Multifractal Analysis of Physiological Signals: A Novel Approach to Optimizing Pacing Strategy in a Pilot Study

Marathons are one of the ultimate challenges of human endeavor. In this paper, we apply recently introduced multifractal techniques which yield a new classification parameter in the processing of physiological data captured on marathon runners. The comparison of their values gives a new insight on the way that runners of different level conduct their run, and ultimately, can be used in order to give advice on how to improve their performance.

The WQN algorithm for EEG artifact removal in the absence of scale invariance

Electroencephalogram (EEG) signals reflect brain activity across different brain states, characterized by distinct frequency distributions. Through multifractal analysis tools, we investigate the scaling behaviour of different classes of EEG signals and artifacts. We show that brain states associated to sleep and general anaesthesia are not in general characterized by scale invariance. The lack of scale invariance motivates the development of artifact removal algorithms capable of operating independently at each scale. We examine here the properties of the wavelet quantile normalization algorithm, a recently introduced adaptive method for real-time correction of transient artifacts in EEG signals. We establish general results regarding the regularization properties of the WQN algorithm, showing how it can eliminate singularities introduced by artefacts, and we compare it to traditional thresholding algorithms. Furthermore, we show that the algorithm performance is independent of the wavelet basis. We finally examine its continuity and boundedness properties and illustrate its distinctive non-local action on the wavelet coefficients through pathological examples.

A review of univariate and multivariate multifractal analysis illustrated by the analysis of marathon runners physiological data

We review the central results concerning wavelet methods in multifractal analysis, which consists in analysis of the pointwise singularities of a signal, and we describe its recent extension to multivariate multifractal analysis, which deals with the joint analysis of several signals; we focus on the mathematical questions that this new techniques motivate. We illustrate these methods by an application to data recorded on marathon runners.

The WQN algorithm to adaptively correct artifacts in the EEG signal

Wavelet quantile normalization (WQN) is a nonparametric algorithm designed to efficiently remove transient artifacts from single-channel EEG in real-time clinical monitoring. Today, EEG monitoring machines suspend their output when artifacts in the signal are detected. Removing unpredictable EEG artifacts would thus allow to improve the continuity of the monitoring. We analyze the WQN algorithm which consists in transporting wavelet coefficient distributions of an artifacted epoch into a reference, uncontaminated signal distribution. We show that the algorithm regularizes the signal. To confirm that the algorithm is well suited, we study the empirical distributions of the EEG and the artifacts wavelet coefficients. We compare the WQN algorithm to the classical wavelet thresholding methods and study their effect on the distribution of the wavelet coefficients. We show that the WQN algorithm preserves the distribution while the thresholding methods can cause alterations. Finally, we show how the spectrogram computed from an EEG signal can be cleaned using the WQN algorithm.

Multifractal analysis of physiological data from marathon runners

We propose an analysis of heart rate marathon runners implemented by computing a multifractal spectrum based on p-exponents. We draw physiological conclusions about their performance. Finally, we link this analysis with the disturbances of the heart rate autoregulation during the marathon, which had been put in evidence up to now only by scales of feeling of marathon runners during the race.