|
|
||||||||
Department of Physiology and Biophysics, The University of Texas Medical Branch, Galveston, Texas 77555-0641
| |
ABSTRACT |
|---|
|
|
|---|
Bronchoconstriction in asthmatic patients is frequently associated with gastroesophageal reflux. However, it is still unclear whether bronchoconstriction originates from the esophagus or from aspiration of the refluxate into the larynx and larger airway. We compared the effect of repeated esophageal and laryngeal instillations of HCl-pepsin (pH 1.0) on tracheal smooth muscle activity in eight anesthetized and artificially ventilated dogs. Saline was used as control. We used pressure in the cuff of an endotracheal tube (Pcuff) as a direct index of smooth muscle activity at the level of the larger airways controlled by vagal efferents. The Pcuff values of the first 60 s after instillations were averaged, and the difference from the baseline values was evaluated. Changes in Pcuff were significantly greater with laryngeal than with esophageal instillations (P = 0.0166). HCl-pepsin instillation into the larynx evoked greater responses than did saline (P = 0.00543), whereas no differences were detected with esophageal instillations. Repeated laryngeal exposure enhanced the responsiveness significantly (P < 0.001). Our data indicate that the larynx is more important than the esophagus as a reflexogenic site for the elicitation of reflex bronchoconstriction in response to acidic solutions.
gastroesophageal reflux; acid-induced laryngitis; laryngeal reflexes; esophageal reflexes
| |
INTRODUCTION |
|---|
|
|
|---|
GASTROESOPHAGEAL REFLUX (GER) is often associated with bronchial asthma (2,19); however, the nature of the association is not fully understood. Although bronchoconstriction has been viewed as a result of gastric refluxate through a vagally mediated reflex (8, 18, 32), it is still controversial whether this reflex originates from the esophagus or the airway. Mendelson (20) was the first to describe "asthmatic-like" reactions induced by aspiration of gastric contents into the airway during induction of general anesthesia (Mendelson syndrome), and he considered aspiration into the airway to be the most important factor for the elicitation of bronchoconstriction. In fact, even if the refluxate does not reach the lower airways, small amounts of aspiration can cause several kinds of reflexes because of the high responsiveness of the larynx (4, 6, 22, 25, 31). This contention is also supported by the observation that acid-induced laryngitis is often seen in GER patients (5, 10, 16, 27).
Conflicting results have been reported on the reflexogenic role of the esophagus in acid-induced bronchoconstriction. Several investigators (17, 18, 23, 26, 29) concluded that esophageal acidification does cause reflex bronchoconstriction, whereas others did not find any substantial evidence for the reactivity to acid solution. In fact, Ekstrom and Tibbling (7) and Wesseling et al. (30) did not find any association of bronchoconstriction with esophageal acidification. The difficulties with these reports are that most of the studies assessed bronchoconstriction by conventional, effort-dependent pulmonary function tests (e.g., peak expiratory flow; forced expiratory volume at 1 s). More direct evidence of reflex bronchoconstriction is desirable for disclosing reflexogenic sites.
Recently, we reported (14) that pressure in the cuff of an endotracheal tube (Pcuff) provides a more sensitive index of airway smooth muscle activity than does total lung resistance, especially when the response is mediated by the vagal efferents. In fact, this index reflects smooth muscle contraction or dilatation of the portion of tracheobronchial tree directly innervated by the vagus (14). We believe that this measurement could more clearly reveal whether the airway or the esophagus is more important for acid-induced reflex bronchoconstriction. The larynx was chosen from the rest of the airways, because it is first exposed to refluxate after the regurgitation has reached the pharynx.
| |
METHODS |
|---|
|
|
|---|
General preparation.
The study was conducted, after approval of the Institutional Animal
Care and Use Committee, on eight healthy mongrel dogs of either sex
(weight 12.3-18.2 kg). The animals were sedated with ketamine (10 mg/kg im) and were anesthetized with a mixture of urethan and
-chloralose (500 and 50 mg/kg iv, respectively). The dog was placed
in a supine position on an operating table. The femoral artery and vein
were catheterized to monitor blood pressure and to administer drugs.
Tracheostomy was established, and an endotracheal tube with a
high-volume, low-pressure cuff (7.5-mm ID; Rüchlit, Waiblingen,
Germany) was inserted in the extrathoracic portion of the trachea. The
cuff was filled with enough distilled water (2-5 ml) to provide a
complete seal with the tracheal wall. A pressure transducer (P10EZ;
Gould, Valley View, OH) was connected to the liquid-filled cuff to
measure Pcuff; the transducer was placed at the same height as the
tracheal cuff. The animal was then artificially ventilated with a
constant-volume-type ventilator (model 607; Harvard Apparatus, Millis,
MA) and paralyzed with doxacurium chloride (2.5 mg iv). This muscle
relaxant has virtually no autonomic effects at the dose used (3, 13). Tidal volume (12-16 ml/kg) and breathing frequency (10-18
breaths/min) were adjusted to maintain end-tidal
CO2 at a concentration of 5.8-6.2% as measured by a precalibrated infrared gas analyzer (Medical Gas Analyzer LB-2; Beckman, Schiller Park, IL).
1 · h
1;
-chloralose, 15 mg · kg
1 · h
1;
doxacurium, 0.5 mg/h). In addition to Pcuff and blood pressure, tracheal airflow and pressure were also obtained by using a no. 1 Fleisch-type pneumotachograph connected to a differential transducer (model 15196; Gould, Hato Rey, Puerto Rico) and a differential transducer (model 16720, Gould) with one port open to atmosphere. All
signals were digitized at 100 Hz per channel with an analog-to-digital converter (AT-CODAS Data-Acquisition Card; Dataq Instruments, Akron,
OH) and stored in an IBM-compatible computer.
Experimental protocol. The larynx and the esophagus were challenged with a solution of hydrochloric acid containing 0.2 g/l pepsin (HCl-P; pH 1.0); saline (0.9% NaCl unbuffered, pH 6.4) was used as control. The order of the challenges was randomized among dogs, between larynx and esophagus, but saline was always given first. A volume of 4 ml was instilled into the larynx with a polyethylene catheter inserted through the tracheal stoma and advanced cranially until the tip reached the larynx. This catheter has multiple side holes over the distal 3 cm to allow the instilled solution to reach a wide area. To minimize the possible mechanical stimulation by the catheter, 10-15 s were allowed between insertion and instillation; in any case, we made sure that Pcuff was in the baseline condition before starting the instillation. For the esophageal instillations (8 ml), the same type of catheter was placed into either the proximal or the distal portion of the esophagus (4 dogs each) and left in situ. The determination of proximal and distal portion of the esophagus was established as follows: a catheter was inserted through the mouth into the esophagus and gently pushed forward until the tip reached the lower esophageal sphincter (the catheter could not be pushed any further). Then the catheter was withdrawn 5 cm for the distal esophageal instillations; proper placement was confirmed postmortem. For the proximal esophageal instillations, the catheter tip was placed midway in the extrathoracic portion of the esophagus; this position was confirmed by direct palpation of the catheter tip across the esophageal wall. All instillations were performed at end-expiratory volume. At 5 min after instillation, the solution was removed by suctioning, and an interval of 10 min was allowed before the next instillation. One experimental session consisted of one saline and one HCl-P instillation into the laryngeal and the esophageal lumina. A total of six sessions was completed in each dog.
Data and statistical analysis.
The response was quantified by calculating the difference between the
average of the Pcuff value in the first 60 s after an instillation and
the corresponding baseline value (
Pcuff). The Pcuff values
corresponding to the three consecutive breaths immediately preceding
the instillation were averaged and was used as the baseline value.
| |
RESULTS |
|---|
|
|
|---|
Figure 1 shows experimental records from
one dog; HCl-P instillation into the larynx clearly increased Pcuff,
whereas instillation into the esophagus did not. Biphasic responses in
Pcuff were often seen with HCl-P instillations into the larynx. The
second phases of the biphasic responses with laryngeal HCl-P
instillations were sustained for ~1-2 min. Figure
2 represents the mean values of
Pcuff
obtained from all the sessions and shows the sustained effects of HCl-P
instillation into the larynx compared with the other types of
instillation. This sustained effect of HCl-P instillations on Pcuff is
more evident after the third experimental sessions. Figure
3 represents the overall results with
statistical comparisons. The responses with the proximal and distal
esophageal instillation were nested, because no visible difference was
observed.
|
|
|
Overall, stronger reflexogenic effects were detected from the larynx than from the esophagus (P = 0.0166). HCl-P elicited stronger responses when instilled into the larynx than into the esophagus (P = 0.00635).
HCl-P laryngeal instillations caused significantly larger airway smooth muscle contraction than did saline (P = 0.00543), whereas no statistical difference was detected for the esophageal instillations. Repeated exposure of the larynx, but not of the esophagus, to HCl-P enhanced the response of airway smooth muscle significantly (P < 0.001).
| |
DISCUSSION |
|---|
|
|
|---|
Our present results indicate a much greater importance of the larynx, compared with the esophagus, as a reflexogenic site in response to HCl-P. Our findings confirm the lack of effect of esophageal acidification on respiratory impedance in asthmatic subjects, as reported by Wesseling et al. (30), and on cough elicitation in cats, as reported by Tatar and Pecova (28). The present results are also in partial agreement with studies by other authors who attributed a significant role of the airway as reflexogenic site in humans (15), cats (29), and rabbits (31). These results are also well supported by our companion study on esophageal receptors (26a), in which 28 esophageal receptors from the cervical vagal nerve were tested, and only three were specifically but poorly activated by HCl-P instillation into the esophagus.
On the other hand, our present findings in anesthetized dogs do not agree with other studies conducted on conscious human subjects (17, 18, 23, 26). Species differences and anesthesia could account for the discrepancy. In particular, depth of anesthesia has been shown to have profound effects on respiratory responses to irritant stimuli (21). In addition, we should also realize that, in most of the studies on human subjects, bronchoconstriction was assessed by conventional pulmonary function tests, such as forced expiratory flow in 1 s, which is generally less specific and sensitive than are direct measurements of smooth muscle activity. In fact, these tests cannot eliminate factors related to the particular efforts of the subjects (1, 14). Our present study instead relies on a direct measurement of smooth muscle contraction in an innervated portion of the airway, which is thus directly involved in reflex responses. Moreover, the large airways give a larger contribution to total airway resistance than do the small ones.
We also found that repeated exposures of the larynx to HCl-P solution significantly enhanced the contractile response of airway smooth muscle. This observation may have clinical significance, because chronic laryngitis is frequently associated with GER (5, 16, 27). Thus, in patients with chronic acid-induced laryngitis, repeated aspirations of gastric content into the larynx might cause increasingly severe bronchoconstriction. Although the present study was not aimed at disclosing the precise mechanisms of this enhancement by repeated HCl-P exposures, we may speculate that inflammatory processes or acid-induced injury of the laryngeal epithelium might be involved (24). However, for two main reasons, we do not think that the epithelial damage directly influenced the response of the tracheal smooth muscle: 1) the increases in Pcuff were reversible and 2) the responses were recorded from a site (trachea) different from that where the instillations were performed (larynx). We might speculate that repeated instillations remove the protective layer of mucus and injure the epithelium, exposing the afferent endings more directly to the irritant stimuli and/or decreasing their response threshold. In any case, the contribution of chronic laryngitis to bronchial asthma has not been fully explored.
Laryngeal HCl-P instillations frequently caused biphasic responses in Pcuff. This type of response was very weak or absent with laryngeal saline instillations. We consider the second phase as a very important factor to explain the difference between HCl-P and saline instillations. In fact, the slopes of the increase in Pcuff immediately after laryngeal saline or HCl-P instillations are similar (Fig. 3). This might suggest that the response was rapidly adapting, possibly mostly due to the mechanical effect of the instillations. The second phase, instead, with its prolonged pattern, could be caused by the chemical stimulation of HCl-P. Similar responses were observed by Bradley et al. (4) with single fiber recordings from the superior laryngeal nerve of the sheep. They reported that the typical response to HCl (pH 2.0) applied to the epiglottis started as a high-frequency discharge, followed by low-frequency discharge and again a high-frequency discharge. The biphasic response could thus originate at the receptor level. In any case, even if their results are not directly applicable to our study, they are consistent with our observations.
Hong and Lee (11) and Hong et al. (12) also have reported a biphasic bronchoconstriction caused by cigarette smoke inhalation in guinea pigs. According to their study, the first phase was induced by a combination of cholinergic reflex and tachykinins, whereas the second phase involved cyclooxygenase metabolites. The involvement of noncholinergic system in the pathogenesis of GER was suggested by Hamamoto et al. (9). They proved that esophageal acid instillation caused neurogenic inflammation of the airways, and a neurokinin-1 receptor antagonist suppressed the response. Therefore, we speculate that the bronchoconstriction induced by HCl-P instillation into the larynx could also involve several mechanisms, including a cholinergic reflex as well as a nonadrenergic, noncholinergic system.
Generally, it is thought that the distal portion of the esophagus is more reactive than is the proximal segment. However, we did not find any difference between the two portions.
Concomitantly with smooth muscle contraction, cardiovascular responses were also noted with laryngeal instillations. Sustained hypertension was commonly seen, and, with HCl-P instillation, asystoles were also occasionally observed. These mechanisms can only be speculated on and go beyond the scope of this study.
In summary, our present results indicate a relatively greater importance of the larynx, compared with the esophagus, as a reflexogenic organ in GER-induced reflex bronchoconstriction. The response caused by laryngeal HCl-P instillation featured a biphasic response of airway smooth muscle contraction as well as an enhancement in magnitude after repeated exposures.
| |
ACKNOWLEDGEMENTS |
|---|
This study was supported by National Heart, Lung, and Blood Institute Grant HL-20122. T. Ishikawa was supported in part by Chiba University Hospital, Chiba, Japan.
| |
FOOTNOTES |
|---|
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. §1734 solely to indicate this fact.
Address for reprint requests and other correspondence: G. Sant'Ambrogio, Dept. of Physiology and Biophysics, The Univ. of Texas Medical Branch, 301 Univ. Blvd., Galveston, TX 77555-0641 (E-mail: gsantamb{at}utmb.edu).
Received 6 July 1998; accepted in final form 7 December 1998.
| |
REFERENCES |
|---|
|
|
|---|
1.
American Thoracic Society.
Lung function testing: selection of reference values and interpretative strategies.
Am. Rev. Respir. Dis.
144:
1202-1218,
1991[Medline].
2.
Ayres, J. G.,
and
J. F. Miles.
Oesophageal reflux and asthma.
Eur. Respir. J.
9:
1073-1078,
1996[Abstract].
3.
Basta, S. J.,
J. J. Savarese,
H. H. Ali,
P. B. Embree,
A. F. Schwartz,
G. D. Rudd,
and
W. B. Wastila.
Clinical pharmacology of doxacurium chloride. A new long-acting nondepolarizing muscle relaxant.
Anesthesiology
69:
478-486,
1988[Medline].
4.
Bradley, R. M.,
H. M. Stedman,
and
C. M. Mistretta.
Superior laryngeal nerve response patterns to chemical stimulation of sheep epiglottis.
Brain Res.
276:
81-93,
1983[Medline].
5.
Cherry, J.,
and
S. I. Margulies.
Contact ulcer of the larynx.
Laryngoscope
78:
1937-1940,
1968[Medline].
6.
Davies, A. M.,
J. S. Koenig,
and
B. T. Thach.
Upper airway chemoreflex responses to saline and water in preterm infants.
J. Appl. Physiol.
64:
1412-1420,
1988
7.
Ekstrom, T.,
and
L. Tibbling.
Gastro-oesophageal reflux and triggering of bronchial asthma: a negative report.
Eur. J. Respir. Dis.
71:
177-180,
1987[Medline].
8.
Gustafsson, P. M.,
N. I. Kjellman,
and
L. Tibbling.
Bronchial asthma and acid reflux into the distal and proximal oesophagus.
Arch. Dis. Child.
65:
1255-1258,
1990[Abstract].
9.
Hamamoto, J.,
H. Kohrogi,
O. Kawano,
H. Iwagoe,
K. Fujii,
N. Hirata,
and
M. Ando.
Esophageal stimulation by hydrochloric acid causes neurogenic inflammation in the airways in guinea pigs.
J. Appl. Physiol.
82:
738-745,
1997
10.
Hanson, D. G.,
P. L. Kamel,
and
P. J. Kahrilas.
Outcomes of antireflux therapy for the treatment of chronic laryngitis.
Ann. Otol. Rhinol. Laryngol.
104:
550-555,
1995[Medline].
11.
Hong, J. L.,
and
L. Y. Lee.
Cigarette smoke-induced bronchoconstriction: causative agents and role of thromboxane receptors.
J. Appl. Physiol.
81:
2053-2059,
1996
12.
Hong, J. L.,
I. W. Rodger,
and
L. Y. Lee.
Cigarette smoke-induced bronchoconstriction: cholinergic mechanisms, tachykinins, and cyclooxygenase products.
J. Appl. Physiol.
78:
2260-2266,
1995
13.
Hou, V. Y.,
C. A. Hirshman,
and
C. W. Emala.
Neuromuscular relaxants as antagonists for M2 and M3 muscarinic receptors.
Anesthesiology
88:
744-750,
1998[Medline].
14.
Ishikawa, T.,
S. Sekizawa,
F. B. Sant'Ambrogio,
and
G. Sant'Ambrogio.
Endotracheal cuff pressure as an index of airway smooth muscle activity: comparison with total lung resistance.
Respir. Physiol.
112:
175-184,
1998[Medline].
15.
Jack, C. I.,
P. M. Calverley,
R. J. Donnelly,
J. Tran,
G. Russell,
C. R. Hind,
and
C. C. Evans.
Simultaneous tracheal and oesophageal pH measurements in asthmatic patients with gastro-oesophageal reflux.
Thorax
50:
201-204,
1995[Abstract].
16.
Jacob, P.,
P. J. Kahrilas,
and
G. Herzon.
Proximal esophageal pH-metry in patients with "reflux laryngitis."
Gastroenterology
100:
305-310,
1991[Medline].
17.
Kjellen, G.,
L. Tibbling,
and
B. Wranne.
Bronchial obstruction after oesophageal acid perfusion in asthmatics.
Clin. Physiol.
1:
285-292,
1981[Medline].
18.
Mansfield, L. E.,
and
M. R. Stein.
Gastroesophageal reflux and asthma: a possible reflex mechanism.
Ann. Allergy Asthma Immunol.
41:
224-226,
1978.
19.
Mays, E. E.
Intrinsic asthma in adults. Association with gastroesophageal reflux.
JAMA
236:
2626-2628,
1976[Abstract].
20.
Mendelson, C. L.
The aspiration of stomach contents into the lung during obstetric anesthesia.
Am. J. Obstet. Gynecol.
52:
191-205,
1946.
21.
Nishino, T.,
K. Hiraga,
T. Mizuguchi,
and
Y. Honda.
Respiratory reflex responses to stimulation of tracheal mucosa in enflurane-anesthetized humans.
J. Appl. Physiol.
65:
1069-1074,
1988
22.
Nishino, T.,
T. Kochi,
and
M. Ishii.
Differences in respiratory reflex responses from the larynx, trachea, and bronchi in anesthetized female subjects.
Anesthesiology
84:
70-74,
1996[Medline].
23.
Perpina, M.,
C. Pellicer,
V. Marco,
J. Maldonado,
and
J. Ponce.
The significance of the reflex bronchoconstriction provoked by gastroesophageal reflux in bronchial asthma.
Eur. J. Respir. Dis.
66:
91-97,
1985[Medline].
24.
Sant'Ambrogio, F. B.,
G. Sant'Ambrogio,
and
K. Chung.
Effects of HCl-pepsin laryngeal instillations on upper airway patency-maintaining mechanisms.
J. Appl. Physiol.
84:
1299-1304,
1998
25.
Sant'Ambrogio, G.,
H. Tsubone,
and
F. B. Sant'Ambrogio.
Sensory information from the upper airway: role in the control of breathing.
Respir. Physiol.
102:
1-16,
1995[Medline].
26.
Schan, C. A.,
S. M. Harding,
J. M. Haile,
L. A. Bradley,
and
J. E. Richter.
Gastroesophageal reflux-induced bronchoconstriction. An intraesophageal acid infusion study using state-of-the-art technology.
Chest
106:
731-737,
1994
26a.
Sekizawa, S.-I.,
T. Ishikawa,
F. B. Sant'Ambrogio,
and
G. Sant'Ambrogio.
Vagal esophageal receptors in anesthetized dogs: mechanical and chemical responsiveness.
J. Appl. Physiol.
86:
1231-1235,
1999
27.
Shaker, R.,
M. Milbrath,
J. Ren,
R. Toohill,
W. J. Hogan,
Q. Li,
and
C. L. Hofmann.
Esophagopharyngeal distribution of refluxed gastric acid in patients with reflux laryngitis.
Gastroenterology
109:
1575-1582,
1995[Medline].
28.
Tatar, M.,
and
R. Pecova.
The effect of experimental gastroesophageal reflux on the cough reflex in anesthetized cats.
Bratisl. Lek. Listy
97:
284-288,
1996[Medline]. (In Slovak.)
29.
Tuchman, D. N.,
J. T. Boyle,
A. I. Pack,
J. Scwartz,
M. Kokonos,
A. R. Spitzer,
and
S. Cohen.
Comparison of airway responses following tracheal or esophageal acidification in the cat.
Gastroenterology
87:
872-881,
1984[Medline].
30.
Wesseling, G.,
R. J. Brummer,
E. F. Wouters,
and
V. G. Ten.
Gastric asthma? No change in respiratory impedance during intraesophageal acidification in adult asthmatics.
Chest
104:
1733-1736,
1993
31.
Wetmore, R. F.
Effects of acid on the larynx of the maturing rabbit and their possible significance to the sudden infant death syndrome.
Laryngoscope
103:
1242-1254,
1993[Medline].
32.
Wright, R. A.,
S. A. Miller,
and
B. F. Corsello.
Acid-induced esophagobronchial-cardiac reflexes in humans.
Gastroenterology
99:
71-73,
1990[Medline].
This article has been cited by other articles:
![]() |
I. M. Lang, S. T. Haworth, B. K. Medda, D. L. Roerig, H. V. Forster, and R. Shaker Airway responses to esophageal acidification Am J Physiol Regulatory Integrative Comp Physiol, January 1, 2008; 294(1): R211 - R219. [Abstract] [Full Text] [PDF] |
||||
![]() |
J. K. M. Lennerz, C. Dentsch, N. Bernardini, T. Hummel, W. L. Neuhuber, and P. W. Reeh Electrophysiological characterization of vagal afferents relevant to mucosal nociception in the rat upper oesophagus J. Physiol., July 1, 2007; 582(1): 229 - 242. [Abstract] [Full Text] [PDF] |
||||
![]() |
B. J. Canning Reflex regulation of airway smooth muscle tone J Appl Physiol, September 1, 2006; 101(3): 971 - 985. [Abstract] [Full Text] [PDF] |
||||
![]() |
J. Vaughan, L. Ngamtrakulpanit, T.N. Pajewski, R. Turner, T-A. Nguyen, A. Smith, P. Urban, S. Hom, B. Gaston, and J. Hunt Exhaled breath condensate pH is a robust and reproducible assay of airway acidity Eur. Respir. J., December 1, 2003; 22(6): 889 - 894. [Abstract] [Full Text] [PDF] |
||||
![]() |
S. Daoui, B. D'Agostino, L. Gallelli, X. Emonds Alt, F. Rossi, and C. Advenier Tachykinins and airway microvascular leakage induced by HCl intra-oesophageal instillation Eur. Respir. J., August 1, 2002; 20(2): 268 - 273. [Abstract] [Full Text] [PDF] |
||||
![]() |
S. K. Field Asthma and Gastroesophageal Reflux : Another Piece in the Puzzle? Chest, April 1, 2002; 121(4): 1024 - 1027. [Full Text] [PDF] |
||||
![]() |
D.-N. Wu, Y. Tanifuji, H. Kobayashi, K. Yamauchi, C. Kato, K. Suzuki, and H. Inoue Effects of Esophageal Acid Perfusion on Airway Hyperresponsiveness in Patients With Bronchial Asthma Chest, December 1, 2000; 118(6): 1553 - 1556. [Abstract] [Full Text] [PDF] |
||||
![]() |
S.-I. Sekizawa, T. Ishikawa, F. B. Sant'Ambrogio, and G. Sant'Ambrogio Vagal esophageal receptors in anesthetized dogs: mechanical and chemical responsiveness J Appl Physiol, April 1, 1999; 86(4): 1231 - 1235. [Abstract] [Full Text] [PDF] |
||||
| ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| HOME | HELP | FEEDBACK | SUBSCRIPTIONS | ARCHIVE | SEARCH | TABLE OF CONTENTS |
| Visit Other APS Journals Online |