Published online before print March 28, 2002, doi: 10.1161/01.RES.0000016960.61087.86
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© 2002 American Heart Association, Inc.
Cellular Biology |
Ionic Current Basis of Electrocardiographic Waveforms
A Model Study
From the Cardiac Bioelectricity Research and Training Center, Department of Biomedical Engineering, Case Western Reserve University, Cleveland, Ohio.
Correspondence to Dr Yoram Rudy, Director, Cardiac Bioelectricity Research and Training Center, 509 Wickenden Bldg, Case Western Reserve University, Cleveland, OH 44106-7207. E-mail yxr{at}po.cwru.edu
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Abstract |
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Body surface electrocardiograms and electrograms recorded from the surfaces of the heart are the basis for diagnosis and treatment of cardiac electrophysiological disorders and arrhythmias. Given recent advances in understanding the molecular mechanisms of arrhythmia, it is important to relate these electrocardiographic waveforms to cellular electrophysiological processes. This modeling study establishes the following principles: (1) voltage gradients created by heterogeneities of the slow-delayed rectifier (IKs) and transient outward (Ito) potassium current inscribe the T wave and J wave, respectively; T-wave polarity and width are strongly influenced by the degree of intercellular coupling through gap-junctions. (2) Changes in [K+]o modulate the T wave through their effect on the rapid-delayed rectifier, IKr. (3) Alterations of IKs, IKr, and INa (fast sodium current) in long-QT syndrome (LQT1, LQT2, and LQT3, respectively) are reflected in characteristic QT-interval and T-wave changes; LQT1 prolongs QT without widening the T wave. (4) Accelerated inactivation of INa on the background of large epicardial Ito results in ST elevation (Brugada phenotype) that reflects the degree of severity. (5) Activation of the ATP-sensitive potassium current, IK(ATP), is sufficient to cause ST elevation during acute ischemia. These principles provide a mechanistic cellular basis for interpretation of electrocardiographic waveforms.
Key Words: electrocardiography • mathematical modeling • long-QT syndrome • Brugada syndrome • ischemia
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Introduction |
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TopAbstractIntroductionMaterials and MethodsResultsDiscussionReferences |
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Body surface electrocardiograms and electrograms recorded from the surfaces of the heart provide information for diagnosis and treatment of cardiac electrophysiological disorders and resulting arrhythmias. In recent years, major advances were made in understanding the molecular and cellular mechanisms of cardiac arrhythmias. Yet, the interpretation of electrocardiographic waveforms remains mostly empirical. It is important, therefore, to establish a mechanistic relationship between the cellular processes and the ECG, so that specific diagnosis of electrophysiological disorders can be made. A pioneering effort in this direction has been the experimental work of Antzelevitch and colleagues,1–4 who used a transmural ventricular wedge preparation to relate electrocardiographic waveforms to the action potential (AP) under a variety of conditions. In this article, we use a theoretical modeling approach to establish the cellular and ion channel basis of ECG waveforms. We use a detailed, physiologically-based model of the ventricular cardiac cell that includes all important ion channels, pumps, and exchangers, and accounts for dynamic concentration changes of Na+, Ca2+, and K+ during the AP. With this model, it is possible to relate ECG patterns to individual membrane ionic currents and AP properties in a deterministic and specific manner. We establish the principles that determine specific morphological properties of electrocardiographic waveforms and provide examples from the long-QT (LQT) syndrome, Brugada syndrome, and acute ischemia.
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Materials and Methods |
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AP propagation was reconstructed as described previously5 in a 1-dimensional fiber of Luo-Rudy dynamic (LRd) model cells.6–9 This reconstruction represents the broad planar wavefront that propagates from endocardium to epicardium during normal ventricular excitation10 resulting from Purkinje network participation. The model also represents AP propagation in the arterially perfused transmural wedge preparation, used by Antzelevitch and colleagues in experimental studies of ECG waveforms.1–4 The fiber formulation takes into account heterogeneities of ion channel expression,8,11 with additional modifications described in the following section. The source program code (in C++) for a single LRd model cell can be downloaded from http://www.cwru.edu/med/CBRTC.
Multicellular 1-Dimensional Fiber Model
The theoretical fiber, of length 1.65 cm, is composed of 165 LRd model cells connected through gap junctions. Transmural heterogeneities of ion channel densities are introduced to represent the 3 ventricular cell types: endocardial (cells 1 to 60), midmyocardial (M cells, cells 61 to 105), and epicardial (cells 106 to 165). Density of IKs (slow-delayed rectifier potassium current) is varied as described previously,8,11 with the lowest in the M cells (density ratios between the slow- and rapid-delayed rectifiers are IKs:IKr=11:1 endocardial, 4:1 midmyocardial, 35:1 epicardial). The transient outward potassium current (Ito) is introduced in epicardial and M cells after the formulation of Dumaine et al.12 The maximum conductance of Ito is set to 0.2125 mS/µF, and 0.25 mS/µF in M and epicardial cells, respectively. Ito is not expressed in endocardial cells.
Gap junction conductance (gj) is homogeneous throughout the fiber, except for a 5-fold decrease at the M-to-epicardium transition region (cells 104 to 107).1 Unless otherwise specified, gj=1.73 µS, resulting in a conduction velocity of 44 cm/s, which is comparable to the average velocity of 44 cm/s recorded in vivo and across the arterially perfused transmural wedge preparation (average thickness of 1.29±0.15 cm).1 A 0.5-ms suprathreshold current stimulus is applied to cell 1 to initiate AP propagation from endocardium to epicardium. To minimize stimulus and end effects, which are restricted to one space constant (about 9 cells),5 only cells 16 to 150 are included in potential computations.
Extracellular Potential
Extracellular unipolar potentials (
e) generated by the fiber in an extensive medium of conductivity 
e, are computed from the transmembrane potential Vm using the following integral expression13
:
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where 
Vm is the spatial gradient of Vm, a is the radius of the fiber, i is the intracellular conductivity, and r is the distance from a source point (x,y,z) to a field point (x',y',z'). e, computed at an "electrode" site 2.0 cm away from the epicardium along the fiber axis, constitutes the presented ECG waveforms.
Protocols
For all simulations, unless specified otherwise, extracellular ionic concentrations are [Na+]o=150 mmol/L, [K+]o=4 mmol/L, and [Ca2+]o= 1.8 mmol/L. Intracellular concentrations are [Na+]i=14.603 mmol/L, [K+]i=140.516 mmol/L, and [Ca2+]i=0.08278 µmol/L at rest and vary dynamically during the AP. The fiber is at resting steady-state before a stimulus is applied. Action potential duration (APD) is measured as the time interval between the occurrence of maximum dVm/dt and 90% repolarization. End of the T wave is determined from the baseline intersection of a linear fit to the steepest portion of the T wave after its peak. All simulations correspond to a temperature of 37°C.
Long-QT and Brugada Syndromes
As described previously,14 LQT syndromes are simulated by reducing the membrane conductance of IKs (LQT1), of IKr (LQT2), or by altering the steady-state inactivation of the fast sodium current INa to generate a late (persistent) current during the AP plateau (LQT3).14,15 The Brugada syndrome is simulated by increasing the rate of fast inactivation of INa, as described by Dumaine et al.12
Acute Myocardial Ischemia
The major change of AP morphology during acute ischemia is caused by activation of the normally dormant ATP-sensitive potassium current, IK(ATP).16 To simulate the associated ECG changes, we incorporate IK(ATP) into the model using the formulation derived previously.16 Greater sensitivity of IK(ATP) to ATP changes in the epicardium17 is accounted for by decreasing the half-maximal saturation point, k0.5, of channel activity of endocardial cells by 75% and of M cells by 50%.
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Results |
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Effects of IKs and Ito Heterogeneities on AP Morphology and ECG Waveforms
Figure 1 relates normal (physiological) transmural AP heterogeneities and their underlying ionic currents to the ECG waveforms. In the normal myocardium, IKr is uniformly distributed across the ventricular wall, IKs density is much lower in the midmyocardium than in either the epicardium or the endocardium, and Ito density increases from endocardium to epicardium. This situation is shown in Figure 1, left column (control), where the small IKs of M cells results in longer APD (APDM=187 ms and APDEpi=148 ms), and Ito produces a notch in the AP during the early repolarization phase (phase 1) in the epicardial and M cells (arrows). Complete repolarization of the epicardium corresponds to the peak of the T wave, whereas repolarization of the midmyocardium corresponds to the end of the T wave. These results are consistent with corresponding experimental observations in the arterially perfused wedge preparation.1–4 Despite the opposite polarity of depolarization and repolarization, the QRS and T wave are both positive (upright). This is because the spatial Vm gradient (
Vm in Equation 1 is determined by the intrinsic APD heterogeneity with only minor modulation by the sequence of activation, because conduction time between inhomogeneous regions (eg, M to epicardium) is small compared with the intrinsic APD differences. Because the transmural APD heterogeneity reflects mostly the heterogeneity of IKs expression, it can be hypothesized that IKs plays a major role in determining the T-wave morphology. To verify this hypothesis (Figure 1, middle column), IKs density in the entire fiber is set equal to the endocardial IKs density under control conditions. For such homogeneous conditions, the sequence of repolarization follows the sequence of activation with the epicardium (rather than midmyocardium) repolarizing last and determining the end of the T wave. This inversion of the repolarization sequence relative to control results in an inversion of the transmural Vm and, therefore, in an inversion of the T wave.
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Figure 1, right column, explores the ionic basis of the J wave (Osborn wave) that appears after the QRS complex. The J wave, present under control conditions, coincides with the notch in the epicardial AP. When Ito, which underlies the notch, is not included in the model (gray traces), the AP notch and J wave disappear, identifying Ito as the ionic current generating the J wave. In the presence of Ito, when the sequence of activation is reversed (epicardial rather than endocardial stimulation), the epicardial AP notch occurs at the time of midmyocardial activation and the J wave is masked by the QRS (not shown). These results are consistent with experimental observations.18
Effects of Varying the Degree of Cell-to-Cell Coupling
Figure 2 examines the effects of varying the degree of intercellular coupling on the ECG. Three degrees of gap-junction coupling are modeled: enhanced (gj=17.3 µS, left), control (gj=1.73 µS, middle), and reduced (gj=0.192 µS, right). A gap junction conductance of 1.73 µS (control) results in propagation velocity of 44 cm/s and conduction time of 30 ms that are in close agreement with the experimental observations of Yan et al1 (44 cm/s and 29.3±1 ms, respectively). The transmural dispersion of repolarization (TDR) is 23 ms (TDR is defined as the interval between the earliest and latest AP repolarization times and can be approximated by the interval between the peak and the end of the T wave).
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Enhanced cell-to-cell communication increases conduction velocity to 69 cm/s and decreases the conduction time across the fiber (conduction time=20 ms) as reflected in the narrow QRS in Figure 2, left column. The short conduction time reduces the effect of the activation sequence on repolarization gradients. The T-wave morphology, therefore, reflects primarily the effect of the intrinsic transmural AP heterogeneity and its orientation is upright (positive) as under conditions of control coupling. Enhanced electrotonic interaction between the well-coupled cells acts to reduce APD differences. This, together with the short transmural conduction time, reduces TDR to 19 ms.
Decreased coupling (gj=0.192 µS) decreases velocity to 14 cm/s and prolongs transmural conduction time to 95 ms (reflected in widening of the QRS). Consequently, the activation sequence rather than intrinsic APD heterogeneities determines the sequence of repolarization and the direction of Vm is reversed compared with control, resulting in an inverted T wave. APD dispersion is increased (TDR=39 ms).
Effects of Changes in Extracellular Potassium Concentration
Figure 3 illustrates the effects of changes in extracellular potassium concentration, [K+]o, on the ECG waveform. [K+]o affects repolarization mostly through its effect on IKr conductance (conductance is proportional to ([K+]o)1/2).7 At [K+]o=2 mmol/L, IKr is reduced relative to control ([K+]o=4 mmol/L). This reduction in repolarizing IKr causes APD prolongation in all cell types. However, the effect is quantitatively greater in M cells, where IKs is small, because the IKr change constitutes a greater percent change of the total repolarizing current (principally, IKr and IKs) in these cells.8 This results in prolongation of the QT interval (QTControl=196 ms and QTHypokalemia=236 ms) and flattening of the T wave relative to control (maximum T-wave amplitude is 0.33 mV and 0.26 mV for control and hypokalemia, respectively), in agreement with experimental2 and clinical observations.19,20 High [K+]o (occurring clinically during acute ischemia16) has an opposite effect. At [K+]o=6 mmol/L, the QT interval (177 ms) is abbreviated, reflecting a shorter epicardial APD, and the T-wave amplitude is accentuated (greater Vm) relative to control (T-wave amplitude: control=0.33 mV and hyperkalemia=0.4 mV). These morphological alterations are observed experimentally as well.2 With respect to control, [K+]o=6 mmol/L results in a slightly narrower QRS, reflecting an increased velocity ("supernormal conduction").21 At higher levels of hyperkalemia, velocity is decreased21 and the QRS is widened (not shown). It should be noted that conductance of IK1, the inward rectifier current, is also proportional to ([K+]o)1/2. However, IK1 has a small effect on the time course of AP repolarization and its modulation by [K+]o changes does not affect the ECG waveform significantly.
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Effects of Ion Channel Mutations: LQT and Brugada Syndromes
Figure 4 shows computed ECG changes caused by 3 types of the LQT syndrome. Reducing IKs or IKr models LQT1 and LQT2, respectively.14 LQT3 is modeled by slowed INa inactivation, leading to the presence of a late INa.14,15 Several degrees of severity (degree of ionic current modification) are simulated for each LQT type. In all cases, the QT interval is prolonged by the mutation, and the prolongation increases with severity.
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Reducing IKs simulates LQT1 (Figure 4, left column). Because IKs is inherently smaller in M cells than in epicardial and endocardial cells, an equal percent reduction of IKs prolongs APD to a lesser extent in M cells than in the other cell types. The net result is a prolongation of the APD of all cell types with decreased APD dispersion. On the ECG, this is reflected in QT-interval prolongation with reduction of TDR (TDR: control=23 ms, 50% IKs=21 ms, 25% IKs=18 ms, and 0% IKs=17 ms).
LQT2 (Figure 4, middle column) is caused by reduced IKr, which causes greater APD prolongation in M cells (as a consequence of their smaller IKs) than in the other cell types. Because M cell repolarization determines the end of the T wave, this nonuniform AP change is reflected in QT-interval prolongation accompanied by widening of the T wave and an increased TDR on the ECG (TDR: control=23 ms, 50% IKr=41 ms, 25% IKr=58 ms, and 0% IKr=91 ms). The greater difference between the M cell AP and the APs of other cell types during the repolarization phase augments Vm and, consequently, the T-wave amplitude. When simulated hypokalemia ([K+]o=2.1 mmol/L) is superimposed on the LQT2 with 50% IKr reduction (Figure 4, LQT2, inset), the T wave becomes notched, as indicated by the arrow. Shimizu et al23 observed similar ECG changes experimentally (Figure 4, bottom row, inset). Superimposing this level of hypokalemia on LQT2 with 50% IKr translates into 36% IKr. This is less severe than LQT2 with 25% and 0% IKr, which do not manifest a notched T wave. Therefore, modification of an ionic current other than IKr by the reduced [K+]o must be involved in inscribing the T-wave notch. To test this hypothesis, the conductance of the inward rectifier potassium current (IK1) was decreased to account for its dependence on ([K+]o)1/2. The combined effects of reduced IK1 and IKr were sufficient to generate a notched T wave.
APD prolongation in LQT3 (Figure 4, right column) is caused by a late mutant INa that shifts the balance of currents during the AP plateau in the inward (depolarizing) direction. As in LQT2, the effect is greater in the M cells. ECG changes caused by late INa (magnitude 0.2% of peak) include widening of the T wave (control=63 ms and LQT3=100 ms), increased T-wave amplitude (control=0.33 mV and LQT3=0.72 mV), and increased TDR (control=23 ms and LQT3=62 ms). The QT-interval prolongation is partly due to late appearance of the T wave (Q- to T-wave onset is 141 ms in control, 157 ms in LQT1, 155 ms in LQT2, and 172 ms in LQT3). These results are consistent with experimental observations.23
Figure 5 illustrates the ECG manifestations of the Brugada syndrome. The T1620M mutation, which accelerates fast inactivation of INa, is introduced following the formulation of Dumaine et al.12 In addition, Ito maximal conductance is increased relative to control, to account for the high Ito density in the right ventricle. Three levels of severity are simulated (Figure 5, from left-to-right): 3-fold increase in Ito density and 1.5 times INa inactivation rate relative to control; 5-fold increase of Ito and 2.5 times INa inactivation rate; and 7-fold increase of Ito and 3.5 times INa inactivation rate. As shown previously,24 it is the balance between Ito (an outward current) and mutant INa (a reduced inward current) that determines the time course and morphology of the AP plateau and repolarization phases in the Brugada syndrome and, therefore, the ECG waveform. In the least severe case (Figure 5, left column), ST-segment elevation with a pronounced J wave is observed, giving the ECG a "saddleback" appearance. With increased severity (Figure 5, middle column), the ECG assumes a "coved" morphology due to T-wave inversion. At the level of the AP, the increased outward direction of the balance between Ito and mutant INa results in a prominent phase 1 notch in the epicardial cells. The reduced Vm generates a large driving force for the L-type calcium current, ICa(L), which is sufficiently augmented (not shown) to prolong the epicardial AP beyond the repolarization times of the M and endocardial cells. The reversed Vm results in an inverted T wave. In the most severe case (Figure 5, right column), the outward balance of currents results in premature repolarization of the epicardial AP and loss of its plateau. Reflecting Vm, the ECG assumes a "triangular" shape.
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h, simulates 3 levels of Brugada syndrome severity. Left, 3-fold increase in Ito density (to simulate the high Ito density in the right ventricle) superimposed with 1.5 times decrease of
Acute Myocardial Ischemia: Effects of IK(ATP) Activation During Hypoxia
Acute myocardial ischemia causes hyperkalemia, acidosis, and hypoxia.16 Reduced level of ATP due to hypoxia activate IK(ATP). Figure 6 presents the effects of IK(ATP) activation on APs and the ECG. Due to greater ATP sensitivity of IK(ATP) in epicardium,17 together with a larger Ito, the epicardial AP plateau is suppressed and APD is abbreviated much more than in the other cell types. Similar to the Brugada syndrome, the large Vm results in a pronounced ST-segment elevation, the hallmark of acute myocardial ischemia.25–27
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Discussion |
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The theoretical approach in this study allows us to establish a direct and specific relationship between cellular ionic processes, the AP, and the morphology of electrocardiographic waveforms. The results demonstrate how alteration of a particular ionic current modifies the transmembrane potential gradient across the ventricular wall (
Vm in Equation 1 and, consequently, the ECG waveforms. This study complements the experimental findings of Antzelevitch et al1–4,12,18,23 and provides, through selected physiological and pathological examples, insights into the principles that relate electrocardiographic observations to underlying ion channel function. It should be emphasized that similar to the transmural wedge experiments,1–4 the simulations presented here only explore electrocardiographic waveforms at a site close to the epicardium during plane-wave propagation from endocardium to epicardium. This model simulates the situation during normal sinus rhythm, where the Purkinje system together with the anisotropic myocardial fiber structure establish a broad wavefront parallel to the endocardial surface that propagates toward the epicardium.10 Under such conditions, the experimental wedge preparation1–4 and the theoretical 1-dimensional fiber used here are adequate models for studying potentials generated by a section of the myocardium at an electrode positioned sufficiently close to the epicardium along the direction of wavefront propagation. Isolating a section of the ventricular wall in this manner facilitates establishing the relationships between the electrocardiographic waveforms, the morphology and properties of the propagating AP, and the underlying cellular ionic processes. However, an electrode sufficiently remote from the myocardium (eg, a body surface ECG electrode) is influenced not only by activity in a section of the myocardium closest to the electrode, but by the distribution of electrical sources in the entire heart. This can be seen clearly in Equation 1 where -Vm (the source of electrocardiographic potentials) is integrated over the entire active tissue where Vm is not zero. The term (1/r) in this equation is a weight factor that acts to emphasize contribution of sources proximal to the electrode relative to those remote from the electrode ("proximity effect"). Under certain circumstances, a precordial electrode can record isolated activity from a proximal section of myocardium. An example in the context of this study is the Brugada syndrome where ST-segment elevation is observed in the right precordial leads.24 These leads are proximal to the right ventricular outflow tract where reduced mutant INa on the background of large Ito suppresses the AP dome to generate a local -Vm and right precordial ST elevation. Such "focusing" of the ECG requires both close proximity and small contribution from activity in other regions of the heart during the same phase of the cardiac cycle. In general, however, such conditions are not met and an ECG electrode records potentials generated by sources in several regions of the heart. The principles established by our simulations and the transmural wedge experiments are derived in simplified models representing an isolated transmural section of the myocardium. However, these principles can be generalized and applied to electrograms and electrocardiograms measured in vivo and provide a mechanistic cellular basis for their interpretation. Recently, we demonstrated that a novel ECG imaging modality (ECGI) can reconstruct epicardial electrograms noninvasively from body surface ECG potentials.28–30 The results of this study are directly applicable to such noninvasive electrograms because, due to proximity, they mostly reflect local activity.
Vm during repolarization is determined by 2 factors: the sequence of activation and local APD. In the (hypothetical) absence of intrinsic electrophysiological heterogeneities, the sequence of repolarization follows the sequence of activation, generating Vm in the opposite direction and a T wave of opposite polarity to the QRS (Figure 1, homogeneous IKs). In the normal myocardium, when AP propagates from endocardium to epicardium at normal velocity (normal sinus rhythm) transmural APD differences due to intrinsic heterogeneity of IKs expression are sufficient to reverse Vm during repolarization and consequently the T wave (Figure 1, control; QRS and T have same polarity). When conduction is sufficiently slow (Figure 2, reduced coupling), the activation sequence determines the sequence of repolarization (intrinsic APD differences are small compared with transmural conduction time). This situation approximates the homogeneous case, and the T-wave polarity is opposite to that of the QRS. Note that in all cases, the peak of the T wave coincides with the time of earliest repolarization (epicardial in control; endocardial for homogeneous IKs and for reduced coupling), whereas the end of the T wave corresponds to latest repolarization (midmyocardial in control; epicardial for homogeneous IKs and for reduced coupling). The results show that transmural IKs heterogeneity is the major determinant of T-wave morphology, whereas presence of Ito in epicardium generates the J wave. Transmural heterogeneity also exists in late INa31 and in the Na+-Ca2+ exchange current.32 Simulations of these heterogeneities (not shown), however, demonstrate only a minimal effect on the ECG waveforms. Another source of heterogeneity is different degrees of electrical loading on repolarizing cells across the transmural regions of the fiber. During endocardial to epicardial conduction, cells in the endocardial region repolarize when other cells are at depolarized potentials, which acts to prolong endocardial APD. The loading effect is opposite in the epicardial region and acts to shorten APD. Therefore, even in a homogeneous tissue, a gradient exists due to loading asymmetry introduced by the propagating AP. In our model, the effect of this functional heterogeneity (not shown) is minimal and does not contribute appreciably to the electrocardiographic waveforms.
The pathological examples were chosen to illustrate important principles in situations where ion channel function is altered by disease. ST-segment elevation is generated by a -Vm directed toward the epicardium during the plateau phase of the AP. Such gradient develops when the epicardial AP plateau is preferentially suppressed. Because the plateau is maintained by a delicate balance between several inward and outward currents,6–9 the ionic basis of ST-segment elevation is not unique and can involve various combinations of processes that shift this balance in the outward (repolarizing) direction. In acute ischemia, we show that IK(ATP) activation with greater ATP sensitivity in epicardial cells17 is sufficient to cause ST elevation. A similar mechanism has been suggested by recent experiments.27 In the Brugada syndrome, accelerated INa inactivation on the background of a large epicardial Ito shifts the balance of currents to cause similar phenomenon and ECG phenotype. Of course, important ECG properties differ between the two pathologies, including sensitivity of specific ECG precordial leads, dependence on heart rate, ß-adrenergic activity, and modulation by drugs. These properties are beyond the principles established here and will be investigated in future studies. The simulated ECG waveforms, however, have sufficient specificity to differentiate between different types of LQT. This is an important demonstration of the potential for using electrocardiographic waveforms to identify a specific channelopathy so that mechanism-based therapy can be administered. The different ECG phenotypes also have physiological and clinical relevance in the context of arrhythmogenesis. For example, LQT1 (IKs channelopathy) prolongs QT without increasing transmural dispersion of repolarization (TDR). This might explain its lower incidence of arrhythmogenesis compared with LQT2 and LQT3,33 where QT prolongation is associated with increased TDR. In the case of the Brugada syndrome (Figure 5), ECG waveforms are indicative of the severity of Na+ channel abnormality. The different morphologies generated by the model as this severity is increased (saddleback, coved, triangular) support the predictions of Antzelevitch based on experimental observations in the transmural wedge preparation.34
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Acknowledgments |
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This study was supported by grants R01-HL-49054 and R37-HL-33343 (to Y. Rudy) from the National Heart, Lung, and Blood Institute.
Received February 7, 2002; revision received March 15, 2002; accepted March 20, 2002.
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