Yoram Rudy

A dynamic model of the cardiac ventricular action potential. I. Simulations of ionic currents and concentration changes.

A mathematical model of the cardiac ventricular action potential is presented. In our previous work, the membrane Na+ current and K+ currents were formulated. The present article focuses on processes that regulate intracellular Ca2+ and depend on its concentration. The model presented here for the mammalian ventricular action potential is based mostly on the guinea pig ventricular cell. However, it provides the framework for modeling other types of ventricular cells with appropriate modifications made to account for species differences. The following processes are formulated: Ca2+ current through the L-type channel (ICa), the Na(+)-Ca2+ exchanger, Ca2+ release and uptake by the sarcoplasmic reticulum (SR), buffering of Ca2+ in the SR and in the myoplasm, a Ca2+ pump in the sarcolemma, the Na(+)-K+ pump, and a nonspecific Ca(2+)-activated membrane current. Activation of ICa is an order of magnitude faster than in previous models. Inactivation of ICa depends on both the membrane voltage and [Ca2+]i. SR is divided into two subcompartments, a network SR (NSR) and a junctional SR (JSR). Functionally, Ca2+ enters the NSR and translocates to the JSR following a monoexponential function. Release of Ca2+ occurs at JSR and can be triggered by two different mechanisms, Ca(2+)-induced Ca2+ release and spontaneous release. The model provides the basis for the study of arrhythmogenic activity of the single myocyte including afterdepolarizations and triggered activity. It can simulate cellular responses under different degrees of Ca2+ overload. Such simulations are presented in our accompanying article in this issue of Circulation Research.

Ionic Mechanisms of Propagation in Cardiac Tissue: Roles of the Sodium and L-type Calcium Currents During Reduced Excitability and Decreased Gap Junction Coupling

In cardiac tissue, reduced membrane excitability and reduced gap junction coupling both slow conduction velocity of the action potential. However, the ionic mechanisms of slow conduction for the two conditions are very different. We explored, using a multicellular theoretical fiber, the ionic mechanisms and functional role of the fast sodium current, INa, and the L-type calcium current, ICa(L), during conduction slowing for the two fiber conditions. A safety factor for conduction (SF) was formulated and computed for each condition. Reduced excitability caused a lower SF as conduction velocity decreased. In contrast, reduced gap junction coupling caused a paradoxical increase in SF as conduction velocity decreased. The opposite effect of the two conditions on SF was reflected in the minimum attainable conduction velocity before failure: decreased excitability could reduce velocity to only one third of control (from 54 to 17 cm/s) before failure occurred, whereas decreased coupling could reduce velocity to as low as 0.26 cm/s before block. Under normal conditions and conditions of reduced excitability, ICa(L) had a minimal effect on SF and on conduction. However, ICa(L) played a major role in sustaining conduction when intercellular coupling was reduced. This phenomenon demonstrates that structural, nonmembrane factors can cause a switch of intrinsic membrane processes that support conduction. High intracellular calcium concentration, [Ca]i, lowered propagation safety and caused earlier block when intercellular coupling was reduced. [Ca]i affected conduction via calcium-dependent inactivation of ICa(L). The increase of safety factor during reduced coupling suggests a major involvement of uncoupling in stable slow conduction in infarcted myocardium, making microreentry possible. Reliance on ICa(L) for this type of conduction suggests ICa(L) as a possible target for antiarrhythmic drug therapy.

Noninvasive electrocardiographic imaging for cardiac electrophysiology and arrhythmia

Over 7 million people worldwide die annually from erratic heart rhythms (cardiac arrhythmias), and many more are disabled. Yet there is no imaging modality to identify patients at risk, provide accurate diagnosis and guide therapy. Standard diagnostic techniques such as the electrocardiogram (ECG) provide only low-resolution projections of cardiac electrical activity on the body surface. Here we demonstrate the successful application in humans of a new imaging modality called electrocardiographic imaging (ECGI), which noninvasively images cardiac electrical activity in the heart. In ECGI, a multielectrode vest records 224 body-surface electrocardiograms; electrical potentials, electrograms and isochrones are then reconstructed on the hearts surface using geometrical information from computed tomography (CT) and a mathematical algorithm. We provide examples of ECGI application during atrial and ventricular activation and ventricular repolarization in (i) normal heart (ii) heart with a conduction disorder (right bundle branch block) (iii) focal activation initiated by right or left ventricular pacing, and (iv) atrial flutter.

Simulation of the Undiseased Human Cardiac Ventricular Action Potential: Model Formulation and Experimental Validation

Cellular electrophysiology experiments, important for understanding cardiac arrhythmia mechanisms, are usually performed with channels expressed in non myocytes, or with non-human myocytes. Differences between cell types and species affect results. Thus, an accurate model for the undiseased human ventricular action potential (AP) which reproduces a broad range of physiological behaviors is needed. Such a model requires extensive experimental data, but essential elements have been unavailable. Here, we develop a human ventricular AP model using new undiseased human ventricular data: Ca2+ versus voltage dependent inactivation of L-type Ca2+ current (ICaL); kinetics for the transient outward, rapid delayed rectifier (IKr), Na+/Ca2+ exchange (INaCa), and inward rectifier currents; AP recordings at all physiological cycle lengths; and rate dependence and restitution of AP duration (APD) with and without a variety of specific channel blockers. Simulated APs reproduced the experimental AP morphology, APD rate dependence, and restitution. Using undiseased human mRNA and protein data, models for different transmural cell types were developed. Experiments for rate dependence of Ca2+ (including peak and decay) and intracellular sodium ([Na+]i) in undiseased human myocytes were quantitatively reproduced by the model. Early afterdepolarizations were induced by IKr block during slow pacing, and AP and Ca2+ alternans appeared at rates >200 bpm, as observed in the nonfailing human ventricle. Ca2+/calmodulin-dependent protein kinase II (CaMK) modulated rate dependence of Ca2+ cycling. INaCa linked Ca2+ alternation to AP alternans. CaMK suppression or SERCA upregulation eliminated alternans. Steady state APD rate dependence was caused primarily by changes in [Na+]i, via its modulation of the electrogenic Na+/K+ ATPase current. At fast pacing rates, late Na+ current and ICaL were also contributors. APD shortening during restitution was primarily dependent on reduced late Na+ and ICaL currents due to inactivation at short diastolic intervals, with additional contribution from elevated IKr due to incomplete deactivation.

Action potential and contractility changes in [Na(+)](i) overloaded cardiac myocytes: a simulation study.

Sodium overload of cardiac cells can accompany various pathologies and induce fatal cardiac arrhythmias. We investigate effects of elevated intracellular sodium on the cardiac action potential (AP) and on intracellular calcium using the Luo-Rudy model of a mammalian ventricular myocyte. The results are: 1) During rapid pacing, AP duration (APD) shortens in two phases, a rapid phase without Na(+) accumulation and a slower phase that depends on [Na(+)](i). 2) The rapid APD shortening is due to incomplete deactivation (accumulation) of I(Ks). 3) The slow phase is due to increased repolarizing currents I(NaK) and reverse-mode I(NaCa), secondary to elevated [Na(+)](i). 4) Na(+)-overload slows the rate of AP depolarization, allowing time for greater I(Ca(L)) activation; it also enhances reverse-mode I(NaCa). The resulting increased Ca(2+) influx triggers a greater [Ca(2+)](i) transient. 5) Reverse-mode I(NaCa) alone can trigger Ca(2+) release in a voltage and [Na(+)](i)-dependent manner. 6) During I(NaK) block, Na(+) and Ca(2+) accumulate and APD shortens due to enhanced reverse-mode I(NaCa); contribution of I(K(Na)) to APD shortening is negligible. By slowing AP depolarization (hence velocity) and shortening APD, Na(+)-overload acts to enhance inducibility of reentrant arrhythmias. Shortened APD with elevated [Ca(2+)](i) (secondary to Na(+)-overload) also predisposes the myocardium to arrhythmogenic delayed afterdepolarizations.

Linking a genetic defect to its cellular phenotype in a cardiac arrhythmia

Advances in genetics and molecular biology have provided an extensive body of information on the structure and function of the elementary building blocks of living systems. Genetic defects in membrane ion channels can disrupt the delicate balance of dynamic interactions between the ion channels and the cellular environment, leading to altered cell function. As ion-channel defects are typically studied in isolated expression systems, away from the cellular environment where they function physiologically, a connection between molecular findings and the physiology and pathophysiology of the cell is rarely established. Here we describe a single-channel-based Markovian modelling approach that bridges this gap. We achieve this by determining the cellular arrhythmogenic consequences of a mutation in the cardiac sodium channel that can lead to a clinical arrhythmogenic disorder (the long-QT syndrome) and sudden cardiac death.

A dynamic model of the cardiac ventricular action potential. II. Afterdepolarizations, triggered activity, and potentiation.

The action potential model presented in our accompanying article in this journal is used to investigate phenomena that involve dynamic changes of [Ca2+]i, as described below. Delayed afterdepolarizations (DADs) are induced by spontaneous Ca2+ release from the sarcoplasmic reticulum (SR), which, in turn, activates both the Na(+)-Ca2+ exchanger (INaCa) and a nonspecific Ca(2+)-activated current (Ins(Ca)). The relative contributions of INaCa and of Ins(Ca) to the generation of DADs are different under different degrees of Ca2+ overload. Early afterdepolarizations (EADs) can be categorized into two types: (1) plateau EADs, resulting from a secondary activation of the L-type Ca2+ current during the plateau of an action potential, and (2) phase-3 EADs, resulting from activation of INaCa and Ins(Ca) by increased [Ca2+]i due to spontaneous Ca2+ release from the SR during the late repolarization phase. Spontaneous rhythmic activity and triggered activity are caused by spontaneous Ca2+ release from the SR under conditions of Ca2+ overload. Postextrasystolic potentiation reflects the time delay associated with translocation of Ca2+ from network SR to junctional SR. The cell is paced at high frequencies to investigate the long-term effects on the intracellular ionic concentrations.

Effects of IKr and IKs heterogeneity on action potential duration and its rate dependence : A simulation study

BACKGROUND A growing body of evidence suggests that heterogeneity of ion channel expression and electrophysiological characteristics is an important property of the ventricular myocardium. The 2 components of the delayed rectifier potassium current, IKr (rapid) and IKs (slow), play a dominant role in the repolarization of the action potential and are important determinants of its duration. METHODS AND RESULTS In this report, the effects of heterogeneities of IKr and IKs on action potential duration (APD) and its rate dependence (adaptation) are studied with the use of the LRd model of a mammalian ventricular cell. Results demonstrate the importance of IKs density variations in heterogeneity of repolarization. Cells with reduced IKs (eg, mid-myocardial M cells) display long APD and steep dependence of APD on rate. Mechanistically, accumulation of IKs activation and increased sodium calcium exchange current, INaCa, secondary to Na+ accumulation at a fast rate underlie the steep APD-rate relation of these cells. When cells are electrotonically coupled in a multicellular fiber through resistive gap junction, APD differences are reduced. The results demonstrate strong dependence of APD heterogeneity on the degree of intercellular coupling even in the normal physiological range. Highly reduced coupling maximizes APD heterogeneity. CONCLUSIONS Heterogeneity of IKs:IKr density strongly influences APD and its rate dependence. However, in the intact myocardium, the degree of gap-junction coupling may be an important factor that determines the manifestation of APD heterogeneity and dispersion of repolarization. The clinical significance of this study is in the context of repolarization abnormalities and associated arrhythmias (eg, long QT syndrome and torsade de pointes).

Genetic and molecular basis of cardiac arrhythmias: impact on clinical management parts I and II

Genetic approaches have succeeded in defining the molecular basis of an increasing array of heart diseases, such as hypertrophic cardiomyopathy and the long-QT syndromes, associated with serious arrhythmias. Importantly, the way in which this new knowledge can be applied to managing patients and to the development of syndrome-specific antiarrhythmic strategies is evolving rapidly because of these recent advances. In addition, the extent to which new knowledge represents a purely research tool versus the extent to which it can be applied clinically is also evolving. The present article represents a consensus report of a meeting of the European Working Group on Arrhythmias. The current state of the art of the molecular and genetic basis of inherited arrhythmias is first reviewed, followed by practical advice on the role of genetic testing in these and other syndromes and the way in which new findings have influenced current understanding of the molecular and biophysical basis of arrhythmogenesis.

Ionic Current Basis of Electrocardiographic Waveforms A Model Study

Body surface electrocardiograms and electrograms recorded from the surfaces of the heart are the basis for diagnosis and treatment of cardiac electrophysiological disorders and arrhythmias. Given recent advances in understanding the molecular mechanisms of arrhythmia, it is important to relate these electrocardiographic waveforms to cellular electrophysiological processes. This modeling study establishes the following principles: (1) voltage gradients created by heterogeneities of the slow-delayed rectifier (IKs) and transient outward (Ito) potassium current inscribe the T wave and J wave, respectively; T-wave polarity and width are strongly influenced by the degree of intercellular coupling through gap-junctions. (2) Changes in [K+]o modulate the T wave through their effect on the rapid-delayed rectifier, IKr. (3) Alterations of IKs, IKr, and INa (fast sodium current) in long-QT syndrome (LQT1, LQT2, and LQT3, respectively) are reflected in characteristic QT-interval and T-wave changes; LQT1 prolongs QT without widening the T wave. (4) Accelerated inactivation of INa on the background of large epicardial Ito results in ST elevation (Brugada phenotype) that reflects the degree of severity. (5) Activation of the ATP-sensitive potassium current, IK(ATP), is sufficient to cause ST elevation during acute ischemia. These principles provide a mechanistic cellular basis for interpretation of electrocardiographic waveforms.