A mathematical algorithm for ECG signal denoising using window analysis

BACKGROUND: The presence of parasite interference signals could cause serious problems in the registration of ECG signals and many works have been done to suppress electromyogram (EMG) artifacts noises and disturbances from electrocardiogram (ECG). Recently, new developed techniques based on global and local transforms have become popular such as wavelet shrinkage approaches (1995) and time-frequency dependent threshold (1998). Moreover, other techniques such as artificial neural networks (2003), energy thresholding and Gaussian kernels (2006) are used to improve previous works. This review summarizes windowed techniques of the concerned issue. METHODS AND RESULTS: We conducted a mathematical method based on two sets of information, which are dominant scale of QRS complexes and their domain. The task is proposed by using a varying-length window that is moving over the whole signals. Both the high frequency (noise) and low frequency (base-line wandering) removal tasks are evaluated for manually corrupted ECG signals and are validated for actual recorded ECG signals. CONCLUSIONS: Although, the simplicity of the method, fast implementation, and preservation of characteristics of ECG waves represent it as a suitable algorithm, there may be some difficulties due to pre-stage detection of QRS complexes and specification of algorithm's parameters for varying morphology cases.     

Analysis of ECG signal denoising method based on S-transform

Electrocardiogram (ECG), a noninvasive technique which is used generally as a primary diagnostic tool for cardiovascular diseases. A cleaned ECG signal provides necessary information about the electrophysiology of the heart diseases and ischemic changes that may occur. However in real situation, noise is often embedded with ECG signal during acquisition. In this paper, a novel ECG signal denoising technique is proposed using Stockwell transform (S-transform). This method is evaluated on several normal and abnormal ECG signals of MIT/BIH arrhythmia database, by artificially adding white Gaussian noises to visually inspected clean ECG recordings. The experimental results demonstrate that the proposed method shows the better signal to noise ratio (SNR), lower root mean square error (RMSE) and percent root mean square difference (PRD) compared to generally used ECG denoising method like wavelet transform.     

Application of higher order statistics for atrial arrhythmia classification

Atrial fibrillation (AF) and atrial flutter (AFL) are the two common atrial arrhythmia encountered in the clinical practice. In order to diagnose these abnormalities the electrocardiogram (ECG) is widely used. The conventional linear time and frequency domain methods cannot decipher the hidden complexity present in these signals. The ECG is inherently a non-linear, non-stationary and non-Gaussian signal. The non-linear models can provide improved results and capture minute variations present in the time series. Higher order spectra (HOS) is a non-linear dynamical method which is highly rugged to noise. In the present study, the performances of two methods are compared: (i) 3rd order HOS cumulants and (ii) HOS bispectrum. The 3rd order cumulant and bispectrum coefficients are subjected to dimensionality reduction using independent component analysis (ICA) and classified using classification and regression tree (CART), random forest (RF), artificial neural network (ANN) and k-nearest neighbor (KNN) classifiers to select the best classifier. The ICA components of cumulant coefficients have provided the average accuracy, sensitivity, specificity and positive predictive value of 99.50%, 100%, 99.22% and 99.72% respectively using KNN classifier. Similarly, the ICA components of HOS bispectrum coefficients have yielded the average accuracy, sensitivity, specificity and PPV of 97.65%, 98.16%, 98.75% and 99.53% respectively using KNN. So, the ICA performed on the 3rd order HOS cumulants coupled with KNN classifier performed better than the HOS bispectrum method. The proposed methodology is robust and can be used in mass screening of cardiac patients.     

Clustering mass spectrometry data using order statistics

Mass spectrometry data is inherently uncertain. Rather than compare peak heights across samples, a comparison can be made of the relative ordering of the peak height across samples. Order statistics are used to provide a distance metric between each ordered list of peak heights from the samples. A principal component analysis is performed on the set of distance vectors to highlight to important components.     

Self-adaptive model-based ECG denoising using features extracted by mean shift algorithm

Denoising of electrocardiogram (ECG) is the fundamental technique for manual or automatic ECG diagnosis. Model-based denoising has attracted initial studies since the ECG dynamical model was established in 2003 and been demonstrated to outperform most model-less denoising methods. The focus of this paper is robust denoising of abnormal ECG signals, which do not satisfy the assumption in previous model-based studies that morphological or physiological variations are small from one beat to another. A mean shift based initializer is proposed to provide a much more robust estimation of initial model parameters for each heart beat. Together with physiological knowledge based wave sub-segmentation and enhanced strategies, the novel initializer has been demonstrated to achieve satisfactory performance for both normal and abnormal heart beats under both white and pink noises. Utilizing records from Massachusetts Institute of Technology (MIT)-Beth Israel Hospital (BIH) database, this paper also applies various filters to denoise noisy signals and the denoising performances verify the availability and efficacy of the proposed denoising method.     

Wavelet threshold based TDL and TDR algorithms for real-time ECG signal compression

In this paper, two novel and simple, target distortion level (TDL) and target data rate (TDR), Wavelet threshold based ECG compression algorithms are proposed for real-time applications. The issues on the use of objective error measures, such as percentage root mean square difference (PRD) and root mean square error (RMSE) as a quality measures, in quality controlled/guranteed algorithm are investigated with different sets of experiments. For the proposed TDL and TDR algorithm, data rate variability and reconstructed signal quality is evaluated under different ECG signal test conditions. Experimental results show that the TDR algorithm achieves the required compression data rate to meet the demands of wire/wireless link while the TDL algorithm does not. The compression performance is assessed in terms of number of iterations required to achieve convergence and accuracy, reconstructed signal quality and coding delay. The reconstructed signal quality is evaluated by correct diagnosis (CD) test through visual inspection. Three sets of ECG data from three different databases, the MIT-BIH Arrhythmia (mita) (F_s=360 Hz, 11 b/sample), the Creighton University Ventricular Tachyarrhythmia (cuvt) (F_s=250 Hz, 12 b/sample) and the MIT-BIH Supraventricular Arrhythmia (mitsva) (F_s=128 Hz, 10 b/sample), are used for this work. For each set of ECG data, the compression ratio (CR) range is defined. The CD value of 100% is achieved for CR ≤12, CR ≤ 8 and CR ≤ 4 for data from mita, cuvt and mitsva databases, respectively. The experimental results demonstrate that the proposed TDR algorithm is suitable for real-time applications.     

Cardiac decision making using higher order spectra

The electrocardiogram (ECG) is the P-QRS-T wave representing the information about the condition of the heart. The shape and size of the ECG signal may contain useful information about the nature of disease afflicting the heart. However, these subtle details cannot be directly monitored by the human eye and may indicate a particular cardiac abnormality. Also, the ECG is highly subjective, the symptoms may appear at random in the time scale. Hence computer assisted methods can help physicians to monitor cardiac health easily and accurately. The ECG signal is nonlinear and non-stationary in nature. These subtle variations can be captured using non-linear dynamical Higher Order Statistics (HOS) techniques. Bispectrum is the third order spectra which captures information beyond mean and standard deviation. In this work we have analyzed five types of beats namely: Normal, Right Bundle Branch Block (RBBB), Left Bundle Branch Block (LBBB), Atrial Premature Contraction (APC) and Ventricular Premature Contraction (VPC). The extracted bispectrum features are subjected to principal component analysis (PCA) for dimensionality reduction. These principal components were fed to four layered feed forward neural network and Least Square-Support Vector Machine (LS-SVM) for automated pattern identification. In our work, we have obtained highest average accuracy of 93.48%, average sensitivity and specificity of 99.27% and 98.31% respectively using LS-SVM with Radial Basis Function (RBF) kernel. Our system is clinically ready to run on large amount of data sets.     

Wavelet threshold based ECG compression using USZZQ and Huffman coding of DSM

In this paper, a new Wavelet threshold based ECG signal compression technique using uniform scalar zero zone quantizer (USZZQ) and Huffman coding on differencing significance map (DSM) is proposed. Wavelet coefficients are selected based on the energy packing efficiency of each sub-band. Significant Wavelet coefficients are quantized with uniform scalar zero zone quantizer. Significance map is created to store the indices of the significant coefficients. This map is encoded efficiently with less number of bits by applying Huffman coding on the differences between indices in the significance map. ECG records from the MIT-BIH arrhythmia database are selected as test data. For the record 117, the proposed technique achieves a compression ratio of 18.7:1 with lower percentage root mean square difference (PRD) compared to other threshold based methods. The proposed technique is tested for MIT-BIH arrhythmia record 119 and a compression ratio of 21.81:1 is achieved with a PRD value of 3.716% which is much lower compared to the reported PRD value of 5.0 and 5.5% of set partitioning in hierarchical tress (SPIHT) and analysis by synthesis ECG compressor (ASEC), respectively. The noise eliminating capability of the proposed technique is also demonstrated in this work. The proposed technique achieves the required compression ratio with less reconstruction error for GSM-based cellular telemedicine system.     

ECG signal compression using ASCII character encoding and transmission via SMS

Software based efficient and reliable ECG data compression and transmission scheme is proposed here. The algorithm has been applied to various ECG data of all the 12 leads taken from PTB diagnostic ECG database (PTB-DB). First of all, R-peaks are detected by differentiation and squaring technique and QRS regions are located. To achieve a strict lossless compression in the QRS regions and a tolerable lossy compression in rest of the signal, two different compression algorithms have used. The whole compression scheme is such that the compressed file contains only ASCII characters. These characters are transmitted using internet based Short Message Service (SMS) and at the receiving end, original ECG signal is brought back using just the reverse logic of compression. It is observed that the proposed algorithm can reduce the file size significantly (compression ratio: 22.47) preserving ECG signal morphology.     

ECG beat classification using PCA,LDA, ICA and Discrete Wavelet Transform

Electrocardiogram (ECG) is the P-QRS-T wave, representing the cardiac function. The information concealed in the ECG signal is useful in detecting the disease afflicting the heart. It is very difficult to identify the subtle changes in the ECG in time and frequency domains. The Discrete Wavelet Transform (DWT) can provide good time and frequency resolutions and is able to decipher the hidden complexities in the ECG. In this study, five types of beat classes of arrhythmia as recommended by Association for Advancement of Medical Instrumentation (AAMI) were analyzed namely: non-ectopic beats, supra-ventricular ectopic beats, ventricular ectopic beats, fusion betas and unclassifiable and paced beats. Three dimensionality reduction algorithms; Principal Component Analysis (PCA), Linear Discriminant Analysis (LDA) and Independent Component Analysis (ICA) were independently applied on DWT sub bands for dimensionality reduction. These dimensionality reduced features were fed to the Support Vector Machine (SVM), neural network (NN) and probabilistic neural network (PNN) classifiers for automated diagnosis. ICA features in combination with PNN with spread value (σ) of 0.03 performed better than the PCA and LDA. It has yielded an average sensitivity, specificity, positive predictive value (PPV) and accuracy of 99.97%, 99.83%, 99.21% and 99.28% respectively using ten-fold cross validation scheme.     

Analysis and automatic identification of sleep stages using higher order spectra

Electroencephalogram (EEG) signals are widely used to study the activity of the brain, such as to determine sleep stages. These EEG signals are nonlinear and non-stationary in nature. It is difficult to perform sleep staging by visual interpretation and linear techniques. Thus, we use a nonlinear technique, higher order spectra (HOS), to extract hidden information in the sleep EEG signal. In this study, unique bispectrum and bicoherence plots for various sleep stages were proposed. These can be used as visual aid for various diagnostics application. A number of HOS based features were extracted from these plots during the various sleep stages (Wakefulness, Rapid Eye Movement (REM), Stage 1-4 Non-REM) and they were found to be statistically significant with p-value lower than 0.001 using ANOVA test. These features were fed to a Gaussian mixture model (GMM) classifier for automatic identification. Our results indicate that the proposed system is able to identify sleep stages with an accuracy of 88.7%.     

Automatic detection of epileptic EEG signals using higher order cumulant features

The unpredictability of the occurrence of epileptic seizures makes it difficult to detect and treat this condition effectively. An automatic system that characterizes epileptic activities in EEG signals would allow patients or the people near them to take appropriate precautions, would allow clinicians to better manage the condition, and could provide more insight into these phenomena thereby revealing important clinical information. Various methods have been proposed to detect epileptic activity in EEG recordings. Because of the nonlinear and dynamic nature of EEG signals, the use of nonlinear Higher Order Spectra (HOS) features is a seemingly promising approach. This paper presents the methodology employed to extract HOS features (specifically, cumulants) from normal, interictal, and epileptic EEG segments and to use significant features in classifiers for the detection of these three classes. In this work, 300 sets of EEG data belonging to the three classes were used for feature extraction and classifier development and evaluation. The results show that the HOS based measures have unique ranges for the different classes with high confidence level (p-value < 0.0001). On evaluating several classifiers with the significant features, it was observed that the Support Vector Machine (SVM) presented a high detection accuracy of 98.5% thereby establishing the possibility of effective EEG segment classification using the proposed technique.     

Vibration and length-dependent flexural rigidity of protein microtubules using higher order shear deformation theory

Microtubules are hollow cylindrical filaments of the eukaryotic cytoskeleton characterized by extremely low shear modulus. A remarkable controversy has occurred in the literature, regarding the length dependence of flexural rigidity of microtubules predicted by the classical elastic beam model. In this study, a higher order shear deformable beam model for microtubules is employed to study unexplained length-dependent flexural rigidity and Young’s modulus of microtubules reported in the literature. The formulation allows for warping of the cross-section of the microtubule and eliminates the need for using arbitrary shear correction coefficients as in other theories. It is showed that vibration frequencies predicted by the present parabolic shear deformation theory (PSDT) are much lower than that given by the approximate isotropic beam model for shorter microtubules, although the two models give almost identical results for sufficiently long microtubules. It is confirmed that transverse shearing and the warping of the cross-section of microtubules are mainly responsible for the length-dependent flexural rigidity of an isolated microtubule reported in the literature, which cannot be explained by the widely used Euler-Bernoulli beam model. Indeed, the length-dependent flexural rigidity predicted by the present model is found to be in qualitative agreement with the existing experimental data ( [Kurachi et al., 1995] and [Pampaloni et al., 2006]). These results recommend that the parabolic shear deformation-beam theory offers a unified simple 1D model, which can capture the length dependence of flexural rigidity and be applied to various static and dynamic problems of microtubule mechanics.     

Cross-linking of U2 snRNA using nitrogen mustard. Evidence for higher order structure.

Nuclear mRNA precursors are spliced by a large macromolecular complex called the spliceosome which contains, in most eucaryotes, five small nuclear RNAs (snRNAs) each in the form of a small ribonucleoprotein particle (the U1, U2, U5, and U4/U6 snRNPs). Although secondary structures have been derived for all five spliceosomal snRNAs based on phylogenetic, biochemical, and genetic data, little tertiary structure information is available. Here we use the general cross-linking reagent nitrogen mustard [bis-(2-chloroethyl)methylamine] to detect tertiary interactions within U2 snRNA. After the cross-linking of deproteinized HeLa nuclear extract, two intramolecularly cross-linked U2 species with anomalous electrophoretic mobility can be detected (X-U2#1 and X-U2#2). The 3' and 5' boundaries of each cross-link were determined by rapid enzymatic RNA sequencing of end-labeled RNA. X-U2#1 is cross-linked between the region U41-U55 and G105 or G106, X-U2#2 between U53 and G97 or G98. We then tested the ability of the two cross-linked species to bind snRNP proteins in vitro (in nuclear extract or S100) and in vivo (in Xenopus oocytes). X-U2#2 reconstituted efficiently both in vitro and in vivo but X-U2#1 did not, as judged by immunoprecipitation with antibodies specific for Sm- and U2-specific proteins. Since the cross-link in X-U2#2 involves the Sm binding site but does not block snRNP assembly, our data strongly suggest that the Sm binding site lies on the surface of the native snRNP.     

Cross-linking of U1 snRNA using nitrogen mustard. Evidence for higher order structure.

Secondary structures for all five spliceosomal small nuclear (sn) RNAs (U1, U2, U4, U5, and U6 snRNAs) have been derived from phylogenetic, biochemical, and genetic data, but tertiary structure information has been more difficult to obtain. Here we have used the general cross-linking reagent nitrogen mustard (bis-(2-chloroethyl)methylamine) to explore the tertiary conformation of naked U1 snRNA. We detected two intramolecularly cross-linked U1 species (X-U1#1 and X-U1#2) after cross-linking of deproteinized HeLa nuclear extract. We determined the cross-linked sites and found that X-U1#1 is cross-linked between the C82-A85 and U129, while X-U1#2 is cross-linked between U105-G108 and A118. We then tested the ability of these two cross-linked species to bind small nuclear ribonucleo-protein (snRNP) proteins in vitro (in HeLa nuclear extract or S100) and in vivo (in Xenopus oocytes). Both X-U1#1 and X-U1#2 were found to reconstitute efficiently in vitro and in vivo, as judged by immunoprecipitation with antibodies specific for Sm and U1-specific proteins. Our data suggest that (i) the Sm-binding site lies on the surface of the native U1 snRNP, since the cross-link in X-U1#1 involves the Sm-binding site but does not block snRNP assembly, and (ii) U1 snRNA may adopt the correct tertiary conformation even in the absence of U1 snRNP proteins.     

Simultaneous multicolor fluorescence cross-correlation spectroscopy to detect higher order molecular interactions using single wavelength laser excitation

Fluorescence cross-correlation spectroscopy is a powerful method for the study of molecular interactions and dynamics in solution and even in living cells. Usually, in the optical setup, either two laser beams have to be superimposed in their respective confocal volumes or two-photon excitation is used for a dual-color detection system. It has been shown recently that fluorescence cross correlation can be achieved with spectrally similar fluorophores using single wavelength excitation fluorescence cross-correlation spectroscopy (SW-FCCS). In this study, we show that SW-FCCS allows the simultaneous excitation of up to three fluorophores in which the cross correlation of their fluctuation signals is detected separately in three detection channels. The experimental and theoretical model to describe triple pairwise cross correlations incorporating cross talk and possible changes in emission characteristics such as quenching upon binding are outlined. The effectiveness of SW-FCCS to detect binding of three interacting partners is experimentally verified with a standard ligand-receptor model, biotin-streptavidin, where differently labeled biotin ligands and their binding to a third-color labeled streptavidin are studied. The cross-correlation amplitudes and their changes with stoichiometric binding are analyzed and the upper limits of dissociation constants are determined. Performed with appropriate negative controls, SW-FCCS can determine interaction patterns between ligands and receptors.