Entropy-Based Multifractal Testing of Heart Rate Variability during Cognitive-Autonomic Interplay

Entropy-based and fractal-based metrics derived from heart rate variability (HRV) have enriched the way cardiovascular dynamics can be described in terms of complexity. The most commonly used multifractal testing, a method using q moments to explore a range of fractal scaling in small-sized and large-sized fluctuations, is based on detrended fluctuation analysis, which examines the power-law relationship of standard deviation with the timescale in the measured signal. A more direct testing of a multifractal structure exists based on the Shannon entropy of bin (signal subparts) proportion. This work aims to reanalyze HRV during cognitive tasks to obtain new markers of HRV complexity provided by entropy-based multifractal spectra using the method proposed by Chhabra and Jensen in 1989. Inter-beat interval durations (RR) time series were obtained in 28 students comparatively in baseline (viewing a video) and during three cognitive tasks: Stroop color and word task, stop-signal, and go/no-go. The new HRV estimators were extracted from the f/α singularity spectrum of the RR magnitude increment series, established from q-weighted stable (log-log linear) power laws, namely: (i) the whole spectrum width (MF) calculated as α_max - α_min; the specific width representing large-sized fluctuations (MF_large) calculated as α₀ - α_q+; and small-sized fluctuations (MF_small) calculated as α_q- - α₀. As the main results, cardiovascular dynamics during Stroop had a specific MF signature while MF_large was rather specific to go/no-go. The way these new HRV markers could represent different aspects of a complete picture of the cognitive-autonomic interplay is discussed, based on previously used entropy- and fractal-based markers, and the introduction of distribution entropy (DistEn), as a marker recently associated specifically with complexity in the cardiovascular control.