Theory, modelling and applications of electrocardiographic mapping

In this thesis, the genesis and applications of electromagnetic signals from the human heart are investigated through theory, modelling, signal processing and clinical studies. One objective of the thesis was to develop and test signal processing methods that would be applicable to multichannel electro- and magnetocardiographic data. A signal processing method based on a type of neural networks called the self-organizing maps is introduced for spatiotemporal analysis of the body surface potential maps produced by the beating heart. This method is capable of utilizing both the spatial morphology of the potential distributions on the body surface as well as their temporal development. A signal processing method aimed at providing a reliable electric baseline for more traditional isointegral analysis of the body surface potential mapping (BSPM) data is also introduced. Another objective of the thesis was to show the utility of electrocardiographic mapping in clinical use. This was demonstrated by applying electro- and magnetocardiographic mapping to evaluation of the propensity to life-threatening arrhythmias in postinfarction patients. Electrocardiographic mapping was found to perform equally well compared to more traditional SA-ECG, but electrocardiographic mapping may be more robust against individual variability in anatomy. A third objective of the thesis was to build a computer model of the human heart that is capable of simulating the normal ventricular activation. The propagation model is based on a bidomain formulation of the cardiac tissue applied to realistic geometry of the ventricles. An anatomically accurate model of the human conduction system that reproduces measured activation sequence of the human heart was developed in this thesis. The body surface potentials and the magnetic fields computed from the simulated activation corresponded to recordings from normal subjects. In summary, the thesis demonstrates the utility of electrocardiographic mapping in clinical use and introduces new signal processing methods that can be applied to this use. Finally, a computer model of the human heart binds together the physiology and anatomy of the human heart and body, classical electromagnetic theory, and computer science to explain the genesis and characteristics of the electromagnetic signals from the human heart.reviewe

Uncertainty Quantification and Reduction in Cardiac Electrophysiological Imaging

Cardiac electrophysiological (EP) imaging involves solving an inverse problem that infers cardiac electrical activity from body-surface electrocardiography data on a physical domain defined by the body torso. To avoid unreasonable solutions that may fit the data, this inference is often guided by data-independent prior assumptions about different properties of cardiac electrical sources as well as the physical domain. However, these prior assumptions may involve errors and uncertainties that could affect the inference accuracy. For example, common prior assumptions on the source properties, such as fixed spatial and/or temporal smoothness or sparseness assumptions, may not necessarily match the true source property at different conditions, leading to uncertainties in the inference. Furthermore, prior assumptions on the physical domain, such as the anatomy and tissue conductivity of different organs in the thorax model, represent an approximation of the physical domain, introducing errors to the inference. To determine the robustness of the EP imaging systems for future clinical practice, it is important to identify these errors/uncertainties and assess their impact on the solution. This dissertation focuses on the quantification and reduction of the impact of uncertainties caused by prior assumptions/models on cardiac source properties as well as anatomical modeling uncertainties on the EP imaging solution. To assess the effect of fixed prior assumptions/models about cardiac source properties on the solution of EP imaging, we propose a novel yet simple Lp-norm regularization method for volumetric cardiac EP imaging. This study reports the necessity of an adaptive prior model (rather than fixed model) for constraining the complex spatiotemporally changing properties of the cardiac sources. We then propose a multiple-model Bayesian approach to cardiac EP imaging that employs a continuous combination of prior models, each re-effecting a specific spatial property for volumetric sources. The 3D source estimation is then obtained as a weighted combination of solutions across all models. Including a continuous combination of prior models, our proposed method reduces the chance of mismatch between prior models and true source properties, which in turn enhances the robustness of the EP imaging solution. To quantify the impact of anatomical modeling uncertainties on the EP imaging solution, we propose a systematic statistical framework. Founded based on statistical shape modeling and unscented transform, our method quantifies anatomical modeling uncertainties and establish their relation to the EP imaging solution. Applied on anatomical models generated from different image resolutions and different segmentations, it reports the robustness of EP imaging solution to these anatomical shape-detail variations. We then propose a simplified anatomical model for the heart that only incorporates certain subject-specific anatomical parameters, while discarding local shape details. Exploiting less resources and processing for successful EP imaging, this simplified model provides a simple clinically-compatible anatomical modeling experience for EP imaging systems. Different components of our proposed methods are validated through a comprehensive set of synthetic and real-data experiments, including various typical pathological conditions and/or diagnostic procedures, such as myocardial infarction and pacing. Overall, the methods presented in this dissertation for the quantification and reduction of uncertainties in cardiac EP imaging enhance the robustness of EP imaging, helping to close the gap between EP imaging in research and its clinical application

Functional Mapping of Three-Dimensional Electrical Activation in Ventricles

University of Minnesota Ph.D. dissertation. 2010. Major: Biomedical Engineering. Advisor: Bin He. 1 computer file (PDF); 139 pages.Ventricular arrhythmias account for nearly 400,000 deaths per year in the United States alone. Electrical mapping of the ventricular activation could facilitate the diagnosis and treatment of arrhythmias, e.g. guiding catheter ablation. To date, both direct mapping and non-contact mapping techniques have been routinely used in electrophysiology labs for obtaining the electrical activity on the endocardial surface. Non-invasive functional mapping methods are also developed to estimate the electrical activity on the epicardium or on both epicardium and endocardium from the body surface measurements. Though successful, the results using above methods are all limited on the surface of the heart and thus cannot directly characterize the cardiac events originating within the myocardial wall. Our group's goal is to develop a functional mapping method to estimate the three-dimensional cardiac electrical activity from either non-invasive body surface potential maps or minimally-invasive intracavitary potential maps, by solving the so-called "inverse problem". Hence the information under the surface of the heart could be revealed to better characterize the cardiac activation. In the present thesis study, the previously developed three-dimensional cardiac electrical imaging (3DCEI) approach has been further investigated. Its function is expanded for not only estimating the global activation sequence but also reconstructing the potential at any myocardial site throughout the ventricle. New algorithms under the 3DCEI scheme are also explored for more powerful mapping capability. The performance of the enhanced 3DCEI approach is rigorously evaluated in both control and diseased swine models when the clinical settings are mimicked. The promising results validate the feasibility of estimating detailed three-dimensional cardiac activation by using the 3DCEI approach, and suggest that 3DCEI has great potential of guiding the clinical management of cardiac arrhythmias in a more efficient way

Magnetocardiography in unshielded environment based on optical magnetometry and adaptive noise cancellation

This thesis proposes and demonstrates the concept of a magnetocardiographic system employing an array of optically-pumped quantum magnetometers and an adaptive noise cancellation for heart magnetic field measurement within a magnetically-unshielded environment. Optically-pumped quantum magnetometers are based on the use of the atomic-spin-dependent optical properties of an atomic medium. An Mxconfiguration- based optically-pumped quantum magnetometer employing two sensing cells containing caesium vapour is theoretically described and experimentally developed, and the dependence of its sensitivity and frequency bandwidth upon the light power and the alkali vapour temperature is experimentally demonstrated. Furthermore, the capability of the developed magnetometer of measuring very weak magnetic fields is experimentally demonstrated in a magnetically-unshielded environment. The adaptive noise canceller is based on standard Least-Mean-Squares (LMS) algorithms and on two heuristic optimization techniques, namely, Genetic Algorithms (GA) and Particle Swarm Optimization (PSO). The use of these algorithms is investigated for suppressing the power line generated 50Hz interference and recovering of the weak magnetic heart signals from a much higher electromagnetic environmental noise. Experimental results show that all the algorithms can extract a weak heart signal from a much-stronger magnetic noise, detect the P, QRS, and T heart features and highly suppress the common power line noise component at 50 Hz. Moreover, adaptive noise cancellation based on heuristic algorithms is shown to be more efficient than adaptive noise canceller based on standard or normalised LMS algorithm in heart features detection

Das inverse Problem der Magnetokardiographie: Aktivierungszeit-Bildgebung mit dem Extended Kalman Filter und dem Unscented Kalman Filter

In order to reconstruct the electrical activity in the heart this work employs the method activation time imaging. In the method first the primary current dipoles distributed on a cubic ventricular grid with a lattice constant of 1.5 mm are calculated from the measured magnetocardiographic signal using standard algorithms for the inverse problem, namely the Weighted Minimum Norm (WMN) or the MUltiple SIgnal Classification (MUSIC). In the next step the activation time of the cubic ventricular cell can be estimated from the maximum of the primary current in the cell. These WMN- and MUSIC-generated activation times act as initial states for the Kalman Filters investigated in this work. Because the number of magnetocardiographic sensors is several orders smaller than the number of primary current dipoles in the heart, the inverse problem for the primary current dipoles doesn't have a unique solution and is highly ill-posed. Consequently, there is a large error between the true simulated activation times and the WMN- and MUSIC-generated activation times. In order to reduce the error between the activation times, in a state-space model a process function is introduced that smoothes the activation time map and states an additional constraint for the activation times. Because the location of the accessory pathway can be found from the minimum of the activation time map, also the localization error for accessory pathways is reduced by the application of the process function. Because both the process function and the MCG signal function are nonlinear and even nonsmooth functions of the activation times, the Extended Kalman Filter (EKF) and the Unscented Kalman Filter (UKF), that are optimized for nonlinear state-space models, are applied to the WMN- and MUSIC-generated initial states.In dieser Arbeit wird zur Rekonstruktion der elektrischen Aktivität des Herzens die Methode activation time imaging untersucht. Hierbei werden zunächst die primären Stromdipole in einem kubischen ventrikulären Gitter aus den Signalen der Sensoren berechnet. Hierfür werden Standardverfahren zur Lösung des inversen Problems verwendet, wie die MUltiple SIgnal Classification (MUSIC) oder das Weighted Minimum Norm (WMN) Verfahren. Aus dem Maximum des Primärstroms einer ventrikulären Zelle kann dann die Aktivierungszeit der Zelle abgeschätzt werden. Die so berechneten Aktivierungszeiten dienen als Anfangszustände für die in der Arbeit verwendeten Kalman Filter. Aufgrund der im Vergleich zur Anzahl der Quellen des Magnetfelds sehr kleinen Anzahl an Sensoren ist das inverse Problem für die primären Stromdipole stark unterbestimmt und nicht eindeutig lösbar. Die mit den Methoden MUSIC und WMN berechneten Aktivierungszeiten weichen daher stark von den tatsächlichen Aktivierungszeiten ab. Es wird daher in einem Zustandsmodell eine Prozessfunktion eingeführt, die eine zusätzliche Nebenbedingung für das inverse Problem darstellt, die Aktivierungszeiten glättet und damit zu einer Verringerung des Fehlers für die Aktivierungszeiten führt. Der mittlere Lokalisierungsfehler für akzessorische Leitungsbahnen wird dabei ebenso verringert, da er aus dem Ort des Minimums der Aktivierungszeiten berechnet werden kann. Da die verwendete Prozessfunktion sowie die Signalfunktion nichtlineare Funktionen der Aktivierungszeiten sind, werden zur Lösung des Zustandsmodells die für nichtlineare Zustandsmodelle optimierten Algorithmen EKF (Extended Kalman Filter) und UKF (Unscented Kalman Filter) verwendet

ECG Imaging of Ventricular Activity in Clinical Applications

ECG imaging was performed in humans to reconstruct ventricular activation patterns and localize their excitation origins. The precision of the non-invasive reconstructions was evaluated against invasive measurements and found to be in line with the state-of-the-art literature. Statistics were produced for various excitation origins and reveal the beat-to-beat robustness of the imaging method

Kalbin Elektriksel Aktivitesinin 3 Boyutlu Transmembran Potansiyel Dağılımları Cinsinden Girişimsiz Olarak Görüntülenmesi

TÜBİTAK EEEAG Proje01.04.2015Vücut yüzeyi potansiyel (VYP) ölçümlerinden kalpteki elektriksel kaynakların kestirilmesine ters elektrokardiografi (EKG) problemi denir. Bu yöntem, ölümcül de olabilecek kalp hastalıklarının teşhisinde ve tedavi planlamasında hekimlere yol gösterme potansiyeline sahiptir. Ancak, bu problem kötü konumlanmış bir problemdir ve ölçümlerdeki az miktarda gürültü bile sınırsız çözümler bulunmasına yol açmaktadır. Bunun üstesinden gelebilmek için literatürde, başta Tikhonov düzenlileştirmesi olmak üzere çeşitli düzenlileştirme yöntemleri uygulanmıştır. Ancak uygulanan her yöntem farklı durumlarda test edilmiştir; henüz hangi yöntemin en iyi yöntem olduğu konusunda fikir birliği sağlanamamıştır. Son zamanlarda, üç boyutlu miyokart dokusunda da detaylı bilgi verebildiği için, transmembran potansiyelleri (TMP) cinsinden ters EKG çözümleri popülerleşmiştir. Ancak henüz bu alanda az sayıda çalışma vardır ve özellikle farklı kalp aritmilerinde farklı yöntemlerin nasıl performans sergileyeceği bilinmemektedir. Bu projede temel amaç, bu açığı kapatmak, farklı elektriksel dağılımlar için literatürdeki belli başlı yöntemlerle ters EKG problemini çözmektir. Bu projede, kapsamlı bir çalışmayla, önerilen yöntemlerin performansları aynı test verisiyle ve aynı kriterler kullanılarak objektif bir şekilde karşılaştırılabilmiştir. Ayrıca farklı aritmiler için TMP benzetimleri ve buna bağlı VYPler elde edildiği için, yöntemlerin bu farklı aritmiler karşısında nasıl bir performans sergilediği de araştırılmıştır. Öncelikle Aliev-Panfilov yöntemiyle farklı kalp aktiviteleri için TMP benzetimleri yapılmış, ardından ileri EKG problemi çözülerek bu dağılımlardan VYP dağılımları bulunmuştur. Bu dağılımlar ters EKG çözümlerinde kullanılmıştır. Uygulanan beş değişik ters EKG çözüm yönteminden her durumda en başarılı yöntemin Bayesian MAP olduğu gözlenmiştir. TTLS, LTTLS ve LSQR yöntemlerinin de uyarım noktalarını ve dalga önünü bulmakta çok kötü performans sergilemediği görülmüştür. Bu proje kapsamında iki ayrı dalda daha literatüre katkı sağlanmıştır. Bunlardan ilki, fiber yönelimlerinin TMP dağılımlarına etkilerinin incelenmesidir. Başka bir kalpten aktarılan fiber yönelimini kullanmanın izotropik varsayım kullanmaktan daha doğru sonuçlar verdiği gözlenmiştir. İkinci katkı da, TMP dağılımları cinsinden FEM yöntemi ile ileri problem çözümünün doğrulamasıdır. Uygun ağ sıklığına ulaşıldığında sayısal çözümün analitik çözüme yakınsadığı gösterilmiştir.Inverse electrocardiography is the estimation of cardiac electrical sources from body surface potential (BSP) measurements. Inverse solutions can guide the physicians for diagnosis and treatment planning of lethal heart diseases. However, inverse problem is ill-posed and even small perturbations in the measurements yield unbounded errors in the solutions. To overcome this difficulty, many regularization approaches have been proposed in literature. However, these methods have been applied and tested under varying conditions in different studies; there is no consensus among researchers on the method with the best performance. Lately, solutions in terms of transmembrane potentials (TMP) have become popular, since they provide information about the electrical activity of the three dimensional myocardium. There are few studies in this area and it is still an open question how different methods will perform under different arrythmia conditions. The main goal in this project is to solve the inverse problem in terms of TMPs, using different approaches but under the same (and diverse) cardiac conditions. First, we obtained TMP distributions for various cardiac electrical activity assumptions using Aliev-Panfilov model. Then we solved the forward ECG problem to obtain the corresponding BSPs, which were later used in the inverse problem solutions. Among the five inverse approaches, Bayesian MAP estimation had the best performance under all conditions. TTLS, LTTLS and LSQR were also successful in finding the initial stimulation points and recovering the wavefront. We made contributions in two more areas in this project. The first one is our study of fiber orientation effects on TMP distributions. We found that even using fiber orientations from a different heart is much better than using the isotropic assumption. The second one is the analytical verification of the FEM based forward problem; with an appropriate mesh size, we showed that the numerical solution converges to the analytical solution

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