Binary symbolic dynamics classifies heart rate variability patterns linked to autonomic modulations
Introduction
The variations of the cardiac interbeat series reflect the complex interplay between the parasympathetic and the sympathetic branch of the autonomic nervous system (ANS). Standard measures in the frequency domain have been linked to the activity of both the branches: high frequency (HF: 0.15–0.4 Hz) oscillations of the cardiac interbeat series reflects parasympathetic modulations whereas low frequency oscillations (LF: 0.04–0.15 Hz) reflect cardiac sympathetic and parasympathetic modulations [1]. Furthermore, the ratio LF/HF is often used as a noninvasive index for the balance between sympathetic and parasympathetic modulations [2]. The usage of these noninvasive indices has stimulated a strong debate whether they effectively reveal the underlying alterations of the ANS [3], [4], [5], [6]. Unfortunately, this analysis is not helpful in deriving information about the patterns as short as few beats (≈10 consecutive interbeat intervals).
The analysis of the cardiac interbeat interval series on short time scales may be accomplished by the analysis of symbolic time series. The instantaneous heart rate can e.g. be symbolized by four different symbols reflecting the closeness of each interbeat interval to the average interbeat interval [7], [8], [9]. The complexity of such symbolic time series may be analyzed using the Shannon or Renyi entropy [7]. Using this kind of symbolization yields additional information in the form of frequencies of specific ‘words’ and forbidden ‘words’ that complements measures of spectral analysis in e.g. patients after myocardial infarction [9]. Another approach of symbolization is the division of the full range of cardiac interbeat intervals (minimum interbeat interval to maximum interbeat interval) into several equidistant classes [10]. Classifying this kind of symbolization with respect to the variations (i.e. frequencies of symbolic patterns with 0, 1 or 2 variations of the symbols) also supplements the information found in traditional frequency domain measures [11], [12]. The analysis of graded head-up tilt data showed that the frequencies of specific symbolic patterns may be used to assess sympathetic and parasympathetic modulations of the ANS [12].
In our group, the succession of accelerations and decelerations of the cardiac interbeat intervals is simply symbolized with two different symbols. Short binary patterns have been extracted from the symbolized series and Approximate Entropy (ApEn) was utilized to measure regularity (complexity) of the extracted patterns [13]. Surprisingly, although the heart rate dynamics of healthy subjects is known to show a high degree of complexity [14], there is a high frequency of regular binary patterns in such subjects (notwithstanding a considerable amount of irregular patterns) [15]. On the contrary, patients with congestive heart failure showed binary patterns characterized by a high level of complexity, which is typical of random behavior. Hence, this approach yields different information when compared to parameters in the frequency domain or parameters derived from nonlinear dynamics.
The appearance of regular binary patterns is closely linked to oscillations of the cardiac interbeat intervals at low frequencies whereas irregular patterns appear due to oscillations of cardiac interbeat intervals at higher frequencies [15]. However, a clear link between the appearance of specific binary patterns to the activity of the sympathetic or parasympathetic branch of the ANS has yet to be demonstrated. In this study, we aim to further clarify this link. For this purpose, we study the cardiac interbeat intervals during an experimental protocol leading to the progressive increase of sympathetic modulation and to the associated gradual decrease of parasympathetic one [16].
Section snippets
Experimental protocol
17 healthy subjects (non-smoker, median age: 28 years, age range 21–54 years, 7 women) were enrolled in the study at the University of Milan. The subjects did not take any medication, nor did they consume any caffeine- or alcohol-containing beverages in 24 h before the recording. While the subjects were on the tilt table, they were supported by two belts at the level of the thigh and the waist. Both feet touched the footrest of the tilt table. The subjects breathed spontaneously but were not
Results
Table 1 lists the mean and standard deviation of the HRV measures. The mean R–R interval was 991 ms during rest and decreased with increasing tilt angle (r=−0.68, see Table 2). The decrease in the average R–R interval was accompanied by a decrease in the measures of the time domain, RMSSD and SDNN, i.e. these measures also showed a negative correlation (r=−0.58, and r=−0.20). In the frequency domain, HF variations () decreased with increasing tilt angle (r=−0.56) whereas LF variations ()
Discussion
The proposed analysis provides a tool, which tracks changes of complexity as a function of different tilt table angles (i.e. different levels of autonomic modulation). In contrast to a previous analysis based on the calculation of complexity of the entire series [21], [22], the observed changes of complexity can be attributed to the presence of specific binary patterns characterized by definite values of complexity. Many regular pattern sets, i.e. regular binary patterns occur more often with
Conflict of interest statement
The authors do not have any conflict of interest.
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