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Interlimb coordination during stepping in the cat: In-phase stepping and gait transitions
Brain Research, 245 (1982) 353-364 Elsevier Biomedical Press
353
Interlimb Coordination During Stepping in the Cat" In-Phase Stepping and Gait Transitions ARTHUR W. ENGLISH and PAUL R. LENNARD
Departments of Anatomy and (P.R.L.) Biology, Emory University, Atlanta, GA 30322 (U.S.A.) (Accepted January 21st, 1982)
Key words: stepping - - interlimb coordination - - gait transitions - - locomotion - - cat - - galloping
The coordination of step cycles between all 4 limbs during in-phase stepping and during transitions to and from alternate stepping was studied in 12 adult cats during repeated overground stepping trials. The temporal spacing of step cycles of the different limbs was determined from analysis of electromyographic (EMG) activity in a single extensor muscle of each limb. Patterns of coordination of the different limbs were established on the basis of the frequency with which phase values separating step cycles were encountered. Steps in which the phasing of step cycles of the two hindlimbs were closer to true in-phase coordination than true alternation (phase between 270 ° and 90 °) and where similar coupling was found in both the preceding and following steps were defined as steady state conditions. Distinct patterns of coordination of forelimb-forelimb and forelimb-hindlimbstep cycles were noted under steady state conditions. During stepping sequences which include transitions either to or from alternate stepping, both gradual and abrupt phase changes were found. The changes in both forelimb-forelimb and forelimb-hindlimbphase relationships were more often gradual than abrupt. Where abrupt changes were encountered in the change in phase relationships between one such limb pair the phase change in the other pair was gradual. Changes in hindlimb-hindlimbphase relationships during transitions were nearly always abrupt. It is concluded that the 4 limbs are coordinated during in-phase stepping according to a few patterns, but that the variability about these patterns makes their association with simple neural circuitry rather speculative. The finding that transitions were most often gradual is interpreted in terms of a state-dependent model of interlimb control, in which the type of transition utilized depends on the strength of neural coupling of step cycles of all 4 limbs at the time that the transition is initiated. INTRODUCTION
h i n d l i m b s are out of phase by between 90 ° a n d 270 ° (ref. 7). Such phase relationships are, by definition,
Several recent studies o f cat interlimb coordination 2,5A°-14,1~,21, using a variety of different approaches a n d methods o f analysis, have indicated that the coupling of h o m o l o g o u s limbs can be utilized to define two overall forms of stepping. Step cycles of the two forelimbs a n d / o r two h i n d l i m b s are coordin a t e d via either some form of a l t e r n a t i o n or are used in-phase. Most of these studies have associated alternate stepping with gaits described as walking a n d t r o t t i n g a n d in-phase stepping with those described as galloping a n d h a l f - b o u n d i n g . T a k i n g a slightly different p o i n t of view, previous work from this l a b o r a t o r y has described alternate stepping as any steps in which the step cycles of the
closer to true a l t e r n a t i o n (180 °) t h a n to true in-phase (0 °) coordination. In-phase c o o r d i n a t i o n was defined as a n y steps in which h i n d l i m b step cycles are between 270 ° a n d 90 ° out of phase*. By analyzing the patterns of c o o r d i n a t i o n of the step cycles of all 4 limbs during alternate stepping, distinct interlimb phase relationships could be described 7. The results o f similar analysis of in-phase stepping were less conclusive. A t b o t h the forelimbs a n d hindlimbs, distinct patterns of in-phase coordination of h o m o l o g o u s limbs were less obvious t h a n for alternate stepping a n d the phase relationships between the forelimb step cycles differed from those of the two hindlimbs. I n steps in which the hind-
* As used in these studies and in the present study, in-phase stepping is defined entirely by the temporal relationship of the step cycles of the two hindlimbs. It is not meant to imply any particular relationship to any of the defined gaits said to be used by cats nor is it intended to imply any particular relationship between step cycles of any of the other pairs of limbs. 0006-8993/82/0000-0000/$02.75 © 1982 Elsevier Biomedical Press
354 limbs were coordinated in-phase, no particular patterns of coordination of the forelimbs and hindlimbs were noted. Two possible explanations for the lack of an appearance of well-defined patterns of interlimb coordination during in-phase stepping were proposed. One factor was the sample sizes used; the number of in-phase steps analyzed was considerably smaller than the number of alternate steps. Since the description of patterns of coordination was made on the basis of the frequency with which phase values were encountered, it was considered possible that a larger sample of in-phase steps might make definition of patterns more clear. Secondly, in the original study, no distinction was made between true, steady state stepping and transitional patterns when the inphase patterns were analyzed. The purpose of this paper is to describe the results of studies aimed at distinguishing between these possibilities. Analysis of interlimb coordination during in-phase stepping which is drawn from a considerably larger data set than previous studies is presented. This analysis includes only steps where in-phase stepping occurs under steady state phase conditions. The transitions to and from steady state conditions were analyzed separately. The results indicate that well-defined patterns of interlimb coordination during in-phase stepping do exist. Transitions between alternate and in-phase stepping are not always abrupt but more often display gradual changes in the phasing of step cycles of the different limbs. MATERIALS AND METHODS The methods of data acquisition and reduction are similar to those reported previously 7. Data were obtained from 12 adult cats run in repeated overground stepping trials. Each trial consisted of multiple passes back and forth along a wooden walkway (1 x 8 m). Animals were encouraged to step along the walkway by rewards with food and/or affection. Aversive reinforcement was never applied. In each experiment, electromyograms were recorded from a single extensor muscle of each limb via percutaneously placed, bipolar, fine wire electrodes. The lateral head of triceps brachii, a forelimb muscle and vastus lateralis, a hindlimb muscle, were chosen for recording because they are superficially placed
and because they are one-joint muscles. During stepping, patterns of electromyographic (EMG) activity in these muscles occur in a consistent relationship to the step cycle of their respective limbs6,S, 17. The rationale for the use of electromyograms in studies of interlimb coordination is discussed in more detail elsewhere 7. All electromyograms were recorded on tape for later analysis. Each pass along the walkway resulted in the recording of a series of phasic EMG bursts from each of the muscles sampled (Fig. I A). The interval between successive terminations of EMG activity in each muscle was determined and used as a measure of step cycle duration (e.g. Fig. IA, SD) for that limb. The duration of each burst (e.g. Fig. 1A, BD) was also determined and the ratio of BD to SD, or duty factor, calculated. Previous studies (see e.g. ref. 7 and citations) have shown that steps at fast speeds tend to be associated with smaller duty factors and slower steps with larger duty factors. To determine the temporal spacing of step cycles of any two different limbs, the absolute latency (e.g. Fig. 1A, L) between successive terminations of EMG activity in the pair was determined and expressed as a function of the duration of the step cycle of the first limb used in the determination, or as phase. Thus the phase between a right forelimb (RF) step cycle and that of the right hindlimb (RH) is the latency between RF and RH divided by the duration of the RF step. Phase values are expressed as degrees to emphasize the continuous nature of their possible distribution. The step cycles of two limbs which are 360 ° out of phase are thus exactly (0 °) in phase. Six sets of phase populations were determined, one for each of the possible combinations of 4 limbs. All measurements were made on strip charts from recorded electromyograms. Data were then entered 2nto a laboratory computer system for subsequent analysis. To study in-phase stepping, only the steps in which the phase between the two hindlimbs ranged between 270 and 90 ° were analyzed. Hindlimb step cycle phase values in this range more closely approach strict in-phase coordination (0°) than strict alternation (180°). Within this subpopulation, two groups of steps were analyzed in more detail. Steady state in-phase stepping, which was defined as those in-phase steps in which hindlimb step cycles of the
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356 step before and the step after were also in-phase, formed one group. Within this group, patterns of interlimb coordination were described on the basis of the frequency with which phase values were encountered. The other group included in-phase steps associated with a transition. In alternate to inphase transitions, hindlimb step cycles of the preceding step were alternating, i.e. phase values ranged from 90 to 270 °. In in-phase to alternate transitions,
the hindlimb-hindlimb phase values of the following step were in this range. Within each of these two subgroups, the phase changes during consecutive steps were determined. In most cases this involved an analysis of 3-step sequences. In a more limited sample, longer sequences, in which the transition occurred near the center of the sequence, were analyzed. The results of analysis of both long and short sequences were similar.
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357 RESULTS
Steady state in-phase stepping The format used in analysis of interlimb stepping patterns is shown in Fig. lB. It shows a circular plot of duty factor vs forelimb-hindlimb phase, in diagrammatic form, to outline the possible patterns of forelimb-hindlimb coordination during steady state in-phase stepping. Duty factor is plotted along the radius, small duty factors (faster stepping speeds) toward the center of the circle. Phase values are plotted about the circumference, beginning at three o'clock (0 ° or 360 °) and increasing in a counterclockwise direction. Four basic patterns are recognized: trotting (phase between ca. 135° and 225°), pacing (phase between ca. 315 ° and 45°), lateral couplet (between ca. 45 ° and 90 ° and its mirror image between 270 ° and 315 °) and diagonal couplet (between ca. 90 ° and 135° and its mirror image between 225 ° and 270°). Stylized figures of stepping cats are shown next to each type of coordination to indicate the coupling of forelimb and hindlimb step cycles at similar times in the cycle of the hindlimbs. The results of analysis of steady state in-phase stepping are shown in Fig. 2. The plots represent a composite of data from all of the cats used in the study. Fig. 2a shows that during steady state in-phase coordination of the hindlimbs, two primary forms of coordination of forelimb step cycles exist. Aggregations of phase values about 90 ° and its mirror image at 270 ° describe these patterns. Phase values are about equally distributed between the two patterns, and in each subgroup they range about 45 ° on either side of the median value. Although this range may seem substantial it is the same or less than that observed when alternate coordination is utilized during overground stepping in individual animals 7. Fig. 2b describes the patterns of coordination of step cycles of the ipsilateral forelimb and hindlimb during steady state in-phase stepping. Three basic types of coordination of homolateral limb step cycles are found. Aggregations of phase values near 180°, 135° and its mirror image at 225 ° account for the majority of the steps analyzed. These represent: (1) a trotting form of forelimb-hindlimb coordination (180 °) where the homolateral limbs are nearly exactly out of phase, and (2) what has been des-
cribed 7 as diagonal couplet coordination (135 °, 225°), where the step cycles of the diagonal limbs are more closely coupled than those of the homolateral limbs. Smaller groupings of steps with phase values between 45 ° and 90 ° and its mirror image (270 ° to 315 °) are also found. These form a third basic type of forelimb-hindlimb coordination. On the basis of gait analysis, Hildebrand 11 has termed phase values in this region lateral couplet coordination, since the step cycles of homolateral limbs are more closely linked than those of the diagonal limbs. Very few steps with forelimb-hindlimb phase values in the region of the plot which might be considered to represent a true pacing form of forelimb-hindlimb coordination (315 ° to 45 °) were found.
Step sequences which include alternate to in-phase transitions The results of analysis of steps which include transition from alternate to in-phase stepping are shown in Figs. 3 and 4. Data were derived from stepping sequences for two consecutive steps in which the hindlimb-hindlimb phase values lay in the in-phase range (270 ° to 90°), but those of the preceding step were in the alternate range, 90 ° to 270 °. Fig. 3 plots the phase relationships between step cycles in the different limbs during such sequences of three consecutive steps. These data have been divided into groups on the basis of the forelimbhindlimb phase relationships found in the final, inphase step of the sequence to make visualization of the transition patterns simpler. The transition from alternate to in-phase occurs between the first and second steps of each panel. Each group of two panels represents the phase relationships of different combinations of limb pairs analyzed in the same 3 step sequences. Individual sequences are identified by the same symbols and lines. The left panels describe the change in phase between step cycles of the two forelimbs, while right panels indicate the change in phase between step cycles of the right forelimb and hindlimb. Similar data were obtained from analysis of the change in phase of the left forelimb and hindlimb step cycles. Fig. 3 demonstrates that the transition from alternate to in-phase stepping usually occurs according to one of two basic types. In most cases transitions are gradual. The change in phase during the
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ALT. - I N - PHASE TRANSITION Fig. 4. Changes in phase relationships of step cycles of the different limbs are shown for sequences of consecutivesteps during whicha transitionfrom alternate to in-phasecoupling of hindlimbstep cyclesoccurs. The solidverticalbars indicate the time of the transition. See text for details. sequence which includes the transition is fairly evenly distributed between steps. Gradual phase changes can involve large magnitude shifts (e.g. Fig. 3, diagonal couplets low final, forelimb-hindlimb, filled circles) or small changes (e.g. Fig. 3, trotting final, forelimb-forelimb, open squares), but are always marked by a smooth change through the sequence. Abrupt changes in phase can also be found during transitional sequences. When the transition is abrupt, the magnitude of the phase change between one pair of steps in the sequence is considerably larger than the change occurring between the
other pair. The larger phase change is sometimes found between the first and second steps (Fig. 3, diagonal couplet high final, forelimb-hindlimb, open circles) and sometimes between the second and third steps (Fig. 3, diagonal couplet low final, forelimb-forelimb, filled circles). A possible third form of phase change is characterized by a change in the direction of the phase change between the first and second steps and the second and third steps. The magnitude of the phase changes may be large and nearly the same for both directions, so that the overall magnitude of the phase change during the sequence may be small (e.g. Fig. 3, diagonal couplet high final, forelimb-forelimb, filled squares). The magnitude of the component changes also may be small (e.g. Fig. 3, trotting final, forelimb-forelimb, filled circles). The former examples are considered forms of abrupt changes because the change in magnitude of each component is great. The latter are considered types of gradual changes, since the component changes are small. An examination of Fig. 3 indicates that alternate to in-phase transitions often involve gradual changes in the phase relationships of the different limbs. Further, in nearly every case of an abrupt change in the phase relationship between one pair of limbs, the change of phase between the other pair of limbs is gradual. This can be seen most easily by comparing sequences of the same symbol in the pairs of plots in each of the groups in Fig. 3. When the transition from alternate to in-phase stepping involves an abrupt change in forelimb-forelimb phase, the change in forelimb-hindlimb phase is gradual. When such a transition results in an abrupt change in forelimb-hindlimb phase, the change in forelimb-forelimb phase is almost always gradual. The observation of gradual changes in phase during transitions from alternate to in-phase stepping which were made from analysis of only 3 steps may be biased by the small number of steps in each sequence. Abrupt changes in phase could occur before or after the 3 steps chosen for analysis. Thus, longer sequences of consecutive steps, in which alternate to in-phase transitions occurred, were analyzed. Representative samples of these longer sequences are shown in Fig. 4. Each panel in Fig. 4 plots phase against the step number in the sequence. The dark vertical bar in each plot marks the place
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361 where the transition from alternate to in-phase occurs. The 3 stepping sequences, indicated by the same symbols and lines, are plotted for different limb combinations in each panel: forelimb-forelimb (top), hindlimb-hindlimb (middle) and forelimbhindlimb (bottom). Fig. 4 shows that the conclusions based on analysis of 3 step sequences hold also for longer sequences of consecutive steps. Both gradual and abrupt changes in the phase relationships between the different limbs are found during transitions from alternate to in-phase stepping. When abrupt phase changes occur between the two forelimbs, the phase change between the forelimbs and hindlimbs is gradual (e.g. Fig. 4, filled triangles). When abrupt changes occur between the forelimbs and hindlimbs, gradual changes are found between the two forelimbs (open circles). Fig. 4 also supports an observation made in the analysis of 3-step sequences but not shown in Fig. 3, that the change in hindlimb-hindlimb phase during alternate to in-phase transitions is always abrupt. The analysis of 3 long sequences suggests that this abrupt change may be preceded by a gradual phase change. However, these observations must be repeated on a larger data set before any significance can be associated with them. Step sequences which include in-phase to alternate transitions Results of analysis of steps which include transitions from in-phase to alternate stepping are shown in Fig. 5. The format is similar to that of Fig. 3. These data were derived from sequences of 3 consecutive steps, in which hindlimb-hindlimb phase values lie in the range of 270° to 90° (in-phase) during the first two steps followed by a step in the range of 90° to 270° (alternate). The transition thus occurs between the second and third steps of the sequence. As in Fig. 3, different two-panel groups are shown, based on the forelimb-hindlimb phase of the initial (in-phase) step. In each pair of panels, the individual symbols and lines indicate data from the same sequences. Fig. 5 demonstrates that, much as in alternate to in-phase transitions, in-phase to alternate transitions are either gradual (e.g. Fig. 5, diagonal couplet initial, forelimb-forelimb, filled squares) or abrupt (e.g. Fig. 5, diagonal couplet initial, forelimb-forelimb, filled triangle or open
star). As noted in alternate to in-phase transitions, "the phase changes which occur during in-phase to alternate transitions are often gradual. Also as in alternate to in-phase transitions, when abrupt phase changes occur between the two forelimbs, the change in forelimb-hindlimb phase tends to be gradual. When abrupt changes in forelimbhindlimb phase occur, the change in forelimb-forelimb phase is gradual. Unlike alternate to in-phase transitions, abrupt phase changes during in-phase to alternate transitions are more common between step cycles of the two forelimbs and more common
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IN-PHASE -ALT. TRANSITION Fig. 6. Changes in phase relationships of step cycles of the different limbs are shown for sequences of consecutive steps during which a transition from in-phase to alternate coupling of hindlimb step cycles occurs. The solid vertical bars indicate the time of the transition. See text for details.
362 when the forelimb-hindlimb phase in the initial step of the sequence was in the diagonal couplet range: Fig. 6 shows a similar analysis of in-phase to alternate transitions carried out on representative longer sequences. The format is similar to that of Fig. 4. The data in this figure indicate that the observations made on three step sequences can be extended to apply to longer sequences. It also indicates that even though in-phase to alternate transitions often involve abrupt shifts in hindlimbhindlimb phase relationships, sometimes gradual phase changes are also encountered (filled triangles). However, the small size of these longer stepping sequences dictates that generalizations concerning these abrupt or gradual transitions should be approached with caution. DISCUSSION It has been argued previously 7 that the identification of interlimb stepping patterns by aggregations of phase values indicates that step cycles of the different limbs are coordinated according to a few, frequently-occurring forms. Substantial variability about these patterns is found, however, so that without additional supporting data, association of these patterns with particular neural pathways must be considered quite speculative. Such conclusions lie between the contrasting positions taken by previous studies of interlimb coordination. These studies either emphasized the tight coupling of step cycles of different limbs and the association of this coupling with the results of studies of long propriospinal neurons1°, v~-15, or have stressed the variability in interlimb timings and pointed to the facultative capability of any neural control mechanisms2,6,20, 21. Both positions have merit, as the present results demonstrate. The coupling of step cycles of the different limbs during in-phase stepping is variable but not so variable that discrete patterns cannot be recognized. The results of the present study indicate that distinct patterns of interlimb coordination during in-phase stepping do exist. Forelimb step cycles are coupled approximately 90 ° out of phase during steady state in-phase stepping. Phase values are aggregated about 90 ° and 270 °, in contrast to the pattern of coupling of forelimb step cycles during
alternate stepping, where phase values were observed about 180°. This coupling of forelimb step cycles is consistent with kinematic observations made of treadmill galloping in cats 5,16,21, where 'the forelimb touchdowns were separated b y . . . slightly more than 25 ~ of a normalized stride' (ref. 21, p. 122). During in-phase coordination, the step cycles of the forelimbs and hindlimbs are coupled via trotting (180°), diagonal couplet (120 °, 240 °) or lateral couplet (60 °, 120°) forms of coordination. The distinction between the trotting and diagonal couplet subpopulations is more marked (e.g. Fig. 2b) than during alternate stepping, so that they might be thought of as distinct patterns rather than subsets of one larger pattern. The presence of a lateral couplet pattern is in contrast to alternate stepping and to previous analysis of interlimb stepping patterns 7,12. However, mean homolateral limb step cycle phase lags in the range of lateral couplet coordination (45 ° to 90 °) have been reported for treadmill galloping 5. No clear-cut tendency was found toward pacing, or in-phase coupling of homolateral limb step cycles. This is in contrast to reports that pacing is commonly encountered during in-phase stepping 13,14. In much the same manner that this type of analysis of interlimb coordination during steady state conditions has proven useful in the establishment of boundary conditions for models of interlimb control, a study of gait transition patterns could provide useful insights for investigations of neural pathways subserving the interactions between the limbs during stepping. The present study found that transitions between alternate and in-phase stepping are most often gradual, resulting in a smooth change in forelimb-forelimb and forelimbhindlimb phase, but also can be abrupt where phase changes are rapid in direction and/or magnitude. When abrupt changes in the phase relationship of one pair of limbs were observed (e.g. between the two forelimbs) the phase changes between the other pair (in this example between the forelimbs and hindlimbs) were gradual. Abrupt phase changes between both of these sets of limbs were not normally encountered. The finding of many examples of gradual phase changes during transitions is in contrast to previous observations reporting a predominance of abrupt
363 changes in the phase relationships between the different limbsrZ, 14. These observations have been used as evidence to support the notion that transitions between modes of stepping constitute transitions from one motor ' p r o g r a m ' to another 14. The different patterns of interlimb coordination observed during stepping were said to be the result of the interaction of these different 'programs'. The suggested neural substrate involved an interaction between long propriospinal and crossed spinal pathways. We argue that these contrasting results emphasize the different conditions under which the data from the two studies were collected. Miller and colleagues confined their observations to treadmill locomotion under quite limited conditions. The present study has used a large data set and examined all of the observed transitions which occurred during overground stepping. Thus the observations of the type of transitions made by Miller et al. may have been a subset of those which have been described above. Indeed, Miller et al. 14 have commented that the abrupt changes in phase which they have observed are not the only strategies used during gait transitions. Data of this type can never by themselves provide a direct indication of which neural pathways control interlimb coordination. We feel, however, that the available evidence points toward the development of an expanded version of the 'program' hypothesis, which specifically includes the consideration of more than the two spinal systems which form the basis of the 'program' hypothesis. We propose that the
observed modes of vertebrate stepping should be defined in terms of the relative strengths of coupling between the neural elements generating stepping movements for all of the different limbs. The strength of coupling between a pair of limbs thus constitutes a state-dependent variable which includes the net effect of all of the converging inputs segmental, crossed spinal, propriospinal, and supraspinal - - to each of a pair of stepping generators. Since all of these parameters have been demonstrated to vary throughout a step cycle 1,3,4,9,18,19, it might be anticipated that the strength oi coupling between any pair of limbs would vary also. One might expect to encounter considerable variability around different interlimb stepping patterns or transition patterns when data are collected from animals stepping overground. Considerably less variability in these patterns might be expected when observations are made under the more restricted conditions of treadmill locomotion. Sources of variability probably involve modulations of interlimb coupling derived from several neuronal systems. However, we feel that this state-dependent model provides a comprehensive basis from which future studies of the neural control of interlimb coordination can be erected.
REFERENCES
analysis of muscular activity in the hindlimb of the cat during unrestrained locom3tion, Acta physioL scand., 75 (1969) 614-630. 7 English, A. W., Interlimb coordination during stepping in the cat: an electromyographic analysis, J. NeurophysioL, 42 (1979) 229-243. 8 English, A. W., An electromyographic analysis of forelimb muscles during overground stepping in the cat, J. exp. Biol., 76 (1978) 105-122. 9 Grillner, S., Locomotion in vertebrates: central mechanisms and reflex interaction, Physiol. Rev., 55 (1975) 247-295. 10 Halbertsma, J., Miller, S. and Van der Meche, F. G. A., Basic programs for the phasing of flexion and extension movements of the limbs during locomotion. In R. M. Herman, S., Grillner, P. S. G. Stein and D. G. Stuart (Eds.), Neural Control of Locomotion, Plenum Press, New York, 1976, pp. 489-518. 11 Hildebrand, M., Analysis of tetrapod gaits: general consJ-
1 Andersson, O., Grillner, S., Lindquist, M. and Zomlefer, M., Peripheral control of the spinal pattern generators for locomotion in cat, Brain Research, 150 (1978) 625-630. 2 Coss, L., Chan, A. K., Goslow, G. E. and Rasmussen, S., Ipsilateral limb variation in cats during overground locomotion, Brain Behav. Evol., 18 (1978) 85-93. 3 Duysens, J., Fluctuations in sensitivity to rhythm resetting effects during the cat's step cycle, Brain Research, 133 (1977) 190-195. 4 Duysens, J., Loeb, G. E. and Weston, B. J., Crossed flexor reflex responses and their reversal in freely walking cats, Brain Research, 197 (1980) 538-542. 5 Eisenstein, B. L., Postillion, F. G., Norgren, K. S. and Wetzel, M. C., Kinematics of treadmill galloping by cats. II. Steady-state coordination under positive reinforcement control, Behav. Biol., 21 (1977) 89-106. 6 Engberg, I. and Lundberg, A., An electromyographic
-
-
ACKNOWLEDGEM ENTS The technical assistance of Margaret NewmanBiggs and Evelyn Manley is greatly appreciated. Support was provided by Grant NS 15452, from the U.S. Public Health Service.
364
12
13
14
15
16
derations, and symmetrical gaits. In R. M. Herman, S. Grillner, P. S. G. Stein and D. G. Stuart (Eds.), Neural Control of Locomotion, Plenum Press, New York, 1976, pp. 203-206. Miller, S. and Van der Meche, F. G. A., Coordinated stepping of all four limbs in the high spinal cat, Brain Research, 109 (1976) 395-398. Miller, S., Van der Burg, J. and Van der Meche, F. G. A., Coordination of movements of the hindlimbs and forelimbs in different forms of locomotion in normal and decerebrate cats, Brain Research, 91 (1975) 217-238. Miller, S., Van der Burg, J. and Van der Meche, F. G. A., Locomotion in the cat: basic programmes of movement, Brain Research, 91 (1975) 239-254. Miller, S., Reitsma, D. J. and Van der Meche, F. G. A., Functional organization of long ascending propriospinal pathways linking lumbosacral and cervical segments in the cat, Brain Research, 62 (1973) 169-188. Norgren, K. S., Seelhorst, E. and Wetzel, M. C., Kinematics of treadmill galloping by cats. I. Steady state coordination under aversive control, Behav. Biol., 21 (1977) 66-88.
17 Rasmussen, S., Chan, A. K. and Goslow, G. E., The cat step cycle: electromyographic patterns for hindlimb muscles during posture and unrestrained locomotion, J. Morph., 155 (1978) 253-270. 18 Rossignol, S. and Gauthier, L., An analysis of mechanisms controlling the reversal of crossed spinal reflexes, Brain Research, 182 (1980) 31-45. 19 Schomburg, E. D., Roesler, J. and Meinck, H. M., Phasedependent transmission in the excitatory propriospinal reflex pathway from forelimb afferents to lumbar motoneurones during fictive locomotion, Neurosci. Lett., 4 (1977) 249-252. 20 Stuart, D. G., Withey, M. C., Wetzel, M. C. and Goslow, G. E., Time constraints for interlimb coordination in the cat during unrestrained locomotion. In R. B. Stein, K. B. Pearson, R. S. Smith and J. B. Redford (Eds.), Control of Posture and Locomotion, Plenum Press, New York, 1973, pp. 537-560. 21 Wetzel, M. C., Anderson, R. C., Brady, T. H. and Norgren, K. S., Kinematics of treadmill galloping by cats. III. Coordination during gait conversions and implications for neural control, Behav. Biol., 21 (1977) 107-127.
353
Interlimb Coordination During Stepping in the Cat" In-Phase Stepping and Gait Transitions ARTHUR W. ENGLISH and PAUL R. LENNARD
Departments of Anatomy and (P.R.L.) Biology, Emory University, Atlanta, GA 30322 (U.S.A.) (Accepted January 21st, 1982)
Key words: stepping - - interlimb coordination - - gait transitions - - locomotion - - cat - - galloping
The coordination of step cycles between all 4 limbs during in-phase stepping and during transitions to and from alternate stepping was studied in 12 adult cats during repeated overground stepping trials. The temporal spacing of step cycles of the different limbs was determined from analysis of electromyographic (EMG) activity in a single extensor muscle of each limb. Patterns of coordination of the different limbs were established on the basis of the frequency with which phase values separating step cycles were encountered. Steps in which the phasing of step cycles of the two hindlimbs were closer to true in-phase coordination than true alternation (phase between 270 ° and 90 °) and where similar coupling was found in both the preceding and following steps were defined as steady state conditions. Distinct patterns of coordination of forelimb-forelimb and forelimb-hindlimbstep cycles were noted under steady state conditions. During stepping sequences which include transitions either to or from alternate stepping, both gradual and abrupt phase changes were found. The changes in both forelimb-forelimb and forelimb-hindlimbphase relationships were more often gradual than abrupt. Where abrupt changes were encountered in the change in phase relationships between one such limb pair the phase change in the other pair was gradual. Changes in hindlimb-hindlimbphase relationships during transitions were nearly always abrupt. It is concluded that the 4 limbs are coordinated during in-phase stepping according to a few patterns, but that the variability about these patterns makes their association with simple neural circuitry rather speculative. The finding that transitions were most often gradual is interpreted in terms of a state-dependent model of interlimb control, in which the type of transition utilized depends on the strength of neural coupling of step cycles of all 4 limbs at the time that the transition is initiated. INTRODUCTION
h i n d l i m b s are out of phase by between 90 ° a n d 270 ° (ref. 7). Such phase relationships are, by definition,
Several recent studies o f cat interlimb coordination 2,5A°-14,1~,21, using a variety of different approaches a n d methods o f analysis, have indicated that the coupling of h o m o l o g o u s limbs can be utilized to define two overall forms of stepping. Step cycles of the two forelimbs a n d / o r two h i n d l i m b s are coordin a t e d via either some form of a l t e r n a t i o n or are used in-phase. Most of these studies have associated alternate stepping with gaits described as walking a n d t r o t t i n g a n d in-phase stepping with those described as galloping a n d h a l f - b o u n d i n g . T a k i n g a slightly different p o i n t of view, previous work from this l a b o r a t o r y has described alternate stepping as any steps in which the step cycles of the
closer to true a l t e r n a t i o n (180 °) t h a n to true in-phase (0 °) coordination. In-phase c o o r d i n a t i o n was defined as a n y steps in which h i n d l i m b step cycles are between 270 ° a n d 90 ° out of phase*. By analyzing the patterns of c o o r d i n a t i o n of the step cycles of all 4 limbs during alternate stepping, distinct interlimb phase relationships could be described 7. The results o f similar analysis of in-phase stepping were less conclusive. A t b o t h the forelimbs a n d hindlimbs, distinct patterns of in-phase coordination of h o m o l o g o u s limbs were less obvious t h a n for alternate stepping a n d the phase relationships between the forelimb step cycles differed from those of the two hindlimbs. I n steps in which the hind-
* As used in these studies and in the present study, in-phase stepping is defined entirely by the temporal relationship of the step cycles of the two hindlimbs. It is not meant to imply any particular relationship to any of the defined gaits said to be used by cats nor is it intended to imply any particular relationship between step cycles of any of the other pairs of limbs. 0006-8993/82/0000-0000/$02.75 © 1982 Elsevier Biomedical Press
354 limbs were coordinated in-phase, no particular patterns of coordination of the forelimbs and hindlimbs were noted. Two possible explanations for the lack of an appearance of well-defined patterns of interlimb coordination during in-phase stepping were proposed. One factor was the sample sizes used; the number of in-phase steps analyzed was considerably smaller than the number of alternate steps. Since the description of patterns of coordination was made on the basis of the frequency with which phase values were encountered, it was considered possible that a larger sample of in-phase steps might make definition of patterns more clear. Secondly, in the original study, no distinction was made between true, steady state stepping and transitional patterns when the inphase patterns were analyzed. The purpose of this paper is to describe the results of studies aimed at distinguishing between these possibilities. Analysis of interlimb coordination during in-phase stepping which is drawn from a considerably larger data set than previous studies is presented. This analysis includes only steps where in-phase stepping occurs under steady state phase conditions. The transitions to and from steady state conditions were analyzed separately. The results indicate that well-defined patterns of interlimb coordination during in-phase stepping do exist. Transitions between alternate and in-phase stepping are not always abrupt but more often display gradual changes in the phasing of step cycles of the different limbs. MATERIALS AND METHODS The methods of data acquisition and reduction are similar to those reported previously 7. Data were obtained from 12 adult cats run in repeated overground stepping trials. Each trial consisted of multiple passes back and forth along a wooden walkway (1 x 8 m). Animals were encouraged to step along the walkway by rewards with food and/or affection. Aversive reinforcement was never applied. In each experiment, electromyograms were recorded from a single extensor muscle of each limb via percutaneously placed, bipolar, fine wire electrodes. The lateral head of triceps brachii, a forelimb muscle and vastus lateralis, a hindlimb muscle, were chosen for recording because they are superficially placed
and because they are one-joint muscles. During stepping, patterns of electromyographic (EMG) activity in these muscles occur in a consistent relationship to the step cycle of their respective limbs6,S, 17. The rationale for the use of electromyograms in studies of interlimb coordination is discussed in more detail elsewhere 7. All electromyograms were recorded on tape for later analysis. Each pass along the walkway resulted in the recording of a series of phasic EMG bursts from each of the muscles sampled (Fig. I A). The interval between successive terminations of EMG activity in each muscle was determined and used as a measure of step cycle duration (e.g. Fig. IA, SD) for that limb. The duration of each burst (e.g. Fig. 1A, BD) was also determined and the ratio of BD to SD, or duty factor, calculated. Previous studies (see e.g. ref. 7 and citations) have shown that steps at fast speeds tend to be associated with smaller duty factors and slower steps with larger duty factors. To determine the temporal spacing of step cycles of any two different limbs, the absolute latency (e.g. Fig. 1A, L) between successive terminations of EMG activity in the pair was determined and expressed as a function of the duration of the step cycle of the first limb used in the determination, or as phase. Thus the phase between a right forelimb (RF) step cycle and that of the right hindlimb (RH) is the latency between RF and RH divided by the duration of the RF step. Phase values are expressed as degrees to emphasize the continuous nature of their possible distribution. The step cycles of two limbs which are 360 ° out of phase are thus exactly (0 °) in phase. Six sets of phase populations were determined, one for each of the possible combinations of 4 limbs. All measurements were made on strip charts from recorded electromyograms. Data were then entered 2nto a laboratory computer system for subsequent analysis. To study in-phase stepping, only the steps in which the phase between the two hindlimbs ranged between 270 and 90 ° were analyzed. Hindlimb step cycle phase values in this range more closely approach strict in-phase coordination (0°) than strict alternation (180°). Within this subpopulation, two groups of steps were analyzed in more detail. Steady state in-phase stepping, which was defined as those in-phase steps in which hindlimb step cycles of the
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356 step before and the step after were also in-phase, formed one group. Within this group, patterns of interlimb coordination were described on the basis of the frequency with which phase values were encountered. The other group included in-phase steps associated with a transition. In alternate to inphase transitions, hindlimb step cycles of the preceding step were alternating, i.e. phase values ranged from 90 to 270 °. In in-phase to alternate transitions,
the hindlimb-hindlimb phase values of the following step were in this range. Within each of these two subgroups, the phase changes during consecutive steps were determined. In most cases this involved an analysis of 3-step sequences. In a more limited sample, longer sequences, in which the transition occurred near the center of the sequence, were analyzed. The results of analysis of both long and short sequences were similar.
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357 RESULTS
Steady state in-phase stepping The format used in analysis of interlimb stepping patterns is shown in Fig. lB. It shows a circular plot of duty factor vs forelimb-hindlimb phase, in diagrammatic form, to outline the possible patterns of forelimb-hindlimb coordination during steady state in-phase stepping. Duty factor is plotted along the radius, small duty factors (faster stepping speeds) toward the center of the circle. Phase values are plotted about the circumference, beginning at three o'clock (0 ° or 360 °) and increasing in a counterclockwise direction. Four basic patterns are recognized: trotting (phase between ca. 135° and 225°), pacing (phase between ca. 315 ° and 45°), lateral couplet (between ca. 45 ° and 90 ° and its mirror image between 270 ° and 315 °) and diagonal couplet (between ca. 90 ° and 135° and its mirror image between 225 ° and 270°). Stylized figures of stepping cats are shown next to each type of coordination to indicate the coupling of forelimb and hindlimb step cycles at similar times in the cycle of the hindlimbs. The results of analysis of steady state in-phase stepping are shown in Fig. 2. The plots represent a composite of data from all of the cats used in the study. Fig. 2a shows that during steady state in-phase coordination of the hindlimbs, two primary forms of coordination of forelimb step cycles exist. Aggregations of phase values about 90 ° and its mirror image at 270 ° describe these patterns. Phase values are about equally distributed between the two patterns, and in each subgroup they range about 45 ° on either side of the median value. Although this range may seem substantial it is the same or less than that observed when alternate coordination is utilized during overground stepping in individual animals 7. Fig. 2b describes the patterns of coordination of step cycles of the ipsilateral forelimb and hindlimb during steady state in-phase stepping. Three basic types of coordination of homolateral limb step cycles are found. Aggregations of phase values near 180°, 135° and its mirror image at 225 ° account for the majority of the steps analyzed. These represent: (1) a trotting form of forelimb-hindlimb coordination (180 °) where the homolateral limbs are nearly exactly out of phase, and (2) what has been des-
cribed 7 as diagonal couplet coordination (135 °, 225°), where the step cycles of the diagonal limbs are more closely coupled than those of the homolateral limbs. Smaller groupings of steps with phase values between 45 ° and 90 ° and its mirror image (270 ° to 315 °) are also found. These form a third basic type of forelimb-hindlimb coordination. On the basis of gait analysis, Hildebrand 11 has termed phase values in this region lateral couplet coordination, since the step cycles of homolateral limbs are more closely linked than those of the diagonal limbs. Very few steps with forelimb-hindlimb phase values in the region of the plot which might be considered to represent a true pacing form of forelimb-hindlimb coordination (315 ° to 45 °) were found.
Step sequences which include alternate to in-phase transitions The results of analysis of steps which include transition from alternate to in-phase stepping are shown in Figs. 3 and 4. Data were derived from stepping sequences for two consecutive steps in which the hindlimb-hindlimb phase values lay in the in-phase range (270 ° to 90°), but those of the preceding step were in the alternate range, 90 ° to 270 °. Fig. 3 plots the phase relationships between step cycles in the different limbs during such sequences of three consecutive steps. These data have been divided into groups on the basis of the forelimbhindlimb phase relationships found in the final, inphase step of the sequence to make visualization of the transition patterns simpler. The transition from alternate to in-phase occurs between the first and second steps of each panel. Each group of two panels represents the phase relationships of different combinations of limb pairs analyzed in the same 3 step sequences. Individual sequences are identified by the same symbols and lines. The left panels describe the change in phase between step cycles of the two forelimbs, while right panels indicate the change in phase between step cycles of the right forelimb and hindlimb. Similar data were obtained from analysis of the change in phase of the left forelimb and hindlimb step cycles. Fig. 3 demonstrates that the transition from alternate to in-phase stepping usually occurs according to one of two basic types. In most cases transitions are gradual. The change in phase during the
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ALT. - I N - PHASE TRANSITION Fig. 4. Changes in phase relationships of step cycles of the different limbs are shown for sequences of consecutivesteps during whicha transitionfrom alternate to in-phasecoupling of hindlimbstep cyclesoccurs. The solidverticalbars indicate the time of the transition. See text for details. sequence which includes the transition is fairly evenly distributed between steps. Gradual phase changes can involve large magnitude shifts (e.g. Fig. 3, diagonal couplets low final, forelimb-hindlimb, filled circles) or small changes (e.g. Fig. 3, trotting final, forelimb-forelimb, open squares), but are always marked by a smooth change through the sequence. Abrupt changes in phase can also be found during transitional sequences. When the transition is abrupt, the magnitude of the phase change between one pair of steps in the sequence is considerably larger than the change occurring between the
other pair. The larger phase change is sometimes found between the first and second steps (Fig. 3, diagonal couplet high final, forelimb-hindlimb, open circles) and sometimes between the second and third steps (Fig. 3, diagonal couplet low final, forelimb-forelimb, filled circles). A possible third form of phase change is characterized by a change in the direction of the phase change between the first and second steps and the second and third steps. The magnitude of the phase changes may be large and nearly the same for both directions, so that the overall magnitude of the phase change during the sequence may be small (e.g. Fig. 3, diagonal couplet high final, forelimb-forelimb, filled squares). The magnitude of the component changes also may be small (e.g. Fig. 3, trotting final, forelimb-forelimb, filled circles). The former examples are considered forms of abrupt changes because the change in magnitude of each component is great. The latter are considered types of gradual changes, since the component changes are small. An examination of Fig. 3 indicates that alternate to in-phase transitions often involve gradual changes in the phase relationships of the different limbs. Further, in nearly every case of an abrupt change in the phase relationship between one pair of limbs, the change of phase between the other pair of limbs is gradual. This can be seen most easily by comparing sequences of the same symbol in the pairs of plots in each of the groups in Fig. 3. When the transition from alternate to in-phase stepping involves an abrupt change in forelimb-forelimb phase, the change in forelimb-hindlimb phase is gradual. When such a transition results in an abrupt change in forelimb-hindlimb phase, the change in forelimb-forelimb phase is almost always gradual. The observation of gradual changes in phase during transitions from alternate to in-phase stepping which were made from analysis of only 3 steps may be biased by the small number of steps in each sequence. Abrupt changes in phase could occur before or after the 3 steps chosen for analysis. Thus, longer sequences of consecutive steps, in which alternate to in-phase transitions occurred, were analyzed. Representative samples of these longer sequences are shown in Fig. 4. Each panel in Fig. 4 plots phase against the step number in the sequence. The dark vertical bar in each plot marks the place
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361 where the transition from alternate to in-phase occurs. The 3 stepping sequences, indicated by the same symbols and lines, are plotted for different limb combinations in each panel: forelimb-forelimb (top), hindlimb-hindlimb (middle) and forelimbhindlimb (bottom). Fig. 4 shows that the conclusions based on analysis of 3 step sequences hold also for longer sequences of consecutive steps. Both gradual and abrupt changes in the phase relationships between the different limbs are found during transitions from alternate to in-phase stepping. When abrupt phase changes occur between the two forelimbs, the phase change between the forelimbs and hindlimbs is gradual (e.g. Fig. 4, filled triangles). When abrupt changes occur between the forelimbs and hindlimbs, gradual changes are found between the two forelimbs (open circles). Fig. 4 also supports an observation made in the analysis of 3-step sequences but not shown in Fig. 3, that the change in hindlimb-hindlimb phase during alternate to in-phase transitions is always abrupt. The analysis of 3 long sequences suggests that this abrupt change may be preceded by a gradual phase change. However, these observations must be repeated on a larger data set before any significance can be associated with them. Step sequences which include in-phase to alternate transitions Results of analysis of steps which include transitions from in-phase to alternate stepping are shown in Fig. 5. The format is similar to that of Fig. 3. These data were derived from sequences of 3 consecutive steps, in which hindlimb-hindlimb phase values lie in the range of 270° to 90° (in-phase) during the first two steps followed by a step in the range of 90° to 270° (alternate). The transition thus occurs between the second and third steps of the sequence. As in Fig. 3, different two-panel groups are shown, based on the forelimb-hindlimb phase of the initial (in-phase) step. In each pair of panels, the individual symbols and lines indicate data from the same sequences. Fig. 5 demonstrates that, much as in alternate to in-phase transitions, in-phase to alternate transitions are either gradual (e.g. Fig. 5, diagonal couplet initial, forelimb-forelimb, filled squares) or abrupt (e.g. Fig. 5, diagonal couplet initial, forelimb-forelimb, filled triangle or open
star). As noted in alternate to in-phase transitions, "the phase changes which occur during in-phase to alternate transitions are often gradual. Also as in alternate to in-phase transitions, when abrupt phase changes occur between the two forelimbs, the change in forelimb-hindlimb phase tends to be gradual. When abrupt changes in forelimbhindlimb phase occur, the change in forelimb-forelimb phase is gradual. Unlike alternate to in-phase transitions, abrupt phase changes during in-phase to alternate transitions are more common between step cycles of the two forelimbs and more common
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7
IN-PHASE -ALT. TRANSITION Fig. 6. Changes in phase relationships of step cycles of the different limbs are shown for sequences of consecutive steps during which a transition from in-phase to alternate coupling of hindlimb step cycles occurs. The solid vertical bars indicate the time of the transition. See text for details.
362 when the forelimb-hindlimb phase in the initial step of the sequence was in the diagonal couplet range: Fig. 6 shows a similar analysis of in-phase to alternate transitions carried out on representative longer sequences. The format is similar to that of Fig. 4. The data in this figure indicate that the observations made on three step sequences can be extended to apply to longer sequences. It also indicates that even though in-phase to alternate transitions often involve abrupt shifts in hindlimbhindlimb phase relationships, sometimes gradual phase changes are also encountered (filled triangles). However, the small size of these longer stepping sequences dictates that generalizations concerning these abrupt or gradual transitions should be approached with caution. DISCUSSION It has been argued previously 7 that the identification of interlimb stepping patterns by aggregations of phase values indicates that step cycles of the different limbs are coordinated according to a few, frequently-occurring forms. Substantial variability about these patterns is found, however, so that without additional supporting data, association of these patterns with particular neural pathways must be considered quite speculative. Such conclusions lie between the contrasting positions taken by previous studies of interlimb coordination. These studies either emphasized the tight coupling of step cycles of different limbs and the association of this coupling with the results of studies of long propriospinal neurons1°, v~-15, or have stressed the variability in interlimb timings and pointed to the facultative capability of any neural control mechanisms2,6,20, 21. Both positions have merit, as the present results demonstrate. The coupling of step cycles of the different limbs during in-phase stepping is variable but not so variable that discrete patterns cannot be recognized. The results of the present study indicate that distinct patterns of interlimb coordination during in-phase stepping do exist. Forelimb step cycles are coupled approximately 90 ° out of phase during steady state in-phase stepping. Phase values are aggregated about 90 ° and 270 °, in contrast to the pattern of coupling of forelimb step cycles during
alternate stepping, where phase values were observed about 180°. This coupling of forelimb step cycles is consistent with kinematic observations made of treadmill galloping in cats 5,16,21, where 'the forelimb touchdowns were separated b y . . . slightly more than 25 ~ of a normalized stride' (ref. 21, p. 122). During in-phase coordination, the step cycles of the forelimbs and hindlimbs are coupled via trotting (180°), diagonal couplet (120 °, 240 °) or lateral couplet (60 °, 120°) forms of coordination. The distinction between the trotting and diagonal couplet subpopulations is more marked (e.g. Fig. 2b) than during alternate stepping, so that they might be thought of as distinct patterns rather than subsets of one larger pattern. The presence of a lateral couplet pattern is in contrast to alternate stepping and to previous analysis of interlimb stepping patterns 7,12. However, mean homolateral limb step cycle phase lags in the range of lateral couplet coordination (45 ° to 90 °) have been reported for treadmill galloping 5. No clear-cut tendency was found toward pacing, or in-phase coupling of homolateral limb step cycles. This is in contrast to reports that pacing is commonly encountered during in-phase stepping 13,14. In much the same manner that this type of analysis of interlimb coordination during steady state conditions has proven useful in the establishment of boundary conditions for models of interlimb control, a study of gait transition patterns could provide useful insights for investigations of neural pathways subserving the interactions between the limbs during stepping. The present study found that transitions between alternate and in-phase stepping are most often gradual, resulting in a smooth change in forelimb-forelimb and forelimbhindlimb phase, but also can be abrupt where phase changes are rapid in direction and/or magnitude. When abrupt changes in the phase relationship of one pair of limbs were observed (e.g. between the two forelimbs) the phase changes between the other pair (in this example between the forelimbs and hindlimbs) were gradual. Abrupt phase changes between both of these sets of limbs were not normally encountered. The finding of many examples of gradual phase changes during transitions is in contrast to previous observations reporting a predominance of abrupt
363 changes in the phase relationships between the different limbsrZ, 14. These observations have been used as evidence to support the notion that transitions between modes of stepping constitute transitions from one motor ' p r o g r a m ' to another 14. The different patterns of interlimb coordination observed during stepping were said to be the result of the interaction of these different 'programs'. The suggested neural substrate involved an interaction between long propriospinal and crossed spinal pathways. We argue that these contrasting results emphasize the different conditions under which the data from the two studies were collected. Miller and colleagues confined their observations to treadmill locomotion under quite limited conditions. The present study has used a large data set and examined all of the observed transitions which occurred during overground stepping. Thus the observations of the type of transitions made by Miller et al. may have been a subset of those which have been described above. Indeed, Miller et al. 14 have commented that the abrupt changes in phase which they have observed are not the only strategies used during gait transitions. Data of this type can never by themselves provide a direct indication of which neural pathways control interlimb coordination. We feel, however, that the available evidence points toward the development of an expanded version of the 'program' hypothesis, which specifically includes the consideration of more than the two spinal systems which form the basis of the 'program' hypothesis. We propose that the
observed modes of vertebrate stepping should be defined in terms of the relative strengths of coupling between the neural elements generating stepping movements for all of the different limbs. The strength of coupling between a pair of limbs thus constitutes a state-dependent variable which includes the net effect of all of the converging inputs segmental, crossed spinal, propriospinal, and supraspinal - - to each of a pair of stepping generators. Since all of these parameters have been demonstrated to vary throughout a step cycle 1,3,4,9,18,19, it might be anticipated that the strength oi coupling between any pair of limbs would vary also. One might expect to encounter considerable variability around different interlimb stepping patterns or transition patterns when data are collected from animals stepping overground. Considerably less variability in these patterns might be expected when observations are made under the more restricted conditions of treadmill locomotion. Sources of variability probably involve modulations of interlimb coupling derived from several neuronal systems. However, we feel that this state-dependent model provides a comprehensive basis from which future studies of the neural control of interlimb coordination can be erected.
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ACKNOWLEDGEM ENTS The technical assistance of Margaret NewmanBiggs and Evelyn Manley is greatly appreciated. Support was provided by Grant NS 15452, from the U.S. Public Health Service.
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