1,721,224 research outputs found
Characterizing histograms of heartbeat interval differences with Gaussian mixture densities
Full text linkIn long-term HRV analysis, it is common choice to study the difference signal IRR(i) = RR(i+1) - RR(i). In this work we first verified the fitting of a Lévy stable distribution on the signals IRR obtained from four databases, available on Physionet. They included normal subjects (N) but also individuals suffering from congestive heart failure (CHF) or showing ST segment changes (ST). The study showed that a L ́evy stable distribution was generally more appropriate on the series than a Gaussian one (N: 1:70+/-0:19; CHF: 1:74+/-0:18; ST: 1:66+/-0:22). The differences between the populations were not significant (p > 5%).
Based on the value of RMSSD on local short intervals, we built a simple Gaussian mixture density for each IRR series. Such mixture densities were able to properly describe the histograms in the databases under analysis. This explanation, which also avoids the necessity of invariant densities with not-finite second moments, might be closer to the physiological situation at hand
Parametric estimation of sample entropy in heart rate variability analysis
No full textIn this paper, a detailed study on the possibility and significance of performing a parametric estimation of sample entropy (SampEn) is proposed. SampEn is a non-linear metric, meant to quantify regularity of a time series. It is widely employed on biomedical signals, especially on heart rate variability. Results relevant to approximate entropy, a related index, are also reported. An analytical expression for SampEn of an autoregressive (AR) model is derived first. Then we study the feasibility of a parametric estimation of SampEn through AR models, both on synthetic and real series. RR series of different lengths are fitted to an AR model and then expected values of SampEn (SampEnμ) are estimated. Values of SampEn, computed from real beat-to-beat interval time series (obtained from 72 normal subjects and 29 congestive heart failure patients), with m = 1 and r = 0.2, are within the standard range of SampEnμ more than 83% (for series length N = 75) and 28% (for N = 1500) of the cases. Surrogate data have been employed to verify if departures from Gaussianity are to account for the mismatch. The work supports the finding that when numerical and parametric estimates of SampEn agree, SampEn is mainly influenced by linear properties of the series. A disagreement, on the contrary, might point those cases where SampEn is truly offering new information, not readily available with traditional temporal and spectral parameters
Development of PDF-ECG : Further steps towards the long-term preservation of clinical electrocardiograms
No full textSample entropy parametric estimation for heart rate variability analysis
Full text linkAims: Sample Entropy (SampEn) is a powerful approach for characterizing heart rate variability regularity. On the other hand, autoregressive (AR) models have been employed for maximum-entropy spectral estimation for more than 40 years. The aim of this study is to explore the feasibility of a parametric approach for SampEn estimation through AR models. We re-analyze the Physionet paroxysmal Atrial Fibrillation (AF) database, where RR series are provided before and after an AF episode, for 25 patients. In particular, we selected short RR series, close to AF episodes, to fit an AR model. Then, theoretical values of SampEn, based on each AR model, were analytically derived (SE th) and also estimated numerically (SEsyn). The value of SampEn (SErr), computed on the 50 RR series with r=0.2×STD, m=1 and N=120, were within the standard range of SEsyn in 30 cases (39 for SEth). This figure increased to 82% of cases, if shorter series were selected (N=75), and if RR series were replaced by surrogates with Gaussian amplitude distribution. Interestingly, without removing ectopic beats, every estimate of SampEn considered was significantly different between pre- and post- AF (SErr: p=0.02; SEsyn: p=0.0024; SEth: p=0.023). When an AR model is appropriate and theoretical estimates differ from numerical ones, a parametric approach might enlighten additional information brought by SampEn
Spectral algorithms for reaction-diffusion equations
Full text linkA collection of codes (in MATLAB & Fortran 77), and examples, for solving reaction-diffusion equations in one and two space dimensions is presented. In areas of the mathematical community spectral methods are used to remove the stiffness associated with the diffusive terms in a reaction-diffusion model allowing explicit high order timestepping to be used. This is particularly valuable for two (and higher) space dimension problems. Our aim here is to provide codes, together with examples, to allow practioners to easily utilize, understand and implement these ideas; we incorporate recent theoretical advances such as exponential time differencing methods and provide timings and error comparisons with other more standard approaches.
The examples are chosen from the literature to illustrate points and queries that naturally arise
Refined estimate of the Dominant T Wave
Full text linkThe Dominant T-wave (DTW) offers an overall view of the venticular repolarization as it reflects the first-order derivative of the transmembrane potential of the myocytes during repolarization (TMPR). DTW can be estimated from the analysis of surface T-waves, which are modeled as a linear combination of DTW and its derivatives. Usually, the contribute of the DTW dominates but, when dispersion of the repolarization times increases (as during pathological conditions) the effects of DTW derivatives can not be neglected. Unfortunately the estimators of DTW proposed so far, do not consider these terms. In this work, an algorithm to estimate the DTW taking into account the second-order derivative of the TMPR curve is introduced. The algorithm was tested on synthetic ECG recordings. When the dispersion of the sources is varied from 10 to 50 ms, the new technique shows an average improvement in the precision of the estimate of the TMPR curve of about 18.9% over previous methods
Theoretical comments on reproducibility and normalization of TWA measures
No full textUsing a simple stochastic model of ventricular repolarization and the equivalent surface source (ESS) model, an electrophysiological formulation relating surface ECG to variations at the myocytes’ level, we recently pointed out a few theoretical results regarding T-wave alternans (TWA). In this paper, stimulated by the comments of John E. Madias on our paper (J Electrocardiol, 2012), we further explored the consequences implied by the theoretical model.
First, we verified the reproducibility of TWA measures, in clinically stable patients repeatedly tested. The sensitivity to displacement was evaluated simulating lead mislocations of up to 20 mm. The numerical simulations were performed on data obtained solving the inverse electrocardiographically problem from three subjects (ECGSIM). The results showed that TWA sensitivity varies across leads, being maximal in V1 and decreases towards V6. Globally, the maximal percent error found was 6.1%. Thus, TWA measures do not seem to add more stringent requirements on lead placement's precision, than the usual diagnostic practice.
Finally, we further discussed the implications of normalizing TWA measures. While clinical studies are necessary to sort out the issue, the theoretical model suggests that normalization might be appropriate only is certain cases
Concurrent clustering and classification for assessing the risk of falling during ageing
No full textDuring ageing, fall prevention represents one of the most sustainable plan of action to promote active ageing and reduce health care costs. To significantly prevent the falls, it is necessary to deploy predictive models that can accurately assess the risk of falling. However, current machine learning methodologies do not offer insights about the rules used for the assessment. Here, we proposed a method capable to concurrently cluster and classify data in the context of fall risk assessment. Such clustering provides support in analyzing the classification performed. We applied the method on a dataset composed by accelerometer signals collected using a wearable sensor from 90 subjects that underwent a Tinetti test (i.e., a clinical scale meant to assess the risk of falling). Thirty-three subjects had a Tinetti score <= 18 and considered has having high risk of falling. A training-validation-test procedure was designed to determine the classification accuracy of the proposed methodology. We evaluated the automatic clustering by observing how the subjects were splitted into three groups. The method achieved a test set accuracy of 0.85. The obtained clusters supported the presence of three macro groups, i.e., low risk, high risk and borderline
Some theoretical results on the observability of repolarization heterogeneity on surface ECG
No full textAssessing repolarization heterogeneity (RH) from surface ECG recording is an open issue in modern electrocardiography, despite the fact that several indexes measured on the T-wave have been proposed and tested. To understand how RH occurring at myocite level is reflected on T-wave shapes, in this paper we propose a mathematical framework that combines a simple statistical model of cardiac repolarization times with the dominant T-wave formalism. Within this framework we compare different T-wave features such as T-wave amplitude, T-wave amplitude variability or QT intervals and we describe mathematically how they are linked to the spatial and temporal components of repolarization heterogeneity
Quantification of Spatial Repolarization Heterogeneity: Testing the Robustness of a New Technique
Full text linkThe V-index is a recently-proposed metric related to repolarization heterogeneity (RH) across the myocardium, a key quantity for the development of arrhythmias. The metric is derived from multi-leads ECG recordings and this paper investigates two of its properties: i) the dependency on the lead system (Frank's orthogonal vs. 12 standard leads); ii) the influence of errors in the location of the T-end position. The first investigation was performed by simulations, using a forward ECG model (ECGSIM). In the lead system of interest, the V-index was computed varying the standard deviation of RH (sv). The results showed that the average bias in the estimate of RH (at σφ = 1 ms) ranged from -20.4±4.0% (sv = 20.6 ms) to -26.3±4.0% (sv = 70.9 ms) for the standard system and from -7.0 ± 4.2% to - 19.0 ± 4.2% for the Frank's one. While the bias diminished, the vulnerability to noise slightly increased. Secondarily, 68 ECGs from the E-OTH-12-0068-010 THEW database were analyzed. To simulate mislocation, the T-end point was consistently moved (±20 ms) around its correct position and the V-index computed. The average differences in the V-index estimates across the population were always smaller than 1%. This is a desirable property, given the discrepancies across methods in locating T-end positions
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