Pergamon Chaos, .Solmns & A'-rac~uls, Vol. 9. No. 3, pp. 507-515, 199X 0 1998 Elsevier Science Ltd. All rights reserved Printed in Great Brit:dn 0960.0779198 $lY.OO+OMl PII: SO960-0779(97)00082-9 Predictability and Nonlinearity of the Heart Rhythm MICHELE BARBI, SANTI CHILLEMI, ANGELO DI GARBO Istituto di Biofisica de1 CNR, Via S. Lorenzo 26, 56127 Pisa, Italy and RITA BALOCCHI, CLARA CARPEGGIANI, MICHELE EMDIN, CLAUDIO MICHELASSI, ENRICA SANTARCANGELO Istituto di Fisiologia Clinica de1 CNR, Via Trieste 41, 56126 Pisa, Italy (Accepted 14 March 1997) Abstract&Sequences of interbeat intervals from 24 subjects in relaxed conditions are analysed by the classical nonlinear prediction method as well as by a direct one, able to estimate the time series nonlinearity. The two approaches yield very similar results, showing that a clear nonlinear behaviour is present in most of the examined sequences. Furthermore, a completely different method, detrended jktuation analysis, is applied to the data. Unexpectedly, the corresponding statistics strongly correlates with the estimators of nonlinearity. 0 1998 Elsevier Science Ltd. All rights reserved 1. INTRODUCTION There is growing interest in the issue of whether both neuronal ensembles [l, 21 and the heart [3,4] generate activities that are irregular yet predictable. In addition, reliable techniques now exist that are capable of exerting control over complex or possibly chaotic biological systems like cardiac tissue [5] and epileptic foci [6]. Since a chaotic system is characterised by its short-term predictability and nonlinearity, the search for these two features in biological time series has become important for the assessment of chaotic behaviour and the comprehension of its physiological meaning. The suggestive hypothesis that the cardiac rhythm may also exhibit the features of deterministic low-dimensional chaos [7] is still under debate [8,9]; so it should be worth investigating some features of the normal sinus rhythm, related to deterministic chaos. In particular, nonlinearity could play an important role. Recently, a number of techniques for making predictions have been developed. Most of them aim to describe the short-term structure of the experimental time series by curves plotting either the normalised prediction error [lo, 111 or the correlation coefficient [12] against the prediction time. These representations are useful to identify extreme behaviours (purely deterministic, or white noise) but are not sufficient to reach clear conclusions in more complicated situations with unknown amounts of autocorrelated noise. Nevertheless, this approach can be a useful tool to detect chaotic behaviour provided suitable controls are carried out simultaneously on the temporal series. Since the hallmark of a chaotic system is a deterministic structure beyond that corresponding to its autocorrelation, an important test is the one based on surrogate data [13]. Surrogate time series are obtained from experimental ones by randomising them in such a way as to preserve certain features (mean, standard deviation, autocorrelation function); or, in other words, by destroying any determinism beyond that implied by second order statistics. Several surrogates are usually created for 507