Implementación y estudio de métodos numéricos para la resolución del problema directo e inverso de la electrocardiografía: modelado de la actividad eléctrica en la superficie del torso

El comportamiento del corazón se rige por su actividad eléctrica, el conocimiento de la cual es indispensable para el correcto diagnóstico de diversas patologías cardiacas. Los sistemas de cartografía eléctrica de superficie permiten estudiar de forma no invasiva los potenciales generados por el corazón. Para ello, es necesaria la correcta resolución del problema inverso de la electrocardiografía. En el presente trabajo, se propone el uso de un nuevo algoritmo iterativo para la resolución del problema inverso en términos de múltiples dipolos móviles. Dicho algoritmo ha sido presentado, testeado y validado.Pedrón Torrecilla, J. (2010). Implementación y estudio de métodos numéricos para la resolución del problema directo e inverso de la electrocardiografía: modelado de la actividad eléctrica en la superficie del torso. http://hdl.handle.net/10251/12804Archivo delegad

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

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

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