Computer modeling and signal analysis of cardiovascular physiology

This dissertation aims to study cardiovascular physiology from the cellular level to the whole heart level to the body level using numerical approaches. A mathematical model was developed to describe electromechanical interaction in the heart. The model integrates cardio-electrophysiology and cardiac mechanics through excitation-induced contraction and deformation-induced currents. A finite element based parallel simulation scheme was developed to investigate coupled electrical and mechanical functions. The developed model and numerical scheme were utilized to study cardiovascular dynamics at cellular, tissue and organ levels. The influence of ion channel blockade on cardiac alternans was investigated. It was found that the channel blocker may significantly change the critical pacing period corresponding to the onset of alternans as well as the alternans’ amplitude. The influence of electro-mechanical coupling on cardiac alternans was also investigated. The study supported the earlier assumptions that discordant alternans is induced by the interaction of conduction velocity and action potential duration restitution at high pacing rates. However, mechanical contraction may influence the spatial pattern and onset of discordant alternans. Computer algorithms were developed for analysis of human physiology. The 12-lead electrocardiography (ECG) is the gold standard for diagnosis of various cardiac abnormalities. However, disturbances and mistakes may modify physiological waves in ECG and lead to wrong diagnoses. This dissertation developed advanced signal analysis techniques and computer software to detect and suppress artifacts and errors in ECG. These algorithms can help to improve the quality of health care when integrated into medical devices or services. Moreover, computer algorithms were developed to predict patient mortality in intensive care units using various physiological measures. Models and analysis techniques developed here may help to improve the quality of health care

ECG analysis and classification using CSVM, MSVM and SIMCA classifiers

Reliable ECG classification can potentially lead to better detection methods and increase accurate diagnosis of arrhythmia, thus improving quality of care. This thesis investigated the use of two novel classification algorithms: CSVM and SIMCA, and assessed their performance in classifying ECG beats. The project aimed to introduce a new way to interactively support patient care in and out of the hospital and develop new classification algorithms for arrhythmia detection and diagnosis. Wave (P-QRS-T) detection was performed using the WFDB Software Package and multiresolution wavelets. Fourier and PCs were selected as time-frequency features in the ECG signal; these provided the input to the classifiers in the form of DFT and PCA coefficients. ECG beat classification was performed using binary SVM. MSVM, CSVM, and SIMCA; these were subsequently used for simultaneously classifying either four or six types of cardiac conditions. Binary SVM classification with 100% accuracy was achieved when applied on feature-reduced ECG signals from well-established databases using PCA. The CSVM algorithm and MSVM were used to classify four ECG beat types: NORMAL, PVC, APC, and FUSION or PFUS; these were from the MIT-BIH arrhythmia database (precordial lead group and limb lead II). Different numbers of Fourier coefficients were considered in order to identify the optimal number of features to be presented to the classifier. SMO was used to compute hyper-plane parameters and threshold values for both MSVM and CSVM during the classifier training phase. The best classification accuracy was achieved using fifty Fourier coefficients. With the new CSVM classifier framework, accuracies of 99%, 100%, 98%, and 99% were obtained using datasets from one, two, three, and four precordial leads, respectively. In addition, using CSVM it was possible to successfully classify four types of ECG beat signals extracted from limb lead simultaneously with 97% accuracy, a significant improvement on the 83% accuracy achieved using the MSVM classification model. In addition, further analysis of the following four beat types was made: NORMAL, PVC, SVPB, and FUSION. These signals were obtained from the European ST-T Database. Accuracies between 86% and 94% were obtained for MSVM and CSVM classification, respectively, using 100 Fourier coefficients for reconstructing individual ECG beats. Further analysis presented an effective ECG arrhythmia classification scheme consisting of PCA as a feature reduction method and a SIMCA classifier to differentiate between either four or six different types of arrhythmia. In separate studies, six and four types of beats (including NORMAL, PVC, APC, RBBB, LBBB, and FUSION beats) with time domain features were extracted from the MIT-BIH arrhythmia database and the St Petersburg INCART 12-lead Arrhythmia Database (incartdb) respectively. Between 10 and 30 PCs, coefficients were selected for reconstructing individual ECG beats in the feature selection phase. The average classification accuracy of the proposed scheme was 98.61% and 97.78 % using the limb lead and precordial lead datasets, respectively. In addition, using MSVM and SIMCA classifiers with four ECG beat types achieved an average classification accuracy of 76.83% and 98.33% respectively. The effectiveness of the proposed algorithms was finally confirmed by successfully classifying both the six beat and four beat types of signal respectively with a high accuracy ratio

Non-invasive fetal electrocardiogram : analysis and interpretation

High-risk pregnancies are becoming more and more prevalent because of the progressively higher age at which women get pregnant. Nowadays about twenty percent of all pregnancies are complicated to some degree, for instance because of preterm delivery, fetal oxygen deficiency, fetal growth restriction, or hypertension. Early detection of these complications is critical to permit timely medical intervention, but is hampered by strong limitations of existing monitoring technology. This technology is either only applicable in hospital settings, is obtrusive, or is incapable of providing, in a robust way, reliable information for diagnosis of the well-being of the fetus. The most prominent method for monitoring of the fetal health condition is monitoring of heart rate variability in response to activity of the uterus (cardiotocography; CTG). Generally, in obstetrical practice, the heart rate is determined in either of two ways: unobtrusively with a (Doppler) ultrasound probe on the maternal abdomen, or obtrusively with an invasive electrode fixed onto the fetal scalp. The first method is relatively inaccurate but is non-invasive and applicable in all stages of pregnancy. The latter method is far more accurate but can only be applied following rupture of the membranes and sufficient dilatation, restricting its applicability to only the very last phase of pregnancy. Besides these accuracy and applicability issues, the use of CTG in obstetrical practice also has another limitation: despite its high sensitivity, the specificity of CTG is relatively low. This means that in most cases of fetal distress the CTG reveals specific patterns of heart rate variability, but that these specific patterns can also be encountered for healthy fetuses, complicating accurate diagnosis of the fetal condition. Hence, a prerequisite for preventing unnecessary interventions that are based on CTG alone, is the inclusion of additional information in diagnostics. Monitoring of the fetal electrocardiogram (ECG), as a supplement of CTG, has been demonstrated to have added value for monitoring of the fetal health condition. Unfortunately the application of the fetal ECG in obstetrical diagnostics is limited because at present the fetal ECG can only be measured reliably by means of an invasive scalp electrode. To overcome this limited applicability, many attempts have been made to record the fetal ECG non-invasively from the maternal abdomen, but these attempts have not yet led to approaches that permit widespread clinical application. One key difficulty is that the signal to noise ratio (SNR) of the transabdominal ECG recordings is relatively low. Perhaps even more importantly, the abdominal ECG recordings yield ECG signals for which the morphology depends strongly on the orientation of the fetus within the maternal uterus. Accordingly, for any fetal orientation, the ECG morphology is different. This renders correct clinical interpretation of the recorded ECG signals complicated, if not impossible. This thesis aims to address these difficulties and to provide new contributions on the clinical interpretation of the fetal ECG. At first the SNR of the recorded signals is enhanced through a series of signal processing steps that exploit specific and a priori known properties of the fetal ECG. More particularly, the dominant interference (i.e. the maternal ECG) is suppressed by exploiting the absence of temporal correlation between the maternal and fetal ECG. In this suppression, the maternal ECG complex is dynamically segmented into individual ECG waves and each of these waves is estimated through averaging corresponding waves from preceding ECG complexes. The maternal ECG template generated by combining the estimated waves is subsequently subtracted from the original signal to yield a non-invasive recording in which the maternal ECG has been suppressed. This suppression method is demonstrated to be more accurate than existing methods. Other interferences and noise are (partly) suppressed by exploiting the quasiperiodicity of the fetal ECG through averaging consecutive ECG complexes or by exploiting the spatial correlation of the ECG. The averaging of several consecutive ECG complexes, synchronized on their QRS complex, enhances the SNR of the ECG but also can suppress morphological variations in the ECG that are clinically relevant. The number of ECG complexes included in the average hence constitutes a trade-off between SNR enhancement on the one hand and loss of morphological variability on the other hand. To relax this trade-off, in this thesis a method is presented that can adaptively estimate the number of ECG complexes included in the average. In cases of morphological variations, this number is decreased ensuring that the variations are not suppressed. In cases of no morphological variability, this number is increased to ensure adequate SNR enhancement. The further suppression of noise by exploiting the spatial correlation of the ECG is based on the fact that all ECG signals recorded at several locations on the maternal abdomen originate from the same electrical source, namely the fetal heart. The electrical activity of the fetal heart at any point in time can be modeled as a single electrical field vector with stationary origin. This vector varies in both amplitude and orientation in three-dimensional space during the cardiac cycle and the time-path described by this vector is referred to as the fetal vectorcardiogram (VCG). In this model, the abdominal ECG constitutes the projection of the VCG onto the vector that describes the position of the abdominal electrode with respect to a reference electrode. This means that when the VCG is known, any desired ECG signal can be calculated. Equivalently, this also means that when enough ECG signals (i.e. at least three independent signals) are known, the VCG can be calculated. By using more than three ECG signals for the calculation of the VCG, redundancy in the ECG signals can be exploited for added noise suppression. Unfortunately, when calculating the fetal VCG from the ECG signals recorded from the maternal abdomen, the distance between the fetal heart and the electrodes is not the same for each electrode. Because the amplitude of the ECG signals decreases with propagation to the abdominal surface, these different distances yield a specific, unknown attenuation for each ECG signal. Existing methods for estimating the VCG operate with a fixed linear combination of the ECG signals and, hence, cannot account for variations in signal attenuation. To overcome this problem and be able to account for fetal movement, in this thesis a method is presented that estimates both the VCG and, to some extent, also the signal attenuation. This is done by determining for which VCG and signal attenuation the joint probability over both these variables is maximal given the observed ECG signals. The underlying joint probability distribution is determined by assuming the ECG signals to originate from scaled VCG projections and additive noise. With this method, a VCG, tailored to each specific patient, is determined. With respect to the fixed linear combinations, the presented method performs significantly better in the accurate estimation of the VCG. Besides describing the electrical activity of the fetal heart in three dimensions, the fetal VCG also provides a framework to account for the fetal orientation in the uterus. This framework enables the detection of the fetal orientation over time and allows for rotating the fetal VCG towards a prescribed orientation. From the normalized fetal VCG obtained in this manner, standardized ECG signals can be calculated, facilitating correct clinical interpretation of the non-invasive fetal ECG signals. The potential of the presented approach (i.e. the combination of all methods described above) is illustrated for three different clinical cases. In the first case, the fetal ECG is analyzed to demonstrate that the electrical behavior of the fetal heart differs significantly from the adult heart. In fact, this difference is so substantial that diagnostics based on the fetal ECG should be based on different guidelines than those for adult ECG diagnostics. In the second case, the fetal ECG is used to visualize the origin of fetal supraventricular extrasystoles and the results suggest that the fetal ECG might in future serve as diagnostic tool for relating fetal arrhythmia to congenital heart diseases. In the last case, the non-invasive fetal ECG is compared to the invasively recorded fetal ECG to gauge the SNR of the transabdominal recordings and to demonstrate the suitability of the non-invasive fetal ECG in clinical applications that, as yet, are only possible for the invasive fetal ECG

Examination of myocardial electrophysiology using novel panoramic optical mapping techniques

Optical mapping of voltage signals has revolutionised the field and study of cardiac electrophysiology by providing the means to visualise changes in electrical activity at a high temporal and spatial resolution from the cellular to the whole heart level under both normal and disease conditions. The aim of this thesis was to develop a novel method of panoramic optical mapping using a single camera and to study myocardial electrophysiology in isolated Langendorff-perfused rabbit hearts. First, proper procedures for selection, filtering and analysis of the optical data recorded from the panoramic optical mapping system were established. This work was followed by extensive characterisation of the electrical activity across the epicardial surface of the preparation investigating time and heart dependent effects. In an initial study, features of epicardial electrophysiology were examined as the temperature of the heart was reduced below physiological values. This manoeuvre was chosen to mimic the temperatures experienced during various levels of hypothermia in vivo, a condition known to promote arrhythmias. The facility for panoramic optical mapping allowed the extent of changes in conduction timing and pattern of ventricular activation and repolarisation to be assessed. In the main experimental section, changes in epicardial electrical activity were assessed under various pacing conditions in both normal hearts and in a rabbit model of chronic MI. In these experiments, there was significant changes in the pattern of electrical activation corresponding with the changes in pacing regime. These experiments demonstrated a negative correlation between activation time and APD, which was not maintained during ventricular pacing. This suggests that activation pattern is not the sole determinant of action potential duration in intact hearts. Lastly, a realistic 3D computational model of the rabbit left ventricle was developed to simulate the passive and active mechanical properties of the heart. The aim of this model was to infer further information from the experimental optical mapping studies. In future, it would be feasible to gain insight into the electrical and mechanical performance of the heart by simulating experimental pacing conditions in the model

The Application of Computer Techniques to ECG Interpretation

This book presents some of the latest available information on automated ECG analysis written by many of the leading researchers in the field. It contains a historical introduction, an outline of the latest international standards for signal processing and communications and then an exciting variety of studies on electrophysiological modelling, ECG Imaging, artificial intelligence applied to resting and ambulatory ECGs, body surface mapping, big data in ECG based prediction, enhanced reliability of patient monitoring, and atrial abnormalities on the ECG. It provides an extremely valuable contribution to the field

Automated Cardiac Rhythm Diagnosis for Electrophysiological Studies, an Enhanced Classifier Approach

INTRODUCTION Heart function can be impaired by rhythm disturbances (cardiac arrhythmia), illustrated by electrocardiogram (ECG) recordings. Computerised arrhythmia diagnosis is well established for ECG’s but less for intracardiac electrophysiological (EP) testing. Accurate diagnosis is pre-requisite for delivering appropriate treatment to patients however existing algorithms misdiagnose a proportion of arrhythmias. Studies suggested artificial intelligence (AI) classifiers are accurate using ECG and intracardiac electrogram features and reviews suggested new features might augment diagnosis. This study aimed to develop an accurate cardiac rhythm diagnostic algorithm for electrophysiological (EP) studies with potential application as a generic rhythm classifier. METHOD An ethically approved prospective clinical study collected clinical history, right atrial and right ventricular intracardiac electrograms, beat-to-beat cardiac stroke volume, body motion and body temperature data during EP studies. An iterative system development life-cycle was used, including knowledge management and classifier development sub-processes. Domain expert knowledge and clinical arrhythmia diagnosis were modelled, synthesised as AI classifiers and used to classify cardiac rhythms. RESULTS Data collected from 65 patients was pre-processed into instances for classifier inputs. Decision tree, naïve Bayes, neural network, support vector machine and inference engine classifiers developed using Matlab showed good performance and were combined as a production system in a mixture-of-experts multi-classifier system. 18 different rhythms were classified, with the naïve Bayes classifier used to classify 11 rhythms, decision tree 4 rhythms, neural network and support vector machine one each, unclassified instances by the inference engine classifier and final class allocation using decision rule. Production system showed overall correct clasification rate 0.960; error 0.040; mean sensitivity 0.855; mean specificity 0.977; mean κ 0.767; mean positive predictive value 0.792; mean negative predictive value 0.975; mean Pearson’s phi 0.787, with P 0.9 for sinus node dysfunction and atrio-ventricular nodal/ junctional tachycardias. Temperature, accelerometry and QT interval were assessed as features by a comparison of algorithm performances with each feature removed and found not to affect classification performance. An evaluation showed 10 beat analysis performed better than 5 beat analysis. CONCLUSIONS Modelling of the clinical diagnosis process produced an AI based mixture-of-experts multi-classifier system, which accurately diagnosed different 18 cardiac rhythms. The naïve Bayes classifier performed best and classified 11 rhythms. Features for clinical symptoms and predisposing factors, atrial electrogram morphology and changes in stroke volume were found to influence rhythm classification. High performances encourage further development and potential future improvements include: a larger sample dataset; inclusion of His and coronary sinus electrograms; data mining for unknown features with significant influence on diagnosis; binary classification. The aim to classify rhythm using artificial intelligence suitable for use during EP studies was satisfied and the research hypothesis that it outperformed current algorithms was accepted. The system was likely to be able to accept updates but needs conversion as a precursor to use in a live clinical environment

Statistical and Graph-Based Signal Processing: Fundamental Results and Application to Cardiac Electrophysiology

The goal of cardiac electrophysiology is to obtain information about the mechanism, function, and performance of the electrical activities of the heart, the identification of deviation from normal pattern and the design of treatments. Offering a better insight into cardiac arrhythmias comprehension and management, signal processing can help the physician to enhance the treatment strategies, in particular in case of atrial fibrillation (AF), a very common atrial arrhythmia which is associated to significant morbidities, such as increased risk of mortality, heart failure, and thromboembolic events. Catheter ablation of AF is a therapeutic technique which uses radiofrequency energy to destroy atrial tissue involved in the arrhythmia sustenance, typically aiming at the electrical disconnection of the of the pulmonary veins triggers. However, recurrence rate is still very high, showing that the very complex and heterogeneous nature of AF still represents a challenging problem. Leveraging the tools of non-stationary and statistical signal processing, the first part of our work has a twofold focus: firstly, we compare the performance of two different ablation technologies, based on contact force sensing or remote magnetic controlled, using signal-based criteria as surrogates for lesion assessment. Furthermore, we investigate the role of ablation parameters in lesion formation using the late-gadolinium enhanced magnetic resonance imaging. Secondly, we hypothesized that in human atria the frequency content of the bipolar signal is directly related to the local conduction velocity (CV), a key parameter characterizing the substrate abnormality and influencing atrial arrhythmias. Comparing the degree of spectral compression among signals recorded at different points of the endocardial surface in response to decreasing pacing rate, our experimental data demonstrate a significant correlation between CV and the corresponding spectral centroids. However, complex spatio-temporal propagation pattern characterizing AF spurred the need for new signals acquisition and processing methods. Multi-electrode catheters allow whole-chamber panoramic mapping of electrical activity but produce an amount of data which need to be preprocessed and analyzed to provide clinically relevant support to the physician. Graph signal processing has shown its potential on a variety of applications involving high-dimensional data on irregular domains and complex network. Nevertheless, though state-of-the-art graph-based methods have been successful for many tasks, so far they predominantly ignore the time-dimension of data. To address this shortcoming, in the second part of this dissertation, we put forth a Time-Vertex Signal Processing Framework, as a particular case of the multi-dimensional graph signal processing. Linking together the time-domain signal processing techniques with the tools of GSP, the Time-Vertex Signal Processing facilitates the analysis of graph structured data which also evolve in time. We motivate our framework leveraging the notion of partial differential equations on graphs. We introduce joint operators, such as time-vertex localization and we present a novel approach to significantly improve the accuracy of fast joint filtering. We also illustrate how to build time-vertex dictionaries, providing conditions for efficient invertibility and examples of constructions. The experimental results on a variety of datasets suggest that the proposed tools can bring significant benefits in various signal processing and learning tasks involving time-series on graphs. We close the gap between the two parts illustrating the application of graph and time-vertex signal processing to the challenging case of multi-channels intracardiac signals

Security and privacy services based on biosignals for implantable and wearable device

Mención Internacional en el título de doctorThe proliferation of wearable and implantable medical devices has given rise to an interest in developing security schemes suitable for these devices and the environment in which they operate. One area that has received much attention lately is the use of (human) biological signals as the basis for biometric authentication, identification and the generation of cryptographic keys. More concretely, in this dissertation we use the Electrocardiogram (ECG) to extract some fiducial points which are later used on crytographic protocols. The fiducial points are used to describe the points of interest which can be extracted from biological signals. Some examples of fiducials points of the ECG are P-wave, QRS complex,T-wave, R peaks or the RR-time-interval. In particular, we focus on the time difference between two consecutive heartbeats (R-peaks). These time intervals are referred to as Inter-Pulse Intervals (IPIs) and have been proven to contain entropy after applying some signal processing algorithms. This process is known as quantization algorithm. Theentropy that the heart signal has makes the ECG values an ideal candidate to generate tokens to be used on security protocols. Most of the proposed solutions in the literature rely on some questionable assumptions. For instance, it is commonly assumed that it possible to generate the same cryptographic token in at least two different devices that are sensing the same signal using the IPI of each cardiac signal without applying any synchronization algorithm; authors typically only measure the entropy of the LSB to determine whether the generated cryptographic values are random or not; authors usually pick the four LSBs assuming they are the best ones to create the best cryptographic tokens; the datasets used in these works are rather small and, therefore, possibly not significant enough, or; in general it is impossible to reproduce the experiments carried out by other researchers because the source code of such experiments is not usually available. In this Thesis, we overcome these weaknesses trying to systematically address most of the open research questions. That is why, in all the experiments carried out during this research we used a public database called PhysioNet which is available on Internet and stores a huge heart database named PhysioBank. This repository is constantly being up dated by medical researchers who share the sensitive information about patients and it also offers an open source software named PhysioToolkit which can be used to read and display these signals. All datasets we used contain ECG records obtained from a variety of real subjects with different heart-related pathologies as well as healthy people. The first chapter of this dissertation (Chapter 1) is entirely dedicated to present the research questions, introduce the main concepts used all along this document as well as settle down some medical and cryptographic definitions. Finally, the objectives that this dissertation tackles down are described together with the main motivations for this Thesis. In Chapter 2 we report the results of a large-scale statistical study to determine if heart signal is a good source of entropy. For this, we analyze 19 public datasets of heart signals from the Physionet repository, spanning electrocardiograms from multiple subjects sampled at different frequencies and lengths. We then apply both ENT and NIST STS standard battery of randomness tests to the extracted IPIs. The results we obtain through the analysis, clearly show that a short burst of bits derived from an ECG record may seem random, but large files derived from long ECG records should not be used for security purposes. In Chapter3, we carry out an análisis to check whether it is reasonable or not the assumption that two different sensors can generate the same cryptographic token. We systematically check if two sensors can agree on the same token without sharing any type of information. Similarly to other proposals, we include ECC algorithms like BCH to the token generation. We conclude that a fuzzy extractor (or another error correction technique) is not enough to correct the synchronization errors between the IPI values derived from two ECG signals captured via two sensors placed on different positions. We demonstrate that a pre-processing of the heart signal must be performed before the fuzzy extractor is applied. Going one step forward and, in order to generate the same token on different sensors, we propose a synchronization algorithm. To do so, we include a runtimemonitoralgorithm. Afterapplyingourproposedsolution,werun again the experiments with 19 public databases from the PhysioNet repository. The only constraint to pick those databases was that they need at least two measurements of heart signals (ECG1 and ECG2). As a conclusion, running the experiments, the same token can be dexix rived on different sensors in most of the tested databases if and only if a pre-processing of the heart signal is performed before extracting the tokens. In Chapter 4, we analyze the entropy of the tokens extracted from a heart signal according to the NISTSTS recommendation (i.e.,SP80090B Recommendation for the Entropy Sources Used for Random Bit Generation). We downloaded 19 databases from the Physionet public repository and analyze, in terms of min-entropy, more than 160,000 files. Finally, we propose other combinations for extracting tokens by taking 2, 3, 4 and 5 bits different than the usual four LSBs. Also, we demonstrate that the four LSB are not the best bits to be used in cryptographic applications. We offer other alternative combinations for two (e.g., 87), three (e.g., 638), four (e.g., 2638) and five (e.g., 23758) bits which are, in general, much better than taking the four LSBs from the entropy point of view. Finally, the last Chapter of this dissertation (Chapter 5) summarizes the main conclusions arisen from this PhD Thesis and introduces some open questions.Programa de Doctorado en Ciencia y Tecnología Informática por la Universidad Carlos III de MadridPresidente: Arturo Ribagorda Garnacho.- Secretario: Jorge Blasco Alis.- Vocal: Jesús García López de la Call

Computational methods for physiological data

Thesis (Ph. D.)--Harvard-MIT Division of Health Sciences and Technology, 2009.Author is also affiliated with the MIT Dept. of Electrical Engineering and Computer Science. Cataloged from PDF version of thesis.Includes bibliographical references (p. 177-188).Large volumes of continuous waveform data are now collected in hospitals. These datasets provide an opportunity to advance medical care, by capturing rare or subtle phenomena associated with specific medical conditions, and by providing fresh insights into disease dynamics over long time scales. We describe how progress in medicine can be accelerated through the use of sophisticated computational methods for the structured analysis of large multi-patient, multi-signal datasets. We propose two new approaches, morphologic variability (MV) and physiological symbolic analysis, for the analysis of continuous long-term signals. MV studies subtle micro-level variations in the shape of physiological signals over long periods. These variations, which are often widely considered to be noise, can contain important information about the state of the underlying system. Symbolic analysis studies the macro-level information in signals by abstracting them into symbolic sequences. Converting continuous waveforms into symbolic sequences facilitates the development of efficient algorithms to discover high risk patterns and patients who are outliers in a population. We apply our methods to the clinical challenge of identifying patients at high risk of cardiovascular mortality (almost 30% of all deaths worldwide each year). When evaluated on ECG data from over 4,500 patients, high MV was strongly associated with both cardiovascular death and sudden cardiac death. MV was a better predictor of these events than other ECG-based metrics. Furthermore, these results were independent of information in echocardiography, clinical characteristics, and biomarkers.(cont.) Our symbolic analysis techniques also identified groups of patients exhibiting a varying risk of adverse outcomes. One group, with a particular set of symbolic characteristics, showed a 23 fold increased risk of death in the months following a mild heart attack, while another exhibited a 5 fold increased risk of future heart attacks.by Zeeshan Hassan Syed.Ph.D