Electrocardiogram Representation Research Articles

Detection of cardiac abnormalities from 12-lead ecg using complex wavelet sub-band features

Aim of the study. This research endeavours to optimize cardiac anomaly detection by introducing a method focused on selecting the most effective Daubechis wavelet families. The principal aim is to differentiate between cardiac states that are normal and abnormal by utilizing longer electrocardiogram (ECG) signal events based on the Apnea ECG dataset. Apnea ECG is often used to detect sleep apnea, a sleep disorder characterized by repeated interruptions in breathing during sleep. By using machine learning methods, such as Principal Component Analysis (PCA) and different classifiers, the goal is to improve the precision of cardiac irregularity identification. Used method. To extract important statistical and sub-band information from lengthy ECG signal episodes, the study uses a novel method that combines discrete wavelet transform with Principal Component Analysis (PCA) for dimension reduction. The methodology focuses on successfully categorizing ECG signals by utilizing several classifiers, including multilayer perceptron (MLP) neural network, Ensemble Subspace K-Nearest Neighbour(KNN), and Ensemble Bagged Trees, together with varied Daubechis wavelet families (db2, db3, db4, db5, db6). Brief Description of Results. The results emphasize the importance of the chosen Daubechis wavelet family, db5, and its superiority in ECG representation. The method distinguishes normal and abnormal ECG signals well on the Physionet Apnea ECG database. The Neural Network-based method accurately recognizes 100% of healthy signals and 97.8% of problematic ones with 98.6% accuracy. Findings. The Ensemble Subspace K-Nearest Neighbour (KNN) and Ensemble Bagged Trees methods got 87.1% accuracy and 0.89 and 0.87 AOC curve values on this dataset, showing that the method works. Precision values of 0.96, 0.86, and 0.86 for MLP Neural Network, KNN Subspace, and Ensemble Bagged Trees confirm their robustness. These findings suggest wavelet families and machine learning can improve cardiac abnormality detection and categorization.

Universal 12-lead ECG representation for signal denoising and cardiovascular disease detection by fusing generative and contrastive learning

With the wide use of electrocardiogram (ECG) technology, more and more ECGs have been collected and stored. However, ECG labeling is costly and laborious, the utilization of unlabeled ECG is still a critical challenge. Self-supervised learning (SSL) is a way to deal with this problem, which can learn representations from unlabeled ECG and use them for downstream tasks. In this study, a novel SSL model that fuses generative learning (denoising autoencoder, DAE) and contrastive learning (CL) is proposed to learn robust representations from unlabeled ECG for downstream denoising and classification. The 12-lead ECGs are separated into one-dimensional single-lead ECGs and ECG-specific noises are added to the original ECGs as the data augmentation method. To improve the model's denoising and feature extraction abilities, the reconstruction loss and contrastive loss are combined during the pretraining phase. In the downstream classification task, a multi-branch network is used to enhance the correlation between different ECG leads. As a result, it improves the denoising performance over the standard DAE by an average of 5.20%. In the classification tasks for the Chapman, PTB-XL, and CPSC2018 databases, compared to existing work, the accuracies in linear probe are increased by at least 2.49%, 1.09%, and 2.61%, respectively. In addition, an SoC (system-on-a-chip) based heterogeneous deployment scheme is designed. It is 13.69–14.26 times faster in inference than pure software deployment and enables real-time detection of ECG signals. The proposed method provides a good way to utilize unlabeled ECG, and the designed deployment scheme has great potential for medical applications.

In-Distribution and Out-of-Distribution Self-Supervised ECG Representation Learning for Arrhythmia Detection.

This paper presents a systematic investigation into the effectiveness of Self-Supervised Learning (SSL) methods for Electrocardiogram (ECG) arrhythmia detection. We begin by conducting a novel analysis of the data distributions on three popular ECG-based arrhythmia datasets: PTB-XL, Chapman, and Ribeiro. To the best of our knowledge, our study is the first to quantitatively explore and characterize these distributions in the area. We then perform a comprehensive set of experiments using different augmentations and parameters to evaluate the effectiveness of various SSL methods, namely SimCRL, BYOL, and SwAV, for ECG representation learning, where we observe the best performance achieved by SwAV. Furthermore, our analysis shows that SSL methods achieve highly competitive results to those achieved by supervised state-of-the-art methods. To further assess the performance of these methods on both In-Distribution (ID) and Out-of-Distribution (OOD) ECG data, we conduct cross-dataset training and testing experiments. Our comprehensive experiments show almost identical results when comparing ID and OOD schemes, indicating that SSL techniques can learn highly effective representations that generalize well across different OOD datasets. This finding can have major implications for ECG-based arrhythmia detection. Lastly, to further analyze our results, we perform detailed per-disease studies on the performance of the SSL methods on the three datasets.

A Novel Detector of Atypical Beats for Early Diagnosis of Heart Diseases Based on the Stacked Beats Representation of 12-lead ECG

We have developed and present in this work a series of algorithms that present a long-duration electrocardiogram (ECG) in a compact form of stacked beats, extracting and visualizing the basic features and facilitating the tedious and time-consuming process of ECG analysis for cardiologists. The expert system based on this representation provides detection of atypical heartbeats, precursors of cardiovascular disease, and their locations in each of the 12 leads. This system was extensively tested with two public databases, MIT-BIH arrhythmia database and China Physiological Signal Challenge (CPSC2018), showing its rapid ECG processing and high efficiency in detecting abnormalities in beat morphology. In particular, tests for atypical beats based on the CPSC2018 database revealed that the set of ECGs marked as normal contains a considerable number of leads with atypical beats. The system is used as a classifier into two classes, normal beats, and atypical beats, the latter being the precursors or indicators of cardiovascular diseases (CVD). It is considered potentially useful for routine studies in groups at high risk of CVD in early stages, as a preventive medicine tool in the public health area. The system allows an intervention of a cardiologist in the intermediate stages of ECG analysis to corroborate the diagnosis in ambiguous cases.

A simple self-supervised ECG representation learning method via manipulated temporal–spatial reverse detection

Learning representations from electrocardiogram (ECG) signals can serve as a fundamental step for different machine learning-based ECG tasks. In order to extract general ECG representations that can be adapted to various downstream tasks, the learning process needs to be based on a general ECG-related task which can be achieved through self-supervised learning (SSL). However, existing SSL approaches either fail to provide satisfactory ECG representations or require too much effort to construct the learning data. In this paper, we propose the T-S reverse detection, a simple yet effective self-supervised approach to learn ECG representations. Inspired by the temporal and spatial characteristics of ECG signals, we flip the original signals horizontally (temporal reverse), vertically (spatial reverse), and both horizontally and vertically (temporal–spatial reverse). Learning is then done by classifying four types of signals including the original one. To verify the effectiveness of the proposed method, we perform a downstream task to detect atrial fibrillation (AF) which is one of the most common ECG tasks. The results show that the ECG representations learned with our method achieve remarkable performance. Furthermore, after exploring the representation feature space and investigating salient ECG locations, we conclude that the temporal reverse is more effective for learning ECG representations than the spatial reverse.

Multi-Domain Variational Autoencoders for Combined Modeling of MRI-Based Biventricular Anatomy and ECG-Based Cardiac Electrophysiology.

Human cardiac function is characterized by a complex interplay of mechanical deformation and electrophysiological conduction. Similar to the underlying cardiac anatomy, these interconnected physiological patterns vary considerably across the human population with important implications for the effectiveness of clinical decision-making and the accuracy of computerized heart models. While many previous works have investigated this variability separately for either cardiac anatomy or physiology, this work aims to combine both aspects in a single data-driven approach and capture their intricate interdependencies in a multi-domain setting. To this end, we propose a novel multi-domain Variational Autoencoder (VAE) network to capture combined Electrocardiogram (ECG) and Magnetic Resonance Imaging (MRI)-based 3D anatomy information in a single model. Each VAE branch is specifically designed to address the particular challenges of the respective input domain, enabling efficient encoding, reconstruction, and synthesis of multi-domain cardiac signals. Our method achieves high reconstruction accuracy on a United Kingdom Biobank dataset, with Chamfer Distances between reconstructed and input anatomies below the underlying image resolution and ECG reconstructions outperforming multiple single-domain benchmarks by a considerable margin. The proposed VAE is capable of generating realistic virtual populations of arbitrary size with good alignment in clinical metrics between the synthesized and gold standard anatomies and Maximum Mean Discrepancy (MMD) scores of generated ECGs below those of comparable single-domain approaches. Furthermore, we observe the latent space of our VAE to be highly interpretable with separate components encoding different aspects of anatomical and ECG variability. Finally, we demonstrate that the combined anatomy and ECG representation improves the performance in a cardiac disease classification task by 3.9% in terms of Area Under the Receiver Operating Characteristic (AUROC) curve over the best corresponding single-domain modeling approach.

Self-supervised ECG pre-training

Background:Real-world medical data, such as electrocardiogram (ECG), often show a long-tail distribution and severe category imbalance, and severely imbalanced data generate bias in deep learning models. In this work, we investigate how to alleviate the problems of label imbalance and inadequate labelling faced by deep learning models when applied to ECG data. Methods:We constructed a short-duration twelve-lead ECG dataset, containing more than 300,000 samples, for morphological recognition based on the actual distribution to evaluate and compare the recognition ability of humans and computers regarding ECG morphology. Two unique ECG data augmentation methods were designed and were combined with a variety of current mainstream self-supervised learning methods, and ultimately, the pre-trained weights were transferred to an 8-class multi-label ECG classification task for evaluation. Results:The experiments showed that self-supervised pre-training relying on negative sample pairs could achieve significantly better ECG representation than baseline, which was significantly effective for alleviating the imbalance in ECG data and reducing the labels of supervised samples. This method effectively utilized a large number of normal ECG samples. Additionally, with the diagnosis of the expert team as ground truth, under the condition of accessing only a small number of labelled samples, these models even performed better than the human ECG doctors participating in the test. Conclusion:The combination of self-supervised learning and unique data augmentation methods in the recognition of ECG morphology can effectively alleviate the long-tail problem and severe data imbalance and can significantly reduce the need for labelled samples in the downstream task.

Diagnostic Interpretation of Non-Uniformly Sampled Electrocardiogram.

We present a set of three fundamental methods for electrocardiogram (ECG) diagnostic interpretation adapted to process non-uniformly sampled signal. The growing volume of ECGs recorded daily all over the world (roughly estimated to be 600 TB) and the expectance of long persistence of these data (on the order of 40 years) motivated us to challenge the feasibility of medical-grade diagnostics directly based on arbitrary non-uniform (i.e., storage-efficient) ECG representation. We used a refined time-independent QRS detection method based on a moving shape matching technique. We applied a graph data representation to quantify the similarity of asynchronously sampled heartbeats. Finally, we applied a correlation-based non-uniform to time-scale transform to get a multiresolution ECG representation on a regular dyadic grid and to find precise P, QRS and T wave delimitation points. The whole processing chain was implemented and tested with MIT-BIH Database (probably the most referenced cardiac database) and CSE Multilead Database (used for conformance testing of medical instruments) signals arbitrarily sampled accordingly to a perceptual model (set for variable sampling frequency of 100–500 Hz, compression ratio 3.1). The QRS detection shows an accuracy of 99.93% with false detection ratio of only 0.18%. The classification shows an accuracy of 99.27% for 14 most frequent MIT-BIH beat types and 99.37% according to AAMI beat labels. The wave delineation shows cumulative (i.e., sampling model and non-uniform processing) errors of: 9.7 ms for P wave duration, 3.4 ms for QRS, 6.7 ms for P-Q segment and 17.7 ms for Q-T segment, all the values being acceptable for medical-grade interpretive software.

Self-Supervised ECG Representation Learning for Emotion Recognition

We exploit a self-supervised deep multi-task learning framework for electrocardiogram (ECG) -based emotion recognition. The proposed solution consists of two stages of learning a) learning ECG representations and b) learning to classify emotions. ECG representations are learned by a signal transformation recognition network. The network learns high-level abstract representations from unlabeled ECG data. Six different signal transformations are applied to the ECG signals, and transformation recognition is performed as pretext tasks. Training the model on pretext tasks helps the network learn spatiotemporal representations that generalize well across different datasets and different emotion categories. We transfer the weights of the self-supervised network to an emotion recognition network, where the convolutional layers are kept frozen and the dense layers are trained with labelled ECG data. We show that the proposed solution considerably improves the performance compared to a network trained using fully-supervised learning. New state-of-the-art results are set in classification of arousal, valence, affective states, and stress for the four utilized datasets. Extensive experiments are performed, providing interesting insights into the impact of using a multi-task self-supervised structure instead of a single-task model, as well as the optimum level of difficulty required for the pretext self-supervised tasks.

Detection of T Wave Peak for Serial Comparisons of JTp Interval.

Electrocardiogram (ECG) studies of drug-induced prolongation of the interval between the J point and the peak of the T wave (JTp interval) distinguished QT prolonging drugs that predominantly block the delayed potassium rectifier current from those affecting multiple cardiac repolarisation ion channel currents. Since the peak of the T wave depends on ECG lead, a “global” T peak requires to combine ECG leads into one-dimensional signal in which the T wave peak can be measured. This study aimed at finding the optimum one-dimensional representation of 12-lead ECGs for the most stable JTp measurements. Seven different one-dimensional representations were investigated including the vector magnitude of the orthogonal XYZ transformation, root mean square of all 12 ECG leads, and the vector magnitude of the 3 dominant orthogonal leads derived by singular value decomposition. All representations were applied to the median waveforms of 660,657 separate 10-s 12-lead ECGs taken from repeated day-time Holter recordings in 523 healthy subjects aged 33.5 ± 8.4 years (254 women). The JTp measurements were compared with the QT intervals and with the intervals between the J point and the median point of the area under the T wave one-dimensional representation (JT50 intervals) by means of calculating the residuals of the subject-specific curvilinear regression models relating the measured interval to the hysteresis-corrected RR interval of the underlying heart rate. The residuals of the regression models (equal to the intra-subject standard deviations of individually heart rate corrected intervals) expressed intra-subject stability of interval measurements. For both the JTp intervals and the JT50 intervals, the curvilinear regression residuals of measurements derived from the orthogonal XYZ representation were marginally but statistically significantly lower compared to the other representations. Using the XYZ representation, the residuals of the QT/RR, JTp/RR and JT50/RR regressions were 5.6 ± 1.1 ms, 7.2 ± 2.2 ms, and 4.9 ± 1.2 ms, respectively (all statistically significantly different; p < 0.0001). The study concludes that the orthogonal XYZ ECG representation might be proposed for future investigations of JTp and JT50 intervals. If the ability of classifying QT prolonging drugs is further confirmed for the JT50 interval, it might be appropriate to replace the JTp interval since with JT50 it appears more stable.

An Efficient Method to Learn Overcomplete Multi-Scale Dictionaries of ECG Signals

The electrocardiogram (ECG) was the first biomedical signal for which digital signal processing techniques were extensively applied. By its own nature, the ECG is typically a sparse signal, composed of regular activations (QRS complexes and other waveforms, such as the P and T waves) and periods of inactivity (corresponding to isoelectric intervals, such as the PQ or ST segments), plus noise and interferences. In this work, we describe an efficient method to construct an overcomplete and multi-scale dictionary for sparse ECG representation using waveforms recorded from real-world patients. Unlike most existing methods (which require multiple alternative iterations of the dictionary learning and sparse representation stages), the proposed approach learns the dictionary first, and then applies a fast sparse inference algorithm to model the signal using the constructed dictionary. As a result, our method is much more efficient from a computational point of view than other existing algorithms, thus becoming amenable to dealing with long recordings from multiple patients. Regarding the dictionary construction, we located first all the QRS complexes in the training database, then we computed a single average waveform per patient, and finally we selected the most representative waveforms (using a correlation-based approach) as the basic atoms that were resampled to construct the multi-scale dictionary. Simulations on real-world records from Physionet’s PTB database show the good performance of the proposed approach.

Towards End-to-End ECG Classification With Raw Signal Extraction and Deep Neural Networks.

This paper proposes deep learning methods with signal alignment that facilitate the end-to-end classification of raw electrocardiogram (ECG) signals into heartbeat types, i.e., normal beat or different types of arrhythmias. Time-domain sample points are extracted from raw ECG signals, and consecutive vectors are extracted from a sliding time-window covering these sample points. Each of these vectors comprises the consecutive sample points of a complete heartbeat cycle, which includes not only the QRS complex but also the P and T waves. Unlike existing heartbeat classification methods in which medical doctors extract handcrafted features from raw ECG signals, the proposed end-to-end method leverages a deep neural network for both feature extraction and classification based on aligned heartbeats. This strategy not only obviates the need to handcraft the features but also produces optimized ECG representation for heartbeat classification. Evaluations on the MIT-BIH arrhythmia database show that at the same specificity, the proposed patient-independent classifier can detect supraventricular- and ventricular-ectopic beats at a sensitivity that is at least 10% higher than current state-of-the-art methods. More importantly, there is a wide range of operating points in which both the sensitivity and specificity of the proposed classifier are higher than those achieved by state-of-the-art classifiers. The proposed classifier can also perform comparable to patient-specific classifiers, but at the same time enjoys the advantage of patient independence.

Inter-Patient ECG Heartbeat Classification with Temporal VCG Optimized by PSO

Classifying arrhythmias can be a tough task for a human being and automating this task is highly desirable. Nevertheless fully automatic arrhythmia classification through Electrocardiogram (ECG) signals is a challenging task when the inter-patient paradigm is considered. For the inter-patient paradigm, classifiers are evaluated on signals of unknown subjects, resembling the real world scenario. In this work, we explore a novel ECG representation based on vectorcardiogram (VCG), called temporal vectorcardiogram (TVCG), along with a complex network for feature extraction. We also fine-tune the SVM classifier and perform feature selection with a particle swarm optimization (PSO) algorithm. Results for the inter-patient paradigm show that the proposed method achieves the results comparable to state-of-the-art in MIT-BIH database (53% of Positive predictive (+P) for the Supraventricular ectopic beat (S) class and 87.3% of Sensitivity (Se) for the Ventricular ectopic beat (V) class) that TVCG is a richer representation of the heartbeat and that it could be useful for problems involving the cardiac signal and pattern recognition.

Using an ECG reference ontology for semantic interoperability of ECG data

In this paper we test the hypothesis that a domain reference ontology of the electrocardiogram (ECG) can be employed in an effective manner to achieve semantic integration between ECG data standards. Several standardization initiatives, namely AHA/MIT-BIH (Physionet), SCP-ECG and HL7 aECG, have led to heterogeneous conceptualizations of the ECG domain. We then argue that a shared anchor, the biomedical reality under scrutiny, can effectively support the semantic integration of these ECG standards into a coherent ECG representation for the sake of a unified Electronic Health Record (EHR) model. Our hypothesis is tested by means of an integration experiment that uses, on the one hand, an ECG Ontology and, on the other hand, elicited conceptual models of the ECG standards. As a conclusion, we attest the hypothesis and also provide an integration table depicting correspondence links between entities in the ECG Ontology and elements in the ECG standards.

An Effective and Efficient Compression Algorithm for ECG Signals With Irregular Periods

This paper presents an effective and efficient preprocessing algorithm for two-dimensional (2-D) electrocardiogram (ECG) compression to better compress irregular ECG signals by exploiting their inter- and intra-beat correlations. To better reveal the correlation structure, we first convert the ECG signal into a proper 2-D representation, or image. This involves a few steps including QRS detection and alignment, period sorting, and length equalization. The resulting 2-D ECG representation is then ready to be compressed by an appropriate image compression algorithm. We choose the state-of-the-art JPEG2000 for its high efficiency and flexibility. In this way, the proposed algorithm is shown to outperform some existing arts in the literature by simultaneously achieving high compression ratio (CR), low percent root mean squared difference (PRD), low maximum error (MaxErr), and low standard derivation of errors (StdErr). In particular, because the proposed period sorting method rearranges the detected heartbeats into a smoother image that is easier to compress, this algorithm is insensitive to irregular ECG periods. Thus either the irregular ECG signals or the QRS false-detection cases can be better compressed. This is a significant improvement over existing 2-D ECG compression methods. Moreover, this algorithm is not tied exclusively to JPEG2000. It can also be combined with other 2-D preprocessing methods or appropriate codecs to enhance the compression performance in irregular ECG cases.

What Is An Electrocardiogram (ECG)?

An electrocardiogram (ECG) is the representation of the electrical activity of the heart (cardiac) muscle as it is recorded from the body surface. This article describes in understandable terms the basics of an ECG. INTRODUCTION An electrocardiogram (ECG) is the representation of the electrical activity of the heart (cardiac) muscle as it is recorded from the body surface. The muscle cells of the heart are linked so closely to one another that electrical impulses can easily spread from one cell to the next. Certain groups of cardiac cells are designed to rapidly transmit electrical activity through the heart. These specialized cells include the atrial conduction tracks, the atrioventricular (AV) node, the bundle of His, the bundle branches, and the distal ventricular conduction system. In the resting state, cardiac muscle cells are “polarized”, with the inside of cells being negatively charged with respect to the outside. This charge is created by having a greater concentration of certain charged particles (ions) on one side of the cell membrane as compared with the other side. For example, the concentration of potassium ions is much higher inside the cells while the concentration of sodium ions is much higher outside. In response to stimuli, movement of these ions occurs, particularly a rapid inward movement of sodium. This causes a rapid loss of internal negative potential and thus generates electricity. This process is known as “depolarization”. The heart has some very specialized cells. The so-called automatic cells of the heart are capable of spontaneous depolarization. They are important in the generation of heart rhythm, and because of this they are also known as pacemaking cells. Under normal conditions, the pacemaking cells in a special area in the upper part of the heart called the sinoatrial (SA or sinus) node depolarize most rapidly and set the heart rate. Other pacemaking cells are situated in the atria (upper chambers of the heart), between the atria and the ventricles (called the AV node), and in the ventricles (lower chambers of the heart). Figure 1 Image 1: A modern ECG machine What Is An Electrocardiogram (ECG)? 2 of 4 Figure 2 Image 2: Recording an ECG from a patient READING A BASIC ECG The first crude ECG was described in 1903 by Willem Einthoven. His procedure has been expanded, and now the probes used to measure electricity (called electrodes) are placed on the right and left arms, left leg, and across the chest wall. Currently there are 12 standardized “leads” for the standard ECG: bipolar leads I, II and III, described by Einthoven, augmented unipolar leads aVR, aVL and aVF and unipolar precordial leads V1-V6. How do these “leads” work and what do they mean? Figure 3 Image 3: A normal ECG with all the different leads When current passes to the positive end of the bipolar (2sided) electrode, it causes a positive deflection, which corresponds to an upward movement of the pen on the ECG paper. Passage of current away from the positive pole of the bipolar electrode causes a negative deflection and a downward movement of the pen on the ECG paper. Current flowing at an oblique angle to the electrode causes smaller deflection, and current flowing perpendicular to the electrode does not cause any deflection in the recorder. Thus each lead “sees” the heart in a different way. This information is recorded on paper as a series of deflections and waves. The distances between the deflections on an ECG are called segments and the distance between waves are called intervals. Figure 4 Image 4: The different ECG segments of a heart beat The P wave represents depolarization of the upper part of the heart, the atria. P wave duration is a measure of the time required for depolarization to spread through the atria to the atrioventricular node. Normal maximum P wave duration is 0.1 seconds. The P-R interval begins at the beginning of the P wave and ends at the peak of the R wave. It represents the time required for an electrical impulse to depolarize the atria and reach the electrical conduction system of lower part of the heart, the ventricular. Normal P-R interval is 0.12 to 0.2 seconds in adults in normal heart rhythm (which is also called sinus rhythm). The QRS complex represents ventricular depolarization. The ST segment is abnormal (elevated or depressed) if the heart lacks oxygen. The T wave is an ECG representation of ventricular repolarization. The Q-T interval represents the time when the heart is unable to be depolarized, also called electrical systole. Heart muscle contraction or mechanical systole usually What Is An Electrocardiogram (ECG)? 3 of 4 begins during the recording of the QRS complex. Commonly encountered ECG abnormalities include:

What Is An Electrocardiogram (ECG)?

An electrocardiogram (ECG) is the representation of the electrical activity of the heart (cardiac) muscle as it is recorded from the body surface. This article describes in understandable terms the basics of an ECG. INTRODUCTION An electrocardiogram (ECG) is the representation of the electrical activity of the heart (cardiac) muscle as it is recorded from the body surface. The muscle cells of the heart are linked so closely to one another that electrical impulses can easily spread from one cell to the next. Certain groups of cardiac cells are designed to rapidly transmit electrical activity through the heart. These specialized cells include the atrial conduction tracks, the atrioventricular (AV) node, the bundle of His, the bundle branches, and the distal ventricular conduction system. In the resting state, cardiac muscle cells are “polarized”, with the inside of cells being negatively charged with respect to the outside. This charge is created by having a greater concentration of certain charged particles (ions) on one side of the cell membrane as compared with the other side. For example, the concentration of potassium ions is much higher inside the cells while the concentration of sodium ions is much higher outside. In response to stimuli, movement of these ions occurs, particularly a rapid inward movement of sodium. This causes a rapid loss of internal negative potential and thus generates electricity. This process is known as “depolarization”. The heart has some very specialized cells. The so-called automatic cells of the heart are capable of spontaneous depolarization. They are important in the generation of heart rhythm, and because of this they are also known as pacemaking cells. Under normal conditions, the pacemaking cells in a special area in the upper part of the heart called the sinoatrial (SA or sinus) node depolarize most rapidly and set the heart rate. Other pacemaking cells are situated in the atria (upper chambers of the heart), between the atria and the ventricles (called the AV node), and in the ventricles (lower chambers of the heart). Figure 1 Image 1: A modern ECG machine What Is An Electrocardiogram (ECG)? 2 of 4 Figure 2 Image 2: Recording an ECG from a patient READING A BASIC ECG The first crude ECG was described in 1903 by Willem Einthoven. His procedure has been expanded, and now the probes used to measure electricity (called electrodes) are placed on the right and left arms, left leg, and across the chest wall. Currently there are 12 standardized “leads” for the standard ECG: bipolar leads I, II and III, described by Einthoven, augmented unipolar leads aVR, aVL and aVF and unipolar precordial leads V1-V6. How do these “leads” work and what do they mean? Figure 3 Image 3: A normal ECG with all the different leads When current passes to the positive end of the bipolar (2sided) electrode, it causes a positive deflection, which corresponds to an upward movement of the pen on the ECG paper. Passage of current away from the positive pole of the bipolar electrode causes a negative deflection and a downward movement of the pen on the ECG paper. Current flowing at an oblique angle to the electrode causes smaller deflection, and current flowing perpendicular to the electrode does not cause any deflection in the recorder. Thus each lead “sees” the heart in a different way. This information is recorded on paper as a series of deflections and waves. The distances between the deflections on an ECG are called segments and the distance between waves are called intervals. Figure 4 Image 4: The different ECG segments of a heart beat The P wave represents depolarization of the upper part of the heart, the atria. P wave duration is a measure of the time required for depolarization to spread through the atria to the atrioventricular node. Normal maximum P wave duration is 0.1 seconds. The P-R interval begins at the beginning of the P wave and ends at the peak of the R wave. It represents the time required for an electrical impulse to depolarize the atria and reach the electrical conduction system of lower part of the heart, the ventricular. Normal P-R interval is 0.12 to 0.2 seconds in adults in normal heart rhythm (which is also called sinus rhythm). The QRS complex represents ventricular depolarization. The ST segment is abnormal (elevated or depressed) if the heart lacks oxygen. The T wave is an ECG representation of ventricular repolarization. The Q-T interval represents the time when the heart is unable to be depolarized, also called electrical systole. Heart muscle contraction or mechanical systole usually What Is An Electrocardiogram (ECG)? 3 of 4 begins during the recording of the QRS complex. Commonly encountered ECG abnormalities include:

Waveform vector analysis of orthogonal electrocardiograms: Quantification and data reduction

Quantification of vectorcardiogram (VCG) analysis by waveform vector analysis (WVA) provides a more stable data base for computer analysis of P, ST and T vectors than does polar-cardiography. Furthermore, compared with data bases composed of Cartesian or polar coordinates of ‘instantaneous’ vectors, it reduces the data and also reduces noise by smoothing. This method is applicable to electrocardiogram (ECG) analysis also. Modified Chebyshev polynomials up to the quaternary term are used as waveform functions for signal representation of scalar ECG, and corresponding waveform coefficients quantify the mean value, gradient, degree of concavity or convexity, biphasic or sigmoid shape, and triphasic or quarternary features. Applied to a vector function of time, the waveform coefficients comprise components of the five vectors—mean (MV), gradient (GV), convex (CV), sigmoid (SV), and quaternary vectors (QV). A waveform power index is derived to express the contribution of each component to overall variation. P, ST, and T vectors of 1,984 rest and exercise VCG of 992 male subjects were analyzed. Representation of the vector function was considered adequate when the approximation error was <25 μV (root mean square; RMS) for each scalar component. In 95% of the records, two waveform vectors adequately reproduced the ST vectors, four were needed for P vectors, and five for T vectors.

ON THE REPRESENTATION OF ELECTROCARDIOGRAMS.

In dealing with the sophisticated statistical analysis of medical signals such as the electrocardiogram (ECG), the first problem one encounters is how to describe each ECG by a few numbers. This is the problem of efficient representation of signals, i.e., to approximate the signal with the smallest number of basis signals while preserving the accuracy of the approximation. This paper begins with a discussion of signal representation in general. The concept of signal space is introduced, which is very helpful in understanding the ideas of signal representation. This portion of the material is of tutorial nature. Attention is then directed to a set of basis components which we have found to be very efficient for ECG representation. These components are the so-called orthonormal exponential signals. An iterative process is developed which enables us to find a set of matched exponents for the representation of all ECGs. With six pairs of such exponentials, the average error of ECG representation (QRS and T waves only, leaving out P wave) is in the vicinity of five per cent. Experimental results will be shown. Using this representation, further statistical analysis may be carried out with ease.