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1Department of Physiological Science and 2Brain Research Institute, University of California, Los Angeles, California; and 3Pavlov Institute of Physiology, St. Petersburg, Russia
Submitted 28 March 2006; accepted in final form 27 June 2006
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ABSTRACT |
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INTRODUCTION |
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Different explanations have been proposed for the alterations observed in the spinal cord after trauma, such as
-motoneuron depression that could explain the loss of the tendon reflex during spinal shock (Weaver et al. 1963
) and
-motoneuron hyperexcitability attributed to the abolishment of supraspinal inhibitory control (Ashby et al. 1974
). It appears that the restoration of spinal cord activity after injury most likely encompasses a range of reorganization strategies involving interneuronal circuits. It has been suggested that a loss of supraspinal control of interneurons may be one reason for the observed changes in the polysynaptic flexor reflexes after injury (Hiersemenzel et al. 2000
). Flexor reflex abolishment during spinal shock may reflect the inhibition of interneuronal activity (Lundberg 1979
). Based on these types of observations, one could reason that the reorganization of spinal circuits after an injury could lead to the restoration of basic spinal cord reflex properties, including interlimb reflexes that could be related to the ability to generate locomotor activity. In fact, an important role of polysynaptic spinal cord reflexes was previously emphasized in the functional organization of the locomotor pattern in rats (Schouenborg 2002
) and cats (Janskowska et al. 1995).
Stepping in spinal animals can be improved by step training (Edgerton et al. 2001
; Fouad et al. 2000
), by epidural spinal cord stimulation (Ichiyama et al. 2005
), and/or by application of neuropharmacological agents that mimic supraspinal excitatory drive (Douglas et al. 1993
; Feraboli-Lohnherr et al. 1999
; Fong et al. 2005
) or reduce inhibition (de Leon et al. 1999
). To understand the importance of these interventions requires identification of the changes that occur in the spinal cord after the injury and the relationship between these changes and the restoration of stepping ability. In the present study, we tested the hypothesis that the restoration of spinal cord reflexes would provide a measure of the functional restoration of the spinal cord networks responsible for generating stepping after a complete spinal cord transection (ST) in adult rats.
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METHODS |
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Surgical procedures
The rats were deeply anesthetized by a combination of ketamine (100 mg/kg) and xylazine (10 mg/kg) administered intraperitoneally (ip) and maintained at a surgical level with supplemental doses of ketamine as needed. All surgeries were performed under aseptic conditions.
Headplug
A small skin incision was made at the midline of the skull. The muscles and fascia were retracted laterally, small grooves were made in the skull with a scalpel, and the skull was thoroughly dried. Two 12-pin Omnetic circular connectors (Omnetics, Minneapolis, MN) with Teflon-coated stainless steel wires (AS632, Cooner Wire, Chatsworth, CA) were securely attached to the skull with screws and dental cement as previously described (Ichiyama et al. 2005
; Roy et al. 1991
).
EMG implants
Skin and fascial incisions were made to expose the bellies of the vastus lateralis (VL), semitendinosus (St), medial gastrocnemius (MG), and tibialis anterior (TA) muscles bilaterally. Using hemostats, the EMG wires were routed subcutaneously from the back incision to the appropriate locations in the hindlimb. Bipolar intramuscular EMG electrodes were inserted into the muscles as described previously (Roy et al. 1991
). The EMG wires were coiled near each implant site to provide stress relief. Stimulation through the headplug was used to verify the proper placement of the electrodes in each muscle.
Spinal cord transection and epidural stimulation electrode implants
A middorsal skin incision was made between T6 and L4 and the paravertebral muscles were retracted as needed. A partial laminectomy was performed at the T8 level and the dura was opened longitudinally. Lidocaine was applied locally and the spinal cord was completely transected as previously described (Talmadge et al. 2002
). A partial laminectomy was then performed at the L2 vertebral level (S1 spinal cord level) and one wire was affixed to the dura at the midline for epidural stimulation using 9.0 suture as previously described (Ichiyama et al. 2005
). A small notch made in the Teflon coating (about 0.51.0 mm) of the wire used for epidural stimulation was placed toward the spinal cord and served as the stimulating electrode. The wire was coiled in the back region to provide stress relief. The Teflon coating (about 1 cm) was stripped from the distal centimeter of one wire that was inserted subcutaneously in the back region and served as a common ground.
All incision areas were irrigated liberally with warm, sterile saline and closed in layers, i.e., investing fascia and then the skin. All closed incision sites were cleaned thoroughly with saline solution. Analgesia was provided by Buprenex (0.5 to 1.0 mg/kg, administered subcutaneously, b.i.d.). The analgesics were initiated before completion of the surgery and continued for a minimum of 2 days. Baytril, a general antibiotic, was added (2 ml/125 ml H2O) into their water bottle for 5 days. The rats were allowed to fully recover from anesthesia in an incubator. The rats were housed individually and the bladders of the spinal rats were expressed manually three times per day for the first 2 wk after surgery and twice per day thereafter. The hindlimbs of the spinal rats were moved passively through a full range of motion once per day to maintain joint mobility.
Stimulation and recording procedures
Testing procedures were started 1 wk after surgery and were performed at 1, 3, 4, and 6 wk post-ST (Fig. 1). Electrophysiological assessments were performed in four control rats. Subsequently, the spinal cords of two of those rats were transected and electrophysiological assessments were made after the transection. In five other rats electrophysiological testing was performed only after ST. Therefore these analyses were performed on four rats in the control condition and on seven rats after ST. All testing was performed when the rats were fully awake, except for the terminal experiment (see following text). The EMG signals were recorded (2,000 Hz), amplified, and filtered (10 to 1,000 Hz band-pass). Stimulation was performed using a Grass S88 Stimulator (Grass Instruments) and a stimulus isolation unit (Grass SIU5, Grass Instruments). Epidural stimulation at S1 was performed by single stimuli (duration of 0.5 ms). Spinal cord reflexes were tested initially by stimulation at 0.2 Hz to determine the stimulus intensityresponse amplitude curve. Averages of seven responses were collected at stimulation intensities between 0.5 and 10 V. The average responses at 0.2 Hz were compared with those at 1, 3, and 5 Hz. Changes in the reflex responses at the different frequencies of stimulation are expressed as a percentage of the response at 0.2 Hz.
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Terminal experiment
After 6 wk of evaluation (Fig. 1), four ST rats were tested for the classical H-reflex/M-response ratio. The rats were anesthetized deeply with ketamine (100 mg/kg) and xylazine (5 mg/kg, ip). A skin incision was made on the lateral aspect of the left leg to expose the soleus muscle and a pair of wires implanted for EMG recordings as described above. A second skin incision was made on the dorsal surface of the left leg from midthigh to slightly below the popliteal fossa. The fascial sheath separating the St and biceps femoris muscles was incised longitudinally to expose the sciatic nerve and its two main branches, i.e., the tibial and peroneal nerves. Using metal pins in the lower lumbar vertebral column and at the malleoli, the left hindlimb was positioned such that partial flexion and extension were possible at the hip, knee, and ankle joints. Silver hook electrodes were placed on the sciatic nerve immediately above its subdivision into the tibial and peroneal nerves and single stimuli (pulse duration of 0.2 ms) were delivered. The cathode was oriented proximal to the anode. The average responses at stimulation frequencies of 1, 3, 5, and 10 Hz and at a pulse duration of 0.5 ms were compared with responses at 0.2 Hz. A 5-min rest interval was allowed between the testing at each stimulation frequency. During testing, the body temperature of the rat was maintained at 36 ± 1°C using a circulating water heating pad and the exposed muscles and nerves were kept moist with warm saline.
Data analysis
All recordings were collected at a range between 0.5 and 10 V. To identify the latencies and amplitudes of a given response, the responses were examined simultaneously at each voltage. The latencies were determined at the threshold voltage at which each type of response appeared. Comparisons of the responses at different voltages were used to identify the onset and amplitude of the early response (ER), middle response (MR), and late response (LR) (Gerasimenko et al. 2006). In each test session, it could be determined that these three responses were modulated differentially, were clearly voltage dependent, and the onset of each of response could be determined consistently (Fig. 2). All electrophysiological recordings from the muscles were analyzed within a 14-ms interval from the stimulus artifact and divided into three windows based on the onset latencies of the three responses, i.e., 1.5 to 6.5 ms for the ER, 6.5 to 10.5 ms for the MR, and 10.5 to 13.5 ms for the LR. The maximum peak-to-peak amplitude of each response was calculated as the average of seven responses and reported as a percentage of the control value. The peak-to-peak amplitude was on the positive slope of the response for the ER and on the negative slope for the MR and LR (Fig. 2). The absolute values of the ER were used for comparisons across time. The control value for the MR was based on the response amplitude before ST for the two rats that were evaluated before and after surgery, and the response amplitude at 1 wk postsurgery for the other seven rats. The LRmax/ERmax ratio was used to evaluate the LR.
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All data are reported as means ± SE. Statistically significant differences were determined using a one-way repeated-measures ANOVA. Values that were not normally distributed were analyzed using the nonparametric KruskalWallis rank test for overall changes and the Wilcoxon sign-rank test to determine differences between the first and last tests. The criterion level for statistical significance was set at P < 0.05 for all analyses.
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RESULTS |
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6 V). The ER appeared at the higher intensities of stimulation (>4 V), with the amplitude increasing with increased stimulus strength (Fig. 2A).
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Restoration of spinal cord reflexes after ST
To compare the three responses before and after ST, two of the seven rats that were spinalized were evaluated before and during the 6 wk after surgery. The perturbation of the ER was not tested at >6 V because of the apparent discomfort to the rat. An example of the changes in the MR from the period before ST and up to 6 wk post-ST are shown for one rat in Fig. 4A. Compared with control values, the MR was facilitated in the distal (>twofold) but not proximal muscles, 1 wk after ST, and continued to increase thereafter. The MR of the distal muscles was facilitated (three- to fourfold) at 6 wk after ST. The LR initially was depressed after surgery, but reappeared about 3 to 5 wk post-ST (Fig. 4B). Although the LR increased after its reappearance, the amplitude remained lower than control even 6 wk post-ST (3060% of pre-ST values).
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When normalized to the values at 0.2 Hz, there was a progressive decrease in the MR amplitude with increasing frequency of stimulation (Fig. 6B). At 5 Hz, the MR amplitudes for the MG, TA, VL, and St were 29, 33, 28, and 50% of the value at 0.2 Hz. The LR also showed a progressive decrease in amplitude with increased frequencies of stimulation such that the values at 3 and 5 Hz were <10% of those at 0.2 Hz for all muscles (Fig. 6C). In contrast, the ER was not significantly affected with increased rates of stimulation.
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To compare the responses produced by S1 epidural stimulation with the classical monosynaptic H-reflex and the direct M-wave, experiments were conducted on four rats 43 days post-ST (Fig. 1). The rats were anesthetized (ketamine, 100 mg/kg body weight), the sciatic nerve was stimulated with single pulses, and the motor responses were monitored in the soleus muscle (see METHODS). Sciatic nerve stimulation produced two motor responses: an M-wave with a latency of 13 ms and an H-reflex with a latency of 57 ms (Fig. 8B). The amplitude of the M-wave was unaffected by varying stimulation frequencies (Fig. 8B), whereas the amplitude of the H-reflex progressively decreased at stimulation frequencies from 0.2 to 10 Hz (Fig. 8A). H-reflex amplitudes at 3, 5, and 10 Hz were respectively 72, 50, and 30% of the amplitude at 0.2 Hz.
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All rats were tested for their ability to step with epidural stimulation once per week post-ST. Stimulation of S1 at 40 Hz failed to produce any rhythmic activity during the first 2 wk post-ST (Fig. 9A). After 3 wk, S1 stimulation evoked a few steps, although the EMG signals were erratic (Figs. 9A and 10A). The mean duration of this rhythmic activity was 8 ± 5 s. After 4 wk, the rhythmic activity between the flexors and extensors within a limb and between the left and right hindlimbs was more coordinated than that after 3 wk. In addition, the mean duration of the bouts of stepping increased to 23 ± 2 s. Stepping performance and the duration of the stepping bouts progressively increased during the next 2 wk, such that the EMG bursts reflected a well-organized stepping pattern and the mean duration of the bouts of stepping was increased to 70 ± 17 s at 42 days postlesion (Fig. 9A). During all evaluation periods, the stepping was characterized as short periods of robust rhythmic activity. It should be noted, however, that despite the robust EMG bursts, and clear swing and stance phases observed within 6 wk after surgery, a high level of weight support (8595% of body weight) was required to generate these stepping patterns.
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DISCUSSION |
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In the present study, we report the responses to similar modes of epidural stimulation before and
6 wk after a complete midthoracic ST. We evaluated the long-term perturbation of the spinal cord reflexes and determined the relationship between the restoration of the ability to step produced by epidural stimulation and the restoration of the spinal cord responses. We found new evidence that provides further insight into the nature of the responses produced by epidural spinal cord stimulation. The major changes observed after ST include the following: a gradual increase of the ER; a facilitation of the MR at all time points studied; and an initial abolishment of the polysynaptic LR during the early stages, followed by a gradual recovery beginning about 3 wk post-ST. Furthermore, the restoration of the ability to step in response to epidural stimulation about 3 wk after surgery coincided with the restoration of the LR. Perhaps the reappearance of these electrically induced polysynaptic reflexes after a spinal cord injury may signify the presence of functional locomotor networks.
The nature of the responses produced by spinal cord epidural stimulation
ER.
The characteristics of the ER are consistent with the direct activation of motor fibers or motoneurons. This response has a short latency (2.53.0 ms) and shows a maximum amplitude with supramaximal stimulation. Theoretically, the short latency of the ER includes only the neuromuscular synaptic delay and the conduction time of the stimulus to the muscle and involves no synaptic delay within the spinal cord. [Note that a synaptic delay in rats has been estimated to be about 2 to 3 ms (Meinck 1976
).] This interpretation would be consistent with the observation that direct spinal cord stimulation at the lumbar level by magnetic field produces a M-wave with a latency of about 1.5 ms (Chiba et al. 2003
). The ER was the only response that was not affected by varying the frequency of stimulation, but was increased with increasing stimulus intensity.
MR.
The MR reflects the behavior of one or more synaptic delays. The MR has a latency of about 5 to 6 ms and is inhibited by increasing either the intensity or the frequency of stimulation. In normal rats the MR was inhibited by Achilles tendon vibration and during double-pulse testing (Gerasimenko et al. 2005). The MR was facilitated at all time points after ST, similar to the behavior of the H-reflex in spinal animals (Reese et al. 2006
; Skinner et al. 1996
; Valero-Cabre et al. 2004
). The latency of the MR that we observed was similar to that of the monosynaptic response to magnetic stimulation of the lumbar enlargement in normal and spinally contused rats (Chiba et al. 2003
). In the present study, stimulation at 5 Hz after 6 wk of ST inhibited the MR by 50 to 70% of control values. Reduction in frequency-dependent depression has been described for the monosynaptic response in ST (Reese et al. 2006
; Skinner et al. 1996
) and contused rats (Lee et al. 2005
; Thompson et al. 1992
). With stimulation at 10 Hz, the H-reflex was almost completely inhibited (7% of control) in control rats, but was maintained at a significantly higher level (56% of control) in ST rats (Skinner et al. 1996
). The lower level of inhibition of the H-reflex after ST may be related to a decrease in presynaptic inhibition on Ia afferents after degeneration of descending tracts (Delwaide 1973
; Thompson et al. 1992
).
To determine whether the main responses produced by S1 stimulation were related to the M-wave and H-reflex, we performed acute terminal experiments under ketamine anesthesia. Single-pulse stimulation of the sciatic nerve produced two responses in the soleus muscle. The latencies of the first (direct M-wave) and second (monosynaptic H-reflex) were about 2 to 3 and 5 to 7 ms, respectively, and correspond to the latencies for the M-wave and H-reflex in the classical testing of the H-reflex in the rat soleus muscle (Chen and Wolpaw 1995
; Wolpaw and Chen 2001
). The MR was inhibited by increasing the stimulus frequency from 1 to 5 Hz at 6 wk post-ST in response to epidural stimulation with the same rats awake or under ketamine anesthesia. The level of inhibition of the H-reflex in response to sciatic nerve stimulation under ketamine anesthesia was similar to the inhibition of the MR noted above. The similar percentage of inhibition for the MR with S1 stimulation and for the H-reflex with sciatic nerve stimulation suggests that there are some common components of these two responses.
LR.
The LR has the longest latency of the three responses (911 ms) and represents a polysynaptic event. The latency difference between the ER and LR was about 6.5 to 8 ms and may correspond to as many as three synaptic delays. With increased stimulus intensity the amplitude of the LR was initially increased and then was completely inhibited at high stimulus intensities. Similar to the MR, the LR was inhibited by Achilles tendon vibration and during double-pulse testing (Gerasimenko et al. 2005). The LR was completely inhibited by stimulation at 3 Hz, whereas the MR was only partially inhibited by stimulation at 5 Hz. These observations may reflect the inhibition of different neural circuits as suggested by Schindler-Ivens and Shields (2000)
.
The LR was abolished in most of the muscles when the animals were tested under ketamine anesthesia. The ability of ketamine, a noncompetitive N-methyl-D-aspartate (NMDA) antagonist, to inhibit NMDA receptors by NMDA channel block and to depress the polysynaptic reflexes is well known. In adult rats, ketamine inhibits NMDA receptors, but has a sparing effect on kainate and
-amino-3-hydroxy-5-methyl-4-isoxazolepropionic acid receptors (Farkas and Ono 1995
). A significant effect of ketamine on NMDA receptors of dorsal horn neurons at a concentration of 5 mg/kg (administered intravenously) was previously reported (Chizh et al. 1997
) and would be expected to have been present at the anesthetic dosages used in the present study. Inhibition of the LR by ketamine suggests a polysynaptic NMDA-dependent origin of the LR. An effect of ketamine on monosynaptic reflexes, however, should also be noted (Farkas and Ono 1995
).
The question is how does the polysynaptic response as induced epidurally relate to the more classically defined reflexes, such as the flexor and crossed extensor reflexes. The flexor reflex pathways contain two to three synapses and are mediated by ipsilateral and contralateral cutaneous afferents from pain and temperature endings (C), touch, temperature, and pain endings (A
), pacinian corpuscles (vibration), touch receptors (A
), and joint receptors (A
). The last two axonal types, i.e., the A
and A
, are thick fibers with diameters between 12 and 20 and 5 and 12 µm, respectively, have a low threshold of activation, and may have responded to the low intensities of stimulation in the present study. Group II and III afferents from the muscle spindles and pressurepain endings also may be considered as afferents that could have mediated the LR as discussed previously (Gerasimenko et al. 2005). Another possible explanation for the LR is a direct activation of interneurons, but because of the high thresholds required to activate these neurons, this seems unlikely. Regardless, it is clear that the LR produced by spinal cord epidural stimulation has a polysynaptic origin. At this time, however, the identification of the polysynaptic chains and their role in spinal cord synaptic organization are unclear.
Changes in the spinal cord responses after ST
The three electrically induced responses were affected differentially post-ST. We found continuously increasing amplitudes of the ER, facilitation of the MR, and an initial disappearance and then a gradual reappearance of the LR beginning at about 3 wk post-ST.
ER.
Inhibition of a direct response after spinal cord injury was previously described in paraplegic humans (Hiersemenzel et al. 2000
) and in spinal rats (Valero-Cabre et al. 2004
). These adaptations can be explained by reversible changes in axonal properties after injury (Agrawal and Fehlings 1996
; LoPachin et al. 1999
) that correspond to inhibition of the M-wave in paraplegic (but not in quadriplegic) patients (Hiersemenzel et al. 2000
). As a result of the high-intensity stimulation required to evoke a direct motor response, we could not evaluate the ER in normal awake rats. However, based on the previous observations noted above, we interpret the increasing ER post-ST as a restoration of the direct response.
MR.
In humans and nonhuman primates there is an inhibition of the H-reflex for a few days after spinal cord injury (Hiersemenzel et al. 2000
). In other species this period has been reported to be shorter, e.g., the inhibition of the H-reflex was about 6 days after spinal cord contusion in rats (Thompson et al. 1993
). In addition, facilitation of the H-reflex within 1 h after a complete ST (T9) in rats without a period of inhibition was reported (Valero-Cabre et al. 2004
). This variability, however, may be related to differences in the type of injury and experimental designs. In our study of complete midthoracic adult spinal rats, the MR was facilitated 1 wk post-ST, being up to two- to threefold higher than in control rats. Facilitation of the monosynaptic reflexes (corresponding to the MR) after a spinal cord injury was previously reported in spinal rats (Chen et al. 2001
; Malmsten 1983
), cats (Hultborn and Malmsten 1983a
), and humans (Hiersemenzel et al. 2000
; Leis et al. 1996
). H-reflex facilitation after a spinal cord injury could be attributed to morpho-functional changes in motoneurons and/or changes at the premotoneuron level arising from disinhibition. The first type of change could include
-motoneuron hyperexcitability arising from changes in the intrinsic properties of the motoneurons (Taylor et al. 1984
), changes in motoneuron morphology, and/or synaptic growth. The second type of change might be attributable to a decrease in presynaptic inhibition (Calancie et al. 1993
; Faist et al. 1999
) and/or a decrease in postactivation depression of transmission from Ia fibers (Nelson et al. 1979
). In rats, the peak facilitation of the H-reflex was observed at 45 days post-ST, after which the amplitude of the H-reflex decreased (Valero-Cabre et al. 2004
). There have been no long-term investigations, however, to determine whether there is an eventual complete restoration of the H-reflex after a spinal cord injury.
LR.
After ST, the LR was abolished for 2 wk. At the beginning of the third week the LR reappeared as a low-amplitude, unstable response and showed a tendency to be restored during the following evaluation periods. The timing of the restoration of the LR in our studies corresponds with the reappearance of polysynaptic reflexes in ST rats. For example, flexor reflexes were inhibited immediately after ST and then restored 2 to 3 wk post-ST (Valero-Cabre et al. 2004
). These authors described different patterns of restoration of the polysynaptic reflexes on the ipsilateral and contralateral sides of the lesion. All ipsilateral and crossed reflex components were abolished immediately after injury except for the ipsilateral reflex components mediated by the thick sensory A
and A
/A
fibers. Over the next 6 wk post-ST, all polysynaptic reflexes mediated ipsilaterally by all axonal types tested increased toward normal. However, the ipsilateral A
- and A
/A
-mediated reflexes increased up to threefold greater than normal. Because we used direct stimulation at the midline of the spinal cord, we most likely activated both ipsilateral and crossed polysynaptic reflex pathways.
Spinal cord reorganization after injury and restoration of stepping ability
After a spinal cord injury in humans, the restoration of polysynaptic flexor reflexes has been reported to coincide with the appearance of the "spastic" phase of recovery and appears to be related to the recovery of
-motoneuron excitability and/or adaptation of interneuronal activity. The interneuronal hypothesis is supported by the fact that there is a lower threshold for flexor reflex activation in injured than in noninjured individuals (Dietz and Muller 2004
; Hiersemenzel 2000). The recovery of complex spinal cord reflexes such as the flexor reflex after an injury may provide a functional basis for the restoration of spinal cord circuits responsible for locomotion. In fact, some of the spinal cord networks that control stepping seem to share the same interneurons that are involved in flexion reflexes, i.e., the spinal circuits involved with the flexor reflex have been suggested to be part of the spinal networks responsible for locomotion (Dietz 2002
; Parise et al. 1997
). Thus several findings support the view that the same spinal pathways are involved in generating the flexor reflex and the swing phase of stepping (Bussel et al. 1989
; Jankowska et al. 1967
; Lundberg 1979
; Nicol et al. 1995
). In the present study, the reappearance of the LR post-ST may reflect the restoration of polysynaptic networks responsible for flexor and cross-extension reflexes that are involved in locomotor circuits. Consistent with this supposition are the results of a recent long-term study reporting the restoration of flexor reflexes in ST rats, most likely reflecting some reorganization of the same spinal pathways (Valero-Cabre et al. 2004
). From this perspective, the stepping patterns in response to epidural stimulation presumably can be attributable to the stimulation of the same afferents as the evoked responses studied in the present paper.
In conclusion, in the present study, the electrophysiological evaluation of the functional chronic state of the spinal cord for 6 wk after a complete, midthoracic ST and of the restoration of epidurally induced locomotor activity was performed. The results show that the restoration of stepping when facilitated by epidural stimulation of the spinal cord coincided with the restoration of late polysynaptic responses. Therefore the electrophysiological assessment of spinal cord reflexes induced by epidural stimulation to facilitate stepping appears to be a useful tool for investigating spinal cord reorganization after a spinal cord injury.
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GRANTS |
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ACKNOWLEDGMENTS |
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FOOTNOTES |
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Address for reprint requests and other correspondence: V. R. Edgerton, Department of Physiological Science, University of California, Los Angeles, 621 Charles E. Young Drive, Los Angeles, CA 90095-1527 (E-mail: vre{at}ucla.edu)
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