Quatrefoil reentry in myocardium: an optical imaging study of the induction mechanism

The physics of heart rhythm disorders

The global burden caused by cardiovascular disease is substantial, with heart disease representing the most common cause of death around the world. There remains a need to develop better mechanistic models of cardiac function in order to combat this health concern. Heart rhythm disorders, or arrhythmias, are one particular type of disease which has been amenable to quantitative investigation. Here we review the application of quantitative methodologies to explore dynamical questions pertaining to arrhythmias. We begin by describing single-cell models of cardiac myocytes, from which two and three dimensional models can be constructed. Special focus is placed on results relating to pattern formation across these spatially-distributed systems, especially the formation of spiral waves of activation. Next, we discuss mechanisms which can lead to the initiation of arrhythmias, focusing on the dynamical state of spatially discordant alternans, and outline proposed mechanisms perpetuating arrhythmias such as fibrillation. We then review experimental and clinical results related to the spatio-temporal mapping of heart rhythm disorders. Finally, we describe treatment options for heart rhythm disorders and demonstrate how statistical physics tools can provide insights into the dynamics of heart rhythm disorders.

R-on-T and the initiation of reentry revisited: Integrating old and new concepts

Initiation of reentry requires 2 factors: (1) a triggering event, most commonly focal excitations such as premature ventricular complexes (PVCs); and (2) a vulnerable substrate with regional dispersion of refractoriness and/or excitability, such as occurs during the T wave of the electrocardiogram when some areas of the ventricle have repolarized and recovered excitability but others have not. When the R wave of a PVC coincides in time with the T wave of the previous beat, this timing can lead to unidirectional block and initiation of reentry, known as the R-on-T phenomenon. Classically, the PVC triggering reentry has been viewed as arising focally from 1 region and propagating into another region whose recovery is delayed, resulting in unidirectional conduction block and reentry initiation. However, more recent evidence indicates that PVCs also can arise from the T wave itself. In the latter case, the PVC initiating reentry is not a separate event from the T wave but rather is causally generated from the repolarization gradient that manifests as the T wave. We call the former an "R-to-T" mechanism and the latter an "R-from-T" mechanism, which are initiation mechanisms distinct from each other. Both are important components of the R-on-T phenomenon and need to be taken into account when designing antiarrhythmic strategies. Strategies targeting suppression of triggers alone or vulnerable substrate alone may be appropriate in some instances but not in others. Preventing R-from-T arrhythmias requires suppressing the underlying dynamic tissue instabilities responsible for producing both triggers and substrate vulnerability simultaneously. The same principles are likely to apply to supraventricular arrhythmias.

Structure and function of the ventricular tachycardia isthmus

Catheter ablation of postinfarction reentrant ventricular tachycardia (VT) has received renewed interest owing to the increased availability of high-resolution electroanatomic mapping systems that can describe the VT circuits in greater detail, and the emergence and need to target noninvasive external beam radioablation. These recent advancements provide optimism for improving the clinical outcome of VT ablation in patients with postinfarction and potentially other scar-related VTs. The combination of analyses gleaned from studies in swine and canine models of postinfarction reentrant VT, and in human studies, suggests the existence of common electroanatomic properties for reentrant VT circuits. Characterizing these properties may be useful for increasing the specificity of substrate mapping techniques and for noninvasive identification to guide ablation. Herein, we describe properties of reentrant VT circuits that may assist in elucidating the mechanisms of onset and maintenance, as well as a means to localize and delineate optimal catheter ablation targets.

Bidomain modeling of electrical and mechanical properties of cardiac tissue

Throughout the history of cardiac research, there has been a clear need to establish mathematical models to complement experimental studies. In an effort to create a more complete picture of cardiac phenomena, the bidomain model was established in the late 1970s to better understand pacing and defibrillation in the heart. This mathematical model has seen ongoing use in cardiac research, offering mechanistic insight that could not be obtained from experimental pursuits. Introduced from a historical perspective, the origins of the bidomain model are reviewed to provide a foundation for researchers new to the field and those conducting interdisciplinary research. The interplay of theory and experiment with the bidomain model is explored, and the contributions of this model to cardiac biophysics are critically evaluated. Also discussed is the mechanical bidomain model, which is employed to describe mechanotransduction. Current challenges and outstanding questions in the use of the bidomain model are addressed to give a forward-facing perspective of the model in future studies.

Slow uniform electrical activation during sinus rhythm is an indicator of reentrant VT isthmus location and orientation in an experimental model of myocardial infarction

BACKGROUND

To validate the predictability of reentrant circuit isthmus locations without ventricular tachycardia (VT) induction during high-definition mapping, we used computer methods to analyse sinus rhythm activation in experiments where isthmus location was subsequently verified by mapping reentrant VT circuits.

METHOD

In 21 experiments using a canine postinfarction model, bipolar electrograms were obtained from 196-312 recordings with 4mm spacing in the epicardial border zone during sinus rhythm and during VT. From computerized electrical activation maps of the reentrant circuit, areas of conduction block were determined and the isthmus was localized. A linear regression was computed at three different locations about the reentry isthmus using sinus rhythm electrogram activation data. From the regression analysis, the uniformity, a measure of the constancy at which the wavefront propagates, and the activation gradient, a measure that may approximate wavefront speed, were computed. The purpose was to test the hypothesis that the isthmus locates in a region of slow uniform activation bounded by areas of electrical discontinuity.

RESULTS

Based on the regression parameters, sinus rhythm activation along the isthmus near its exit proceeded uniformly (mean r²= 0.95±0.05) and with a low magnitude gradient (mean 0.37±0.10mm/ms). Perpendicular to the isthmus long-axis across its boundaries, the activation wavefront propagated much less uniformly (mean r²= 0.76±0.24) although of similar gradient (mean 0.38±0.23mm/ms). In the opposite direction from the exit, at the isthmus entrance, there was also less uniformity (mean r²= 0.80±0.22) but a larger magnitude gradient (mean 0.50±0.25mm/ms). A theoretical ablation line drawn perpendicular to the last sinus rhythm activation site along the isthmus long-axis was predicted to prevent VT reinduction. Anatomical conduction block occurred in 7/21 experiments, but comprised only small portions of the isthmus lateral boundaries; thus detection of sinus rhythm conduction block alone was insufficient to entirely define the VT isthmus.

CONCLUSIONS

Uniform activation with a low magnitude gradient during sinus rhythm is present at the VT isthmus exit location but there is less uniformity across the isthmus lateral boundaries and at isthmus entrance locations. These factors may be useful to verify any proposed VT isthmus location, reducing the need for VT induction to ablate the isthmus. Measured computerized values similar to those determined herein could therefore be assistive to sharpen specificity when applying sinus rhythm mapping to localize EP catheter ablation sites.

Label-free conduction velocity mapping and gap junction assessment of functional iPSC-Cardiomyocyte monolayers

Cardiac conduction is an important function of the heart. To date, accurate measurement of conduction velocity (CV) in vitro is hindered by the low spatial resolution and poor signal-to-noise ratio of microelectrode arrays (MEAs), or the cytotoxicity and end-point analysis of fluorescence optical imaging. Here, we have developed a new label-free method based on defocused brightfield imaging to quantify CV by analyzing centroid displacements and contraction trajectories of each cardiomyocyte in a monolayer of human stem cell-derived cardiomyocytes (iPSC-CMs). Our data revealed that the time delay between intracellular calcium release and the initiation of cell contraction is highly consistent across cardiomyocytes; however, the duration a cell takes to reach its maximum beating magnitude varies significantly, proving that the time delay in excitation-contraction coupling is largely constant in iPSC-CMs. Standard calcium imaging of the same iPSC-CM populations (~10⁶ cells) was conducted for comparison with our label-free method. The results confirmed that our label-free method was capable of achieving highly accurate CV mapping (17.64 ± 0.89 cm/s vs. 17.95 ± 2.29 cm/s, p-value>0.1). Additionally, our method effectively revealed various shapes in cell beating pattern. We also performed label-free CV mapping on disease-specific iPSC-CM monolayers with plakophilin-2 (PKP2) knockdown, which effectively quantified their low CV values and further validated the arrhythmogenic role of PKP2 mutation in arrhythmogenic right ventricular cardiomyopathy (ARVC) through the disruption of cardiac conduction. The label-free method offers a cytotoxic-free technique for long-term measurement of dynamic beating trajectories, beating propagation and conduction velocities of cardiomyocyte monolayers.

Optical Mapping

Optical mapping of electrical activity in the heart is based on voltage-sensitive and lipophilic fluorescence dyes. Optical signals recorded from cardiac cells correlate well with their transmembrane potentials. High spatiotemporal resolution, wide field mapping, and high sensitivity to transmembrane potential enable detailed characterization of action potential initiation and propagation. Optical mapping is used to study complex patterns of excitation propagation, including propagation across the sinoatrial and atrioventricular nodes and during atrial and ventricular arrhythmias.Optical mapping is used to study the role of reentrant activity in atrial and ventricular fibrillation.

Source-Sink Mismatch Causing Functional Conduction Block in Re-Entrant Ventricular Tachycardia

Ventricular tachycardia (VT) caused by a re-entrant circuit is a life-threatening arrhythmia that at present cannot always be treated adequately. A realistic model of re-entry would be helpful to accurately guide catheter ablation for interruption of the circuit. In this review, models of electrical activation wavefront propagation during onset and maintenance of re-entrant VT are discussed. In particular, the relationship between activation mapping and maps of transition in infarct border zone thickness, which results in source-sink mismatch, is considered in detail and supplemented with additional data. Based on source-sink mismatch, the re-entry isthmus can be modeled from its boundary properties. Isthmus boundary segments with large transitions in infarct border zone thickness have large source-sink mismatch, and functional block forms there during VT. These alternate with segments having lesser thickness change and therefore lesser source-sink mismatch, which act as gaps, or entrance and exit points, to the isthmus during VT. Besides post-infarction substrates, the source-sink model is likely applicable to other types of volumetric changes in the myocardial conducting medium, such as when there is presence of fibrosis or dissociation of muscle fibers.

Effect of anisotropy on ventricular vulnerability to unidirectional block and reentry by single premature stimulation during normal sinus rhythm in rat heart

Single high-intensity premature stimuli when applied to the ventricles during ventricular drive of an ectopic site, as in Winfree's "pinwheel experiment," usually induce reentry arrhythmias in the normal heart, while single low-intensity stimuli barely do. Yet ventricular arrhythmia vulnerability during normal sinus rhythm remains largely unexplored. With a view to define the role of anisotropy on ventricular vulnerability to unidirectional conduction block and reentry, we revisited the pinwheel experiment with reduced constraints in the in situ rat heart. New features included single premature stimulation during normal sinus rhythm, stimulation and unipolar potential mapping from the same high-resolution epicardial electrode array, and progressive increase in stimulation strength and prematurity from diastolic threshold until arrhythmia induction. Measurements were performed with 1-ms cathodal stimuli at multiple test sites (n = 26) in seven rats. Stimulus-induced virtual electrode polarization during sinus beat recovery phase influenced premature ventricular responses. Specifically, gradual increase in stimulus strength and prematurity progressively induced make, break, and graded-response stimulation mechanisms. Hence unidirectional conduction block occurred as follows: 1) along fiber direction, on right and left ventricular free walls (n = 23), initiating figure-eight reentry (n = 17) and tachycardia (n = 12), and 2) across fiber direction, on lower interventricular septum (n = 3), initiating spiral wave reentry (n = 2) and tachycardia (n = 1). Critical time window (55.1 ± 4.7 ms, 68.2 ± 6.0 ms) and stimulus strength lower limit (4.9 ± 0.6 mA) defined vulnerability to reentry. A novel finding of this study was that ventricular tachycardia evolves and is maintained by episodes of scroll-like wave and focal activation couplets. We also found that single low-intensity premature stimuli can induce repetitive ventricular response (n = 13) characterized by focal activations.NEW & NOTEWORTHY We performed ventricular cathodal point stimulation during sinus rhythm by progressively increasing stimulus strength and prematurity. Virtual electrode polarization and recovery gradient progressively induced make, break, and graded-response stimulation mechanisms. Unidirectional conduction block occurred along or across fiber direction, initiating figure-eight or spiral wave reentry, respectively, and tachycardia sustained by scroll wave and focal activations.

Probing the Electrophysiology of the Developing Heart

Many diseases that result in dysfunction and dysmorphology of the heart originate in the embryo. However, the embryonic heart presents a challenging subject for study: especially challenging is its electrophysiology. Electrophysiological maturation of the embryonic heart without disturbing its physiological function requires the creation and deployment of novel technologies along with the use of classical techniques on a range of animal models. Each tool has its strengths and limitations and has contributed to making key discoveries to expand our understanding of cardiac development. Further progress in understanding the mechanisms that regulate the normal and abnormal development of the electrophysiology of the heart requires integration of this functional information with the more extensively elucidated structural and molecular changes.

Optical Imaging of Cardiac Action Potential

This chapter reviews the major milestones and scientific achievements facilitated by optical imaging of the action potential in the heart over more than four decades since its introduction. We discuss the limitations of this technique, which sometimes are not fully recognized; the unresolved issues, such as motion artifacts, and the newest developments and future directions.

Nonlinear and Stochastic Dynamics in the Heart

In a normal human life span, the heart beats about 2 to 3 billion times. Under diseased conditions, a heart may lose its normal rhythm and degenerate suddenly into much faster and irregular rhythms, called arrhythmias, which may lead to sudden death. The transition from a normal rhythm to an arrhythmia is a transition from regular electrical wave conduction to irregular or turbulent wave conduction in the heart, and thus this medical problem is also a problem of physics and mathematics. In the last century, clinical, experimental, and theoretical studies have shown that dynamical theories play fundamental roles in understanding the mechanisms of the genesis of the normal heart rhythm as well as lethal arrhythmias. In this article, we summarize in detail the nonlinear and stochastic dynamics occurring in the heart and their links to normal cardiac functions and arrhythmias, providing a holistic view through integrating dynamics from the molecular (microscopic) scale, to the organelle (mesoscopic) scale, to the cellular, tissue, and organ (macroscopic) scales. We discuss what existing problems and challenges are waiting to be solved and how multi-scale mathematical modeling and nonlinear dynamics may be helpful for solving these problems.

The strength-interval curve in cardiac tissue

The bidomain model describes the electrical properties of cardiac tissue and is often used to simulate the response of the heart to an electric shock. The strength-interval curve summarizes how refractory tissue is excited. This paper analyzes calculations of the strength-interval curve when a stimulus is applied through a unipolar electrode. In particular, the bidomain model is used to clarify why the cathodal and anodal strength-interval curves are different, and what the mechanism of the “dip” in the anodal strength-interval curve is.

MECHANISM OF ANODE BREAK EXCITATION IN THE HEART: THE RELATIVE INFLUENCE OF MEMBRANE AND ELECTROTONIC FACTORS

Two hypotheses for the mechanism of anode break excitation in cardiac tissue are electrotonic interaction between adjacent regions of depolarization and hyperpolarization, and a hyperpolarization-activated membrane current, if. We incorporate membrane kinetics proposed for if into the bidomain model with unequal anisotropy ratios. During unipolar stimulation, we find that:

(1) The mechanisms of cathode make, cathode break, and anode make excitation are insensitive to if.

(2) Both electrotonic interactions and if contribute to anode break excitation. In our simulations, if makes the dominant contribution.

(3) Electrotonic interactions cause the "dip" in the anodal strength-interval curve.

(4) Following anode break excitation, the wave front propagates in the direction perpendicular to the fibers.

(5) if improves the agreement between the measured and calculated strength-interval curves.

We suggest three experiments to determine the mechanism of anode break excitation: measure the site and timing of initial excitation, or use drugs to suppress if.

Intracellular calcium and the mechanism of anodal supernormal excitability in langendorff perfused rabbit ventricles

BACKGROUND

Anodal stimulation hyperpolarizes the cell membrane and increases the intracellular Ca(2+) (Ca(i)) transient. This study tested the hypothesis that the maximum slope of the Ca(i) decline (-(dCa(i)/dt)(max)) corresponds to the timing of anodal dip on the strength-interval curve and the initiation of repetitive responses and ventricular fibrillation (VF) after a premature stimulus (S(2)).

METHODS AND RESULTS

We simultaneously mapped the membrane potential (V(m)) and Ca(i) in 23 rabbit ventricles. A dip in the anodal strength-interval curve was observed. During the anodal dip, ventricles were captured by anodal break excitation directly under the S(2) electrode. The Ca(i) following anodal stimuli is larger than that following cathodal stimuli. The S(1)-S(2) intervals of the anodal dip (203±10 ms) coincided with the -(dCa(i)/dt)(max) (199±10 ms, P=NS). BAPTA-AM (n=3), inhibition of the electrogenic Na(+)-Ca(2+) exchanger current (I(NCX)) by low extracellular Na(+) (n=3), and combined ryanodine and thapsigargin infusion (n=2) eliminated the anodal supernormality. Strong S(2) during the relative refractory period (n=5) induced 29 repetitive responses and 10 VF episodes. The interval between S(2) and the first non-driven beat was coincidental with the time of -(dCa(i)/dt)(max).

CONCLUSIONS

Larger Ca(i) transient and I(NCX) activation induced by anodal stimulation produces anodal supernormality. The time of maximum I(NCX) activation is coincidental to the induction of non-driven beats from the Ca(i) sinkhole after a strong premature stimulation.

Probing field-induced tissue polarization using transillumination fluorescent imaging

Despite major successes of biophysical theories in predicting the effects of electrical shocks within the heart, recent optical mapping studies have revealed two major discrepancies between theory and experiment: 1), the presence of negative bulk polarization recorded during strong shocks; and 2), the unexpectedly small surface polarization under shock electrodes. There is little consensus as to whether these differences result from deficiencies of experimental techniques, artifacts of tissue damage, or deficiencies of existing theories. Here, we take advantage of recently developed near-infrared voltage-sensitive dyes and transillumination optical imaging to perform, for the first time that we know of, noninvasive probing of field effects deep inside the intact ventricular wall. This technique removes some of the limitations encountered in previous experimental studies. We explicitly demonstrate that deep inside intact myocardial tissue preparations, strong electrical shocks do produce considerable negative bulk polarization previously inferred from surface recordings. We also demonstrate that near-threshold diastolic field stimulation produces activation of deep myocardial layers 2-6 mm away from the cathodal surface, contrary to theory. Using bidomain simulations we explore factors that may improve the agreement between theory and experiment. We show that the inclusion of negative asymmetric current can qualitatively explain negative bulk polarization in a discontinuous bidomain model.

Virtual electrodes and the induction of fibrillation in Langendorff-perfused rabbit ventricles: the role of intracellular calcium

A strong premature electrical stimulus (S(2)) induces both virtual anodes and virtual cathodes. The effects of virtual electrodes on intracellular Ca(2+) concentration ([Ca(2+)](i)) transients and ventricular fibrillation thresholds (VFTs) are unclear. We studied 16 isolated, Langendorff-perfused rabbit hearts with simultaneous voltage and [Ca(2+)](i) optical mapping and for vulnerable window determination. After baseline pacing (S(1)), a monophasic (10 ms anodal or cathodal) or biphasic (5 ms-5 ms) S(2) was applied to the left ventricular epicardium. Virtual electrode polarizations and [Ca(2+)](i) varied depending on the S(2) polarity. Relative to the level of [Ca(2+)](i) during the S(1) beat, the [Ca(2+)](i) level 40 ms after the onset of monophasic S(2) increased by 36+/-8% at virtual anodes and 20+/-5% at virtual cathodes (P<0.01), compared with 25+/-5% at both virtual cathode-anode and anode-cathode sites for biphasic S(2). The VFT was significantly higher and the vulnerable window significantly narrower for biphasic S(2) than for either anodal or cathodal S(2) (n=7, P<0.01). Treatment with thapsigargin and ryanodine (n=6) significantly prolonged the action potential duration compared with control (255+/-22 vs. 189+/-6 ms, P<0.05) and eliminated the difference in VFT between monophasic and biphasic S(2), although VFT was lower for both cases. We conclude that virtual anodes caused a greater increase in [Ca(2+)](i) than virtual cathodes. Monophasic S(2) is associated with lower VFT than biphasic S(2), but this difference was eliminated by the inhibition of the sarcoplasmic reticulum function and the prolongation of the action potential duration. However, the inhibition of the sarcoplasmic reticulum function also reduced VFT, indicating that the [Ca(2+)](i) dynamics modulate, but are not essential, to ventricular vulnerability.

Detection of the diastolic pathway, circuit morphology, and inducibility of human postinfarction ventricular tachycardia from mapping in sinus rhythm

OBJECTIVE

The purpose of this study was to determine whether sinus rhythm activation maps could be used to detect the origin and characteristics of reentrant ventricular tachycardia in postinfarction patients.

METHODS

In each of 11 post-myocardial infarction patients, unipolar electrograms were acquired at 256 virtual endocardial sites using noncontact mapping. Electrograms were marked for activation time and mapped on a three-dimensional grid. Spatial differences in sinus rhythm activation time were correlated to isthmus characteristics and to activation through the diastolic pathway during tachycardia on the basis of the presence of contiguous lines of slow conduction and block.

RESULTS

Twenty tachycardia morphologies were analyzed. Fourteen sustained reentrant circuit morphologies occurred in nine patients, with dual morphologies having a shared isthmus occurring in five of nine patients. Dual morphologies were caused by changes in entrance-exit point location about a common isthmus. One transient circuit morphology of <10 beats occurred in three of nine patients also having sustained reentry. The estimated isthmus determined from sinus rhythm activation overlapped the diastolic pathway determined from tachycardia maps with 83.8% sensitivity and 89.2% specificity. The mean difference in sinus rhythm activation time across the isthmus border was larger in transient compared with sustained morphologies (32.8 +/- 9.5 ms vs. 22.8 +/- 1.8 ms), with smaller isthmus size (4.8 +/- 1.1 cm(2) vs. 10.0 +/- 1.1 cm(2); P < .05), narrower entrance-exit points (7.0 +/- 1.5 mm vs. 9.3 +/- 0.8 mm; P < .05), and greater activation time difference across them (16.3 +/- 3.5 ms vs. 10.1 +/- 1.0 ms; P < .05).

CONCLUSION

In post-myocardial infarction patients, the reentry isthmus can be localized in the endocardial border zone from sinus rhythm activation maps. Nonsustained reentry occurs when isthmus size is small and entrance-exit points are narrow and more electrically discontinuous.

The pinwheel experiment revisited: effects of cellular electrophysiological properties on vulnerability to cardiac reentry

In normal heart, ventricular fibrillation can be induced by a single properly timed strong electrical or mechanical stimulus. A mechanism first proposed by Winfree and coined the “pinwheel experiment” emphasizes the timing and strength of the stimulus in inducing figure-of-eight reentry. However, the effects of cellular electrophysiological properties on vulnerability to reentry in the pinwheel scenario have not been investigated. In this study, we extend Winfree's pinwheel experiment to show how the vulnerability to reentry is affected by the graded action potential responses induced by a strong premature stimulus, action potential duration (APD), and APD restitution in simulated monodomain homogeneous two-dimensional tissue. We find that a larger graded response, longer APD, or steeper APD restitution slope reduces the vulnerable window of reentry. Strong graded responses and long APD promote tip-tip interactions at long coupling intervals, causing the two initiated spiral wave tips to annihilate. Steep APD restitution promotes wave front-wave back interaction, causing conduction block in the central common pathway of figure-of-eight reentry. We derive an analytical treatment that shows good agreement with numerical simulation results.

Calcium transient dynamics and the mechanisms of ventricular vulnerability to single premature electrical stimulation in Langendorff-perfused rabbit ventricles

BACKGROUND

Single strong premature electrical stimulation (S(2)) may induce figure-eight reentry. We hypothesize that Ca current-mediated slow-response action potentials (APs) play a key role in the propagation in the central common pathway (CCP) of the reentry.

METHODS

We simultaneously mapped optical membrane potential (V(m)) and intracellular Ca (Ca(i)) transients in isolated Langendorff-perfused rabbit ventricles. Baseline pacing (S(1)) and a cathodal S(2) (40-80 mA) were given at different epicardial sites with a coupling interval of 135 +/- 20 ms.

RESULTS

In all 6 hearts, S(2) induced graded responses around the S(2) site. These graded responses propagated locally toward the S(1) site and initiated fast APs from recovered tissues. The wavefront then circled around the refractory tissue near the site of S(2). At the side of S(2) opposite to the S(1), the graded responses prolonged AP duration while the Ca(i) continued to decline, resulting in a Ca(i) sinkhole (an area of low Ca(i)). The Ca(i) in the sinkhole then spontaneously increased, followed by a slow V(m) depolarization with a take-off potential of -40 +/- 3.9 mV, which was confirmed with microelectrode recordings in 3 hearts. These slow-response APs then propagated through CCP to complete a figure-eight reentry.

CONCLUSION

We conclude that a strong premature stimulus can induce a Ca(i) sinkhole at the entrance of the CCP. Spontaneous Ca(i) elevation in the Ca(i) sinkhole precedes the V(m) depolarization, leading to Ca current-mediated slow propagation in the CCP. The slow propagation allows more time for tissues at the other side of CCP to recover and be excited to complete figure-eight reentry.

Preshock phase singularity and the outcome of ventricular defibrillation

BACKGROUND

Phase singularity (PS) is a topological defect that serves as a source of ventricular fibrillation (VF). Whether or not the quantity of preshock PS determines defibrillation outcome is unclear.

OBJECTIVE

The purpose of this study was to test the hypothesis that the number of PSs at the time of shock is an important factor that determines the shock outcome.

METHODS

Isolated, perfused rabbit hearts (n = 7) were optically mapped with a potentiometric dye (di-4-ANNEPS). Shocks were delivered during short (10 seconds) and long (1 minute) VF, and the outcome was classified as successful type A (immediate termination), type B (postshock repetitive responses before termination), and unsuccessful.

RESULTS

When shock strengths of 50% probability of successful defibrillation (DFT50) +/- 50 V were given in short VF, the types A and B and unsuccessful shocks were associated with a preshock PS number of 0.3 +/- 0.4, 1.4 +/- 0.3, and 1.5 +/- 0.4 (P <.01 by analysis of variance) and shock strengths of 205 +/- 77, 207 +/- 65, and 173 +/- 74 V (P <.01), respectively. When the same shocks were applied during long VF, the PS numbers were 1.7 +/- 0.5, 3.0 +/- 0.5, and 3.5 +/- 0.6, respectively (P <.01), and the shock strengths were 282 +/- 100, 283 +/- 135, and 256 +/- 126 V, respectively (P <.01). If we only analyze shocks with strength at DFT(50), the preshock PS number was still significantly different for short VF (0.6 +/- 0.5, 1.6 +/- 0.9, and 1.5 +/- 0.8; P <.05) and for long VF (1.4 +/- 0.5, 2.7 +/- 0.6, and 2.7+/-1.3; P <.05), respectively. All preshock PSs were eliminated by shocks. However, rapid repetitive activity was then reinitiated in unsuccessful and type B successful shocks but not in type A successful shocks.

CONCLUSIONS

A low number or an absence of preshock PS was associated with type A successful defibrillation. There was no difference in preshock PS numbers between unsuccessful and type B successful defibrillation.

Cathodal stimulation in the recovery phase of a propagating planar wave in the rabbit heart reveals four stimulation mechanisms

The stimulation of cardiac tissue in the recovery phase has significant importance in relation to reentry induction. In the theoretical experiment proposed by Winfree, termed the 'pinwheel' experiment, a point stimulus (S2) is applied in the wake of a freely propagating planar wave (S1). Reentry induced from this S1-S2 pinwheel protocol has been observed experimentally in heart preparations. However, in these experiments, which focused on activation outcomes, only mapping of extracellular voltages has been conducted. The lack of transmembrane potential (Vm) distribution data makes it impossible to analyse the underlying stimulation mechanisms which precede the reentry induction. In this work we sought to elucidate the stimulation mechanisms throughout the heart cycle using the pinwheel protocol. We examined the cardiac tissue responses during and immediately after cathodal stimulation in the refractory wake of a propagating planar wave. The voltage-sensitive dye di-4-ANEPPS was utilized to measure Vm directly from quasi two-dimensional preparations of cryoablated Langendorff-perfused rabbit hearts. Four stimulation mechanisms were observed that depended on the Vm magnitude during S2 cathodal stimulation. Make stimulation always occurred during diastolic stimulation. When stimulation was at the beginning of the relative refractory period (RRP), transitional make-break stimulation was detected. During the RRP the excitation was due to the break mechanism. While approaching the effective refractory period (ERP), the tissue response is characterized by a damped wave mediated response. These four stimulation mechanisms were observed in all hearts whether the S1 planar wave propagation was parallel or perpendicular to the fibre direction. This study is the first examination of Vm and the stimulation mechanisms throughout the cardiac cycle using the pinwheel protocol, and the results have implications in the development and improvement of pacing protocols for artificial cardiostimulators.

Influence of anisotropic conduction properties in the propagation of the cardiac action potential

Anisotropy, the property of being directionally dependent, is ubiquitous in nature. Propagation of the electrical impulse in cardiac tissue is anisotropic, a property that is determined by molecular, cellular, and histological determinants. The properties and spatial arrangement of connexin molecules, the cell size and geometry, and the fiber orientation and arrangement are examples of structural determinants of anisotropy. Anisotropy is not a static property but is subject to dynamic functional regulation, mediated by modulation of gap junctional conductance. Tissue repolarization is also anisotropic. The relevance of anisotropy extends beyond normal propagation and has important implications in pathological states, as a potential substrate for abnormal rhythms and reentry.

Quatrefoil Reentry Caused by Burst Pacing

BACKGROUND

Experiments and clinical studies have shown that high-frequency (burst) pacing can induce reentry and fibrillation without a strong shock. We hypothesize that a train of weak stimuli induces quatrefoil reentry, and investigate the mechanism and threshold for this mode of reentry induction.

METHODS

We apply a train of weak stimuli at different pacing rates to determine the threshold necessary to induce quatrefoil reentry. Numerical calculations are used to simulate cardiac tissue, based on the bidomain model with unequal anisotropy ratios. We consider both anodal and cathodal stimuli.

RESULTS

Quatrefoil reentry is initiated using much smaller currents during burst pacing (0.9 mA) compared to a single premature pulse (8.6 mA). As we varied the pacing rate, we observed reentry at the border between different modes of phase locking, such as between 1:1 and 2:1 responses.

CONCLUSION

Burst pacing can significantly reduce the threshold for reentry. However, the extreme sensitivity of reentry induction to the exact number of stimuli in the pulse train makes the method difficult to use as a consistent, reproducible way to induce reentry.

The effect of the cut surface during electrical stimulation of a cardiac wedge preparation

Optical mapping from the cut surface of a "wedge preparation" allows observation inside the heart wall, below the epicardium or endocardium. We use numerical simulations based on the bidomain model to illustrate how the transmembrane potential is influenced by the cut surface. The distribution of transmembrane potential around a unipolar cathode depends on the fiber angle. For intermediate angles, hyperpolarization appears on only one side of the electrode, and is large and widespread.

The effect of the fiber curvature gradient on break excitation in cardiac tissue

BACKGROUND

Break excitation has been hypothesized as a mechanism for the initiation of reentry in cardiac tissue. One way break excitation can occur is by virtual electrodes formed due to a curving fiber geometry. In this article, we are concerned with the relationship between the peak gradient of fiber curvature and the threshold for break stimulation and the initiation of reentry.

METHODS

We calculate the maximum gradient of fiber curvature for different scales of fiber geometry in a constant tissue size (20x20 mm), and also examine the mechanisms by which reentry initiation fails.

RESULTS

For small peak gradients, reentry fails because break excitation does not occur. For larger peak gradients, reentry fails because break excitation fails to develop into full-scale reentry. For strong stimuli above the upper limit of vulnerability, reentry fails because the break excitation propagates through the hyperpolarized region and then encounters refractory tissue, causing the wave front to die.

Fluorescence imaging of cardiac propagation: spectral properties and filtering of optical action potentials

Fluorescence imaging using voltage-sensitive dyes is an important tool for studying electrical propagation in the heart. Yet, the low amplitude of the voltage-sensitive component in the fluorescence signal and high acquisition rates dictated by the rapid propagation of the excitation wave front make it difficult to achieve recordings with high signal-to-noise ratios. Although spatially and temporally filtering the acquired signals has become de facto one of the key elements of optical mapping, there is no consensus regarding their use. Here we characterize the spatiotemporal spectra of optically recorded action potentials and determine the distortion produced by conical filters of different sizes. On the basis of these findings, we formulate the criteria for rational selection of filter characteristics. We studied the evolution of the spatial spectra of the propagating wave front after epicardial point stimulation of the isolated, perfused right ventricular free wall of the pig heart stained with di-4-ANEPPS. We found that short-wavelength (<3 mm) spectral components represent primarily noise and surface features of the preparation (coronary vessels, fat, and connective tissue). The time domain of the optical action potential spectrum also lacks high-frequency components (>100 Hz). Both findings are consistent with the reported effect of intrinsic blurring caused by light scattering inside the myocardial wall. The absence of high-frequency spectral components allows the use of aggressive low-pass spatial and temporal filters without affecting the optical action potential morphology. We show examples where the signal-to-noise ratio increased up to 150 with <3% distortion. A generalization of our approach to the rational filter selection in various applications is discussed.

Intracellular Calcium Dynamics and Anisotropic Reentry in Isolated Canine Pulmonary Veins and Left Atrium

Background— Rapid activations due to either focal discharge or reentry are often present during atrial fibrillation (AF) in the pulmonary veins (PVs). The mechanisms of these rapid activations are unclear.

Methods and Results— We studied 7 isolated, Langendorff-perfused canine left atrial (LA) and PV preparations and used 2 cameras to map membrane potential alone (Vm, n=3) or Vm and intracellular calcium simultaneously (Ca i , n=4). Rapid atrial pacing induced 26 episodes of focal discharge from the proximal PVs in 5 dogs. The cycle lengths were 223±52 ms during ryanodine infusion (n=13) and 133±59 ms during ryanodine plus isoproterenol infusion (n=13). The rise of Ca i preceded Vm activation at the sites of focal discharge in 6 episodes of 2 preparations, compatible with voltage-independent spontaneous Ca i release. Phase singularities during pacing-induced reentry clustered specifically at the PV-LA junction. Periodic acid-Schiff (PAS) stain identified large cells with pale cytoplasm along the endocardium of PV muscle sleeves. There were abrupt changes in myocardial fiber orientation and increased interstitial fibrosis in the PV and at the PV-LA junction.

Conclusions— PV muscle sleeves may develop voltage-independent Ca i release, resulting in focal discharge. Focal discharge may also be facilitated by the presence of PAS-positive cells that are compatible with node-like cells. During reentry, phase singularities clustered preferentially at sites of increased anisotropy such as the PV-LA junction. These findings suggest that focal discharge caused by spontaneous calcium release and anisotropic reentry both contribute to rapid activations in the PVs during AF.

Ventricular Tachycardia Duration and Form Are Associated with Electrical Discontinuities Bounding the Core of the Reentrant Circuit

BACKGROUND

Successful prediction of reentrant ventricular tachycardia duration and form from sinus-rhythm electrogram signals in canine hearts is relevant to clinical studies, to potentially improve catheter ablation treatment during EP study.

METHODS/RESULTS

Following LAD ligation of canine hearts, activation maps were constructed from 312 border zone sites 4-5 days postinfarction. When reentrant ventricular tachycardia was inducible via programmed stimulation, the core of the circuit was defined on the maps as the enclosed area formed by the adjoining lines of slowest conduction and block bounding the protected region of the reentrant circuit. The number, location, and width of points of entrance or exit of the activation wavefront about the core were determined. Core perimeter location was then marked on the sinus-rhythm activation map, and the difference in activation time at opposite recording sites along the core perimeter was measured. Mean sinus-rhythm activation was highly discontinuous along the core perimeter in 10 transient reentry experiments (30.1 +/- 4.4 ms), moderately discontinuous in 13 sustained experiments (16.7 +/- 1.8 ms), and only slightly discontinuous in 5 noninducible experiments (9.7 +/- 1.7 ms). For transient versus sustained experiments, the entrance/exit points were narrower (mean: 6.5 +/- 1.0 mm vs 9.5 +/- 1.8 mm) with larger sinus-rhythm discontinuity across them (mean: 23.8 +/- 6.0 ms vs 11.8 +/- 2.1 ms). As core size increased, so did the number of entrance/exits present during reentry (P < 0.001). With increasing core size, four-loop (quatrefoil) reentry was frequently observed.

CONCLUSIONS

Whether reentrant ventricular tachycardia will be inducible in the canine infarct border zone, and its duration and form, is associated with the characteristics of electrical discontinuities present about the core perimeter.

Correction of motion artifact in cardiac optical mapping using image registration

Cardiac motion is one of the main sources of artifacts in epifluorescence imaging experiments. It can cause significant error in electrophysiological measurements such as action potential duration. We present a novel approach that uses image registration based on maximization of mutual information to correct for in-plane cardiac motion in such experiments. The approach is relatively fast (a few seconds per frame) and is performed entirely post acquisition. The image registration approach is an alternative to traditional approaches such as mechanical restraint of the heart or addition of chemical uncouplers. Our results show that the image registration method significantly reduces motion-related artifacts in experimental data.

Refractory Gradient is Responsible for the Increase in Ventricular Vulnerability Under Sodium Channel Blockade

BACKGROUND

Previous studies have shown that sodium channel (I(Na)) blockade increases ventricular vulnerability; however, there were differences in the degree of the increase. Because the vulnerable window (VW) is altered by the type of preshock refractory gradient (RG), the hypothesis was that the differences in the arrhythmogenesis of I(Na) blockade result from the different types of preshock RG employed.

METHODS AND RESULTS

Simulations of regio(Na)l electric shock following constant pacing stimuli in 2-dimensional bidomain myocardial sheets under I(Na) blockade were conducted using 3 types of preshock RG: longitudinally tilted (LRG), transversely tilted (TRG), and non-tilted RG (NRG). The increase in the degree of I(Na) blockade almost linearly decreased the conduction velocity. The action potential duration in the LRG and TRG cases was non-linearly shortened with the increase in INa blockade because of electrotonic influences, whereas in the case of NRG it was slightly prolonged. In both LRG and TRG cases, the VW for reentry induction by electric shock was considerably widened by the INa blockade; however, this was not the case for NRG in which the VW was rather narrowed by the INa blockade.

CONCLUSION

The type of preshock RG alters the degree of the increase in ventricular vulnerability under INa blockade.

Optical imaging of the heart

Optical techniques have revolutionized the investigation of cardiac cellular physiology and advanced our understanding of basic mechanisms of electrical activity, calcium homeostasis, and metabolism. Although optical methods are widely accepted and have been at the forefront of scientific discoveries, they have been primarily applied at cellular and subcellular levels and considerably less to whole heart organ physiology. Numerous technical difficulties had to be overcome to dynamically map physiological processes in intact hearts by optical methods. Problems of contraction artifacts, cellular heterogeneities, spatial and temporal resolution, limitations of surface images, depth-of-field, and need for large fields of view (ranging from 2x2 mm2 to 3x3 cm2) have all led to the development of new devices and optical probes to monitor physiological parameters in intact hearts. This review aims to provide a critical overview of current approaches, their contributions to the field of cardiac electrophysiology, and future directions of various optical imaging modalities as applied to cardiac physiology at organ and tissue levels.

Dynamics of virtual electrode-induced scroll-wave reentry in a 3D bidomain model

Functional reentry in the heart can be caused by a wave front of excitation rotating around its edge. Previous simulations on the basis of monodomain cable equations predicted the existence of self-sustained, vortex-like wave fronts (scroll waves) rotating around a filament in three dimensions. In our simulations, we used the more accurate bidomain model with modified Beeler-Reuter ionic kinetics to study the dynamics of scroll-wave filaments in a 16 x 8 x 1.5-mm slab of ventricular tissue with straight fibers. Wave fronts were identified as the areas with inward current. Their edges represented the filaments. Both transmural and intramural reentries with I- and U-shaped filaments, respectively, were obtained by the S1-S2 point stimulation protocol through the virtual electrode-induced phase singularity mechanism. The filaments meandered along elongated trajectories and tended to attach to the tissue boundaries exposed to air (no current flow) rather than to the bath (zero extracellular potential). They completely detached from electroporated (zero transmembrane potential) boundaries. In our simulations, the presence of the bath led to generation of only U-shaped filaments, which survived for the 1.5-mm-thick slab but not for the slabs of 0.5- or 3-mm thicknesses. Thus boundary conditions may be another determinant of the type and dynamics of reentry.

Art Winfree and the bidomain model of cardiac tissue

This paper reviews Art Winfree's contributions to the bidomain model of cardiac tissue. Specifically, he first predicted quatrefoil reentry, he showed that an S1 refractory gradient is not required for an S2 stimulus to induce reentry, and his work on spiral wave meandering led to studies on how the path of the tip of a spiral wave is influenced by tissue anisotropy.

High resolution magnetic images of planar wave fronts reveal bidomain properties of cardiac tissue

We magnetically imaged the magnetic action field and optically imaged the transmembrane potentials generated by planar wavefronts on the surface of the left ventricular wall of Langendorff-perfused isolated rabbit hearts. The magnetic action field images were used to produce a time series of two-dimensional action current maps. Overlaying epifluorescent images allowed us to identify a net current along the wavefront and perpendicular to gradients in the transmembrane potential. This is in contrast to a traditional uniform double-layer model where the net current flows along the gradient in the transmembrane potential. Our findings are supported by numerical simulations that treat cardiac tissue as a bidomain with unequal anisotropies in the intra- and extracellular spaces. Our measurements reveal the anisotropic bidomain nature of cardiac tissue during plane wave propagation. These bidomain effects play an important role in the generation of the whole-heart magnetocardiogram and cannot be ignored.

Synthesis of voltage-sensitive fluorescence signals from three-dimensional myocardial activation patterns

Voltage-sensitive fluorescent dyes are commonly used to measure cardiac electrical activity. Recent studies indicate, however, that optical action potentials (OAPs) recorded from the myocardial surface originate from a widely distributed volume beneath the surface and may contain useful information regarding intramural activation. The first step toward obtaining this information is to predict OAPs from known patterns of three-dimensional (3-D) electrical activity. To achieve this goal, we developed a two-stage model in which the output of a 3-D ionic model of electrical excitation serves as the input to an optical model of light scattering and absorption inside heart tissue. The two-stage model permits unique optical signatures to be obtained for given 3-D patterns of electrical activity for direct comparison with experimental data, thus yielding information about intramural electrical activity. To illustrate applications of the model, we simulated surface fluorescence signals produced by 3-D electrical activity during epicardial and endocardial pacing. We discovered that OAP upstroke morphology was highly sensitive to the transmural component of wave front velocity and could be used to predict wave front orientation with respect to the surface. These findings demonstrate the potential of the model for obtaining useful 3-D information about intramural propagation.

Basic mechanisms of cardiac impulse propagation and associated arrhythmias

Propagation of excitation in the heart involves action potential (AP) generation by cardiac cells and its propagation in the multicellular tissue. AP conduction is the outcome of complex interactions between cellular electrical activity, electrical cell-to-cell communication, and the cardiac tissue structure. As shown in this review, strong interactions occur among these determinants of electrical impulse propagation. A special form of conduction that underlies many cardiac arrhythmias involves circulating excitation. In this situation, the curvature of the propagating excitation wavefront and the interaction of the wavefront with the repolarization tail of the preceding wave are additional important determinants of impulse propagation. This review attempts to synthesize results from computer simulations and experimental preparations to define mechanisms and biophysical principles that govern normal and abnormal conduction in the heart.

Spatiotemporal correlation between phase singularities and wavebreaks during ventricular fibrillation

Phase Singularity and Wavebreak.

INTRODUCTION

Phase maps and the detection of phase singularities (PSs) have become a well-developed method for characterizing the organization of ventricular fibrillation (VF). How precisely PS colocalizes with wavebreak (WB) during VF, however, is unknown.

METHODS AND RESULTS

We performed optical mapping of 27 episodes of VF in nine Langendorff-perfused rabbit hearts. A WB is a point where the activation wavefront and the repolarization waveback meet. A PS is a site where its phase is ambiguous and its neighboring pixels exhibit a continuous phase progression from -pi to +pi. The correlation coefficient between the number of WBs and PSs was 0.78 +/- 0.09 for each heart and 0.81 for all VF episodes (P < 0.001), indicating a significant temporal correlation. We then superimposed the WBs and PSs for every 100 frames of each episode. These maps showed a high degree of spatial colocalization. To quantify spatial colocalization, the spatial shifts between the cumulative maps of WBs and PSs in corresponding frames were calculated by automatic alignment to obtain maximum overlap between these two maps. The spatial shifts were 0.04 +/- 0.31 mm on the x-axis and 0.06 +/- 0.27 mm on the y-axis over a 20 x 20 mm2 mapped field, indicating highly significant spatial correlation.

CONCLUSION

Phase mapping provides a convenient and robust approach to quantitatively describe wave propagation and organization during VF. The close spatiotemporal correlation between PSs and WBs establishes that PSs are a valid alternate representation of WB during VF and further validated the use of phase mapping in the study of VF dynamics.

A mathematical model for electrical stimulation of a monolayer of cardiac cells

Background

The goal of our study is to examine the effect of stimulating a two-dimensional sheet of myocardial cells. We assume that the stimulating electrode is located in a bath perfusing the tissue.

Methods

An equation governing the transmembrane potential, based on the continuity equation and Ohm's law, is solved numerically using a finite difference technique.

Results

The sheet is depolarized under the stimulating electrode and is hyperpolarized on each side of the electrode along the fiber axis.

Conclusions

The results are similar to those obtained previously by Sepulveda et al. (Biophys J, 55: 987–999, 1989) for stimulation of a two-dimensional sheet of tissue with no perfusing bath present.

Effects of Elevated Extracellular Potassium Ion Concentration on Anodal Excitation of Cardiac Tissue

INTRODUCTION

Anodal excitation of cardiac tissue occurs by two mechanisms: "make" and "break." Anodal strength-interval curves are divided into two sections, with break excitation occurring at short intervals and make at long intervals. Our goal is to determine how an elevated extracellular potassium ion concentration, [K]o, affects the mechanism of anodal excitation and influences the anodal strength-interval curve.

METHODS AND RESULTS

Computer simulations of unipolar stimulation were performed using the bidomain model, with membrane kinetics governed by the Luo-Rudy model. The diastolic threshold for anodal stimulation first decreased and then increased with increasing [K]o, reaching a minimum value at [K]o = 12 mM. The mechanism for diastolic anodal excitation was make for all [K]o values except 13.3 mM, in which case it was break. For low [K]o (4 and 8 mM) the break section of the anodal strength-interval contained a "dip," but for high [K]o (12 and 13 mM), the dip disappeared.

CONCLUSION

High [K]o predisposes cardiac tissue to break excitation, which is thought to play an important role in reentry induction and defibrillation. Because fibrillation raises extracellular [K]o levels, break excitation may play a more important role in defibrillation than is suggested by simulations and experiments using normal [K]o values.

Interaction dynamics of a pair of vortex filament rings

Vortex filament-filament interactions are believed to underlie lethal arrhythmias in cardiac tissue but their dynamics remain poorly understood. We numerically replicate an experimentally postulated reentrant filament configuration as a pair of adjacent circular filaments (scroll rings) with common symmetry axes and varying initial radii and separation distances. The interaction properties are quantified in terms of the scroll-ring lifetime T(L) and direction of initial velocity V0. Two cases were examined, differing only in the direction of the wave around the filament, and observed drastic differences in T(L) between the cases as the separation distance between the rings was decreased. We conclude that ring interactions present unexpected behaviors associated with competing interaction and decay mechanisms.

Nonlinear effects in subthreshold virtual electrode polarization

Introduction of the virtual electrode polarization (VEP) theory suggested solutions to several century-old puzzles of heart electrophysiology including explanation of the mechanisms of stimulation and defibrillation. Bidomain theory predicts that VEPs should exist at any stimulus strength. Although the presence of VEPs for strong suprathreshold pulses has been well documented, their existence at subthreshold strengths during diastole remains controversial. We studied cardiac membrane polarization produced by subthreshold stimuli in 1) rabbit ventricular muscle using high-resolution fluorescent imaging with the voltage-sensitive dye pyridinium 4-[2-[6-(dibutylamino)-2-naphthalenyl]-ethenyl]-1-(3-sulfopropyl)hydroxide (di-4-ANEPPS) and 2) an active bidomain model with Luo-Rudy ion channel kinetics. Both in vitro and in numero models show that the common dog-bone-shaped VEP is present at any stimulus strength during both systole and diastole. Diastolic subthreshold VEPs exhibited nonlinear properties that were expressed in time-dependent asymmetric reversal of membrane polarization with respect to stimulus polarity. The bidomain model reveals that this asymmetry is due to nonlinear properties of the inward rectifier potassium current. Our results suggest that active ion channel kinetics modulate the transmembrane polarization pattern that is predicted by the linear bidomain model of cardiac syncytium.

Sympathetic nerve sprouting, electrical remodeling, and increased vulnerability to ventricular fibrillation in hypercholesterolemic rabbits

Whether hypercholesterolemia (HC) can induce proarrhythmic neural and electrophysiological remodeling is unclear. We fed rabbits with either high cholesterol (HC, n=10) or standard (S, n=10) chows for 12 weeks (protocol 1), and with HC (n=12) or S (n=10) chows for 8 weeks (protocol 2). In protocol 3, 10 rabbits were fed with various protocols to observe the effects of different serum cholesterol levels. Results showed that the serum cholesterol levels were 2097+/-288 mg/dL in HC group and 59+/-9 mg/dL in S group for protocol 1 and were 1889+/-577 mg/dL in HC group and 50+/-21 mg/dL in S group for protocol 2. Density of growth-associated protein 43- (GAP43) and tyrosine hydroxylase- (TH) positive nerves in the heart was significantly higher in HC than S in protocol 1. Compared with S, HC rabbits had longer QTc intervals, more QTc dispersion, longer action potential duration, increased heterogeneity of repolarization and higher peak calcium current (ICa) density (14.0+/-3.1 versus 9.1+/-3.4 pA/pF; P<0.01) in protocol 1 and 2. Ventricular fibrillation was either induced or occurred spontaneously in 9/12 of hearts of HC group and 2/10 of hearts in S group in protocol 2. Protocol 3 showed a strong correlation between serum cholesterol level and nerve density for GAP43 (R2=0.94; P<0.001) and TH (R2=0.91; P<0.001). We conclude that HC resulted in nerve sprouting, sympathetic hyperinnervation, and increased ICa. The neural and electrophysiological remodeling was associated with prolonged action potential duration, longer QTc intervals, increased repolarization dispersion, and increased ventricular vulnerability to fibrillation.

Effects of elevated extracellular potassium on the stimulation mechanism of diastolic cardiac tissue

During cardiac disturbances such as ischemia and hyperkalemia, the extracellular potassium ion concentration is elevated. This in turn changes the resting transmembrane potential and affects the excitability of cardiac tissue. To test the hypothesis that extracellular potassium elevation also alters the stimulation mechanism, we used optical fluorescence imaging to examine the mechanism of diastolic anodal unipolar stimulation of cardiac tissue under 4 mM (normal) and 8 mM (elevated) extracellular potassium. We present several visualization methods that are useful for distinguishing between anodal-make and anodal-break excitation. In the 4-mM situation, stimulation occurred by the make, or stimulus-onset, mechanism that involved propagation out of the virtual cathodes. For 8-mM extracellular potassium, the break or stimulus termination mechanism occurred with propagation out of the virtual anode. We conclude that elevated potassium, as might occur in myocardial ischemia, alters not only stimulation threshold but also the excitation mechanism for anodal stimulation.

Use of topological charge to determine filament location and dynamics in a numerical model of scroll wave activity

The unique time course of an excitable element in cardiac tissue can be represented as the phase of its trajectory in state space. A phase singularity is defined as a spatial point where the surrounding phase values changes by a total of 2 pi, thereby forming the organizing center for a reentrant excitatory wave, a phenomenon which occurs in cardiac fibrillation. In this paper, we describe a methodology to detect the singular filament in numeric simulations of three-dimensional (3-D) scroll waves by using the concept of topological charge. Here, we use simple two-variable models of cardiac activity to construct the state space, generate the phase field, and calculate the topological charge as a summation of 3-D convolution operations. We illustrate the usage of the algorithm on the basic dynamics of vortex ring filament behavior as well as the more complex spatiotemporal behavior observed in fibrillation. We also compare the motion of filament wavetips as determined by the phase field produced by two-variable state space and single-variable, time-delay embedded state space. Finally, we examine the state spaces produced by a more complex three-variable model. We conclude that the use of state-space analysis, along with the unique properties of topological charge, allows for a novel means of filament localization.

Anode-break excitation during end-diastolic stimulation is explained by half-cell double layer discharge

The phenomenon of anodal-break excitation during end-diastolic stimulation of the heart was discovered many years ago by B. Hoffman. Yet, the existence and mechanistic explanation of this effect remain controversial. We sought to confirm its existence and to determine a possible role of half-cell potential. We used isolated Langendorff-perfused rabbit hearts (n = 6) which were stained with di-4-ANEPPS and perfused with 15-mM butanedione monoxime (BDM). Transmembrane potentials were optically recorded at the left ventricular epicardium with a high spatial and temporal resolution (200 microm/343 micros) near the tip of a 120-microm platinum-iridium Teflon-coated unipolar pacing electrode to detect virtual electrode polarization and to reconstruct an activation pattern. Hearts were paced at a cycle length of 300 ms by anodal square pulses with an amplitude of 0.1-10 mA and a duration of 5-60 ms. Data revealed that the anodal-break excitation does exists and is accompanied by an overshoot in the recordings of the pacing current. Addition of a diode in the stimulation circuit eliminated both the overshoot and the break excitation. The findings suggest that a half-cell surface potential at the pacing electrode metal-saline interface may influence the pacing currents during unipolar anodal cardiac stimulation providing "break"-like activation. We also confirmed that the threshold of "break"-like excitation is lower than make-excitation. We suggest that further exploration of this effect is needed in order to design improved multiphasic pacing waveforms.

Artifacts, assumptions, and ambiguity: Pitfalls in comparing experimental results to numerical simulations when studying electrical stimulation of the heart

Insidious experimental artifacts and invalid theoretical assumptions complicate the comparison of numerical predictions and observed data. Such difficulties are particularly troublesome when studying electrical stimulation of the heart. During unipolar stimulation of cardiac tissue, the artifacts include nonlinearity of membrane dyes, optical signals blocked by the stimulating electrode, averaging of optical signals with depth, lateral averaging of optical signals, limitations of the current source, and the use of excitation-contraction uncouplers. The assumptions involve electroporation, membrane models, electrode size, the perfusing bath, incorrect model parameters, the applicability of a continuum model, and tissue damage. Comparisons of theory and experiment during far-field stimulation are limited by many of these same factors, plus artifacts from plunge and epicardial recording electrodes and assumptions about the fiber angle at an insulating boundary. These pitfalls must be overcome in order to understand quantitatively how the heart responds to an electrical stimulus. (c) 2002 American Institute of Physics.