INTRODUCTION

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION REFERENCES

VENTRICULAR FIBRILLATION (VF) accounts for over 220,000 sudden cardiac deaths per year in the United States alone, and atrial fibrillation (AF) is a common arrhythmia afflicting as many as 5% of Americans over the age of 65 (19) and accounting for one-third of strokes in the elderly. Whereas VF episodes in high-risk patients can be aborted by implantable cardiodefibrillators, the ability to maintain sinus rhythm in patients with AF using currently available drugs is limited, such that clinical therapy is often confined to ventricular rate control and anticoagulation to prevent thromboemboli or catheter ablation to attempt cure in a select group of patients (16). Recent experimental and modeling studies in ventricular muscle suggest that dynamically induced instabilities in cardiac wave fronts, in addition to preexisting heterogeneities, can contribute to the wave break that fuels fibrillation (11, 15, 27-29, 32, 35). Electrical restitution of the action potential (AP) duration (APD) and conduction velocity (CV) in ventricular muscle has been shown to be a key factor regulating this dynamical instability. In ventricular cell models, spiral reentry quickly breaks up into a complex multiple spiral VF-like state if the slope of APD restitution curve is steep (>1) over a sufficiently wide range of diastolic intervals (DI). If this range of DIs is narrowed, the spiral wave remains intact but still hypermeanders chaotically. Only when the slope of APD restitution is <1 everywhere does the spiral wave stabilize to quasiperiodic meander or stationary behavior (11, 27, 28). This type of wave break arises solely from the dynamics of cardiac propagation and is related to steep APD restitution causing oscillations in wavelength before localized wave break (28), without any requirement for fixed heterogeneities in the tissue.

In atrial tissue, the effects of electrical restitution on the dynamical instability of atrial wave fronts have not been characterized and should not be assumed to essential for wave break-perpetuating fibrillation for several reasons. First, the atrium has a complex geometry, including the atrial appendages, the pectinate muscle network, fossa ovalis, and specialized tissues such as the crista terminalis and Bachmann's bundle as well as multiple orifices for veins, arteries, and valves (14). Recent modeling using simplified approximations to structures such as the pectinate muscles and crista terminalis have shown that these anatomic structures may support AF initiation and maintenance (8, 12, 34). Second, atrial tissue displays substantial regional electrophysiological heterogeneity in AP morphology, degree of anisotropy (such as the crista terminalis), and CV (with slow conduction at the inferior vena cava/tricuspid isthmus and perisinus nodal and atrioventricular nodal regions). The atrial AP has a complex morphology and, depending on heart rate and other factors, can show a spike-and-dome appearance, a triangular shape with no sustained plateau, or ventricular-like AP plateau (10, 30). These features may create substantial dispersion of refractoriness (10), which, coupled with slow conduction, provides a substrate for wave break and reentry. Over four decades ago, modeling studies (21) showed how such preexisting electrophysiological heterogeneities such as dispersion of refractoriness could promote AF. Finally, the electrophysiological and structural properties of the atrium become significantly remodeled by the process of AF itself (1, 4, 6, 7, 13, 22, 33), including increased effective refractory period (ERP) heterogeneity (9), so that AF is likely to become chronic if it persists for more than several weeks.

The purpose of this simulation study was to investigate the role of electrical restitution on wave front stability, emphasizing simulated atrial tissue using a realistic physiological human atrial cell model. Two detailed mathematical models of the human atrial AP, both incorporating intracellular Ca²⁺ dynamics as well as ionic currents, have been published, by Courtemanche et al. (3) and by Nygren et al. (23). Although based on comparably rigorous experimental data, the two models have different AP shapes and electrophysiological properties, and thus may be relevant to different regions of the human atrium. The detailed comparison of ionic properties in both the Nygren model and Courtemanche model can be found in Ref. 24. In simulated two-dimensional (2-D) homogeneous tissue, a spiral wave initiated using the Nygren model remains intact, whereas in the Courtemanche model the spiral wave breaks up (24). Because one focus of this study was to examine whether modifying atrial electrical restitution can increase wave stability, we choose the Courtemanche model as our single cell model. Also, because the complex morphology of the atrial AP makes APD measurement more equivocal than in the ventricle, we examined whether ERP restitution could be used as a substitute for APD restitution in atrial as well as ventricular tissue.

Glossary

2-D	Two-dimensional
3-D	Three-dimensional
tmax	Maximum time step
tmin	Minimum time step
y	Time constant of a given gating variable
AF	Atrial fibrillation
AP	Action potential
APD	Action potential duration
APD50	Time from onset of depolarization until the cell repolarizes to 50% repolarization
APD90	Time from onset of depolarization until the cell repolarizes to 90% repolarization
APD32 mV	Portion of the cardiac cycle during which V  32 mV
APD62 mV	Portion of the cariac cycle during which V  62 mV
Cm	Total capacitance
CL	Cycle length
CV	Conduction velocity
[Ca2+]i	Intracellular Ca2+ concentration
D	Isotropic diffusion coefficient
DI	Diastolic interval
E	Equilibrium potential of a given ionic channel
ECG	Electrocardiogram
ERP	Effective refractory period
f	Gating variable
fCa	Gating variable
F	Faraday's constant
g	Conductance of a given ionic channel
Gsi	Maximum conductance of L-type Ca2+ channel
h	Gating variable
ICa,b	Ca2+ background current
ICa,L	Slow inward L-type Ca2+ current
Iion	Total ionic current
IK1	Time-independent K+ current
IKr	Rapid delayed outward K+ current
IKs	Slow delayed outward K+ current
IKur	Ultrarapid delayed outward K+ current
INa	Fast inward Na+ current
INa,b	Na+ background current
INaCa	Na+/Ca2+ exchanger current
INaK	Na+-K+ pump current
IpCa	Sarcolemmal Ca2+ pump current
Istim	Stimulus current
Ito	Transient outward K+ current
j	Gating variable
JSR	Junctional sarcoplasmic reticulum
[K+]i	Intracellular K+ concentration
LR1	Phase 1 of the Luo-Rudy model
m	Gating variable
n	Number
NSR	Nonjunctional sarcoplasmic reticulum
[Na+]i	Intracellular Na+ concentration
Oa	Gating variable
Oi	Gating variable
PCL	Pacing cycle length
PDE	Partial differential equation
R	Gas constant
SR	Sarcoplasmic reticulum
t	Time
T	Temperature
Ua	Gating variable
Ui	Gating variable
V	Transmembrance potential
VF	Ventricular fibrillation
X	Na+, K+, or Ca2+
Xr	Gating variable
Xs	Gating variable
[X]i	Intracellular concentration of Na+, K+, or Ca2+
[X]o	Extracellular concentration of Na+, K+, or Ca2+
y	A given gating variable
y	Steady state of a given gating variable
z	Equal to 1, 1, or 2 for Na+, K+, or Ca2+, respectively

	METHODS

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION REFERENCES

Human atrial model. Cardiac cells are resistively connected by gap junctions between cells. Ignoring the detailed structure of real tissue, we consider a homogeneous continuous conduction model in which

(1)

where V is the transmembrane potential, C_m is the total capacitance, and D is the isotropic diffusion coefficient determined by gap junction resistance, surface-to-volume ratio, and membrane capacitance. Here we use C_m = 100 pF and D = 0.001 cm²/ms. I_ion is the total ionic current from the Courtemanche model (3), which is given by

(2)

where I_Na = g_Nam³hj(V  E_Na) and is the fast inward Na⁺ current; I_Ca,L = g_Ca,Ldff_Ca(V  65) and is the slow inward L-type Ca²⁺ current; I_Kr = g_KrX_r(V  E_K)/1 + exp[(V + 15)/22.4] and is the rapid delayed outward K⁺ current; I_Ks = g_KsX(V  E_K) and is the slow delayed outward K⁺ current; I_to = g_toOO_i(V  E_K) and is the transient outward K⁺ current; I_Kur = 0.005 + 0.05/{1 + exp[(V  15)/13]} and is the ultrarapid delayed outward K⁺ current; and I_K1 = g_K1(V  E_K)/{1 + exp[0.07(V + 80)]} and is the time-independent K⁺ current. The ionic gating variables m, h, j, d, f, f_Ca, X_r, X_s, O_a, O_i, U_a, and U_i are all governed by Hodgkin-Huxley-type differential equations

(3)

where y represents the appropriate gating variable. The detailed formulations of the ionic exchange currents, background currents, and their gating constants can be found in Courtemanche et al. (3). The driving force for E_Na, E_Ca, and E_K all have the formulation E_X = (RT/zF)[log ([X]_o/[X]_i)], where [X]_o and [X]_i are the extracellular and intracellular concentrations for X = Na⁺, K⁺, or Ca²⁺ and z = 1, 1, or 2 for Na⁺, K⁺, or Ca²⁺, respectively.

Computer simulations. Numerical simulations were performed in the isolated cell, one-dimensional (1-D) cable, and 2-D tissue. To simulate a single cell, we integrated the following ordinary differential equation

(4)

where I_stim is the external stimulus current. We used a square wave stimulus (29 pA/pF × 2 ms) at a constant frequency. We used a fourth-order Runge-Kutta method to integrate Eq. 4 with a fixed time step = 0.01 ms.

(5)

Electrophysiological measurements. APD restitution refers to the relationship between APD and the previous DI. In standard terminology, APD₅₀ and APD₉₀ are the times from the onset of depolarization until the cell repolarizes to 50% and 90% of the full AP amplitude, respectively. In this modeling study, we used a voltage threshold crossing method to measure APD, approximating APD₉₀ with APD_{62 mV}, defined as the portion of the cardiac cycle (in ms) during which V  62 mV, and DI as the portion during which V   62 mV. APD₅₀ was analogously approximated by APD_{32 mV}, using 32 mV as the voltage threshold. APD_{62 mV} and APD_{32 mV} yielded values close to the true APD₉₀ and APD₅₀ values. APD_{62 mV} and APD_{32 mV} were measured in both single cells and 1-D tissue using an S1S2 pacing protocol in which a premature S2 stimulus scanning diastole was delivered after pacing with an S1 stimulus for 200 beats at a given CL. The pacing site for the 1-D cable simulations was located at the left boundary of the cable, and the recording site was located 1 cm away. CV restitution is defined as the relation between the propagated speed of the S2 AP and the corresponding DI.

	RESULTS

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION REFERENCES

APD restitution in the single cell. Under control conditions with parameters set to their original values (3), Fig. 1A shows that the Courtemanche human atrial model had a resting membrane potential near 81 mV and diastolic [Ca²⁺]_i  0.1 µM. AP shape and APD varied with the PCL, with a more prominent "spike-and-dome" appearance to the plateau at longer PCLs. APD_{62 mV} was similar (264 ms) at PCLs of 1,000 and 600 ms, but shortened to 242 ms at a PCL of 400 ms. The 400 ms PCL was also associated with mild resting membrane potential depolarization, a modest increase in diastolic [Ca²⁺]_i, and a decrease in peak systolic [Ca²⁺]_i.

View larger version (22K): [in this window] [in a new window]   Fig. 1.   Effect of PCL on the atrial AP (left) and [Ca2+]i (right) in the single cell atrial model. PCLs are 1,000 ms (dashed-dotted line), 600 ms (dashed line), and 400 ms (solid line). A: control; B: ICa,L blocked by 65%; C: ICa,L blocked by 90%. See Glossary for abbreviations.

62 mV

32 mV

62 mV

32 mV

32 mV

62 mV

32 mV

View larger version (19K): [in this window] [in a new window]   Fig. 2.   Single cell APD restitution as a function of PCL. A: S1S2 protocol for measuring APD restitution. APs are superimposed as the S1S2 coupling interval is progressively shortened. B and C: APD62 mV (left) and APD32 mV (right) of the S2 beats versus the DI, showing APD restitution curves for PCL = 400 ms (solid line), 600 ms (dashed line), and 1,000 ms (dashed-dotted line) for the control case (B) and with ICa,L blocked by 90% (C), respectively. For reference, the dotted line indicates a slope of 1. See Glossary for abbreviations.

62 mV

32 mV

62 mV

32 mV

View larger version (22K): [in this window] [in a new window]   Fig. 3.   Superimposed APs (A) and intracellular Ca2+ transients (B) of the the last S1 beat and the S2 beat delivered at an S1S2 coupling interval of 500 ms for three different PCLs: 400 ms (solid line), 600 ms (dashed line), and 1,000 ms (dashed-dotted line). See Glossary for abbreviations.

APD and CV restitution in 1-D tissue. In cardiac tissue, coupling of myocytes to neighboring cells generates diffusive currents that affect APD restitution and other electrophysiological properties. In addition, CV restitution is an important determinant of wave stability (26, 31) and cannot be measured in a single cell. To address these issues, we paced a 1-D cable (equivalent to a planar wave in 2-D or 3-D) and scanned diastole with premature S2 beats. APD restitution and CV restitution were measured 1 cm from the pacing site by plotting APD and local CV as functions of DI (see METHODS).

62 mV

32 mV

62 mV

32 mV

62 mV

32 mV

32 mV

62 mV

View larger version (23K): [in this window] [in a new window]   Fig. 4.   APD32 mV (left), APD62 mV (middle), and ERP (right) restitution curves at different PCLs (400, 600, and 1,000 ms) obtained in a one-dimensional cable of cells using the S1S2 method under the following conditions. A: control; B: ICa,L blocked by 46%; C: ICa,L blocked by 65%; D: ICa,L blocked by 65% and IKs and IKr increased ninefold. Dotted line, reference line with slope of 1. See Glossary for abbreviations.

View larger version (14K): [in this window] [in a new window]   Fig. 5.   Corresponding CV restitution curves for the same parameters as in Fig. 4. See Fig. 4 legend for details. See Glossary for abbreviations.

ERP restitution versus APD restitution. The APD_{32 mV} and APD_{62 mV} restitution curves in Figs. 2 and 4 had markedly different shapes and slopes, making the characterization of the APD restitution slope highly dependent on the repolarization level used to define APD. This ambiguity arose largely because PCL and premature stimuli had complex effects on the spike-and-dome morphology of the atrial AP plateau, which affects APD_{32 mV} to a greater extent than APD_{62 mV}. To develop a more consistent criterion for atrial restitution steepness, we examined ERP restitution, because wave break in fibrillation results directly from wave fronts encountering still-refractory tissue. ERP restitution was measured using an S1S2S3 protocol (see METHODS) and correlated with both APD restitution and spiral wave stability.

32 mV

62 mV

62 mV

View larger version (42K): [in this window] [in a new window]   Fig. 6.   Correlation of APD32 mV, APD62 mV, and ERP restitution with spiral wave behavior in simulated 2-D ventricular tissue using the LR1 ventricular cell model. Gsi was increased from 0 to 0.065 as indicated to progressively steep the slope of APD and ERP restitution, with Na = 23, K = 0.705, K1 = 0.6047, and other parameters at their original values. A: APD32 mV (dashed line) and APD62 mV (solid line) restitution curves; B: ERP restitution; C: gray scale (white = depolarized; black = repolarized) snapshots of membrane voltage 2 s after initiation of a spiral wave by cross-field stimulation in homogeneous isotropic 2-D tissue. The trajectory of the spiral wave tip is shown on the right. As the slopes of APD32 mV, APD62 mV, and ERP restitution become progressively steeper, spiral wave behavior transitions from nearly stable (first row), to quasiperiodically meander (second row), to chaotic hypermeander (third row), to spontaneous breakup (fourth row). See Glossary for abbreviations.

62 mV

32 mV

Spiral reentry behavior in 2-D atrial tissue and correlation with electrical restitution. For the control parameter settings of the Courtemanche model, a spiral wave initiated with cross-field stimulation spontaneously broke up into multiple spiral waves that were self-sustaining provided that the 2-D tissue exceeded a critical size (Fig. 7C). For tissue sizes smaller than the critical size, breakup either did not occur, or occurred transiently, with the tissue eventually becoming quiescent (Fig. 7, A and B). The critical tissue size was ~16.5 × 16.5 cm², which was obtained empirically by numerical simulation. For 10 × 10- and 15 × 15-cm² tissues (Fig. 7, A and B), the spiral wave tip moved irregularly toward the boundary before the first wave break occurred and disappeared from the boundary, terminating reentry. In these two cases, the tissue became quiescent after 5 and 8 s, respectively, with the exact duration depending strongly on the conditions used to initiate the spiral wave. Although no wave break occurred in Fig. 7, A and B, the contours of both the wave back and wave front were irregular, reflecting their dynamical instability. For 20 × 20-cm² tissue (Fig. 7C), the initiated spiral wave broke into complex multiple wavelets after several seconds, which were sustained throughout the 25-s simulation.

View larger version (47K): [in this window] [in a new window]   Fig. 7.   Spiral reentry in simulated homogeneous isotropic 2-D atrial tissue for control parameter settings of the Courtemanche atrial cell model. Gray scale (white = depolarized; black = repolarized) snapshots of membrane voltage at the times indicated after initiation of the spiral wave by cross-field stimulation are shown. A-C: tissue size of 10 × 10 cm2 (A), 15 × 15 cm2 (B), and 20 × 20 cm2 (C). Only in C does the tissue size exceed the critical mass required to sustain a fibrillation-like state. See Glossary for abbreviations.

View larger version (68K): [in this window] [in a new window]   Fig. 8.   Spiral wave behavior in simulated 2-D homogeneous isotropic tissue, corresponding to the APD32 mV, APD62 mV, and ERP restitution curves in Fig. 4, A-D. Left, gray scale (white = depolarized; black = repolarized) snapshots of membrane voltage at the times indicated after initiation of the spiral wave by cross-field stimulation. Right, trajectories of the spiral tip and the pseudo-ECGs. A: control case, showing spiral wave breakup; B: ICa,L blocked by 46%, showing chaotic hypermeander; C: ICa,L blocked by 65%, showing quasiperiodic meander; D: ICa,L blocked by 65% and IKs and IKr increased ninefold, showing a completely stable spiral wave. The tissue sizes (20 × 20 cm2 in A, 10 × 10 cm2 in B, and 5 × 5 cm2 in C and D) exceeded the critical sizes required for sustained reentry for the parameter settings in each case. See Glossary for abbreviations.

62 mV

62 mV

62 mV

62 mV

	DISCUSSION

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION REFERENCES

In this study, we investigated the role of electrical restitution on spiral wave stability in simulated homogeneous atrial and ventricular 2-D tissue using the Courtemanche atrial model and the Luo-Rudy phase 1 ventricular AP model, respectively. Our major conclusions can be summarized as follows. First, in the physiologically detailed (including intracellular Ca²⁺ dynamics) Courtemanche atrial AP model, APD restitution curves are qualitatively as well as quantitatively sensitive to the level of repolarization used to define APD. This arises primarily from the complex rate sensitivity of the spike-and-dome configuration of the atrial AP plateau and effects of the intracellular Ca²⁺ transient on ionic currents affecting the APD. These factors tend to have larger effects on APD_{32 mV} (~APD₅₀) than on APD_{62 mV} (~APD₉₀), which leads to ambiguities in attempting to correlate APD restitution slope with spiral wave behavior. In addition, considerable regional variations in atrial AP morphology, particularly with respect to the spike-and-dome feature, are likely to add further site-dependent variability to atrial APD restitution measurements. ERP restitution and CV restitution in atrial tissue, however, can be characterized with similar reliability as in ventricular tissue. Second, to circumvent ambiguities in atrial APD restitution, we reasoned that wave breaks that promote fibrillation occur primarily when waves encounter areas of increased refractoriness. Thus ERP restitution slope might be an equivalent or superior measure of dynamic wave stability than APD restitution slope. We validated this concept first in ventricular tissue using the Luo-Rudy guinea pig ventricular AP model and then applied the same test to atrial tissue. We found that ERP restitution slope correlated better with APD_{62 mV} restitution than with APD_{32 mV} restitution and was highly predictive of spiral wave behavior. For the tissue with steep ERP restitution slope (>1), an initiated spiral wave either broke up or exhibited chaotically hypermeandering tip motion, depending on the range of DIs with ERP restitution slope >1. When ERP restitution slope was flat (<1 for all DIs), a single spiral wave remained intact with either quasiperiodic meandering or stable tip motion, as we and others have previously reported for APD₉₀ restitution in ventricular AP models (15, 27). These findings support the general validity of ERP restitution slope as a measure of dynamic wave stability in both ventricular and atrial tissue. A caveat, however, is that in our study, we modulated ERP slope specifically by altering I_Ca,L, I_Kr, and I_Ks. Similar effects on ERP restitution steepness can be achieved by modifying other combinations of different currents, and we did not directly demonstrate their equivalence with respect to spiral wave behavior. However, previous simulation studies have demonstrated that APD restitution slope is a robust global system parameter controlling spiral wave stability, i.e., that the manipulations of specific ionic currents used to alter restitution slope are not critically important, only their net effect on restitution slope (28). This has been demonstrated in a wide variety of models, ranging from simple phenomenological two- and three-variable models, such as the Karma models (15), to intermediate models, such as the Beeler-Reuter model (5), to physiologically detailed models, such as the various Luo-Rudy versions (18).

The advantage of using ERP restitution in place of APD restitution is that ambiguities about restitution slope arising from effects of the level of repolarization chosen to define APD are eliminated. This is important not only in the atrium, but also potentially in regions of ventricle exhibiting spike-and-dome AP morphology, such as the epicardium. In addition, ERP restitution can be obtained using extracellular pacing/recording electrodes, without an absolute need for accurate measurement of the transmembrane AP by microelectrode, optical dye, or monophasic AP recording techniques. This should facilitate electrical restitution measurements in clinical studies, in which the monophasic AP catheter is the only option for measuring APD restitution and is more cumbersome than extracellular electrogram recordings. Although the DI cannot be measured directly from extracellular electrograms, it can be readily estimated from the ERP during the basic S1 pacing (i.e., the ERP of the S2 beat). On the other hand, a disadvantage of ERP restitution is that it requires a pacing intervention (the S3 beat) at each site at which ERP is to be measured, making high resolution spatial mapping of electrical restitution impractical and inferior to optical mapping of APD restitution in the experimental setting. We are currently investigating whether the need for the S3 beat can be eliminated by using activation-recovery intervals to estimate local ERP (20).

There are several limitations in this modeling study. First, we modified I_Ca,L, I_Ks, and I_Kr to produce altered ERP restitution slopes and spiral wave behaviors without a primary consideration of whether these interventions had existing physiological counterparts. In principle, however, similar changes could be reproduced experimentally by drugs (which may not exist currently but potentially could be developed), because they all involved modulating simulated real ionic currents. Second, to achieve sustained spiral reentry for the control case, we also had to use a larger tissue size than the realistic atrium. However, this is consistent with the observation that when AF is induced in the normal atrium, it is typically nonsustained. Third, APD, ERP, and CV restitution are not unique relationships, but depend on factors such as wave front curvature and memory. Thus electrical restitution experienced by wave fronts during fibrillation may be different from electrical restitution properties measured by extrastimulus or rapid pacing methods. Although electrical restitution measured by the extrastimulus method is only an approximation of that during fibrillation, our findings substantiate that from a practical standpoint the relationship is close enough to provide useful information for assessing wave stability. This is illustrated in Table 1, which demonstrates if the range of DIs visited during spiral wave reentry corresponded to the range of DIs with APD restitution slope >1, the spiral wave reentry was unstable (i.e., in the hypermeander or breakup regimes).

A fourth limitation of this study relates to tissue characteristics. To maximize computational efficiency, we used the minimum tissue size required to support sustained reentry, which varied for different spiral wave phenotypes. In this model, however, we substantiated that increasing tissue size beyond the minimum size did not change the spiral wave phenotype, suggesting that the primary role of tissue borders was to extinguish wave fronts rather than create new ones. Below the critical size, the phenotype was also the same, but reentry was nonsustained, consistent with the critical mass hypothesis validated in experimental studies (17). In addition, to isolate dynamically induced effects of electrical restitution on wave stability from the effects of preexisting heterogeneities, we simulated 2-D homogeneous atrial and ventricular tissue rather than 3-D heterogeneous tissue. It is well known that preexisting electrophysiological/anatomic features in 3-D tissue, such as tissue anisotropy, fiber rotation, and complex anatomic structures, affect the stability of the spiral wave reentry (8, 12, 14, 34). In addition, the atrial AP varies substantially from region to region, producing preexisting dispersion of refractoriness affecting spiral wave stability (10, 30). Although our findings indicate that electrical restitution in the atrium is a potentially important determinant of wave stability, they do not address the relative importance of restitution-based wave break compared with heterogeneity-based wave break in AF. At the present time, the role of restitution-based wave break in the maintenance of AF remains controversial, with some investigators believing that wavebreak is an epiphenomenon (2) rather than the engine of fibrillation, as proposed in the original multiple wavelet hypothesis (21). If wave break is the engine of AF, however, our previous modeling work (35) has documented a synergistic relationship between electrical restitution parameters and preexisting tissue heterogeneity in promoting wave break. Specifically, we found that for a given level of preexisting electrophysiological/anatomic heterogeneity, wave break was more easily induced as restitution-based dynamic instability increased. Together, these observations suggest that reducing dynamic instability by flattening APD or ERP restitution may have therapeutic potential for preventing AF and VF. This strategy will need to be tested in future studies using realistic heterogeneous models of atrial and ventricular tissue and then validated in experimental AF and VF models.