Unscented Kalman Filter for Unobservable Parameter Estimation in Heart Cell Signals

One interesting feature of biological systems is that minor subcellular changes can cause alterations at the whole organ level. In the heart, the random dynamics of cell membrane ion channels contributes to beat-to-beat repolarization variability, which has been related to proarrhythmic risk. Inference of unobservable cellular parameters, such as the number of channels, is key to characterize such random ion channel dynamics. In this work, a methodology based on the use of Unscented Kalman Filters is proposed to infer the number of channel from action potential signals, like those commonly recorded experimentally

Theroetical Analysis of Autonomic Nervous System Effects on Cardiac Elestrophysiology and its Relationship with Arrhythmic Risk

Las enfermedades cardiovasculares representan la principal causa de mortalidad y morbilidad en las sociedades industrializadas. Un porcentaje significativo de las muertes asociadas a estas enfermedades está relacionado con el desarrollo de arritmias cardíacas, siendo éstas definidas como anomalías en el funcionamiento eléctrico del corazón.Tres son los elementos principales que están involucrados en el desarrollo de las arritmias: un sustrato arritmogénico, un desencadenante y factores de modulación. El Sistema Nervioso Autónomo (SNA) es el más relevante de estos factores moduladores.El SNA está compuesto por dos ramas, simpática y parasimpática, que encierta medida actúan de forma antagónica entre sí. La posibilidad de revelar cómo el sistema nervioso simpático modula la actividad ventricular y participa en el desarrollo de arritmias, tal y como se ha observado experimentalmente, podría ser crucial para avanzar en el diseño de nuevas terapias clínicas dirigidas a prevenir o tratar estas anomalías rítmicas.Esta tesis investiga y analiza la variabilidad espacio-temporal de la repolarización ventricular humana, su modulación por el sistema nervioso simpático, los mecanismos que subyacen a incrementos notables en dicha variabilidad y la relación que existe con la generación de arritmias ventriculares. Para ello, se proponen metodología que combinan el procesado de señales ventriculares y el modelado in silico de miocitos ventriculares humanos. Los modelos in silico desarrollados incluyen descripciones teóricas acopladas de la electrofisiología, la dinámica del calcio, el estiramiento mecánico y la señalización -adrenérgica. Para tener en cuenta la variabilidad temporal(latido a latido) de la repolarización, se añade estocasticidad en las ecuaciones que definen la apertura y cierre de los canales iónicos de las principales corrientes activas durante la fase de repolarización del potencial de acción (AP), es decir, durante el retorno de la célula al estado de reposo después de una excitación. Por otro lado, para tener en cuenta la variabilidad espacial (célula a célula) de la repolarización, se construye y calibra una población de modelos representativos de diferentes características celulares utilizando para ellos datos experimentales disponibles. La investigación teórica y computacional de este estudio, combinada con el procesado de señales ventriculares tanto clínicas como experimentales, sienta las bases para futuros estudios que tengan como objetivo mejorar los métodos de estratificación del riesgo arrítmico y guiar la búsqueda de terapias antiarrítmicas más eficaces.En el Capítulo 2, se construye una población de modelos computacionales estocásticos representativos de células ventriculares humanas, los cuales se calibran experimentalmente.Estos modelos combinan la electrofisiología, la mecánica y la señalización-adrenérgica y se utizan para caracterizar de modo teórico la variabilidadespacio-temporal. La calibración de los modelos se basa en rangos experimentales de una serie de marcadores derivados del AP que describen su duración, amplitud y morfología.Mediante el uso de esta población de modelos estocásticos de AP se reproducenlas interacciones descritas experimentalmente entre un tipo particular de variabilidad temporal, asociada con las oscilaciones de baja frecuencia (LF) de la duración del AP (APD), y la variabilidad global latido a latido de la repolarización (BVR) en respuesta a un incremento de la actividad simpática. Además en este capítulo, se han estudiado los mecanismos iónicos que esán detrás de los incrementos simultáneos de ambos fenómenos y se ha demostrado que dichos mecanismos están asociados con la disminución de las corrientes rectificadora de entrada y rectificadora retardada rápida de K+ y a su vez de la corriente de Ca2+ tipo-L. Finalmente, se ha probado que niveles elevados de oscilaciones de baja frecuencia del APD y de BVR en ventrículos enfermosconducen a inestabilidades eléctricas y al desarrollo de eventos arritmogénicos.En el Capítulo 3, se investiga el retardo necesario para la manifestación de las oscilaciones LF del APD, como una forma particular de variabilidad de repolarización, en los miocitos ventriculares en respuesta a la provocación simpática. Mediante el uso de una población calibrada experimentalmente de modelos de AP ventriculares humanos, como en el Capítulo 2, se ha demostrado que esta latencia oscilatoria está asociada con la cinética lenta de fosforilación de la corriente rectificadora retardada lenta de K+ (IKs) en respuesta a la estimulación -adrenérgica. La estimulación previa de los receptores reduce sustancialmente el tiempo requerido para el desarrollo de oscilaciones de LF. Además, se ha demostrado que lapsos de tiempo cortos están íntimamente relacionados con mayores magnitudes oscilatorias del APD, medidas en elCapítulo 3, particularmente en células susceptibles de desarrollar eventos arritmogénicos en respuesta a la estimulación simpática.La calibración experimental de la población de modelos utilizados en los Capítulos 2 y 3 no garantiza que cada modelo de la población construida represente las medidas de un cardiomiocito ventricular humano individual. Es por esta razón que en el Capítulo 4 se desarrolla una metodología novedosa para construir poblaciones computacionales de modelos celulares ventriculares humanos que recapitulen más fielmente las evidencias experimentales disponibles. La metodología propuesta se basa en la formulación de representaciones estado-espacio no lineales y en el uso del filtro de Kalman (UKF) para la estimación de los parámetros y las variables de estado de un modelo AP estocástico subyacente para cada señal de potencial dada como entrada.Las pruebas realizadas sobre series de potencial sintéticas y experimentales demuestran que esta metodología permite establecer una correspondencia entre las trazas AP de entrada y los conjuntos de parámetros del modelo (conductancias de corriente iónicas) y las variables de estado (variables relacionadas con la apertura/cierre de los canales iónicos y concentraciones iónicas intracelulares). A su vez, se ha demostrado que la metodología propuesta es robusta y adecuada para la investigación de la variabilidad espacio-temporal en la repolarización ventricular humana.En el Capítulo 5 se proponen varias mejoras a la metodología desarrollada en elCapítulo 4 para estimar con mayor precisión los parámetros y las variables de estado de los modelos estocásticos de células ventriculares humanas a partir de señales individuales de AP dadas como entradas, y a su vez para reducir el tiempo de convergencia a fin de proporcionar una estimación más rápida. Las mejoras se han basado en el uso combinado del método UKF, presentado en el Capítulo 4, junto con el método Double Greedy Dimension Reduction (DGDR) con generación automática de biomarcadores.Además de estimar las conductancias de las corrientes iónicas en condiciones basales, el enfoque presentado en este capítulo también proporciona el conjunto de niveles de fosforilación inducidos por la estimulación -adrenérgica, contribuyendo así al análisis de patrones de repolarización espacio-temporal con y sin modulación autonómica.En conclusión, esta tesis presenta novedosas metodologías enfocadas hacia lacaracterización de la variabilidad espacio-temporal de la repolarización ventricular humana, el análisis de sus mecanismos subyacentes y la determinaci´ón de la relación entre aumentos en la variabilidad y el mayor riesgo de sufrir arritmias ventriculares y muerte súbita cardíaca. Se desarrollan conjuntos de modelos computacionales estocásticos celulares humanos con representación de la electrofisiología ventricular, la mecánica y la señalización -adrenérgica para analizar la variabilidad global de larepolarización, latido a latido y célula a célula, así como de un tipo particular de variabilidad en forma de oscilaciones de baja frecuencia. Para reproducir fielmente los patrones de variabilidad medidos experimentalmente de manera individual, se proponen metodologías para construir poblaciones de modelos AP ventriculares humanos donde los parámetros y las variables de estado de cada modelo se estiman a partir de una serie de potencial de entrada dada. Estos modelos personalizados abren la puerta a una investigación más robusta de las causas y consecuencias de la variabilidad espacio-temporal de la repolarización ventricular humanCardiovascular diseases represent the main cause of mortality and morbidity in industrialized societies. A significant percentage of deaths associated with these diseases is related to the generation of cardiac arrhythmias, defined as abnormalities in the electrical functioning of the heart. Three major elements are involved in the development of arrhythmias, which include an arrhythmogenic substrate, a trigger and modulating factors. The Autonomic Nervous System (ANS) is the most relevant of these modulators. The ANS is composed of two branches, sympathetic and parasympathetic, which to a certain extent act antagonistically to each other. The possibility of revealing how the sympathetic nervous system modulates the activity of the ventricles (lower heart chambers) and participates in the development of arrhythmias, as reported experimentally, could be crucial to advance in the design of new clinical therapies aimed at preventing or treating these rhythm abnormalities. This thesis investigates spatio-temporal variability of human ventricular repolarization, its modulation by the sympathetic nervous system, the mechanisms behind highly elevated variability and the relationship to the generation of ventricular arrhythmias. To that end, methodologies combining signal processing of ventricular signals and in silico modeling of human ventricular myocytes are proposed. The developed in silico models include coupled theoretical descriptions of electrophysiology, calcium dynamics, mechanical stretch and -adrenergic signaling. To account for temporal (beat-to-beat) repolarization variability, stochasticity is added into the equations defining the gating of the ion channels of the main currents active during action potential (AP) repolarization, i.e. during the return of the cell to the resting state after an excitation. To account for spatial (cell-to-cell) repolarization variability, a population of models representative of different cellular characteristics are constructed and calibrated based on available experimental data. The theoretical computational research of this study, combined with the processing of clinical and experimental ventricular signals, lays the ground for future studies aiming at improving arrhythmic risk stratification methods and at guiding the search for more efficient anti-arrhythmic therapies. In Chapter 2, a population of experimentally-calibrated stochastic human ventricular computational cell models coupling electrophysiology, mechanics and -adrenergic signaling are built to investigate spatio-temporal variability. Model calibration is based on experimental ranges of a number of AP-derived markers describing AP duration, amplitude and shape. By using the proposed population of stochastic AP models, the experimentally reported interactions between a particular type of temporal variability associated with low-frequency (LF) oscillations of AP duration (APD) and overall beat-to-beat variability of repolarization (BVR) in response to enhanced sympathetic activity are reproduced. Ionic mechanisms behind correlated increments in both phenomena are investigated and found to be related to downregulation of the inward and rapid delayed rectifier K+ currents and the L-type Ca2+ current. Concomitantly elevated levels of LF oscillations of APD and BVR in diseased ventricles are shown to lead to electrical instabilities and arrhythmogenic events. In Chapter 3, the time delay for manifestation of LF oscillations of APD, as a particular form of repolarization variability, is investigated in ventricular myocytes in response to sympathetic provocation. By using an experimentally-calibrated population of human ventricular AP models, as in Chapter 2, this oscillatory latency is demonstrated to be associated with the slow phosphorylation kinetics of the slow delayed rectifier K+ current IKs in response to -adrenergic stimulation. Prior stimulation of -adrenoceptors substantially reduces the time required for the development of LF oscillations. In addition, short time lapses are shown to be related to large APD oscillatory magnitudes, as measured in Chapter 2, particularly in cells susceptible to develop arrhythmogenic events in response to sympathetic stimulation. The experimental calibration of the population of models used in Chapter 2 and Chapter 3, despite ensuring that simulated population measurements lie within experimental limits, does not guarantee that each model in the constructed population represents the experimental measurements of an individual human ventricular cardiomyocyte. It is for that reason that in Chapter 4 a novel methodology is developed to construct computational populations of human ventricular cell models that more faithfully recapitulate individual available experimental evidences. The proposed methodology is based on the formulation of nonlinear state-space representations and the use of the Unscented Kalman Filter (UKF) to estimate parameters and state variables of an underlying stochastic AP model given any input voltage trace. Tests performed over synthetic and experimental voltage traces demonstrate that this methodology successfully renders a one-to-one match between input AP traces and sets of model parameters (ionic current conductances) and state variables (ionic gating variables and intracellular concentrations). The proposed methodology is shown to be robust for investigation of spatio-temporal variability in human ventricular repolarization. Chapter 5 improves the methodology developed in Chapter 4 to more accurately estimate parameters and state variables of stochastic human ventricular cell models from individual input voltage traces and to reduce the converge time so as to provide faster estimation. The improvements are based on the combined use of the UKF method of Chapter 4 together with Double Greedy Dimension Reduction (DGDR) method with automatic generation of biomarkers. Additionally, on top of estimating ionic current conductances at baseline conditions, the approach presented in this chapter also provides a set of -adrenergic-induced phosphorylation levels, thus contributing to the analysis of spatio-temporal repolarization patterns with and without autonomic modulation. In conclusion, this thesis presents novel methodologies for characterization of spatio-temporal variability of human ventricular repolarization, for dissection of its underlying mechanisms and for ascertainment of the relationship between elevated variability and increased risk for ventricular arrhythmias and sudden cardiac death. Sets of stochastic human computational cell models with representation of ventricular electrophysiology, mechanics and -adrenergic signaling are developed and used to analyze overall beat-to-beat and cell-to-cell repolarization variability as well as a particular type of variability in the form of LF oscillations. To faithfully reproduce experimentally measured variability patterns in a one-to-one manner, methodologies are proposed to construct populations of human ventricular AP models where the parameters and state variables of a model are estimated from a given input voltage trace. These personalized models open the door to more robust investigation of the causes and consequences of spatio-temporal variability of human ventricular repolarization.<br /

Time Course of Low-Frequency Oscillatory Behavior in Human Ventricular Repolarization Following Enhanced Sympathetic Activity and Relation to Arrhythmogenesis

Background and Objectives: Recent studies in humans and dogs have shown that ventricular repolarization exhibits a low-frequency (LF) oscillatory pattern following enhanced sympathetic activity, which has been related to arrhythmic risk. The appearance of LF oscillations in ventricular repolarization is, however, not immediate, but it may take up to some minutes. This study seeks to characterize the time course of the action potential (AP) duration (APD) oscillatory behavior in response to sympathetic provocations, unveil its underlying mechanisms and establish a potential link to arrhythmogenesis under disease conditions. Materials and Methods: A representative set of human ventricular computational models coupling cellular electrophysiology, calcium dynamics, β-adrenergic signaling, and mechanics was built. Sympathetic provocation was modeled via phasic changes in β-adrenergic stimulation (β-AS) and mechanical stretch at Mayer wave frequencies within the 0.03–0.15 Hz band. Results: Our results show that there are large inter-individual differences in the time lapse for the development of LF oscillations in APD following sympathetic provocation, with some cells requiring just a few seconds and other cells needing more than 3 min. Whereas, the oscillatory response to phasic mechanical stretch is almost immediate, the response to β-AS is much more prolonged, in line with experimentally reported evidences, thus being this component the one driving the slow development of APD oscillations following enhanced sympathetic activity. If β-adrenoceptors are priorly stimulated, the time for APD oscillations to become apparent is remarkably reduced, with the oscillation time lapse being an exponential function of the pre-stimulation level. The major mechanism underlying the delay in APD oscillations appearance is related to the slow IKs phosphorylation kinetics, with its relevance being modulated by the IKs conductance of each individual cell. Cells presenting short oscillation time lapses are commonly associated with large APD oscillation magnitudes, which facilitate the occurrence of pro-arrhythmic events under disease conditions involving calcium overload and reduced repolarization reserve. Conclusions: The time course of LF oscillatory behavior of APD in response to increased sympathetic activity presents high inter-individual variability, which is associated with different expression and PKA phosphorylation kinetics of the IKs current. Short time lapses in the development of APD oscillations are associated with large oscillatory magnitudes and pro-arrhythmic risk under disease conditions

Time Course of Low-Frequency Oscillatory Behavior in Human Ventricular Repolarization Following Enhanced Sympathetic Activity and Relation to Arrhythmogenesis

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Complex Interaction Between Low-Frequency APD Oscillations and Beat-to-Beat APD Variability in Humans Is Governed by the Sympathetic Nervous System

Background: Recent clinical, experimental and modeling studies link oscillations of ventricular repolarization in the low frequency (LF) (approx. 0.1 Hz) to arrhythmogenesis. Sympathetic provocation has been shown to enhance both LF oscillations of action potential duration (APD) and beat-to-beat variability (BVR) in humans. We hypothesized that beta-adrenergic blockade would reduce LF oscillations of APD and BVR of APD in humans and that the two processes might be linked. Methods and Results: Twelve patients with normal ventricles were studied during routine electrophysiological procedures. Activation-recovery intervals (ARI) as a conventional surrogate for APD were recorded from 10 left and 10 right ventricular endocardial sites before and after acute beta-adrenergic adrenergic blockade. Cycle length was maintained constant with right ventricular pacing. Oscillatory behavior of ARI was quantified by spectral analysis and BVR as the short-term variability. Beta-adrenergic blockade reduced LF ARI oscillations (8.6 ± 4.5 ms2 vs. 5.5 ± 3.5 ms2, p = 0.027). A significant correlation was present between the initial control values and reduction seen following beta-adrenergic blockade in LF ARI (rs = 0.62, p = 0.037) such that when initial values are high the effect is greater. A similar relationship was also seen in the beat-to beat variability of ARI (rs = 0.74, p = 0.008). There was a significant correlation between the beta-adrenergic blockade induced reduction in LF power of ARI and the witnessed reduction of beat-to-beat variability of ARI (rs = 0.74, p = 0.01). These clinical results accord with recent computational modeling studies which provide mechanistic insight into the interactions of LF oscillations and beat-to-beat variability of APD at the cellular level. Conclusion: Beta-adrenergic blockade reduces LF oscillatory behavior of APD (ARI) in humans in vivo. Our results support the importance of LF oscillations in modulating the response of BVR to beta-adrenergic blockers, suggesting that LF oscillations may play role in modulating beta-adrenergic mechanisms underlying BVR

Data-driven Identification of Stochastic Model Parameters and State Variables: Application to the Study of Cardiac Beat-to-beat Variability

Enhanced spatiotemporal ventricular repolarization variability has been associated with ventricular arrhythmias and sudden cardiac death, but the involved mechanisms remain elusive. In this paper, a methodology for estimation of parameters and state variables of stochastic human ventricular cell models from input voltage data is proposed for investigation of repolarization variability. Methods: The proposed methodology formulates state-space representations based on developed stochastic cell models and uses the unscented Kalman filter to perform joint parameter and state estimation. Evaluation over synthetic and experimental data is presented. Results: Results on synthetically generated data show the ability of the methodology to: first, filter out measurement noise from action potential (AP) traces; second, identify model parameters and state variables from each of those individual AP traces, thus allowing robust characterization of cell-to-cell variability; and, third, replicate statistical population''s distributions of input AP-based markers, including dynamic markers quantifying beat-to-beat variability. Application onto experimental data demonstrates the ability of the methodology to match input AP traces while concomitantly inferring the characteristics of underlying stochastic cell models. Conclusion: A novel methodology is presented for estimation of parameters and hidden variables of stochastic cardiac computational models, with the advantage of providing a one-to-one match between each individual AP trace and a corresponding set of model characteristics. Significance: The proposed methodology can greatly help in the characterization of temporal (beat-to-beat) and spatial (cell-to-cell) variability in human ventricular repolarization and in ascertaining the corresponding underlying mechanisms, particularly in scenarios with limited available experimental data

Mechanisms underlying interactions between low-frequency oscillations and beat-to-beat variability of celullar ventricular repolarization in response to sympathetic stimulation:Implications for arrhythmogenesis

Background and Objectives: Enhanced beat-to-beat variability of ventricular repolarization (BVR) has been linked to arrhythmias and sudden cardiac death. Recent experimental studies on human left ventricular epicardial electrograms have shown that BVR closely interacts with low-frequency (LF) oscillations of activation recovery interval during sympathetic provocation. In this work human ventricular computational cell models are developed to reproduce the experimentally observed interactions between BVR and its LF oscillations, to assess underlying mechanisms and to establish a relationship with arrhythmic risk. Materials and Methods: A set of human ventricular action potential (AP) models covering a range of experimental electrophysiological characteristics was constructed. These models incorporated stochasticity in major ionic currents as well as descriptions of ß-adrenergic stimulation and mechanical effects to investigate the AP response to enhanced sympathetic activity. Statistical methods based on Automatic Relevance Determination and Canonical Correlation Analysis were developed to unravel individual and common factors contributing to BVR and LF patterning of APD in response to sympathetic provocation. Results: Simulated results reproduced experimental evidences on the interactions between BVR and LF oscillations of AP duration (APD), with replication of the high inter-individual variability observed in both phenomena. ICaL, IKr and IK1 currents were identified as common ionic modulators of the inter-individual differences in BVR and LF oscillatory behavior and were shown to be crucial in determining susceptibility to arrhythmogenic events. Conclusions: The calibrated family of human ventricular cell models proposed in this study allows reproducing experimentally reported interactions between BVR and LF oscillations of APD. Ionic factors involving ICaL, IKr and IK1 currents are found to underlie correlated increments in both phenomena in response to sympathetic provocation. A link to arrhythmogenesis is established for concomitantly elevated levels of BVR and its LF oscillations