Detrended fluctuation analysis in a simple spreadsheet as a tool for teaching fractal physiology

Abstract

Fractal physiology demonstrated growing interest over the last decades among physiologists, neuroscientists, and clinicians. Many physiological systems coordinate themselves for reducing variability and maintain a steady state. When recorded over time, the output signal exhibits small fluctuations around a stable value. It is becoming increasingly clear that these fluctuations, in most free-running healthy systems, are not simply due to uncorrelated random errors and possess interesting properties, one of which is the property of fractal dynamics. Fractal dynamics model temporal processes in which similar patterns occur across multiple timescales of measurement. Smaller copies of a pattern are nested within larger copies of the pattern, a property termed scale invariance. It is an intriguing process that may deserve attention for implementing curricular development for students to reconsider homeostasis. Teaching fractal dynamics needs to make calculating resources available for students. The present paper offers a calculating resource that uses a basic formula and is executable in a simple spreadsheet. The spreadsheet allows computing detrended fluctuation analysis (DFA), the most frequently used method in the literature to quantify the fractal-scaling index of a physiological time series. DFA has been nicely described by the group at Harvard that designed it; the authors made the C language source available. Going further, it is suggested here that a guide to build DFA step by step in a spreadsheet has many advantages for teaching fractal physiology and beyond: 1) it promotes the DIY (do-it-yourself) in students and highlights scaling concepts; and 2) it makes DFA available for people not familiarized with executing code in C language.

Detrended Fluctuation, Coherence, and Spectral Power Analysis of Activation Rearrangement in EEG Dynamics During Cognitive Workload

“…Furthermore, the recent introduction of DFA technique for heart rate variability measuring appears to provide improved prognostic methods of cardiovascular diseases diagnostics by calculating the alpha fractal scaling component (Willson et al, 2002; Chiang et al, 2016). As it was noted by Arsac and Deschodt-Arsac (2018), in the last decade there has been a growing interest in fractal physiology among neuroscientists and clinicians. Many physiological systems coordinate themselves to reduce variability and maintain a steady-state.…”

Correlation between heart rate variability and polysomnography-derived scores of obstructive sleep apnea

“…Al-Angari and Sahakian ( 2007) study also found a significant reduction in SampEn in patients with OSA, supporting the notion that these patients have a more predictable heart rate oscillation. Altogether, those findings with DFA and entropy indicate that patients with OSA have altered fractal dynamics and decreased unpredictability of heart rate oscillations, a condition consistent with loss of physiological complexity in patients with OSA (Goldberger et al, 2002;Burggren and Monticino, 2005;Porta et al, 2007a;Arsac and Deschodt-Arsac, 2018). Although none of the asymmetry indices were found different among groups, the acceleration capacity is decreased in patients with moderate OSA.…”

Adaptive Capacities and Complexity of Heart Rate Variability in Patients With Chronic Obstructive Pulmonary Disease Throughout Pulmonary Rehabilitation

“…After artifact correction, a series of 256 R-R intervals was retained for each participant under each experimental condition for subsequent analyses, in accordance with previous guidelines ( Shaffer and Ginsberg, 2017 ) and in order to have the same number of intervals for each subject ( Ribeiro et al, 2018 ). Series of R-R intervals were linearly detrended before evaluating their complexity, in accordance with standard methodology ( Peng et al, 1995 ; Delignières et al, 2005 ; Arsac and Deschodt-Arsac, 2018 ).…”

“…DFA was used because it provides reliable results for “short” time series, especially for 256 data ( Almurad and Delignières, 2016 ; Liddy and Haddad, 2018 ). The DFA methodology was previously described ( Delignières et al, 2005 ; Almurad and Delignières, 2016 ; Arsac and Deschodt-Arsac, 2018 ; Liddy and Haddad, 2018 ). To sum up, DFA analyses the relationship between the average fluctuation amplitude and the size of the observation window where these fluctuations are measured.…”