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.