The Role of the Hyperpolarization-Activated Inward Current$I_rm f$in Arrhythmogenesis: A Computer Model Study

Atrial fibrillation is the most common cardiac arrhythmia. Structural cardiac defects such as fibrosis and gap junction remodeling lead to a reduced cellular electrical coupling and are known to promote atrial fibrillation. It has been observed that the expression of the hyperpolarization-activated current$I_ f$is increased under pathological conditions. Recent experimental data indicate a possible contribution of$I_ f$to arrhythmogenesis. In this paper, the role of$I_ f$in action potential propagation in normal and in pathological tissue is investigated by means of computer simulations. The effect of diffuse fibrosis and gap junction remodeling is simulated by reducing cellular coupling nonuniformly. As expected, the conduction velocity decreases when cellular coupling is reduced. In the presence of$I_ f$the conduction velocity increases both in normal and in pathological tissue. In our simulations, ectopic activity is present in regions with high expression of$I_ f$and is facilitated by cellular uncoupling. We conclude that an increased$I_ f$may facilitate propagation of the action potential. Hence,$I_ f$may prevent conduction slowing and block. Overexpression of$I_ f$may lead to ectopic activity, especially when cellular coupling is reduced under pathological conditions.     

Modulation of spiral-wave dynamics and spontaneous activity in a fibroblast/myocyte heterocellular tissue--a computational study

Fibroblasts make for the most common nonmyocyte cells in the human heart and are known to play a role in structural remodeling caused by aging and various pathological states, which can eventually lead to cardiac arrhythmias and fibrillation. Gap junction formed between fibroblasts and myocytes have been recently described and were shown to alter the cardiac electrical parameters, such as action potential duration and conduction velocity, in various manners. In this study, we employed computational modeling to examine the effects of fibroblast-myocyte coupling and ratio on automaticity and electrical wave conduction during reentrant activity, with specific emphasis on dynamic phenomena and stability. Our results show that fibroblast density and coupling impact wave frequency in a biphasic way, first increasing wave frequency and then decreasing it. This can be explained by the dual role of the fibroblast cell as a current sink or a current source, depending on the coupled myocytes intracellular potential. We have also demonstrated that wave stability as manifested by the spiral-wave tip velocity and reentrant activity lifespan depends on fibroblast-myocyte coupling and ratio in a complex way. Finally, our study describes the required conditions in which spontaneous activity can occur, as a result of the fibroblasts depolarizing the myocytes' resting potential sufficiently to induce rhythmic pulses without any stimulation applied.     

Electrical coupling and impulse propagation in anatomically modeledventricular tissue

Computer simulations were used to study the role of resistive couplings on flat-wave action potential propagation through a thin sheet of ventricular tissue. Unlike simulations using continuous or periodic structures, this unique electrical model includes random size cells with random spaced longitudinal and lateral connections to simulate the physiologic structure of the tissue. The resolution of the electrical model is ten microns, thus providing a simulated view at the subcellular level. Flat-wave longitudinal propagation was evaluated with an electrical circuit of over 140,000 circuit elements, modeling a 0.25 mm by 5.0 mm sheet of tissue. An electrical circuit of over 84,000 circuit elements, modeling a 0.5 mm by 1.5 mm sheet was used to study flat-wave transverse propagation. Under normal cellular coupling conditions, at the macrostructure level, electrical conduction through the simulated sheets appeared continuous and directional differences in conduction velocity, action potential amplitude and V˙_max were observed. However, at the subcellular level (10 μm) unequal action potential delays were measured at the longitudinal and lateral gap junctions and irregular wave-shapes were observed in the propagating signal. Furthermore, when the modeled tissue was homogeneously uncoupled at the gap junctions conduction velocities decreased as the action potential delay between modeled cells increased. The variability in the measured action potential was most significant in areas with fewer lateral gap junctions, i.e., lateral gap junctions between fibers were separated by a distance of 100 μm or more     

Propagation of depolarization and repolarization processes in themyocardium-an anisotropic model

A three-dimensional finite-elements model of the left and right ventricles has been developed to study the process of myocardial electrical activation. The experimentally measured velocity is known to depend on membrane processes, the cellular shape, fiber orientation, and the interaction with neighboring cells. The simulated process is, therefore, governed by the geometry and by the directional conduction velocity at each point in the myocardial volume. The geometry of the ventricles is described by ellipsoidal shape, and divided to layers and sections, each filled with "cells" of preassigned properties. It allows for taking into account the local orientation of the myocardial fibers and their distributed velocities and refractory periods. The values are Gaussly distributed around the mean, and the mean and variance differ at each section. A conduction network of Purkinje "cells" is included on the endocardial surface. The anisotropic properties are demonstrated during simulation of an abnormal cardiac cycle, when propagating is initiated at an ectopic ventricular site. Ischemia is simulated by low conduction velocities in the ischemic zone and wide dispersion of values in nearby locations; automaticity is described by restimulating "cells" in the injured area; the dangerous effects of a premature beat leading to reentry are simulated by reduction of propagation velocity in "cells" that are reactivated while they repolarize. The different activation patterns are calculated throughout the myocardium and on its surface. The generated surface activation maps are not sensitive to minute changes in location of the foci of activation within the normal conduction system. The maps show sensitivity to pathological velocities, ischemic areas, and the existence of ectopic foci.(ABSTRACT TRUNCATED AT 250 WORDS)     

Effects of gap junction conductance on dynamics of sinoatrial nodecells: two-cell and large-scale network models

A computational model of single rabbit sinoatrial (SA) node cells has been revised to fit data on regional variation of rabbit SA node cell oscillation properties. The revised model simulates differences in oscillation frequency. Maximum diastolic potential, overshoot potential, and peak upstroke velocity observed in cells from different regions of the node. Dynamic properties of electrically coupled cells, each with different intrinsic oscillation frequency, are studied as a function of coupling conductance. Simulation results demonstrate at least four distinct regimes of behavior as coupling conductance is varied: (a) independent oscillation (G_c<1 pS); (b) complex oscillation (1⩽G_c<220 pS); (c) frequency, but not waveform entrainment (G_c⩾220 pS); and (d) frequency and waveform entrainment (G_c⩾50 nS). The conductance of single cardiac myocyte gap junction channels is about 50 pS. These simulations therefore show that very few gap junction channels between each cell are required for frequency entrainment. Analyses of large-scale SA node network models implemented on the Connection Machine CM-200 supercomputer indicate that frequency entrainment of large networks is also supported by a small number of gap junction channels between neighboring cells     

Action Potential Collision in Heart Tissue-Computer Simulations and Tissue Expenrments

The electrical effects of action potential collision were studied using a computer simulation of one-dimensional action potential propagation and tissue experiments from isolated cardiac Purkinje strands and papillary muscles. The effects of collision, when compared to normal one-way propagation, included quantitative changes in all of the measured indexes of action potential upstroke and repolarization. These changes can be attributed to spatiotemporal changes in the net membrane current. Parameter sensitivity and analytic techniques identified five factors which determine the collision-induced decrease in action potential area: conduction velocity, action potential height, cable radius, specific intracellular resistivity, and the specific membrane resistance during action potential repolarization. The simulations demonstrated that collision effects were independent of inhomogeneity in action potential duration, the spatial extent of the collision effects was greater than the passive space constant, and certain simulated abnormal conditions (e. g., discontinuous propagation, ischemic tissue) increased the magnitude of the collision effects. The tissue experiments supported the simulations regarding the changes in action potential configuration directly at and on each side of the collision site. Elevated [K+]0 increased the changes in action potential duration in both tissue preparations. In papillary muscles, collision effects in the transverse direction were confined to a narrower region than collision effects in the longitudinal direction with no difference in the peak magnitude of the changes. Action potential collision is a common occurrence in the heart.     

Estimation of conduction velocity vector fields from epicardialmapping data

An automated method to estimate vector fields of propagation velocity from observed epicardial extracellular potentials is introduced. The method relies on fitting polynomial surfaces T(x,y) to the space-time (x,y,t) coordinates of activity, Both speed and direction of propagation are computed from the gradient of the local polynomial surface. The components of velocity, which are total derivatives, are expressed in terms of the partial derivatives which comprise the gradient of T. The method was validated on two-dimensional (2-D) simulations of propagation and then applied to cardiac mapping data. Conduction velocity was estimated at multiple epicardial locations during sinus rhythm, pacing, and ventricular fibrillation (VF) in pigs. Data were obtained via a 528-channel mapping system from 23×22 and 24×21 arrays of unipolar electrodes sutured to the right ventricular epicardium. Velocity estimates are displayed as vector fields and are used to characterize propagation qualitatively and quantitatively during both simple and complex rhythms     

Comparative simulation of excitation and body surfaceelectrocardiogram with isotropic and anisotropic computer heart models

Comparative simulations between isotropic and anisotropic computer heart models were conducted to study the effects of myocardial anisotropy on the excitation process of the heart and on body surface electrocardiogram. The isotropic heart model includes atria, ventricles, and a special conduction system, and is electrophysiologically specified by parameters relative to action potential, conduction velocity, automaticity, and pacing. The anisotropic heart model was created by incorporating rotating fiber directions into the ventricles of the isotropic heart model. The orientation of the myocardial fibers in the ventricles of the model was gradually rotated counterclockwise from the epicardial layer to the endocardial layer for a total rotation of 90°. The anisotropy of conduction velocity and intracellular electric conductivity was included in the simulation. Comparative simulations of the normal heart, LBBB, and RBBB showed no significant differences between the two models in the excitation processes of the whole heart or in the body surface electrocardiograms. However, it was easier to induce ventricular fibrillation in the anisotropic model than in the isotropic model. The comparative simulation is useful for investigating the effects of myocardial anisotropy at the whole heart level and for evaluating limitations of the isotropic heart model     

A technique to track individual motor unit action potentials in surface EMG by monitoring their conduction velocities and amplitudes

The speed of propagation of an action potential along a muscle fiber, its conduction velocity (CV), can be used as an indication of the physiological or pathological state of the muscle fiber membrane. The motor unit action potential (MUAP), the waveform resulting from the spatial and temporal summation of the individual muscle fiber action potentials of that motor unit (MU), propagates with a speed referred to as the motor unit conduction velocity (MUCV). This paper introduces a new algorithm, the MU tracking algorithm, which estimates MUCVs and MUAP amplitudes for individual MUs in a localized MU population using SEMG signals. By tracking these values across time, the electrical activity of the localized MU pool can be monitored. An assessment of the performance of the algorithm has been achieved using simulated SEMG signals. It is concluded that this analysis technique enhances the suitability of SEMG for clinical applications and points toward a future of noninvasive diagnosis and assessment of neuromuscular disorders.     

Bidirectional Nerve Refractory Characteristics in Simulations of Direct and Remote Stimulation

The effects of remote stimulation on the refractory characteristics of myelinated nerve fibers were investigated using computer simulations of nerve action potentials, in response to spatially separated conditioning and test stimuli. The behavior of the test action potential was strongly influenced by its direction of propagation relative to that of the conditioning action potential. Under certain conditions, the variation of relative refractory period with conduction velocity (CV) changed from inverse, for propagation in opposing directions, to direct, for propagation in the same direction. A similar directionally dependent result occurred in the study of relative refractory period as a function of stimulus intensity. At certain interstimulus intervals, the test stimulus elicited action potentials which would conduct in the direction opposite to the conditioning action potential, but would not conduct in the wake of that conditioning action potential. These results are explained in terms of the spatial spread of stimulus current resulting from distant placement of the stimulating electrode in a volume conductor. Clinical repercussions of these results for correction of refractory period in collision neurography are discussed.     

Interaction of specialized cardiac conduction system with antiarrhythmic drugs: a simulation study

The use of antiarrhythmic drugs is common to treat heart rhythm disorders. Computational modeling and simulation are promising tools that could be used to investigate the effects of specific drugs on cardiac electrophysiology. In this paper, we study the multiscale effects of dofetilide, a drug that blocks IKr, from cellular to organ level paying special attention to its effect on heart structures, in particular the specialized cardiac conduction system (CCS). We include a model of the CCS in a patient-specific anatomical ventricular model and study the drug effects in simulations with and without a CCS. Results confirmed the expected effects of dofetilide at cellular level, increasing the action potential duration, and at organ level, prolonging the QT segment. Notable differences are shown between models with and without the CCS on action potential duration distributions. These techniques show the importance of heart heterogeneity and the global effects of the interaction of drugs with cardiac structures.     

A logical state model of reentrant ventricular activation

The ventricular surface of the heart was modeled as two-dimensional, 4096 element, network of cells connected logically to each other. An ischemic area was represented by a central core of prolonged refractoriness, distributed into eccentrically-layered elliptical contours such that refractoriness declined along varying gradients to the surrounding normal area. Propagation of cardiac action potentials was stimulated by five sequential states ranging from activation to inactivation. Reentrant activation was induced by premature stimulation of the network and resembled a "figure 8" type reentry seen experimentally. Activation patterns of reentry appeared as two propagation wavefronts which traveled around the ends of a continuous line of functional conduction block, merged into a single wavefront, then conducted slowly along a retrograde path to reactivate a region proximal to the block. Reentry could be prevented by modifying the distribution of recovery of excitability through stimulation at two strategically located sites during basic rhythm. Prevention occurred when the second site was situated in an area of prolonged refractoriness, just distal to the line of block. These simulations indicate that reentrant activation is characterized by the formation of long lines of conduction block which occur along a border of steeply graded refractoriness, and retrograde slow conduction which occurs along a more shallow refractory gradient. The occurrence of reentry is dependent on: 1) the coupling interval of the premature stimulus, 2) the location of the stimulus relative to the maximum refractory gradient, and 3) the activation sequence of the basic paced beats. Thus, this paper presents an efficient logical state model of cardiac activation which simulates experimentally observed activation patterns of reentry and its prevention.     

Influence of electrical coupling on early after depolarizations inventricular myocytes

Computer modeling is used to study the effect of electrical coupling between a myocardial zone where early after-depolarizations (EADs) can develop and the normal neighboring tissue. The effects of such coupling on EAD development and on the likelihood of EAD propagation as an ectopic beat are studied. The influence on EAD formation is investigated by approximating two partially coupled myocardial zones modeled as two active elements coupled by a junctional resistance R. For R values lower than 800 Ω cm², the action potentials are transmitted to the coupled element, and for R values higher than 850 Ω cm² they are blocked. In both ranges of R, when the electrical coupling increases, the EADs appear at more negative takeoff potentials with higher amplitudes and upstrokes. The EADs are not elicited if the electrical coupling is too high. In a separate model of two one-dimensional cardiac fiber segments partially coupled by a resistance R, critical R values exist, between 42 and 54 Ω cm² that facilitate EAD propagation. These results demonstrate that in myocardial zones favorable to the formation of EAD, the electrical coupling dramatically affects initiation of EAD and its spread to the neighboring tissue     

Simulation of QRST integral maps with a membrane-based computer heart model employing parallel processing

The simulation of the propagation of electrical activity in a membrane-based realistic-geometry computer model of the ventricles of the human heart, using the governing monodomain reaction-diffusion equation, is described. Each model point is represented by the phase 1 Luo-Rudy membrane model, modified to represent human action potentials. A separate longer duration action potential was used for the M cells found in the ventricular midwall. Cardiac fiber rotation across the ventricular wall was implemented via an analytic equation, resulting in a spatially varying anisotropic conductivity tensor and, consequently, anisotropic propagation. Since the model comprises approximately 12.5 million points, parallel processing on a multiprocessor computer was used to cut down on simulation time. The simulation of normal activation as well as that of ectopic beats is described. The hypothesis that in situ electrotonic coupling in the myocardium can diminish the gradients of action-potential duration across the ventricular wall was also verified in the model simulations. Finally, the sensitivity of QRST integral maps to local alterations in action-potential duration was investigated.     

Ultrasonically actuated silicon microprobes for cardiac signal recording

In this paper, we report on ultrasonically actuated silicon thin microprobes that successfully penetrated canine cardiac tissue in vitro, and recorded the electrophysiological signals from multiple sites simultaneously within the heart wall. The penetration force--maximum force encountered by the probe during penetration--is found to reduce with increasing ultrasonic driving voltage, on both excised canine right ventricular muscle and chicken breast muscle. The rate of force decrease varies with tissue type and microprobe dimension. With ultrasonic actuation, the silicon microprobes are inserted into isolated perfused canine heart without breakage or significant buckling, under 10Vpp actuating voltage. Recordings were obtained from isolated perfused canine heart during pacing, following the induction of ventricular tachycardia, and during the transition from ventricular tachycardia to ventricular fibrillation. Local conduction velocity of 0.60 +/- 0.03 m/s was observed from the multichannel recordings from the canine right ventricular wall under epicardial pacing. The application of the ultrasonic microprobes in cardiac electrophysiology study can provide information for reconstruction of electrical wave propagation within the heart, which is important to understanding the mechanisms of cardiac arrhythmias.     

Identification of cardiac rhythm features by mathematical analysis of vector fields

Automated techniques for locating cardiac arrhythmia features are limited, and cardiologists generally rely on isochronal maps to infer patterns in the cardiac activation sequence during an ablation procedure. Velocity vector mapping has been proposed as an alternative method to study cardiac activation in both clinical and research environments. In addition to the visual cues that vector maps can provide, vector fields can be analyzed using mathematical operators such as the divergence and curl. In the current study, conduction features were extracted from velocity vector fields computed from cardiac mapping data. The divergence was used to locate ectopic foci and wavefront collisions, and the curl to identify central obstacles in reentrant circuits. Both operators were applied to simulated rhythms created from a two-dimensional cellular automaton model, to measured data from an in situ experimental canine model, and to complex three-dimensional human cardiac mapping data sets. Analysis of simulated vector fields indicated that the divergence is useful in identifying ectopic foci, with a relatively small number of vectors and with errors of up to 30 degrees in the angle measurements. The curl was useful for identifying central obstacles in reentrant circuits, and the number of velocity vectors needed increased as the rhythm became more complex. The divergence was able to accurately identify canine in situ pacing sites, areas of breakthrough activation, and wavefront collisions. In data from human arrhythmias, the divergence reliably estimated origins of electrical activity and wavefront collisions, but the curl was less reliable at locating central obstacles in reentrant circuits, possibly due to the retrospective nature of data collection. The results indicate that the curl and divergence operators applied to velocity vector maps have the potential to add valuable information in cardiac mapping and can be used to supplement human pattern recognition.     

Computer modeling of ventricular rhythm during atrial fibrillation and ventricular pacing

We propose a unified atrial fibrillation (AF)-ventricular pacing (VP) (AF-VP) model to demonstrate the effects of VP on the ventricular rhythm during atrial fibrillation AF. In this model, the AV junction (AVJ) is treated as a lumped structure characterized by refractoriness and automaticity. Bombarded by random AF impulses, the AVJ can also be invaded by the VP-induced retrograde wave. The model includes bidirectional conduction delays in the AVJ and ventricle. Both refractory period and conduction delay of the AVJ are dependent upon its recovery time. The electrotonic modulation by blocked impulses is also considered in the model. Our simulations show that, with proper parameter settings, the present model can account for most principal statistical properties of the RR intervals during AF. We further demonstrate that the AV conduction property and the ventricular rate in AF depend on both AF rate and the degree of electrotonic modulation in the AVJ. Finally, we show that multilevel interactions between AF and VP can generate various patterns of ventricular rhythm that are consistent with previous experimental observations.     

Effect of variation in membrane excitability on propagation velocity of simulated action potentials for cardiac muscle and smooth muscle in the electric field model for cell-to-cell transmission of excitation

We have previously published several studies on the propagation of simulated action potentials (APs) of cardiac muscle and smooth muscle using the PSpice program. Those studies were done on single chains of five to ten cells in length to examine longitudinal propagation between the cells, either not connected by gap-junction (g.j) channels or connected by various numbers of channels. In addition, transverse propagation was examined between parallel chains (two to five chains) not connected by g.j. channels. In all those studies, the myocardial cells and smooth muscle cells (SMCs) were unintentionally somewhat hyperexcitable by virtue of the values inserted into the GTABLEs of the PSpice program. Because transmission of excitation from cell to cell occurred very well in the absence of g.j. channels, by virtue of the electric field (EF) generated in the narrow junctional clefts (negative cleft potential V/sub JC/), the present study was carried out, in which the cells were made hypo-excitable by altering the GTABLE values. Three levels of excitability of the cardiac cells and SMC were examined: 1) high; 2) intermediate; and 3) low. It was found that propagation of excitation, both longitudinally and transversely, can occur by the EF mechanism alone, even when the excitability of the cells was low. Therefore, the EF mechanism alone can account for propagation of excitation in cardiac muscles and smooth muscles that do not possess gap junctions. In those cases in which gap junctions do exist and are functioning, the EF mechanism would act in parallel and thereby increase the safety factor for conduction.     

Optimization of the latching pulse for dynamic flip-flop sensors

Analysis of dynamic IGFET flip-flop charge sensors shows that the optimum latching waveform is an initial voltage step followed by a ramp of gradually increasing slope. Latchup time is approximately inversely proportional to the initial voltage imbalance. Capacitive coupling between the two sides of the flip-flop generates a voltage excursion of the off-side even when there is no off-side conduction. With a 10-V latching ramp, the off-side is no off-side conduction. With a 10-V latching ramp, the off-side voltage excursion is typically about 2 V, and full latchup is attained in about 75 ns for an initial imbalance of 0.5 V. If a small off-side conduction is allowed, then latchup time can be reduced by a factor of two or more. The penalty is a few tenths of a volt added excursion of the off-side voltage. Computer circuit simulations were used to verify the analytic derivations.