Rectification of the Background Potassium Current
A Determinant of Rotor Dynamics in Ventricular Fibrillation
Ventricular fibrillation (VF) is the leading cause of sudden cardiac death. Yet, the mechanisms of VF remain elusive. Pixel-by-pixel spectral analysis of optical signals was carried out in video imaging experiments using a potentiometric dye in the Langendorff-perfused guinea pig heart. Dominant frequencies (peak with maximal power) were distributed throughout the ventricles in clearly demarcated domains. The fastest domain (25 to 32 Hz) was always on the anterior left ventricular (LV) wall and was shown to result from persistent rotor activity. Intermittent block and breakage of wavefronts at specific locations in the periphery of such rotors were responsible for the domain organization. Patch-clamping of ventricular myocytes from the LV and the right ventricle (RV) demonstrated an LV-to-RV drop in the amplitude of the outward component of the background rectifier current (IB). Computer simulations suggested that rotor stability in LV resulted from relatively small rectification of IB (presumably IK1), whereas instability, termination, and wavebreaks in RV were a consequence of strong rectification. This study provides new evidence in the isolated guinea pig heart that a persistent high-frequency rotor in the LV maintains VF, and that spatially distributed gradients in IK1 density represent a robust ionic mechanism for rotor stabilization and wavefront fragmentation.
Ventricular fibrillation (VF) is traditionally attributed to multiple randomly wandering electrical wavelets, ever changing in direction and number.1 However, a new idea based on theoretical2 and experimental3 studies postulates that “rotors” are the major organizing centers of fibrillation. Thus, two divergent mechanisms for the maintenance of VF have come to light. Some workers propose that VF results from the instability of rotors, which ultimately leads to their breakup.4,5 Alternatively, other investigators hypothesize that fibrillation is maintained by wavefronts emanating at an exceedingly high frequency from a relatively stable rotor.6–9 Accordingly, fibrillatory conduction is the result of the interaction of such wavefronts with anatomical and functional obstacles, and not the breakup of the source.
Consistent with the stable source hypothesis, recent studies demonstrated spatiotemporal periodicities10 and domain-like distribution of excitation frequencies11 during VF. Such results suggested that VF may have an underlying organization. Using high-resolution optical mapping, we present new evidence in the isolated Langendorff-perfused guinea pig heart that demonstrates that VF may be the result of a highly periodic reentrant source, which may remain stable for more than 100 rotations. Moreover, using the patch-clamp technique and computer simulations, we demonstrate for the first time that regional differences in an inward rectifier current may provide an ionic mechanism for the localization of the source and the establishment of a consistent gradient of excitation frequencies during VF.
Materials and Methods
Detailed descriptions of the approaches used in the experiments, computer simulations, and analyses are presented in the online expanded Materials and Methods section, available in the data supplement at http://www.circresaha.org.
Spatial Distribution of Dominant Frequencies
Figure 1 shows an example of the frequency analysis performed on the optical recordings of the fibrillating heart (see online Materials and Methods for details). In Figure 1A, the rapid and irregular ECG is typical of VF. Figure 1B shows the dominant frequency (DF) map.11 The DFs are clustered in several distinctive and smooth regions termed “domains.” Here, the right ventricular (RV) DFs range between 10 and 16 Hz, with 14 Hz (light green) constituting the largest domain on the epicardial surface; the left ventricular (LV) frequencies range between 14 and 26 Hz. Note that the highest frequency (26 Hz) is on the anterior LV wall (red). Thus, in contrast to the complex propagation patterns during VF, the distribution of DFs is simple. Moreover, the ventricles are activated at different rates, which results in a gradient of excitation frequencies.
The presence of rapid frequencies (>20 Hz, cycle length (CL) <50 ms) on the anterior LV wall is intriguing and implies that the guinea pig action potential (AP) is highly plastic, since the paced (1 Hz) AP duration is ≈200 ms.12 To independently confirm the extremely rapid frequencies during VF in the LV, we recorded electrical activity with an intracellular floating microelectrode (3 mol/L KCl, 20 MΩ). Five-second recordings from the RV and the LV, obtained 5 minutes after the initiation of VF, were analyzed. AP CLs were measured from a 1-second segment chosen at random. Figure 1C shows representative APs. For this episode, the mean AP CLs were 38.6 (≈26 Hz) and 64.12 ms (≈16 Hz) for LV and RV, respectively, which correlated well with the optical data. In 4 microelectrode experiments, CLs on the anterior LV wall (36.96±3.9 ms; mean±SD) were significantly briefer than CLs on the RV free wall (63.92±17.16 ms; P=0.011).
Quantification of Dominant-Frequency Maps
The DF domain configuration (Figure 1B) was consistent across experiments. To quantify this finding, we constructed DF maps in nine hearts, which were subsequently aligned, rescaled, and averaged (see online Materials and Methods for details). Figure 2A shows the composite DF maps of the anterior (left) and posterior (right) surfaces. Here, the average DFs are also organized in domains. Moreover, the locus of the fastest domain is the anterior LV wall (mean DF=26 Hz) and is much faster than the RV (mean DF=15 Hz). To substantiate the difference, six sites in the RV were compared with six sites in the fastest domain (marked 1 to 12), across the nine hearts. Based on post hoc comparisons using Scheffe’s test, no differences (P>>0.05) were found among DFs within the RV (eg, 2 versus 5) or within the LV (eg, 8 versus 11). However, DFs at RV sites were significantly different (10−3>P>10−8) from DFs at LV sites (eg, 5 versus 9).
The standard deviation (SD) of the mean DFs for each pixel was used to construct an SD map (Figure 2B). The SD is lowest (0 to 2 Hz) in the free walls of the ventricles and is largest in the periphery and in between the major domains. Hence, both domain organization and hierarchy of frequency gradients are preserved among animals.
Nature of the Fastest DFs
In Figure 3A, we present the ECG from another heart during VF. In Figure 3B, the DF map shows the LV-to-RV gradient of DFs. Further analysis demonstrated that in fact a relatively stable high-frequency rotor was responsible for the fastest DF domain in the LV. Figure 3C shows snapshots of the rotor at 4 different times during one rotation. In this example, the rotor was on the epicardial surface for ≈150 rotations at 32 Hz (see online data supplement for videoclip of this VF episode). Thus, the activity of a high-frequency rotor gave rise to the fastest DF domain in this heart.
To establish the contribution of rotor activity to the fast frequency domain in the other eight hearts, 11 rotors were identified. We calculated the frequency of each rotor and correlated it with the fastest DF. A strong correlation (R=0.95) existed between the two parameters, suggesting that the rotor was the main contributor to the frequency of the fastest domain. However, despite the stability of the highest frequency domain in the LV, and the excellent correlation between the rotation frequencies and the highest DFs, inspection of the LV epicardium revealed rotors of variable persistence (range, 4 to 150 rotations). Thus, while it is likely that all dominant rotors remained in the anterior LV wall, some probably took an intramural position13 and thus were hidden from view.
Fibrillatory Conduction as a Mechanism for VF
Phase analysis aids in the identification of the center of rotation and highlights wavebreaks occurring when fronts collide with refractory tails or other obstacles.7,8,10 Figure 4 shows a series of phase maps (see online Materials and Methods for technical details) of the anterior wall depicting the behavior of the same rotor as in Figure 3, for one complete rotation. Colors reflect phases of the AP: upstroke is colored green, plateau is blue and violet, and refractory tail is red and yellow. A phase singularity (PS) point is the location at which all phases (ie, colors) converge, and the continuous spatial changes reflect the full cycle of excitation, repolarization, and recovery.7 Numbers identify PSs (eg, PS 1 marks the center of rotation) and are used to track the activity. The maps show that PS 1 is stable and that the wavelet it flanks serves as a source of new wavelets in its surrounding. At t=0 ms, 4 PSs are present on the epicardial surface defining 2 distinct waves; PSs 1 and 2 flank the source wave, and PSs 3 and 4 flank a daughter wavelet. As the source wave continues to rotate, it breaks in its periphery producing new wavelets. This is evident at t=5 ms when the source wave originally bounded by PSs 1 and 2 breaks up at PS 5. The source is then flanked by PSs 1 and 5, and a new wavelet bounded by PSs 2 and 6 is generated. The process continues as the source wave (now bounded by PSs 1 and 5) undergoes further breakup at PS 7, giving rise to a new wavelet bounded by PSs 5 and 8 at t=10 ms. Some of the wavelets formed undergo decremental conduction and die. For example, the wavelet flanked by PSs 2 and 6, which is visibly formed as the result of the rotation and breakup of the arm of the rotor, dies between t=15 and t=20 ms. Others undergo one or more rotations and then terminate spontaneously by collision with another wavefront (data not shown). Still others (eg, PSs 5 and 8) exit the field and vanish elsewhere. Clearly, the breakup of waves from a stable high-frequency source gives rise to complex patterns of activation, consistent with VF.
Spatial Distribution of Phase Singularities
From the foregoing, it is evident that a high-frequency stationary rotor may be a source of PSs and wavelets. To understand the relation between DF domains and PSs, we characterized the spatial distribution of PSs by marking their location for 1 second during VF. Figure 5A outlines the DF domains (black lines) shown in Figure 3 with a superimposed spatial histogram of PSs (colored squares). The black circle marks the center of rotation. Most PSs are located near the boundaries of the DF domains suggesting that wavebreaks occur near those boundaries. Close to the source, activation of the LV is 1:1, but at an intermediate distance, corresponding to the boundaries of the fastest domain, wavebreaks and intermittent block develop. Beyond such boundaries, slower DF domains are created where excitation is again periodic, albeit at a slower frequency. Figure 5B shows optical APs and corresponding frequency spectra obtained by fast Fourier transformation (FFT) of signals from 3 sites marked in panel Figure 5A (black squares). At site a, located within the 32-Hz domain, the regular morphology of the optical APs and the single narrow frequency peak indicate 1:1 activation. In contrast, at site b, located at the boundary between the fastest and slowest domains, the optical APs are irregular. The small-amplitude depolarizations (marked by arrows) reflect intermittent blockade of impulses initiated within the fastest domain. Their timing coincided with the presence of PSs. Intermittent block and wavebreaks are also reflected in the spectrum, which shows two distinct peaks (13 and 32 Hz) whose similar amplitudes depict the almost equal contribution of both fast and slow domains at that location. A number of smaller peaks in the power spectrum reflect the contribution of the other neighboring domains, namely those corresponding to 18, 20, and 27 Hz. Similar to site a, at site c, located within the 13-Hz domain in the RV, the regular morphology of the APs and the single narrow peak in the spectrum suggest that this region is activated rhythmically at the slower frequency. Therefore, the data suggest that spatially distributed wavebreaks and conduction block may be a mechanism for the formation of DF domains.
Quantification of Spatial Distribution and PS Lifespan
To determine whether wavebreaks constitute a general mechanism for the formation of DF domains, we further identified the position of PSs in six experiments (see online Materials and Methods for details). Figure 5C outlines the major DF domains (black lines) of the anterior composite DF map (Figure 2A). Superimposed on that image is the composite spatial histogram of PSs (colored squares). Once again, the majority of PSs occurred at the boundary of the fastest domain. We also measured the lifespan of PSs7 and hence indirectly the lifespan of wavelets. During VF, the mean lifespan of PSs was 22 ms (range, 3.2 to 100 ms), with 50% of the PSs lasting <15 ms. Further analysis revealed that the average lifespan of PSs in the fastest frequency domain was 43.5 ms (range, 3.3 to 275.6 ms), whereas the average lifespan of PSs elsewhere was significantly briefer at 17.1 ms (range, 1.7 to 80.2 ms; P=0.00016) with 50% of PSs lasting <13.6 ms. Given that the rotation period for the rotors in the LV is 37.04±3.8 ms, the short lifespan and location of the majority of PSs suggest that they are the result of breakup from distant periodic sources and, therefore, most likely not maintaining VF. Overall, the data further support our conclusion that wavebreaks and spatially distributed intermittent block are responsible for the domain-like distribution of DFs.
The Background Current
Simulations previously demonstrated the importance of the background inward rectifier current (IK1) in the establishment of fast and stable reentry.9 Thus, we hypothesized that the stabilization of the high-frequency rotor in the LV may result from chamber-specific differences in IK1. We used the whole-cell voltage-clamp technique to characterize the background current in the RV and the LV and relate its spatial distribution to the excitation frequencies and stability. Figure 6A shows the I-V relations of the background current, IB, (most likely IK1, see Technical Limitations) of two different cells from the LV and the RV in the same heart. The outward conductance of IB is clearly larger in the LV cell than in the RV cell. Similar results were obtained for 19 LV cells and 18 RV cells from 10 hearts. Figure 6B shows the mean I-V relations. Clearly, the outward conductance is significantly higher in the LV than the RV (−50 mV: RV 5.3±0.4; LV 7.4±0.6 pA/pF, P=0.009).
To understand the effect of the difference in the LV and RV background currents on VF dynamics, we used the respective experimental mean IB (Figure 6B), in a 2-dimensional computer model (see online Materials and Methods for details on the model and its parameters). Figure 7A shows simulated steady-state I-V relations (IK1) for the LV (solid line) and RV (broken line), superimposed on the corresponding experimental data (see Figure 6), and the respective simulated single-cell APs obtained at 1 Hz. The reduced outward component of IK1 in the RV resulted in a longer AP than the LV. Figure 7B shows four snapshots of the simulations (3×3-cm2 sheets) with the inward rectifying properties of the RV (top frames) and the LV (bottom frames), ie, small and large IK1, respectively. Strong rectification in the RV model resulted in unstable, ie, self-terminating reentry. In contrast, the smaller degree of rectification in the LV model resulted in a stable and persistent high-frequency rotor (33 Hz, CL=30 ms). Hence, the relatively large outward component of the background current may play an important role in stabilizing reentry in the LV.
To more closely approximate the experimental situation, we combined the two models. Two representative frames of a simulation using a 6×6-cm2 sheet containing the LV in the center (2×2 cm2), and the RV in the periphery are shown in Figure 7C. In both frames, the stationary vortex in the LV gives rise to waves that propagate into the RV. However, dynamic nonuniformity results in wavefront fragmentation, decremental conduction, and intermittent block, with occasional formation of short-lived rotors near the edges of the sheet (see online data supplement for videoclips). Such rotors are either invaded by incoming waves or they self-terminate (Figure 7B). To quantify such behavior, we carried out additional simulations using sheets of three different RV sizes, in which we documented the formation of 20 randomly chosen rotors (PSs) and measured their lifespan. The size (2×2 cm2) and central position of the LV were kept constant, while the total size of the sheet was changed. When the sheet was 4×4 cm2, the lifespan of the PSs in the RV was 73±93 ms (mean±SD) with a median of 27 ms. When a sheet of 6×6 cm2 was used, the lifespan of PSs in the RV was 61±83 ms (median=34 ms). Finally, when the sheet was 8×8 cm2, the lifespan of PSs in the RV became 109±139 ms (median=45 ms). In addition, while the LV rotor CL was 30 ms, the RV rotors that lasted at least one rotation had a CL of 40 to 50 ms. The somewhat longer lifespan of the RV rotors in the simulations than in the experiments most likely reflects the proximity of the rotors to the boundaries of the sheet, which protected them from invasion and annihilation by incoming wavefronts from the LV. Obviously such boundaries do not exist in the experimental situation. Nevertheless, these data demonstrate that while rotors did form in the simulated RV, they were always slower and relatively short-lived, regardless of the size of the sheet.
In Figure 7D, we present a DF map of the 6×6-cm2 LV-RV model, to allow for quantitative comparison with the experimental results. As in the experiments, there is a sharp drop in DF from 33 Hz in the LV to 17 to 20 Hz in the RV. Overall, these data support the idea that the amplitude of the outward component of the background current plays a role in establishing the maximum allowable rate of local activation during VF.
The major finding of this study is that VF in the isolated guinea pig heart is characterized by a consistent gradient in dominant activation frequency from the LV to the RV. Such a gradient may result from a significant difference in the density of the background current, presumably IK1, between the two ventricles. Further, the high-frequency activity found in the LV is likely to result from persistent rotors that sustain VF. The finding of chamber-specific differences in the background current was demonstrated numerically to represent a possible ionic mechanism for the stabilization of the high-frequency rotors in the LV, along with wavefront fragmentation in their periphery, and for the relative low-frequency activity elsewhere, including the RV.
Mechanisms of VF
Previously, Rogers et al14 found reentry in ≈30% of VF cases in pig hearts; it was mostly short-lived, and tended to cluster, although in different regions across animals. Although other potential mechanisms cannot be ruled out, such results are consistent with the idea that VF is maintained by stable source(s), with fibrillatory conduction of the waves that emanate from them. Indeed, recent data showed that fibrillatory conduction is present during VF in the rabbit heart7,8 and in the isolated sheep ventricular preparations.11 Those studies demonstrated that rapidly emanating wavefronts from reentrant sources propagate throughout the ventricles and intermittently block, giving rise to wavelets, and DF domains. Consequently, fibrillatory conduction from a stable source may account for the complex patterns of wavefront propagation, together with the organization that is documented in VF.14,15 Our analysis of the lifespan of PSs, which result from fibrillatory conduction and reflect the lifespan of wavelets, suggests that they are too brief (mean lifespan ≈17 ms) to maintain VF. Additionally, their location in the periphery of the fastest domain (see Figures 2 and 5⇑) is consistent with wavebreaks and block of waves emanating from a high-frequency source.
Gradients of excitation frequency have been shown to exist both during atrial fibrillation in sheep16,17and dogs18 and VF in swine.19 Our study in the guinea pig heart is the first to show a highly consistent localization of a stable high-frequency source in the LV. Moreover, this study is the first to describe the maintenance of fibrillation with a correlation to its stationary properties, namely, the LV-to-RV gradient of excitation frequencies. The finding that ionic current differences between the RV and the LV are also highly consistent suggests an ionic mechanism for the formation of a relatively stable high-frequency source in the LV and for the establishment of an LV-to-RV frequency gradient.
Mechanisms of Rapid Reentry and Rotor Stability
During VF, the activation rate is significantly faster than that achievable by either pacemaker activity or rapid pacing.20 Similarly, in our experiments, rotors have significantly briefer CLs (≈30 to 40 ms) than expected from the guinea pig heart whose action potential duration (APD) is ≈200 ms during sinus rhythm.12 Computer simulations suggest that extremely fast rotors may be the result of the strong repolarizing influence exerted by their core, which activates IK1 and leads to extreme abbreviation of the APD in its proximity.21 However, with increasing distance from the core, this influence weakens and APD progressively increases. Consequently, the tissue close to the core achieves very brief CLs, whereas far from the core the myocardium cannot conduct at the rate of the rotor and nonuniform (ie, other than 1:1) conduction develops. In theory, this effect may provide a basis for the results shown in Figure 5 demonstrating that propagation near the rotor was 1:1, and that, at a certain distance from the rotor, intermittent block and wavebreaks developed and slower DF domains were formed. Nevertheless, this mechanism does not explain the consistent localization of the rotors to the anterior free wall of the LV.
Regional differences in currents,22 influencing repolarization, may influence the dynamic behavior of rotors and thus arrhythmias.23 We focused on differences in IK1 density in the LV and the RV because, in addition to controlling the APD, a large IK1 stabilizes the rotor.21 This reasoning is further supported by our current simulations. Upon the incorporation of the experimental I-V relation of IB into our ionic model, the large outward conductance in the LV produced both the necessary abbreviation of the APD for the establishment of high-frequency activity and stability in terms of persistence of the rotor. In contrast, the model with small outward conductance of IB, simulating the RV, was unable to sustain stable reentry. These results confirm previously published computer simulations, which demonstrated that when the outward component of IB is small, the wavetail close to the core propagates more slowly than the wavefront.21 Consequently, wavefront-wavetail interactions develop, producing meandering and eventual termination due to collision with the edges of the sheet (Figure 7B). When the LV and RV models were coupled (Figure 7C), the LV sustained stable reentry. In contrast, wavefront fragmentation, decremental conduction, and intermittent block were most notable in the RV.
These data suggest that the larger amplitude of the LV background conductance may stabilize the rotor in the LV by reducing the APD near the core, thus leading to a decrease in the degree of wavefront-wavetail interactions. On the other hand, the stronger rectification of IB in the RV should prolong APD. Consequently, the RV will be unable to conduct at the frequency of the stable source in the LV (see Figure 1). This does not imply, however, that the RV is incapable of undergoing reentry. Rather, the large difference in the outward component of IK1 suggests that, if rotors are formed in the RV, their frequency will be relatively slow and they will be less stable than in the LV.
Structural Mechanisms of Rotor Stabilization
Kim et al24 suggested that source-sink mismatch between a papillary muscle and the ventricular wall may serve to anchor the rotor. Thus, the two papillary muscles in the LV of the guinea pig heart, which insert in the LV apex and anterior LV wall, may conceivably help to stabilize the rotor. However, in contrast to the experiments of Kim et al24 in which reentry was often terminated by the other wavelets that existed during VF, we observed that the reentrant source remains stable within the field of view as long as 150 rotations, at least in one case (Figure 3). Nevertheless, as 3-dimensional scroll waves are predicted to align their filaments according to the myocardial fibers,13 we cannot rule out the possibility that structures in the LV may somehow stabilize the reentrant circuit.
Other Ion Channels and VF
The demonstration of differences in IK1 density in the LV and the RV myocytes seemed sufficient to account for many aspects of VF dynamics and allowed us to reproduce very closely the experimental results using computer models in which other channels are uniformly distributed. Nevertheless, Beaumont et al9 demonstrated that INa has a major role in the stabilization of spiral-wave reentry and modulates the transition from VF to monomorphic ventricular tachycardia (MVT). Thus, we cannot exclude a role of INa characteristics in the dynamics observed. Similarly, ICa blockade was demonstrated to stabilize reentry and convert VF to MVT by reducing rotor frequency and wavefront fragmentation.8 Consequently, we cannot discount the involvement of ICa in the observed phenomena. Moreover, while we focused on structurally normal hearts, in diseased hearts, other currents (eg, IKATP) may play an important role in the manifestation of the arrhythmia.25
Fibrillation in Other Species
In the present study, we clearly supported the hypotheses that, in the structurally normal guinea pig heart, a stable reentrant source is the underlying mechanism of VF, and that the stabilization of the source and complexity seen in VF may be the result of regional differences in potassium currents. Nevertheless, fibrillation may span a spectrum of mechanisms. For example, Gray et al10 demonstrated that theoretically each rotor occupies a minimum area. Thus, small hearts, eg, guinea pig and rabbit, can accommodate only a few (1 or 2) rotors, whereas in larger hearts, eg, sheep, dogs, and humans, a greater number of rotors may exist during VF. Moreover, the electrophysiological properties of myocytes of different species vary greatly,22 and such heterogeneity across species again may influence rotor behavior and arrhythmia manifestation. Therefore, the frequencies observed here, which are significantly faster in comparison to the DF frequencies reported in other species,8,10,19 may be due to the unique ionic makeup of the guinea pig myocytes. Finally, in particular hearts, a single drifting rotor may produce fibrillatory dynamics, whereas in other hearts, a stable source within the ventricles may be responsible for VF, and still in other hearts, larger numbers of stable or drifting rotors may coexist, with each dominating a region of the ventricle and thus producing fibrillation. These alternatives are not mutually exclusive in that vortex-like reentry is most likely underlying fibrillation.
The limitations of optical mapping and signal analysis have been discussed at length elsewhere.7,8,26 The current density-voltage relationship of IB recorded here shows a reversal potential of −84 mV and inward rectification, which suggests that IB is predominantly IK1.27 However, potential contaminants may be present (eg, INa). However, this is very unlikely since IB was activated by a slow ramp (1.6 mV/s), which probably inactivated fast inward sodium channels. In addition, in a subset of experiments (5 cells), there was no significant difference in the current before and after administration of tetrodotoxin (30 μmol/L). Further, the use of nifedipine (2 μmol/L) eliminates contamination by the L-type calcium current. Because no sodium ions were included in the pipette solution, the activity of the Na+-K+ pump was minimal.27 Finally, because the pipette solution contained 5 mmol/L of EGTA and no calcium ions, the activity of the Na+-Ca2+ exchanger should also be minimal.27 We therefore believe that the background current IB is mostly IK1. However, it will be necessary to carry out single-channel studies with the appropriate pharmacological treatments to firmly establish this. Finally, the limitations of the computer model are described elsewhere.9 However, please note that sarcolemmal currents, such as inactivation of the calcium current, the sodium-calcium exchanger, and the calcium pump, although important in the regulation of APD, were not incorporated here because when there are too many parameters, the model becomes underdetermined with respect to the experimental data.9
This work was supported by grants PO1 HL39707 and HL60843 from the NHLBI and grants from the NIH (1S10RR12917) and the Whitaker Foundation (to J.B.). We thank Jiang Jiang, Fan Yang, Robert Morton, Matthew Brunson, and Ploy Siripornsawan for assistance; Janet Jackson for secretarial support; and Dr Eduardo Solessio for insightful discussions. Simulations were performed at supercomputer centers of Boston University, UC San Diego, and on a Sun E6500 at SUNY Upstate Medical University.
Original received June 11, 2001; revision received October 15, 2001; accepted October 15, 2001.
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