Highest dominant frequency and rotor positions are robust markers of driver location during noninvasive mapping of atrial fibrillation: A computational study

[EN] BACKGROUND Dominant frequency (DF) and rotor mapping have been proposed as noninvasive techniques to guide localization of drivers maintaining atrial fibrillation (AF). OBJECTIVE The purpose of this study was to evaluate the robustness of both techniques in identifying atrial drivers noninvasively under the effect of electrical noise or model uncertainties. METHODS Inverse-computed DFs and phase maps were obtained from 30 different mathematical AF simulations. Epicardial highest dominant frequency (HDF) regions and rotor location were compared with the same inverse-computed measurements after addition of noise to the ECG, size variations of the atria, and linear or angular deviations in the atrial location inside the thorax. RESULTS Inverse-computed electrograms (EGMs) individually correlated poorly with the original EGMs in the absence of induced uncertainties (0.45 +/- 0.12) and were worse with 10-dB noise (0.22 +/- 0.11), 3-cm displacement (0.01 +/- 0.02), or 36 degrees rotation (0.02 +/- 0.03). However, inverse-computed HDF regions showed robustness against induced uncertainties: from 82% +/- 18% match for the best conditions, down to 73% +/- 23% for 10-dB noise, 77% +/- 21% for 5-cm displacement, and 60% +/- 22% for 36 degrees rotation. The distance from the inverse-computed rotor to the original rotor was also affected by uncertainties: 0.8 +/- 1.61 cm for the best conditions, 2.4 +/- 3.6 cm for 10-dB noise, 4.3 +/- 3.2 cm for 4-cm displacement, and 4.0 +/- 2.1 cm for 36 degrees rotation. Restriction of rotor detections to the HDF area increased rotor detection accuracy from 4.5 +/- 4.5 cm to 3.2 +/- 3.1 cm (P < .05) with 0-dB noise. CONCLUSION The combination of frequency and phase-derived measurements increases the accuracy of noninvasive localization of atrial rotors driving AF in the presence of noise and uncertainties in atrial location or size.This work was supported in part by grants from Generalitat Valenciana (ACIF/2013/021); Instituto de Salud Carlos III-FEDER (Fondo Europeo de Desarrollo Regional) and Ministerio de Ciencia e Innovacion (PI13-01882, PI13-00903, PI14/00857, PI16/01123, IJCI-2014-22178, DTS16/00160 and Red RIC RD12.0042.0001); Spanish Society of Cardiology (Clinical Research Grant 2015); and the National Heart, Lung, and Blood Institute (P01-HL039707, P01-HL087226, and Q1 R01-HL118304). Dr. Atienza served on the advisory board of Medtronic and Sorin. Dr. Berenfeld received research support from Medtronic and St. Jude Medical; and is a cofounder and Scientific Officer of Rhythm Solutions, Inc., Research and Development Director for S.A.S. Volta Medical, and consultant to Acutus Medical. All other authors have reported that they have no relationships relevant to the contents of this paper to disclose.Rodrigo Bort, M.; Climent, AM.; Liberos Mascarell, A.; Fernandez-Aviles, F.; Berenfeld, O.; Atienza, F.; Guillem Sánchez, MS. (2017). Highest dominant frequency and rotor positions are robust markers of driver location during noninvasive mapping of atrial fibrillation: A computational study. Heart Rhythm. 14(8):1224-1233. https://doi.org/10.1016/j.hrthm.2017.04.017S1224123314

Study on Parameter Optimization for Support Vector Regression in Solving the Inverse ECG Problem

The typical inverse ECG problem is to noninvasively reconstruct the transmembrane potentials (TMPs) from body surface potentials (BSPs). In the study, the inverse ECG problem can be treated as a regression problem with multi-inputs (body surface potentials) and multi-outputs (transmembrane potentials), which can be solved by the support vector regression (SVR) method. In order to obtain an effective SVR model with optimal regression accuracy and generalization performance, the hyperparameters of SVR must be set carefully. Three different optimization methods, that is, genetic algorithm (GA), differential evolution (DE) algorithm, and particle swarm optimization (PSO), are proposed to determine optimal hyperparameters of the SVR model. In this paper, we attempt to investigate which one is the most effective way in reconstructing the cardiac TMPs from BSPs, and a full comparison of their performances is also provided. The experimental results show that these three optimization methods are well performed in finding the proper parameters of SVR and can yield good generalization performance in solving the inverse ECG problem. Moreover, compared with DE and GA, PSO algorithm is more efficient in parameters optimization and performs better in solving the inverse ECG problem, leading to a more accurate reconstruction of the TMPs

Estimación de la geometría ventricular a partir de medidas de ecografía transtorácica para la resolución del problema inverso de la electrocaerdiografía

Descripción El problema inverso de la electrocardiografía (ECG imaging, ECGi) permite identificar los patrones de conducción eléctrica en el corazón tanto en las modalidades invasivas como no invasivas. Esta técnica ya ha demostrado que permite identificar los patrones de conducción intrínsecos en pacientes con insuficiencia cardiaca para programar terapias de resincronización cardiaca. Actualmente en el grupo COR del Instituto ITACA estamos simplificando el proceso de obtención de datos de ECGi para utilizar imágenes de ecografía en lugar de imágenes de tomografía axial computerizada o resonancia magnética. Sin embargo, hasta la fecha hemos aplicado estos procesos de simplificación del ECGi para estudiar arritmias auriculares. El objetivo del presente trabajo final de máster es implementar una interfaz gráfica de usuario para poder estimar un mallado tridimensional de los ventrículos a partir de dimensiones estimables desde ecografías transtorácicas para ser utilizado en la resolución del problema inverso de la electrocardiografía. Nuestra hipótesis es que a partir de una cantidad finita de medidas de los ventrículos y el torso obtenidas mediante ecografía transtorácica es posible estimar la anatomía de los dos ventrículos y resolver el problema inverso de la electrocardiografía con una resolución comparable a las técnicas del estado del arte. El objetivo del presente trabajo es desarrollar una aplicación informática para que un usuario no especializado pueda estimar la geometría y ubicación tridimensional de los ventrículos para la resolución del problema inverso de la electrocardiografía. Tareas: T1.- Revisión bibliográfica sobre el problema inverso de la electrocardiografía y aplicaciones de la literatura en la resincronización cardiaca. T2.- Familiarización con los algoritmos actuales de estimación de las cavidades exteriores auriculares a partir de medidas de ecografía transtorácica, incluyendo la corrección de la distorsión producida por el ecógrafo. T3.- Implementación de algoritmos para la estimación de las cavidades ventriculares exteriores a partir de medidas de ecografía transtorácica. Se segmentarán los ventrículos de al menos dos sujetos (TAC o MRI) y se identificarán los cortes y medidas necesarios para obtener una estimación del volumen completo como adaptación de un modelo anatómico de librería. T4.- Desarrollo de una interfaz gráfica de usuario para la obtención de una geometría estimada de los ventrículos de un paciente a partir de un número limitado de ecografías transtorácicas. T5. Cuantificación de la precisión del algoritmo implementado en relación con el estado del arte. Se medirán las isocronas calculadas con modelos ventriculares completos de al menos 10 pacientes y modelos estimados a partir de un subconjunto de medidas y al menos en 1 paciente se contarán con datos de ecografías transtorácicas para validación. T5.- Redacción de la memoria y preparación de la presentación.Description The inverse problem of electrocardiography (ECG imaging, ECGi) allows the identification of electrical conduction patterns in the heart in both invasive and non-invasive modalities. This technique has already shown that it allows the identification of intrinsic driving patterns in patients with heart failure to program cardiac resynchronization therapies. Currently in the COR group of the ITACA Institute we are simplifying the process of obtaining ECGi data to use ultrasound images instead of computerized axial tomography or magnetic resonance imaging. However, to date we have applied these ECGi simplification processes to study atrial arrhythmias. The objective of the present master's thesis is to implement a graphical user interface to be able to estimate a three-dimensional meshing of the ventricles from estimable dimensions from transthoracic ultrasound to be used in the resolution of the inverse problem of electrocardiography. Our hypothesis is that from a finite amount of measurements of the ventricles and the torso obtained by transthoracic ultrasound, it is possible to estimate the anatomy of the two ventricles and solve the inverse problem of electrocardiography with a resolution comparable to state of the art techniques. . The aim of this paper is to develop a computer application so that a non-specialized user can estimate the geometry and three-dimensional location of the ventricles for the resolution of the inverse problem of electrocardiography. Chores: T1.- Bibliographic review on the inverse problem of electrocardiography and applications of the literature on cardiac resynchronization. T2.- Familiarization with the current algorithms for estimating the external atrial cavities from transthoracic ultrasound measurements, including correction of the distortion produced by the ultrasound. T3.- Implementation of algorithms for the estimation of external ventricular cavities from transthoracic ultrasound measurements. The ventricles of at least two subjects (TAC or MRI) will be segmented and the cuts and measurements necessary to obtain an estimate of the complete volume as an adaptation of an anatomical library model will be identified. T4.- Development of a graphical user interface for obtaining an estimated geometry of the ventricles of a patient from a limited number of transthoracic ultrasounds. T5 Quantification of the accuracy of the algorithm implemented in relation to the state of the art. Isochrones calculated with complete ventricular models of at least 10 patients and models estimated from a subset of measurements will be measured and at least 1 patient will have transthoracic ultrasound data for validation. T5.- Writing of the memory and preparation of the presentation.Larrea Broch, AC. (2018). Estimación de la geometría ventricular a partir de medidas de ecografía transtorácica para la resolución del problema inverso de la electrocaerdiografía. http://hdl.handle.net/10251/114188TFG

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 identification of atrial fibrillation drivers

Atrial fibrillation (AF) is one of the most common cardiac arrhythmias. Nowadays the fibrillatory process is known to be provoked by the high-frequency reentrant activity of certain atrial regions that propagates the fibrillatory activity to the rest of the atrial tissue, and the electrical isolation of these key regions has demonstrated its effectiveness in terminating the fibrillatory process. The location of the dominant regions represents a major challenge in the diagnosis and treatment of this arrhythmia. With the aim to detect and locate the fibrillatory sources prior to surgical procedure, non-invasive methods have been developed such as body surface electrical mapping (BSPM) which allows to record with high spatial resolution the electrical activity on the torso surface or the electrocardiographic imaging (ECGI) which allows to non-invasively reconstruct the electrical activity in the atrial surface. Given the novelty of these systems, both technologies suffer from a lack of scientific knowledge about the physical and technical mechanisms that support their operation. Therefore, the aim of this thesis is to increase that knowledge, as well as studying the effectiveness of these technologies for the localization of dominant regions in patients with AF. First, it has been shown that BSPM systems are able to noninvasively identify atrial rotors by recognizing surface rotors after band-pass filtering. Furthermore, the position of such surface rotors is related to the atrial rotor location, allowing the distinction between left or right atrial rotors. Moreover, it has been found that the surface electrical maps in AF suffer a spatial smoothing effect by the torso conductor volume, so the surface electrical activity can be studied with a relatively small number of electrodes. Specifically, it has been seen that 12 uniformly distributed electrodes are sufficient for the correct identification of atrial dominant frequencies, while at least 32 leads are needed for non-invasive identification of atrial rotors. Secondly, the effect of narrowband filtering on the effectiveness of the location of reentrant patterns was studied. It has been found that this procedure allows isolating the reentrant electrical activity caused by the rotor, increasing the detection rate for both invasive and surface maps. However, the spatial smoothing caused by the regularization of the ECGI added to the temporal filtering causes a large increase in the spurious reentrant activity, making it difficult to detect real reentrant patterns. However, it has been found that maps provided by the ECGI without temporal filtering allow the correct detection of reentrant activity, so narrowband filtering should be applied for intracavitary or surface signal only. Finally, we studied the stability of the markers used to detect dominant regions in ECGI, such as frequency maps or the rotor presence. It has been found that in the presence of alterations in the conditions of the inverse problem, such as electrical or geometrical noise, these markers are significantly more stable than the ECGI signal morphology from which they are extracted. In addition, a new methodology for error reduction in the atrial spatial location based on the curvature of the curve L has been proposed. The results presented in this thesis showed that BSPM and ECGI systems allows to non-invasively locate the presence of high-frequency rotors, responsible for the maintenance of AF. This detection has been proven to be unambiguous and robust, and the physical and technical mechanisms that support this behavior have been studied. These results indicate that both non-invasive systems provide information of great clinical value in the treatment of AF, so their use can be helpful for selecting and planning atrial ablation procedures.La fibrilación auricular (FA) es una de las arritmias cardiacas más frecuentes. Hoy en día se sabe que el proceso fibrilatorio está provocado por la actividad reentrante a alta frecuencia de ciertas regiones auriculares que propagan la actividad fibrilatoria en el resto del tejido auricular, y se ha demostrado que el aislamiento eléctrico de estas regiones dominantes permite detener el proceso fibrilatorio. La localización de las regiones dominantes supone un gran reto en el diagnóstico y tratamiento de la FA. Con el objetivo de poder localizar las fuentes fibrilatorias con anterioridad al procedimiento quirúrgico, se han desarrollado métodos no invasivos como la cartografía eléctrica de superficie (CES) que registra con gran resolución espacial la actividad eléctrica en la superficie del torso o la electrocardiografía por imagen (ECGI) que permite reconstruir la actividad eléctrica en la superficie auricular. Dada la novedad de estos sistemas, existe una falta de conocimiento científico sobre los mecanismos físicos y técnicos que sustentan su funcionamiento. Por lo tanto, el objetivo de esta tesis es aumentar dicho conocimiento, así como estudiar la eficacia de ambas tecnologías para la localización de regiones dominantes en pacientes con FA. En primer lugar, ha visto que los sistemas CES permiten identificar rotores auriculares mediante el reconocimiento de rotores superficiales tras el filtrado en banda estrecha. Además, la posición de los rotores superficiales está relacionada con la localización de dichos rotores, permitiendo la distinción entre rotores de aurícula derecha o izquierda. Por otra parte, se ha visto que los mapas eléctricos superficiales durante FA sufren una gran suavizado espacial por el efecto del volumen conductor del torso, lo que permite que la actividad eléctrica superficial pueda ser estudiada con un número relativamente reducido de electrodos. Concretamente, se ha visto que 12 electrodos uniformemente distribuidos son suficientes para una correcta identificación de frecuencias dominantes, mientras que son necesarios al menos 32 para una correcta identificación de rotores auriculares. Por otra parte, también se ha estudiado el efecto del filtrado en banda estrecha sobre la eficacia de la localización de patrones reentrantes. Así, se ha visto que este procedimiento permite aislar la actividad eléctrica reentrante provocada por el rotor, aumentando la tasa de detección tanto para señal obtenida de manera invasiva como para los mapas superficiales. No obstante, este filtrado temporal sobre la señal de ECGI provoca un gran aumento de la actividad reentrante espúrea que dificulta la detección de patrones reentrantes reales. Sin embargo, los mapas ECGI sin filtrado temporal permiten la detección correcta de la actividad reentrante, por lo el filtrado debería ser aplicado únicamente para señal intracavitaria o superficial. Por último, se ha estudiado la estabilidad de los marcadores utilizados en ECGI para detectar regiones dominantes, como son los mapas de frecuencia o la presencia de rotores. Se ha visto que en presencia de alteraciones en las condiciones del problema inverso, como ruido eléctrico o geométrico, estos marcadores son significativamente más estables que la morfología de la propia señal ECGI. Además, se ha propuesto una nueva metodología para la reducción del error en la localización espacial de la aurícula basado en la curvatura de la curva L. Los resultados presentados en esta tesis revelan que los sistemas de CES y ECGI permiten localizar de manera no invasiva la presencia de rotores de alta frecuencia. Esta detección es univoca y robusta, y se han estudiado los mecanismos físicos y técnicos que sustentan dicho comportamiento. Estos resultados indican que ambos sistemas no invasivos proporcionan información de gran valor clínico en el tratamiento de la FA, por lo que su uso puede ser de gran ayuda para la selección y planificaciLa fibril·lació auricular (FA) és una de les arítmies cardíaques més freqüents. Hui en dia es sabut que el procés fibrilatori està provocat per l'activitat reentrant de certes regions auriculars que propaguen l'activitat fibril·latoria a la resta del teixit auricular, i s'ha demostrat que l'aïllament elèctric d'aquestes regions dominants permet aturar el procés fibrilatori. La localització de les regions dominants suposa un gran repte en el diagnòstic i tractament d'aquesta arítmia. Amb l'objectiu de poder localitzar fonts fibril·latories amb anterioritat al procediment quirúrgic s'han desenvolupat mètodes no invasius com la cartografia elèctrica de superfície (CES) que registra amb gran resolució espacial l'activitat elèctrica en la superfície del tors o l'electrocardiografia per imatge (ECGI) que permet obtenir de manera no invasiva l'activitat elèctrica en la superfície auricular. Donada la relativa novetat d'aquests sistemes, existeix una manca de coneixement científic sobre els mecanismes físics i tècnics que sustenten el seu funcionament. Per tant, l'objectiu d'aquesta tesi és augmentar aquest coneixement, així com estudiar l'eficàcia d'aquestes tecnologies per a la localització de regions dominants en pacients amb FA. En primer lloc, s'ha vist que els sistemes CES permeten identificar rotors auriculars mitjançant el reconeixement de rotors superficials després del filtrat en banda estreta. A més, la posició dels rotors superficials està relacionada amb la localització d'aquests rotors, permetent la distinció entre rotors de aurícula dreta o esquerra. També s'ha vist que els mapes elèctrics superficials durant FA pateixen un gran suavitzat espacial per l'efecte del volum conductor del tors, el que permet que l'activitat elèctrica superficial pugui ser estudiada amb un nombre relativament reduït d'elèctrodes. Concretament, s'ha vist que 12 elèctrodes uniformement distribuïts són suficients per a una correcta identificació de freqüències dominants auriculars, mentre que són necessaris almenys 32 per a una correcta identificació de rotors auriculars. D'altra banda, també s'ha estudiat l'efecte del filtrat en banda estreta sobre l'eficàcia de la localització de patrons reentrants. Així, s'ha vist que aquest procediment permet aïllar l'activitat elèctrica reentrant provocada pel rotor, augmentant la taxa de detecció tant pel senyal obtingut de manera invasiva com per als mapes superficials. No obstant això, aquest filtrat temporal sobre el senyal de ECGI provoca un gran augment de l'activitat reentrant espúria que dificulta la detecció de patrons reentrants reals. A més, els mapes proporcionats per la ECGI sense filtrat temporal permeten la detecció correcta de l'activitat reentrant, per la qual cosa el filtrat hauria de ser aplicat únicament per a senyal intracavitària o superficial. Per últim, s'ha estudiat l'estabilitat dels marcadors utilitzats en ECGI per a detectar regions auriculars dominants, com són els mapes de freqüència o la presència de rotors. S'ha vist que en presència d'alteracions en les condicions del problema invers, com soroll elèctric o geomètric, aquests marcadors són significativament més estables que la morfologia del mateix senyal ECGI. A més, s'ha proposat una nova metodologia per a la reducció de l'error en la localització espacial de l'aurícula basat en la curvatura de la corba L. Els resultats presentats en aquesta tesi revelen que els sistemes de CES i ECGI permeten localitzar de manera no invasiva la presència de rotors d'alta freqüència. Aquesta detecció és unívoca i robusta, i s'han estudiat els mecanismes físics i tècnics que sustenten aquest comportament. Aquests resultats indiquen que els dos sistemes no invasius proporcionen informació de gran valor clínic en el tractament de la FA, pel que el seu ús pot ser de gran ajuda per a la selecció i planificació de procediments d'ablació auricular.Rodrigo Bort, M. (2016). Non-invasive identification of atrial fibrillation drivers [Tesis doctoral]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/75346TESISPremios Extraordinarios de tesis doctorale

Deconvolution of Quantized-Input Linear Systems: An Information-Theoretic Approach

The deconvolution problem has been drawing the attention of mathematicians, physicists and engineers since the early sixties. Ubiquitous in the applications, it consists in recovering the unknown input of a convolution system from noisy measurements of the output. It is a typical instance of inverse, ill-posed problem: the existence and uniqueness of the solution are not assured and even small perturbations in the data may cause large deviations in the solution. In the last fifty years, a large amount of estimation techniques have been proposed by different research communities to tackle deconvolution, each technique being related to a peculiar engineering application or mathematical set. In many occurrences, the unknown input presents some known features, which can be exploited to develop ad hoc algorithms. For example, prior information about regularity and smoothness of the input function are often considered, as well as the knowledge of a probabilistic distribution on the input source: the estimation techniques arising in different scenarios are strongly diverse. Less effort has been dedicated to the case where the input is known to be affected by discontinuities and switches, which is becoming an important issue in modern technologies. In fact, quantized signals, that is, piecewise constant functions that can assume only a finite number of values, are nowadays widespread in the applications, given the ongoing process of digitization concerning most of information and communication systems. Moreover, hybrid systems are often encountered, which are characterized by the introduction of quantized signals into physical, analog communication channels. Motivated by such consideration, this dissertation is devoted to the study of the deconvolution of continuous systems with quantized input; in particular, our attention will be focused on linear systems. Given the discrete nature of the input, we will show that the whole problem can be interpreted as a paradigmatic digital transmission problem and we will undertake an Information-theoretic approach to tackle it. The aim of this dissertation is to develop suitable deconvolution algorithms for quantized-input linear systems, which will be derived from known decoding procedures, and to test them in different scenarios. Much consideration will be given to the theoretical analysis of these algorithms, whose performance will be rigorously described in mathematical terms

Multiscale Modeling of the Ventricles: From Cellular Electrophysiology to Body Surface Electrocardiograms

This work is focused on different aspects within the loop of multiscale modeling: On the cellular level, effects of adrenergic regulation and the Long-QT syndrome have been investigated. On the organ level, a model for the excitation conduction system was developed and the role of electrophysiological heterogeneities was analyzed. On the torso level a dynamic model of a deforming heart was created and the effects of tissue conductivities on the solution of the forward problem were evaluated

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

Deconvolution of Quantized-Input Linear Systems : an Information-Theoretic Approach

The deconvolution problem has been drawing the attention of mathematicians, physicists and engineers since the early sixties. Ubiquitous in the applications, it consists in recovering the unknown input of a convolution system from noisy measurements of the output. It is a typical instance of inverse, ill-posed problem: the existence and uniqueness of the solution are not assured and even small perturbations in the data may cause large deviations in the solution. In the last fifty years, a large amount of estimation techniques have been proposed by di fferent research communities to tackle deconvolution, each technique being related to a peculiar engineering application or mathematical set. In many occurrences, the unknown input presents some known features, which can be exploited to develop ad hoc algorithms. For example, prior information about regularity and smoothness of the input function are often considered, as well as the knowledge of a probabilistic distribution on the input source: the estimation techniques arising in diff erent scenarios are strongly diverse. Less eff ort has been dedicated to the case where the input is known to be aff ected by discontinuities and switches, which is becoming an important issue in modern technologies. In fact, quantized signals, that is, piecewise constant functions that can assume only a fi nite number of values, are nowadays widespread in the applications, given the ongoing process of digitization concerning most of information and communication systems. Moreover, hybrid systems are often encountered, which are characterized by the introduction of quantized signals into physical, analog communication channels. Motivated by such consideration, this dissertation is devoted to the study of the deconvolution of continuous systems with quantized input; in particular, our attention will be focused on linear systems. Given the discrete nature of the input, we will show that the whole problem can be interpreted as a paradigmatic digital transmission problem and we will undertake an Information-theoretic approach to tackle it. The aim of this dissertation is to develop suitable deconvolution algorithms for quantized-input linear systems, which will be derived from known decoding procedures, and to test them in diff erent scenarios. Much consideration will be given to the theoretical analysis of these algorithms, whose performance will be rigorously described in mathematical terms

Effect of cardiac motion on solution of the electrocardiography inverse problem

Previous studies of the ECG inverse problem often assumed that the heart was static during the cardiac cycle; consequently, a time-dependent geometrical error was thought to be unavoidably introduced. In this paper, cardiac motion is included in solutions to the electrocardiographic inverse problem. Cardiac dynamics are simulated based on a previously developed biventricular model that coupled the electrical and mechanical properties of the heart, and simulated the ventricular wall motion and deformation. In the forward computation, the heart surface source model method is employed to calculate the epicardial potentials from the action potentials, and then, the simulated epicardial potentials are used to calculate body surface potentials. With the inclusion of cardiac motion, the calculated body surface potentials are more reasonable than those in the case of static assumption. In the epicardial potential-based inverse studies, the Tikhonov regularization method is used to handle ill-posedness of the ECC inverse problem. The simulation results demonstrate that the solutions obtained from both the static ECG inverse problem and the dynamic ECG inverse problem approaches are approximately the same during the QRS complex period, due to the minimal deformation of the heart in this period. However, with the most obvious deformation occurring during the ST-T segment, the static assumption of heart always generates something akin to geometry noise in the ECG inverse problem causing the inverse solutions to have large errors. This study suggests that the inclusion of cardiac motion in solving the ECG inverse problem can lead to more accurate and acceptable inverse solutions