|
|
||||||||
1 Department of Otolaryngology,
Head and Neck Surgery, Saga Medical School, 5-1-1
Nabeshima, Saga 849, Japan;
2 Albert Einstein College of
Medicine, Reflex responses of hypoglossal motoneurons innervating the
geniohyoid (GH) and thyrohyoid (TH) muscles from the superior laryngeal
(SLN) and vestibular nerves and their behaviors during fictive
swallowing and vomiting were examined by recording both the
extracellular activities of 11 single cells in the hypoglossal nucleus
and GH and TH muscle nerve activity in eight decerebrate, paralyzed,
and artificially ventilated cats. The majority of TH motoneurons were
either active and/or exhibited shortened antidromic latencies
during early expiration. In contrast, GH motoneurons did not exhibit
any respiratory-related activity. Electrical single-shock stimulation
of the SLN never evoked an excitatory reflex response on GH or TH
motoneurons but rather evoked inhibitory responses on the THs. Unlike
other hypoglossal motoneurons, GH and TH motoneurons do not appear to
receive vestibular inputs. However, they can exhibit robust activities
during fictive swallowing and vomiting, particularly during expulsion.
Thus these motoneurons may play an important role in airway protection
during swallowing and vomiting but not in controlling upper airway
patency regulated by vestibular afferents.
thyrohyoid muscle; geniohyoid muscle; hypoglossal nucleus; superior
laryngeal nerve; vestibular respiratory reflex
THE GENIOHYOID (GH) and thyrohyoid (TH) muscles connect
the hyoid bone to, respectively, the mandible and the thyroid
cartilage, a main component of the laryngeal framework. These muscles
can be involved in various upper airway and digestive behaviors,
including swallowing (12, 16), vomiting (9), and vocalization (8). During swallowing in particular, synergistic activation of these hyoid
muscles plays a cardinal role both in the closing of the laryngeal
vestibule by elevating the entire larynx rostroventrally (12, 16, 22)
and in the resulting opening of the upper esophageal sphincter (2, 16).
During vomiting, TH motoneurons have been shown to fire phasically in
between successive retching bursts and to exhibit vigorously
exaggerated activity during the end of the expulsion stage, suggesting
a possible mechanism for closing the laryngeal orifice during expulsion
similar to that of swallowing (26). The GH muscle is known to exhibit
strong activity during expulsion (9).
Apart from such elaborate motor sequences as swallowing and vomiting,
more simple and direct "elementary" reflexes from the superior
laryngeal nerve (SLN) (3) and vestibular respiratory reflexes in the
upper airway musculature (4, 19, 21, 31) may possibly involve GH and
TH. These motoneurons are located in the hypoglossal nucleus, except
for some TH motoneurons reportedly located in the cat ventral horn at
C1 (17). Although there are many reports that hypoglossal motoneurons
in general respond to vestibular inputs (13, 14, 19), it is unknown if
GH and TH motoneurons in particular are influenced by the vestibular system. In addition, the entire hypoglossal (XII) nerve and some XII
motoneurons, which particularly innervate the genioglossal muscle, are
known to exhibit inspiratory activity (6, 10, 18). It is very likely
that the GH and TH motoneurons also receive respiratory inputs, because
the activities of these hyoid muscles greatly affect upper airway
patency (28, 30).
Thus, whereas the hyoid muscles can be involved in multifarious
behaviors, no attention has been paid to their individual motoneurons
in regard to the respective reflex responses and behaviors. In addition
to its relevancy for better understanding the functional roles of these
muscles in various behaviors, it is relevant for understanding the
underlying neural circuitry to know whether the same motoneuron can be
involved in different reflexes and behaviors. In this study we
examined reflex responses of hypoglossal GH and TH motoneurons from the
SLN and vestibular nerve and their behaviors during fictive swallowing
and vomiting by recording both extracellular single cell activities in
the hypoglossal nucleus and the entire activities of the GH and TH
muscle nerves in the decerebrate and paralyzed cat.
All the procedures used in this study conform to the National
Institutes of Health Guide for the Care and Use of Laboratory Animals and were approved by The Rockefeller University Animal Care and Use Committee.
Data were obtained from eight adult cats of either sex, which were
midcollicularly decerebrated under isoflurane anesthesia, paralyzed
with gallamine triethiodide, and artificially ventilated to maintain
end-tidal CO2 at 4-6%.
Neurograms of the TH and GH muscle nerves as well as C5 phrenic nerve,
L1 abdominal muscle nerve, and the pharyngeal branch of the vagus
(Ph-X), which innervates pharyngeal constrictor muscles, were recorded
on the right side using bipolar cuff electrodes to examine the
laryngeal and vestibular reflexes and behaviors during fictive
swallowing and vomiting. The TH muscle nerve was dissected near the
hyoid bone; the GH muscle nerve was dissected beneath the mylohyoid
muscle as a branch of the hypoglossal nerve. Both of them were
identified using electrical nerve stimulation to elicit a twitch of
only the target muscle (26). Unit activities of TH and GH motoneurons
were also recorded extracellularly in the hypoglossal nucleus on the
right side using glass micropipettes (impedance 3-5 M Anesthesia was discontinued after the completion of all surgical
procedures and at least 1 h before data collection. The recording data
from the nerves and single motoneurons were saved at sampling frequencies of 1 and 50 kHz, respectively, using a Cambridge Electronic Design 1401-plus data interface and Spike 2 software in conjunction with a Power Macintosh 8100/110 computer.
TH and GH nerve activity.
During resting respiration, both the GH and TH nerves were usually
almost silent. In only three out of eight cats, a weak activity of the
TH nerve was observed during the early expiratory phase (Fig.
1A,
left). This early expiratory
activity of TH was enhanced by stimulating the SLN at an intensity
below the threshold for inducing swallowing.
![]()
ABSTRACT
Top
Abstract
Introduction
Methods
Results
Discussion
References
![]()
INTRODUCTION
Top
Abstract
Introduction
Methods
Results
Discussion
References
![]()
METHODS
Top
Abstract
Introduction
Methods
Results
Discussion
References
), and
fast green dye was deposited electrophoretically through the recording
micropipette to localize histologically the recording sites. Recorded
cells were identified as TH and GH motoneurons by antidromic activation from the TH and GH nerves, respectively, the same nerves used for
recording. The antidromic spikes were confirmed by collision with
spontaneous spikes or those elicited during swallowing or vomiting, if
possible. Antidromic latency variations (11) were measured at different
phases of the respiratory cycle to evaluate possible respiratory inputs
to the motoneurons by delivering antidromic stimuli to the GH and TH
nerves at 2-5 Hz. During testing of the antidromic latency
variation, end-tidal CO2 was
maintained strictly at 4.5-5.0%. The vestibular nerve on the left
side was stimulated, as described previously (20), to induce vestibular
respiratory reflexes, using trains of two to five pulses, 0.2-ms pulse
width, 3-ms interpulse interval, repetition rate of one stimulus train every 0.8-0.9 s, delivered at random with respect to the
respiratory cycle, at an intensity between 75 and 375 µA (5 times the
threshold for evoking a volley recorded from the medial longitudinal
fasciculus and always less than the threshold for current spread to the
facial nerve, the closest nontarget nerve, as was tested with trains of
50 pulses before paralysis of the animal). The SLN on the right side
(ipsilateral to the cell recording side) was stimulated to induce both
elementary laryngeal reflexes (3) (using repetitive single pulses of
0.2-ms pulse width at an intensity between 50 and 150 µA, 3-5
times the threshold for evoking inhibitory reflex response on the
phrenic nerve, repetition interval 1.3 s delivered at random with
respect to the respiratory cycle) and fictive swallowing (using trains
of 0.2-ms pulses, 2-30 Hz, 50-200 µA). Fictive swallowing was identified by the burst activity of the Ph-X or TH nerve (5, 26).
The vagus nerves were stimulated just rostral to the diaphragm (using
trains of 0.3-ms pulses, 25 Hz, 0.5-2 mA) to induce fictive vomiting, which was identified by a characteristic series of bursts of
coactivation of phrenic and abdominal muscle nerve discharge (15).
![]()
RESULTS
Top
Abstract
Introduction
Methods
Results
Discussion
References

View larger version (46K):
[in a new window]
Fig. 1.
Typical examples of nerve activities during resting respiration
(A,
left), fictive vomiting
(B,
left), and swallowing
(B,
right) and reflex responses to right
superior laryngeal nerve (SLN) (single shock stimuli of 5 times
threshold intensity for phrenic nerve inhibition;
A,
middle) and left vestibular nerve
(VN) (trains of 5 pulses at 3-ms interval of 5 times threshold
intensity for medial longitudinal fasciculus evoked potential;
A,
right) stimulation (stim). Large
artifacts are seen in synchrony with stimulation pulses. Reflex
response traces shown in A, middle, and
A, right represent average of 116 and 108 sweeps,
respectively. In B, retching phase is
delineated by left 2 vertical dashed
lines, and beginning and end of expulsion are indicated by solid lines.
Stages 1, 2,
and 3 of expulsion are also delineated
by dashed lines. Fictive swallowing was induced by repetitive SLN
stimulation at 2 Hz (B,
right). All nerves were recorded on
right side. All recordings were obtained in same cat; gains are
indicated in parentheses compared with recording during respiration.
Abd, L1 abdominal muscle nerve; GH, geniohyoid muscle nerve; Phr, C5
phrenic nerve; TH, thyrohyoid muscle nerve.
|
TH and GH motoneuronal activity. We recorded unit activities of seven TH and four GH motoneurons, which were antidromically activated from their corresponding nerves with latencies between 1.1 and 1.3 ms (mean ± SD = 1.2 ± 0.1 ms) and 1.0 and 1.7 ms (1.3 ± 0.3 ms), respectively. All the motoneurons were capable of following repetitive stimulation of 300 Hz or more. Antidromic activation was also confirmed by the collision test for all but three cells (2 THs and 1 GH) that showed neither spontaneous discharge nor swallowing or vomiting activities. All TH cells recorded were located in the caudal part of the XII nucleus between 0.6 and 1.2 mm caudal to the obex, whereas GH cells were located more rostrally in the XII nucleus between the level of the obex and 1.9 mm rostral to it. We could not record even antidromic field potentials more caudally in the C1 ventral horn, where some TH motoneurons have been reported (17). None of the TH or GH cells exhibited evoked responses to SLN or vestibular nerve stimulation even though reflex responses were simultaneously recorded on the phrenic and abdominal nerves.
Motoneuronal behaviors observed during fictive swallowing (for all 11 cells) and during fictive vomiting (for 4 GH and 5 TH cells) are summarized in Table 1. Five out of seven TH and three out of four GH cells showed burst activities during fictive swallowing (Fig. 2, Aa and Ba); the remaining three motoneurons were silent. During fictive vomiting, the behaviors of individual motoneurons were more varied than the corresponding whole nerve activities. Three out of five TH cells tested and two out of four GH cells were silent throughout the vomiting period. The behavior of both of the TH motoneurons that were active during vomiting resembled the behavior of the whole TH nerve in that the cells were active both during the interretch period and mainly during stage 3 of expulsion (cf. Fig. 2Aa and Fig. 1B). Whereas the whole GH nerve was mainly active during the interretch phase (Fig. 1B) as well as during expulsion, one GH motoneuron was active during retching bursts (Fig. 2Ba), whereas another was active during the interretch phase. During expulsion, one GH motoneuron fired throughout most of the expulsion period, starting in stage 1, similar to the GH nerve (Fig. 2Ba); the other GH motoneuron was active during stage 2 and 3.
|
| |
DISCUSSION |
|---|
|
|
|---|
The present study has investigated whether the hypoglossal hyoid, GH and TH, motoneurons are involved in a number of upper-airway behaviors, including swallowing, vomiting, and respiration and SLN and vestibular reflexes. Most of these motoneurons can be multifunctional; however, individual motoneurons differ in regard to the variety of behaviors in which they are involved. The recording sites of the GH and TH motoneurons in our data are consistent with previous anatomic results, with the exception of the possibility of a caudal extension of the TH motor pool into the upper cervical ventral horn. The results of previous anatomic studies were inconsistent concerning the location of TH motoneurons, which were reported to exist in the caudal hypoglossal nucleus and C1 ventral horn (17), the rostral part of the region from the caudal hypoglossal nucleus down into the ventral horn of C2 (7), only in the caudal hypoglossal nucleus of the medulla (25), or only in C1 and C2 (29) or none being observed within the hypoglossal nucleus (24). Although the number of neurons recorded in the present experiment is small, our results suggest that TH motoneurons exist mostly in the caudal hypoglossal nucleus, because even an antidromic field potential from the TH nerve could not be recorded in the C1 ventral horn.
We have recently demonstrated characteristic TH nerve activities during fictive swallowing and vomiting (26). The burst activity of the GH nerve during fictive swallowing is similar to that of TH, although the GH burst starts 20-80 ms before the TH burst. This tendency, which is also observed in actual swallowing (3), can be assumed to be part of the centrally programmed output proper to swallowing because there was an absence of actual movement and proprioceptive sensory feedback in our paralyzed preparation. It was, however, also recognized in our study that swallowing burst activity was not invoked in all GH and TH motoneurons, although a swallowing active motoneuron always exhibited a burst of activity every time swallowing occurred. In contrast to the similarity of the swallowing activities, neural activities during the expulsion phase of fictive vomiting are different between TH and GH motoneurons. GH motoneurons are activated chiefly from the later part of stage 1 expulsion with a transient exaggeration during stage 3, whereas TH motoneurons exhibit a burst activity mainly during stage 3. These findings are consistent with previously described electromyogram (EMG) activities during actual vomiting (9) and suggest the difference of functional roles between the TH and GH muscles during the expulsion phase of vomiting. The GH may assist the opening of the upper esophageal sphincter (2) to facilitate expulsion of vomitus (9) during stage 1 and 2 expulsion. The TH burst activity together with the GH exaggerated activity seems to be important for the closure of the laryngeal vestibule to protect the lower airway during stage 3, when pharyngeal constrictors squeeze the pharyngeal cavity and clean the hypopharynx (9, 26), in a similar manner to that during swallowing (12, 22).
Afferents from the SLN induce airway protective reflexes. A single pulse electrical stimulus to the SLN elicits short latency reflexive EMG activities on upper airway muscles, known as the elementary reflexes (3). Such elementary reflexes were reported to exist not only in laryngeal muscles but also in the GH, TH, and other oropharyngeal muscles in anesthetized animals (3). However, our present results from the decerebrate and paralyzed cat have revealed that a single shock stimulus to the SLN does not evoke excitatory reflex responses corresponding to the elementary reflexes on the GH and TH muscles but rather evokes inhibitory responses observed only on TH but not GH motoneurons. This finding is consistent with results from a recent EMG study using the decerebrate and spontaneously breathing cat (23).
Vestibular respiratory reflexes are thought to act to maintain airway patency and to compensate for mechanical constraints on respiration that may arise during movements and changes in posture (31). Electrical stimulation of the vestibular nerve produces widespread, bilateral reflex responses that can be recorded from respiratory nerves to upper airway, thoracic, diaphragm, and abdominal muscles (20, 21). The responses typically consist of a combination of increased and decreased respiratory nerve activity. Although there is much evidence that hypoglossal motoneurons receive vestibular inputs (4, 13, 14, 19, 21, 27), the present study strongly suggests that the GH and TH motoneurons are not involved in vestibular-upper airway reflexes. Thus these results indicate that only selected hypoglossal motoneurons innervating certain tongue muscles, e.g., the genioglossal muscle, whose activity can greatly affect upper airway resistance (30), receive vestibular signals.
The present study has also demonstrated that the majority of TH motoneurons receive excitatory inputs during the early expiratory phase, as evidenced by actual motoneuronal discharge and/or the shortening of antidromic latencies (11) during the early expiratory phase. GH motoneurons, on the other hand, did not exhibit any respiratory-related activity. In contract, other hypoglossal motoneurons are known to have inspiratory activities (6, 10, 18). Although most TH motoneurons were silent during resting respiration in our artificially ventilated preparation, it is possible that more may be recruited to help regulate airway resistance under hypercapnic conditions or other respiratory facilitation (1). Although the functional significance of TH activation during early expiration remains to be clarified, it may help to brake expiratory airflow, similar to the function of the laryngeal adductors during early expiration.
Perspectives
The GH and TH muscles connect the hyoid bone to, respectively, the mandible and the thyroid cartilage, a main component of the laryngeal framework. These muscles may play an important role in airway protection during swallowing and vomiting but not in controlling upper airway patency regulated by vestibular afferents, although TH motoneurons may receive excitatory inputs during the early expiratory phase. Individual TH and GH motoneurons can be multifunctional, but they are not homogeneous in regard to the upper airway behaviors in which they are involved. This study provides distinct evidence that multifunctional cranial motoneurons common to different behaviors other than respiration exist in the mammalian brain stem. However, it remains to be determined whether such motoneurons are driven directly by different central pattern generator (CPG) cells or by common interneurons that belong to different CPGs for individual behaviors. Similarly, we may also need to reevaluate multifunctionality or heterogeneity of other upper airway motoneurons such as cells in the nucleus ambiguus.| |
ACKNOWLEDGEMENTS |
|---|
We thank Drs. Bill J. Yates and Keisuke Shiba for comments on the manuscript.
| |
FOOTNOTES |
|---|
This study was supported by National Institute of Neurological Disorders and Stroke Grant NS-20585 and by National Institute on Deafness and Other Communication Disorders Grant DC-02644.
Address for reprint requests: A. D. Miller, The Rockefeller Univ., Box 79, 1230 York Ave., New York, NY 10021-6399.
Received 2 September 1997; accepted in final form 15 December 1997.
| |
REFERENCES |
|---|
|
|
|---|
1.
Adachi, T., T. Umezaki, T. Matsuse, and T. Shin. Changes in
laryngeal muscle activities during hypercapnia in the cat.
Otolaryngol. Head Neck Surg. In press.
2.
Asoh, R.,
and
R. K. Goyal.
Manometry and electromyography of the upper esophageal sphincter in the opposum.
Gastroenterology
74:
514-520,
1978[Medline].
3.
Doty, R. W.,
and
J. F. Bosma.
An electromyographic analysis of reflex of deglutition.
J. Neurophysiol.
19:
44-60,
1956
4.
Elmund, J.,
J. P. Bowman,
and
R. J. Morgan.
Vestibular influence on tongue activity.
Exp. Neurol.
81:
126-140,
1983[Medline].
5.
Grélot, L.,
J. C. Barillot,
and
A. L. Bianchi.
Pharyngeal motoneurones: respiratory-related activity and responses to laryngeal afferents in the decerebrate cat.
Exp. Brain Res.
78:
336-344,
1989[Medline].
6.
Hwang, J.-C.,
D. J. Bartlett,
and
W. M. St. John.
Characterization of respiratory-modulated activity of hypoglossal motoneurons.
J. Appl. Physiol.
55:
793-798,
1983
7.
Kirzinger, A.,
and
U. Jurgens.
Motoneuronal location of external laryngeal and hyoid muscles involved in primate phonation.
J. Hirnforsch.
35:
559-565,
1994[Medline].
8.
Kirzinger, A.,
and
U. Jurgens.
Role of extralaryngeal muscles in phonation of subhuman primates.
J. Comp. Physiol. [A]
175:
215-222,
1994[Medline].
9.
Lang, I. M.,
S. K. Sarna,
and
W. J. Dodds.
Pharyngeal, esophageal, and proximal gastric responses associated with vomiting.
Am. J. Physiol.
265 (Gastrointest. Liver Physiol. 28):
G963-G972,
1993
10.
Laursen, A. M.,
and
J. C. Rekling.
Electrophysiological properties of hypoglossal motoneurons of guinea-pigs studied in vitro.
Neuroscience
30:
619-637,
1989[Medline].
11.
Lipski, J.
Antidromic activation of neurones as an analytic tool in the study of the central nervous system.
J. Neurosci. Methods
4:
1-32,
1981[Medline].
12.
Maeyama, T.
Experimental investigation of the function of the intrinsic and extrinsic laryngeal muscles during deglutition, especially for elevation of the larynx.
Otol. Fukuoka
21:
787-807,
1975.
13.
Mameli, O.,
and
E. Tolu.
Vestibular ampullar modulation of hypoglossal neurons.
Physiol. Behav.
37:
773-775,
1986[Medline].
14.
Mameli, O.,
E. Tolu,
F. Melis,
and
M. A. Caria.
Labyrinthine projection to the hypoglossal nucleus.
Brain Res. Bull.
20:
83-88,
1988[Medline].
15.
Miller, A. D.,
L. K. Tan,
and
I. Suzuki.
Control of abdominal and expiratory intercostal muscle activity during vomiting: role of ventral respiratory group expiratory neurons.
J. Neurophysiol.
57:
1854-1866,
1987
16.
Miller, A. J.
Deglutition.
Physiol. Rev.
62:
129-184,
1982
17.
Miyazaki, T.,
Y. Yoshida,
M. Hirano,
T. Shin,
and
T. Kanaseki.
Central location of the motoneurons supplying the thyrohyoid and the geniohyoid muscles as demonstrated by horseradish peroxidase method.
Brain Res.
219:
423-427,
1981[Medline].
18.
Richard, C. A.,
and
M. R. Harper.
Respiratory-related activity in hypoglossal neurons across sleep-waking status in cats.
Brain Res.
542:
167-170,
1991[Medline].
19.
Rossiter, C. D.,
and
B. J. Yates.
Vestibular influences on hypoglossal nerve activity in the cat.
Neurosci. Lett.
211:
25-28,
1996[Medline].
20.
Shiba, K.,
M. S. Siniaia,
and
A. D. Miller.
Role of ventral respiratory group bulbospinal expiratory neurons in vestibular-respiratory reflexes.
J. Neurophysiol.
76:
2271-2279,
1996
21.
Siniaia, M. S.,
and
A. D. Miller.
Vestibular effects on upper airway musculature.
Brain Res.
736:
160-164,
1996[Medline].
22.
Spiro, J.,
J. K. Rendell,
and
T. Gay.
Activation and coordination patterns of the suprahyoid muscles during swallowing.
Laryngoscope
104:
1376-1382,
1994[Medline].
23.
Sugimoto, T., K. Narikawa, S. Takagi, T. Umezaki, and T. Shin.
Effects of medullary longitudinal split on symmetrical pharyngeal
swallowing in cats. Jap. J. Physiol. 47, Suppl. 2: S172, 1997.
24.
Uemura, M.,
K. Matsuda,
M. Kume,
Y. Takeuchi,
R. Matsushima,
and
N. Mizuno.
Topographical arrangement of hypoglossal motoneurons: an HRP study in the cat.
Neurosci. Lett.
13:
99-104,
1979[Medline].
25.
Ueyama, T.,
T. Satoda,
T. Tashiro,
and
N. Mizuno.
The distribution of infrahyoid motoneurons in the cat: a retrograde horseradish peroxidase study.
Anat. Embryol. (Berl.)
177:
445-450,
1988[Medline].
26.
Umezaki, T., K. Shiba, Y. Zheng, and A. D. Miller.
Upper airway motor outputs during vomiting versus swallowing in
the decerebrate cat. Brain Res. In press.
27.
Umezaki, T.,
Y. Zheng,
K. Shiba,
and
A. D. Miller.
Role of nucleus retroambigualis in respiratory reflexes evoked by superior laryngeal and vestibular nerve afferents and in emesis.
Brain Res.
769:
347-356,
1997[Medline].
28.
Van de Graaff, W. B.,
S. B. Gottfried,
J. Mitra,
E. van Lunteren,
N. S. Cherniack,
and
K. P. Strohl.
Respiratory function of hyoid muscles and hyoid arch.
J. Appl. Physiol.
57:
197-204,
1984
29.
Van der Sprenkel, H. B.
The hypoglossal nerve in an embryo of Erinaceus europaeus.
J. Comp. Neurol.
36:
219-270,
1924.
30.
Van Lunteren, E.,
and
K. P. Strohl.
The muscles of the upper airways.
Clin. Chest Med.
7:
171-188,
1986[Medline].
31.
Yates, B. J.,
and
A. D. Miller.
Vestibular respiratory regulation.
In: Neural Control of the Respiratory Muscles, edited by A. D. Miller,
A. L. Bianchi,
and B. P. Bishop. Boca Raton, FL: CRC, 1996, p. 271-283.
This article has been cited by other articles:
![]() |
M. Yokoba, H. G. Hawes, and P. A. Easton Geniohyoid muscle function in awake canines J Appl Physiol, August 1, 2003; 95(2): 810 - 817. [Abstract] [Full Text] [PDF] |
||||
![]() |
A. Jean Brain Stem Control of Swallowing: Neuronal Network and Cellular Mechanisms Physiol Rev, April 1, 2001; 81(2): 929 - 969. [Abstract] [Full Text] [PDF] |
||||
| ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| HOME | HELP | FEEDBACK | SUBSCRIPTIONS | ARCHIVE | SEARCH | TABLE OF CONTENTS |
| Visit Other APS Journals Online |