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1Department of Physical Therapy, University of Delaware, Newark, Delaware; 2Kennedy Krieger Institute, Baltimore, Maryland; and 3Department of Neuroscience, 4Department of Neurology, and 5Department of Physical Medicine and Rehabilitation, Johns Hopkins University School of Medicine, Baltimore, Maryland
Submitted 24 January 2005; accepted in final form 8 June 2005
| ABSTRACT |
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| INTRODUCTION |
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The use of a split-belt treadmill, where the belt beneath each foot is independently controlled, allows for the systematic manipulation and study of interlimb coordination. Decerebrate or spinal cats can walk on a split-belt treadmill, where one hindlimb is made to go faster than the others, by prolonging stance and shortening swing on the "slow" hindlimb, and vice versa on the "fast" hindlimb (Forssberg et al. 1980
; Kulagin and Shik 1970
). This suggests that either sensory or motor information from one limb affects the control of the opposite limb's movement. A one-to-one stepping pattern is predominantly seen for lower speed ratios (e.g., 2:1), although cats sometimes switch strategies at high ratios (e.g., 3:16:1), taking two or three steps on the fast limb for each step on the slow limb. Similar findings have been reported during supported stepping in human infants (Thelen et al. 1987
; Yang et al. 2004
). Human adults can also rapidly adjust stance and swing times during split-belt walking (Dietz et al. 1994
) but have not been reported to produce multiple stepping on the fast leg at higher speed ratios. Collectively, these results show that both quadrupeds and bipeds can make basic adjustments in stance and swing times to maintain an alternating pattern with legs moving at different speeds. Spinal circuits are capable of generating this pattern in cats, and the one-to-one relationship between limbs can be temporarily changed under extreme situations in cats and infants.
Little is known about locomotor adaptation and storage of new patterns (as identified by the presence of aftereffects) in humans. Prokop et al. (1995)
have shown that a very short (45 strides) bout of practice on a split-belt treadmill allows subjects to make more rapid adjustments to each leg's stance and swing times on subsequent exposures to split-belt walking. This practice effect did not transfer when the slow and fast limbs were switched, suggesting a limb specific mechanism (Prokop et al. 1995
). Practice on a split-belt treadmill also alters the perception of leg speed during walking (Jensen et al. 1998
). Other types of locomotor adaptations are known to occur, although they do not involve alterations in interlimb coordination. Treadmill running can cause an aftereffect of inadvertently jogging forward when asked to jog in place (eyes closed) on solid ground (Anstis 1995
). Stepping in place on a rotating treadmill can cause curved trajectories on solid ground; this podokinetic after-rotation (PKAR) is thought to be caused by a recalibration of the proprioceptive relationship between the trunk and stance limb yaw rotations (Earhart et al. 2002
; Gordon et al. 1995
; Weber et al. 1998
).
In this study, we investigated the adaptability of the locomotor pattern in adults using a single 10-min session of practice on a split-belt treadmill. We hypothesized that the pattern within each individual limb (i.e., intralimb parameters) would change rapidly to accommodate the treadmill but would not necessarily adapt or show aftereffects. Specifically, the leg on the faster belt was expected to produce a kinematic pattern identical to fast symmetric walking and vice versa for the leg on the slower belt. In contrast, we expected that the pattern between legs (i.e., interlimb parameters) would adapt and subsequently show aftereffects. Interlimb coordination might adapt to optimize the relative movement between legs, given the novel task mechanics associated with coupling a fast pattern on one leg with a slow pattern on the other. We also asked whether adaptation is influenced by the difference in training speeds between the two legs. We expected the largest adaptation and aftereffect when the speed ratio between the two legs is greatest. Preliminary results have been presented in abstract form (Reisman et al. 2004
).
| METHODS |
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OPTOTRAK (Northern Digital, Waterloo, Canada) sensors were used to record three-dimensional position data from both sides of the body. Infrared emitting diodes (IREDs) were placed bilaterally (Fig. 1) on the foot (5th metatarsal head), ankle (lateral malleolus), knee (lateral joint space), hip (greater trochanter), pelvis (iliac crest), and shoulder (acromion process). Foot contacts were determined using four contact switches per foot: two placed on the forefoot and two on the heel. Voltages reflecting treadmill belt speeds were recorded directly from treadmill motor output. Marker position and analog data (foot switches and treadmill speed) were synchronized and sampled simultaneously using OPTOTRAK software at 100 and 1,000 Hz, respectively.
Data analysis
Three-dimensional marker position data were low-pass filtered at 6 Hz. Custom software written in MATLAB (Mathworks) was used for all analyses. Stride time was determined from the foot switches and is defined as the period from one foot contact to the next on the same limb. A stride contains both stance (foot contact to lift-off) and swing (lift-off to next foot contact) phases. We refer to the limb on the slow belt in the split-belt period as the "slow limb" and the limb on the fast belt as the "fast limb." Joint angles were calculated such that flexion was positive and extension was negative (Fig. 1). Limb orientation angle (Bosco and Poppele 2002
) was calculated as the angle between the vertical and the vector from the hip marker to the fifth metatarsal marker.
We calculated intralimb (i.e., those measured from a single leg) and interlimb (i.e., those where the measurement depended on both legs) kinematic variables. Intralimb parameters were as follows. 1) Stride lengtha modified version of stride length for the treadmill was calculated as the distance traveled by the ankle marker in the anterior-posterior direction from initial contact to lift-off of one limb; a stride length ratio (fast/slow) was also calculated to assess symmetry. 2) Percent stance timethe duration of stance phase expressed as a percentage of the stride time; a stance time ratio (fast/slow) was also calculated to assess symmetry. 3) Relative timing of peak joint anglesthe latency between peak angles occurring for all combinations of hip, knee, and ankle joint pairs. We found peak hip extension, knee flexion, and ankle extension (plantar-flexion) within a limb and calculated the relative timing between peaks. These peaks were chosen because they were the most salient peaks within a stride time (foot contact to foot contact). All times are expressed as a percent of stride time.
Interlimb parameters were as follows. 1) Step lengtha modified version of step length for the treadmill was calculated as the anterior-posterior distance between the ankle marker of each leg at heel strike of the leading leg; fast step length refers to the step length measured at fast leg heel strike and slow step length refers to step length measured at slow leg heel-strike. 2) Percent double limb support timethe time when both feet are in contact with the floor expressed as a percentage of the stride time for each leg. There are two periods of double support per stride cycle and we define slow double support as occurring at the end of the slow limb's stance (i.e., the time from fast leg foot contact to slow leg lift-off), and fast double support at the end of the fast limb's stance (i.e., the time from slow leg foot contact to fast leg lift-off). A double support ratio (fast/slow) was also calculated to assess symmetry. 3) Limb orientation at weight transferthe angle of the leading limb at opposite limb lift-off. 4) Limb angle phasethe point in the slow limb cycle (i.e., time from peak limb extension to the subsequent peak limb extension) at which the fast limb reaches peak extension. We chose to calculate limb angle phasing because the limb angle represents the entire orientation of the limb, which is particularly important for foot placement and weight transfer in bipedal gait. We used a dual referent analysis method for phase calculations (Berkowitz and Stein 1994
). This is superior to single referent techniques in situations where the duty cycle of the referent (i.e., slow) leg changes (e.g., peak flexion time varies within the extension-flexion cycle). It ensures that changes in the referent duty cycle will not produce shifts in phase values obtained (Berkowitz and Stein 1994
); this is of issue if the percent stance and swing time change over experimental periods (thus varying the relative duration of flexor and extensor phases). We defined a phase of 0.0 and 1.0 for subsequent peaks in slow limb extension and 0.5 for peak slow limb flexion (see Fig. 7A). The following equations were used to calculate the phase of fast limb extension with respect to the slow limb (Berkowitz and Stein 1994
)
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63% of the final adaptation. Thus our measure of the rate is an estimation of the number of strides for a subject to proceed approximately two-thirds of the way through the adaptation process.
Statistical analyses were completed using the averages of the first five strides baseline, the first and last five strides of the adaptation period (early and late adaptation, respectively), and the first and last five strides of the postadaptation period (early and late postadaptation, respectively). We will refer to the baseline period when both belts are tied at the slow speed as both slow and the period when the belts are tied at the fast speed as both fast. For all kinematic variables except phasing, we used a repeated measures ANOVA with condition (2:1, 3:1, or 4:1) as the between-subjects variable and testing period (both slow baseline, early adaptation, late adaptation, early post-adaptation, and late postadaptation) as the within-subjects variable. When the ANOVA yielded a significant effect, post hoc analyses were completed using a Tukey HSD test. For phasing, we calculated the mean vector and the angular deviation (circular equivalent of the SD) and used the Watson's U2 test (Batschelet 1981
) to test for significant differences between testing periods. Statistica (StatSoft, Tulsa, OK) and MATLAB were used for all statistical analyses.
| RESULTS |
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Subjects maintained a one-to-one stepping pattern (i.e., alternating steps with 2 double support periods and no airborne periods) during all experiments, regardless of speed ratio. Only one subject took one double step in mid-air at the very beginning of the split-belt period in the 4:1 speed condition. To maintain one-to-one stepping, the stride times (i.e., stance + swing) of each leg were equivalent for all phases of the experiment (P = 0.931). Stride times of both legs shortened during the both fast period and during split-belt walking (P < 0.05 for both).
Although stride times were equivalent for all periods, the percent time in stance, swing, and double support changed in different ways. Figure 2 shows a Hildebrand style time plot, with time on the x-axis and stride number increasing vertically along the y-axis. At baseline, stance, swing, and double support times were equal for both legs. Early in adaptation the stride times were shorter overall, and the fast leg had a shorter stance time, longer swing time, and a shorter double limb support time compared with the slow leg. In late adaptation, double limb support times became equal, but stance and swing times did not change appreciably. In early postadaptation, there was a substantial aftereffect in double limb support times, opposite of that seen in early adaptation. However, stance and swing times switched back to baseline values rapidly. In the late postadaptation period, the temporal pattern returned to baseline values, with equal stance, swing, and double limb support times for both legs.
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0.05), with a post hoc difference between the both slow and early adaptation periods (both P
0.05). There was a small change from early to late adaptation that did not reach statistical significance, but no difference between the both slow baseline and early postadaptation periods (i.e., no aftereffect). We concluded that intralimb timing was only slightly changed by split-belt practice but showed no evidence of an aftereffect. The aftereffects are very important because they show that the subject was actually learning and storing a new pattern versus just changing the pattern in response to the treadmill.
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0.66, with fast peak extension after slow peak flexion. During early adaptation, limb phasing values were reduced (i.e., closer to being exactly out of phase). By late adaptation, limb phasing increased, but not fully to the baseline level, and in early postadaptation, the opposite shift in phasing occurred. Circular statistical analysis of group data revealed significant differences between the both slow and early adaptation periods (P < 0.05, Fig. 7C) and between the both slow and early postadaptation periods (P < 0.05, Fig. 7C). Another important feature of walking is the orientation of the limbs at different points in the cycle. We measured limb orientation at weight transfer (i.e., when the opposite leg just lifts off) because this is a critical point in the cycle for stability. If the limb is too flexed at weight transfer, the body may be too far behind the limb, and if it is too extended, the body may move too far forward of the limb; either can lead to instability. We found adaptive alterations in each limb's position at weight transfer during split-belt walking. Figure 8A shows a stick figure of the limb orientations at weight transfer from a subject walking in the 4:1 condition. During the both slow period, the slow and fast limbs accept weight in a similar position (Fig. 8A, cf. top and bottom). In early adaptation, the slow limb accepts weight in slightly more flexion (Fig. 8A, top), and the fast limb accepts weight in much more extension (Fig. 8A, bottom). By late adaptation, both limbs accept weight in a similar position. There is a robust aftereffect postadaptation, with slow and fast limbs showing the opposite effect as seen in early adaptation. Group data showing the difference between the two limbs' position at weight transfer is shown in Fig. 8B. There was a significant main effect for period (P < 0.001, Fig. 8B), and post hoc testing revealed that the slow limb was significantly more flexed than the fast limb at weight transfer in early adaptation compared with the both slow period (P < 0.001). This difference diminished during adaptation (P < 0.001) and reversed in early postadaptation such the fast limb was significantly more flexed than the slow limb at weight transfer (P < 0.001, Fig. 8B). There was no effect of the speed ratio on this measure.
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| DISCUSSION |
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Previous studies of cats, human infants, and adults have focused on basic temporal and spatial features of split-belt walking, without addressing inter- versus intralimb differences or adaptation and storage of a new pattern (Dietz et al. 1994
; Forssberg et al. 1980
; Jensen et al. 1998
; Kulagin and Shik 1970
; Prokop et al. 1995
; Thelen et al. 1987
; Yang et al. 2004
). All studies have shown speed appropriate changes in intralimb parameters such as stance and swing times on the split-belt treadmill, similar to what we report here. Adult humans have also been shown to require several strides to change stance (and swing) times when they first encounter the split-belt treadmill (Prokop et al. 1995
). In contrast, we found that these parameters changed almost immediately, and further showed no aftereffects in them after split-belt training. One difference between the studies is that we stopped and started the treadmill between each period (i.e., belts tied vs. split), whereas they switched from tied to split-belt walking midstream; this midstream transition may have required a few strides to switch to the split-belt pattern. Only one study in cats has looked for the presence or absence of motor aftereffects after split-belt walking and found adaptive changes in double support times (Ito et al. 1998
). Here we show for the first time that there are differences between the adaptability of intra and interlimb coordination during human bipedal gait.
Similar adaptation studies have been done for arm movements, although fewer exist for walking. Adaptation occurs for changes in load during catching (Lang and Bastian 1999
), altered dynamics during reaching (Lackner and Dizio 1994
; Shadmehr and Mussa-Ivaldi 1994
), and altered gaze direction from prisms during reaching and walking (Martin et al. 1996b
; Morton and Bastian 2004b
). These processes are similar to the split-belt adaptation in that they occur within a single session of practice and they result in aftereffects when the perturbation is removed. They are different from the split-belt adaptation in that adapted parameters are intralimb and are related to another perturbation like altered dynamics or gaze direction. Of interest is that lesion studies have shown that all of these adaptations seem to require the cerebellum (Lang and Bastian 1999
; Martin et al. 1996a
; Maschke et al. 2004
; Smith and Shadmehr 2004
), with the exception of Coriolis perturbations (Lackner and Dizio 1994
), for which patient performance has not been tested. Another type of locomotor adaptation has been reported when walking on a rotating treadmill (Gordon et al. 1995
; Weber et al. 1998
). Similar to our results, this adaptation occurs within a short time (15 min) and results in a robust aftereffect. One important difference is that podokinetic adaptation is thought to alter the relationship between the trunk and stance limb yaw rotations with no change in interlimb coordination; split-belt adaptation alters interlimb relationships. It may be that very different systems are involved in these processes: one that alters body orientation relative to the feet versus one that alters phase between the legs.
Adaptations such as these require error information to drive the changes that take place. As error is reduced, the adaptation is complete. We expect that the error signal for split-belt should reflect some difference between the limbs. Errors in limb phasing or relative orientation might drives this process. We think it is less likely that kinematic parameters at single joints drive the process because they change very little during adaptation and show minimal aftereffects, which are needed to drive the readaptation process.
Pattern generation and split-belt walking
There are three results from this study that speak to the organization of putative pattern-generating circuits in adult humans. First, we see relatively invariant patterns of intralimb joint motion timing, regardless of whether the two legs walk at the same or different speeds. This result is present for all joint pairs within a limb, but strongest for timing between hip and knee, probably because of greater biomechanical coupling, but possibly because of greater neural coupling, of these two joints. This shows that there are circuits that can drive intralimb kinematics in an invariant way, independent of changes in interlimb coordination. One interpretation is that there are separate pattern-generating circuits for each of the two legs, although these can be coupled somewhat flexibly. Consistent with this, other animals seem to show preservation of basic intralimb patterns (e.g., rostral and pocket scratch in turtle), even when they are performed as a mixed-form interlimb pattern, where one limb makes a rostral scratch and the other a pocket scratch (Field and Stein 1997
).
Second, our subjects maintain a 1:1 interlimb stepping pattern on the treadmill, regardless if the speeds were 2:1, 3:1, or 4:1. Only one subject took one 2:1 "air" step on the first step in the 4:1 speed condition. This finding is different from that for split-belt treadmill walking in spinal walking cats or supported infant stepping; both spontaneously produce multiple stepping on one limb relative to the other at the speed ratios that we tested (Forssberg et al. 1980
; Thelen et al. 1987
; Yang et al. 2004
). Other animals, such as spinal turtle, also produce 2:1 interlimb coordination patterns during scratching and swimming movements (Field and Stein 1997
). It is possible that our results are different because of a mechanical need to have a 1:1 ratio for better stability and balance during adult bipedal walking. It should be noted, however, that our subjects did hold onto a safety bar that was more than sufficient to reduce balance demands (Jeka and Lackner 1994
), so they theoretically were not required to produce this pattern to maintain upright stability. We have also found (unpublished observations) that subjects can make themselves adopt a 2:1 stepping pattern, although they comment that this requires conscious effort and "doesn't feel as much like walking, more like trying to learn a dance step." Therefore we suspect that there is a strong bias toward 1:1 interlimb neural coupling between circuits that control the two legs during walking in adults.
Third, our main finding is that interlimb motor parameters gradually adapt during split-belt walking. Changes in interlimb parameters paralleled the behavioral observation of a limp in early adaptation, a reduced limp in late adaptation, and the opposite limp postadaptation (after training). This adaptation took longer for larger speed ratios and is in line with the subjective experience of the participants, who all felt like their gait became more natural during adaptation and felt the opposite asymmetry postadaptation. Thus in the adult human nervous system, interlimb coordination can be independently controlled and modified without necessarily altering many aspects of intralimb coordination. This also suggests that neural elements that control interlimb coordination are dissociable from those that control intralimb coordination during human bipedal walking.
Why adapt interlimb coordination?
Adaptation of the interlimb parameters largely restored symmetry to the gait cycle. There are several reasons why this might occur. First, symmetry has inherent advantages for stability. Even though subjects held onto the safety bar, which greatly improves balance (Jeka and Lackner 1994
), they still may optimize gait parameters to reduce the likelihood of becoming unstable. For example, equalizing double support during adaptation allows for comparable transition times between stance and swing on each leg. Adapting the angle of the leading limb at weight transfer is critical; this is the time when the body's center of mass is propelled forward toward the forefoot (Perry 1992
). If the weight-accepting limb is too extended, the body's center of mass may be propelled too far forward of the foot and if it is too flexed, the center of mass may lie too far behind the foot; both situations reduce stability and could lead to falling. Second, symmetric walking patterns are probably more efficient than asymmetric patterns. For example, it is known that in amputees and persons with hemiparesis, the greater the gait asymmetry, the slower the walking speed (Brandstater et al. 1983
; Donker and Beek 2002
; Roth et al. 1997
; Titianova et al. 2003
), and slower walking is associated with greater energy costs (Zamparo et al. 1995
). Third, neural interlimb coupling mechanisms might be biased toward producing symmetric patterns for walking. It is known that there are phase-dependent responses in one leg based on the activity of the contralateral leg during other reciprocal leg movements like cycling (Ting et al. 2000
). In this task, it is possible that similar phase-dependent influences of one leg on the other lead to the changes observed in the interlimb parameters. This may be a direct consequence of the organization of circuits that generate interlimb patterns.
Note that the interlimb parameters that adapt are not necessarily independent, but can be simultaneously altered by phase shifting one limb's movement relative to the other. In our experiments, limb angle phasing changed in early adaptation because of altered stance and swing times. Specifically, there were earlier peaks in the limb extension angle on the fast leg because of a shorter stance time and later peaks in the limb extension angle on the slow leg because of a longer stance time. Limb angle phasing adapted slowly and showed aftereffects in the postadaptation phase. Theoretically, even small shifts in phase can produce robust changes in interlimb parameters that are comparable with what we see in the early split-belt condition of our experiments (i.e., early adaptation). This is shown in Fig. 10, which shows the right and left limb angles for both legs moving at the same speed (0.5 m/s, Fig. 10A); the phase is 0.63, with symmetric double support times and limb angles at weight transfer. Figure 10B shows the same data after we manually introduced a phase shift similar to what we saw early in 3:1 walking (double referent shift of 0.06 to produce a phase of 0.57). This manipulation makes the double support times and limb angles at weight acceptance asymmetric, and the pattern is similar to early split-belt walking. In addition, this example also shows that asymmetric gait patterns may exist, even when stance/swing times are symmetric.
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We predict that the nervous system should have a means to estimate and adjust phase between the limbs and detect errors in this relationship. We expect that sensory information or motor command information from both of the limbs is necessary for this process. Sensory information about hip angle and loading from the ipsilateral limb affects transitions from stance to swing (Duysens and Pearson 1980
; Grillner and Rossignol 1978
; Pang and Yang 2000
). Afferent feedback from a given limb also strongly affects the contralateral limb in spinal cat (Giuliani and Smith 1987
), human pedaling movements (Ting et al. 1998
, 2000
), and walking (Verschueren et al. 2002
). The motor state of one limb, even under isometric conditions, can also alter contralateral limb activity during cyclic movements like human pedaling (Ting et al. 2000
) .
It is possible that spinal networks could be used to adaptively adjust phasing between the limbs. In spinal turtle, removal of hemisegments of the spinal cord changes bilateral patterns that occur during fictive scratching (Stein et al. 1995
), with deletions of contralateral extensor activity. Thus interlimb flexionextension phasing is disrupted by a lesion of only one side of the spinal cord. Stein et al. (1995)
suggested that the neural elements that coordinate interlimb phase are embedded in pattern generators in a bilateral shared core of the spinal cord.
Another possibility is that supraspinal centers are involved. More specifically, there is good evidence to suggest that the cerebellum could be important for this adaptation. It receives information about the state of spinal pattern generating circuits (through ventral spinocerebellar pathways) and the sensory state of the limbs bilaterally (through dorsal spinocerebellar pathways), allowing it to compare intended leg movements with actual leg motions and elicit corrections. Dorsal spinocerebellar neurons also carry information about limb angles (Bosco and Poppele 2002
) and respond to ipsi- or contralateral stepping (Poppele et al. 2003
). A large percentage of dorsal spinocerebellar neurons also showed bipedal interactions, modulating with movement of both limbs (Poppele et al. 2003
); these cells could theoretically carry information about interlimb phasing, although this was not specifically tested. Brain stem neurons of the vestibulospinal and reticulospinal pathways of cats are also active with extensor and flexor phases of locomotion, and the modulation of these neurons with the locomotor cycle is disrupted with cerebellar damage (Orlovsky 1972a
,b
). It is also known that decerebrate cats that can normally adapt double support times to the split-belt treadmill cannot do so after disruption of activity in the cerebellar vermis through NO deprivation (Yanagihara and Kondo 1996
). Finally, our preliminary studies in humans with cerebellar damage show that they do not adapt interlimb parameters during split-belt walking and show little or no aftereffects from practice (Morton and Bastian 2004a
).
We have not yet tested whether split-belt treadmill walking generalizes to other contexts. For example, it is important to know if this adaptation induces aftereffects in any parameters during overground walking, where stance speed is no longer constrained by the treadmill. Aftereffects in intralimb parameters like stride length might be expressed overground, causing subjects to walk in a curved trajectory, which is not possible when walking on a treadmill. Overground aftereffects after treadmill training have been observed in other types of locomotor tasks, such as circular treadmill walking (Gordon et al. 1995
; Weber et al. 1998
) and treadmill running (Anstis 1995
), although neither paradigm tests reorganization of motor patterns between the legs. The extent of generalization to other forms of locomotion, such as backward walking or running, is also important because it indicates whether the adaptation is caused by alterations of neural circuits specific for forward walking or shared circuits used for generation of multiple locomotor patterns.
In conclusion, the results of this study reveal, for the first time, that after walking on a split-belt treadmill, healthy human adults show a new motor pattern of locomotor interlimb coordination when the belts are returned to the same speed. This indicates that during split-belt walking, subjects adapted and stored new patterns of interlimb coordination. This adaptation was observed in the locomotor parameters whose values are calculated from the time and position of both limbs during the gait cycle. Adaptation of these parameters seems to restore some symmetry to the gait cycle that is important for stability and efficiency. In contrast, other parameters, like stance time, stride length, and intralimb joint timing, do not adapt slowly over training and showed no after-effect in the postadaptation period. These results are exciting because they raise the possibility that asymmetric gait patterns resulting from some types of CNS damage could be remediated with specific adaptive rehabilitation strategies using a split-belt treadmill. These results also suggest that the adult nervous system employs separate processes to change and store different locomotor parameters. We speculate that the differences in these processes may be related to the varying complexity of the parameters, task demands, and/or the level of supraspinal control necessary for their adaptation.
| GRANTS |
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| ACKNOWLEDGMENTS |
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| FOOTNOTES |
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1 The Supplementary Material for this article (a video) is available online at http://jn.physiology.org/cgi/content/full/00089.2005/DC1. ![]()
Address for reprint requests and other correspondence: A. J. Bastian, Rm. G-04, Kennedy Krieger Inst., 707 N. Broadway, Baltimore, MD 21205 (E-mail: bastian{at}kennedykrieger.org)
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