Multiscale Entropy Analysis of Physiological Time Series Signals

Abstract

Healthy physiological regulation is thought to produce time series with complex, multiscale structure, while disease
and aging are associated with a loss of this complexity that single-scale entropy measures can fail to detect. We
applied multiscale entropy analysis, computing sample entropy across temporal coarse-graining scales 1 through
20, to de-identified interbeat-interval recordings from 214 subjects drawn from three groups: 86 young healthy
adults (mean age 28.4 years), 79 older healthy adults (mean age 67.1 years), and 49 age-matched patients with
congestive heart failure (mean age 66.8 years), each recording spanning a minimum of 4 hours of continuous
ambulatory monitoring. Complexity index, defined as the area under the multiscale entropy curve across all 20
scales, was highest in young healthy adults (12.84 ± 1.63), intermediate in older healthy adults (10.21 ± 1.79), and
lowest in the heart failure group (6.47 ± 2.05), with all three pairwise group differences significant (one-way ANOVA
F(2,211) = 154.7, p < 0.001; post hoc Tukey tests p < 0.001 for all pairs). Single-scale sample entropy at scale 1,
equivalent to conventional short-timescale entropy analysis, distinguished the heart failure group from young
healthy adults (Cohen's d = 1.14) but showed substantially weaker separation between young and older healthy
adults (Cohen's d = 0.31, p = 0.04), whereas the multiscale complexity index separated these same two healthy
groups with much larger effect size (Cohen's d = 1.58, p < 0.001), indicating that multiscale analysis captured
age-related complexity loss largely invisible to single-scale entropy. Complexity loss was concentrated at
intermediate-to-large coarse-graining scales, corresponding to timescales of roughly 10-20 heartbeats: entropy at
scale 5 and above accounted for 71% of the total between-group variance in complexity index, compared to only
8% attributable to scale 1 alone. A logistic regression classifier using complexity index alone distinguished heart
failure patients from age-matched healthy adults with an area under the receiver operating characteristic curve of
0.91, compared to 0.76 for a classifier using scale-1 sample entropy alone. These findings support multiscale
entropy, particularly its intermediate-to-large-scale components, as a substantially more sensitive marker of both
healthy aging and pathological autonomic dysfunction than conventional single-scale entropy measures.