Heartbeat Dynamics Analysis under Cold-Pressure Test using Wavelet p-Leader Non-Gaussian Multiscale Expansions.

Multiscale and multifractal (MF) analyses have been proven an effective tool for the characterisation of heartbeat dynamics in physiological and pathological conditions. However, pre-processing methods for the unevenly sampled heartbeat interval series are known to affect the estimation of MF properties. In this study, we employ a recently proposed method based on wavelet p-leaders MF spectra to estimate MF properties from cardiovascular variability series, which are also pre-processed through an inhomogeneous point-process modelling. Particularly, we exploit a non-Gaussian multiscale expansion to study changes in heartbeat dynamics as a response to a sympathetic elicitation given by the cold-pressor test. By comparing MF estimates from raw heartbeat series and the point-process model, results suggest that the proposed modelling provides features statistically discerning between stress and resting condition at different time scales. These findings contribute to a comprehensive characterization of autonomic nervous system activity on cardiovascular control during cold-pressor elicitation.

Wavelet p-Leader Non-Gaussian Multiscale Expansions for EEG series: an Exploratory Study on Cold-Pressor Test.

Brain dynamics recorded through electroencephalography (EEG) have been proven to be the output of a nonstationary and nonlinear system. Thus, multifractality of EEG series has been exploited as a useful tool for a neurophysiological characterization in health and disease. However, the role of EEG multifractality under peripheral stress is unknown. In this study, we propose to make use of a novel tool, the recently defined non-Gaussian multiscale analysis, to investigate brain dynamics in the range of 4-8Hz following a cold-pressor test versus a resting state. The method builds on the wavelet p-leader multifractal spectrum to quantify different types of departure from Gaussian and linear properties, and is compared here to standard linear descriptive indices. Results suggest that the proposed non-Gaussian multiscale indices were able to detect expected changes over the somatosensory and premotor cortices, over regions different from those detected by linear analyses. They further indicate that preferred responses for the contralateral somatosensory cortex occur at scales 2.5s and 5s. These findings contribute to the characterization of the so-called central autonomic network, linking dynamical changes at a peripheral and a central nervous system levels.

Multiscale properties of instantaneous parasympathetic activity in severe congestive heart failure: A survivor vs non-survivor study.

Multifractal analysis of cardiovascular variability series is an effective tool for the characterization of pathological states associated with congestive heart failure (CHF). Consequently, variations of heartbeat scaling properties have been associated with the dynamical balancing of nonlinear sympathetic/vagal activity. Nevertheless, whether vagal dynamics has multifractal properties yet alone is currently unknown. In this study, we answer this question by conducting multifractal analysis through wavelet leader-based multiscale representations of instantaneous series of vagal activity as estimated from inhomogeneous point process models. Experimental tests were performed on data gathered from 57 CHF patients, aiming to investigate the automatic recognition accuracy in predicting survivor and non-survivor patients after a 4 years follow up. Results clearly indicate that, on both CHF groups, the instantaneous vagal activity displays power-law scaling for a large range of scales, from ≃ 0.5s to ≃ 100s. Using standard SVM algorithms, this information also allows for a prediction of mortality at a single-subject level with an accuracy of 72.72%.

Point-process high-resolution representations of heartbeat dynamics for multiscale analysis: A CHF survivor prediction study.

Multiscale analysis of human heartbeat dynamics has been proved effective in characterizeing cardiovascular control physiology in health and disease. However, estimation of multiscale properties can be affected by the interpolation procedure used to preprocess the unevenly sampled R-R intervals derived from the ECG. To this extent, in this study we propose the estimation of wavelet coefficients and wavelet leaders on the output of inhomogeneous point process models of heartbeat dynamics. The RR interval series is modeled using probability density functions (pdfs) characterizing and predicting the time until the next heartbeat event occurs, as a linear function of the past history. Multiscale analysis is then applied to the pdfs' instantaneous first order moment. The proposed approach is tested on experimental data gathered from 57 congestive heart failure (CHF) patients by evaluating the recognition accuracy in predicting survivor and non-survivor patients, and by comparing performances from the informative point-process based interpolation and non-informative spline-based interpolation. Results demonstrate that multiscale analysis of point-process high-resolution representations achieves the highest prediction accuracy of 65.45%, proving our method as a promising tool to assess risk prediction in CHF patients.

P-leader multifractal analysis and sparse SVM for intrapartum fetal acidosis detection.

Interpretation and analysis of intrapartum fetal heart rate, enabling early detection of fetal acidosis, remains a challenging signal processing task. Among the many strategies that were used to tackle this problem, scale-invariance and multifractal analysis stand out. Recently, a new and promising variant of multifractal analysis, based on p-leaders, has been proposed. In this contribution, we use sparse support vector machines applied to p-leader multifractal features with a double aim: Assessment of the features actually contributing to classification; Assessment of the contribution of non linear features (as opposed to linear ones) to classification performance. We observe and interpret that the classification rate improves when small values of the tunable parameter p are used.

Intrapartum fetal heart rate classification from trajectory in Sparse SVM feature space.

Intrapartum fetal heart rate (FHR) constitutes a prominent source of information for the assessment of fetal reactions to stress events during delivery. Yet, early detection of fetal acidosis remains a challenging signal processing task. The originality of the present contribution are three-fold: multiscale representations and wavelet leader based multifractal analysis are used to quantify FHR variability ; Supervised classification is achieved by means of Sparse-SVM that aim jointly to achieve optimal detection performance and to select relevant features in a multivariate setting ; Trajectories in the feature space accounting for the evolution along time of features while labor progresses are involved in the construction of indices quantifying fetal health. The classification performance permitted by this combination of tools are quantified on a intrapartum FHR large database (≃ 1250 subjects) collected at a French academic public hospital.

Nearest-neighbor based wavelet entropy rate measures for intrapartum fetal heart rate variability.

The interpretation and analysis of intrapartum fetal heart rate (FHR), enabling early detection of fetal acidosis, remains a challenging signal processing task. The ability of entropy rate measures, amongst other tools, to characterize temporal dynamics of FHR variability and to discriminate non-healthy fetuses has already been massively investigated. The present contribution aims first at illustrating that a k-nearest neighbor procedure yields estimates for entropy rates that are robust and well-suited to FHR variability (compared to the more commonly used correlation-integral algorithm). Second, it investigates how entropy rates measured on multiresolution wavelet and approximation coefficients permit to improve classification performance. To that end, a supervised learning procedure is used, that selects the time scales at which entropy rates contribute to discrimination. Significant conclusions are obtained from a high quality scalp electrode database of nearly two thousands subjects collected in a French public university hospital.

Multiscale wavelet p-leader based heart rate variability analysis for survival probability assessment in CHF patients.

A priori discrimination of high mortality risk amongst congestive heart failure patients constitutes an important clinical stake in cardiology and involves challenging analyses of the temporal dynamics of heart rate variability (HRV). The present contribution investigates the potential of a new multifractal formalism, constructed on wavelet p-leader coefficients, to help discrimination between survivor and non survivor patients. The formalism, applied to a high quality database of 108 patients collected in a Japanese hospital, enables to assess the existence of multifractal properties amongst congestive heart failure patients and to reveal significant differences in the multiscale properties of HRV between survivor and non survivor patients, for scales ranging from approximately 60 to 250 beats.

Low dimensional manifold embedding for scattering coefficients of intrapartum fetale heart rate variability.

Intrapartum fetal surveillance for early detection of fetal acidosis in clinical practice focuses on reducing neonatal morbidity via early detection. It is the subject of on going research studies attempting notably to improve detection performance by reducing false positive rate. In that context, the present contribution tailors to fetal heart rate variability analysis a graph-based dimensionality reduction procedure performed on scattering coefficients. Applied to a high quality and well-documented database constituted by obstetricians from a French academic hospital, the low dimensional embedding enables to distinguish between the temporal dynamics of healthy and acidotic fetuses, as well as to achieve satisfactory detection performance detection compared to those obtained by the clinical-benchmark FIGO criteria.

Scale-Free and Multifractal Time Dynamics of fMRI Signals during Rest and Task.

Scaling temporal dynamics in functional MRI (fMRI) signals have been evidenced for a decade as intrinsic characteristics of ongoing brain activity (Zarahn et al., 1997). Recently, scaling properties were shown to fluctuate across brain networks and to be modulated between rest and task (He, 2011): notably, Hurst exponent, quantifying long memory, decreases under task in activating and deactivating brain regions. In most cases, such results were obtained: First, from univariate (voxelwise or regionwise) analysis, hence focusing on specific cognitive systems such as Resting-State Networks (RSNs) and raising the issue of the specificity of this scale-free dynamics modulation in RSNs. Second, using analysis tools designed to measure a single scaling exponent related to the second order statistics of the data, thus relying on models that either implicitly or explicitly assume Gaussianity and (asymptotic) self-similarity, while fMRI signals may significantly depart from those either of those two assumptions (Ciuciu et al., 2008; Wink et al., 2008). To address these issues, the present contribution elaborates on the analysis of the scaling properties of fMRI temporal dynamics by proposing two significant variations. First, scaling properties are technically investigated using the recently introduced Wavelet Leader-based Multifractal formalism (WLMF; Wendt et al., 2007). This measures a collection of scaling exponents, thus enables a richer and more versatile description of scale invariance (beyond correlation and Gaussianity), referred to as multifractality. Also, it benefits from improved estimation performance compared to tools previously used in the literature. Second, scaling properties are investigated in both RSN and non-RSN structures (e.g., artifacts), at a broader spatial scale than the voxel one, using a multivariate approach, namely the Multi-Subject Dictionary Learning (MSDL) algorithm (Varoquaux et al., 2011) that produces a set of spatial components that appear more sparse than their Independent Component Analysis (ICA) counterpart. These tools are combined and applied to a fMRI dataset comprising 12 subjects with resting-state and activation runs (Sadaghiani et al., 2009). Results stemming from those analysis confirm the already reported task-related decrease of long memory in functional networks, but also show that it occurs in artifacts, thus making this feature not specific to functional networks. Further, results indicate that most fMRI signals appear multifractal at rest except in non-cortical regions. Task-related modulation of multifractality appears only significant in functional networks and thus can be considered as the key property disentangling functional networks from artifacts. These finding are discussed in the light of the recent literature reporting scaling dynamics of EEG microstate sequences at rest and addressing non-stationarity issues in temporally independent fMRI modes.

Adaptive multiscale complexity analysis of fetal heart rate.

Per partum fetal asphyxia is a major cause of neonatal morbidity and mortality. Fetal heart rate monitoring plays an important role in early detection of acidosis, an indicator for asphyxia. This problem is addressed in this paper by introducing a novel complexity analysis of fetal heart rate data, based on producing a collection of piecewise linear approximations of varying dimensions from which a measure of complexity is extracted. This procedure specifically accounts for the highly non-stationary context of labor by being adaptive and multiscale. Using a reference dataset, made of real per partum fetal heart rate data, collected in situ and carefully constituted by obstetricians, the behavior of the proposed approach is analyzed and illustrated. Its performance is evaluated in terms of the rate of correct acidosis detection versus the rate of false detection, as well as how early the detection is made. Computational cost is also discussed. The results are shown to be extremely promising and further potential uses of the tool are discussed. MATLAB routines implementing the procedure will be made available at the time of publication.

Methodology for multifractal analysis of heart rate variability: from LF/HF ratio to wavelet leaders.

The present contribution aims at proposing a comprehensive and tutorial introduction to the practical use of wavelet Leader based multifractal analysis to study heart rate variability. First, the theoretical background is recalled. Second, practical issues and pitfalls related to the selection of the scaling range or statistical orders, minimal regularity, parabolic approximation of spectrum and parameter estimation, are discussed. Third, multifractal analysis is connected explicitly to other standard characterizations of heart rate variability: (mono)fractal analysis, Hurst exponent, spectral analysis and the HF/LF ratio. This review is illustrated on real per partum fetal ECG data, collected at an academic French public hospital, for both healthy fetuses and fetuses suffering from acidosis.

Assessing erectile neurogenic dysfunction from heart rate variability through a Generalized Linear Mixed Model framework.

BACKGROUND: The low (LF) vs. high (HF) frequency energy ratio, computed from the spectral decomposition of heart beat intervals, has become a major tool in cardiac autonomic system control and sympatho-vagal balance studies. The (statistical) distributions of response variables designed from ratios of two quantities, such as the LF/HF ratio, are likely to non-normal, hence preventing e.g., from a relevant use of the t-test. Even using a non-parametric formulation, the solution may be not appropriate as the test statistics do not account for correlation and heteroskedasticity, such as those that can be observed when several measures are taken from the same patient. OBJECTIVES: The analyses for such type of data require the application of statistical models which do not assume a priori independence. In this spirit, the present contribution proposes the use of the Generalized Linear Mixed Models (GLMMs) framework to assess differences between groups of measures performed over classes of patients. METHODS: Statistical linear mixed models allow the inclusion of at least one random effect, besides the error term, which induces correlation between observations from the same subject. Moreover, by using GLMM, practitioners could assume any probability distribution, within the exponential family, for the data, and naturally model heteroskedasticity. Here, the sympatho-vagal balance expressed as LF/HF ratio of patients suffering neurogenic erectile dysfunction under three different body positions was analyzed in a case-control protocol by means of a GLMM under gamma and Gaussian distributed responses assumptions. RESULTS: The gamma GLMM model was compared with the normal linear mixed model (LMM) approach conducted using raw and log transformed data. Both raw GLMM gamma and log transformed LMM allow better inference for factor effects, including correlations between observations from the same patient under different body position compared to the raw LMM. The gamma GLMM provides a more natural distribution assumption of a response expressed as a ratio. CONCLUSIONS: A gamma distribution assumption intrinsically models quadratic relationships between the expected value and the variance of the data avoiding prior data transformation. SAS and R source code are available on request.

Assessment of cardiovascular autonomic control by the empirical mode decomposition.

OBJECTIVES: Heart-rate variability (HRV) is an interesting tool for assessing cardiac autonomic system control, but nonstationarities raise problematic issues. The objective of this paper is to show that adapted signal processing tools may cope with nonstationary situations and improve the analysis of HRV. METHODS: We propose to use the recent method of Empirical Mode Decomposition (EMD), so as to analyze the cardiac sympatho-vagal balance on automatically extracted modes. The method, which is fully data-adaptive, consists in an iterative decomposition based on the idea that any signal can be locally represented as an oscillation superimposed to a more regular trend. When a signal is composed of distinct nonstationary components, EMD therefore achieves a time-varying filtering which effectively separates them. RESULTS: The method has been applied to situations where postural changes occur, provoking instantaneous changes in heart rate as a result of autonomic modifications. In the considered application where the sympatho-vagal balance is quantified by comparing the low-frequency (LF) and high-frequency (HF) components of RR intervals, EMD automatically achieves a separation of these components upon which further processing can be carried. Visualizing the decomposition in the time-frequency plane, we can identify local events due to the postural changes, and we can assess a (time-varying) HF vs. LF discrimination without resorting to some fixed high-pass/low-pass filtering. CONCLUSION: Assessing cardiovascular autonomic control by resorting to LF/HF measurements may prove difficult in nonstationary situations where the use of a priori fixed filters can be questioned. Because it is both local and fully data-adaptive, EMD appears as an appealing and versatile pre-processing technique for overcoming some of the limitations that conventional spectral methods are faced with in nonstationary situations.