Purkinje and ventricular contributions to endocardial activation sequence in perfused rabbit right ventricle.

Interactions between peripheral conduction system and myocardial wave fronts control the ventricular endocardial activation sequence. To assess those interactions during sinus and paced ventricular beats, we recorded unipolar electrograms from 528 electrodes spaced 0.5 mm apart and placed over most of the perfused rabbit right ventricular free wall endocardium. Left ventricular contributions to electrograms were eliminated by cryoablating that tissue. Electrograms were systematically processed to identify fast (P) deflections separated by >2 ms from slow (V) deflections to measure P-V latencies. By using this criterion during sinus mapping (n = 5), we found P deflections in 22% of electrograms. They preceded V deflections at 91% of sites. Peripheral conduction system wave fronts preceded myocardial wave fronts by an overall P-V latency magnitude that measured 6.7 +/- 3.9 ms. During endocardial pacing (n = 8) at 500 ms cycle length, P deflections were identified on 15% of electrodes and preceded V deflections at only 38% of sites, and wave fronts were separated by a P-V latency magnitude of 5.6 +/- 2.3 ms. The findings were independent of apical, basal, or septal drive site. Modest changes in P-V latency accompanied cycle length accommodation to 125-ms pacing (6.8 +/- 2.6 ms), although more pronounced separation between wave fronts followed premature stimulation (11.7 +/- 10.4 ms). These results suggested peripheral conduction system and myocardial wave fronts became functionally more dissociated after premature stimulation. Furthermore, our analysis of the first ectopic beats that followed 12 of 24 premature stimuli revealed comparable separation between wave fronts (10.7 +/- 5.5 ms), suggesting the dissociation observed during the premature cycles persisted during the initiating cycles of the resulting arrhythmias.

Transient outward current modulates discontinuous conduction in rabbit ventricular cell pairs.

OBJECTIVE: While several studies have demonstrated that the L-type calcium current maintains discontinuous conduction, the contribution of the transient outward current (I(to)) to conduction remains unclear. This study evaluated the effects of I(to) inhibition on conduction between ventricular myocytes. METHODS: An electronic circuit with a variable resistance (R(j)) was used to electrically couple single epicardial myocytes isolated from rabbit right ventricle. We inhibited I(to) with 4-aminopyridine superfusion, rate-acceleration, or premature stimulation to evaluate the subsequent effects on conduction delay and the critical R(j), which was quantified as the highest R(j) that could be imposed before conduction failed. RESULTS: I(to) inhibition significantly enhanced conduction in all cell pairs (n=23). Pharmacologic inhibition of I(to) resulted in a 32+/-5% decrease in conduction delay and a 36+/-7% increase in critical R(j). Similarly, reduction of the basic cycle length from 2 to 0.5 s resulted in a 31+/-3% decrease in conduction delay and a 31+/-3% increase in critical R(j). Finally, premature action potentials conducted with a 41+/-4% shorter conduction delay and a 73+/-24% higher critical R(j) than basic action potentials. CONCLUSIONS: I(to) inhibition significantly enhanced conduction across high R(j). These results suggest I(to) may contribute to rate-dependent conduction abnormalities.

Effects of electrode-myocardial separation on cardiac stimulation in conductive solution.

INTRODUCTION: Effects of a conductive bath and electrode-myocardial separation on cardiac stimulation have not been elucidated. These factors may play a role in endocardial catheter stimulation or defibrillation. METHODS AND RESULTS: We studied effects of a bath and separation on transmembrane voltage changes during stimulation (deltaVm) and excitation thresholds in rabbit hearts, cultured rat cardiac cell monolayers, and cardiac bidomain computer models. Similar to previous epicardial measurements with no bath, a dogbone pattern of deltaVm during stimulation was found in bathed epicardium and right ventricular septal endocardium and in models of bathed anisotropic myocardium. Electrode-myocardial separation altered spatial distributions of deltaVm, moved reversals of the sign of deltaVm farther from the stimulation epicenter, and decreased aspect ratio of deltaVm (i.e., length/width of dogbone contours of deltaVm). The separation increased thresholds and reduced maximal deltaVm, while deltaVm at sites away from maxima increased or decreased. Anodal thresholds in models initially were larger than those in experiments and decreased when models were altered to include nonuniform cellular coupling. Existence of nonuniformity in monolayers was indicated by irregular excitation patterns. CONCLUSION: Electrode-myocardial separation alters spatial distributions of deltaVm, which may impact on arrhythmia induction by altering distributions of states of deltaVm-sensitive ion channels. The results also indicate that excitation thresholds may depend on tissue nonuniformities.

Functional reentry's influence on intracellular calcium in the LRd membrane equations.

This paper examines relationships between transmembrane potential (Vm), [Ca2+]i dependent membrane ionic currents, and [Ca2+]i handling by the sarcoplasmic reticulum (SR) in a two-dimensional model of cardiac tissue. Luo-Rudy dynamic (LRd) membrane equations were used because they include detailed formulations for triggered SR Ca2+ release dependent on membrane Ca2+ influx (CICR) and for spontaneous SR Ca2+ release following calsequestrin buffer overload (SCR). Reentry's rapid rate (110-ms cycle length) elevated [Ca2+]i and limited CICR, which in turn promoted SCR that occurred at intervals of 320-350 ms, was preferential at sites located inside the functional center, and destabilized the reentrant activation sequence. Although adjustment of LRd parameters for SR Ca2+ modified SCR interval and peak [Ca2+]i in voltage clamp simulations with a command waveform representing Vm time course within the functional center, SCR persisted. Using the same command waveform, SCR also occurred with an alternate SR Ca2+ formulation that represented subcellular details underlying CICR. LRd parameter adjustments to promote CICR and limit SCR in subsequent reentry simulations failed to eliminate SCR completely, as they modulated SCR intervals in a manner consistent with the voltage clamp simulations. Taken together, our findings support a destabilizing influence of functional reentry on [Ca2+]i handling. However, [Ca2+]i instabilities did not always fractionate depolarization wavefronts during reentry. Fractionation depended, in part, upon CICR and SCR parameters in the LRd formulation for SR Ca2+ release.

Distributed computing for membrane-based modeling of action potential propagation.

Action potential propagation simulations with physiologic membrane currents and macroscopic tissue dimensions are computationally expensive. We, therefore, analyzed distributed computing schemes to reduce execution time in workstation clusters by parallelizing solutions with message passing. Four schemes were considered in two-dimensional monodomain simulations with the Beeler-Reuter membrane equations. Parallel speedups measured with each scheme were compared to theoretical speedups, recognizing the relationship between speedup and code portions that executed serially. A data decomposition scheme based on total ionic current provided the best performance. Analysis of communication latencies in that scheme led to a load-balancing algorithm in which measured speedups at 89 +/- 2% and 75 +/- 8% of theoretical speedups were achieved in homogeneous and heterogeneous clusters of workstations. Speedups in this scheme with the Luo-Rudy dynamic membrane equations exceeded 3.0 with eight distributed workstations. Cluster speedups were comparable to those measured during parallel execution on a shared memory machine.

Electrotonic suppression of early afterdepolarizations in isolated rabbit Purkinje myocytes.

Many studies suggest that early afterdepolarizations (EADs) arising from Purkinje fibers initiate triggered arrhythmias under pathological conditions. However, electrotonic interactions between Purkinje and ventricular myocytes may either facilitate or suppress EAD formation at the Purkinje-ventricular interface. To determine conditions that facilitated or suppressed EADs during Purkinje-ventricular interactions, we coupled single Purkinje myocytes and aggregates isolated from rabbit hearts to a passive model cell via an electronic circuit with junctional resistance (R(j)). The model cell had input resistance (R(m,v)) of 50 M Omega, capacitance of 39 pF, and a variable rest potential (V(rest,v)). EADs were induced in Purkinje myocytes during superfusion with 1 microM isoproterenol. Coupling at high R(j) to normally polarized V(rest,v) established a repolarizing coupling current during all phases of the Purkinje action potential. This coupling current preferentially suppressed EADs in single cells with mean membrane resistance (R(m,p)) of 297 M Omega, whereas EAD suppression in larger aggregates with mean R(m,p) of 80 M Omega required larger coupling currents. In contrast, coupling to elevated V(rest,v) established a depolarizing coupling current during late phase 2, phase 3, and phase 4 that facilitated EAD formation and induced spontaneous activity in single Purkinje myocytes and aggregates. These results have important implications for arrhythmogenesis in the infarcted heart when reduction of the ventricular mass due to scarring alters the R(m,p)-to-R(m,v) ratio and in the ischemic heart when injury currents are established during coupling between polarized Purkinje myocytes and depolarized ventricular myocytes.

Beat-to-beat repolarization variability in ventricular myocytes and its suppression by electrical coupling.

Single ventricular myocytes paced at a constant rate and held at a constant temperature exhibit beat-to-beat variations in action potential duration (APD). In this study we sought to quantify this variability, assess its mechanism, and determine its responsiveness to electrotonic interactions with another myocyte. Interbeat APD(90) (90% repolarization) of single cells was normally distributed. We thus quantified APD(90) variability as the coefficient of variability, CV = (SD/mean APD(90)) x 100. The mean +/- SD of the CV in normal solution was 2.3 +/- 0.9 (132 cells). Extracellular TTX (13 microM) and intracellular EGTA (14 mM) both significantly reduced the CV by 44 and 26%, respectively. When applied in combination the CV fell by 54%. In contrast, inhibition of the rapid delayed rectifier current with L-691,121 (100 nM) increased the CV by 300%. The CV was also significantly reduced by 35% when two normal myocytes were electrically connected with a junctional resistance (R(j)) of 100 MOmega. Electrical coupling (R(j) = 100 MOmega) of a normal myocyte to one producing early afterdepolarization (EAD) completely blocked EAD formation. These results indicate that beat-to-beat APD variability is likely mediated by stochastic behavior of ion channels and that electrotonic interactions act to limit temporal dispersion of refractoriness, a major contributor to arrhythmogenesis.

Optical transmembrane potential recordings during intracardiac defibrillation-strength shocks.

BACKGROUND: The prolongation of the action potential after defibrillation-strength shocks is believed to be a critical component of defibrillation. The response of the transmembrane potential to the shock may affect this prolongation. We studied the effects of an intracardiac shock on the transmembrane potential and action potential duration at multiple sites on the epicardium using a voltage-sensitive dye and optical mapping system. METHODS AND RESULTS: A laser scanner recorded optical action potentials with voltage-sensitive dye at 63 spots on both the left and right ventricles of six isolated, perfused rabbit hearts. Hearts were paced with epicardial point stimulation followed by the delivery of a 2 A and 20 ms rectangular waveform shock during the relative refractory period. The shock was given between right atrial and right ventricular electrodes. Of 621 total spots analyzed, 241 spots hyperpolarized and 76 spots depolarized with a right ventricular anode, whereas 159 spots hyperpolarized and 145 spots depolarized with a right ventricular cathode (P < 0.05). Both hyperpolarized and depolarized spots exhibited prolonged action potential duration, although prolongation was greater with depolarizing responses (16.7 +/- 9 ms vs. 13.3 +/- 13.4 ms, p<0.001). Hyperpolarized and depolarized spots were not randomly distributed, but clustered into regions. The size of the hyperpolarized regions was larger than the depolarized regions with RV anodal stimulation (27 +/- 20 spots/hyperpolarized region vs. 8.5 +/- 9 spots/depolarized region, p < 0.03) but not with RV cathodal stimulation. With reversal of electrode polarity, spots hyperpolarized near the shocking electrodes frequently did not reverse polarization but remained hyperpolarized. CONCLUSIONS: Distinct regions of either polarization occur during intracardiac defibrillation-strength shocks. Although hyperpolarizing membrane responses were observed more often than depolarizing responses, depolarizing membrane polarization resulted in greater action potential prolongation. The absence of sign change in polarization in some regions with shocks of opposite polarities suggests that nonlinear intrinsic membrane properties are operative during strong electrical stimulation.

Review of mechanisms by which electrical stimulation alters the transmembrane potential.

Electrical stimuli pace, cardiovert, or defibrillate the heart by changing transmembrane potential (deltaVm). Recent simulation studies provide insights into mechanisms by which stimuli establish deltaVm. This review attempts a nonmathematical description of these mechanisms. We start with the cable model in which the intracellular core conductor is bounded by a highly resistive and capacitive membrane that separates the intracellular and extracellular spaces. Intracellular and extracellular resistances are assumed to vary linearly with position. Although this model predicts anodal extracellular stimuli hyperpolarize adjacent tissue and cathodal extracellular stimuli depolarize that tissue, it fails to reproduce regions of opposite deltaVm distant from the electrodes. We then consider the sawtooth model in which microscopic discontinuities in intracellular resistance represent gap junctions. While model studies with such discontinuities demonstrate large deltaVm at cell ends, experimental validation of such deltaVm remains elusive. Extending the analysis to the two- and three-dimensional syncytium, we also consider the bidomain model in which intracellular, extracellular, and interstitial currents are explicitly characterized. Differences in resistance to these currents gives rise to virtual electrodes, which are experimentally observed regions of large deltaVm that arise distant from the stimulating electrode. Distant deltaVm regions are also evident when macroscopic discontinuities in intracellular resistance are introduced into the bidomain model. Such discontinuities are associated with clefts or scars that give rise to "secondary sources." Albeit the cable model offers remarkable insight the bidomain model and the concept of secondary sources provide a more complete understanding of membrane excitation, especially when combined into a unifying activating function.

Modulation of repolarization in rabbit Purkinje and ventricular myocytes coupled by a variable resistance.

Purkinje-ventricular junctions (PVJs) have been implicated as potential sites of arrhythmogenesis, in part because of the dispersion of action potential duration (APD) between Purkinje (P) and ventricular (V) myocytes. To characterize electrotonic modulation of APD as a function of junctional resistance (Rj), we coupled single isolated rabbit P and V myocytes with an electronic circuit. In seven of eight PV myocyte pairs, both APDs shortened on coupling at Rj = 50 MOmega. This was in contrast to modulation of APD in paired ventricular myocytes, which demonstrated APD shortening of the intrinsically longer action potential and APD prolongation of the intrinsically shorter action potential. Companion computer simulations, performed to suggest possible mechanisms for the paradoxical shortening of the V action potential in paired P and V myocytes, showed that the difference in intrinsic peak plateau potentials (Vpp) of the P and V myocytes determined whether the V action potential shortened or prolonged on coupling. This difference in Vpp caused a large, repolarizing coupling current to flow to the V myocyte, contributing to early inactivation of the L-type calcium current and early activation of the inward rectifier current. These results suggest that intrinsic differences in phase 1 repolarization could yield differing patterns of APD shortening or prolongation in the network of subendocardial PVJs, leaving some PVJs vulnerable to conduction of premature stimuli while other PVJs remain refractory.

Spatial changes in the transmembrane potential during extracellular electric stimulation.

The purpose of this study was to determine the spatial changes in the transmembrane potential caused by extracellular electric field stimulation. The transmembrane potential was recorded in 10 guinea pig papillary muscles in a tissue bath using a double-barrel microelectrode. After 20 S1 stimuli, a 10-ms square wave S2 shock field with a 30-ms S1-S2 coupling interval was given via patch shock electrodes 1 cm on either side of the tissue during the action potential plateau. Two shock strengths (2.1+/-0.2 and 6.5+/-0.6 V/cm) were tested with both shock polarities. The recording site was moved across the tissue along fibers with either 200 micrometer (macroscopic group [n=5], 12 consecutive recording sites over a 2. 2-mm tissue length in each muscle) or 20 micrometer (microscopic group [n=5], 21 consecutive recording sites over a 0.4-mm tissue length in each muscle) between adjacent recording sites. In the macroscopic group, the portion of the tissue toward the anode was hyperpolarized, whereas the portion toward the cathode was depolarized, with 1 zero-potential crossing from hyperpolarization to depolarization present near the center of the tissue. In the microscopic group, only 1 zero-potential crossing was observed in the center region of the tissue, whereas, away from the center, only hyperpolarization was observed toward the anode and depolarization toward the cathode. Although these results are consistent with predictions from field stimulation of continuous representations of myocardial structure, ie, the bidomain and cable equation models, they are not consistent with the prediction of depolarization-hyperpolarization oscillation from representations based on cellular-level resistive discontinuities associated with gap junctions, ie, the sawtooth model.

A model study of intramural dispersion of action potential duration in the canine pulmonary conus.

Regional gradients of action potential duration (APD) due to electrophysiological differences between endocardial, midmyocardial, and epicardial myocytes may exist across the ventricular wall. In addition, activation sequence-induced gradients of APD may occur if intramural fiber rotation accelerates or decelerates the depolarization wave front. To investigate relative contributions of regional and activation sequence-induced gradients to intramural APD dispersion, we simulated action potential propagation in two-dimensional models with idealized geometries representing the canine pulmonary conus. Ionic currents for endocardial myocytes were described using the Luo-Rudy membrane equations. Modifications to I(Ks) approximated action potentials of epicardial and midmyocardial cells. Spatial coupling was modeled with a bidomain representation of tissue structure that included unequal anisotropic conductivity ratios. Activation sequence-induced gradients reached 69 ms cm(-1) during a nonuniform activation sequence where the change in orientation between endocardial and epicardial fibers accelerated the depolarization wave front. Regional gradients reached 133 ms cm(-1) at the boundary between endocardial and midmyocardial cells. When regional and activation sequence-induced gradients were oriented in opposite directions, overall APD dispersion decreased. When the gradients were oriented in the same direction, overall dispersion measured as high as 202 ms cm(-1). This gradient exceeded values previously estimated as sufficient to induce cardiac arrhythmia during premature stimulation and suggests that regional and activation sequence-induced gradients increase arrhythmia vulnerability in the presence of other arrhythmogenic conditions.

Conduction between isolated rabbit Purkinje and ventricular myocytes coupled by a variable resistance.

Conduction at the Purkinje-ventricular junction (PVJ) demonstrates unidirectional block under both physiological and pathophysiological conditions. Although this block is typically attributed to multidimensional electrotonic interactions, we examined possible membrane-level contributions using single, isolated rabbit Purkinje (P) and ventricular (V) myocytes coupled by an electronic circuit. When we varied the junctional resistance (Rj) between paired V myocytes, conduction block occurred at lower Rj values during conduction from the smaller to larger myocyte (115 +/- 59 M omega) than from the larger to smaller myocyte (201 +/- 51 M omega). In Purkinje-ventricular myocyte pairs, however, block occurred at lower Rj values during P-to-V conduction (85 +/- 39 M omega) than during V-to-P conduction (912 +/- 175 M omega), although there was little difference in the mean cell size. Companion computer simulations, performed to examine how the early platea currents affected conduction, showed that P-to-V block occurred at lower Rj values when the transient outward current was increased or the calcium current was decreased in the model P cell. These results suggest that intrinsic differences in phase 1 repolarization can contribute to unidirectional block at the PVJ.

Myocardial discontinuities: a substrate for producing virtual electrodes that directly excite the myocardium by shocks.

BACKGROUND: Theoretical models suggest that an electrical stimulus causes regions of depolarization and hyperpolarization on either side of a myocardial discontinuity. This study determined experimentally whether an artificial discontinuity gives rise to an activation front in response to an electrical stimulus, consistent with the creation of such polarized regions. METHODS AND RESULTS: After a thoracotomy in six dogs, a 504-unipolar-electrode plaque was sutured to the right ventricular epicardium to map activations. From a line electrode parallel to one side of the plaque, 10 S1 stimuli were delivered, followed by S2 and S3 stimuli (S1S1, S1S2, S2S3 interval=300 ms). S1 and S3 stimuli were 25 mA; 5-ms S2 stimuli of both polarities were initially 25 mA and increased in 25 mA increments. The plaque was removed, and a transmural incision was made through the ventricular wall in the middle of the mapped region and sutured closed. The plaque was replaced and the stimulation protocol repeated. Before the incision, S2 stimuli directly activated tissue only near the stimulation site. An activation front arose at the border of the directly activated region and propagated across the plaque. As the S2 stimulus strength was increased, the size of the directly activated region increased. After the incision, sufficiently large S2 stimuli caused direct activation of tissue adjacent to the transmural incision as well as at the stimulation site. Activation fronts that arose adjacent to the transmural incision either propagated proximally toward the stimulation site and collided with the activation front originating from the stimulation wire or propagated distally away from the incision. Minimum S2 stimulus strengths activating areas adjacent to the incision were only 45+/-14% (cathode) and 39+/-18% (anode) of the strengths required to directly activate the same area before the incision was formed (P<.05). CONCLUSIONS: Myocardial discontinuities can give rise to activation fronts after a stimulus, suggesting the presence of polarized regions adjacent to the discontinuity.

Contributions of the specialized conduction system to the activation sequence in the canine pulmonary conus.

This study was designed to characterize the relative contributions of the specialized conduction system and the myocardial architecture to the ventricular activation sequence. In animal experiments, the activation sequence within a 14 x 14-mm region on each surface of the pulmonary conus from isolated canine hearts was determined from electrograms recorded during ventricular drives applied at the periphery of the measurement region. Recordings were obtained simultaneously from electrode arrays mounted on the endocardium and epicardium. Activation sequences were determined before and after the right ventricular cavity was bathed with a dilute Lugol-normal Tyrode (LNT) solution that selectively inhibited excitation of Purkinje cells. Simulations of action potential propagation in three-dimensional models (14.4 mm long x 7.2 mm wide x 3.6 mm thick) that included the major features of the midwall architecture were performed to aid in the interpretation of the experimental findings. During endocardial pacing (7 animals, 43 total drives), LNT application markedly prolonged the endocardial (13.7 +/- 1.3 ms) and epicardial (5.7 +/- 1.0 ms) activation sequences. However, epicardial isochrone maps constructed with electrograms recorded before LNT application showed no signs of multiple breakthrough sites and, with the exception of overall timing, closely resembled isochrone maps constructed with electrograms recorded after LNT application. During epicardial pacing (9 animals, 55 total drives), LNT application prolonged the endocardial (3.7 +/- 0.6 ms) and epicardial (1.9 +/- 0.6 ms) activation sequences much less dramatically than during endocardial pacing, suggesting a primary contribution of myocardial architecture. However, in those instances where nonuniform anisotropy slowed epicardial expansion of the depolarization wavefront, the specialized conduction system contributed to the activation sequence to a greater extent.

Effects of premature beats on repolarization of postextrasystolic beats.

BACKGROUND: A short-long-short sequence of cycle lengths predisposes to reentrant tachyarrhythmias. There is limited information about the effects of premature ventricular contractions (PVCs) on repolarization of postextrasystolic depolarizations (PEDs). Such information would contribute to understanding the mechanism for facilitating reentry with short-long-short cycle lengths. METHODS AND RESULTS: We introduced PVCs, over a range of coupling intervals and during a range of basic drive cycle lengths (BCLs), and determined PED repolarization. Our results from whole-animal experiments, isolated cell studies, and computer simulations are reported. In the whole-animal experiments, PED refractory periods (RPs) were longer than RPBCL. The greatest difference between RPPED and RPBCL (delta RPmax) occurred after short coupling interval PVCs and was 4.3 +/- 0.8, 4.2 +/- 0.8, and 2.1 +/- 0.5 ms (mean +/- SEM) during drives with short, intermediate, and long BCLs, respectively. The diastolic interval preceding the PED (DIPED) was inversely related to the coupling interval between the basic drive beat and the PVC and directly related to RPPED. PED action potential durations (APDs) of isolated canine myocytes were 9.8 +/- 4.9 ms (mean +/- SEM) longer than APD BCL (n = 19). The DiFrancesco-Noble membrane equations were used in simulations of action potential propagation in a one-dimensional cable, with stimulation protocols duplicating those in the animal experiments. PVCs prolonged APDPED, and APDPED was prolonged more during short than during long BCL drives. There was a direct relation between DIPED and APDPED. Analysis of the membrane currents over the time course of the PVCs and PEDs suggested that the ionic basis for PED repolarization prolongation was the interaction of Ito and Ik. Hyperpolarizing constant-current injections introduced immediately after the spike of isolated myocyte action potentials caused APD prolongation. This observation is consistent with the Ito and Ik interaction causing PED repolarization prolongation. CONCLUSIONS: PED repolarization prolongation could provide sites for unidirectional block to propagation of PVCs after PEDs and could facilitate initiation of reentrant tachyarrhythmias after short-long-short sequences of cycle lengths.

Effects of activation sequence on the spatial distribution of repolarization properties.

The electrotonic effects of activation spread on the spatial distribution of repolarization properties were studied in animal experiments and with computer simulations. Refractory periods (RPs) were measured at 36 sites within a 1.0 cm2 region of the epicardial surface of the canine pulmonary conus during 37 drives in 11 experiments. In each experiment three or four sites along the perimeter of the region bounding the RP test sites were driven. Activation propagated uniformly during some and nonuniformly during other drives in the same animals. In general, RPs were distributed uniformly when activation spread uniformly and nonuniformly when activation spread nonuniformly. The authors observed RP differences as large as 16 ms between sites with 2 mm separation during drive from some epicardial sites in these normal canine hearts. Indices of nonuniformity of activation and of relative RP values were used to quantify the relation between nonuniformity of activation spread and the spatial distribution of the RP. There was a significant negative correlation between nonuniformity of activation and RP indices during the 19 drives in which activation spread nonuniformly. This indicated that RPs were relatively long at sites where activation spread decelerated and relatively short at sites where activation spread accelerated. When nonuniform activation spread was simulated by introducing high-resistance barriers in a model with fixed anisotropic conductivities, there were marked spatial variations in action potential duration. The spatial variations in action potential duration were negatively correlated to acceleration and deceleration of activation spread. The major new finding of this study is that the spatial distributions of RPs are markedly affected by activation spread. Since both characteristics of activation sequence and nonuniformity of RP distributions have roles in reentrant arrhythmias, the findings suggest that some sites of origin of premature activity may be more arrhythmogenic than others. The findings may also explain why ventricular tachycardia can sometimes be initiated from one but not from other sites in patients undergoing electrophysiologic testing.

Computer simulations of three-dimensional propagation in ventricular myocardium. Effects of intramural fiber rotation and inhomogeneous conductivity on epicardial activation.

Three-dimensional membrane-based simulations of action potential propagation in ventricular myocardium were performed. Specifically, the effects of the intramural rotation of the fiber axes and inhomogeneous conductivity on the timing and pattern of epicardial activation were examined. Models were built, with approximately 400,000 microscopic elements arranged in rectangular parallelepipeds in each model. Simulations used the nonlinear Ebihara and Johnson membrane equations for the fast sodium current. Constructed models had histological features of ventricular myocardium. All models were anisotropic. In a subset of the models, an abrupt intramural rotation of the fiber axes was included. This feature was also combined with randomly distributed inhomogeneous conductivity and regions of high transverse resistance to represent nonuniform anisotropy in a further subset of the models. Epicardial stimuli were applied for each simulation. Three-dimensional activation patterns and epicardial isochron maps were constructed from the simulations. We noted that the rotation of fiber axes accelerated epicardial activation distant from the stimulus site. The inhomogeneous conductivity caused regional acceleration and deceleration of activation spread. We also noted features of epicardial activation that resulted from the fiber rotation, and the inhomogeneous conductivity corresponded to that observed in maps from experimental animals.

Cardiac propagation simulation.

We have completed a range of membrane-based simulations of action potential propagation in two- and three-dimensional models of ventricular myocardium. The two-dimensional simulations included a bidomain representation of the myocardium which explicitly characterized the component volume conductors in the intracellular, interstitial, and extracellular spaces. With these simulations, we studied the contribution of the extracellular volume conductor to transmural myocardial propagation during depolarization. We also used two-dimensional bidomain simulations to study the effect of the interstitial volume conductor in the setting of planar myocardial depolarization with nominal and extreme tissue conductivities. Our three-dimensional simulations included a monodomain representation of the myocardium which characterized the three component volume conductors as a single lumped conductor. With these simulations, we examined the effects of the intramural rotation of the fiber axes on the timing and pattern of activation. To achieve practical solution times, we extended numerical techniques from previous reports and developed a range of new techniques applicable to this class of problems. Simulations of the depolarization wavefront used the nonlinear Ebihara and Johnson membrane equations for the fast sodium current as the membrane model. Simulations of the full action potential cycle combined the Ebihara and Johnson fast sodium current with the Beeler and Reuter membrane equations. Our results demonstrated that the individual volume conductors and the rotation of fiber axes have unique and identifiable consequences on the electrical activation in models of ventricular myocardium.

Computer simulations of activation in an anatomically based model of the human ventricular conduction system.

Simulations of the electrical activity during excitation were performed in an anatomically based model of the human ventricular conduction system. Each of the 33,000 elements of this model represented a unit bundle of Purkinje or atrioventricular nodal tissue. The Ebihara-Johnson model for sodium defined the active membrane characteristics. Using a combination of new and existing modeling techniques, simulations of excitation were completed in approximately 5 min CPU time on an IBM 3090 at the Cornell National Supercomputer Facility. Activation times at sites in the model were compared to experimental measurements for the excitation of the ventricular myocardium on the endocardial surface. These "literature-based" times were estimated from a number of reported human heart mapping studies. Initially, the times fit poorly. The major factor for the discrepancy was the conduction velocities of the elements, which were a result of the physical and electrical parameters derived from a review of histologic and electrical properties studies. In addition, there was a latency between activation of the system in the left ventricle of the model and that in the right ventricle when compared to the experimental work. When the times were scaled to adjust for the conduction velocity and ventricular latency effects, the match between the simulation and literature-based times was much improved. Quantitative comparison between normalized times resulted in correlation coefficients CCF = 0.76 for the right ventricle and CCF = 0.64 for the left ventricle.