A reliability analysis of cardiac repolarization time markers

In vivo human sock-mapping validation of a simple model that explains unipolar electrogram morphology in relation to conduction-repolarization dynamics

INTRODUCTION

The unipolar electrogram (UEG) provides local measures of cardiac activation and repolarization and is an important translational link between patient and laboratory. A simple theoretical model of the UEG was previously proposed and tested in silico.

METHOD AND RESULTS

The aim of this study was to use epicardial sock-mapping data to validate the simple model's predictions of unipolar electrogram morphology in the in vivo human heart. The simple model conceptualizes the UEG as the difference between a local cardiac action potential and a position-independent component representing remote activity, which is defined as the average of all action potentials. UEGs were recorded in 18 patients using a multielectrode sock containing 240 electrodes and activation (AT) and repolarization time (RT) were measured using standard definitions. For each cardiac site, a simulated local action potential was generated by adjusting a stylized action potential to fit AT and RT measured in vivo. The correlation coefficient (cc) measuring the morphological similarity between 13,637 recorded and simulated UEGs was cc  =  0.89 (0.72-0.95), median (Q₁ -Q₃ ), for the entire UEG, cc  =  0.90 (0.76-0.95) for QRS complexes, and cc  =  0.83 (0.58-0.92) for T-waves. QRS and T-wave areas from recorded and simulated UEGs showed cc> 0.89 and cc> 0.84, respectively, indicating good agreement between voltage isochrones maps. Simulated UEGs accurately reproduced the interaction between AT and QRS morphology and between RT and T-wave morphology observed in vivo.

CONCLUSIONS

Human in vivo whole heart data support the validity of the simple model, which provides a framework for improving the understanding of the UEG and its clinical utility.

Interactions between Activation and Repolarization Restitution Properties in the Intact Human Heart: In-Vivo Whole-Heart Data and Mathematical Description

BACKGROUND

The restitution of the action potential duration (APDR) and conduction velocity (CVR) are mechanisms whereby cardiac excitation and repolarization adapt to changes in heart rate. They modulate the vulnerability to dangerous arrhythmia, but the mechanistic link between restitution and arrhythmogenesis remains only partially understood.

METHODS

This paper provides an experimental and theoretical study of repolarization and excitation restitution properties and their interactions in the intact human epicardium. The interdependence between excitation and repolarization dynamic is studied in 8 patients (14 restitution protocols, 1722 restitution curves) undergoing global epicardial mapping with multi-electrode socks before open heart surgery. A mathematical description of the contribution of both repolarization and conduction dynamics to the steepness of the APDR slope is proposed.

RESULTS

This study demonstrates that the APDR slope is a function of both activation and repolarization dynamics. At short cycle length, conduction delay significantly increases the APDR slope by interacting with the diastolic interval. As predicted by the proposed mathematical formulation, the APDR slope was more sensitive to activation time prolongation than to the simultaneous shortening of repolarization time. A steep APDR slope was frequently identified, with 61% of all cardiac sites exhibiting an APDR slope > 1, suggesting that a slope > 1 may not necessarily promote electrical instability in the human epicardium. APDR slope did not change for different activation or repolarization times, and it was not a function of local baseline APD. However, it was affected by the spatial organization of electrical excitation, suggesting that in tissue APDR is not a unique function of local electrophysiological properties. Spatial heterogeneity in both activation and repolarization restitution contributed to the increase in the modulated dispersion of repolarization, which for short cycle length was as high as 250 ms. Heterogeneity in conduction velocity restitution can translate into both activation and repolarization dispersion and increase cardiac instability. The proposed mathematical formulation shows an excellent agreement with the experimental data (correlation coefficient r = 0.94) and provides a useful tool for the understanding of the complex interactions between activation and repolarization restitution properties as well as between their measurements.

Ventricular stimulus site influences dynamic dispersion of repolarization in the intact human heart

Spatial variation of restitution in relation to varying stimulus site is poorly defined in the intact human heart. Repolarization gradients were shown to be dependent on site of activation with epicardial stimulation promoting significant transmural gradients. Steep restitution slopes were predominant in the normal ventricle.

The spatial variation in restitution properties in relation to varying stimulus site is poorly defined. This study aimed to investigate the effect of varying stimulus site on apicobasal and transmural activation time (AT), action potential duration (APD) and repolarization time (RT) during restitution studies in the intact human heart. Ten patients with structurally normal hearts, undergoing clinical electrophysiology studies, were enrolled. Decapolar catheters were placed apex to base in the endocardial right ventricle (RV_endo) and left ventricle (LV_endo), and an LV branch of the coronary sinus (LV_epi) for transmural recording. S1–S2 restitution protocols were performed pacing RV_endo apex, LV_endo base, and LV_epi base. Overall, 725 restitution curves were analyzed, 74% of slopes had a maximum slope of activation recovery interval (ARI) restitution (S_max) > 1 (P < 0.001); mean S_max = 1.76. APD was shorter in the LV_epi compared with LV_endo, regardless of pacing site (30-ms difference during RV_endo pacing, 25-ms during LV_endo, and 48-ms during LV_epi; 50th quantile, P < 0.01). Basal LV_epi pacing resulted in a significant transmural gradient of RT (77 ms, 50th quantile: P < 0.01), due to loss of negative transmural AT-APD coupling (mean slope 0.63 ± 0.3). No significant transmural gradient in RT was demonstrated during endocardial RV or LV pacing, with preserved negative transmural AT-APD coupling (mean slope −1.36 ± 1.9 and −0.71 ± 0.4, respectively). Steep ARI restitution slopes predominate in the normal ventricle and dynamic ARI; RT gradients exist that are modulated by the site of activation. Epicardial stimulation to initiate ventricular activation promotes significant transmural gradients of repolarization that could be proarrhythmic.

Regional segmentation of ventricular models to achieve repolarization dispersion in cardiac electrophysiology modeling

The electrocardiogram (ECG) is one of the most significant outputs of a computational model of cardiac electrophysiology because it relates the numerical results to clinical data and is a universal tool for diagnosing heart diseases. One key features of the ECG is the T-wave, which is caused by longitudinal and transmural heterogeneity of the action potential duration (APD). Thus, in order to model a correct wave of repolarization, different cell properties resulting in different APDs must be assigned across the ventricular wall and longitudinally from apex to base. To achieve this requirement, a regional parametrization of the heart is necessary. We propose a robust approach to obtain the transmural and longitudinal segmentation in a general heart geometry without relying on ad hoc procedures. Our approach is based on auxiliary harmonic lifting analyses, already used in the literature to generate myocardial fiber orientations. Specifically, the solution of a sequence of Laplace boundary value problems allows parametrically controlled segmentation of both heart ventricles. The flexibility and simplicity of the proposed method is demonstrated through several representative examples, varying the locations and extents of the epicardial, midwall, and endocardial layers. Effects of the control parameters on the T-wave morphology are illustrated via computed ECGs.

Measurement bias in activation-recovery intervals from unipolar electrograms

The activation-recovery interval (ARI) calculated from unipolar electrograms is regularly used as a convenient surrogate measure of local cardiac action potential durations (APD). This method enables important research bridging between computational studies and in vitro and in vivo human studies. The Wyatt method is well established as a theoretically sound method for calculating ARIs; however, some studies have observed that it is prone to a bias error in measurement when applied to positive T waves. This article demonstrates that recent theoretical and computational studies supporting the use of the Wyatt method are likely to have underestimated the extent of this bias in many practical experimental recording scenarios. This work addresses these situations and explains the measurement bias by adapting existing theoretical expressions of the electrogram to represent practical experimental recording configurations. A new analytic expression for the electrogram's local component is derived, which identifies the source of measurement bias for positive T waves. A computer implementation of the new analytic model confirms our hypothesis that the bias is systematically dependent on the electrode configuration. These results provide an aid to electrogram interpretation in general, and this work's outcomes are used to make recommendations on how to minimize measurement error.

A fully implicit finite element method for bidomain models of cardiac electromechanics

We propose a novel, monolithic, and unconditionally stable finite element algorithm for the bidomain-based approach to cardiac electromechanics. We introduce the transmembrane potential, the extracellular potential, and the displacement field as independent variables, and extend the common two-field bidomain formulation of electrophysiology to a three-field formulation of electromechanics. The intrinsic coupling arises from both excitation-induced contraction of cardiac cells and the deformation-induced generation of intra-cellular currents. The coupled reaction-diffusion equations of the electrical problem and the momentum balance of the mechanical problem are recast into their weak forms through a conventional isoparametric Galerkin approach. As a novel aspect, we propose a monolithic approach to solve the governing equations of excitation-contraction coupling in a fully coupled, implicit sense. We demonstrate the consistent linearization of the resulting set of non-linear residual equations. To assess the algorithmic performance, we illustrate characteristic features by means of representative three-dimensional initial-boundary value problems. The proposed algorithm may open new avenues to patient specific therapy design by circumventing stability and convergence issues inherent to conventional staggered solution schemes.

Mathematical modeling and simulation of ventricular activation sequences: implications for cardiac resynchronization therapy

Next to clinical and experimental research, mathematical modeling plays a crucial role in medicine. Biomedical research takes place on many different levels, from molecules to the whole organism. Due to the complexity of biological systems, the interactions between components are often difficult or impossible to understand without the help of mathematical models. Mathematical models of cardiac electrophysiology have made a tremendous progress since the first numerical ECG simulations in the 1960s. This paper briefly reviews the development of this field and discusses some example cases where models have helped us forward, emphasizing applications that are relevant for the study of heart failure and cardiac resynchronization therapy.