR interval and arterial pressure oscillations in humans’,Circulation,93, pp. 1527–1532
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Faes, L., Nollo, G. & Antolini, R. Experimental approach for testing the uncoupling between cardiovascular variability series. Med. Biol. Eng. Comput. 40, 565–570 (2002). https://doi.org/10.1007/BF02345456
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/BF02345456