Biotic Patterns of Heart Rate Variation
The above figure compares wavelet plots, recurrence plots and embedding plots of time series of heartbeat intervals,
of chaotic and biotic patterns generated with the process equation. These and other techniques show that the pattern
of heart rate variation is biotic rather than chaotic.
Heart rate variation, a hallmark of cardiac health, appears to be random or chaotic. However, nonlinear dynamic
analysis reveals distinct patterns in the apparently erratic series of heartbeat intervals (RRI: R to R intervals
in the electrocardiogram) of healthy subjects. Similar patterns, that we call biotic, can be generated by the process
equation At+1 = At + g sinAt and variants such as At+1 = At +
g sinAt-1. Complement plots
reveal a regular pattern of concentric rings in RRI series and in integer biotic series, absent in chaotic or random
series. Recurrence plots of RRIs and of biotic series show episodic patterns ("complexes"), while chaotic
series present stable, uniform patterns. In RRI series and in computer-generated bios, recurrence rate is lower
than observed with randomized copies of the series; this feature is an operational definition of novelty, which
is absent in most chaotic series. RRI series and computer-generated biotic series resemble 1/f noise in wavelet
plot patterns and low Hurst exponents (indicating anti-persistence). Bios represents a new and distinct class of
patterns that meets the definition of chaos, and adds features of novelty, division in time-limited complexes in
recurrence and wavelet plots, and (for integer data) ring patterns in complement plots. RRI series display a biotic
pattern approximated by equations that model bipolar feedback.
 
Complement plots of a series of 8000 RRI from a healthy 27 y/o woman
(top). X axis: cosine of RRI; Y axis: sine of RRI. Bottom: complement plots of computer generated series scaled
to integer values within the range obtaining in RRI series: 1/f noise, biotic pattern generated by the process
equation with delay At+1 = At + g * sinAt-1 for g = 3.1, and chaotic and biotic series generated by the process
equation At+1 = At
+ g * sinAt for g 3.7 and 4.7 respectively.
References
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Prepared by Hector Sabelli
Date: August 1999
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