Characterization of Spatio-Temporal Cardiac Action Potential Variability at Baseline and Under ß-Adrenergic Stimulation by Combined Unscented Kalman Filter and Double Greedy Dimension Reduction.

OBJECTIVE: Elevated spatio-temporal variability of human ventricular repolarization has been related to increased risk for ventricular arrhythmias and sudden cardiac death, particularly under ß-adrenergic stimulation ( ß-AS). This work presents a methodology for theoretical characterization of temporal and spatial repolarization variability at baseline conditions and in response to ß-AS. For any measured voltage trace, the proposed methodology estimates the parameters and state variables of an underlying human ventricular action potential (AP) model by combining Double Greedy Dimension Reduction (DGDR) with automatic selection of biomarkers and the Unscented Kalman Filter (UKF). Such theoretical characterization can facilitate subsequent characterization of underlying variability mechanisms. MATERIAL AND METHODS: Given an AP trace, initial estimates for the ionic conductances in a stochastic version of the baseline human ventricular O'Hara et al. model were obtained by DGDR. Those estimates served to initialize and update model parameter estimates by the UKF method based on formulation of an associated nonlinear state-space representation and joint estimation of model parameters and state variables. Similarly, ß-AS-induced phosphorylation levels of cellular substrates were estimated by the DGDR-UKF methodology. Performance was tested by building an experimentally-calibrated population of virtual cells, from which synthetic AP traces were generated for baseline and ß-AS conditions. RESULTS: The combined DGDR-UKF methodology led to 25% reduction in the error associated with estimation of ionic current conductances at baseline conditions and phosphorylation levels under ß-AS with respect to individual DGDR and UKF methods. This improvement was not at the expense of higher computational load, which was diminished by 90% with respect to the individual UKF method. Both temporal and spatial AP variability of repolarization were accurately characterized by the DGDR-UKF methodology. CONCLUSIONS: A combined DGDR-UKF methodology is proposed for parameter and state variable estimation of human ventricular cell models from available AP traces at baseline and under ß-AS. This methodology improves the estimation performance and reduces the convergence time with respect to individual DGDR and UKF methods and renders a suitable approach for computational characterization of spatio-temporal repolarization variability to be used for ascertainment of variability mechanisms and its relation to arrhythmogenesis.

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

OBJECTIVE: 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.

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 (r s = 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 (r s = 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 (r s = 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.

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, ß-adrenergic signaling, and mechanics was built. Sympathetic provocation was modeled via phasic changes in ß-adrenergic stimulation (ß-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 ß-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 ß-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 I Ks phosphorylation kinetics, with its relevance being modulated by the I Ks 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 I Ks current. Short time lapses in the development of APD oscillations are associated with large oscillatory magnitudes and pro-arrhythmic risk under disease conditions.