Heart Rate Fragmentation: A Symbolic Dynamical Approach

Abstract

Background: We recently introduced the concept of heart rate fragmentation along with a set of metrics for its quantification. The term was coined to refer to an increase in the percentage of changes in heart rate acceleration sign, a dynamical marker of a type of anomalous variability. The effort was motivated by the observation that fragmentation, which is consistent with the breakdown of the neuroautonomic-electrophysiologic control system of the sino-atrial node, could confound traditional short-term analysis of heart rate variability. Objective: The objectives of this study were to: (1) introduce a symbolic dynamical approach to the problem of quantifying heart rate fragmentation; (2) evaluate how the distribution of the different dynamical patterns ("words") varied with the participants' age in a group of healthy subjects and patients with coronary artery disease (CAD); and (3) quantify the differences in the fragmentation patterns between the two sample populations. Methods: The symbolic dynamical method employed here was based on a ternary map of the increment NN interval time series and on the analysis of the relative frequency of symbolic sequences (words) with a pre-defined set of features. We analyzed annotated, open-access Holter databases of healthy subjects and patients with CAD, provided by the University of Rochester Telemetric and Holter ECG Warehouse (THEW). Results: The degree of fragmentation was significantly higher in older individuals than in their younger counterparts. However, the fragmentation patterns were different in the two sample populations. In healthy subjects, older age was significantly associated with a higher percentage of transitions from acceleration/deceleration to zero acceleration and vice versa (termed "soft" inflection points). In patients with CAD, older age was also significantly associated with higher percentages of frank reversals in heart rate acceleration (transitions from acceleration to deceleration and vice versa, termed "hard" inflection points). Compared to healthy subjects, patients with CAD had significantly higher percentages of soft and hard inflection points, an increased percentage of words with a high degree of fragmentation and a decreased percentage of words with a lower degree of fragmentation. Conclusion: The symbolic dynamical method employed here was useful to probe the newly recognized property of heart rate fragmentation. The findings from these cross-sectional studies confirm that CAD and older age are associated with higher levels of heart rate fragmentation. Furthermore, fragmentation with healthy aging appears to be phenotypically different from fragmentation in the context of CAD.

Keywords: aging; coronary artery disease; fragmentation; heart rate variability; symbolic dynamics; vagal tone.

Figure 1

Examples of respiratory sinus arrhythmia and anomalous (fragmented) sinus rhythm. Electrocardiograms (Holter lead) from a healthy subject (first row) and a patient with coronary artery disease (CAD) (second row), both from the present study. Normal-to-normal (NN) sinus interval time series from the healthy subject (third row, left) and the patient with CAD (third row, right). The fluctuation patterns of the former time series are characteristic of phasic (respiratory) sinus arrhythmia, while that of the latter are indicative of an abnormal, non-phasic sinus arrhythmia (Costa et al., 2017). Positive and negative changes in the value of the NN intervals, corresponding to heart rate decelerations and accelerations were mapped to symbols “−1” and “1,” respectively. Symbol “0” is used to represent intervals in which heart rate did not change. To assist in visual comparisons, pale gray backgrounds are used for data from the healthy subject and light red for data from the patient with CAD, respectively. The symbolic mapping of the differences between consecutive NN intervals for the ECG of the healthy subject (first 16 intervals) along with the first four words that were derived from this sequence are shown on the bottom left. The first word “−1−111” contains one hard inflection point. It belongs to the group W₁ and, more specifically, to the subgroup ${\mathrm{\text{W}}}_1^{\mathrm{\text{H}}}$. The following three words, “−1110,” “110−1,” and “10−1−1” contain two inflection points. Therefore, they belong to group W₂. However, the first word (“−1110”) belongs to the subgroup ${\mathrm{\text{W}}}_2^{\mathrm{\text{M}}}$ since it contains one hard and one soft inflection point; the second (“110−1”) and the third (“10−1−1”) words belong to the subgroup ${\mathrm{\text{W}}}_2^{\mathrm{\text{S}}}$ since they present two soft inflection points. The panels on the bottom right show the percentage of words in each group for the healthy subject (left) and patient with CAD (right). Note a substantially higher percentage of fragmented words for the patient with CAD than for the healthy subject. The abbreviation “a.u.” stands for arbitrary units.

Figure 2

Schematic representation of all (#81) different words of length 4 with an alphabet of 3 symbols. The symbols “/”, “\”, and “−” represent heart rate acceleration, deceleration and no change, respectively. Words were grouped by the number and type of inflection points. The labels, 0–80, shown in parentheses, are the decimal value of the ternary representation of each pattern using the symbols “2” if ΔNN_i < 0, “1” if ΔNN_i > 0 and “0” if ΔNN_i = 0. For example, the label for the word comprising 4 consecutive accelerations, i.e., the word 2222, is 80 (= 2 × 3³+2 × 3²+2 × 3¹+2 × 3⁰). Abbreviations: W, word subgroup. The subscript and superscript of W indicate, respectively, the number and the type of inflection points, hard (H), soft (S) or a combination of hard and soft (M, mixed) that the words in that subgroup contain.

Figure 3

Relationship between the percentage of words with no inflection points (W₀), one (W₀), two (W₀) and three (W₀) inflection points and the participants' age for the healthy subjects (blue) and those with coronary artery disease (CAD, red) during the 24-h (A), putative awake (B) and putative sleep (C) periods. Symbols and lines represent, respectively, word percentages for each subject and the regression lines derived from linear regression analyses controlled for the average NN interval. In each plot, the rates of change of the outcome variables per year of age for the healthy subjects and the patients with CAD are indicated in blue and red, respectively.