How random is your heart beat?

We measure the content of random uncorrelated noise in heart rate variability using a general method of noise level estimation using a coarse grained entropy. We show that usually - except for atrial fibrillation - the level of such noise is within 5 - 15% of the variance of the data and that the variability due to the linearly correlated processes is dominant in all cases analysed but atrial fibrillation. The nonlinear deterministic content of heart rate variability remains significant and may not be ignored.Comment: see http://urbanowicz.org.p

ECG-based estimation of respiratory modulation of AV nodal conduction during atrial fibrillation

Information about autonomic nervous system (ANS) activity may be valuable for personalized atrial fibrillation (AF) treatment but is not easily accessible from the ECG. In this study, we propose a new approach for ECG-based assessment of respiratory modulation in AV nodal refractory period and conduction delay. A 1-dimensional convolutional neural network (1D-CNN) was trained to estimate respiratory modulation of AV nodal conduction properties from 1-minute segments of RR series, respiration signals, and atrial fibrillatory rates (AFR) using synthetic data that replicates clinical ECG-derived data. The synthetic data were generated using a network model of the AV node and 4 million unique model parameter sets. The 1D-CNN was then used to analyze respiratory modulation in clinical deep breathing test data of 28 patients in AF, where a ECG-derived respiration signal was extracted using a novel approach based on periodic component analysis. We demonstrated using synthetic data that the 1D-CNN can predict the respiratory modulation from RR series alone ($\rho$ = 0.805) and that the addition of either respiration signal ($\rho$ = 0.830), AFR ($\rho$ = 0.837), or both ($\rho$ = 0.855) improves the prediction. Results from analysis of clinical ECG data of 20 patients with sufficient signal quality suggest that respiratory modulation decreased in response to deep breathing for five patients, increased for five patients, and remained similar for ten patients, indicating a large inter-patient variability.Comment: 20 pages, 7 figures, 5 table

Mixing Bandt-Pompe and Lempel-Ziv approaches: another way to analyze the complexity of continuous-states sequences

In this paper, we propose to mix the approach underlying Bandt-Pompe permutation entropy with Lempel-Ziv complexity, to design what we call Lempel-Ziv permutation complexity. The principle consists of two steps: (i) transformation of a continuous-state series that is intrinsically multivariate or arises from embedding into a sequence of permutation vectors, where the components are the positions of the components of the initial vector when re-arranged; (ii) performing the Lempel-Ziv complexity for this series of `symbols', as part of a discrete finite-size alphabet. On the one hand, the permutation entropy of Bandt-Pompe aims at the study of the entropy of such a sequence; i.e., the entropy of patterns in a sequence (e.g., local increases or decreases). On the other hand, the Lempel-Ziv complexity of a discrete-state sequence aims at the study of the temporal organization of the symbols (i.e., the rate of compressibility of the sequence). Thus, the Lempel-Ziv permutation complexity aims to take advantage of both of these methods. The potential from such a combined approach - of a permutation procedure and a complexity analysis - is evaluated through the illustration of some simulated data and some real data. In both cases, we compare the individual approaches and the combined approach.Comment: 30 pages, 4 figure

Nonlinear trend removal should be carefully performed in heart rate variability analysis

$\bullet$ Background : In Heart rate variability analysis, the rate-rate time series suffer often from aperiodic non-stationarity, presence of ectopic beats etc. It would be hard to extract helpful information from the original signals. 10 $\bullet$ Problem : Trend removal methods are commonly practiced to reduce the influence of the low frequency and aperiodic non-stationary in RR data. This can unfortunately affect the signal and make the analysis on detrended data less appropriate. $\bullet$ Objective : Investigate the detrending effect (linear \& nonlinear) in temporal / nonliear analysis of heart rate variability of long-term RR data (in normal sinus rhythm, atrial fibrillation, 15 congestive heart failure and ventricular premature arrhythmia conditions). $\bullet$ Methods : Temporal method : standard measure SDNN; Nonlinear methods : multi-scale Fractal Dimension (FD), Detrended Fluctuation Analysis (DFA) \& Sample Entropy (Sam-pEn) analysis. $\bullet$ Results : The linear detrending affects little the global characteristics of the RR data, either 20 in temporal analysis or in nonlinear complexity analysis. After linear detrending, the SDNNs are just slightly shifted and all distributions are well preserved. The cross-scale complexity remained almost the same as the ones for original RR data or correlated. Nonlinear detrending changed not only the SDNNs distribution, but also the order among different types of RR data. After this processing, the SDNN became indistinguishable be-25 tween SDNN for normal sinus rhythm and ventricular premature beats. Different RR data has different complexity signature. Nonlinear detrending made the all RR data to be similar , in terms of complexity. It is thus impossible to distinguish them. The FD showed that nonlinearly detrended RR data has a dimension close to 2, the exponent from DFA is close to zero and SampEn is larger than 1.5 -- these complexity values are very close to those for 30 random signal. $\bullet$ Conclusions : Pre-processing by linear detrending can be performed on RR data, which has little influence on the corresponding analysis. Nonlinear detrending could be harmful and it is not advisable to use this type of pre-processing. Exceptions do exist, but only combined with other appropriate techniques to avoid complete change of the signal's intrinsic dynamics. 35 Keywords $\bullet$ heart rate variability $\bullet$ linear / nonlinear detrending $\bullet$ complexity analysis $\bullet$ mul-tiscale analysis $\bullet$ detrended fluctuation analysis $\bullet$ fractal dimension $\bullet$ sample entropy

Assessment of ventricular repolarization instability and cardiac risk stratification in different pathological and abnormal conditions

Cardiovascular diseases (CVDs) represents the leading cause of mortality worldwide [1,2]. These pathological conditions are mainly characterized by a structurally abnormal heart, that is, a vulnerable substrate, prone to the abnormal generation and/or propagation of the electrical impulse, determining the onset of ventricular arrhythmias, which can result in sudden cardiac death (SCD) [3]. In this context, the assessment of ventricular repolarization from the electrocardiogram (ECG) signal has been shown to provide with valuable information for risk stratification and several electrocardiographic indices have been proposed in the literature [4]. The main objective of this thesis is to propose methodological advances for the assessment of ventricular repolarization instability in pathological and abnormal conditions. These contributions are aimed at improving the prediction of ventricular arrhythmias and, consequently, better identifying SCD risk. In particular, we have addressed this objective by developing robust methodologies for the assessment of T-wave alternans (TWA) and ventricular repolarization instability, in invasive and non-invasive cardiac signals, that have been evaluated in both experimental and clinical conditions. In the first part of the thesis, TWA was simultaneously characterized (prevalence, magnitude, time-course, and alternans waveform) in body-surface ECG and intracardiac electrograms (EGMs) signals during coronary artery occlusion. Signals from both body surface ECG and intracardiac EGMs recorded from 4 different anatomical heart locations (coronary sinus, epicardial space and left and right ventricles) were analyzed following a multilead strategy. Leads were linearly combined using the periodic component analysis (πCA) [5], which maximizes the 2-beat periodicity (TWA periodicity) content present on the available leads. Then the Laplacian Likelihood Ratio method (LLRM) [6] was applied for TWA detection and estimation. A sensitivity study for TWA detection from the 5 different locations of leads was performed, revealing that it is the combination of the ECG leads that better performs. In addition, this multilead approach allowed us to find the optimal combination of intracardiac leads usable for in-vivo monitorization of TWA directly from an implantable device, with a sensitivity comparable to the ECG analysis. These results encourage further research to determine the feasibility of predicting imminent VT/VF episodes by TWA analysis implemented in implantable cardioverter defibrillator’s (ICD) technology.Then, we have studied the potential changes induced by a prolonged exposure to simulated microgravity on ventricular repolarization in structurally normal hearts. It is well known that this environmental condition affects the control of autonomic and cardiovascular systems [7], with a potential increase on cardiac electrical instability. The effects of short- (5 days), mid- (21 days) and long- (60 days) exposure to simulated microgravity on TWA using the head-down bed-rest (HDBR) model [8] were assessed. TWA was evaluated before (PRE), during and after (POST) the immobilization period, by the long-term averaging technique in ambulatory ECG Holter recordings [9]. Additionally, we proposed an adapted short-term averaging approach for shorter, non-stationary ECG signals obtained during two stress manoeuvres (head-up tilt-table and bicycle exercise tests). Both approaches are based on the multilead analysis used in the previous study. The absence of significant changes between PRE and POST-HDBR on TWA indices suggests that a long-term exposure to simulated microgravity is not enough to induce alterations in healthy myocardial substrate up to the point of reflecting electrical instability in terms of TWA on the ECG. Finally, methodological advances were proposed for the assessment of ventricular repolarization instability from the ECG signal in the presence of sporadic (ventricular premature contractions, VPCs) and sustained (atrial fibrillation) rhythm disturbances.On the one hand, a methodological improvement for the estimation of TWA amplitude in ambulatory ECG recordings was proposed, which deals with the possible phase reversal on the alternans sequence induced by the presence of VPCs [10]. The performance of the algorithm was first evaluated using synthetic signals. Then, the effect of the proposed method in the prognostic value of TWA amplitude was assessed in real ambulatory ECG recordings from patients with chronic heart failure (CHF). Finally, circadian TWA changes were evaluated as well as the prognostic value of TWA at different times of the day. A clinical study demonstrated the enhancement in the predictive value of the index of average alternans (IAA) [9] for SCD stratification. In addition, results suggested that alternans activity is modulated by the circadian pattern, preserving its prognostic information when computed just during the morning, which is also the day interval with the highest reported SCD incidence. Thus, suggesting that time of the day should be considered for SCD risk prediction. On the other hand, the high irregularity of the ventricular response in atrial fibrillation (AF) limits the use of the most common ECG-derived markers of repolarization heterogeneity, including TWA, under this clinical condition [11]. A new method for assessing ventricular repolarization changes based on a selective averaging technique was developed and new non-invasive indices of repolarization variation were proposed. The positive impact in the prognostic value of the computed indices was demonstrated in a clinical study, by analyzing ECG Holter recordings from CHF patients with AF. To the best of our knowledge, this is the first study that attempts a non-invasive SCD stratification of patients under AF rhythm by assessing ventricular repolarization instability from the ECG signal. To conclude, the research presented in this thesis sheds some light in the identification of pro-arrhythmic factors, which plays an important role in adopting efficient therapeutic strategies. In particular, the optimal configuration for real-time monitoring of repolarization alternans from intracardiac EGMs, together with the prognostic value of the proposed non-invasive indices of alternans activity and ventricular instability variations in case of AF rhythms demonstrated in two clinical studies, would increase the effectiveness of (ICD) therapy. Finally, the analysis of ECG signals recorded during HDBR experiments in structurally healthy hearts, also provides interesting information on cardiovascular alterations produced in immobilized or bedridden patients.<br /

Rotor detection in atrial fibrillation

Atrial fibrillation (AF) is one of the most common arrhythmias in the clinical practice. Catheter ablation method was developed more than 20 years ago as an approach to terminate this rhythm disorder. Since its outbreak, this technique obtained international acceptance among the clinicians, and technological advances in this field increased its safety while reducing the procedure duration. However, there is no perfect AF treatment procedure described yet, since the understanding of the driving and sustaining AF mechanisms remains poor, with pulmonary vein isolation being the most common ablation strategy. Several theories try to explain the initiating and maintenance mechanisms of the AF, ranging from multiple wavelets propagating at random in the atria to ectopic focus fired from the pulmonary veins. Alternatively, spatiotemporal stable sources (rotors) have been proposed as the maintenance mechanism of AF. The most representative characteristic of a rotor is the re-entry spiral-like propagation pattern that the electrical wavefront exhibits as it propagates. The assessment of its presence and posterior ablation of the sites where rotors anchor might improve the success of AF ablation. Technical solutions emerged focusing on the rotor assessment problem. They base their methods on the reconstruction of the atrial activity using multi-electrode catheters and phase maps, in which they detect singularity points, the sites where rotors spin. The ablation of these sites showed promising results, but the difficulty to reproduce the results by other authors increased the controversy on this technique. In this Thesis we address the rotor detection problem in the time domain as opposed to current methods based on the phase domain of the signals. We develop a new method to identify local activation times (LATs) in unipolar electrograms (EGMs) recorded with multi-electrode catheters. We propose a new filtering scheme to enhance the activation component of the EGM while considerably reducing the presence of noise in the signal. This signal processing method reects the real activity of the tissue in contact with the electrode. It opposes the Hilbert transform (HT) used to extract the phase component of the signal, that do not correlate well with the temporal activations. With the EGM LATs we perform a spatial interpolation translating the electrode positions of the catheter into a regular 2D grid. This way we generate isochronal maps revealing the electrical wavefronts in the atrium. What is more, this step guarantees compatibility with multi-electrode catheters, not restricting the method to specific models. With the isochronal maps, we develop a new rotor detection algorithm based on the optical flow of the wavefront dynamics, and a rotation pattern match. Additionally, we develop a new method based on Granger's causality to estimate the directionality of the wavefronts, that provides an additional indicator for rotational patterns. We validate the methods using in silico and real AF signals. We implement these methods into a system that can assess the presence of rotational activation sites in the atrium. Our system is able to operate in realtime with multi-electrode catheters of different topologies in contact with the atrial wall. We integrate signal acquisition and processing in our system, allowing direct acquisition of the signals without requiring signal exportation from a recording device, which delays the clinical procedure. We address the computational time handicap by designing parallelizable signal processing steps. We employ multi-core processors and GPU based code to distribute the computations and minimize the processing times, achieving near real-time results. The results presented in this Thesis provide a new technical solution to detect the presence of rotational activity (rotors) in AF patients in real-time. Although the presence of rotational activity is itself controversial, we individually validate each of the steps of the procedure and obtain evidence of the presence of rotational activity in AF patients. The system has been also found useful to characterize the atrial sites where rotational activity was found in terms of spatial and voltage distribution. The results of this Thesis provide a new alternative to existing methods based on phase analysis and open a new research line in the detection of the mechanisms sustaining AF.La fibrilación auricular (FA) es una de las arritmias más comunes en la práctica clínica. Para tratar de terminar esta fibrilación en pacientes se desarrollo el método de ablación con catéter hace ya más de 20 años. Desde su puesta en marchar esta técnica ha ido ganando aceptación internacional por parte de la comunidad médica, y los avances tecnológicos desarrollados en esta línea han aumentado la seguridad y disminuido la duración del procedimiento. Sin embargo todavía no existe un tratamiento perfecto para tratar la FA, debido en parte a que el conocimiento de los mecanismos que inician y sostienen la fibrilación son limitados. Como método de ablación el aislamiento de las venas pulmonares prevalece como el más empleado en la práctica, pero se hace necesario el desarrollo de nuevos métodos para hacer frente al problema de la FA. Distintas teorías tratan de explicar los mecanismos de inicio y mantenimiento de la FA, desde unas basadas en la propagación de múltiples frentes de onda aleatorios en las aurículas, hasta las que basan su hipótesis en focos ectópicos disparados principalmente desde las venas pulmonares, entre otras teorías. Recientemente, una de estas teorías basada en fuentes espacio-temporalmente estables (rotores) se propuso como mecanismo de mantenimiento de la FA. La característica más representativa de un rotor es su patrón de reentrada en forma de espiral que realiza el frente de onda eléctrico en el tejido auricular. La evaluación de la presencia de rotores y la posterior de los sitios en los que se encuentren puede mejorar el éxito de la ablación en pacientes con FA. En vista de esta tendencia por la búsqueda de rotores se desarrollaron soluciones técnicas para la evaluación de zonas que alberguen actividad rotacional. Sus técnicas se basan en la reconstrucción de la actividad auricular empleando catéteres multi-electrodo y detectando puntos de singularidad en mapas de phase, esto es la posición en la aurícula en la que el rotor gira. La ablación de estos puntos mostró resultados prometedores, pero la dificultad por replicar los resultados por parte de otros autores incremento la controversia con respecto a esta técnica. En esta Tesis abordamos el problema de la detección de rotores en el dominio del tiempo, oponiéndonos a las técnicas actuales basadas en el dominio de la fase de las señales. Para ello hemos desarrollado un nuevo para identificar tiempos de activación local en electrogramas unipolares registrados con catéteres multi-electrodo. Para ello proponemos un nuevo método de filtrado para realzar la activación del electrograma reduciendo considerablemente la presencia de ruido en la señal. Con este procesado de la señal extraemos y reflejamos la actividad real del tejido en contacto con el electrodo. Al mismo tiempo nos oponemos a la transformada de Hilbert empleada para calcular la componente de fase de la señal, que es sabido no tiene una buena correlación con las activaciones temporales. Con los electrogramas y los tiempos de activación locales aplicamos una interpolación espacial logrando trasladar la posición de los electrodos en el catéter a una rejilla regular en 2D. Mediante este paso generamos mapas isócronos que reconstruyen los frentes de onda eléctricos que se propagan en la aurícula. Además, la interpolación nos permite garantizar una compatibilidad con otros catéteres multi-electrodos, no restringiendo el uso de nuestro método a modelos específicos. Con los mapas isócronos hemos desarrollado un nuevo algoritmo de detección de rotores basado en el flujo óptico de la dinámica del frente de onda que hacemos coincidir con un patrón de rotación. Adicionalmente hemos desarrollado un nuevo método basad en la causalidad propuesta por Granger para estimar la dirección de los frentes de propagación, que sirve como indicador adicional para encontrar patrones de activación rotacional. Hemos validado todos y cada uno de los métodos empleando señales in silico así como señales reales de pacientes con FA. En la parte de aplicación, hemos implementado los métodos en un sistema que evalúa la presencia de actividad rotacional en la aurícula. Nuestro sistema opera en tiempo real siendo compatible con catéteres multi-electrodo de diferentes topologías asegurando contacto con la pared auricular. Para evitar sobreextender el procedimiento clínico, hemos integrado las partes de adquisición y procesado de señal conjuntamente, lo que nos permite un registro de las señales directo sin viii necesidad de requerir un exportado adicional desde un sistema de registro. Para hacer frente al objetivo de presentar los resultados en tiempo real hemos diseñado todos los pasos de procesado de señal para que sean paralelizables. Para ello empleamos procesadores multinúcleo y código para ejecutar en tarjetas gráficas (GPUs) para distribuir las computaciones y minimizar el tiempo de procesado, logrando resultados en quasi tiempo real. Hemos empleado el sistema de detección de rotores para estudiar la distribución espacial y de voltaje de los sitios que muestran actividad rotacional en la aurícula. Aunque la presencia de actividad rotacional es en sí misma controvertida, hemos validad individualmente todos y cada uno de los pasos descritos obteniendo evidencia de la presencia de actividad rotacional en pacientes con FA.Programa Oficial de Doctorado en Multimedia y ComunicacionesPresidente: Pablo Laguna Lasaosa.- Secretario: Pablo Martínez Olmos.- Vocal: Batiste Andreu Martínez Climen