Published online before print June 23, 2005, doi: 10.1161/01.RES.0000174429.00987.17
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© 2005 American Heart Association, Inc.
Integrative Physiology |
Differences Between Left and Right Ventricular Chamber Geometry Affect Cardiac Vulnerability to Electric Shocks
From the Tulane University (B.R., N.A.T), New Orleans, La; Washington University (L.L., I.R.E.), St. Louis, Mo; and Washington and Lee University (J.C.E.), Lexington, Va. The current affiliation for B.R. is Oxford University Computing Laboratory, Oxford, UK.
Correspondence to Natalia Trayanova, Department of Biomedical Engineering, Lindy Boggs Center, Suite 500, Tulane University, New Orleans, LA 70118. E-mail nataliat{at}tulane.edu
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Abstract |
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Although effects of shock strength and waveform on cardiac vulnerability to electric shocks have been extensively documented, the contribution of ventricular anatomy to shock-induced polarization and postshock propagation and thus, to shock outcome, has never been quantified; this is caused by lack of experimental methodology capable of mapping 3-D electrical activity. The goal of this study was to use optical imaging experiments and 3-D bidomain simulations to investigate the role of structural differences between left and right ventricles in vulnerability to electric shocks in rabbit hearts. The ventricles were paced apically, and uniform-field, truncated-exponential, monophasic shocks of reversed polarity were applied over a range of coupling intervals (CIs) in experiment and model. Experiments and simulations revealed that reversing the direction of externally-applied field (RV– or LV– shocks) alters the shape of the vulnerability area (VA), the 2-D grid encompassing episodes of arrhythmia induction. For RV– shocks, VA was nearly rectangular indicating little dependence of postshock arrhythmogenesis on CI. For LV– shocks, the probability of arrhythmia induction was higher for longer than for shorter CIs. The 3-D simulations demonstrated that these effects stem from the fact that reversal of field direction results in relocation of the main postshock excitable area from LV wall (RV– shocks) to septum (LV– shocks). Furthermore, the effect of septal (but not LV) excitable area in postshock propagation was found to strongly depend on preshock state. Knowledge regarding the location of the main postshock excitable area within the 3-D ventricular volume could be important for improving defibrillation efficacy.
Key Words: ventricles • virtual electrode polarization • reentry • excitable area • arrhythmia induction
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Introduction |
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Defibrillation and cardiac vulnerability to electric shocks are strongly linked. A large body of research has demonstrated that ventricular fibrillation induction with an electric shock in sinus rhythm and defibrillation are driven by the same mechanisms.1–3 Furthermore, it has become a standard in the clinical practice of defibrillation to use the upper limit of vulnerability (ULV), which approximates the defibrillation threshold,4–8 in programming the implantable cardioverter/defibrillator. Therefore, complete understanding of the mechanisms by which a defibrillation shock fails in terminating lethal arrhythmias and subsequent optimization of the clinical procedure of defibrillation benefits from the knowledge regarding the factors that contribute to and alter cardiac vulnerability to electric shocks.
Strength of the shock and its waveform are important factors affecting ventricular vulnerability to electric shocks. Equally important is the multifaceted ventricular structure with its convoluted geometry and complex fiber architecture. It provides a pathway through which the shock current flows; it also channels the propagation of the postshock activations. Whereas the effects of shock waveform and strength on cardiac vulnerability have been extensively documented,9–11 the contribution of ventricular anatomical features to shock-induced polarization and postshock propagation and thus, to shock outcome, has never been analyzed. Understanding this contribution could provide the background for rational rather than trial-and-error design of new shock delivery systems that can target specific critical ventricular structures, thus achieving the most favorable postshock behavior and resulting in a significant decrease in defibrillation threshold.
The goal of this study is to investigate the role of ventricular anatomy, and specifically, the geometrical differences between left and right ventricles (LV and RV), in vulnerability to electric shocks. Because spatial nonuniformity of the applied electric field has been implicated in generating shock-induced polarization in addition to polarization stemming from tissue geometry and fibrous structure12,13 and is, thus, a factor in shock outcome, a uniform applied field (as delivered by large external plate electrodes) is used here. In this case, reversal of shock polarity acts only to change the direction of the current flow through the ventricular chambers. This allows us to examine, for the same magnitude and configuration of the applied field, how differences between left and right ventricular chamber anatomy result in differences in shock-induced transmembrane potential changes and postshock electrical activity, and thus, in shock outcome. Of particular importance is knowledge regarding the location of the main postshock excitable area formed typically by deexcitation of previously refractory myocardium14–19 in a large portion of the ventricular volume. Postshock wavefront propagation through the main postshock excitable area is characterized with long uninterrupted pathways13,16 allowing for the recovery of the surrounding myocardium. Therefore, the main postshock excitable area is directly responsible for the global electrical behavior of the ventricles after the shock and ultimately, for shock outcome. Because shock-induced virtual electrode polarization has been shown theoretically to depend on fiber curvature with respect to the direction of the applied field,18 we hypothesize that reversing the direction of the electric field will change the location of the main postshock excitable area within the rabbit ventricles.
To understand the role of ventricular anatomy in postshock electrical behavior, the global 3-D activity in the ventricles needs to be analyzed. Whereas optical mapping techniques provide high-resolution information regarding epicardial activity, the methodology is insufficient in resolving depth information. For instance, postshock activations could remain undetected optically if they propagate intramurally without a signature on the epicardium.20 Thus, it is paramount to also use alternative approaches in gaining insight into the electrical behavior within the tissue depth. Our group has recently developed a realistic computer model of stimulation/defibrillation in the rabbit heart; simulations of arrhythmia induction with this model have the unique ability to provide information regarding the 3-D postshock activity in the ventricles.17,21 Therefore, to fully elucidate the role of ventricular anatomy in shock-induced vulnerability, this study uses a combination of optical mapping experiments and 3-D computer simulations.
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Materials and Methods |
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Experimental Preparation
Hearts of young rabbits (New Zealand White, 1 to 3 months, n=5; Harlan, Indianapolis, Ind) were removed and placed into a temperature-controlled Langendorff perfusion system. The hearts were perfused with oxygenated Tyrode’s solution containing 2,3-Butanedione Monoxime (BDM, Fisher Scientific) to prevent motion artifacts and stained with the voltage sensitive dye di-4-ANEPPS (Molecular Probes). An optical mapping system was used to record activity on the anterior wall of the ventricles, as previously described.14,19
Computational Model
The anatomically-based rabbit ventricular model (Figure 1A) described in a previous study17 was used. In brief, the myocardial mesh was generated from data by Vetter and McCulloch,22 which incorporate realistic geometry and fiber orientation. The model also included representation of the blood in the ventricular cavities and the perfusing bath. Electrical activity in the myocardium was simulated using the bidomain equations. The Beeler–Reuter model modified for defibrillation23 was used to represent the kinetics of the ionic currents. Simulations were performed using a semiimplicit finite element method with a variable time step as previously described.24
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Protocol for Determining the Vulnerability Area
In simulations and experiments, the ventricles were paced at the apex. To ensure uniform applied field, in both approaches the shocks were delivered via 2 large planar electrodes located at the vertical walls of the perfusion chamber (Figure 1). Consistent with the goal of the study, examining the change in cardiac vulnerability on reversal of field direction necessitated the use of monophasic shocks in both simulations and experiments (8-ms-long truncated-exponential waveforms of 65% tilt). The shocks were applied over a range of coupling intervals (CIs, measured with respect to the last pacing stimulus). An example of preshock transmembrane potential distribution on the epicardium of the rabbit model is shown in Figure 1A. The square in Figure 1B represents the field of view of the optical mapping system (16x16 mm2).
The applied electric field was referred to as RV– when the electrode near the RV was used as the cathode and the one near the LV was the grounding electrode. The opposite electrode orientation was referred to as LV–. Shock strength (SS) referred to the leading-edge value of the electric field between the electrodes.
Vulnerability areas (VAs), ie, areas on a 2-D grid that encompass episodes of reentry induction for various SSs and CIs, were determined for both field directions in simulations and in experiments. The tachyarrhythmia was considered sustained if the shock application induced more than 6 beats of postshock activation.9
For each field direction, the ULV was estimated as the highest shock strength that induced sustained arrhythmia. The vulnerable window was estimated to be the interval in time between the lowest and the highest CI at which a sustained arrhythmia was induced.
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Vulnerability Areas
In experiments, the vulnerable window was found to extend from 116±8.9 to 184±16.7 ms for RV–, and from 116±16.7 to 188±17.9 ms for LV– shocks. Mean ULV was 12.2±1.6 V/cm and 11±2.1 V/cm for RV– and LV– shocks, respectively. Figure 2A depicts, for both field directions, the probability of tachyarrhythmia induction for each combination of CI and SS derived from all experiments. As in reference 9, to combine data from different experiments, SS and CI were represented as deviations from the ULV and the longest CI in the vulnerable window (CImax), respectively (Figure 2A). Figure 2A demonstrates that probability of arrhythmia induction is distributed differently over SSs and CIs for the 2 field directions. For RV– shocks, probability of arrhythmia induction larger than 0.2 (ie, occurring in at least 2 rabbits) was documented for a wide range of CIs (CI-CImax from 0 to –80 ms) and for SSs ranging from 0 to –6 V/cm SS-ULV. For LV– shocks, probability of arrhythmia induction larger than 0.2 was found to concentrate within a much narrower CI range (CI-CImax from 0 to –40 ms); indeed, for LV– shocks, 65.5% of arrhythmia induction episodes occurred for CI-CImax from 0 to –20 ms, whereas for RV–polarity only 44.7% of arrhythmia episodes were induced within this CI range. In addition, in all hearts examined, ULV occurred at CImax for LV– shocks, and over a range of CIs for RV– shocks.
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Figure 2B presents VAs for both field directions as obtained from the rabbit ventricular model. For RV– shocks (ULV=9.6 V/cm), consistent with the experimental data, VA extends over a broad CI range, from 0 to –60 ms CI-CImax (CImax=130 ms) and for SS ranging 0 to –6.4 V/cm SS-ULV. In addition, as in the experiment, it has a somewhat rectangular shape. Reversing field direction (ULV=12.7 V/cm) alters VA shape in a manner similar to experimental data: the majority of arrhythmias are induced at long CIs, from 0 to –20 ms CI-CImax (CImax=105 ms) and ULV is reached at CImax. Furthermore, in simulations as in experiments, only shocks of strength <–8 V/cm induce arrhythmia when applied at short CIs (CI-CImax<–20 ms).
Transmembrane Potential Distribution on the Epicardium at Shock End
The correspondence between experimental and model VAs is qualitatively very good, as demonstrated by Figure 2. Below, we also demonstrate agreement between simulation and experiment regarding the general pattern of epicardial transmembrane potential distribution at shock-end.
Figure 3 presents typical examples of anterior shock-end epicardial transmembrane potential distributions in the rabbit ventricles in experiments (A) and simulations (B) for various SSs and CIs. The white squares in Figure 3B indicate the field of view of the optical mapping system. As in reference 25, CIs are expressed as a percentage of action potential duration (%APD). For RV– shocks, in both experiments and simulations, the epicardium is depolarized in the vicinity of the cathode, whereas the LV epicardium is negatively polarized (Figure 3, left); reversing field direction switches, overall, the location of these 2 areas (Figure 3, right). The pattern of shock-end epicardial transmembrane potential distribution is qualitatively similar among all rabbit hearts for the corresponding SSs and CIs (data not shown) and demonstrates good agreement with the simulation results (potential distribution within the white square in Figure 3B). Note that the agreement between experiment and simulation regarding the shock-end transmembrane potential distribution is expected to be only qualitative because of depth averaging in the optical signal26–28 (ie, agreement only with regard to the pattern of shock-induced positive and negative polarization and not with respect to polarization magnitude). As demonstrated previously, depth averaging results in a significantly diminished optical signal magnitude27,28 (for instance, optical signal maximum positive and negative polarization in the field of view is 27.8 and –66.9 mV for the RV– shock of 8V/cm, 50%APD and 13 and –51.26 mV for an LV– shock of 8V/cm, 50%APD, both shown in Figure 3A, versus 280 and –110 mV for the RV– shock of 6.4V/cm, 51%APD and 160 and –140 mV for the LV– shock of 6.4V/cm, 51%APD, both presented in Figure 3B).
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Effect of Chamber Anatomy on Shock-End Transmembrane Potential Distribution Within the 3-D Ventricular Volume
In this section we elucidate the mechanisms underlying the change in vulnerability on reversal of the direction of applied field, which can only be achieved through realistic simulations of 3-D electrical activity. The rabbit ventricular model was used to first analyze the differences in the 3-D shock-end transmembrane distributions between the 2 cases. Figure 4 presents such information for episodes inside and outside the VA. For RV– shocks (Figure 4, left), one observes that increasing SS by 6.4 V/cm from below to above the ULV for the same CI, ie, moving vertically across the VA border (compare episode b to episode a), results in an increase in the areas strongly depolarized by the shock (
20 mV, red color) as demonstrated by both the epicardial and transmural transmembrane potential maps (Figure 4A); the trend remains the same when CI is increased (compare episodes c and d). This observation is quantified in Figure 4B, where the amount of ventricular tissue experiencing shock-end potentials >+20 mV and <–90 mV (calculated as percentage of all nodes in the ventricular volume) is plotted as a function of CI for the 2 SSs (SS–ULV/±3.2 V/cm) used to generate the images in Figure 4A. It shows that when SS is increased from below-ULV (triangles) to above-ULV (squares), the amount of tissue strongly depolarized at shock-end increases dramatically (from 47.7% to 74.1% of tissue volume for CI-CImax=–50 ms and from 24.8% to 75.1% for CI-CImax=–15 ms). This is the tissue volume which remains refractory for a significant period of time after the shock, blocking propagation of postshock activations. In addition, the area that is fully deexcited at shock-end and through which postshock activations will freely propagate (nodes below –90 mV) is also extended on increased SS, although to a much smaller degree (from 10.4% to 22.2% for CI-CImax=–50 ms and from 19.0% to 22.2% for CI-CImax=–15 ms). The plot shows that these trends remain the same regardless of CI.
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Furthermore, the simulation results in Figure 4A demonstrate that for this orientation of the applied field, regardless of SS or CI, the main postshock excitable area is always within the LV wall (deep blue areas). This is also underscored by the postshock transmembrane potential maps in Figure 5, top: 20 ms after shock-end, propagation has just traversed (case a, same as in Figure 4A) or proceeds through (case b, same as in Figure 4A) the LV wall. At shock-end, the septum is either mildly or strongly positively polarized for shocks below or above the ULV (Figure 4A), respectively, and is not an avenue for postshock propagation. The shock-end negative polarization in the RV is a thin stripe in a thin wall; thus, the RV is not a major structure for postshock propagation (see also Figure 5, top, 20 ms panel).
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The increase, for RV– shocks, in the amount of strongly depolarized tissue for all above-ULV shocks, as demonstrated by Figure 4A and 4B, leads, for these SSs, to blockade of the propagation through the LV wall by surrounding tissue that is in extended refractoriness, resulting in a failure of the shock to induce arrhythmia. This is shown in Figure 5, top. In case a, the entire ventricles are refractory 20 ms postshock after a rapid propagation through the excitable areas, and the shock fails to induce arrhythmia. In case b, large LV–wall excitable areas remain at 20 ms postshock; by the time the wavefronts propagate through them, the rest of the myocardium recovers, allowing reentry to be established. Two rotors are induced, 1 counterclockwise and 1 clockwise, on the anterior and posterior sides of the ventricles, respectively, with a common pathway in the apex. The same reentrant pattern was observed in the experiment as documented by the example activation map shown in Figure 6, left. This behavior is similar for every CI in the VA, hence the nearly rectangular shape of the VA for RV– shocks.
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Figure 4C and 4D presents analysis of the shock-end Vm distribution for LV– shocks; here the effect of increased SS is different for short versus long CIs. First, in regard to the amount of strongly depolarized tissue, for intermediate and long CIs (ie, intermediate and small CI-CImax), the behavior is different from the one for RV– shocks (compare episode d to episode c in Figure 4A and 4C for both directions of the applied field, separated by the same difference in SS); here, the amount of tissue strongly depolarized changes little as SS increases, thus the 6.4 V/cm change in SS results in an episode within the VA. Figure 4D provides quantification of this observation: only a 16.2% increase is found from episode d to episode c for LV– shocks. In contrast, for short CIs (large CI-CImax), one notices a significant increase in the amount of strongly depolarized tissue, particularly in the transmural slices. As shown quantitatively in Figure 4D, from episode b to episode a, the amount of strongly depolarized tissue is increased by 46.1%. In the latter case, the increase in the amount of strongly depolarized tissue is also accompanied by a slight decrease in the excitable area (compare episodes a and b), whereas the opposite is true for episodes corresponding to long CIs.
Second, for LV– shocks the main postshock excitable area relocates to the septum, the other thick wall in the ventricles (Figure 4C). For episodes within the VA, as shown in Figure 5, bottom, a septal excitable area is still present 20 ms after shock (episodes b and c), ultimately resulting in the establishment of reentry. The reentrant circuit is a figure-of-eight on the anterior and another on the posterior with a common pathway in the LV, and is also evident in the experimental activation map in Figure 6, right. The pattern of the reentry is indeed determined by the initial postshock propagation, here through the septum, resulting in subsequent activation through both free walls.
The septal excitable area is, however, minor and thus inconsequential in episode a of Figure 4C and 4D; it is no longer present 20 ms after shock (Figure 5a, bottom) resulting in complete recovery of the ventricles. The noticeable increase in the area strongly depolarized by the shock in this case, as shown in Figure 4D, is indeed attributable to the depolarization of the septal tissue, causing a no-arrhythmia-induction outcome of episode a and thus altering the VA shape. Therefore, for LV– shocks, the unusual behavior of the septum for short CIs and large SSs results in a VA shape that differs from the one for RV– shocks.
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Discussion |
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This combined computer simulation and optical mapping study investigates the role of ventricular anatomy, and specifically, the differences between LV and RV, in vulnerability to electric shocks. Our results demonstrate that reversing the direction of the applied field alters the VA shape and the probability of arrhythmia induction throughout the VA. For RV– shocks, the VA shape is nearly rectangular indicating little or no dependence of postshock arrhythmogenesis on CI. For LV– shocks, the probability of arrhythmia induction is higher for longer CIs (short CI-CImax) than for shorter. In addition, for RV– shocks, the CI at which the ULV is reached varies among experiments in the range from 0 to –40 ms CI-CImax, whereas for LV– shocks the ULV is always reached at CImax. This behavior is confirmed by the simulation results.
The 3-D simulations using the anatomically based rabbit model revealed that for RV– shocks, regardless of SS or CI, the main postshock excitable area is always located in the thick LV wall. Immediate postshock activations always originate and propagate through it, although such propagation may or may not result in reentry. Increasing SS from within the VA to above the ULV is associated, for all CIs, with a significant enlargement of the areas strongly depolarized by the shock (55% to 202.8%, depending on CI), indicating a dramatic increase in the occurrence of postshock propagation block.
Reversing the direction of the applied field leads to a change in the location of the main excitable area; it is now in the septum, the other thick wall in the ventricles. In addition, reversing the field direction results in a much smaller increase in the areas strongly depolarized by the shock for the same increase in SS (by 
16% for the majority of the episodes in the VA). A noticeable exception to these trends is the behavior at short CIs (large CI-CImax) where the ventricles are vulnerable to reentry for low SSs only. The 3-D simulations revealed that the septal transmembrane potential distribution at shock-end is responsible for this change in behavior: the majority of the septum is depolarized in this case, surrounding the small apical postshock excitable area on all sides and blocking wavefront propagation.
Why is septal shock-end behavior different in this case? Shock-induced transmembrane potential in the myocardium is a function of the underlying fibrous structure.13 Rapid changes in fiber orientation as well as other tissue heterogeneities lead to localized changes in shock-induced transmembrane potential.13,18,29,30 A recent study by Ikeda et al31 on the role of ventricular structural complexities in maintaining VF reported, by means of histological sectioning, that tissue structure nonuniformities were much more evident in the interventricular septum as compared with the LV and RV walls. This finding is consistent with the structure of the rabbit ventricular model of Vetter and McCulloch22 used in the present study; the change in fiber orientation in the model is locally much more rapid in the ventricular septum than in the other walls. Indeed, a calculation of the passive polarization in the 3-D volume of the rabbit ventricles19 by our group revealed alternating-in-sign regions of membrane polarization in the septum (Figure 11 in reference 19). The postshock behavior of a myocardial region characterized with rapid spatial change in polarization is much more likely to depend on the preshock state of the tissue, ie, on the CI at which the shock is delivered (unpublished results). This is manifested as a difference in the excitable area induced by strong shocks for short and long CIs, as demonstrated by Figure 4D, episodes a and c.
The location of the main excitable area (within the LV free wall for RV–, and within the septum for LV– shocks) also results in different reentrant patterns for shocks within the VA. Indeed, the thin RV wall becomes refractory soon after the shock for both field directions (Figure 5) and is never a major postshock propagation avenue; postshock activation always proceeds through the thick septal or LV walls. In the case of LV wall propagation, the postshock reentrant circuit is a scroll wave on each side of the ventricles (posterior/anterior) with a common apical pathway (Figure 5b-top). This is because of the fact that after propagating through the LV wall, the activation extends toward the recovering RV wall and septum, establishing a rotor on each side (Figure 5b, top). In the case of postshock propagation through the septum, both LV and RV walls become excitable after a certain recovery period, resulting in the establishment of a figure-of-eight reentry on each side of the ventricles (altogether a quatrefoil reentry, Figure 5b and 5c, bottom).
The combination of optical mapping experiments and 3-D computer simulation studies provides, as demonstrated by the present research, a unique opportunity to explore cardiac electrical behavior after a defibrillation shock. The simulations provide information regarding behavior in the depth of the ventricular walls (including the septum) not achievable by any imaging technique thus far. For instance, similar to previous studies,19 our theoretical and experimental results demonstrate that 2 large areas of opposite-in-sign transmembrane potential are induced on the epicardium following applied fields of opposite direction (Figure 3). For LV– shocks, judging from the epicardial maps only, one might expect that, at shock-end, the interaction between these 2 areas will result in break excitations in the apical region leading to a scroll wave on the anterior (and possibly, another on the posterior), with chirality dependent on the direction of the field, in a manner similar to the response to RV– shocks. However, the present study demonstrates that the ventricular walls could exhibit complex midmyocardial transmembrane potential distributions at shock-end (Figure 4), which are not predictable from the epicardial maps. Therefore, the information regarding shock-induced polarization and postshock activity in the 3-D volume of the ventricles, as provided by the bidomain simulations, is critical to understanding the mechanisms by which a shock results (or not) in arrhythmia generation.
This study reveals that ventricular anatomy plays a major role in shock-induced electrical behavior, and thus, in the outcome of a defibrillation shock. The difference in the thickness of the ventricular walls is ultimately manifested as a preferential location of the postshock excitable area. In addition, the location of this area determines the types of postshock reentrant circuits. The present study purposefully used a uniform applied field and a (truncated-exponential) monophasic shock waveform to reveal the basic contribution of cardiac anatomy to 3-D postshock behavior; in this manner the contribution was not masked by applied field nonuniformity and additional nonlinear effects associated with biphasic defibrillation waveform shape. The findings of the study are directly applicable to external defibrillation with monophasic shocks. They are also very relevant to ICD electrode configurations and biphasic waveforms. In these more complex cases, a main postshock excitable area(s) will still be developed within the 3-D volume of the tissue; it will be at least partially determined by cardiac anatomy. Identifying the location of the main postshock excitable area could be very important for improving clinical defibrillation efficacy because its eradication can be specifically targeted by auxiliary small-magnitude shocks, resulting in a dramatic decrease in defibrillation threshold. Finally, our results indicate that the thickness of the ventricular walls is an important factor in shock-induced arrhythmogenesis, and thus, the insight provided by this research might be important in understanding the reasons behind the elevated defibrillation threshold in patients with hypertrophy.32
Limitations
The limitations of the ventricular rabbit model and of the experimental techniques used in this study have been described elsewhere.14,17 These include limitations of the membrane model, lack of small-scale tissue heterogeneities in the rabbit model, and the use of BDM as excitation-contraction uncoupler in experiments. Furthermore, only an apical pacing site was used in this study. Whereas previous research from our team has demonstrated that the origin of postshock reentry is determined solely by the shock, its survival depends on pacing site,33 thus the VA shapes could be different for a different pacing site. However, differences in VAs between RV–and LV– shocks are expected to remain because they are determined by ventricular chamber anatomy, which is not changed. None of these limitations are, however, expected to alter the basic conclusions of this combined simulation/experimental study regarding the role of the 3-D ventricular anatomy in the spatiotemporal response to applied electric fields and shock-induced arrhythmogenesis.
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Acknowledgments |
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This work was supported by National Institutes of Health grants HL063195 (N.T.), HL074283 (I.E.), and HL067322 (I.E.) and grants from the Whitaker Foundation and the W.M. Keck Foundation (J.E.).
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Footnotes |
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Original received April 6, 2005; revision received June 8, 2005; accepted June 9, 2005.
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