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.
Highlights
Heart rate analysis and heart rate variability (HRV) analysis has proven to be a useful adjunct feature for clinical medicine (Javorka et al, 2008; Huikuri et al, 2009; Hu et al, 2010; Lake, 2011)
Entropy-derived measures including Sample Entropy, Multiscale Entropy (MSE), and Rényi Entropy have been applied for early identification of sepsis and analysis of diabetes and cardiovascular diseases (CVD) (Oida et al, 1999; Lake et al, 2002; Costa and Healy, 2003; Lake, 2006; Valencia et al, 2009; Cornforth et al, 2015; Kohnert et al, 2018; Jelinek et al, 2019)
The non-crucial events can be either the ordinary Poisson events or events generated by Type I 1/f -noise
Summary
Heart rate analysis and heart rate variability (HRV) analysis has proven to be a useful adjunct feature for clinical medicine (Javorka et al, 2008; Huikuri et al, 2009; Hu et al, 2010; Lake, 2011). Descriptive features sensitive to characteristics of a time series need to be understood in terms of their explanatory power of the process they are measuring. Entropy-derived measures including Sample Entropy, Multiscale Entropy (MSE), and Rényi Entropy have been applied for early identification of sepsis and analysis of diabetes and cardiovascular diseases (CVD) (Oida et al, 1999; Lake et al, 2002; Costa and Healy, 2003; Lake, 2006; Valencia et al, 2009; Cornforth et al, 2015; Kohnert et al, 2018; Jelinek et al, 2019). Applying a coarse-graining procedure to the experimental time series of the interbeat fluctuations (RR intervals) provides a mathematical model to describe the bio-signal associated with heart rate fluctuations
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