|
|
||||||||
The Journal of Neurophysiology Vol. 88 No. 4 October 2002, pp. 1675-1684
Copyright ©2002 by the American Physiological Society
Department of Neurobiology and Anatomy, University of Rochester, Rochester New York 14642
| |
ABSTRACT |
|---|
|
|
|---|
Sobotka, Stanislaw, Wei Zuo, and James L. Ringo. Is the Functional Connectivity Within Temporal Lobe Influenced By Saccadic Eye Movements?. J. Neurophysiol. 88: 1675-1684, 2002. Local evoked potentials (LEPs), recorded in response to electrical stimulation, were used to study functional connectivity between different sites of the temporal lobe. Permanent electrodes were implanted in anterior and posterior positions of both inferotemporal cortex (IT) and hippocampal formation (HF). In each experimental session, one of these four sites was stimulated and LEPs were recorded in the others. Clear LEPs were found in the anterior and posterior IT sites in response to stimulation of the anterior as well as posterior HF. Bidirectional connections (as judged by the potentials) were found between the anterior and posterior sites of the same structure (IT or HF). The timing of the LEPs indicates that much of the response was carried in multisynaptic circuits. Stimulation delivered just after the monkey made a saccade produced larger late components in the LEPs than the same stimulation delivered without a saccade. The influence was maximal when the delay between the end of the saccade and the electrical stimulation was in the range of 50-100 ms. This saccadic modulation of the functional connectivity was observed within IT (bidirectional) and between posterior HF and IT (unidirectional).
| |
INTRODUCTION |
|---|
|
|
|---|
In natural conditions, the neural circuitry underpinning visual memory and high level vision operates on a pulsatile data stream caused by the saccades used to reposition the eyes. While exploring their visual environment, monkeys make two to four saccades each second. These saccades are the only eye movement used to bring new images to the fovea. Other eye movements are used to stabilize vision.
Saccades dramatically influence the visual data stream. Each saccade produces a break in the visual information flow into the cortex. Following each saccade, the image on and near the fovea, critical for object vision, often bears no relation to that image existing prior to the saccade. Thus in at least many cases, it would seem logical for the system to treat a saccade as a fresh starting point from which to begin object identification and memory access.
The sorts of processing tasks that make sense within the
fixation period and those that make sense between fixation
periods are different. Given a system that predominantly used spike
rates to convey information, within a fixation period it would be
reasonable to integrate all available spikes to create the highest
possible signal-to-noise ratio. In contrast, summation across fixations on different objects would simply reduce resolution. At the beginning of a fixation period, a system should clear any neural circuitry that
engages in summation within a fixation period because the data that
would be in the circuitry would be from the previous fixation period
and, at least in many cases, inappropriate. Similarly, the breaks
caused by saccades would appear to be important for a system that used
a temporal spike code for information transmission. As suggested by
others (Kayama et al. 1979
; Richmond and Optican 1987
), the beginning of a fixation period could be the
reference point for neural processing schemes, which use the temporal
pattern of activity to carry information. It would not be at all
surprising, moreover, if the neural circuitry made comparisons and
associations (of some currently unknown sort) among the series of
objects identified by a series of fixations. Such processing would seem
likely to benefit if the fixation boundaries were unambiguously marked off.
The preceding text is not to suggest that we currently have a good
model of how visual processing and visual memory operates within and
between fixations. The point is simply that, as a general strategy,
synchronizing the processing to the pulsatile nature of the main data
input seems inherently sensible and possible. Existence of such a
system predicts that saccades would modulate the functional
connectivity between ventral temporal lobe sites. It was the purpose of
the present work to test that prediction. Because the ventromedial
temporal lobe appears to play a major role in higher-order visual
perception and memory processes (Eacott et al. 1994
;
Gaffan 1994
; Horel et al. 1987
;
Riches et al. 1991
), it would appear to be a plausible
place to test the prediction.
In our previous studies, we showed that saccadic eye movements could
generate event-related potentials (Sobotka and Ringo 1997
) and modulate single-unit activity (Ringo et al.
1994
; Sobotka et al. 1997
) in the medial and
ventral temporal lobe regions. In an illuminated environment, these
effects could be, at least partly, caused by a shift of the visual
image on the retina. However, we found both effects (saccade-related
potentials and saccadic modulation of single units) in the medial
temporal lobe in full darkness. Results from these studies encouraged
us to pursue the idea of saccadic control over visual memory and high
level visual functions in the temporal lobe.
In the current experiments, we delivered a short electric stimulus to an electrode at one site and recorded the local potentials from another site in the ventral temporal lobe. We compared the amplitudes of the potentials evoked in response to the pulse delivered when there had been no recent saccade, with the amplitudes of the potentials evoked by the pulse delivered soon after a saccade had been completed. These experiments were designed to measure if saccades modulate connectivity in inferotemporal cortex and the hippocampal formation, that is, to test a prediction of the hypothesis the saccades exert control over the functions of this region.
| |
METHODS |
|---|
|
|
|---|
Subjects
Two adult monkeys, Macaca nemestrina (4.5-5.5 kg), were used in the experiment. All procedures and methods of this study were reviewed and approved by the appropriate institutional animal care and use committee. All surgeries were performed under sterile conditions while the animals were anesthetized with secobarbital. The animals received postoperative antibiotics and analgesics.
Each monkey had a scleral search coil implanted under the conjunctiva
of one eye to record the eye position (Judge et al. 1980
).
Four small bundles of platinum-iridium electrodes were implanted stereotactically into the right hemisphere, aimed at anterior and posterior sites in inferotemporal cortex (IT) and the hippocamapal formation (HF). The electrodes were constructed from 200-µm wires, covered with paralene, then ground to a tip with an approximately 45° angle. Three or four electrodes formed a bundle and were glued together. The distance between adjacent tips was 2 mm. The same electrodes could be used both for the recording of evoked potentials and for delivering electrical stimulation to the brain. One bundle of four electrodes was implanted in the anterior and one into the posterior HF. One bundle of three electrodes was implanted in the anterior and one into posterior IT. For other experiments, additional electrodes were aimed at the anterior and posterior basal forebrain and medial septum. These additional electrodes were not used in any way in the experiments reported here.
All electrodes were soldered into a 25-pin connector. This connector and the connector for the eye-coil system were cemented to the skull with dental acrylic and this mass was attached to the skull by titanium (0.5 mm) and stainless steel (0.86 mm) screws.
During the course of the experiments, the monkeys had restricted access to water in their home cages. They received the necessary fluids as rewards in the behavioral task. Hydration levels were carefully monitored. Free water access was allowed at least once each week.
Histology
After experimentation, electrolytic lesions were made to
facilitate verification of electrode positions. DC anodal current (1 mA) was delivered to the deepest electrodes for 60 s (a skull screw was used as a cathode). One week later the animals were killed
with an overdose of barbiturate and perfused transcardially with saline
followed by 10% formalin. The brains were blocked in situ, extracted,
embedded in wax, sectioned, and stained. The electrodes' positions
(derived from histological data, and confirmed by magnetic resonance
imaging) presented on standard brain drawings from the atlas of
Winters et al. (1969)
are shown on the Fig. 1. The use of permanent electrodes made
recovery of their positions relatively easy.
|
Procedure
The animals performed a two-choice visual discrimination task. This allowed sets of recordings of responses evoked by electrical stimulation to be obtained in the midst of a normal operation of the neuronal circuitry and in a reasonably aroused and repeatable state.
During recording, each monkey was seated in a primate chair in a dark room. The head was held by a padded face mask mounted over the snout and by a plate behind the head preventing withdrawal. Thirty-two centimeters in front of the monkey there was a computer screen (Sony GDM-20E01) on which images were presented during recording sessions. Images were presented on the screen by an IBM-compatible computer with multimedia software (Grasp, Paul Mace Software). A second similar computer with commercial recording software (Datawave, Longmont, CO) was used to control the experiment (electrical stimulation and juice reward delivery, data acquisition etc.).
Images
The single green letters "p" and "d" were used as visual images in the visual discrimination task. The image "d" was a 180° rotation of the image "p." One image from the pair (p) was chosen as a positive GO stimulus, the other as a negative NO-GO stimulus.
Each session consisted of 50-300 trials. At the beginning of each trial, an image (approximately 2° diam) was presented for 2 s. The center of the image was 7.5° to the left, right, up, or down from the center of the screen. For each trial, the presentation position was randomly determined. The image was presented only when the monkey's gaze was outside this position. The task of the monkey was to make a saccade to the GO image and then hold this eye position (inside a 3° radius window) for 0.6 s. The correct response was rewarded with a drop of fruit juice. The NO-GO image was not associated with any reward. After a randomly determined interval of darkness (from 4 to 10 s), a new trial was begun.
Occasionally, a very-low-intensity dot (0.5° diam) was presented in one of the same four places where visual images could appear. This was also treated as a GO image, a saccade to and a maintained fixation on the dot was rewarded with a drop of juice. The purpose of the faint dot was to encourage visual search and eye movements during the intervals of full darkness when the data presented in this paper were collected.
Saccades
A magnetic eye coil system (Robinson 1963
) was
used to record saccadic eye movements. Changes in the position of gaze,
which met both of the following criteria, were treated as saccades: at
least a 5° difference in eye position between the beginning and the
end of a 50-ms period and no more than a 1° change in eye position
during the proceeding 200 ms.
Electrical stimulation
Four independent constant current isolation units provided
electrical stimulation. The units, modified from a design of Murray Bloom (Gallistel 1981
), were battery powered and
electrically isolated from their inputs (via photoemitter-photodetector
pairs) and from each other. Stimulation was delivered with 0.2-ms pulse to the electrode tips, which were 2 mm apart. Immediately after each
stimulation pulse, the stimulating electrodes were shorted together to
bleed off any charge build-up during the stimulation. This was done to
minimize the risk of hydrolysis (Doty and Bartlett 1981
).
Stimulation current was usually set to 1 mA (experiments 1, 2, and 4, see the description of experiments in the Table 1). This current is much larger than typically used with microelectrodes because our electrode tips are much larger and thus require higher total current levels to achieve a similar current density.
|
In a separate study (experiment 3) on the influence of stimulation intensity on the amplitude of EPs, 0.25- to 3-mA currents were used. In this experiment, LEP recording was repeated seven times with stimulation current set to 0.25, 0.5, 1, 1.5, 2, 2.5, and 3 mA. The on-line electroencephalographic (EEG) monitoring showed no afterdischarges. On no occasion was a motor seizure elicited by the electrical stimulation nor was there any visible motor reaction. Before the first recording session with each stimulation pair of electrodes, a series of single pulses was delivered with different intensities (up to 3 mA). There was no visible motor or eye movement reaction elicited by this stimulation.
Stimulation delivery
LEPs were recorded in response to a single 0.2-ms electrical pulse. This pulse could be delivered in darkness either 100 ms after a saccade or, for comparison, when no saccade was made during the preceding 0.5 s. In no case was stimulation delivered if stimulation had occurred within the previous 0.5 s. In 50% of trials (control trials), electrical stimulus was not delivered. Whether or not stimulation was given and what type of stimulation was delivered (with or without saccade) was determined randomly.
While most work was done with LEPs collected in the dark, LEPs were also collected in some sessions during the time of image presentation in which case the pulse was delivered 100 ms after the first saccade landed on the image.
In experiment 2, the influence of delay between the end of the saccade and the electrical pulse on LEP was studied. In this experiment, before each trial, the stimulus delay time was randomly selected from a limited pool of delays, 50, 100, 150, 200, 300, and 500 ms.
LEPs
Four amplifiers and filters (0.1 Hz to 1 kHz, 9 dB/octave roll-off) were used to record potentials from multiple pairs of electrodes. A computer running a commercial software package (Datawave) was used for data acquisition. During each experimental session (typically 100 min), brain potentials and horizontal and vertical eye positions were recorded with a sampling rate of 0.5 kHz.
Initial selection of stimulation and recording electrodes
Data were collected from both monkeys for each combination of stimulation and recording pair of electrodes. In each bundle of three or four electrodes, all adjacent (2 mm apart) electrodes made pairs. Each electrode of a pair was used as cathode (i.e., both polarities of pulse were tried). From all combinations of stimulation and recording pairs, eight that produced the clearest LEPs in both monkeys were chosen. If the stimulation of one site (e.g., anterior HF) and recording from the other site produced a clear LEP for more than one combination of stimulation-recording pairs, only one combination that produced the best LEP was selected.
Analysis
In the present paper, only the LEPs collected in full darkness (in the intertrial interval between presentations of different visual images: the letters p and d or a weak spot of light) were analyzed. Data were analyzed off-line with user written programs and the SAS statistical package. To avoid problems of data selection, all data from any given experiment was used in the statistical analysis.
| |
RESULTS |
|---|
|
|
|---|
Behavioral data
TRAINING. The monkeys were trained to discriminate between the letters p (GO image) and d (NO-GO image) until they reached a criterion of at least a 30% difference between correct and incorrect GO responses during two consecutive sessions. It was a relatively difficult task for the monkeys. One monkey needed six sessions of 300 trials each to learn this task (96% correct GO vs. 48% incorrect GO). The other monkey needed 22 such sessions (93 vs. 61%, respectively).
BEHAVIORAL PERFORMANCE DURING DIFFERENT STIMULATION INTENSITY. Behavioral data collected in the experiment 3 (effect of stimulation intensity on amplitude of LEPs) were analyzed to test if electrical stimulation used in the present study disturbed the monkeys performance. This was the only experiment of the present study in which we used currents greater than 1 mA. Seven sessions were run, each with a different pulse intensity (currents from 0.25 to 3 mA) for each of eight stimulated regions.
The analysis showed that the monkeys' performance was not significantly effected by the strength of electrical stimulation. Specifically, regression analysis showed that stimulation current was not a statistically significant predictor of monkey's performance (mean number of correct GO and NO-GO responses, averaged from 2 monkeys) in any of eight stimulated regions (all P > 0.01). The performance level (mean percent of correct GO and NO-GO responses, averaged across the 2 monkeys and 8 stimulation regions and 6 stimulation intensities) was 71.4% (69.2% for 0.25 mA, 71.7% for 0.5 mA, 67.5% for 1 mA, 71.4% for 1.5 mA, 72.3% for 2 mA, 72.1% for 2.5 mA, and 75.2% for 3 mA). Averaged standard error for individual stimulation intensity was equal 4.6.Evoked potentials
ACTIVE CONNECTIONS. The potentials evoked at each location by electrical stimulation at the other locations were examined. Clear evoked potentials were found in anterior and posterior IT to the stimulation of anterior as well as posterior HF. Bidirectional connections (as judged by evoked potentials) were found between the anterior and posterior part of IT and also of the HF. The eight combinations, which produced the strongest evoked potentials in both monkeys, were chosen for further studies (see Fig. 2).
|
DESCRIPTION. Each averaged evoked potential had one (or, in a few cases, 2) prominent components with peak latency between 75 and 250 ms (see Fig. 3). The early portion of the LEP was contaminated by artifact from the electrical stimulus (see Fig. 4) and was not analyzed. Components were selected for further analysis by visual inspection of all sets of tracings of evoked potentials. The investigator who made this selection was not aware of which potentials were evoked by stimulation delivered after saccades and which were delivered when no saccades were made during the preceding 0.5 s. The peak amplitude of the selected components was the measure used in our comparisons.
|
|
COMPARISON BETWEEN THE LEP TO AN ELECTRICAL PULSE DELIVERED EITHER 100 MS AFTER A SACCADE OR WITHOUT A SACCADE. Stimulation delivered with a short delay after a saccade (100 ms) produced a larger late component of the LEP (peak latency between 75 and 250 ms) than the same stimulation delivered without a saccade (see Fig. 5 and Table 2). The most significant difference was found when the posterior HF was stimulated and a recording was made from anterior or posterior IT. Also, the stimulation of one portion (anterior or posterior) of IT produced a substantial difference in LEPs recorded from the other portion of IT. The weakest effect (if any) was found when anterior HF was stimulated.
|
|
INFLUENCE OF DELAY TIME BETWEEN A SACCADE AND AN ELECTRICAL PULSE. The late component of the LEPs (peak latency between 75 and 250 ms) was largest when the interval between the end of the saccade and the electrical stimulation was either 50 or 100 ms. This amplitude was found to decrease with an increase of this delay time (see Fig. 6).
|
|
INFLUENCE OF INTENSITY OF ELECTRICAL PULSE. Small LEPs were recorded to a pulse of 0.25 or 0.5 mA (see Fig. 7). The amplitude of the LEP increased with stimulation intensity until it appeared to reach a saturation level (between 1.5 and 2.5 mA). The relation between the amplitude of evoked potentials and intensity of stimulation seems to be approximately linear around 1 mA.
|
EVENT-RELATED POTENTIALS TO A SACCADE.
A study from our laboratory (Sobotka and Ringo 1997
)
showed that spontaneous saccades themselves could evoke event-related potential (ERP) in the medial temporal cortex. This raises the question
whether this ERP is a simple explanation of the difference between LEPs
to the electrical pulse delivered after saccades and without saccades.
|
LOCALIZATION OF EPS GENERATORS. We performed an additional experiment (experiment 4) to examine whether the EPs were generated by local brain structures or whether they were less specific and reflected activity of more distant brain areas (i.e., asking if these EPs were really LEPs). In this experiment, we compared EPs recorded with the monopolar method, from different electrodes belonging to the same bundle (2 bundles of 4 electrodes were implanted into HF and 2 bundles of 3 electrodes implanted in IT). Two connected skull screws above parietal cortex were used as a reference electrode. Monopolar recordings from neighboring electrodes showed large difference in number, amplitudes, and polarity of EP components. Evoked potentials, which were recorded with bipolar methods, from pairs (2 mm apart) showed the same range of amplitudes as the subtraction of EPs recorded monopolarly (see Fig. 9). These observations suggest a proximal localization of sources generating EPs.
|
COMPARISON BETWEEN LEPS AFTER IPSILATERAL AND CONTRALATERAL EYE MOVEMENTS. In an attempt to characterize this phenomenon, we investigated if the gross direction of the saccadic eye movement (ipsilateral or contralateral, in respect to studied hemisphere) effects the strength of saccadic modulation of the LEPs we recorded. For this analysis, we used data collected in experiment 3 in which modulation effect of a saccade (when the saccade preceded the electrical pulse) was repeatedly studied (for 7 different intensity of stimulation). Sixteen sets of recording (each set consisted of 7 sessions with different intensity of electrical stimulation) were collected (8 combinations of "stimulation-recording" regions in 2 monkeys).
All classifying saccades, which after 100 ms were followed by electrical pulse, were sorted according to the direction of the horizontal coordinate of eye movement into two groups. For each of stimulation intensity, which produced clear LEP (from 5 to 7 levels in 0.25- to 3-mA range), we calculated contrast between LEPs following ipsilateral and contralateral saccade: Contrast = (C
I)/(C + I),
where C was amplitude of LEPs if the saccade was made toward
the visual field contralateral to studied hemisphere and I
was amplitude of LEPs if the saccade was made toward the ipsilateral
visual field.
To confirm that this testing method is capable of revealing
statistically significant differences (i.e., to test its statistical power), we compared contrasts between LEPs following saccades with
those in which the pulse was delivered in the absence of a saccade:
Contrast = (S
N)/(S + N), where S was amplitude of LEPs if saccade was
made (ipsilateral or contralateral) and N was amplitude of
LEPs if no saccade was made.
From 16 recording sets (8 combinations of stimulation- recording
regions in 2 monkeys), 13 sets produced clear LEPs.
In 9 of these 13 sets, a saccade preceding electrical pulse produced
statistically significant (P < 0.01, t-test) increase of LEP amplitude (average contrast from 13 sessions = 0.305),
In none of these 13 sets did the LEP amplitudes differ significantly
between those following ipsilateral saccades compared with those
following contralateral saccades (average contrast = 0.032).
Therefore it seems that whereas saccades produce substantial facilitation in connectivity between temporal regions the gross left-right direction of the saccade is less important.
AMPLITUDE OF RESPONSE TO ELECTRICAL STIMULATION BEFORE THE ONSET OF SACCADE. In an attempt to determine if a saccade after the electrical stimulation could influence the LEPs, we also compared LEPs in the following two situations: when the monkey made a saccade immediately after the electrical stimulation (between 0 and 100 ms after) and when the monkey did not make any eye movement during at least 0.5 s after electrical pulse delivery.
In this comparison, we used only responses which were recorded when there was no saccade before the stimulation (for 500 ms). We found no consistent difference in the amplitudes recorded under the two conditions. Of course this result should be treated with some caution because of substantial variability of LEPs averaged from small number of available cases in which our monkeys made saccades soon after electrical stimulation. A representative example is illustrated in Fig. 10.
|
| |
DISCUSSION |
|---|
|
|
|---|
In the present study, we analyzed the amplitude of local potentials evoked by a short electrical pulse delivered to one area and recorded from another area of the medial temporal lobe. We showed that the amplitude of late components of these LEPs were significantly larger if the pulse was given soon after the end of a saccadic eye movement (experiment 1). This amplitude decreased with increased time between the end of a saccade and the stimulation pulse (experiment 2). The increased amplitude of evoked potentials to the pulse delivered soon after a saccade was observed for a broad range of stimulation intensities (experiment 3).
These experiments were designed to test a prediction of the general hypothesis that saccades serve to frame the visual inputs from individual fixations and acting as such a framework would modulate the neuronal circuitry (INTRODUCTION). That hypothesis does appear supported, however, the data do not provide any clear indication as to exactly what modulation of the visual processing the saccades perform. Those critical details must await future work.
Additional analysis, in which we investigated if the lateral direction of eye movement affects the strength of saccadic modulation of functional connectivity did not uncover significant difference between saccades made toward ipsilateral compared with those made toward contralateral visual fields. This lack of lateral directionality might not be surprising as the receptive fields in temporal cortex are usually large and bilateral.
There are other potentially confounding or methodological interpretations of the saccade-related modification of the LEPs that can be considered. These are as follows. It is conceivable that the electrical stimulation, besides sending excitation to recorded region, also produce small seizures, which in turn modify signal propagation. Saccades then would have their effect by modifying this seizure.
There are several reasons why this interpretation is not plausible in explaining the result observed in the present study. First, we continuously monitored the local EEG activity when running the study and did not observe any sign of seizure or afterdischarge evoked by electrical stimulation. Second, we could not find any behavioral result from the electrical stimulation either from changing performance on the task or any noticeable motor effects in our monkeys. Furthermore, no EEG or behavioral evidence of seizures occurred despite using a broad range of stimulation intensities, up to one (3 mA), three times the level at which the bulk of the present results were gathered.
Because the data presented in the present paper were collected in the
dark, the increase in amplitude of evoked potentials soon after a
saccade could not have been evoked by the shift of visual image on the
retina. A further possible objection to the conclusion of saccadic
modulation of functional connectivity in the present work is that, as
found in our previous experiment (Sobotka and Ringo
1997
), there are ERPs to the saccade in absence of electrical
stimulation. These potentials could be recorded in the dark. Thus is
might seem possible that this increase in amplitude of the LEPs
following a saccade might be explained by the addition of the ERPs
produced by the saccade itself (added to the ordinary LEP caused by
electrical stimulation). However, the results of the present study
showed that the amplitude of the evoked potential to electrical
stimulation delivered soon after a saccade was significantly greater
than the amplitude derived from adding together the evoked potential to
electrical stimulation delivered without a saccade and the ERP to a
saccade itself. These results indicate that just after the end of a
saccade there is a modulation of the connectivity within the medial
temporal cortex.
Our recordings were made in the medial temporal lobe (hippocampal formation and inferotemporal cortex), areas that usually are associated with high level memory and visual perception. A significant increase of the amplitude of evoked potentials to electrical stimulation just after a saccade in these regions suggest that this effect may play a substantial role there in mnemonic and perceptual processing.
| |
ACKNOWLEDGMENTS |
|---|
Sincere thanks are due to M. Diltz and S. O'Neill for expert technical assistance.
This work was supported by National Institute of Child Health and Human Development Grant HD-36032.
| |
FOOTNOTES |
|---|
Address for reprint requests: S. Sobotka, Dept. of Neurobiology and Anatomy, Box 603, University of Rochester Medical Center, 601 Elmwood Ave., Rochester NY 14642 (E-mail: Stanislaw_Sobotka{at}urmc.rochester.edu).
Received 29 December 2000; accepted in final form 24 June 2002.
| |
REFERENCES |
|---|
|
|
|---|
This article has been cited by other articles:
![]() |
K. P. Purpura, S. F. Kalik, and N. D. Schiff Analysis of Perisaccadic Field Potentials in the Occipitotemporal Pathway During Active Vision J Neurophysiol, November 1, 2003; 90(5): 3455 - 3478. [Abstract] [Full Text] [PDF] |
||||
| ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| HOME | HELP | FEEDBACK | SUBSCRIPTIONS | ARCHIVE | SEARCH | TABLE OF CONTENTS |
| Visit Other APS Journals Online |