Abstract
A unifying general approach to measure regularity, synchronisation and co-ordination is proposed. This approach is based on conditional entropy and is specifically designed to deal with a small amount of data (a few hundred samples). Quantitative and reliable indexes of regularity, synchronisation and co-ordination (ranging from 0 to 1) are derived in a domain (i.e. the information domain) different from time and frequency domains. The method is applied to evaluate regularity, synchronisation and co-ordination among cardiovascular beat-to-beat variability signals during sympathetic activation induced by head-up tilt (T), during the perturbing action produced by controlled respiration at 10, 15 and 20 breaths/min (CR10, CR15 and CR20), and after peripheral muscarinic blockade provoked by the administration of low and high doses of atropine (LD and HD). It is found that: (1) regularity of the RR interval series is around 0.209; (2) this increases during T, CR10 and HD; (3) the systolic arterial pressure (SAP) series is more regular (0.406) and its regularity is not affected by the specified experimental conditions; (4) the muscle sympathetic (MS) series is a complex signal (0.093) and its regularity is not influenced by HD and LD; (5) the RR interval and SAP series are significantly, though weakly, synchronised (0.093) and their coupling increases during T, CR10 and CR15; (6) the RR interval and respiration are coupled (0.152) and their coupling increases during CR10; (7) SAP and respiration are significantly synchronised (0.108) and synchronisation increases during CR10; (8) MS and respiration are uncoupled and become coupled (0.119) after HD; (9) the RR interval, SAP and respiration are significantly co-ordinated (0.118) and co-ordination increases during CR10 and CR15; (10) during HD the co-ordination among SAP, MS and the respiratory signal is larger than that among the RR interval, SAP, MS and the respiratory signal, thus indicating that the RR interval contributes towards reducing co-ordination.
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References
Anderson, B., Kenney, R. A., andNeil, E. (1950): “The role of the chemoreceptors of the carotid and aortic regions in the production of Mayer waves’,Acta Physiol. Scand.,20, pp. 203–220
Brown, T. E., Beightol, L. A., Kob, J., andEckberg, D. L. (1993): ‘Important influence of respiration on human RR interval power spectra is largely ignored’,J. Appl. Physiol.,75, pp. 2310–2317
Cooke, W. H., Hoag, J. B., Crossman, A. A., Kuusela, T. A., Tahvanainen, K. U. O., andEckberg, D. L. (1999): ‘Human responses to upright tilt: a window on central autonomic integration’,J. Physiol.,517, pp. 617–628
Glass, L., andMackey, M. C. (1988): ‘From clock to chaos. The rhythms of life’ (University Press, Princeton, NJ)
Grassberger, P., andProcaccia, I. (1983): ‘Measuring the strangeness of strange attractors’,Physica D,9, pp. 189–208
Guevara, M. R., (1997): ‘Chaos in electrophysiology’, inBillette, J., andLeBlanc, A. R. (Eds), ‘Concepts and techniques in bioelectric measurements: is the medium carrying the message?’ (Editions de l'École Polytechnique, Montréal), pp. 67–87
Guyton, A. C., andHarris, J. H. (1951): ‘Pressoreceptor-autonomic oscillation: a probable cause of vasomotor waves’,Am. J. Physiol.,165, pp. 158–166
Hoyer, D., Bauer, R., Walter, B., andZwiener, U. (1998): ‘Estimation of nonlinear couplings on the basis of complexity and predictability: a new method applied to cardiorespiratory co-ordination’,IEEE Trans. Biomed. Eng.,45, pp. 545–552
Kelso, S. (1995): ‘Dynamic pattern’ (MIT Press, Cambridge, Massachusetts).
Koepchen, H. P. (1991): ‘Physiology of rhythms and control systems: an integrative approach’ inHaken, H., andKoepchen, H. P. (Eds), ‘Rhythms in physiological systems’ (Springer-Verlag, Berlin), pp. 3–20
Meyer, J. U., Limdbom, L., andIntiglietta, M. (1987): ‘Coordinated diameter oscillations at arteriolar bifurcation in skeletal muscle’,Am. J. Physiol.,253, pp. H568-H573
Miyakawa, K. (1988): ‘Mechanisms of blood pressure oscillation caused by central nervous system ischemic response’,Jpn. J. Physiol.,38, pp. 399–425
Montano, N., Gnecchi-Ruscone, T., Porta, A., Lombardi, F., Pagani, M., andMalliani, A. (1994): ‘Power spectrum analysis of heart rate variability to assess changes in sympatho-vagal balance during graded orthostatic tilt’,Circulation,90, pp. 1826–1831
Montano, N., Pagani, M., Porta, A., Cogliati, C., Malliani, A., Narkiewicz, K., Abboud, F. M., Birkett, C., andSomers, V. K. (1998): ‘Vagotonic effects of atropine modulate spectral oscillations of sympathetic nerve activity’,Circulation,98, pp. 1394–1399
Oppenheim, A. V. andSchafer, R. W. (1975): ‘Digital signal processing’ (Prentice Hall, Englewood Cliffs, New Jersey)
Pagani, M., Lombardi, F., Guzzetti, S., Rimoldi, O., Furlan, R., Pizzinelli, P., Sandrone, G., Malfatto, 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
Pagani, M., Montano, N., Porta, A., Malliani, A., Abboud, F. M., Birkett, C., andSomers, V. K. (1997): ‘Relationship between spectral components of cardiovascular variabilities and direct measures of muscle sympathetic nerve activity in humans’,Circulation,95, pp. 1441–1448
Palus, M. (1997): ‘Detecting phase synchronisation in noisy systems’,Phys. Lett. A,235, pp. 341–351
Papoulis, A. (1984): ‘Probability, random variables and stochastic processes’ (McGraw-Hill, New York)
Pincus, S. M. (1995): ‘Approximated entropy (ApEn) as a complexity measure’,Chaos,5, pp. 110–117
Porta, A. (1998): ‘Multivariate method based on conditional entropy estimate for measuring regularity, synchronisation and co-ordination in cardiovascular variability signals’. PhD Thesis, Dipartimento di Bioingegneria, Politecnico di Milano
Porta, A., Baselli, G., Liberati, D., Montano, N., Cogliati, C., Gnecchi-Ruscone, T., Malliani, A., andCerutti, S. (1998a): ‘Measuring regularity by means of a corrected conditional entropy in sympathetic outflow’,Biol. Cybern.,78, pp. 71–78
Porta, A., Baselli, G., Lombardi, F., andCerutti, S. (1998b): ‘Quantifying regularity and synchronisation by using entropy rates in the cardiovascular variability data’ in ‘Information processing and management of uncertainty’ (EDK, Paris), pp. 555–561
Porta, A., Baselli, G., Lombardi, F., Montano, N., Malliani, A., andCerutti, S. (1999): ‘Conditional entropy approach for the evaluation of the coupling strength’,Biol. Cybern.,81, pp. 119–129
Preiss, G., andPolosa, C. (1974): ‘Patterns of sympathetic neuron activity associated with Mayer waves’,Am. J. Physiol.,226, pp. 724–730
Rapp, P. E. (1987): ‘Why are so many biological systems periodic?,Prog. Neurobiol.,29, pp. 261–273
Singer, W. (1993): ‘Synchronisation of cortical activity and its putative role in information processing and learning,Annu. Rev. Physiol.,55, pp. 349–374
Theiler, J., Eubank, S., Longtin, A., Galdrikian, J., andFarmer, D. (1992): ‘Testing for nonlinearity in time series: the method of surrogate data’,Physica D,58, pp. 77–94
Wallin, B. G., (1983): ‘Intraneural recording and autonomic function in man’ inBannister, R. (Ed.): ‘Autonomic failure’ (Oxford University Press, London), pp. 36–51
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Porta, A., Guzzetti, S., Montano, N. et al. Information domain analysis of cardiovascular variability signals: Evaluation of regularity, synchronisation and co-ordination. Med. Biol. Eng. Comput. 38, 180–188 (2000). https://doi.org/10.1007/BF02344774
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DOI: https://doi.org/10.1007/BF02344774