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1Department of Sport Science and 2Clinical Neurology and Neurophysiology, University of Freiburg, Freiburg, Germany
Submitted 16 November 2005 ; accepted in final form 30 March 2006
| ABSTRACT |
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86 ms after perturbation, postural compensatory responses are cortically mediated. posture; transcranial magnetic stimulation; H reflex; transcortical reflex loop; soleus
| METHODS |
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General experimental procedure.
The subjects stood in upright position with both legs on a treadmill (Woodway). The platform was accelerated with 60 m/s2 in posterior direction. The mechanical stimulus had translatory amplitude of 15 cm with a rise time of 50 ms. This evoked several reflex peaks in the Sol EMG. Reflex latencies were calculated with respect to the onset of ankle movement, which was measured by an ankle goniometer (Penny and Giles). According to their latencies, the first three reflex peaks were termed SLR, MLR, and LLR. SLR onset was defined as the first deflection in the EMG that exceeded the level of the mean background activity during standing by three times its standard deviation. The onsets and peaks of MLR and LLR were determined on the basis of the SLR onset and previously reported latencies and durations of SLR, MLR, and LLR (18, 25, 41, 51). The time interval for the MLR peak was set from 60 to 85 ms to exclude monosynaptic reflex responses as well as transcortical loops. Petersen et al. (41) calculated the minimum conduction time for a transcortical reflex loop as the sum of the latency of the somatosensory-evoked cortical potential and the latency of the MEP. Without considering the time which is necessary for central processing, the minimum conduction time would be 79 ms. Because the LLR response in their study had a mean onset latency of 94 ms, the authors suggested that the delay required for central processing of the afferent input was
15 ms. However, as demonstrated by Toft et al. (54), the latency of the LLR response is highly dependent on the contraction level: high muscle contractions could reduce the latency by 8 ms on average. Taking this into account, the conduction time of a transcortical loop would be as short as 86 ms (10). Therefore, each reflex peak exceeding 85 ms after the onset of ankle movement was termed LLR. In subjects without distinct MLR a second peak of the LLR (LLR2) was examined. Consequently, the first three reflex peaks of each subject were investigated using TMS and peripheral nerve stimulation. Four conditions were tested: 1) stance perturbation alone to elicit SLR, MLR, and LLR; 2) stance perturbation + electrical stimulation (Sol H reflexes) to assess spinal excitability at SLR and LLR peaks; 3) stance perturbation + subthreshold TMS to assess corticospinal excitability at SLR, MLR, and LLR peaks; and 4) stance perturbation + soleus H reflex (= test reflex) + subthreshold TMS (= conditioning stimulus) to assess excitability of specific corticospinal pathways at SLR, MLR, and LLR peaks.
The peaks of the MEPs as well as the peaks of the soleus H reflexes were triggered to coincide with the peaks of SLR, MLR, or LLR (see Fig. 1). Subjects underwent
300 perturbations. In each trial, muscular activation and upright position were carefully controlled by visualizing the pressure distribution of the feet and the corresponding EMG activity of the lower limb. Subjects also received visual feedback on their standing position to ensure a constant starting position before each trial.
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H-reflex recording. For H-reflex stimulation, an electrical stimulator (Digitimer DS 7, Hertfordshire, UK) was used to generate single square-wave pulses of 500-µs duration. The H reflex of the Sol was elicited with the cathode (2-cm diameter) placed over the tibial nerve in the popliteal fossa. The anode (10 cm x 5 cm) was positioned below the patella.
H-reflex recruitment curves were only recorded at the peak of SLR and LLR because in most subjects distinct MLR peaks were absent. The electrical stimulation was timed so that the H-reflex peak coincided with the peak of the first (SLR) and the third reflex component (LLR), respectively (see Fig. 1). Recruitment curves were displayed online with specially adapted software (LabView, National Instruments). For each subject the maximal M response (Mmax) and the maximal H-reflex size (Hmax) were determined at SLR and LLR.
TMS.
TMS was applied over the left motor cortex using a Magstim 200 (Magstim, Dyfed, UK) with a 90-mm circular coil. The stimulus waveform was monophasic and had a pulse width of 200 µs. For each subject, the initial stimulation point was set
0.5 cm anterior to the vertex and over the midline. The final position for the stimulation was determined by moving the coil anterior and left from the vertex while MEP size of Sol and TA were monitored on an oscilloscope. The optimal position for eliciting MEPs in the TA and Sol with minimal intensity was marked on the scalp with a felt pen. During relaxed sitting, the lowest stimulation intensity at which TA potentials of peak-to-peak amplitudes greater than 100 µV were evoked in at least three of five trials was taken as the resting threshold. Resting threshold was determined in the TA because it was not possible to assess the motor threshold (MT) at rest in the Sol in all subjects. For Sol, an active MT was determined during perturbation at SLR. Stimulation intensity was then adjusted to be just below this active MT (0.9 MT).
During perturbation, the coil was fixed by using a special halo vest (50). The stimulus intensity was adjusted to be subthreshold for the active Sol at SLR. Coil position and MEP size were repeatedly checked throughout the experiment while stimulus strength was kept constant (0.9 MT of active MT). TMS was timed so that the peaks of the MEPs arrived in the Sol at the same time as SLR, MLR, or LLR peaks. Root mean square values from surface EMGs of the right Sol were calculated 20 ms around each reflex peak (27) (see Fig. 1). At SLR, MLR, and LLR, MEPs were compared with the background EMG. It was expected that differences in the cortical and/or spinal excitability between the three stimulation points will result in a modulation of the MEP amplitudes (41).
H reflex as a test reflex.
The size of the test H reflex was measured as the peak-to-peak amplitude and was expressed as a percentage of Mmax. It has been demonstrated earlier that the susceptibility of the H reflex to conditioning depends on the size of the control reflex (11). Therefore, it was ensured that the test reflex always had the same size of
20% of the maximal M response and that it was on the ascending portion of the H reflex recruitment curve. By this methodological approach, it was possible to adjust the control H reflexes to equivalent sizes at SLR, MLR, and LLR (see Fig. 1). Accordingly, the susceptibility of the test H reflexes for facilitation or inhibition induced by a constant conditioning stimulus should be the same for SLR, MLR, and LLR. Thus any differences in conditioned H-reflex size induced by a constant cortical stimulus should be attributable to changes in the excitability of direct or indirect corticospinal pathways.
H reflex conditioned by TMS. For the H-reflex conditioning, peripheral nerve stimulation and subthreshold TMS were combined with the postural task on the treadmill. Thereby, the effect of transcranial pulses can add up with voluntary drive and thus modulate on the Sol H reflex during perturbation. The stimulus intensity was expressed in relation to maximum stimulator output and remained constant throughout the experiment.
Depending on the time interval between TMS and H reflex, H-reflex amplitude is either facilitated or inhibited (see Fig. 2). Negative interstimulus intervals (ISI) indicate that the control H reflex is released before TMS. The latency for the TMS volley to arrive at the motoneuron is some milliseconds shorter than the arrival time of the peripheral compound potential. Accordingly, the earliest effect of the descending corticospinal volley on the H reflex can be found when the H reflex is released
24 ms before TMS (ISI 2 to 4). This earliest observable H-reflex facilitation can (at least within the first 0.51 ms after its onset) most likely be attributed to the influence of direct monosynaptic projections from the motor cortex to spinal motoneurons of TA and Sol muscle (40, 42). Approximately 2 ms after the onset of facilitation, the conditioned H reflex is depressed (see Fig. 2). This inhibition was proposed to be caused by disynaptic reciprocal inhibition through Ia inhibitory interneurons (40, 42). If TMS precedes the H-reflex stimulation, a long-lasting inhibition occurs in motor tasks like walking or dynamic voluntary plantar flexion (42). This inhibition is assumed to rely on the activation of polysynaptic corticospinal pathways (42). To detect the onset of the short-latency facilitation and the long-lasting inhibition, ISIs between 8 and +15 ms were tested in intervals of 1 ms (short-latency facilitation) and 3 ms (long-lasting inhibition) during dynamic plantar flexion on an ankle ergometer (see Fig. 2). The facilitating and inhibitory ISIs were determined for each subject and used in the perturbed stance task to assess excitability in the fastest as well as in slower, polysynaptic corticospinal pathways.
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Statistical analysis. Data were analyzed by ANOVA. Differences were evaluated by a post hoc multiple range test (Tukey). Differences between values at selected points in time were compared by a paired two-sided test (parametric). Correlation between MEP facilitation and facilitation of conditioned H reflexes was determined by using the Pearson correlation coefficient. SPSS 13.0 software was used for statistical analysis. Data are presented as group mean values ± SE, if not indicated differently.
| RESULTS |
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Reflex latencies. Reflex peak latencies of SLR, MLR, and LLR were determined with respect to the beginning of ankle movement (Table 1). The respective latencies from the initiation of ankle movement to the onset of the reflex response were also presented in Table 1. Short- and long-latency responses were seen in all subjects. Clear peaks corresponding to a MLR could be observed in five subjects.
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When comparing the effects of H-reflex facilitation with negative ISIs and the MEP-facilitation at LLR the effects of the TMS on the H reflex were almost twice as large as those on the background EMG (142 vs. 88% increase, P < 0.01; expressed in percentage of the background EMG activity). The Pearson correlation coefficient for conditioned H and MEP facilitation was r = 0.71 (P < 0.01). In contrast, there were no significant differences in the facilitation of H reflexes and MEPs at SLR and MLR [SLR: 14 vs. 11%, r = 0.34, not significant (NS); MLR: 26 vs. 26%, r = 0.71, NS]. Regarding the effects obtained with positive ISIs, there were no significant correlations at all (SLR, r = 0.26, NS; MLR, r = 0.30, NS; LLR, r = 0.44, NS).
Temporal onset of conditioning effects. Facilitatory effects were obtained for negative ISIs only. For peaks with latencies exceeding 85 ms, TMS pulses induced an increase in the H-reflex amplitude and also in EMG activity. For the H reflex, this temporal onset is illustrated in Fig. 6, where the size of the conditioned H reflex is expressed in percentage of the control H reflex on the y-axis. The latency of the respective reflex peak is shown on the x-axis. For all subjects, all single values obtained with negative ISIs are presented. In 13 of 16 subjects who showed LLRs between 85 and 100 ms, the effect of the TMS on the H reflex induced significantly more facilitation at LLR than at SLR (P < 0.05). Conditioning effects at LLRs later than 100 ms were always greater than conditioning effects at SLRs (P < 0.001).
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| DISCUSSION |
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H-reflex recruitment curves. H-reflex recruitment curves were recorded to assess the spinal excitability. The significantly greater Hmax-to-Mmax ratios at LLR compared with SLR can be caused by pre- or postsynaptic mechanisms. Because the size of the SLRs and LLRs were similar, the background EMG activity and thus the excitability of the motoneuronal pool should be comparable, too. Accordingly, the observed changes in H-reflex size between SLR and LLR were most likely not due to changes on the postsynaptic side of the H-reflex pathway. More likely, a reduction in presynaptic inhibition of Ia afferents may cause the increase of the H reflex at LLR. Hereby, an afferent volley of the same size would excite a greater number of motoneurons and consequently increase the H reflex. Short-term alterations in presynaptic inhibition have been demonstrated during gait, during changes in postural orientation (supine vs. stance), and at the onset and execution of voluntary movements (15, 22, 28, 35). Iles (23) showed that a cortically induced decrease in presynaptic inhibition of Ia afferents to Sol occurred during voluntary contraction of the Sol. This suggests that the motoneuron activation and the presynaptic inhibition of Ia afferents targeting onto this motoneuronal pool were mediated via the same cortical site. Actually, cortically induced decreases in presynaptic inhibition of Ia afferents were only seen when corticospinal and peripheral Ia volleys targeted to the same motoneurons (36). It was concluded that corticospinal activation of a motoneuron led to a reduction in presynaptic inhibition of Ia afferents projecting onto this target motoneuron (36). Accordingly, changes in the corticospinal drive would influence presynaptic inhibition of the Ia afferents and thus enhance the H-reflex excitability.
Facilitation of MEPs. Several studies indicated alterations in corticospinal excitability during voluntary tasks like walking (43, 50) and tonic isometric ankle dorsi- and plantar flexion (37, 40). Corticospinal excitability was also increased during involuntary reflex responses caused by muscular stretch of the TA (41). In the present study, Sol MEPs were highly facilitated at long-latency reflex responses compared with SLR and MLR peaks, although neither the background EMG nor the stimulus intensities varied. Because TMS was subthreshold to elicit MEPs at SLR, it can be assumed that additional corticospinal activation associated with the postural task was responsible for the increased susceptibility of Sol to TMS at LLR.
In previous studies, changes in the corticospinal excitability during balance tasks were controversially discussed. Keck et al. (26) observed MEP modulations in the TA during the time course of perturbation that were accompanied by changes in background EMG activity. Different from the present study the relation of perturbation induced background EMG and MEP remained unchanged in the analyzed time frames. The critical time period for the occurrence of transcortical reflexes (70120 ms after onset of platform movement) was not analyzed in detail. The same study reported clear differences between a voluntary foot dorsiflexion task and the postural response. The voluntary foot dorsiflexion was accompanied by a premovement facilitation of the MEP. Because no premovement facilitation of the MEP occurred during the postural task, the authors concluded that the TA compensatory response after perturbation is predominantly organized on a spinal level. Lavoie and coworkers (29) compared MEPs evoked during a "postural task" with MEPs elicited during a "volitional task." Subjects were instructed to maintain different standing postures: "standing quietly on both feet in neutral position," "lean forward," and "standing on tiptoe." MEPs of the Sol elicited under the postural task were compared with MEPs produced during voluntary tonic contraction while subjects were seated (volitional task). The main result revealed a strong correlation of background EMG and MEP size in both tasks. In view of the absence of any differences, the authors concluded that the volitional task as well as the postural task are equally under the control of the motor cortex. However, several studies indicated a close link between background EMG activity and MEP amplitude (47). Therefore, the same modulation of the MEPs during volitional and postural task in the study of Lavoie et al. (29) may be attributed to changes in the excitability of spinal or corticospinal neurons rather than to alterations in cortical excitability (31, 55). Furthermore, it has to be considered that there was no clear onset of the postural response and that the rise time of the MEP was long enough to allow several pathways to contribute to its facilitation. Accordingly it was argued that the modulation of motor responses evoked by TMS revealed only the net effect of the activation of several different corticospinal projections (42). Consequently, excitability changes assessed by TMS alone can hardly be attributed to specific structures of the CNS.
Solopova et al. (52) elicited MEPs and H reflexes in the Sol either while subjects stood on a rigid floor or while they balanced on a movable platform that was capable of producing translational-rotational movements in the sagittal direction. MEPs increased significantly when subjects were exposed to the stance instability on the movable platform, whereas the H reflex tended to decrease. From these results the authors concluded that the motor cortex underwent "substantial functional reorganization under unstable support conditions" to regulate the body position. However, the results of Solopova et al. could also be explained by changes in excitability on an interneuron and/or subcortical level (39). Thus the TMS-induced facilitation of MEPs observed in our study may also be mediated by subcortical and/or spinal structures. However, the comparison of excitability changes on the spinal and corticospinal level reveals moderate facilitations for the H-reflex amplitudes at LLR (+21 ± 5%), whereas MEP amplitudes were much more strongly increased (+78 ± 11%). To validate the assumption of such a corticospinal contribution a more reliable method is required. Conditioning of the H reflex with TMS allows the localization of the site where the change in facilitation occurred (37, 40). This method provides a high temporal resolution by which different corticospinal pathways can be separated (39).
H-reflex conditioning by TMS. It was assumed that the first possible influence affecting the H reflex by TMS is mediated through direct monosynaptic corticospinal projections with the highest conduction velocities (40). The existence of such projections has been confirmed for monkeys (45) and is assumed for humans (7). To assess the influence of direct projections, the facilitation evoked by TMS had to be measured within the initial 0.51 ms after its onset to avoid contamination by activation of indirect pathways to the motoneurons (39). Previous studies have demonstrated that changes in the excitability of corticospinal projections, responsible for the earliest facilitation of spinal motoneurons, were task related (39). In dynamic movements like walking or dynamic plantar flexion, direct corticospinal pathways can easily be activated probably owing to an increased cortical excitability (42).
Relevance of direct corticospinal projections during perturbed stance.
In the present study, the conditioned Sol H reflexes were unchanged for negative ISIs at SLR and MLR, whereas at LLR H reflexes were significantly increased with respect to the control H reflex. Because H-reflex amplitudes were always adjusted to be
20% of Mmax, alterations in motoneuronal excitability during the course of perturbation were unlikely to be the reason for the H-reflex facilitation. Therefore, the facilitation can rather be attributed to an enhanced contribution of direct monosynaptic corticospinal projections, provided that the ISI was short enough to exclude nonmonosynaptic effects. Assuming monosynaptic effects, there are two conceivable mechanisms: the facilitation may either result from a change in excitability at a cortical level or it could be influenced by a reduction in presynaptic inhibition of the terminals of the descending corticospinal fibers. The latter assumption is improbable, because several studies indicated that the descending fibers in humans and cats are free from presynaptic inhibition (4, 14, 38, 48). As a consequence, we suggest that changes in the facilitatory effect of TMS during the time course of perturbation reflect alterations in excitability of cortical motoneurons.
Relevance of slow corticospinal projections during perturbed stance. When TMS preceded the H-reflex stimulation, no effects on the H reflex could be noticed during perturbation. Because slower or polysynaptic projections are supposed to be responsible for effects at these ISIs (42), they seem to be of minor relevance for this task. Several authors observed a strong facilitation for ISIs ranging from 2.6 to almost 25 ms during stance and during tonic plantar flexion (40, 42). In contrast, long-lasting inhibitory effects were described in dynamic tasks like walking and dynamic plantar flexion for positive ISIs (onsets ranging from 3 to 16 ms) (42). The stance perturbation task in the present study seems to be closer to standing than to walking. On the other hand, it can be seen as a transition from a static to a dynamic task involving brisk and short compensatory reactions. The present results could show neither facilitation nor inhibition of slow corticospinal projections. This may indicate that the slow projections are less relevant for the perturbation task. This is further emphasized by the observation that MEP facilitation at LLR was only correlated with conditioning effects obtained with negative ISIs whereas there was no relationship with positive ISIs. Thus the MEP volley at LLR seems to be mainly influenced by excitability changes of cortical neurons responsible for direct corticospinal projections.
Temporal onset of transcortical contribution to the perturbation response. The present study analyzed the organization of the successive reflex responses in the soleus muscle with respect to their transcortical nature. For the lower leg a transcortical contribution was confirmed for the LLR of the TA muscle (9, 41, 57). Petersen et al. (41) and Christensen et al. (9) investigated the time course of spinal and corticospinal excitability changes of the reflex response after stretch of the TA muscle in a seated position and during walking, respectively (9, 41). In those studies the different reflex components M1 (corresponding to SLR), M2 (MLR), and M3 (LLR) were analyzed with regard to the onset of corticospinal facilitation. The facilitatory effects at the M1 and M2 component were negligible. Strong facilitation was reported when the MEP was superimposed with the M3 response. Thereby, enhanced corticospinal excitability was observed from 85 ms onward with a maximum at 95 ± 9 ms in the study of Petersen and coworkers and from 90 ms onward with a peak at 110 ms in Christensen et al.'s work. In both studies it was concluded that a transcortical reflex pathway may contribute to the generation of the long-latency TA stretch response. This assumption was confirmed by Van Doornik et al. (57), who applied subthreshold TMS to M2 and M3. Low stimulus intensities activated intracortical inhibitory circuits and thereby suppressed motor cortical output. The M3 response of the TA was depressed to a greater extent than M2. This observation verified that M3 of the TA muscle is at least partly transcortical in origin.
Regarding the Sol muscle, such a transcortical influence on the LLR has not been shown. Previous studies demonstrated that it is not possible to compare the organization of muscular responses in different muscles (41, 53). Thus the results obtained for the TA cannot be transferred to the Sol muscle. On the basis of the differences of corticomotoneural input to TA and Sol (7, 8), it was even suggested that transcortical pathways play no or only a minor role in the generation of the long-latency reflex in the Sol muscle (44). In contrast, Sinkjaer et al. (51) suggested a transcortically mediated LLR in the Sol. However, this cortical influence was apparent at much longer latencies (peak latency of 114 ms) than reported for the TA muscle [8590 ms; (9, 41)].
To assess the time course of excitability changes in the Sol muscle in the present study, the conditioning effects on the H reflex were illustrated relative to their latencies (Fig. 6). Neither MEPs nor conditioned H reflexes were facilitated at SLR and MLR. On the basis of the latency, it is assumed that the SLR peaks were mainly mediated monosynaptically via Ia afferents, whereas reflex peaks between 60 and 85 ms are consistent with the MLR (41). This response is mediated at least partly by a group II spinal pathway (18, 49). However, only in five subjects distinct reflex peaks could be distinguished in this time range. This supports the observation of Christensen et al. (9), who applied stretches to the dorsiflexors during walking and received small and variable responses during this time interval. The authors favored the explanation that the pathway, responsible for mediating the MLR, may be depressed in walking, leading to small and prolonged responses. The absence of distinct MLR in most subjects may alternatively be explained by a depression of the MLR response in this postural regulation task.
In the present study, Sol MEPs and conditioned H reflexes were facilitated from 85 ms onward. This indicates a transcortical mediation of these LLRs with similar latencies as observed for the TA (9, 41, 57). This is noteworthy because Sol and TA muscles were assumed to be different with regard to their corticospinal projections and, thus, in their organization of the LLR (44). The distribution of corticospinal pathways is considered to be far less pronounced in the Sol than in the TA. Some studies observed large monosynaptic peaks in peristimulus time histograms (PSTHs) of TA motor units, whereas the response peaks of soleus motor units were either absent or poorly defined (7, 8). On the basis of these results, it could be assumed that the cortical connections to the soleus muscle involve mostly polysynaptic pathways, whereas the TA receives strong monosynaptic input. However, more recent studies provided evidence for relevant monosynaptic corticospinal input to Sol motoneurons (3, 32, 56). Maertens de Noordhout et al. (32) determined the rise time of monosynaptic excitatory postsynaptic potentials in TA and Sol. The rise times were 1.13 ms for the TA and 1.14 ms for the Sol, indicating similar positioning of corticomotoneuronal synapses onto the two populations of motoneurons. Analyzing PSTHs, Bawa et al. (3) showed that although the strength of the corticomotoneural connections was higher in the TA, the occurrence of these pathways was similar in TA and Sol. Therefore, from the present data, it is concluded that these monosynaptic projections are responsible for facilitation of conditioned H-reflexes at LLR during dynamic posture control.
Nonetheless, the question remains whether the LLR peaks were triggered by somatosensory input or by vestibular information. The vestibular system provides both sensory characteristics (58) and motor projections (6), which potentially enable the vestibular system to trigger and modulate automatic postural responses in the lower extremity (for review, see Ref. 1). However, there is strong evidence that EMG responses in the Sol after fast translational perturbations are not triggered by the vestibular system. Horizontal displacement is more likely processed via spinal proprioceptive pathways (13), whereas EMG activity induced by platform rotation is mainly attributed to vestibulospinal mechanisms (2). Moreover, the strong short-latency facilitation of the H reflex by subthreshold TMS in our study argues against an involvement of vestibulospinal pathways that would be slower because of polysynaptic transmission. Additionally, several studies indicated that the vestibulospinal reflex system is predominantly involved in the compensation of slow body sway rather than in postural reactions after fast translatory displacements (5, 34). Most convincingly, this can be concluded from the comparison of patients with different deficiencies: Postural responses were delayed in subjects with sensory neuropathy, whereas no deficits could be observed in patients with vestibular loss (21, 24). Therefore, the vestibular system may affect the amplitude of the postural response but not the temporal characteristics (20).
For these reasons it seems justified to assume that in the present study, the vestibular system did not affect the latencies of the reflex peaks. Thus facilitation from 86 ms onward is probably triggered by somatosensory signals, indicating the involvement of a transcortical loop in the postural compensatory response of the Sol muscle.
Functional implications. Results of PSTHs suggested a weighted excitatory input from corticomotoneural connections to the Sol (3). In addition, reduced speed of dynamic voluntary contractions was shown to be related to lesions of the pyramidal tract in monkeys (19). Because of their high firing rate around the onset of muscular activation, corticomotoneural projections were thought to be important for the initiation and execution of voluntary dynamic contractions (16, 30). The present results indicate that the large-diameter component of the corticospinal tract may also be of functional relevance for the fast and reflexive control of posture and gait and not only for fine voluntary movements. Different from voluntary movements, the initial part of the muscular response during perturbation is mediated by spinal pathways. After 85 ms the muscular output can apparently be influenced by cortical structures via direct monosynaptic projections. Thus, as it was pointed out for the tibialis muscle in walking (9), cortical control through a transcortical reflex loop may play an important role for the Sol in postural tasks.
| GRANTS |
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| FOOTNOTES |
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The costs of publication of this article were defrayed in part by the payment of page charges. The article must therefore be hereby marked "advertisement" in accordance with 18 U.S.C. Section 1734 solely to indicate this fact.
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