|
|
||||||||
Department of Physiology, Université de Montréal, Montreal, Quebec, Canada
Submitted 6 December 2004; accepted in final form 4 March 2005
| ABSTRACT |
|---|
|
|
|---|
| INTRODUCTION |
|---|
|
|
|---|
Less is known concerning the nature of the cortical contribution to the control of the hindlimb during locomotion, although it is clear, especially in humans, that the integrity of the motor cortex is important. For example, motor cortical infarct (Knutsson and Richards 1979
) or interruption of the corticospinal pathway (Nathan 1994
) each leads to severe paresis or even paralysis of the lower limbs, making walking difficult or impossible. Moreover, transcranial electrical and magnetic stimulation (Capaday et al. 1999
; Petersen et al. 1998
, 2001
; Schubert et al. 1997
) and imaging (Fukuyama et al. 1997
; Hanakawa et al. 1999
; Malouin et al. 2003
; Miyai et al. 2001
) studies all support a contribution of the motor cortex to human locomotion.
Damage to the corticospinal system in non-human primates, cats, and rats (Bucy et al. 1966
; Chambers and Liu 1957
; Eidelberg and Yu 1981
; Jiang and Drew 1996
; Laursen and Wiesendanger 1966
; Lawrence and Kuypers 1968
; Metz et al. 1998
; Muir and Wishaw 1999; Schucht et al. 2002
; Vilensky et al. 1997
) produces only transient deficits in hindlimb locomotor behavior over a flat surface. Under more challenging circumstances, however, the importance of the motor cortex for ensuring appropriate hindlimb function is evident (Drew et al. 1996
, 2002
; Schucht et al. 2002
). In addition, the few single-unit recording studies that have examined discharge characteristics of neurons in the hindlimb representation of the motor cortex have shown that pyramidal tract neurons increase their discharge rates during tasks in which cats are required to step over obstacles attached to a treadmill belt (Drew et al. 2002
; Widajewicz et al. 1994
) as well as during rhythmical or discrete voluntary movements of the hindlimb in the primate (Neafsey 1980
; Sahrmann et al. 1984
).
Although there is evidence that the motor cortex contributes to the control of hindlimb locomotion, the nature of that contribution remains unclear, particularly with respect to its relative strength and specificity. For instance, although several studies suggest a differential contribution to the control of the proximal and distal hindlimb in non-human primates (Hatanaka et al. 2001
; Wise and Tanji 1981
) and rats (Donoghue and Wise 1982
; Neafsey et al. 1986
), one of the major studies in the cat reports that the motor cortex exerts a global influence on the hindlimb in its entirety (Nieoullon and Rispal-Padel 1976
). Moreover, although stimulation of the motor cortex has been demonstrated to reset the locomotor rhythm in reduced preparations (Degtyarenko et al. 1993
; Leblond et al. 2001
; Orlovsky 1972
), there is little indication whether this is so in the intact animal or whether the nature of the resetting is similar to that observed during stimulation of the forelimb representation of the motor cortex (Rho et al. 1999
).
Clarification of these issues is important as most locomotor studies concentrate on the hindlimb because of the greater accessibility of lumbar spinal circuits (Rossignol 1996
). Similarly, most studies on reflex pathways, even in the intact animal, concentrate on the hindlimb (Pearson et al. 1999
; Rossignol et al. 1988
; Wolpaw et al. 1993
). Moreover, the fact that the hindlimbs and the forelimbs are used in a very similar manner in quadrupedal locomotion provides an opportunity for a comparative examination of the relative contribution of cortical control to the different limbs that is not available in other tasks in other species and especially in primates. We therefore used ICMS to examine the contribution of the motor cortex on the structure and timing of the pattern of electromyographic (EMG) activity observed in the hindlimbs during treadmill locomotion. The results suggest that in all important aspects the cortical contribution to regulation of the hindlimb during locomotion is similar to that for the forelimbs.
| METHODS |
|---|
|
|
|---|
Experiments were carried out on five male cats (weights: 4.25.5 kg) trained to walk at a comfortable and constant speed (circa 0.350.45 m/s) on a treadmill. Cats were carefully selected on the basis of their willingness to walk for uninterrupted periods of
20 min.
Surgical procedures
The motor cortex was stimulated in three cats (MC2325). The pyramidal tract was stimulated in four cats (MC24-27).
In cats MC23 and MC24, microwire electrodes were chronically implanted into the hindlimb representation of the motor cortex. Anesthesia was induced with a mix of ketamine hydrochloride (30 mg/kg im) and acepromazine maleate and was maintained with additional doses of ketamine hydrochloride (5 mg/kg iv) as needed to maintain a constant heart rate and a lack of corneal reflex. Microwire electrodes (Tri-ML insulated stainless steel: 25 µm diam) attached to a miniature connector (Neuralynx: EIB27) were manually inserted, one at a time, into the posterior bank of the cruciate sulcus that contains the hindlimb representation of the motor cortex (Armstrong and Drew 1984b
; Nieoullon and Rispal-Padel 1976
; Widajewicz et al. 1994
). By using ketamine anesthesia for this procedure, we were able to ensure appropriate positioning of the microwires by recording neuronal activity and examining the responses evoked by ICMS as the wires were inserted. The cortex was covered with a hemostatic material (Sterispon) and the microwire connector was attached to the cat's cranium with dental acrylic. In one cat (MC25), a recording chamber was positioned over the motor cortex (Drew 1988
, 1993
; Widajewicz et al. 1994
) to allow comparison of the responses evoked with tungsten microelectrodes with those evoked by cortical microwires. Penicillin (Novopharm: 40000 UI/kg iv) and analgesics (buprenorphine hydrochloride: 5 µg/kg) were provided at the beginning and at the end of each surgery, and for
48 h following surgeries. Antibiotics (cephadroxil: 100200 mg/day) were administrated daily for the duration of the experiment.
One to 2 wk after recovery from the initial surgery, the cats were anesthetized with isoflurane (23% with oxygen) to complete the surgical procedures. Microwires electrodes were implanted in the pyramidal tract at P7 (Drew 1993
) in two of the cats used for the cortical microstimulation (MC24 and MC25) as well as in two additional cats (MC26-27) to allow comparison with the responses evoked by ICMS. Multiple pairs of Teflon-insulated, braided stainless steel wires were implanted into selected muscles of the fore- and hindlimbs to record EMG activity in all cats. In the forelimb, electrodes were implanted bilaterally into cleidobrachialis (ClB), protactor of the shoulder and flexor of the elbow and triceps brachii, lateral head (TriL), extensor of the elbow. In the hindlimb, electrodes were always inserted bilaterally into: extensor digitorum brevis (EDB), dorsiflexor of the hindpaw digits; extensor digitorum longus (EDL), dorsiflexor of the digits and flexor of the foot; lateral and medial heads of the gastrocnemius (GL and GM), extensors of the ankle; anterior head of the sartorius (Srt), a hip flexor; semitendinosus (St), a knee flexor; tibialis anterior (TA), an ankle flexor; and vastus lateralis (VL), a knee extensor. In some cats, electrodes were additionally implanted into the following muscles contralateral to the cortical stimulation sites: flexor digitorum longus (FDL; MC23-24), ventroflexor of the digits and extensor of the foot; and soleus (Sol; MC25-27), extensor of the ankle. Recovery and postoperative procedures were as before.
All surgical and experimental procedures followed the recommendations of the Canadian Council for the Protection of Animals and were approved by the local ethics committee.
Protocol
In the cat with a recording chamber, the electrode was slowly advanced into layer V of the motor cortex, which was identified by the presence of neurons that were antidromically activated by stimulation of the pyramidal tract (Armstrong and Drew 1984a
). Intra-cortical microstimulation (cathodal current, 11 pulses at 330 Hz, pulse duration 0.2 ms,
35 µA) was then applied while the cat was held gently in a prone position to test the threshold and the nature of the evoked responses in the contralateral hindlimb. Evoked EMG responses were digitized on-line at a frequency of 5 kHz for 25 ms before and 150 ms after the onset of the stimulus train. EMGs were band-pass filtered between 100 Hz and 3 kHz.
The animal was then placed onto the treadmill to assess the effects of microstimulation during locomotion. Trains of stimuli (identical to those used for stimulation at rest) were delivered at a range of current strengths of 535 µA (5 µA steps) at a delay of 50 ms after the onset of activity in the sartorius (i.e., at swing onset). Subsequently trains of stimuli at 25 µA were applied at different times throughout the step cycle. Ten to fifteen repetitions were made at each delay in the following order: 50-150-300-500-700-900-0-100-200-400-600-800, and 1,000 ms after the onset of the activity in the Srt. All responses were recorded and digitized on-line as in the preceding text. In addition, a continuous record of the EMG activity during locomotion was also digitized at 1 kHz. Last, longer trains of stimuli (200-ms duration) were delivered to determine the cortical contribution to the cycle timing. Trains of stimuli were applied in every fifth step cycle at each delay (5 repetitions at each stimulus delay) using the same order as detailed in the preceding text.
Penetrations were made in a grid pattern separated by a minimum of 0.5 mm in both the anteroposterior and mediolateral planes. To aid histological reconstruction, small electrolytic lesions (20 µA, DC cathodal current) were made in layer V in selected penetrations.
A similar recording protocol was used for cats with microwires chronically implanted in the motor cortex and in the pyramid. For some of these cortical microwires, it was possible to record antidromically activated cells in layer V. However, as these wires could not be adjusted to ensure that they were in the optimal location, we did not use a constant intensity for these experiments but rather adjusted the strength of the stimulus to a level that evoked clear responses in flexor muscles during the swing phase of locomotion.
Data analysis
Data were analyzed as previously described (Rho et al. 1999
). In brief, the data obtained with the cat at rest were computer-rectified and averaged. The onset and offset of cortically evoked EMG responses were determined manually using the interval of confidence (P < 0.01) of the standard error of the mean (SE) of the prestimulus period as a guideline. The amplitude of the net evoked responses was computed by subtracting the area of the prestimulus EMG responses (for an identical period of time) from the selected evoked EMG responses. The latency, duration, and amplitude of the net evoked responses were computed and plotted.
For the data in which short trains of stimuli were applied during locomotion, control and stimulated cycles were manually identified in reference to the onset of the Srt. The step cycle was subdivided into ten equal phases (groups) synchronized on the onset of the sartorius (see Fig. 1). The responses evoked by stimuli in each phase were averaged and plotted on a display monitor. The average activity from a similar time period taken from unstimulated cycles was superimposed on this display (Fig. 1) (Drew and Rossignol 1984
). The onset and offset of the response was determined manually using the interval of confidence (P < 0.01) of the SE of the control activity during the identical phase of the unstimulated cycles as a guideline. Evoked responses were included in the analysis if their latency was
50 ms and their duration exceeded 5 ms. We defined two types of responses. Primary responses, regardless of sign, were those that occurred before any other change in activity. Secondary responses were those in which the latency was <50 ms but that occurred after a primary response. At some phases of the step cycle the secondary response was sometimes evoked in the absence of a primary response; we continue to refer to such responses as secondary responses. For example, in Fig. 3B, a short-latency, primary, increase in activity is evoked in EDB in late stance together with a later, secondary, decrease in activity. In early stance, however, only the longer latency decrease in activity is observed; the latter is, therefore referred to as a secondary response.
|
|
|
Histology
At the end of the experimental manipulations, the cats were deeply anesthetized with sodium pentobarbitol (Somnotol 40 mg/kg) and perfused per cardium. The brains were sectioned and stained with cresyl violet.
| RESULTS |
|---|
|
|
|---|
Short trains of ICMS were applied throughout the hindlimb representation of the motor cortex using either microwires (n = 18 sites) or glass-insulated tungsten electrodes (n = 16 sites). Stimulation with the cat held gently on the experimenter's lap and with the hindlimb unsupported evoked brief, twitch movements involving one or more joints of the hindlimb at all 34 sites (Table 1). At just suprathreshold current intensities, the most common effect was a brief movement of two joints (18/34 sites: 53%) normally the knee and the ankle (16/18 sites: 89%). In a relatively high proportion of sites (13/34: 38%), stimulation at low intensities evoked responses around a single joint, most frequently the ankle (9/13: 69%). At the other sites (3/34, 9%), the stimulation evoked movement of all three joints (hip, knee, and ankle). No movements were evoked in either the contralateral forelimb or in the ipsilateral hindlimb by stimuli at any of the loci. Similarly, stimuli with the cat at rest did not produce evoked EMG responses in the muscles recorded in these two limbs although weak responses were occasionally observed during locomotion. The following report is, therefore based primarily on the effects evoked in the contralateral hindlimb.
|
All of the stimulated sites were located within the caudal bank of the cruciate sulcus. Figure 2A illustrates tracings of two histological sections taken from cat MC25 showing electrode penetrations terminating in layer V (dotted line) within the caudal bank of the cruciate sulcus. The approximate location of all 16 sites at which stimulation was applied in this cat are illustrated in the pseudo-3D representation of Fig. 2B (see Widajewicz et al. 1994
). Similar regions of the motor cortex were stimulated in cats MC23 and MC24, as illustrated in Fig. 2, C and D.
|
PHASE-DEPENDENT NATURE OF THE RESPONSES. Figure 3 illustrates representative examples of the effects evoked by ICMS at different phases of the locomotor cycle via a tungsten microelectrode (current strength 25 µA: Fig. 3A) and a microwire (current strength 35 µA: Fig. 3B). Each of the electrodes was verified to be in layer V of the cortex by the presence of neurons discharging antidromically to stimulation of the pyramidal tract. Stimulation through the cortical electrodes during the swing phase evoked short latency primary responses in the flexor muscles, St and TA and was without effect in the EDB and the GM. In contrast, during the early and late stance phases, primary responses were absent or smaller in St and TA and the stimulation produced a clear decrease in the level of activity of the GM that was more pronounced in late stance; there was also a long-latency, secondary decrease in activity in the TA in the example in Fig. 3A (early stance). The responses in the EDB were more complex. Clear primary increases in activity were seen in late stance in the example in Fig. 3B and in early stance in the example in Fig. 3A; there was also a weak increase in the level of activity in the EDB in early stance in the example in Fig. 3B (not significant) that was followed by a secondary decrease. As the results evoked by the two different methods were generally similar (see DISCUSSION), they will be treated together except where differences occur.
The phase-dependant nature of the EMG responses evoked in these four muscles, as well as in several others recorded in the same experiment as in Fig. 3B, is illustrated in Fig. 4. Maximal responses in the hip, knee, and ankle flexor muscles, St, TA, EDL, and Srt were observed during the swing phase (phases 0.10. 3) and at the end of stance (phases 0.91.0; Fig. 4, AC). In the paw dorsiflexor, EDB, increased responses were maximal at the end of swing (phase 3) and again in late stance (phases 0.81.0; Fig. 4D). Secondary, longer latency decreases in EMG activity were evoked in EDB, EDL, and Srt during the swing phase. In extensor muscles, primary increases in activity were observed in the GM and GL at the end of the swing phase (Fig. 4E), and decreases in activity were observed during stance in all four recorded extensor muscles (Fig. 4, E and F).
Figure 5 illustrates that the responses evoked by the stimulation were reproducible from cat to cat, especially for the primary responses. As for the single example illustrated in Fig. 4, primary increases in the flexor muscles St and TA were always present during the swing phase and at the end of stance (
91% of cortical sites; Table 2). Similar responses were seen in the EDL and Srt. The responses in EDB were more variable. In MC24, they were observed predominantly during stance, although some responses were observed during swing, whereas in MC25, they were predominant in late swing. This difference in response is probably related to the difference in the pattern of activity in the EDB. In the illustrated extensor, GM, as well as in all other extensor muscles (FDL, VL, GL, Sol), the predominant effect was a decrease in activity during the stance phase. Increases in activity were seen in some sites at the end of swing and very occasionally, as in MC25, during early stance.
|
|
The latencies of the responses evoked at different phases of the step cycle are summarized in Table 2. In the flexor muscles, primary increased responses were always evoked at short latency (average values
16 ms) during the swing phase. When responses were evoked in flexor muscles during stance, responses were always smaller and at longer latency than those evoked during swing.
In the extensor muscles, the primary increased responses evoked during swing were at longer latencies (
21 ms) than those evoked in flexor muscles. During stance, the averaged latency of the primary decrease in activity ranged from 19.7 ms in FDL to 31.8 ms in Sol.
Responses in both flexor and extensor muscles were generally evoked at longer latency at rest than during locomotion.
Effects of current strength
Figure 6 illustrates the effect of modifying the current strength on the cortically evoked EMG responses during the early swing phase of the step cycle. In the illustrated example, stimulation of the motor cortex through a tungsten electrode at the standard intensity of 25 µA (Fig. 6A, middle) activated muscles acting around all of the major joints of the hindlimb. At 10 µA similar activation patterns were evoked in the three illustrated flexor muscles but there was no longer a significant response in the VL. At 35 µA, the amplitudes of the evoked responses were increased in all four illustrated muscles. As shown in Fig. 6B (left), at this site all of the recorded flexor muscles (solid lines) were recruited at the lowest strengths used, while extensors (dotted lines) were recruited at slightly higher intensities. Subsequently, as stimulus strength was increased there was a relatively monotonic increase in the amplitude of the evoked responses in all of the muscles over the limited range of intensities that we employed.
|
The percentage of recorded contralateral hindlimb flexor and extensor muscles recruited at different intensities of ICMS during the swing phase of the step cycle is summarized in Fig. 6C for all sites from all three cats. In cat MC25, in which ICMS was applied through tungsten electrodes, stimulation at 15 µA recruited almost 75% of the total complement of flexor muscles while stimulation at 25 µA recruited 95%. In other words, stimulation at 25 µA was sufficient to recruit nearly all of the flexor muscles that we recorded in all 16 sites that were stimulated. Similar results were observed for the microwire stimulation in cat MC23 in which 75% of flexor muscles were recruited at 25 µA, and there was only a slight increase after this (note that some flexor muscles in some sites were not activated even at 150 µA). The results from cat MC24 were slightly different in that there was a relatively large jump in the frequency of flexor muscles recruited at 50 µA (57%) to the proportion recruited at 75 µA (82%). The differences between these two cats was mainly caused by the fact that very few responses were evoked in the Srt from any of the stimulated sites in cat MC24.
Specificity of the responses evoked by ICMS
Although a number of cortical sites produced movement only at a single joint, most sites produced movement at multiple joints (Table 1). Moreover, even in sites in which movement was produced at a single joint, the stimulation frequently activated multiple muscles. However, even though several muscles were activated, the relative amplitude of the responses evoked in different muscles varied according to the stimulated site. For instance, Fig. 7 illustrates the responses evoked in four hindlimb flexor muscles by stimulation of three different sites (AC, respectively) distributed within the hindlimb representation of the motor cortex from the same cat (MC25). At rest, stimulation at 25 µA at cortical site A evoked a flexion of the hip, at site B, the same stimulation evoked a strong knee flexion, whereas at site C, it evoked a weak flexion of the ankle. At all three sites threshold was between 10 and 15 µA. These mechanical effects were largely reflected in the evoked EMG responses that we recorded. Stimulation of site A evoked a response only in the Srt, whereas stimulation at site B evoked strong responses in the St, together with relatively weaker responses in Srt and TA. Stimulation at site C evoked no response in the St but weak responses in Srt, TA, and EDB; the latter muscle was not activated from either of the other two sites when the cat was not walking.
|
Thus while at rest, the mechanical effects of the microstimulation were relatively well reflected in the relative magnitudes of the evoked responses, locomotion produced changes in excitability that tended to mask these differences.
Nonetheless, there were differences in the relative effects of the stimulated sites on representative flexor muscles during locomotion as demonstrated by the density plots of Fig. 8. In this figure, the stimulated sites in each cat have been placed in order according to the magnitude of the responses evoked in the St. Thus those sites producing the largest responses in St are found at the bottom of the display and are concentrated to the left which represents the swing phase (phases 0.00.3). The same order of sites is maintained for the other displayed muscles. This illustrates that while the sites that produced the largest responses in the St in cat MC25 generally also evoked large responses in the Srt, there were other sites that had relatively little effect on the St and yet evoked large responses in Srt. In cat MC24, the sites producing the largest responses in St produced relatively small responses in the TA, and vice versa. Similarly, some of the sites producing responses in the EDB had only minimal effects on the St, Srt, or TA (not illustrated).
|
The responses evoked by stimulation of the pyramidal tract (PT) are plotted in Fig. 9. In general, stimulation of the PT in all four cats tested (MC2427) evoked phase-dependent responses in all muscles that were similar to those evoked from the more discrete stimulation of individual cortical sites (compare with Fig. 5). Responses in flexor muscles were largest during swing and responses in extensors were increased at the end of swing and decreased during stance. The only discrepancy that was observed was the lack of any response in St during the swing phase of locomotion from stimulation of the PT in cat MC24. The reason for this discrepancy is not known.
|
Long trains of stimuli during different phases of the locomotor cycle were applied in 12/16 cortical sites in cat MC25 and 5/8 cortical sites in cat MC24. During swing, the stimulation invariably produced a hyperflexion of the contralateral hindlimb, whereas the same stimulation during stance was either without a visible behavioral effect or produced a curtailment of stance and initiated a premature flexion of the hindlimb. In the representative example illustrated in Fig. 10A, stimulation during swing produced increases in the amplitude and the duration of both Srt (Fig. 10D) and St but had no effect on the overall duration of the step cycle at these times (Fig. 10, B and C). The same stimulation during stance (Fig. 10A, middle and bottom) led to a significant decrease in the duration of the extensor muscle, GM (Fig. 10E), and the initiation of a new burst of activity in the St and the Srt. This caused a significant decrease in the duration of the step cycle (to
70% of control values) which was reset by the stimulation (compare subsequent cycles in Fig. 10A, middle and bottom).
|
|
|
| DISCUSSION |
|---|
|
|
|---|
General considerations
Most of these experiments were performed with the microwire electrodes used in our current studies of the long-term plastic changes in corticospinal efficacy that occur following cutaneous denervation of the hindpaw (Bretzner and Drew 2003
). As with most experiments in which microwires are used, one of the limitations of this method is the inability to modify the location of the electrode once it has been implanted. In contrast to experiments using moveable microelectrodes it is therefore, not possible to displace the electrode to ensure that the tip is located in the optimal region for eliciting motor activity, namely within layer V (Asanuma 1975
; Asanuma and Sakata 1967
; Porter and Lemon 1993
). Nevertheless, some of the microwire electrodes used in this study were positively identified to be within layer V by the presence of antidromic activity produced by stimulation of the pyramidal tract and most others were identified as being in the gray matter by the presence of multiunit neuronal activity. Moreover, there was no qualitative difference between the results obtained with stimulation of these microwire electrodes and those obtained from the experiments with a moveable tungsten microelectrode. The more elevated thresholds obtained for the microwire electrodes are to be expected based on the inability to specifically localize them and the larger exposed areas of these electrodes compared with glass-insulated tungsten microelectrodes (Armstrong and Drew 1985a
). The following discussion therefore makes no distinction between the results obtained using the two different types of electrode.
Phase dependence of the evoked responses
Stimulation of the hindlimb representation of the motor cortex led to clear phase-dependent responses in which stimulation during swing evoked increased activity in flexor muscles but had relatively minor effects in extensor muscles, whereas stimulation in stance had little effect on flexor muscles and generally decreased activity in the extensor muscles. The major exceptions to this generalization were the increased responses that were frequently seen in the extensor muscles at the end of swing and the onset of stance and the complex pattern of activity in the EDB. Indeed, responses in the latter muscle varied in different cats and seemed to depend on the exact pattern of activity in the muscle during locomotion (Fig. 5). This pattern of activity is very similar to that observed in the extensor digitorum communis muscle in the forelimb (Rho et al. 1999
) and suggests that the pattern of activity, and excitability, of some of the distal muscles is more flexible than that of more proximal muscles.
Overall, the pattern of responses that was observed in hindlimb flexor and extensor muscles in this study was similar to that detailed for the forelimb in previous studies (Armstrong and Drew 1985b
), suggesting that the cortex has a similar capacity for modulating the activity of hindlimb muscles during locomotion as for the forelimbs. We have previously suggested that most of the phase dependence from cortical stimulation is the result of the rhythmic changes in excitability of the interneuronal networks in the spinal cord that are activated by the descending corticospinal volley (Rho et al. 1999
). Nonetheless, there is also the possibility that changes in cortical excitability produced by step-related changes in discharge activity may also influence the magnitude of the evoked responses (Petersen et al. 1998
). However, the finding that the responses evoked by stimulating the PT, which should be relatively uninfluenced by changes in cortical excitability, were almost identical to those obtained from stimulating the motor cortex supports the contention that the phase dependency is determined more by the state and excitability of the spinal interneuronal pathways than on the excitability of the cortex itself. This does not imply that changes in cortical excitability do not contribute to this process only that the excitability changes in spinal circuits are sufficient to produce the phase-dependent response.
It is also interesting to note that the responses evoked by stimulation of the pyramidal tract were not substantially greater that those evoked by stimulation of the motor cortex and this despite the fact that stimulation of the pyramidal tract should activate a much greater number of axons. Indeed, not only were the effects not greater but we normally employed currents of
100 µA simply to have responses of a comparable magnitude to those evoked from small regions of the cortex by currents of
25 µA. This difference was not simply a function of badly positioned electrodes. Histological examination showed that the electrodes were appropriately positioned, and we were able to antidromically activate pyramidal tract neurons in all cats. Instead, the results suggest that the activation of multiple corticospinal fibers, originating from different regions of the cortex, might result in conflicting signals at the spinal level. The results that we observe would therefore represent the strongest of these signals.
Reset of the step cycle
To compensate for unexpected changes in the environment, animals must be able to modify the timing of the step cycle to lengthen or shorten stride, and, in extreme conditions, they must be able to interrupt, or reset, the step cycle and start a new one. Previous studies have shown that stimulation of the forelimb representation of the motor cortex is able to produce such changes in the forelimb in intact animals (Armstrong and Drew 1985b
; Rho et al. 1999
). The present results show that the hindlimb representation of the motor cortex has a similar, although slightly reduced, capacity to reset the hindlimb cycle. In our previous studies in which we stimulated the forelimb representation of the motor cortex (Rho et al. 1999
), stimulation during the stance phase of the step cycle could shorten the cycle by up to 38% (mean 65%). Indeed, in that study, 17/32 of the sites produced a reduction of the step cycle that was >25% (i.e., reduced to 75% of the control value), whereas in the present study, the greatest reduction that we observed was 26% and the mean reduction was 15%. Although it is possible that this reduced capacity for modifying the cycle might be due to the limited number of sites that we examined, examination of the data in Fig. 11 and comparison with Fig. 10 in Rho et al. (1999)
, suggests an overall reduction in the capacity of the motor cortex to modify hindlimb cycle duration.
Interestingly, the changes in hindlimb cycle duration were relatively independent of major changes in the forelimbs. This suggests that under normal circumstances, coordinated changes in step cycle duration would require simultaneous activation of both the forelimb and hindlimb representations of the motor cortex. Such simultaneous activation might also be required to produce reductions in hindlimb cycle duration of the same order as those observed from stimulation of the forelimb representation (Rho et al. 1999
).
The results obtained from this cortical stimulation differ from some of those obtained in reduced cat preparations in which, by definition, only the PT could be stimulated. Although our results agree with those obtained in thalamic and mesencephalic cats walking on a treadmill (Orlovsky 1972
) as well as those obtained in the fictive preparation by Degtyarenko et al. (1993)
, they are somewhat different from some of those reported by Leblond et al. (2001)
. In particular, although stimulation during the swing phase in the intact cat always evoked increased flexor activity in our study, as it did in the studies by Orlovsky (1972)
and Degtyarenko et al. (1993)
, Leblond et al. (2001)
found stimulation sites that curtailed the flexion phase and initiated an extension. The reason for these differences is not clear. However, it is not likely to be a difference between stimulation of the motor cortex and of the PT, as stimulation of the PT in the intact cat produced similar results to those obtained from cortical stimulation. Moreover, Orlovsky and Degtyarenko also obtained their results from stimulating the PT. One possibility is that the location of the electrodes in the PT might be a factor. Leblond et al. (2001)
specifically looked for areas producing an extensor bias. In our study, the PT electrodes were placed stereotaxically and fixed in place. Moreover, we emphasize that similar results were also obtained from all 17 electrodes positioned in the motor cortex in the two cats and that none of these sites caused a curtailment of flexor activity. It is also possible that the lack of any phasic peripheral afferent feedback makes the spinal neuronal networks more open to perturbation from central sources. For example, stimulation of the reticular formation in the intact (Drew 1991b
) or decerebrate, walking (Drew and Rossignol 1984
) cat has much less influence over step cycle timing that the same stimulation does during fictive locomotion (Perreault et al. 1994
). Similar effects can also be seen from red nucleus stimulation, which does not change cycle timing in the intact cat (Rho et al. 1999
) but which does during fictive locomotion (Degtyarenko et al. 1993
).
Specificity of the responses
Nieoullon and Rispal-Padel (1976)
previously reported that stimulation of the hindlimb representation of the cat motor cortex evokes global effects in which the whole hindlimb is flexed even at threshold levels. This is in contrast to the forelimb in which threshold stimulation more frequently produces movement around a single joint (Armstrong and Drew 1984b
; Nieoullon and Rispal Padel 1976
). In this study, we also found that microstimulation at threshold levels frequently activated movement around two or more hindlimb joints. However, we also found several sites at which threshold stimulation activated only a single joint, much as is the situation with stimulation of the forelimb representation of the motor cortex. Even so, the proportion of sites eliciting activity around a single joint (38%) was reduced compared with the 60% reported for the forelimb by Armstrong and Drew (1984b)
; even though the latter were stimulating at a constant strength of 35 µA. Nevertheless, the results do show that the motor cortex can exert differential control over the hindlimb as in other species (see INTRODUCTION) and as for the forelimb. The differences between the results obtained here possibly reflect differences in stimulus intensity (with respect to the study of Nieoullon and Rispal-Padel 1976
) and differences in the regions of the hindlimb representation that were stimulated [mostly in the bank of the cruciate sulcus in this study compared with mostly superficially in the study of Armstrong and Drew (1984b)
]. Indeed, most of the sites producing a movement around a single joint were found quite deep within the cruciate sulcus and, in most cases, single-joint responses were restricted to the ankle. The more specific nature of the responses in this study is also in agreement with the results from the unit recording study of Widajewicz et al. (1994)
showing neurons discharging in phase with the activity of different groups of muscles.
Some of the more overt specificity was lost during locomotion as the increased excitability of the spinal circuits resulted in increased recruitment compared with that seen in the resting cat (see. Fig. 7). Even in this situation, however, there were clear differences in the relative amplitude of the responses evoked in different muscles. This is seen in both Figs. 7 and 8, which show that in some sites the relative amplitude in muscles such as the TA and the Srt was relatively larger than that in St and in others relatively smaller. This demonstrates that in some sites, the motor cortex can differentially activate muscles acting around different joints, whereas in others, it activates muscles acting all joints, albeit with relatively different potency. It is unlikely that the activation of multiple muscles acting around more than one joint is caused by excessive stimulus intensities as multiple responses were evoked from most cortical sites even at strengths of 1015 µA and increasing stimulus intensity resulted in relatively low supplementary recruitment (see Fig. 6D). Given the relatively low spread of current that might be expected at these low intensities (Stoney et al. 1968
), even allowing for trans-synaptic activation, the results suggest that a restricted area of cortex will activate a large number of hindlimb muscles. This again is similar to the result obtained from stimulation of the forelimb representation of the motor cortex (Armstrong and Drew 1985a
,b
).
A schematic summary of the way in which the hindlimb representation of the motor cortex may act to modify locomotor activity in the hindlimbs is illustrated in Fig. 12. This emphasizes that the output from different regions of the hindlimb representation has the capacity to modulate interneuronal networks influencing hindlimb muscles acting around several hindlimb joints. At the same time, the results show that the strength of this modulation is not equal but that some regions will influence muscles acting around the hip more than those at the knee while others will show the opposite pattern. Regions modulating more distal regions are more selective than those activating more proximal regions. Microstimulation of these same regions also influence the timing of the cycle, and in this case, we found effects on cycle duration from several different regions, including those influencing the structure of both more proximal and more distal musculature.
|
It is clear that in the process of evolution, the motor cortex has become more and more associated with the control of the forelimb and particularly of the wrist and hand (Heffner and Masterton 1975
; Kuypers 1981
; Lawrence and Kuypers 1968
; Nudo and Masterton 1990
; Phillips 1986
). Although this process is at its clearest in humans and non-human primates, there is also evidence showing that the corticospinal projections to the lumbar enlargements are smaller than those to the cervical enlargements in most species and, in some species are even absent (Heffner and Masterton 1975
). In agreement with this, in most mammals, including the cat, the hindlimb representation of the motor cortex is normally smaller than that of the forelimb. Despite the difference in the overall magnitude of the projection, however, the results in this paper suggest that the nature of the contribution of the motor cortex to the control of the hindlimbs is qualitatively the same as that for the forelimbs. This is especially true for its capacity to modify the level of activity in a wide selection of muscles acting around different joints of the hindlimb and, moreover, of its capacity to differentially modulate activity around these joints. The results also show that the motor cortex maintains a similar capacity to modulate cycle timing of the hindlimb as it does for the forelimb although there might be a quantitative difference in the strength of this capacity. Moreover, the results from stimulating with the long trains supports our previous contention (Widajewicz et al. 1994
) that the motor cortex may control movements of the hindlimbs independently of the forelimbs. Overall, the results presented in this report argue in favor of a substantial contribution of the corticospinal system to the regulation of the hindlimbs during locomotion in cats. It is highly likely that a similar contribution is made to the control of human locomotion, particularly in light of the devastating effects of motor cortical lesion on human locomotion.
| GRANTS |
|---|
|
|
|---|
| ACKNOWLEDGMENTS |
|---|
|
|
|---|
Present address of F. Bretzner: International Collaboration on Repair Discoveries (ICORD), Dept. of Zoology, 6270 University Blvd., Vancouver, British Columbia V6T 1Z4, Canada.
| FOOTNOTES |
|---|
Address for reprint requests and other correspondence: T. Drew, Dept. of Physiol, Université de Montréal, PO Box 6128, Station Centre-ville, Montréal, Québec H3C 3J7, Canada (E-mail: Trevor.Drew{at}umontreal.ca)
| REFERENCES |
|---|
|
|
|---|
Amos A, Armstrong DM, and Marple-Horvat DE. Changes in the discharge patterns of motor cortical neurons associated with volitional changes in stepping in the cat. Neurosci Lett 109: 107112, 1990.[CrossRef][Web of Science][Medline]
Armstrong DM. Supraspinal contributions to the initiation and control of locomotion in the cat. Prog Neurobiol 26: 273361, 1986.[CrossRef][Web of Science][Medline]
Armstrong DM and Drew T. Discharges of pyramidal tract and other motor cortical neurons during locomotion in the cat. J Physiol 346: 471495, 1984a.
Armstrong DM and Drew T. Topographical localisation in the motor cortex of the cat for somatic afferent responses and evoked movements. J Physiol 350: 3354, 1984b.
Armstrong DM and Drew T. Electromyographic responses evoked in muscles of the forelimb by intracortical stimulation in the cat. J Physiol 367: 309326, 1985a.
Armstrong DM and Drew T. Forelimb electromyographic responses to motor cortex stimulation during locomotion in the cat. J Physiol 367: 327351, 1985b.
Asanuma H and Sakata H. Functional organisation of a cortical efferent system examined with focal depth stimulation in cats. J Neurophysiol 30: 3554, 1967.
Asanuma H. Recent developments in the study of the columnar arrangement of neurons within the motor cortex. Physiol Revs 55: 143156, 1975.
Beloozerova IN and Sirota MG. The role of the motor cortex in the control of accuracy of locomotor movements in the cat. J Physiol 461: 125, 1993.
Bretzner F and Drew T. Locomotor plasticity following unilateral cutaneous denervation of the hindpaw in the cat. Soc Neurosci Abstr 2003.
Bucy PC, Ladpli R, and Ehrlich A. Destruction of the pyramidal tract in the monkey: the effects of bilateral section of the cerebral peduncles. J Neurosurg 25: 120, 1966.[Web of Science][Medline]
Capaday C, Lavoie BA, Barbeau H, Schneider C, and Bonnard M. Studies on the corticospinal control of human walking. I. Responses to focal transcranial magnetic stimulation of the motor cortex. J Neurophysiol 81: 129139, 1999.
Chambers WW and Liu CN. Cortico-spinal tract of the cat. An attempt to correlate the pattern of degeneration with deficits in reflex activity following neocortical lesions. J Comp Neurol 108: 2355, 1957.[CrossRef][Web of Science][Medline]
Degtyarenko AM, Zavadskaya TV, and Baev KV. Mechanisms of supraspinal correction of locomotor activity generator. Neuroscience 52: 323332, 1993.[CrossRef][Web of Science][Medline]
Donoghue JP and Wise SP. The motor cortex of the rat: cytoarchitecture and microstimulation mapping. J Comp Neurol 212: 7688, 1982.[CrossRef][Web of Science][Medline]
Drew T. Motor cortical cell discharge during voluntary gait modification. Brain Res 457: 181187, 1988.[CrossRef][Web of Science][Medline]
Drew T. Visuomotor coordination in locomotion. Current Opinion in Neurobiol 1: 652657, 1991a.
Drew T. Functional organization within the medullary reticular formation of the intact unanaesthetized cat. III. Microstimulation during locomotion. J Neurophysiol 66: 919938, 1991b.
Drew T. Motor cortical activity during voluntary gait modifications in the cat. I. Cells related to the forelimbs. J Neurophysiol 70: 179199, 1993.
Drew T, Jiang W, Kably B, and Lavoie S. Role of the motor cortex in the control of visually triggered gait modifications. Can J Physiol Pharmacol 74: 426442, 1996.[CrossRef][Web of Science][Medline]
Drew T, Jiang W, and Widajewicz W. Contributions of the motor cortex to the control of the hindlimbs during locomotion in the cat. Brain Res Brain Res Rev 40: 178191, 2002.[CrossRef][Medline]
Drew T and Rossignol S. Phase dependent responses evoked in limb muscles by stimulation of the medullary reticular formation during locomotion in thalamic cats. J Neurophysiol 52: 653675, 1984.
Eidelberg E and Yu J. Effects of corticospinal lesions upon treadmill locomotion by cats. Exp Brain Res 43: 101103, 1981.[Web of Science][Medline]
Fukuyama H, Ouchi Y, Matsuzaki S, Nagahama Y, Yamauchi H, Ogawa M, Kimura J, and Shibasaki H. Brain functional activity during gait in normal subjects: a SPECT study. Neurosci Lett 228: 183186, 1997.[CrossRef][Web of Science][Medline]
Hanakawa T, Katsumi Y, Fukuyama H, Honda M, Hayashi T, Kimura J, and Shibasaki H. Mechanisms underlying gait disturbance in Parkinson's disease. A single photon emission computed tomography study. Brain 122: 12711282, 1999.
Hatanaka N, Nambu A, Yamashita A, Takada M, and Tokuno H. Somatotopic arrangement and corticospinal inputs of the hindlimb region of the primary motor cortex in the macaque monkey. Neurosci Res 40: 922, 2001.[CrossRef][Web of Science][Medline]
Heffner R and Masterton B. Variations in form of the pyramidal tract and its relationship to digital dexterity. Brain Behav Evol 12: 161200, 1975.[Web of Science][Medline]
Jiang W and Drew T. Effects of bilateral lesions of the dorsolateral funiculi and dorsal columns at the level of the low thoracic spinal cord on the control of locomotion in the adult cat. I. Treadmill walking. J Neurophysiol 76: 849866, 1996.
Knutsson E and Richards C. Different types of disturbed motor control in gait of hemiparetic patients. Brain 102: 405430, 1979.
Kuypers HGJM. The organization of the "motor system." Int J Neurol 4: 7891, 1963.
Kuypers HGJM. Anatomy of the descending pathways. In: Handbook of Neurophysiology, edited by Brooks V. Bethesda, MD: Am. Physiol. Soc., 1981, vol. II, part 1, p. 597666.
Laursen AM and Wiesendanger M. Motor deficits after transection of a bulbar pyramid in the cat. Acta Physiol Scand 68: 118126, 1966.
Lawrence DG and Kuypers HGJM. The functional organization of the motor system in the monkey. I. The effects of bilateral pyramidal lesions. Brain 91: 115, 1968.
Leblond H, Menard A, and Gossard JP. Corticospinal control of locomotor pathways generating extensor activities in the cat. Exp Brain Res 138: 173184, 2001.[CrossRef][Web of Science][Medline]
Liddell EGT and Phillips CG. Pyramidal section in the cat. Brain 67: 19, 1944.
Malouin F, Richards CL, Jackson PL, Dumas F, and Doyon J. Brain activations during motor imagery of locomotor-related tasks: a PET study. Hum Brain Mapp 19: 4762, 2003.[CrossRef][Web of Science][Medline]
Metz GAS, Dietz V, Schwab ME, and Van de Meent H. The effects of unilateral pyramidal tract section on hindlimb motor performance in the rat. Behav Brain Res 96: 3746, 1998.[CrossRef][Web of Science][Medline]
Miyai I, Tanabe H, Sase H, Eda H, Oda I, Konishi I, Tsunazawa Y, Suzuki T, Yanagida T, and Kubota K. Cortical mapping of gait in humans: a near infra-red spectroscopic topography study. NeuroImage 14: 11861192, 2001.[CrossRef][Web of Science][Medline]
Muir GD and Whishaw IQ. Complete locomotor recovery following corticospinal tract lesions: measurement of ground reaction forces during overground locomotion in rats. Behav Brain Res 103: 4553, 1999.[CrossRef][Web of Science][Medline]
Nathan PW. Effects on movement of surgical incisions into the human spinal cord. Brain 117: 337346, 1994.
Neafsey EJ. Precentral cortical zones related to flexion and extension in two hindlimb movements in the monkey. Brain Res 198: 453459, 1980.[CrossRef][Web of Science][Medline]
Neafsey EJ, Bold EL, Haas G, Hurley-Gius KM, Quirk G, Sievert CF, and Terreberry RR. The organization of the rat motor cortex: a microstimulation mapping study. Brain Res Rev 11: 7796, 1986.
Nieoullon A and Rispal-Padel L. Somatotopic localisation in cat motor cortex. Brain Res 105: 405422, 1976.[CrossRef][Web of Science][Medline]
Nudo RJ and Masterton RB. Descending pathways to the spinal cord. IV. Some factors related to the amount of cortex devoted to the corticospinal tract. J Comp Neurol 296: 584597, 1990.[CrossRef][Web of Science][Medline]
Orlovsky GN. The effect of different descending systems on flexor and extensor activity during locomotion. Brain Res 40: 359371, 1972.[CrossRef][Web of Science][Medline]
Pearson KG, Fouad K, and Misiaszek JE. Adaptive changes in motor activity associated with functional recovery following muscle denervation in walking cats. J Neurophysiol 82: 370381, 1999.
Perreault M-C, Rossignol S, and Drew T. Microstimulation of the medullary reticular formation during fictive locomotion. J Neurophysiol 71: 229245, 1994.
Petersen N, Christensen LOD, and Nielsen J. The effect of transcranial magnetic stimulation on the soleus H reflex during human walking. J Physiol 513: 599610, 1998.
Petersen N, Butler JE, Marchand-Pauvert V, Fisher R, Ledebt A, Pyndt HS, Hansen NL, and Nielsen JB. Suppression of EMG activity by transcranial magnetic stimulation in human subjects during walking. J Physiol 537: 651656, 2001.
Phillips CG. Movements of the Hand. Liverpool, UK: Liverpool University Press, 1986.
Porter R and Lemon R. Corticospinal Function and Voluntary Movement. Oxford: Clarendon, 1993.
Rho M-J, Lavoie S, and Drew T. Effects of red nucleus microstimulation on the locomotor pattern and timing in the intact cat: a comparison with the motor cortex. J Neurophysiol 81: 22972315, 1999.
Rossignol S. Neural control of stereotypic limb movements. In: Handbook of Physiology. Regulation and Integration of Multiple Systems, edited by Rowell LB and Sheperd JT. Bethesda, MD: Am. Physiol. Soc., 1996, sect. 12, p. 173216.
Rossignol S, Lund JP, and Drew T. The role of sensory inputs in regulating patterns of rhythmical movements in higher vertebrates: a comparison between locomotion, respiration, and mastication. In: Neural control of rhythmic movements in vertebrates, edited by Cohen AH, Rossignol S and Grillner S. New York: Wiley, 1988, p. 201283.
Sahrmann SA, Clare MH, Montgomery EB Jr, and Landau WM. Motor cortical neuronal activity patterns in monkeys performing several force tasks at the ankle. Brain Res 310: 5566, 1984.[CrossRef][Web of Science][Medline]
Schubert M, Curt A, Jensen L, and Dietz V. Corticospinal input in human gait: modulation of magnetically evoked motor responses. Exp Brain Res 115: 234246, 1997.[CrossRef][Web of Science][Medline]
Schucht P, Raineteau O, Schwab ME, and Fouad K. Anatomical correlates of locomotor recovery following dorsal and ventral lesions of the rat spinal cord. Exp Neurol 176: 143153, 2002.[CrossRef][Web of Science][Medline]
Stoney SD, Thompson WD, and Asanuma H. Excitation of pyramidal tract cells by intracortical microstimulation: effective extent of stimulating current. J Neurophysiol 31: 659669, 1968.
Vilensky JA, Gilman S, Dunn EA, and Wilson WJ. Utilization of the Denny-Brown collection: differential recovery of forelimb and hind limb stepping after extensive unilateral cerebral lesions. Behav Brain Res 82: 223233, 1997.[CrossRef][Web of Science][Medline]
Widajewicz W, Kably B, and Drew T. Motor cortical activity during voluntary gait modifications in the cat. II. Cells related to the hindlimbs. J Neurophysiol 72: 20702089, 1994.
Wise SP and Tanji J. Supplementary and precentral motor cortex: contrast in responsiveness to peripheral input in the hindlimb area of the unanesthetized monkey. J Comp Neurol 195: 433451, 1981.[CrossRef][Web of Science][Medline]
Wolpaw JR, Herchenroder PA, and Carp JS. Operant conditioning of the primate H-reflex: factors affecting the magnitude of change. Exp Brain Res 97: 3139, 1993.[Web of Science][Medline]
This article has been cited by other articles:
![]() |
J. T. Choi, E. P. G. Vining, D. S. Reisman, and A. J. Bastian Walking flexibility after hemispherectomy: split-belt treadmill adaptation and feedback control Brain, March 1, 2009; 132(3): 722 - 733. [Abstract] [Full Text] [PDF] |
||||
![]() |
D. M. Griffin, H. M. Hudson, A. Belhaj-Saif, and P. D. Cheney Stability of Output Effects from Motor Cortex to Forelimb Muscles in Primates J. Neurosci., February 11, 2009; 29(6): 1915 - 1927. [Abstract] [Full Text] [PDF] |
||||
![]() |
S. Giszter, M. R. Davies, A. Ramakrishnan, U. I. Udoekwere, and W. J. Kargo Trunk Sensorimotor Cortex Is Essential for Autonomous Weight-Supported Locomotion in Adult Rats Spinalized as P1/P2 Neonates J Neurophysiol, August 1, 2008; 100(2): 839 - 851. [Abstract] [Full Text] [PDF] |
||||
![]() |
K. Stecina and E. Jankowska Uncrossed actions of feline corticospinal tract neurones on hindlimb motoneurones evoked via ipsilaterally descending pathways J. Physiol., April 1, 2007; 580(1): 119 - 132. [Abstract] [Full Text] [PDF] |
||||
![]() |
D. A. McVea and K. G. Pearson Long-Lasting, Context-Dependent Modification of Stepping in the Cat After Repeated Stumbling-Corrective Responses J Neurophysiol, January 1, 2007; 97(1): 659 - 669. [Abstract] [Full Text] [PDF] |
||||
![]() |
N. Krouchev, J. F. Kalaska, and T. Drew Sequential Activation of Muscle Synergies During Locomotion in the Intact Cat as Revealed by Cluster Analysis and Direct Decomposition J Neurophysiol, October 1, 2006; 96(4): 1991 - 2010. [Abstract] [Full Text] [PDF] |
||||
![]() |
S. Rossignol Plasticity of connections underlying locomotor recovery after central and/or peripheral lesions in the adult mammals Phil Trans R Soc B, September 29, 2006; 361(1473): 1647 - 1671. [Abstract] [Full Text] [PDF] |
||||
![]() |
D. L. Boothe, A. H. Cohen, and T. W. Troyer Temporal Correlations in Stochastic Models of Double Bursting During Simulated Locomotion J Neurophysiol, March 1, 2006; 95(3): 1556 - 1570. [Abstract] [Full Text] [PDF] |
||||
![]() |
F. Bretzner and T. Drew Changes in Corticospinal Efficacy Contribute to the Locomotor Plasticity Observed After Unilateral Cutaneous Denervation of the Hindpaw in the Cat J Neurophysiol, October 1, 2005; 94(4): 2911 - 2927. [Abstract] [Full Text] [PDF] |
||||
![]() |
F. Bretzner and T. Drew Motor Cortical Modulation of Cutaneous Reflex Responses in the Hindlimb of the Intact Cat J Neurophysiol, July 1, 2005; 94(1): 673 - 687. [Abstract] [Full Text] [PDF] |
||||
| ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| HOME | HELP | FEEDBACK | SUBSCRIPTIONS | ARCHIVE | SEARCH | TABLE OF CONTENTS |
| Visit Other APS Journals Online |