Quantifying Non-Stationarity with Information Theory.

We introduce an index based on information theory to quantify the stationarity of a stochastic process. The index compares on the one hand the information contained in the increment at the time scale τ of the process at time t with, on the other hand, the extra information in the variable at time t that is not present at time t-τ. By varying the scale τ, the index can explore a full range of scales. We thus obtain a multi-scale quantity that is not restricted to the first two moments of the density distribution, nor to the covariance, but that probes the complete dependences in the process. This index indeed provides a measure of the regularity of the process at a given scale. Not only is this index able to indicate whether a realization of the process is stationary, but its evolution across scales also indicates how rough and non-stationary it is. We show how the index behaves for various synthetic processes proposed to model fluid turbulence, as well as on experimental fluid turbulence measurements.

Distance to Healthy Metabolic and Cardiovascular Dynamics From Fetal Heart Rate Scale-Dependent Features in Pregnant Sheep Model of Human Labor Predicts the Evolution of Acidemia and Cardiovascular Decompensation.

The overarching goal of the present work is to contribute to the understanding of the relations between fetal heart rate (FHR) temporal dynamics and the well-being of the fetus, notably in terms of predicting the evolution of lactate, pH and cardiovascular decompensation (CVD). It makes uses of an established animal model of human labor, where 14 near-term ovine fetuses subjected to umbilical cord occlusions (UCO) were instrumented to permit regular intermittent measurements of metabolites lactate and base excess, pH, and continuous recording of electrocardiogram (ECG) and systemic arterial blood pressure (to identify CVD) during UCO. ECG-derived FHR was digitized at the sampling rate of 1,000 Hz and resampled to 4 Hz, as used in clinical routine. We focused on four FHR variability features which are tunable to temporal scales of FHR dynamics, robustly computable from FHR sampled at 4 Hz and within short-time sliding windows, hence permitting a time-dependent, or local, analysis of FHR which helps dealing with signal noise. Results show the sensitivity of the proposed features for early detection of CVD, correlation to metabolites and pH, useful for early acidosis detection and the importance of coarse time scales (2.5-8 s) which are not disturbed by the low FHR sampling rate. Further, we introduce the performance of an individualized self-referencing metric of the distance to healthy state, based on a combination of the four features. We demonstrate that this novel metric, applied to clinically available FHR temporal dynamics alone, accurately predicts the time occurrence of CVD which heralds a clinically significant degradation of the fetal health reserve to tolerate the trial of labor.

Kullback-Leibler divergence measure of intermittency: Application to turbulence.

For generic systems exhibiting power law behaviors, and hence multiscale dependencies, we propose a simple tool to analyze multifractality and intermittency, after noticing that these concepts are directly related to the deformation of a probability density function from Gaussian at large scales to non-Gaussian at smaller scales. Our framework is based on information theory and uses Shannon entropy and Kullback-Leibler divergence. We provide an extensive application to three-dimensional fully developed turbulence, seen here as a paradigmatic complex system where intermittency was historically defined and the concepts of scale invariance and multifractality were extensively studied and benchmarked. We compute our quantity on experimental Eulerian velocity measurements, as well as on synthetic processes and phenomenological models of fluid turbulence. Our approach is very general and does not require any underlying model of the system, although it can probe the relevance of such a model.

Mutual information for intrapartum fetal heart rate analysis.

The analysis of the temporal dynamics in intrapartum fetal heart rate (FHR), aiming at early detection of fetal acidosis, constitutes an intricate signal processing task, that continuously receives significant research efforts. Entropy and entropy rates, envisaged as measures of complexity, often computed via popular implementations referred to as Approximate Entropy (ApEn) or Sample Entropy (SampEn), have regularly been reported as significant features for intrapartum FHR analysis. The present contribution aims to show how mutual information enhances characterization of FHR temporal dynamics and improves fetal acidosis detection performance. To that end, mutual information is first connected to ApEn and SampEn both conceptually and with respect to estimation procedure. Second, mutual information, ApEn and SampEn are computed on a large (≃ 1000 subjects) and documented database of FHR data, collected in a French academic hospital. Reported results show that the use of mutual information permits to significantly outperform ApEn and SampEn for acidosis detection, during any stage of labor.

Comparative Multifractal Analysis of Dynamic Infrared Thermograms and X-Ray Mammograms Enlightens Changes in the Environment of Malignant Tumors.

There is growing evidence that the microenvironment surrounding a tumor plays a special role in cancer development and cancer therapeutic resistance. Tumors arise from the dysregulation and alteration of both the malignant cells and their environment. By providing tumor-repressing signals, the microenvironment can impose and sustain normal tissue architecture. Once tissue homeostasis is lost, the altered microenvironment can create a niche favoring the tumorigenic transformation process. A major challenge in early breast cancer diagnosis is thus to show that these physiological and architectural alterations can be detected with currently used screening techniques. In a recent study, we used a 1D wavelet-based multi-scale method to analyze breast skin temperature temporal fluctuations collected with an IR thermography camera in patients with breast cancer. This study reveals that the multifractal complexity of temperature fluctuations superimposed on cardiogenic and vasomotor perfusion oscillations observed in healthy breasts is lost in malignant tumor foci in cancerous breasts. Here we use a 2D wavelet-based multifractal method to analyze the spatial fluctuations of breast density in the X-ray mammograms of the same panel of patients. As compared to the long-range correlations and anti-correlations in roughness fluctuations, respectively observed in dense and fatty breast areas, some significant change in the nature of breast density fluctuations with some clear loss of correlations is detected in the neighborhood of malignant tumors. This attests to some architectural disorganization that may deeply affect heat transfer and related thermomechanics in breast tissues, corroborating the change to homogeneous monofractal temperature fluctuations recorded in cancerous breasts with the IR camera. These results open new perspectives in computer-aided methods to assist in early breast cancer diagnosis.

Wavelet-based multifractal analysis of dynamic infrared thermograms to assist in early breast cancer diagnosis.

Breast cancer is the most common type of cancer among women and despite recent advances in the medical field, there are still some inherent limitations in the currently used screening techniques. The radiological interpretation of screening X-ray mammograms often leads to over-diagnosis and, as a consequence, to unnecessary traumatic and painful biopsies. Here we propose a computer-aided multifractal analysis of dynamic infrared (IR) imaging as an efficient method for identifying women with risk of breast cancer. Using a wavelet-based multi-scale method to analyze the temporal fluctuations of breast skin temperature collected from a panel of patients with diagnosed breast cancer and some female volunteers with healthy breasts, we show that the multifractal complexity of temperature fluctuations observed in healthy breasts is lost in mammary glands with malignant tumor. Besides potential clinical impact, these results open new perspectives in the investigation of physiological changes that may precede anatomical alterations in breast cancer development.

Self-similar anisotropic texture analysis: the hyperbolic wavelet transform contribution.

Textures in images can often be well modeled using self-similar processes while they may simultaneously display anisotropy. The present contribution thus aims at studying jointly selfsimilarity and anisotropy by focusing on a specific classical class of Gaussian anisotropic selfsimilar processes. It will be first shown that accurate joint estimates of the anisotropy and selfsimilarity parameters are performed by replacing the standard 2D-discrete wavelet transform with the hyperbolic wavelet transform, which permits the use of different dilation factors along the horizontal and vertical axes. Defining anisotropy requires a reference direction that needs not a priori match the horizontal and vertical axes according to which the images are digitized; this discrepancy defines a rotation angle. Second, we show that this rotation angle can be jointly estimated. Third, a nonparametric bootstrap based procedure is described, which provides confidence intervals in addition to the estimates themselves and enables us to construct an isotropy test procedure, which can be applied to a single texture image. Fourth, the robustness and versatility of the proposed analysis are illustrated by being applied to a large variety of different isotropic and anisotropic self-similar fields. As an illustration, we show that a true anisotropy built-in self-similarity can be disentangled from an isotropic self-similarity to which an anisotropic trend has been superimposed.

A wavelet-based method for local phase extraction from a multi-frequency oscillatory signal.

One of the challenges in analyzing neuronal activity is to correlate discrete signal, such as action potentials with a signal having a continuous waveform such as oscillating local field potentials (LFPs). Studies in several systems have shown that some aspects of information coding involve characteristics that intertwine both signals. An action potential is a fast transitory phenomenon that occurs at high frequencies whereas a LFP is a low frequency phenomenon. The study of correlations between these signals requires a good estimation of both instantaneous phase and instantaneous frequency. To extract the instantaneous phase, common techniques rely on the Hilbert transform performed on a filtered signal, which discards temporal information. Therefore, time-frequency methods are best fitted for non-stationary signals, since they preserve both time and frequency information. We propose a new algorithmic procedure that uses wavelet transform and ridge extraction for signals that contain one or more oscillatory frequencies and whose oscillatory frequencies may shift as a function of time. This procedure provides estimates of phase, frequency and temporal features. It can be automated, produces manageable amounts of data and allows human supervision. Because of such advantages, this method is particularly suitable for analyzing synchronization between LFPs and unitary events.

Respiratory cycle as time basis: an improved method for averaging olfactory neural events.

In the mammalian olfactory system, neural activity appears largely modulated by respiration. Accurate analysis of respiratory synchronized activity is precluded by the variability of the respiratory frequency from trial to trial. Thus, the use of respiratory cycle as the time basis for measuring cell responses was developed about 20 years ago. Nevertheless, averaging oscillatory component of the activity remains a challenge due to their rhythmic features. In this paper, we present a new respiratory monitoring setup based on the measurement of micropressure changes induced by nasal airflow in front of the nostril. Improvements provided by this new monitoring setup allows automatic processing of respiratory signals in order to extract each respiratory period (expiration and inspiration). The time component of these periods, which can differ from trial to trial, is converted into a phase component defined as [-pi, 0] and [0, pi] for inspiration and expiration, respectively. As opposed to time representation, the phase representation is common to all trials. Thus, this phase representation of the respiratory cycle is used as a normalized time basis permitting to collect results in a standardized data format across different animals and providing new tools to average oscillatory components of the activity.