Mechanisms linking electrical alternans and clinical ventricular arrhythmia in human heart failure.

BACKGROUND: Mechanisms of ventricular tachycardia (VT) and ventricular fibrillation (VF) in patients with heart failure (HF) are undefined. OBJECTIVE: The purpose of this study was to elucidate VT/VF mechanisms in HF by using a computational-clinical approach. METHODS: In 53 patients with HF and 18 control patients, we established the relationship between low-amplitude action potential voltage alternans (APV-ALT) during ventricular pacing at near-resting heart rates and VT/VF on long-term follow-up. Mechanisms underlying the transition of APV-ALT to VT/VF, which cannot be ascertained in patients, were dissected with multiscale human ventricular models based on human electrophysiological and magnetic resonance imaging data (control and HF). RESULTS: For patients with APV-ALT k-score >1.7, complex action potential duration (APD) oscillations (≥2.3% of mean APD), rather than APD alternans, most accurately predicted VT/VF during long-term follow-up (+82%; -90% predictive values). In the failing human ventricular models, abnormal sarcoplasmic reticulum (SR) calcium handling caused APV-ALT (>1 mV) during pacing with a cycle length of 550 ms, which transitioned into large magnitude (>100 ms) discordant repolarization time alternans (RT-ALT) at faster rates. This initiated VT/VF (cycle length <400 ms) by steepening apicobasal repolarization (189 ms/mm) until unidirectional conduction block and reentry. Complex APD oscillations resulted from nonstationary discordant RT-ALT. Restoring SR calcium to control levels was antiarrhythmic by terminating electrical alternans. CONCLUSION: APV-ALT and complex APD oscillations at near-resting heart rates in patients with HF are linked to arrhythmogenic discordant RT-ALT. This may enable novel physiologically tailored, bioengineered indices to improve VT/VF risk stratification, where SR calcium handling and spatial apicobasal repolarization are potential therapeutic targets.

Accelerating cardiac bidomain simulations using graphics processing units.

Anatomically realistic and biophysically detailed multiscale computer models of the heart are playing an increasingly important role in advancing our understanding of integrated cardiac function in health and disease. Such detailed simulations, however, are computationally vastly demanding, which is a limiting factor for a wider adoption of in-silico modeling. While current trends in high-performance computing (HPC) hardware promise to alleviate this problem, exploiting the potential of such architectures remains challenging since strongly scalable algorithms are necessitated to reduce execution times. Alternatively, acceleration technologies such as graphics processing units (GPUs) are being considered. While the potential of GPUs has been demonstrated in various applications, benefits in the context of bidomain simulations where large sparse linear systems have to be solved in parallel with advanced numerical techniques are less clear. In this study, the feasibility of multi-GPU bidomain simulations is demonstrated by running strong scalability benchmarks using a state-of-the-art model of rabbit ventricles. The model is spatially discretized using the finite element methods (FEM) on fully unstructured grids. The GPU code is directly derived from a large pre-existing code, the Cardiac Arrhythmia Research Package (CARP), with very minor perturbation of the code base. Overall, bidomain simulations were sped up by a factor of 11.8 to 16.3 in benchmarks running on 6-20 GPUs compared to the same number of CPU cores. To match the fastest GPU simulation which engaged 20 GPUs, 476 CPU cores were required on a national supercomputing facility.

Solvers for the cardiac bidomain equations.

The bidomain equations are widely used for the simulation of electrical activity in cardiac tissue. They are especially important for accurately modeling extracellular stimulation, as evidenced by their prediction of virtual electrode polarization before experimental verification. However, solution of the equations is computationally expensive due to the fine spatial and temporal discretization needed. This limits the size and duration of the problem which can be modeled. Regardless of the specific form into which they are cast, the computational bottleneck becomes the repeated solution of a large, linear system. The purpose of this review is to give an overview of the equations and the methods by which they have been solved. Of particular note are recent developments in multigrid methods, which have proven to be the most efficient.

Excitation of a cardiac muscle fiber by extracellularly applied sinusoidal current.

INTRODUCTION: The goal of this study was to examine the effect of AC currents on a cardiac fiber. The study is the second in a series of two articles devoted to the subject. The initial study demonstrated that low-strength sinusoidal currents can cause hemodynamic collapse without inducing ventricular fibrillation. The present modeling study examines possible electrophysiologic mechanisms leading to such hemodynamic collapse. METHODS AND RESULTS: A strand of cardiac myocytes was subjected to an extracellular sinusoidal current stimulus. The stimulus was located 100 microm over one end. Membrane dynamics were described by the Luo-Rudy dynamic model. Examination of the interspike intervals (ISI) revealed that they were dependent on the phase of the stimulus and, as a result, tended to take on discrete values. The frequency dependency of the current threshold to induce an action potential in the cable had a minimum, as has been found experimentally. When a sinus beat was added to the cable, the sinus beat dominated at low-stimulus currents, whereas at high currents the time between action potentials corresponded to the rate observed in a cable without the sinus beat. In between there was a transition region with a wide dispersion of ISIs. CONCLUSION: The following phenomena observed in the initial study were reproduced and explained by the present simulation study: insignificant effect of temporal summation of subthreshold stimuli, frequency dependency of the extrasystole threshold, discrete nature of the ISI, and increase in regularity of the ISI with increasing stimulus strength.

Reentry in a morphologically realistic atrial model.

INTRODUCTION: Atrial fibrillation is the most common cardiac arrhythmia. In ablation procedures, identification of the reentrant pathways is vital. This has proven difficult because of the complex morphology of the atria. The purpose of this study was to ascertain the role of specific anatomic structures on reentry induction and maintenance. METHOD AND RESULTS: A computationally efficient, morphologically realistic, computer model of the atria was developed that incorporates its major structural features, including discrete electrical connections between the right and left atria, physiologic fiber orientation in three dimensions, muscle structures representing the crista terminalis (CT) and pectinate muscles, and openings for the veins and AV valves. Reentries were induced near the venous openings in the left and right atria, the mouth of the coronary sinus, and the free wall of the right atrium. The roles of certain muscular structures were ascertained by selectively removing the structures and observing how the propagation of activity was affected. CONCLUSION: (1) The muscular sheath of the coronary sinus acts as a pathway for a reentrant circuit and stabilizes any circuits that utilize the isthmus near the inferior vena cava. (2) Poor trans-CT coupling serves to stabilize flutter circuits. (3) Wall thickness is an important factor in the propagation of electrical activity, especially in the left atrium. (4) The openings of the inferior and superior venae cavae form natural anatomic anchors that make reentry easier to initiate by allowing for smaller ectopic beats to induce reentry.

Effect of fibre rotation on the initiation of re-entry in cardiac tissue.

Transmural rotation of cardiac fibres can have a big influence on the initiation of re-entry in the heart. However, owing to computational demands, this has not been fully explored in a three-dimensional model of cardiac tissue that has a microscopic description of membrane currents, such as the Luo-Rudy model. Using a previously described model that is computationally fast, re-entry in three-dimensional blocks of cardiac tissue is induced by a cross-shock protocol, and the activity is examined. In the study, the effect of the transmural fibre rotation is ascertained by examining differences between a tissue block with no rotation and ones with 1, 2 and 3 degrees of rotation per fibre layer. The direction of the re-entry is significant in establishing whether or not re-entry can be induced, with clockwise re-entry being easier to initiate. Owing to the rotating anisotropy that results in preferential propagation along the fibre axis, the timing of the second stimulus in the cross-shock protocol has to be changed for different rates of fibre rotation. The fibre rotation either increases or decreases the window of opportunity for re-entry, depending on whether the activation front is perpendicular or parallel to the fibre direction. By varying the transmural extent of the S2, it is found that a deeper stimulus has to be applied to the blocks with fibre rotation to create re-entry. Increasing the transmural resistance also tends to reduce the extent of the S2 required to induce re-entry. Results suggest that increasing fibre rotation reduces the susceptibility of the tissue to re-entry, but that more complex spatiotemporal patterns are possible, e.g. stable figure-of-eight re-entries and transient rotors. Three mechanisms of re-entry annihilation are identified: front catchup, filling of the excitable gap and core wander.

Intercellular coupling mediated by potassium accumulation in peg-and-socket junctions.

Coupling of smooth muscle cells is important for coordination of gastrointestinal motility. Small structures called peg-and-socket junctions (PSJs) have been found between muscle cells and may play a role in electrical coupling due to extracellular potassium accumulation in the narrow cleft between the muscle cells. A model was developed in which an electrical boundary element model of the cell morphology is used in conjunction with a finite difference model which described ionic fluxes and diffusion of extracellular potassium in the PSJ. The boundary element model used a combination of triangular and cylindrical elements to reduce computational demand while ensuring accuracy. Barrier kinetics were used to model the underlying ionic transport mechanisms. Seven ionic transport mechanisms were used to create the transmembrane voltage waveform. Results indicate that PSJs may produce significant coupling between smooth muscle cells under appropriate conditions. Coupling increased exponentially with increasing length and with decreasing intercellular gap.

Electrophysiological basis of mono-phasic action potential recordings.

Monophasic action potentials (MAPs) have been recorded for over a century, however, the exact mechanism responsible for their genesis has yet to be elucidated fully. The goal of the paper is to examine the physical basis of MAP recordings. MAP recordings are simulated by modelling a three-dimensional block of cardiac tissue. The effect of the MAP electrode is modelled by introducing a large, non-specific leakage conductance to the small region under the electrode. From the spread of the electrical activity, the equivalent extracellular current flow can be efficiently determined. These computed current sources are then input into a boundary element model of the tissue to determine the surface potentials. Finally, differences in surface potentials are used to compute waveforms that closely resemble MAP recordings. By varying model parameters, the mechanisms responsible for the MAP are determined, and a theory is put forward that can account for all observations. It is hypothesised that the leakage current causes the formation of a double-layer potential with a strength equal to the difference in transmembrane voltage between the regions under the electrode and those outside the electrode, leading to a recorded potential that mimics the transmembrane voltage outside the electrode region, although offset. Based on experimental MAP recordings, an equivalent leakage channel with a conductance of 0.1 mS cm-2 and a reversal potential of -43 mV is introduced by the electrode.

Computationally efficient model for simulating electrical activity in cardiac tissue with fiber rotation.

Transmural rotation of cardiac fibers may have a large influence on the initiation, stabilization, and termination of several life threatening cardiac arrhythmias. However, three-dimensional modeling of reentry in cardiac tissue is computationally demanding, as a tissue on the order of centimeters in size must be used to sustain reentry and several seconds must be simulated. Numerical accuracy requires time steps on the order of microseconds and spatial discretization on the order of microns. Consequently, the resultant numerical systems are extremely large. In this article, a computationally efficient model of a three-dimensional block of cardiac tissue with fiber rotation is presented. Computational speedup is achieved by using a discrete cable model which allowed for system order reduction, and also by using a scheme for tracking the activation wave front which identified regions requiring integration with a small time step. Simulating 1.2 s of activity of the approximately 2 x 10(6) cells constituting a block measuring 2.0 x 4.0 x 0.29 cm was performed in 26 h. Effects of model parameters on performance are discussed. The effect of fiber rotation on the spread of electrical activity after point source stimulation and a cross shock protocol is clearly demonstrated.

Role of cellular orientation in electrical coupling between gastrointestinal smooth muscle.

Electrical fields produced during depolarization as well as low resistance pathways through gap junctions have been proposed as electrical coupling mechanisms serving to coordinate electrical control activity in gastrointestinal smooth muscle. The differing orientations of the longitudinal and circular muscle layers offer many possible configurations for cells coupled by electrical fields. The boundary element method is used to investigate coupling, with respect to both gap junctions and field effects for ellipsoidal and cylindrical cells. Physiological considerations allow the possibility of aggregates of cells with coordinated electrical activity. The effect of multiple source cells on field coupling is also modeled. Results indicate that even small gap junctional conductances are effective for coupling of smooth muscle and that field coupling is most efficacious when the ellipsoidal cells are coupled side by side and when cylindrical cells are coupled end to end.

Mechanisms of electrical coupling between pyramidal cells.

Direct electrical coupling between neurons can be the result of both electrotonic current transfer through gap junctions and extracellular fields. Intracellular recordings from CA1 pyramidal neurons of rat hippocampal slices showed two different types of small-amplitude coupling potentials: short-duration (5 ms) biphasic spikelets, which resembled differentiated action potentials and long-duration (>20 ms) monophasic potentials. A three-dimensional morphological model of a pyramidal cell was employed to determine the extracellular field produced by a neuron and its effect on a nearby neuron resulting from both gap junctional and electric field coupling. Computations were performed with a novel formulation of the boundary element method that employs triangular elements to discretize the soma and cylindrical elements to discretize the dendrites. An analytic formula was derived to aid in computations involving cylindrical elements. Simulation results were compared with biological recordings of intracellular potentials and spikelets. Field effects produced waveforms resembling spikelets although of smaller magnitude than those recorded in vitro. Gap junctional electrotonic connections produced waveforms resembling small-amplitude excitatory postsynaptic potentials. Intracellular electrode measurements were found inadequate for ascertaining membrane events because of externally applied electric fields. The transmembrane voltage induced by the electric field was highly spatially dependent in polarity and wave shape, as well as being an order of magnitude larger than activity measured at the electrode. Membrane voltages because of electrotonic current injection across gap junctions were essentially constant over the cell and were accurately depicted by the electrode. The effects of several parameters were investigated: 1) decreasing the ratio of intra to extracellular conductivity reduced the field effects; 2) the tree structure had a major impact on the intracellular potential; 3) placing the gap junction in the dendrites introduced a time delay in the gap junctional mediated electrotonic potential, as well as deceasing the potential recorded by the somatic electrode; and 4) field effects decayed to one-half of their maximum strength at a cell separation of approximately 20 micron. Results indicate that the in vitro measured spikelets are unlikely to be mediated by gap junctions and that a spikelet produced by the electric field of a single source cell has the same waveshape as the measured spikelet but with a much smaller amplitude. It is hypothesized that spikelets are a manifestation of the simultaneous electric field effects from several local cells whose action potential firing is synchronized.

Efficient and accurate computation of the electric fields of excitable cells.

The numerical computation of the electric fields produced by excitable cells is important in many applications. Traditionally, a potential formulation was used. An integral formulation based on the differentiation of Green's theorem, which solves directly for the electric field, is presented herein. This is desirable because the electric field is proportional to current density, which can be calculated on the cell membrane. Fredholm equations of the second kind are produced, which are more appropriate than are those of the first kind (produced by formulations based on potential). Analytic formulae are presented to calculate the required matrix entries for zeroth order triangular elements that are generally used for field computations in boundary element methods. Results indicated that significantly more accurate answers may be obtained with significantly less computation by formulating the problem directly in terms of electric field as opposed to potential. This approach has the additional advantage that, for equal intracellular and extracellular conductivities, only one matrix must be generated, and no system of simultaneous equations must be solved; this drastically reduces storage and computation requirements. Examples are given to illustrate this technique and to compare the electric field formulation with the potential formulation.

The effect of morphological interdigitation on field coupling between smooth muscle cells.

The electrical control activity (ECA) in the distal stomach, small intestine, and colon has been modeled by populations of coupled nonlinear oscillators. Coupling has traditionally been explained through gap junctions, but gap junctions alone are inadequate, as they are not always present or cannot account for the observed behavior. Coupling through extracellular electric fields has been proposed as another coupling path which may work instead of, or in conjunction with, gap junctions. A morphological structure, the interdigitation, is studied for its effect on fields produced by a spherical cell. Using boundary element methods, the potential produced by a cell and the transmembrane potential induced in an adjacent cell are considered. Computer simulation results indicate that the presence of an interdigitation between two neighboring cells produces a 60% increase in extracellular potential and a 50% increase in induced transmembrane voltage. The interdigitation length is the most important factor, with radius playing a very small part in determining peak values of potential and voltage. These interdigitation fields may be of appreciable magnitude with regard to coupling. Also, the upstroke phase of the ECA can play a major role in intercellular communication.

Effects of the propagation velocity of a surface depolarization wave on the extracellular potential of an excitable cell.

Extracellular electric fields have been proposed as a mechanism for electrical coupling between excitable cells. This study deals with the extracellular potential produced by an isolated excitable spherical cell due to a traveling depolarization wave on the cell's surface. Both uniform and nonuniform propagation velocity profiles are considered. Using boundary element methods, the extracellular potential was computed. The polarity of the extracellular potential was found to be space-dependent. The peak extracellular potential increased when a) the propagation velocity decreased, b) the rise time of the depolarization decreased, and c) the extracellular resistivity increased.