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

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 mu, with mu < 3 generating non-stationary behavior. The non-stationary condition is characterized by two regimes of the IPL index: (a) perennial non-stationarity, with 1 < mu < 2 and (b) slow evolution toward the stationary regime, with 2 < mu < 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 mu = 2. The complexity of cognitive tasks is associated with the mental effort required to address a difficult task, which leads to an increase of mu with increasing task difficulty. On this basis we explore the conjecture that disease evolution leads the IPL index mu moving from the healthy condition mu = 2 toward the border with Gaussian statistics with mu = 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 mu from the border with perennial variability, mu = 2, to the border with Gaussian statistics, mu = 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.

Automated summary

The study emphasizes the importance of crucial events in physiological dynamics, where they are defined as short-term turbulence phenomena with waiting time distribution density. The index of the distribution determines the stability of the process, with healthy physiological processes being closer to the non-stationary regime. Disease progression is observed to shift the IPL index towards Gaussian statistics, providing a new index for assessing disease severity.