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Background Ventricular tachyarrhythmias are often preceded by short sequences of premature ventricular complexes. In a previous study, a restitution-based computational model predicted which sequences of stimulated premature complexes were most likely to induce ventricular fibrillation in canines in vivo. However, the underlying mechanism, based on discordant-alternans dynamics, could not be verified in that study. The current study seeks to elucidate the mechanism by determining whether the spatiotemporal evolution of action potentials and initiation of ventricular fibrillation in in vitro experiments are consistent with model predictions. Methods and Results Optical mapping voltage signals from canine right-ventricular tissue (n=9) were obtained simultaneously from the entire epicardium and endocardium during and after premature stimulus sequences. Model predictions of action potential propagation along a 1-dimensional cable were developed using action potential duration versus diastolic interval data. The model predicted sign-change patterns in action potential duration and diastolic interval spatial gradients with posterior probabilities of 91.1%, and 82.1%, respectively. The model predicted conduction block with 64% sensitivity and 100% specificity. A generalized estimating equation logistic-regression approach showed that model-prediction effects were significant for both conduction block ( P<1×10 -15 , coefficient 44.36) and sustained ventricular fibrillation ( P=0.0046, coefficient, 1.63) events. Conclusions The observed sign-change patterns favored discordant alternans, and the model successfully identified sequences of premature stimuli that induced conduction block. This suggests that the relatively simple discordant-alternans-based process that led to block in the model may often be responsible for ventricular fibrillation onset when preceded by premature beats. These observations may aid in developing improved methods for anticipating block and ventricular fibrillation.

Finding appropriate values for parameters in mathematical models of cardiac cells is a challenging task. Here, we show that it is possible to obtain good parameterizations in as little as 30-40 s when as many as 27 parameters are fit simultaneously using a genetic algorithm and two flexible phenomenological models of cardiac action potentials. We demonstrate how our implementation works by considering cases of "model recovery" in which we attempt to find parameter values that match model-derived action potential data from several cycle lengths. We assess performance by evaluating the parameter values obtained, action potentials at fit and non-fit cycle lengths, and bifurcation plots for fidelity to the truth as well as consistency across different runs of the algorithm. We also fit the models to action potentials recorded experimentally using microelectrodes and analyze performance. We find that our implementation can efficiently obtain model parameterizations that are in good agreement with the dynamics exhibited by the underlying systems that are included in the fitting process. However, the parameter values obtained in good parameterizations can exhibit a significant amount of variability, raising issues of parameter identifiability and sensitivity. Along similar lines, we also find that the two models differ in terms of the ease of obtaining parameterizations that reproduce model dynamics accurately, most likely reflecting different levels of parameter identifiability for the two models.

Aims: Human action potentials in the Brugada syndrome have been characterized by delayed or even complete loss of dome formation, especially in the right ventricular epicardial layers. Such a repolarization pattern is believed to trigger phase-2 reentry (P2R); however, little is known about the conditions necessary for its initiation. This study aims to determine the specific mechanisms that facilitate P2R induction in Brugada-affected cardiac tissue in humans., Methods: Ionic models for Brugada syndrome in human epicardial cells were developed and used to study the induction of P2R in cables, sheets, and a three-dimensional model of the right ventricular free wall., Results: In one-dimensional cables, P2R can be induced by adjoining lost-dome and delayed-dome regions, as mediated by tissue excitability and transmembrane voltage profiles, and reduced coupling facilitates its induction. In two and three dimensions, sustained reentry can arise when three regions (delayed-dome, lost-dome, and normal epicardium) are present., Conclusions: Not only does P2R induction by Brugada syndrome require regions of action potential with delayed-dome and lost-dome, but in order to generate a sustained reentry from a triggered waveback multiple factors are necessary, including heterogeneity in action potential distribution, tissue coupling, direction of stimulation, the shape of the late plateau, the duration of lost-dome action potentials, and recovery of tissue excitability, which is predominantly modulated by tissue coupling.

Background: Electric excitability in the ventricular wall is influenced by cellular electrophysiology and passive electric properties of the myocardium. Action potential (AP) rise time, an indicator of myocardial excitability, is influenced by conduction pattern and distance from the epicardial surface. This study examined AP rise times and conduction velocity as the depolarizing wavefront approaches the epicardial surface., Methods and Results: Two-photon excitation of di-4-aminonaphthenyl-pyridinum-propylsulfonate was used to measure electric activity at discrete epicardial layers of isolated Langendorff-perfused rabbit hearts to a depth of 500 μm. Endo-to-epicardial wavefronts were studied during right atrial or ventricular endocardial pacing. Similar measurements were made with epi-to-endocardial, transverse, and longitudinal pacing protocols. Results were compared with data from a bidomain model of 3-dimensional (3D) electric propagation within ventricular myocardium. During right atrial and endocardial pacing, AP rise time (10%-90% of upstroke) decreased by ≈50% between 500 and 50 μm from the epicardial surface, whereas conduction velocity increased and AP duration was only slightly shorter (≈4%). These differences were not observed with other conduction patterns. The depth-dependent changes in rise time were larger at higher pacing rates. Modeling data qualitatively reproduced the behavior seen experimentally and demonstrated a parallel reduction in peak I(Na) and electrotonic load as the wavefront approaches the epicardial surface., Conclusions: Decreased electrotonic load at the epicardial surface results in more rapid AP upstrokes and higher conduction velocities compared with the bulk myocardium. Combined effects of tissue depth and pacing rate on AP rise time reduce conduction safety and myocardial excitability within the ventricular wall.

This paper describes a systematic approach to suppressing cardiac alternans in simulated Purkinje fibers using localized current injections. We investigate the controllability and observability of the periodically paced Noble model for different locations of the recording and control electrodes. In particular, we show that the loss of controllability causes the failure of the control approach introduced by Echebarria and Karma [Chaos 12, 923 (2002)] for longer fiber lengths. Furthermore, we explain how the optimal locations for the recording and control electrodes and the timing of the feedback current can be selected, accounting for both linear and nonlinear effects, effectively doubling the length of fibers that can be controlled with previous methods.

Increased dispersion of action potential duration across cardiac tissue has long been considered an important substrate for the development of most electrical arrhythmias. Although this dispersion has been studied previously by characterizing the static intrinsic gradients in cellular electrophysiology and dynamical gradients generated by fast pacing, few studies have concentrated on dispersions generated solely by structural effects. Here we show how boundaries and geometry can produce spatially dependent changes in action potential duration (APD) in homogeneous and isotropic tissue, where all the cells have the same APD in the absence of diffusion. Electrotonic currents due to coupling within the tissue and at the tissue boundaries can generate dispersion, and the profile of this dispersion can change dramatically depending on tissue size and shape, action potential morphology, tissue dimensionality, and stimulus frequency and location. The dispersion generated by pure geometrical effects can be on the order of tens of milliseconds, enough under certain conditions to produce conduction blocks and initiate reentrant waves., (Copyright © 2011 Elsevier Ltd. All rights reserved.)

Modeling the dynamics of wave propagation in human ventricular tissue and studying wave stability require models that reproduce realistic characteristics in tissue. We present a minimal ventricular (MV) human model that is designed to reproduce important tissue-level characteristics of epicardial, endocardial and midmyocardial cells, including action potential (AP) amplitudes and morphologies, upstroke velocities, steady-state action potential duration (APD) and conduction velocity (CV) restitution curves, minimum APD, and minimum diastolic interval. The model is then compared with three previously published human ventricular cell models, the Priebe and Beuckelmann (PB), the Ten Tusscher-Noble-Noble-Panfilov (TNNP), and the Iyer-Mazhari-Winslow (IMW). For the first time, the stability of reentrant waves for all four models is analyzed, and quantitative comparisons are made among the models in single cells and in tissue. The PB, TNNP, and IMW models exhibit quantitative differences in APD and CV rate adaptation, as well as completely different reentrant wave dynamics of quasi-breakup, stability, and breakup, respectively. All the models have dominant frequencies comparable to clinical values except for the IMW model, which has a large range of frequencies extending beyond the clinical range for both ventricular tachycardia (VT) and ventricular fibrillation (VF). The TNNP and IMW models possess a large degree of short-term memory and we show for the first time the existence of memory in CV restitution. The MV model also can be fitted to reproduce the dynamics of other models and is computationally more efficient: the times required to simulate the MV, TNNP, PB and IMW models follow the ratio 1:31:50:8084.

A perspective on systems containing many action potential waves that, individually, are prone to spiral wave breakup is proposed. The perspective is based on two quantities, "predator" and "prey," which we define as the fraction of the system in the excited state and in the excitable but unexcited state, respectively. These quantities exhibited a number of properties in both simulations and fibrillating canine cardiac tissue that were found to be consistent with a proposed theory that assumes the existence of regions we call "domains of influence," each of which is associated with the activity of one action potential wave. The properties include (i) a propensity to rotate in phase space in the same sense as would be predicted by the standard Volterra-Lotka predator-prey equations, (ii) temporal behavior ranging from near periodic oscillation at a frequency close to the spiral wave rotation frequency ("type-1" behavior) to more complex oscillatory behavior whose power spectrum is composed of a range of frequencies both above and, especially, below the spiral wave rotation frequency ("type-2" behavior), and (iii) a strong positive correlation between the periods and amplitudes of the oscillations of these quantities. In particular, a rapid measure of the amplitude was found to scale consistently as the square root of the period in data taken from both simulations and optical mapping experiments. Global quantities such as predator and prey thus appear to be useful in the study of multiple spiral wave systems, facilitating the posing of new questions, which in turn may help to provide greater understanding of clinically important phenomena such as ventricular fibrillation.

The extensive development of detailed mathematical models of cardiac myocyte electrophysiology in recent years has led to a proliferation of models, including many that model the same animal species and specific region of the heart and thus would be expected to have similar properties. In this paper we review and compare two recently developed mathematical models of the electrophysiology of canine ventricular myocytes. To clarify their similarities and differences, we also present studies using them in a range of preparations from single cells to two-dimensional tissue. The models are compared with each other and with new and previously published experimental results in terms of a number of their properties, including action potential morphologies; transmembrane currents during normal heart rates and during alternans; alternans onsets, magnitudes, and cessations; and reentry dynamics of spiral waves. Action potential applets and spiral wave movies for the two canine ventricular models are available online as supplemental material. We find a number of differences between the models, including their rate dependence, alternans dynamics, and reentry stability, and a number of differences compared with experiments. Differences between models of the same species and region of the heart are not unique to these canine models. Similar differences can be found in the behavior of two models of human ventricular myocytes and of human atrial myocytes. We provide several possible explanations for the differences observed in models of the same species and region of the heart and discuss the implications for the applicability of models in addressing questions of mechanism in cardiac electrophysiology.

Background: The relationships between action potential duration (APD) and conduction velocity (CV) to the previous diastolic interval (DI) are known as the APD and CV restitution relationships. There is considerable debate regarding the importance of these relationships in the development and stability of reentry., Objectives: The purpose of this study was to increase the understanding of the ionic basis for restitution during reentry., Methods: APD and CV were studied numerically during one-dimensional reentry as ring length (L) was shortened. A three-state variable model (u, v, w) was used to analyze the effect of gating variables of the fast (v) and slow (w) currents on the spatial and temporal dynamics of transmembrane potential (u). Three parameter sets were used corresponding to three APD and CV restitution curves., Results: Sustained spatial oscillations of APD and CV larger than the ring length were observed in two of the parameter sets (cytochalasin-D model [CYTO] and model 3 [M3]) before block occurred at L = 6 cm. The last model (diacetyl monoxime [DAM]) resulted in uniform APD and CV for all L until block occurred at L = 3 cm. Multivalued APD and CV restitution relationships due to "dephasing" of w and v with DI were observed in M3 and CYTO simulations. Overall, these dynamics could be explained by the wavelength-to-ring length ratio and the sensitivity of APD on the value of the gating variables w and v., Conclusion: Propagation stability is mostly controlled by APD sensitivity to w, but the APD restitution slope does not always reflect this sensitivity. The interaction of the dynamic history (i.e., memory) of the fast and slow currents and electrotonic effects resulted in multivalued restitution curves.

Background: The relationships between action potential duration (APD) and conduction velocity (CV) to the previous diastolic interval (DI) are known as the APD and CV restitution relationships. There is considerable debate regarding the importance of these relationships in the development and stability of reentry., Objectives: The purpose of this study was to increase the understanding of the ionic basis for restitution during reentry., Methods: APD and CV were studied numerically during one-dimensional reentry as ring length (L) was shortened. A three-state variable model (u, v, w) was used to analyze the effect of gating variables of the fast (v) and slow (w) currents on the spatial and temporal dynamics of transmembrane potential (u). Three parameter sets were used corresponding to three APD and CV restitution curves., Results: Sustained spatial oscillations of APD and CV larger than the ring length were observed in two of the parameter sets (cytochalasin-D model [CYTO] and model 3 [M3]) before block occurred at L = 6 cm. The last model (diacetyl monoxime [DAM]) resulted in uniform APD and CV for all L until block occurred at L = 3 cm. Multivalued APD and CV restitution relationships due to "dephasing" of w and v with DI were observed in M3 and CYTO simulations. Overall, these dynamics could be explained by the wavelength-to-ring length ratio and the sensitivity of APD on the value of the gating variables w and v., Conclusion: Propagation stability is mostly controlled by APD sensitivity to w, but the APD restitution slope does not always reflect this sensitivity. The interaction of the dynamic history (i.e., memory) of the fast and slow currents and electrotonic effects resulted in multivalued restitution curves.

We examine the utility of the action potential (AP) duration (APD) restitution curve slope in predicting the onset of electrical alternans when electrotonic and memory effects are considered. We develop and use two ionic cell models without memory that have the same restitution curve with slope >1 but different AP shapes and, therefore, different electrotonic effects. We also study a third cell model that incorporates short-term memory of previous cycle lengths, so that it has a family of S1-S2 restitution curves as well as a dynamic restitution curve with slope >1. Our results indicate that both electrotonic and memory effects can suppress alternans, even when the APD restitution curve is steep. In the absence of memory, electrotonic currents related to the shape of the AP, as well as conduction velocity restitution, can affect how alternans develops in tissue and, in some cases, can prevent its induction entirely, even when isolated cells exhibit alternans. When short-term memory is included, alternans may not occur in isolated cells, despite a steep APD restitution curve, and may or may not occur in tissue, depending on conduction velocity restitution. We show for the first time that electrotonic and memory effects can prevent conduction blocks and stabilize reentrant waves in two and three dimensions. Thus we find that the slope of the APD restitution curve alone does not always well predict the onset of alternans and that incorporating electrotonic and memory effects may provide a more useful alternans criterion.