Diffusion Entropy vs. Multiscale and Rényi Entropy to Detect Progression of Autonomic Neuropathy

Abstract

We review the literature to argue the importance of the occurrence of crucial events in the dynamics of physiological processes. Crucial events are interpreted as short time intervals of turbulence, and the time distance between two consecutive crucial events is a waiting time distribution density with an inverse power law (IPL) index μ, with μ < 3 generating non-stationary behavior. The non-stationary condition is characterized by two regimes of the IPL index: (a) perennial non-stationarity, with 1 < μ < 2 and (b) slow evolution toward the stationary regime, with 2 < μ < 3. Human heartbeats and brain dynamics belong to the latter regime, with healthy physiological processes tending to be closer to the border with the perennial non-stationary regime with μ = 2. The complexity of cognitive tasks is associated with the mental effort required to address a difficult task, which leads to an increase of μ with increasing task difficulty. On this basis we explore the conjecture that disease evolution leads the IPL index μ moving from the healthy condition μ = 2 toward the border with Gaussian statistics with μ = 3, as the disease progresses. Examining heart rate time series of patients affected by diabetes-induced autonomic neuropathy of varying severity, we find that the progression of cardiac autonomic neuropathy (CAN) indeed shifts μ from the border with perennial variability, μ = 2, to the border with Gaussian statistics, μ = 3 and provides a novel, sensitive index for assessing disease progression. We find that at the Gaussian border, the dynamical complexity of crucial events is replaced by Gaussian fluctuation with long-time memory.

Biophotons and Emergence of Quantum Coherence—A Diffusion Entropy Analysis

“…In the recent past the DEA method has been applied to a wide variety of problems, from the study of amino acid sequences in DNA [ 50 ], to Mozart’s music [ 51 , 52 ] up to the progression of autonomic neuropathy [ 53 ] looking for the heartbeat signal. Here, for the first time, this approach is applied to the biophotons emitted from germinating seeds.…”

“…It is also important to notice that the authors of Ref. [ 53 ], who analyzed the heartbeats of patients under the influence of autonomic neuropathy, found that the increasing severity of this disease has the effect of making μ move from the healthy condition close to μ = 2 to the border with ordinary statistical physics, μ = 3, while the spectrum keeps the character of 1/f noise. It is so because the physiological system moves from a complexity condition generated by crucial events to a complexity condition characterized by the FBM infinite memory.…”

“…[ 14 ] is indeed an important ingredient of the physiological mechanism of information coding, transmission, and processing in the nervous system. However, we do not rule out the connection with self-organized criticality that may be the source of the joint action of the infinite FBM memory and crucial events [ 53 ]. We shall explore this important issue by comparing the transition to FBM induced by autonomic neuropathy disease in human beings [ 53 ] to the hypotheses of stress signaled by biophoton emission [ 63 , 64 ].…”

“…However, we do not rule out the connection with self-organized criticality that may be the source of the joint action of the infinite FBM memory and crucial events [ 53 ]. We shall explore this important issue by comparing the transition to FBM induced by autonomic neuropathy disease in human beings [ 53 ] to the hypotheses of stress signaled by biophoton emission [ 63 , 64 ]. We hope that the present paper may contribute to shedding further light on the role played by biophotons on these processes.…”

Complexity and Entropy in Physiological Signals (CEPS): Resonance Breathing Rate Assessed Using Measures of Fractal Dimension, Heart Rate Asymmetry and Permutation Entropy

“…As well as the introduction of many more measures, other changes to CEPS since its first version include the ability to modify data (normalisation, binarisation, interpolation, coarse-graining, addition of coloured and other noises, data segmentation with or without overlapping windows, resampling and detrending), as well as an analysis section for displaying plots and results from multidimensional or graphical measures (currently only two [8,9]. Other measures also in course of implementation include diffusion entropy [10,11], Emergence, Self-Organization and Complexity [12]. At the end of the article, we have included a list of the more than 200 abbreviations used.…”