Abstract
It has been shown that fluctuation of human heartbeat intervals (heart rate variability, HRV) reflects variations in autonomic nervous system activity. We studied HRV at simulated altitudes of over 6000 m from Holter electrocardiograms recorded during the Operation Everest II study (Houston et al. 1987). Stationary, ∼30-min segments of HRV data from six subjects at sea level and over 6000m were supplied to (1) spectral analysis to evaluate sympathetic and parasympathetic nervous system (SNS, PNS) activity, (2) the analysis of Poincaré section of the phase space trajectory reconstructed on a delayed coordinate system to evaluate whether there was fluctuation with deterministic dynamics, (3) the estimation of the correlation dimension to evaluate a static property of putative attractors, and (4) the analysis of nonlinear predictability of HRV time series which could reflect a dynamic property of the attractor. Unlike HRV at sea level, the recordings at over 6000 m showed a strong periodicity (period of about 20 s) with small cycle-to-cycle perturbation. When this perturbation was expressed on a Poincaré section, it seemed to be likely that the perturbation itself obeyed a deterministic law. The correlation dimensions of these recordings showed low dimensional values (3.5 ± 0.4, mean±SD), whereas those of the isospectral surrogates showed significantly (P < 0.05) higher values (5.3 ±0.5) with embedding dimensions of 5.6 ± 0.9. At over 6000 m, the correlation coefficients between the observed and the predicted time series with the prediction time of < 4 beats were significantly (P < 0.01) higher than those for the surrogate data, whereas there was no significant difference in the nonlinear predictability between the observed and the surrogate data at sea level. The results of the spectral analyses showed that, at over 6000 m, there was hardly any power > 0.15 Hz in the HRV spectra possibly due to PNS withdrawal. Hence, these deterministic and/or chaotic dynamics might be mediated by variations in SNS activity at over 6000 m.
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References
Albano AM, Meunch J, Schwartz C, Mees AI, Rapp PE (1988) Singular-value decomposition and the Grassberger-Procaccia algorithm. Phys Rev A 38:3017–3026
Anholm JD, Powles ACP, Downey III R, Houston CS, Sutton JR, Bonnet MH, Cymerman A (1992) Operation Everest II: arterial oxygen saturation and sleep at extreme simulated altitude. Am Rev Respir Dis 145:817–826
Babloyantz A, Destexhe A (1988) Is the normal heart a periodic oscillator? Biol Cybern 58:203–211
Berger RD, Saul JP, Cohen RJ (1989) Transfer function analysis of autonomic regulation. I. Canine atrial rate response. Am J Physiol 256:H142-H152
Broomhead DS, King GP (1986) Extracting qualitative dynamics from experimental data. Physica D 20:217–236
Casdagli M (1991) Chaos and deterministic versus stochastic nonlinear modelling. J R Stat Soc B 54:303–328
Farmer JD (1982) Chaotic attractors of an infinite-dimensional dynamical system. Physica D 4:366–393
Fraser AM, Swinney HL (1986) Independent coordinates for strange attractors from mutual information. Phys Rev A 33:1134–1140
Glass L, Mackey MC (1988) From clocks to chaos. The rhythms of life. Princeton University Press, Princeton, NJ
Glass L, Malta CP (1990) Chaos in multi-looped negative feedback systems. J Theor Biol 145:217–223
Goldberger AL (1991) Is the normal heartbeat chaotic or homeostatic? News Physiol Sci 6:87–91
Grassberger P (1986) Do climatic attractors exist? Nature 326:609–612
Grassberger P, Procaccia I (1983) Measuring the strangeness of strange attractors. Physica D 9:189–208
Hartley LH, Vogel JA, Crutz JC (1974) Reduction of maximal exercise heart rate at altitude and its reversal with atropine. J Appl Physiol 36:362–365
Holzfuss J, Mayer-Kress G (1986) An approach to error-estimation in the application of dimension algorithms. In: Mayer-Kress G (ed) Dimensions and entropies in chaotic systems. Quantification of complex behavior. Springer, Berlin Heidelberg New York, pp 114–122
Houston CS, Sutton JR, Cymerman A, Reeves JT (1987) Operation Everest II: Man at extreme altitude. J Appl Physiol 68:877–882
Kennel MB, Brown R, Ararbanel HDI (1992) Determining embedding dimension for phase-space reconstruction using a geometrical construction. Phys Rev A 45:3403–3411
Kobayashi M, Musha T (1982) 1/f Fluctuation of heartbeat period. IEEE Trans Biomed Eng 29:456–457
Mackey MC, Milton JG (1987) Dynamical diseases. Ann N Y Acad Sci 504:16–32
Malconian M, Hultgren H, Nitta M, Anholm J, Houston C, Fails H (1990) The sleep electrocardiogram at extreme altitudes (Operation Everest II). Am J Cardiol 65:1014–1020
Malliani A, Pagani M, Lombardi F, Cerutti S (1991) Cardiovascular neural regulation explored in the frequency domain. Circulation 84:482–492
Mannerville P (1980) Intermittency, self-similarity and 1/f spectrum in dissipative dynamical systems. J Phys 41:1235–1243
Mayes-Kress G, Yates FE, Benton L, Keidel M, Tirsch W, Pöpel SJ, Geist K (1988) Dimensional analysis of nonlinear oscillations in brain, heart, and muscle. Math Biosci 90:155–182
Osborne AR, Provenzale A (1989) Finite correlation dimension for stochastic systems with power-law spectra. Physica D 35:357–381
Pincus SM (1991) Approximate entropy as a measure of system complexity. Proc Natl Acad Sci USA 88:2297–2301
Ruella D (1990) Deterministic chaos: the science and the fiction. Proc R Soc London Ser A 427:241–248
Saul JP (1990) Beat-to-beat variations of heart rate reflect modulation of cardiac autonomic outflow. News Physiol Sci 5:32–37
Schiff SJ, Chang T (1992) Differentiation of linearly correlated noise from chaos in a biologic system using surrogate data. Biol Cybern 67:387–393
Sugihara G, May RM (1990) Nonlinear forecasting as a way of distinguishing chaos from measurement error in time series. Nature 344:734–741
Theiler J (1986) Spurious dimension from correlation algorithms applied to limited time-series data. Phys Rev A 34:2427–2432
Theiler J, Eubank S, Longtin A, Galdrikian B, Farmer JD (1992) Testing for nonlinearity in time series: the method of surrogate data. Physica D 58:77–94
Thompson JMT, Stewart HB (1986) Nonlinear dynamics and chaos. Wiley, New York
Tsuda I, Tahara T, Iwanaga H (1992) Chaotic pulsation in human capillary vessels and its dependence on mental and physical conditions. Int J Bifurcation Chaos 2:313–324
Wales DJ (1991) Calculating the rate of loss of information from chaotic time series by forecasting. Nature 350:485–488
West JB, Peters Jr RM, Aksnes G, Maret KH, Milledge JS, Schoene RB (1986) Nocturnal periodic breathing at altitudes of 6300 and 8050m. J Appl Physiol 61:280–287
Yamamoto Y, Hughson RL (1991) Coarse-graining spectral analysis: new method for studying heart rate variability. J Appl Physiol 71:1143–1150
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Present address and address for correspondence: Laboratory for Exercise Physiology and Biomechanics, Faculty of Education, University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113, Japan
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Yamamoto, Y., Hughson, R.L., Sutton, J.R. et al. Operation Everest II: An indication of deterministic chaos in human heart rate variability at simulated extreme altitude. Biol. Cybern. 69, 205–212 (1993). https://doi.org/10.1007/BF00198960
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DOI: https://doi.org/10.1007/BF00198960