Mathematical Modeling of Stress Using Fractal Geometry; The Power Laws and Fractal Complexity of Stress

Abstract

In this study, we analyze the physiological data during real-world driving tasks to determine whether driver’s relative stress is mono-fractal or multi-fractal. We use the PhysioNet database including long term ECG recordings from 15 healthy volunteers, taken while they were driving on a prescribed route including city streets and highways in and around Boston, Massachusetts. The vibration analysis such as power spectral densities (PSD) analysis has been performed to estimate the exponent from realizations of these pro- cesses and to find out if the signal of interest exhibits a power-law PSD. Multifractal dynamics of heartbeat interval signals have been assessed by multifractal spectrum analysis to explore the possibility that ECG recordings belong to class of multi-fractal process for which a large number of scaling exponents are re- quired to characterize their scaling structures. We apply Higuchi algorithm to find the fractal complexity of each cardiac rhythm for different time intervals. According to our analysis, we investigate that driver’s ECG signals under relative stress follows fractal behavior unlike control healthy signals which are multi-fractal. Our findings provide a comprehensive framework for detect stress and differentiate people who experience stress with normal people without stress which is crucial in finding the best diagnostic and controlling strat- egy in fight against many health problems due to stress, such as high blood pressure, heart disease, obesity and diabetes. Moreover, being able to recognize stress can help us to manage it.