David J. Christini

Real-Time Linux Dynamic Clamp: A Fast and Flexible Way to Construct Virtual Ion Channels in Living Cells

AbstractWe describe a system for real-time control of biological and other experiments. This device, based around the Real-Time Linux operating system, was tested specifically in the context of dynamic clamping, a demanding real-time task in which a computational system mimics the effects of nonlinear membrane conductances in living cells. The system is fast enough to represent dozens of nonlinear conductances in real time at clock rates well above 10 kHz. Conductances can be represented in deterministic form, or more accurately as discrete collections of stochastically gating ion channels. Tests were performed using a variety of complex models of nonlinear membrane mechanisms in excitable cells, including simulations of spatially extended excitable structures, and multiple interacting cells. Only in extreme cases does the computational load interfere with high-speed “hard” real-time processing (i.e., real-time processing that never falters). Freely available on the worldwide web, this experimental control system combines good performance, immense flexibility, low cost, and reasonable ease of use. It is easily adapted to any task involving real-time control, and excels in particular for applications requiring complex control algorithms that must operate at speeds over 1 kHz.

A Computational Model to Predict the Effects of Class I Anti-Arrhythmic Drugs on Ventricular Rhythms

Two- and three-dimensional models of cardiac excitability based on sodium channel kinetics can predict the adverse effects of class I anti-arrhythmic drugs. Crowdsourcing the Heart for Drug Screening The old way: Consult a specialist to answer your question. The new way: Consult a crowd of generalists who in the aggregate can come up with a better answer. The old way—testing drugs on single cardiac cells in vitro—has not worked well for screening out potential anti-arrhythmia agents that can occasionally block conduction in the heart or exacerbate arrhythmia, serious problems that cause sudden death in treated patients. Instead, Moreno et al. have called on the crowd by building a model of heart tissue that includes many cardiac cells and their interactions. When anti-arrhythmia drugs are “applied” to the model’s beating heart tissue—but not when they are applied to the single cardiac cells that make up the model—the drugs that cause side effects, and the concentrations at which they do so, are revealed, results that the authors were able to validate experimentally. The model starts with the detailed kinetics of the heart’s sodium channels, first in the context of a single cell, then in two- and three-dimensional cardiac tissue. The authors compared the action of lidocaine, a class 1B anti-arrhythmic drug not known to cause conduction block, and flecainide, a prototypical class 1C drug that carries a warning from the Food and Drug Administration. In the modeled analyses of single cardiac cells, both drugs slowed excitability at concentrations that matched those used in patients, but the cells retained the ability to generate action potentials. But when the model incorporated coupled groups of cells, the behavior of the drugs diverged. Lidocaine lowered excitability without causing block, but at the higher concentrations (used clinically), flecainide caused serious conduction block when heart rates reached 160 beats per minute. Experiments in rabbit heart confirmed the results of the model. In scaled-up, 500 by 500 groups of cells, the authors’ model could also successfully predict the tendency of flecainide, but not lidocaine, to make the heart extra sensitive to heartbeats occurring too early or too late, an effect that causes even more severe arrhythmias in patients when they take anti-arrhythmia drugs. Again, experiments in rabbit hearts replicated the model’s predictions, as did simulations of anatomically accurate human hearts derived from magnetic resonance imaging images. The ability of this sophisticated model of living cardiac tissue to replicate the clinical adverse effects of lidocaine and flecainide is promising, but it will be necessary to validate its performance with other drugs to understand how to deploy it most effectively. Ideally, such models will be useful for screening out potential arrhythmic drugs that promote conduction block or exacerbate arrhythmias. Such a view of how drugs affect the collective activity of cardiac cells should help in these situations in which the cure proves more deadly than the disease. A long-sought, and thus far elusive, goal has been to develop drugs to manage diseases of excitability. One such disease that affects millions each year is cardiac arrhythmia, which occurs when electrical impulses in the heart become disordered, sometimes causing sudden death. Pharmacological management of cardiac arrhythmia has failed because it is not possible to predict how drugs that target cardiac ion channels, and have intrinsically complex dynamic interactions with ion channels, will alter the emergent electrical behavior generated in the heart. Here, we applied a computational model, which was informed and validated by experimental data, that defined key measurable parameters necessary to simulate the interaction kinetics of the anti-arrhythmic drugs flecainide and lidocaine with cardiac sodium channels. We then used the model to predict the effects of these drugs on normal human ventricular cellular and tissue electrical activity in the setting of a common arrhythmia trigger, spontaneous ventricular ectopy. The model forecasts the clinically relevant concentrations at which flecainide and lidocaine exacerbate, rather than ameliorate, arrhythmia. Experiments in rabbit hearts and simulations in human ventricles based on magnetic resonance images validated the model predictions. This computational framework initiates the first steps toward development of a virtual drug-screening system that models drug-channel interactions and predicts the effects of drugs on emergent electrical activity in the heart.

Mechanism Underlying Initiation of Paroxysmal Atrial Flutter/Atrial Fibrillation by Ectopic Foci A Simulation Study

Background— The mechanisms underlying paroxysmal atrial flutter/atrial fibrillation initiation by ectopic foci from various locations are unclear. Methods and Results— We used parallel computational techniques to study an anatomically accurate 3-dimensional atrial structure incorporating a detailed ionic-current model of an atrial myocyte. At the single-cell level, upregulation of the L-type Ca2+ current ICa,L steepened restitution curves of action potential duration and conduction velocity compared with the control. Spontaneous firings of ectopic foci, coupled with sinus activity, produced dynamic spatial dispersions of repolarization, including discordant alternans, which caused conduction block and reentry only for the elevated ICa,L case. For each foci location, a vulnerable window for atrial flutter/atrial fibrillation induction was identified as a function of the coupling interval and focus cycle length. For ectopic foci in the pulmonary veins and left atrium, the site of conduction block and reentry gradually shifted, as a function of coupling interval, from the right atrium to the interatrial area and finally to the left atrium. The size of the vulnerable window was largest for pulmonary vein foci, becoming markedly smaller for right atrial foci, especially those near the sinoatrial node. Conclusions— These findings suggest that a mechanism of dynamically induced repolarization dispersion, especially discordant alternans, underlies the induction of atrial flutter/atrial fibrillation by atrial ectopic foci. The sites and likelihood of reentry induction varied according to ectopic focus location and timing, with the largest vulnerable window corresponding to the pulmonary vein region.

Targeted deletion of kcne2 impairs ventricular repolarization via disruption of IK,slow1 and Ito,f

Mutations in human KCNE2, which encodes the MiRP1 potassium channel ancillary subunit, associate with long QT syndrome (LQTS), a defect in ventricular repolarization. The precise cardiac role of MiRP1 remains controversial, in part, because it has marked functional promiscuity in vitro. Here, we disrupted the murine kcne2 gene to define the role of MiRP1 in murine ventricles. kcne2 disruption prolonged ventricular action potential duration (APD), suggestive of reduced repolarization capacity. Accordingly, kcne2 (−/−) ventricles exhibited a 50% reduction in IK,slow1, generated by Kv1.5—a previously unknown partner for MiRP1. Ito,f, generated by Kv4 α subunits, was also diminished, by ~25%. Ventricular MiRP1 protein coimmunoprecipitated with native Kv1.5 and Kv4.2 but not Kv1.4 or Kv4.3. Unexpectedly, kcne2 (−/−) ventricular membrane fractions exhibited 50% less mature Kv1.5 protein than wild type, and disruption of Kv1.5 trafficking to the intercalated discs. Consistent with the reduction in ventricular K+ currents and prolonged ventricular APD, kcne2 deletion lengthened the QTc under sevoflurane anesthesia. Thus, targeted disruption of kcne2 has revealed a novel cardiac partner for MiRP1, a novel role for MiRPs in α subunit targeting in vivo, and a role for MiRP1 in murine ventricular repolarization with parallels to that proposed for the human heart.—Roepke, T. K., Kontogeorgis, A., Ovanez, C., Xu, X., Young, J. B., Purtell, K., Goldstein, P. A., Christini, D. J., Peters, N. S., Akar, F. G., Gutstein, D. E., Lerner, D. J., Abbott, G. W. Targeted deletion of kcne2 impairs ventricular repolarization via disruption of IK,slow1 and Ito,f. FASEB J. 22, 3648–3660 (2008)

Nonlinear-dynamical arrhythmia control in humans

Nonlinear-dynamical control techniques, also known as chaos control, have been used with great success to control a wide range of physical systems. Such techniques have been used to control the behavior of in vitro excitable biological tissue, suggesting their potential for clinical utility. However, the feasibility of using such techniques to control physiological processes has not been demonstrated in humans. Here we show that nonlinear-dynamical control can modulate human cardiac electrophysiological dynamics by rapidly stabilizing an unstable target rhythm. Specifically, in 52/54 control attempts in five patients, we successfully terminated pacing-induced period-2 atrioventricular-nodal conduction alternans by stabilizing the underlying unstable steady-state conduction. This proof-of-concept demonstration shows that nonlinear-dynamical control techniques are clinically feasible and provides a foundation for developing such techniques for more complex forms of clinical arrhythmia.

Exploiting mathematical models to illuminate electrophysiological variability between individuals

Abstract  Across individuals within a population, several levels of variability are observed, from the differential expression of ion channels at the molecular level, to the various action potential morphologies observed at the cellular level, to divergent responses to drugs at the organismal level. However, the limited ability of experiments to probe complex interactions between components has hitherto hindered our understanding of the factors that cause a range of behaviours within a population. Variability is a challenging issue that is encountered in all physiological disciplines, but recent work suggests that novel methods for analysing mathematical models can assist in illuminating its causes. In this review, we discuss mathematical modelling studies in cardiac electrophysiology and neuroscience that have enhanced our understanding of variability in a number of key areas. Specifically, we discuss parameter sensitivity analysis techniques that may be applied to generate quantitative predictions based on considering behaviours within a population of models, thereby providing novel insight into variability. Our discussion focuses on four issues that have benefited from the utilization of these methods: (1) the comparison of different electrophysiological models of cardiac myocytes, (2) the determination of the individual contributions of different molecular changes in complex disease phenotypes, (3) the identification of the factors responsible for the variable response to drugs, and (4) the constraining of free parameters in electrophysiological models of heart cells. Together, the studies that we discuss suggest that rigorous analyses of mathematical models can generate quantitative predictions regarding how molecular‐level variations contribute to functional differences between experimental samples. These strategies may be applicable not just in cardiac electrophysiology, but in a wide range of disciplines.

Effects of electrical and structural remodeling on atrial fibrillation maintenance: A simulation study

Atrial fibrillation, a common cardiac arrhythmia, often progresses unfavourably: in patients with long-term atrial fibrillation, fibrillatory episodes are typically of increased duration and frequency of occurrence relative to healthy controls. This is due to electrical, structural, and contractile remodeling processes. We investigated mechanisms of how electrical and structural remodeling contribute to perpetuation of simulated atrial fibrillation, using a mathematical model of the human atrial action potential incorporated into an anatomically realistic three-dimensional structural model of the human atria. Electrical and structural remodeling both shortened the atrial wavelength - electrical remodeling primarily through a decrease in action potential duration, while structural remodeling primarily slowed conduction. The decrease in wavelength correlates with an increase in the average duration of atrial fibrillation/flutter episodes. The dependence of reentry duration on wavelength was the same for electrical vs. structural remodeling. However, the dynamics during atrial reentry varied between electrical, structural, and combined electrical and structural remodeling in several ways, including: (i) with structural remodeling there were more occurrences of fragmented wavefronts and hence more filaments than during electrical remodeling; (ii) dominant waves anchored around different anatomical obstacles in electrical vs. structural remodeling; (iii) dominant waves were often not anchored in combined electrical and structural remodeling. We conclude that, in simulated atrial fibrillation, the wavelength dependence of reentry duration is similar for electrical and structural remodeling, despite major differences in overall dynamics, including maximal number of filaments, wave fragmentation, restitution properties, and whether dominant waves are anchored to anatomical obstacles or spiralling freely.

Application of linear and nonlinear time series modeling to heart rate dynamics analysis

The linear autoregressive (AR) model is often used to investigate the pathophysiologic mechanisms controlling heart rate (HR) dynamics. This study implemented parametric models new to this field to determine if a more appropriate HR dynamics modeling structure exists. The linear AR and autoregressive-moving average (ARMA) models, and the nonlinear polynomial autoregressive (PAR) and bilinear (BL) models were fit to instantaneous HR time series obtained from nine subjects in the supine position. Model orders were determined by the Akaike Information Criteria (AIC). Model residual variance was used as the primary intermodel comparison criterion, with significance evaluated by a /spl lambda//sup 2/ distributed statistic. The BL model best represented the HR dynamics, as its residual variance was significantly (p<0.05) smaller than that of the corresponding AR model for nine out of nine data sets. In all cases, the BL model had a smaller residual variance than either the ARMA or PAR models. The bilinear model was ineffective at data forecasting, however, the authors show that this cannot reflect BL model validity because poor prediction is inherent to the BL model structure. The apparent superiority of the nonlinear bilinear model suggests that future heart rate dynamics studies should put greater emphasis on nonlinear analyses.<<ETX>>

Introduction: Mapping and control of complex cardiac arrhythmias.

This paper serves as an introduction to the Focus Issue on mapping and control of complex cardiac arrhythmias. We first introduce basic concepts of cardiac electrophysiology and describe the main clinical methods being used to treat arrhythmia. We then provide a brief summary of the main themes contained in the articles in this Focus Issue. In recent years there have been important advances in the ability to map the spread of excitation in intact hearts and in laboratory settings. This work has been combined with simulations that use increasingly realistic geometry and physiology. Waves of excitation and contraction in the heart do not always propagate with constant velocity but are often subject to instabilities that may lead to fluctuations in velocity and cycle time. Such instabilities are often treated best in the context of simple one- or two-dimensional geometries. An understanding of the mechanisms of propagation and wave stability is leading to the implementation of different stimulation protocols in an effort to modify or eliminate abnormal rhythms. (c) 2002 American Institute of Physics.

Dynamical Mechanism for Subcellular Alternans in Cardiac Myocytes

Rationale: Cardiac repolarization alternans is an arrhythmogenic rhythm disturbance, manifested in individual myocytes as a beat-to-beat alternation of action potential durations and intracellular calcium transient magnitudes. Recent experimental studies have reported “subcellular alternans,” in which distinct regions of an individual cell are seen to have counterphase calcium alternations, but the mechanism by which this occurs is not well understood. Although previous theoretical work has proposed a possible dynamical mechanism for subcellular alternans formation, no direct evidence for this mechanism has been reported in vitro. Rather, experimental studies have generally invoked fixed subcellular heterogeneities in calcium-cycling characteristics as the mechanism of subcellular alternans formation. Objective: In this study, we have generalized the previously proposed dynamical mechanism to predict a simple pacing algorithm by which subcellular alternans can be induced in isolated cardiac myocytes in the presence or absence of fixed subcellular heterogeneity. We aimed to verify this hypothesis using computational modeling and to confirm it experimentally in isolated cardiac myocytes. Furthermore, we hypothesized that this dynamical mechanism may account for previous reports of subcellular alternans seen in statically paced, intact tissue. Methods and Results: Using a physiologically realistic computational model of a cardiac myocyte, we show that our predicted pacing algorithm induces subcellular alternans in a manner consistent with theoretical predictions. We then use a combination of real-time electrophysiology and fluorescent calcium imaging to implement this protocol experimentally and show that it robustly induces subcellular alternans in isolated guinea pig ventricular myocytes. Finally, we use computational modeling to demonstrate that subcellular alternans can indeed be dynamically induced during static pacing of 1D fibers of myocytes during tissue-level spatially discordant alternans. Conclusion: Here we provide the first direct experimental evidence that subcellular alternans can be dynamically induced in cardiac myocytes. This proposed mechanism may contribute to subcellular alternans formation in the intact heart.