|
|
||||||||
1 Division of Cardiology, Department of Medicine, Cedars-Sinai Medical Center, and 2 Division of Cardiology, Departments of Medicine, Physiology, and Physiological Science and the Cardiovascular Research Laboratory, University of California at Los Angeles School of Medicine, Los Angeles, California 90048-1865; and 3 Department of Physics and Astronomy, Vanderbilt University, Nashville, Tennessee 37235
| |
ABSTRACT |
|---|
|
|
|---|
The effects of acute amiodarone infusion on dynamics of ventricular fibrillation (VF) are unclear. Six isolated swine right ventricles (RVs) were studied in vitro. Activation patterns during VF were mapped optically, whereas action potentials were recorded with a glass microelectrode. At baseline, VF was associated with frequent spontaneous wave breaks. Amiodarone (2.5 µg/ml) reduced spontaneous wave breaks and increased the cycle length (CL) of VF from 83.3 ± 17.8 ms at baseline to 118.4 ± 25.8 ms during infusion (P < 0.05). Amiodarone increased the reentrant wave front CL (114.4 ± 15.5 vs. 78.2 ± 19.0 ms, P < 0.05) and central core area (4.1 ± 3.8 vs. 0.9 ± 0.3 mm2, P < 0.05). Within 30 min of infusion, VF terminated (n = 1), converted to ventricular tachycardia (VT) (n = 1) or continued at a slower rate (n = 4). Amiodarone flattened the APD restitution curves. We conclude that amiodarone reduced spontaneous wave breaks. It might terminate VF or convert VF to VT. These effects were associated with the flattening of APD restitution slope and increased core size of reentrant wave fronts.
optical mapping; action potential duration restitution; sudden death; pharmacology; antiarrhythmic agents
| |
INTRODUCTION |
|---|
|
|
|---|
INTRAVENOUS AMIODARONE is a commonly used antiarrhythmic agent in the treatment of life-threatening ventricular tachyarrhythmia (13). However, few studies have examined the mechanisms by which amiodarone is effective against ventricular fibrillation (VF). We (27) previously proposed that transition from ventricular tachycardia (VT) to VF is a transition to spatiotemporal chaos, with similarities to the quasi-periodic route to chaos seen in fluid turbulence. In this scenario, chaos results from the interaction of multiple causally independent oscillatory motions. Computer simulations and animal experiments suggest that the destabilizing oscillatory motions during spiral-wave reentry arise from restitution properties of action potential duration (APD). Modifying APD restitution characteristics can prevent spiral-wave breakup in simulated cardiac tissue, suggesting that drugs with similar effects in real cardiac tissue may have antifibrillatory efficacy (the restitution hypothesis). Intravenous amiodarone is effective in treating patients with life-threatening ventricular arrhythmias and is now included in the new American Heart Association guidelines for advanced cardiopulmonary life support (7). The purpose of this study was to investigate the mechanisms underlying antifibrillatory effects of amiodarone and to determine whether flattening of APD restitution may be involved in its antifibrillatory actions.
| |
METHODS |
|---|
|
|
|---|
The research protocol was approved by the institutional animal care and use committee and followed the guidelines of the American Heart Association. The details of the isolated right ventricle (RV) preparation have been reported elsewhere (9). Briefly, six farm pigs (25-32 kg) were anesthetized and the hearts were removed. The RV was placed in tissue bath with the epicardial side up and was perfused with oxygenated Tyrode solution (37.0 ± 0.5°C, pH 7.4 ± 0.5) through the right coronary artery. The composition of the Tyrode solution was the following (in mM): 125.0 NaCl, 4.5 KCl, 0.5 MgCl2, 0.54 CaCl2, 1.2 NaH2PO4, 24.0 NaHCO3, 5.5 glucose, and 50 mg/l albumin. Two bipolar electrodes were attached to the epicardial surface: one for continuous recording and the other for pacing. Two Endotak defibrillation electrodes (Guidant) were placed on two opposing sides of the tissue bath for electrical defibrillation.
Optical mapping system.
We stained four of six RVs and optically mapped the patterns of
epicardial activation. The optical mapping system used in the present
study was similar to the one described previously (15).
Fluorescence from RV epicardium was elicited by a solid state,
frequency doubled laser (Verdi, Coherent) at a wavelength of 532 nm.
Laser light was delivered to the RV with the use of multiple 1-mm
optical fibers (model SP-SF-960, FIS). The RVs were stained for 20 min
with
4-[
-2(di-n-butylamino)-6-naphthyl]vinyl]pyridinium (di-4-ANEPPS; Molecular Probes) 10 µmol/l in the perfusate. The emitting fluorescence was imaged with a 12-bit digital charge-coupled device camera (model CA-D1-0128T, Dalsa) through a 600-nm
long-pass glass filter (model R60, Nikon) and a 25-mm/f0.85 video lens
(model CF25L, Fujinon). Video images at 128 × 128 pixels were
acquired over 30 × 30 mm2 at 2.3 ms/frame and were
transferred to a personal computer with a frame grabber (Imaging
Technology). An excitation-contraction uncoupler was not used in the
current study. We recorded 2.3 s of data during each acquisition.
Transmembrane potential recordings and the APD restitution
curves.
Transmembrane potentials (TMPs) were recorded from an epicardial site
using a standard glass microelectrode (9) or pure iridium
metal microelectrode (18). For APD measurements, a
custom-written program selected as time of activation ( phase
0) if the voltage change over time (dV/dt) at that time
was greater than both of its temporal neighbors and that the
dV/dt was
5 V/s. The program then looked forward in time
to determine AP peak (voltage greater than both neighbors) and looked
backward in time to determine baseline (voltage less than both
neighbors). The voltage difference between the peak and the baseline
was the AP amplitude. The program then looked forward in time from the
AP peak until the voltage dropped by a value equal to 90% of the AP
amplitude. That time is the time of 90% repolarization and the
temporal difference between phase 0 and 90% repolarization
is the APD90. The diastolic interval (DI) was defined as
the difference between 90% repolarization and the onset of the next
activation. Cycle length (CL) was defined by the temporal difference
between consecutive activations. Manual editing was then performed to
eliminate noise.
|
0, we either omitted
those data (first method) or manually estimated the negative DI, as shown in Fig. 1D (second method). The APD restitution curve
was estimated by single exponential fitting with the use of ORIGIN software (Microcal).
Study protocol. In all isolated RVs, spontaneous VF occurred during the isolation procedure and persisted in the tissue bath. The patterns of activation were mapped while TMPs were simultaneously recorded. Four RVs were defibrillated to allow APD recordings during dynamic pacing. VF was then reinitiated by rapid pacing. Amiodarone (2.5 µg/ml) was then added to the perfusate for 30 min. TMP recordings and optical mapping studies were repeated at 3-min intervals. Reversibility of the effects of amiodarone was assessed with drug-free Tyrode perfusion for 60 min. Inducibility of VF was then tested by electrical stimulation, using the dynamic and fixed rate rapid pacing (CL as short as 50 ms) protocols.
Data analysis. Reentrant wave fronts were identified, and the sizes of their cores were measured by tracing the path of the wave break points. If the path led to a closed loop, then the area encircled by this loop was used as the core size (16). The mean number of wavelets per frame was obtained from the number of wavelets observed every 100 frames (230 ms apart). Density of wavelets was obtained by dividing the number of wavelets by the mapped area (3 cm × 3 cm). The incidence of spontaneous wave breaks was the ratio between the total number of wave breaks observed divided by the total duration of VF analyzed.
Statistical analysis.
Data are presented as means ± SD. Student's t-tests
were used to compare means. Analysis of variance with a Newman-Keuls
test was used when multiple comparisons were performed. A P
value
0.05 was considered significant.
| |
RESULTS |
|---|
|
|
|---|
Table 1 summarizes the results of
the study. At pacing CL of 400 ms, amiodarone significantly decreased
the maximum derivative of voltage relation to time
[(dV/dt)max], prolonged the APD90 and increased the effective refractory period (Table 1).
|
Effects of amiodarone infusion on VF. VF CL, APD90, and DI were prolonged by amiodarone infusion (Table 1). At the end of 30-min infusion, amiodarone resulted in the conversion from VF to VT in 1 RV and VF termination in 1 RV. In the remaining 4 RVs, VF continued at a slower rate. At that time we replaced the perfusate with amiodarone-free Tyrode solution to evaluate the reversibility of the effect of the drug. However, during the drug-free washout period, the VF and VT CLs continued to lengthen and eventually all RVs became quiescent. We then attempted to reinduce VF up to 1 h after the beginning of washout. In no RV was the VF inducible.
Amiodarone infusion progressively increased CL, reduced the density of wavelets, and the incidence of spontaneous wave breaks (Table 1). Single-cell TMP recordings showed that amiodarone resulted in a reduction of the low amplitude and fast activations in VF, leading to the transition to VT or to a slower CL VF (Fig. 1). We identified 11, 4, and 3 reentrant wave fronts in VF episodes shown in Fig. 1, A-C. There was a progressive increase of the CL of reentrant wave front after amiodarone infusion (Table 1). Video images revealed the effects of amiodarone on wave dynamics during VF. At baseline, VF was characterized by the presence of multiple irregular wave fronts and spontaneous wave breaks (Fig. 2, top). These gave rise to the irregular TMP recordings (Fig. 1A). Figure 2, bottom, illustrates typical activation patterns during amiodarone infusion. A single wave front propagated from the bottom right to the top left corner of Fig. 2. The wavelet propagates repeatedly without breaking, leading in this example to complete elimination of spontaneous wave breaks in the mapped region and a decrease in the number of wavelets. These changes also gave rise to the periodic activity in the TMP recordings (Fig. 1C).
|
|
Effects of amiodarone on APD restitution.
Figure 4A shows action
potential recordings at baseline (left) and during
amiodarone infusion (Fig. 4A, right). During
dynamic pacing, the pacing intervals were fixed for eight beats
(S1), followed by an abrupt shortening of pacing interval.
The first beat of the shortened interval is equivalent to a premature
stimulus (S2). This figure shows the AP induced by the last
two S1 and the S2. The shortest
S1/S2 achieved at baseline was 160/150 ms, with
a corresponding S2 APD of 113 ms. During amiodarone
infusion, the shortest S1/S2 increased to
200/190 ms, resulting in an S2 APD of 148 ms. Figure
4B shows an example of dynamic APD restitution curve.
Amiodarone increased the APD at all diastolic intervals. Amiodarone
significantly reduced the maximum slope of APD90
restitution curve. It also appeared to have increased the shortest DI
achieved during dynamic pacing. However, the latter increase was not
statistically significant (Table 1). Figure
5 shows examples of APD restitution curves during VF at baseline and during amiodarone infusion while RV
was still fibrillating. Amiodarone flattened the slope of
APD90 restitution curve, particularly at short DIs. Table 1
shows the effects of amiodarone infusion in all RVs studied. The DIs
associated with the maximum slope of APD90 restitution
curve at baseline and during amiodarone infusion were <10 ms (Table
1).
|
|
| |
DISCUSSION |
|---|
|
|
|---|
In this study we demonstrated that amiodarone infusion reduced the slope of the APD restitution curve, enlarged the core of reentrant wave front and suppressed spontaneous wave breaks in VF. These changes were associated with a decreased number of wavelets, the termination of VF, or the transition from VF to VT.
Mechanism of antiarrhythmic drug action.
An explanation for the antifibrillatory action of amiodarone is its
-blocking effects (8). Because the RVs were isolated from the rest of the body, they were not influenced by the systemic sympathetic activity. However, local sympathetic nerve terminals might
still be active during VF. It is therefore possible that some of the
antifibrillatory effects of amiodarone in swine RV were due to
-blocking effects.
Comparing amiodarone with bretylium and verapamil. Bretylium and verapamil are also effective in flattening the restitution curve (5, 20) but are less useful than amiodarone in treating or preventing clinical VF in human patients. Bretylium (10) results in norepinephrine release during initial administration. It also results in significant orthostatic hypotension and is therefore poorly tolerated. For verapamil to flatten the restitution curve, a concentration of 1,000-3,000 ng/ml is needed (2, 20). This concentration is at least twice as high as what can be achieved with a maximum oral dose of verapamil (120 mg every 6 h) (25). These data indicate that a very high (or toxic) dose of verapamil is needed to reach a serum concentration sufficient to flatten the restitution curve. In comparison, we showed in this study that amiodarone 2.5 µg/ml may flatten restitution curve and exerts significant effects on the patterns of activation in VF. This serum concentration can be easily achieved with 5 mg/kg intravenous amiodarone (6). Therefore, amiodarone is clinically more useful than verapamil or bretylium in treating patients with VT and VF.
Limitation of the study. The first limitation is that acute effects of amiodarone cannot be reversed. Therefore, we were not able to test whether or not the effects of amiodarone are reversible on washout. A second limitation is that we used isolated normal RV in the study. It is unclear whether or not the results are applicable to diseased human hearts. A third limitation is that calcium channel blockers (20) and bretylium (5) are also known to flatten APD restitution. However, these drugs are not as effective as amiodarone in treating human VF. Therefore, flattening of APD restitution may only partially explain the antifibrillatory effects of amiodarone.
In conclusion, amiodarone infusion reduced spontaneous wave breaks and the density of VF wavelets. It might terminate VF or convert VF to VT. These effects were associated with the flattening of APD restitution slope and increased the core size of reentrant wave fronts.| |
ACKNOWLEDGEMENTS |
|---|
We thank Juliana Cho Glick and Wyeth-Ayerst Laboratories for providing amiodarone used in the study. We also thank Scott Lamp for the data analysis software, Avile McCullen and Meiling Yuan for technical assistance, and Elaine Lebowitz for secretarial assistance.
| |
FOOTNOTES |
|---|
This study was supported by a grant from Cedars-Sinai Electrocardiographic Heart Beat Organization Foundation and Sweepstakes Award (to H. S. Karagueuzian), a Pauline and Harold Price Endowment (to P.-S. Chen), and the Laubisch and the Kawata Endowments (to J. N. Weiss). This study was also supported in part by National Heart, Lung, and Blood Institute Grants P50-HL-52319 and HL-66389, American Heart Association Grants 9750623N and 9950464N, by University of California Tobacco-Related Disease Research Program Grant 9RT-0041, and by the Ralph M. Parsons Foundation, Los Angeles, CA.
Address for reprint requests and other correspondence: P.-S. Chen, Rm. 5342, Cedars-Sinai Medical Center, 8700 Beverly Blvd., Los Angeles, CA 90048-1865 (E-mail: chenp{at}cshs.org).
The costs of publication of this article were defrayed in part by the payment of page charges. The article must therefore be hereby marked "advertisement" in accordance with 18 U.S.C. Section 1734 solely to indicate this fact.
10.1152/ajpheart.00633.2001
Received 19 July 2001; accepted in final form 12 November 2001.
| |
REFERENCES |
|---|
|
|
|---|
1.
Cao, JM,
Qu Z,
Kim YH,
Wu TJ,
Garfinkel A,
Weiss JN,
Karagueuzian HS,
and
Chen PS.
Spatiotemporal heterogeneity in the induction of ventricular fibrillation by rapid pacing: importance of cardiac restitution properties.
Circ Res
84:
1318-1331,
1999
2.
Colatsky, TJ,
and
Hogan PM.
Effects of external calcium, calcium channel-blocking agents, and stimulation frequency on cycle length-dependent changes in canine cardiac action potential duration.
Circ Res
46:
543-552,
1980
3.
Follmer, CH,
Aomine M,
Yeh JZ,
and
Singer DH.
Amiodarone-induced block of sodium current in isolated cardiac cells.
J Pharmacol Exp Ther
243:
187-194,
1987
4.
Frame, LH,
and
Simson MB.
Oscillations of conduction, action potential duration, and refractoriness. A mechanism for spontaneous termination of reentrant tachycardias.
Circulation
78:
1277-1287,
1988
5.
Garfinkel, A,
Kim YH,
Voroshilovsky O,
Qu Z,
Kil JR,
Lee MH,
Karagueuzian HS,
Weiss JN,
and
Chen PS.
Preventing ventricular fibrillation by flattening cardiac restitution.
Proc Natl Acad Sci USA
97:
6061-6066,
2000
6.
Ikeda, N,
Nademanee K,
Kannan R,
and
Singh BN.
Electrophysiologic effects of amiodarone: experimental and clinical observation relative to serum and tissue drug concentrations.
Am Heart J
108:
890-898,
1984[ISI][Medline].
7.
International Guidelines 2000 for CPR and ECC.
Part 6: advanced cardiovascular life support: section 5: pharmacology I: agents for arrhythmias.
Circulation
102:
I112-I128,
2000[Medline].
8.
Kadish, AH,
Chen RF,
Schmaltz S,
and
Morady F.
Magnitude and time course of
-adrenergic antagonism during oral amiodarone therapy.
J Am Coll Cardiol
16:
1240-1245,
1990[Abstract].
9.
Kim, YH,
Garfinkel A,
Ikeda T,
Wu TJ,
Athill CA,
Weiss JN,
Karagueuzian HS,
and
Chen PS.
Spatiotemporal complexity of ventricular fibrillation revealed by tissue mass reduction in isolated swine right ventricle. Further evidence for the quasiperiodic route to chaos hypothesis.
J Clin Invest
100:
2486-2500,
1997[ISI][Medline].
10.
Koch-Weser, J.
Prevention of sudden coronary death by chronic antiarrhythmic therapy.
Adv Cardiol
25:
206-228,
1978[Medline].
11.
Kodama, I,
Kamiya K,
and
Toyama J.
Cellular electropharmacology of amiodarone.
Cardiovasc Res
35:
13-29,
1997
12.
Koller, ML,
Riccio ML,
and
Gilmour RF, Jr.
Dynamic restitution of action potential duration during electrical alternans and ventricular fibrillation.
Am J Physiol Heart Circ Physiol
275:
H1635-H1642,
1998
13.
Kudenchuk, PJ,
Cobb LA,
Copass MK,
Cummins RO,
Doherty AM,
Fahrenbruch CE,
Hallstrom AP,
Murray WA,
Olsufka M,
and
Walsh T.
Amiodarone for resuscitation after out-of-hospital cardiac arrest due to ventricular fibrillation.
N Engl J Med
341:
871-878,
1999
14.
Lee, MH,
Lin SF,
Ohara T,
Omichi C,
Okuyama Y,
Chudin E,
Garfinkel A,
Weiss JN,
Karagueuzian HS,
and
Chen PS.
Effects of diacetyl monoxime and cytochalasin D on ventricular fibrillation in swine right ventricles.
Am J Physiol Heart Circ Physiol
280:
H2689-H2696,
2001
15.
Lin, SF,
Roth BJ,
and
Wikswo JP, Jr.
Quatrefoil reentry in myocardium: an optical imaging study of the induction mechanism.
J Cardiovasc Electrophysiol
10:
574-586,
1999[ISI][Medline].
16.
Mandapati, R,
Asano Y,
Baxter WT,
Gray R,
Davidenko J,
and
Jalife J.
Quantification of effects of global ischemia on dynamics of ventricular fibrillation in isolated rabbit heart.
Circulation
98:
1688-1696,
1998
17.
Nolasco, JB,
and
Dahlen RW.
A graphic method for the study of alternation in cardiac action potentials.
J Appl Physiol
25:
191-196,
1968
18.
Omichi, C,
Lee MH,
Ohara T,
Naik AM,
Wang NC,
Karagueuzian HS,
and
Chen PS.
Comparing cardiac action potentials recorded with metal and glass microelectrodes.
Am J Physiol Heart Circ Physiol
279:
H3113-H3117,
2000
19.
Rensma, PL,
Allessie MA,
Lammers WJEP,
Bonke FIM,
and
Schalij MJ.
Length of excitation wave and susceptibility to reentrant atrial arrhythmias in normal conscious dogs.
Circ Res
62:
395-410,
1988
20.
Riccio, ML,
Koller ML,
and
Gilmour RFJ
Electrical restitution and spatiotemporal organization during ventricular fibrillation.
Circ Res
84:
955-963,
1999
21.
Samie, FH,
Mandapati R,
Gray RA,
Watanabe Y,
Zuur C,
Beaumont J,
and
Jalife J.
A mechanism of transition from ventricular fibrillation to tachycardia: effect of calcium channel blockade on the dynamics of rotating waves.
Circ Res
86:
684-691,
2000
22.
Sheldon, RS,
Hill RJ,
Cannon NJ,
and
Duff HJ.
Amiodarone: biochemical evidence for binding to a receptor for class I drugs associated with the rat cardiac sodium channel.
Circ Res
65:
477-482,
1989
23.
Ujhelyi, MR,
Sims JJ,
and
Miller AW.
Induction of electrical heterogeneity impairs ventricular defibrillation: an effect specific to regional conduction velocity slowing.
Circulation
100:
2534-2540,
1999
24.
Voroshilovsky, O,
Qu Z,
Lee MH,
Ohara T,
Fishbein GA,
Huang HL,
Swerdlow CD,
Lin SF,
Garfinkel A,
Weiss JN,
Karagueuzian HS,
and
Chen PS.
Mechanisms of ventricular fibrillation induction by 60-Hz alternating current in isolated swine right ventricle.
Circulation
102:
1569-1574,
2000
25.
Walsh, P.
Physician's Desk Reference. Montvale, NJ: Medical Economics, 2001, p. 2981.
26.
Wang, J,
Feng J,
and
Nattel S.
Class III antiarrhythmic drug action in experimental atrial fibrillation. Differences in reverse use dependence and effectiveness between d-sotolol and the new antiarrhythmic drug ambasilide.
Circulation
90:
2032-2040,
1994
27.
Weiss, JN,
Garfinkel A,
Karagueuzian HS,
Qu Z,
and
Chen PS.
Chaos and the transition to ventricular fibrillation: a new approach to antiarrhythmic drug evaluation.
Circulation
99:
2819-2826,
1999
28.
Yabek, SM,
Kato R,
and
Singh BN.
Effects of amiodarone and its metabolite, desethylamiodarone, on the electrophysiologic properties of isolated cardiac muscle.
J Cardiovasc Pharmacol
8:
197-207,
1986[ISI][Medline].
This article has been cited by other articles:
![]() |
M. Hayashi, S. Takatsuki, P. Maison-Blanche, A. Messali, A. Haggui, P. Milliez, A. Leenhardt, and F. Extramiana Ventricular Repolarization Restitution Properties in Patients Exhibiting Type 1 Brugada Electrocardiogram With and Without Inducible Ventricular Fibrillation J. Am. Coll. Cardiol., March 25, 2008; 51(12): 1162 - 1168. [Abstract] [Full Text] [PDF] |
||||
![]() |
S. M. Narayan, M. R. Franz, G. Lalani, J. Kim, and A. Sastry T-Wave Alternans, Restitution of Human Action Potential Duration, and Outcome J. Am. Coll. Cardiol., December 18, 2007; 50(25): 2385 - 2392. [Abstract] [Full Text] [PDF] |
||||
![]() |
S. Iravanian and D. J. Christini Optical mapping system with real-time control capability Am J Physiol Heart Circ Physiol, October 1, 2007; 293(4): H2605 - H2611. [Abstract] [Full Text] [PDF] |
||||
![]() |
G. A. Ng, K. E. Brack, V. H. Patel, and J. H. Coote Autonomic modulation of electrical restitution, alternans and ventricular fibrillation initiation in the isolated heart Cardiovasc Res, March 1, 2007; 73(4): 750 - 760. [Abstract] [Full Text] [PDF] |
||||
![]() |
S. F. Mironov, F. J. Vetter, and A. M. Pertsov Fluorescence imaging of cardiac propagation: spectral properties and filtering of optical action potentials Am J Physiol Heart Circ Physiol, July 1, 2006; 291(1): H327 - H335. [Abstract] [Full Text] [PDF] |
||||
![]() |
S. C. Hao, D. J. Christini, K. M. Stein, P. N. Jordan, S. Iwai, O. Bramwell, S. M. Markowitz, S. Mittal, and B. B. Lerman Effect of {beta}-adrenergic blockade on dynamic electrical restitution in vivo Am J Physiol Heart Circ Physiol, July 1, 2004; 287(1): H390 - H394. [Abstract] [Full Text] [PDF] |
||||
![]() |
E. M. Cherry and F. H. Fenton Suppression of alternans and conduction blocks despite steep APD restitution: electrotonic, memory, and conduction velocity restitution effects Am J Physiol Heart Circ Physiol, June 1, 2004; 286(6): H2332 - H2341. [Abstract] [Full Text] [PDF] |
||||
![]() |
P. Kirchhof, H. Degen, M. R. Franz, L. Eckardt, L. Fabritz, P. Milberg, S. Laer, J. Neumann, G. Breithardt, and W. Haverkamp Amiodarone-Induced Postrepolarization Refractoriness Suppresses Induction of Ventricular Fibrillation J. Pharmacol. Exp. Ther., April 1, 2003; 305(1): 257 - 263. [Abstract] [Full Text] |
||||
| ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| HOME | HELP | FEEDBACK | SUBSCRIPTIONS | ARCHIVE | SEARCH | TABLE OF CONTENTS |
| Visit Other APS Journals Online |