Dynamical Analysis of Biological Signals with the 0–1 Test: A Case Study of the PhotoPlethysmoGraphic (PPG) Signal

Abstract

The 0–1 test distinguishes between regular and chaotic dynamics for a deterministic system using a time series as a starting point without appealing to any state space reconstruction method. A modification of the 0–1 test allows for the determination of a more comprehensive range of signal dynamic behaviors, particularly in the field of biological signals. We report the results of applying the test and study with more details the PhotoPlethysmoGraphic (PPG) signal behavior from different healthy young subjects, although its use is extensible to other biological signals. While mainly used for heart rate and blood oxygen saturation monitoring, the PPG signal contains extensive physiological dynamics information. We show that the PPG signal, on a healthy young individual, is predominantly quasi-periodic on small timescales (short span of time concerning the dominant frequency). However, on large timescales, PPG signals yield an aperiodic behavior that can be firmly chaotic or a prior transition via an SNA (Strange Nonchaotic Attractor). The results are based on the behavior of well-known time series that are random, chaotic, aperiodic, periodic, and quasi-periodic.

From Frequency Content to Signal Dynamics Using DNNs

“…Because of averaging such a large time window, these dynamic collateral behaviors, whose physiological impact is evident, are masked. Nevertheless, this study reinforces the hypothesis already suggested in previous works [9,10] of the multi-dynamic (multiscale) character present in the PPG signal. In some way, this dynamic multiscalability confirms the information transfer from large to small timescales, whereby a wide variety of subsystems contribute to the regulatory mechanisms of the cardiovascular system.…”

“…The generated signals contain 150,000 points or observations (samples). Their dynamic congruence was verified using a previously formulated procedure [10]. The spectrum of dynamical behaviors could exhibit most of the dynamical behaviors found in the phenomena of the natural world, except for the fruitful dynamism present in the dynamical transitions between stable regimes.…”

“…3. It is important to recall that the analysis of the dynamics of time series using DNNs is not usually studied by the scientific community, as far as the authors know, but from other perspectives [10,26,33,49].…”

“…Understanding signal dynamics makes it possible to conjecture the mechanisms that trigger its generation and, consequently, develop mathematical functional models that increasingly support more reliable reproductions and predictions. Among the sources of data that have been the subject of dynamic studies, there are medical imaging and volumes [1], voice signals [2], radio signals [3], and, more specifically, biological signals, such as EEG [4,5], ECG [6], the EMG [7], and PPG signals [8][9][10] which are the focus of the present work.…”

“…Some ap-proaches directly tackle the modeling of the morphology of the PPG signal [28][29][30][31][32]. In previous work, we looked at the behavior of the PPG signal dynamics from a stochastic perspective by modifying the 0-1 test [10]. We also carried on with the study of its chaoticity level using methods based on DNNs [9].…”