Linguistic Analysis of the Human Heartbeat Using Frequency and Rank Order Statistics

Complex physiologic signals may carry unique dynamical signatures that are related to their underlying mechanisms. We present a method based on rank order statistics of symbolic sequences to investigate the profile of different types of physiologic dynamics. We apply this method to heart rate fluctuations, the output of a central physiologic control system. The method robustly discriminates patterns generated from healthy and pathologic states, as well as aging. Furthermore, we observe increased randomness in the heartbeat time series with physiologic aging and pathologic states and also uncover nonrandom patterns in the ventricular response to atrial fibrillation.

Figure 1

(a) Schematic illustration of the mapping procedure for 8-bit words from part of a 2 h heartbeat time series. (b) Probability distribution of every 8-bit word. The word index ranges from 0 to $2^m-1$ for $m$-bit words. For our example of $m=8$, there is a total of 256 possible words. The word (11000110) shown in (a) is labeled as word $198$ ($=128+64+4+2$). (c) Rank ordered probability plotted on a log-log scale. The linear regime (for rank $\le 50$) is reminiscent of Zipf’s law for natural languages [2].

Figure 2

Rank order comparison of two cardiac interbeat interval time series from the same subject. For each word, its rank in the first time series is plotted against its rank in the second time series. The dashed diagonal line indicates the case where the rank order of words for both time series is identical.

Figure 3

A rooted phylogenetic tree generated according to the distances between different groups. White noise indicates a simulated uncorrelated random time series. The distance ($D$) between any two groups is the summation of the horizontal lengths along the shortest path on the tree that connects them. For example, the distance is 0.211 between healthy young and healthy elderly groups.

Figure 4

Representative interbeat time series for (a) a healthy subject, and (b) a subject with congestive heart failure (CHF). (c) Rank order comparison of the time series in (a) and its randomized surrogate. (d) Rank order comparison of the time series in (b) and its randomized surrogate. The narrower scattering of (d) compared to (c) implies that heartbeat fluctuations in the congestive heart failure subject are more comparable to random than that of the healthy subject. Both (c) and (d) are results for the case $m=8$.

Figure 5

Nonrandomness index ($m=8$) of the interbeat interval time series derived from healthy young and elderly subjects, subjects with congestive heart failure (CHF), subjects with atrial fibrillation (AF), and artificial time series of uncorrelated noise. Values are given as mean $\pm$ standard deviation.