The Cat Step Cycle: Electromyographic Patterns for Hindlimb Muscles during Posture and Unrestrained Locomotion S. RASMUSSEN,' A. K. CHAN2.4AND G. E. GOSLOW, JR.3 I Department of Physical Education (60121, Department of Engineermg and Department of Biological Sciences, Northern Arizona Uniuersity, Flagstaff, Arizona 86011

ABSTRACT The telemetered electromyographic activity (EMG) of select hindlimb muscles of unrestrained cats during standing, walking, trotting, and galloping have been recorded. Simultaneous cinematographic records permitted close correlation of muscle activity and locomotor behavior. In general, the pattern of extensor activity of the ankle, knee, and hip during locomotion is fairly consistent, while that of the flexors is more variable. Changes in basic EMG patterns from walk, to trot, t o gallop are most evident in the two-jointed muscles associated with the knee and hip. Progressively greater variation of activity onset and cessation can be seen among extensor muscle groups from the walk, to trot, to gallop. Co-activation of the joint extensors and flexors, especially of the hip, a t the end of the stance phase (E3)is slight in the walk, moderate in the trot, and considerable in the gallop. These EMG changes are necessary to meet the demands imposed upon the musculature a t the faster gaits, particularly galloping, which include limb rigidity as related t o loading, momentum as related to the limb's directional change from the stance phase to the swing phase, and lower spinal movements. The peroneal muscles of the ankle and the gluteal muscles of the hip show extensor activity and act as joint stabilizers during locomotion. Both biceps femoris anterior muscle and biceps femoris posterior muscle show consistent hip extensor patterns a t all gaits. During quiet standing, extensor activity about the knee, ankle, and metatarsophalangeal joints is evident; but the hip extensor and flexor musculature is remarkably silent. EMG data for unrestrained cats are compared t o those of dogs on a treadmill (Tokuriki, '73a,b, '74; Wentink, '76) and those recorded fromdecerebrate cats (mesencephalic preparation) during controlled locomotion (Gambaryan et al., '71). The EMG patterns from decerebrate cats are more consistent a t the walk and gallop within functional groups of muscles a t the ankle, knee, and hip than the EMG patterns observed in unrestrained cats or animals moving on a treadmill. Muscular contraction produces the force by which animals position and rhythmically move their limbs. This simple idea becomes complicated when one considers the number of muscles in each limb, and the coordination of force and timing of muscular contraction necessary to produce a smooth locomotor act. The nervous system directs this coordination, and electromyograms (EMGs) record the resulting electrical activity of the muscles. Engberg ('64) and Engberg and Lundberg ('69) combined EMG with cinematography to J. MORPH. (1978)155: 253-270.

study the activity of hindlimb muscles in cats during unrestrained locomotion. This excellent study resulted in data that have been used for several years in interpreting the demands imposed on the nervous system to direct peripheral events in locomotion. The present study, designed to compliment and expand that work, presents averaged EMGs from select hindlimb muscles of unrestrained cats during standing, walking, trotting, and gal' Present address: Department of Electrical Engineering, Texas A & M University, College Station, Texas 77843.

253

254

S. RASMUSSEN, A. K. CHAN A N D G. E . GOSLOW. J R

used to implant t h e electrode in t h e muscle of interest. When t h e needle was extracted, t h e hook on the end of the electrode wire held the wire in place in t h e muscle. The copper ball was inserted into t h e animal's rectum to serve a s a reference electrode. To avoid hinderance of the animal's normal gait, only one muscle was implanted most of the time; on occasion two muscles were implanted and their activities during locomotion studied simultaneously. Location of t h e wire electrode was verified by stimulation immediately after implantation and again after the recording session. The correctness of electrode implantation was verified by palpation or observation of expected muscular action. Small frequency-modulated transmitters were used to transmit the electrical signals from t h e muscles. These transmitters (18g including batteries) were carried in elastic belts by the animals. The coaxial cables leading from the electrodes to the transmitters were lightly taped in place. The transmitted electrical signal from the muscle was received by a frequency-modul a t e d radiowave receiver a n d processed through a preamplifier and a bandpass filter. The filter was used to reduce movement artifact and extraneous electrical interference. The filter was adjusted to allow the passage of METHODS signals between 20 and 200 Hz. The EMGs Seven cats weighing 2-5 kg were trained to were recorded on a pen recorder. A signal to move on a 6-m curved ramp with a background noise ratio of about 2 to 1 was used when grid ruled into 10-cm squares. Cooperative in- analyzing t h e data t o designate the beginning dividuals were chosen and encouraged to per- or end of a particular muscle's contractile form by using food as a reward. The animals activity. were filmed with a 16-mm camera at 62 To facilitate simultaneous cinematographic frames per second (2-msec exposure each 16.1 and EMG records a magnetic reed switch was msec). A 75 mm f-1.5 lens was used. To reduce attached externally to t h e drive shaft of the parallax the background grid was bowed into a camera (Gans, '66). This switch generated a semicircle with a radius of 6.7 m. The cats small electrical pulse each time the shutter of moved parallel to t h e grid on tightly woven t h e camera opened. This signal, when discarpet. played on the recorder, allowed synchronizaThe telemetered EMG techniques have been tion of each frame on t h e film with a corredescribed elsewhere (Chan e t al., '77). Briefly, sponding time interval of electrical activity a n enamelled silver wire electrode of 100 p m from the cat muscle. diameter was connected to t h e center conducLimitations of camera speed, where actual tor of a light and flexible coaxial cable, with a behavioral events may have occurred anycopper ball of 1-1.6 cm diameter connected t o where within t h e 16.1-msec interval between the other conductor of the cable (Engberg, frames, a r e recognized. In order t o minimize '64). The free end of the wire, with about 0.5 analysis errors, criteria for film and EMG mm of the enamel insulation scraped off, was analysis were established. The criteria for threaded through the lumen of a 26-gauge choosing lift-off were t h a t t h e animal's foot hypodermic needle. The remainder of the fine was just clear of the carpeted surface or t h a t wire and t h e attached cable was passed along the animal was no longer bearing any of his the outside of the needle. The needle was then body weight on t h a t foot, as evidenced by a

loping. With the aid of simultaneous cinematographic records, these data a r e related to the temporal and physical events of t h e step cycle. The use of a treadmill for t h e study of quadruped locomotion provides for controlled stepping movements, but there are differences in some step cycle parameters of treadmill and overground locomotion (Wetzel e t al., '75). Extensive EMG studies of t h e hindlimb of dogs running on a treadmill, however, have been made by Tokuriki ('73a,b, '74) and Wentink ('76). Severin et al. ('67) described a n experimental preparation where stepping movements a t a variety of gaits could be sustained by continuous stimulation of t h e mesencephalon of decerebrate cats suspended over a moving treadmill. Gambaryan e t al. ('71) studied the EMG patterns for select hindlimb muscles in this mesencephalic preparation, and his work has become quite useful for t h e study of the neural control of locomotion (Herman e t al., '76; Shik and Orlovski, '76; Wetzel and Stuart, '76). Detailed comparisons of EMGs obtained under these conditions of locomotion to those from unrestrained animals, who have not undergone radical surgery, should be made so t h a t the possible EMG alterations resulting from treadmill running and radical preparation can be evaluated.

255

HINDLIMB ELECTROMYOGRAPHY

lower spinal angle, shown in figure lC,is that angle formed by the horizontal and a line from the crest of the ilium t o the tuberosity of the ischium. This angle decreases as the lower spine extends both in E3 and in the F phase of the gallop. The knee also continues to extend in the F phase of the gallop. This extension results from the continued backward motion of the leg following thrust-off a t the end of the previous E3. Throughout the rest of F the hip undergoes flexion, while the lower spine reaches a plateau of extension before commencing its own flexion. During E’ the hip remains relatively stable, while the lower spine begins its full extension. During E3 lower spine and hip are again in phase during a continued forceful extension. The EMG data, expressed as percentages of total stride time, for the walking, trotting, and galloping gaits are presented in table 1 and figures 2, 3, and 4. Table 1 contains muscle names and abbreviations and the numerS.D.) for the EMG data ical values (mean presented graphically in figures 2, 3 and 4. The data are shown with the ankle musculature a t the top of the figures because the actions of these muscles are least complex. This allows for a more direct and conclusive RESULTS discussion in preparation for the more compliThe EMG activity patterns observed in this cated situations encountered with the two study are interpreted with reference to the joint muscles of the knee and hip. The activity Philippson step cycle (’05). This step cycle is patterns of the muscles are presented in summarized in figure 1, and select joint angle figures 2, 3, and 4, with the ankle extensor changes are also presented in figure 1. The muscles listed as a group under that joint, joint angle data are from a previous study then the ankle flexor muscles, and so on. Some by Goslow et al. (’73) and the methods for muscles, such as the peroneal muscles and the measuring all the joint angles of concern are gluteal muscles whose actions are not so didescribed in that study. It is only necessary to rect, are placed between short horizontal lines repeat here the way the hip joint angles and in the left column in the figures. The large bar the lower spinal angles are measured. The hip represents the average activity interval for joint angle is measured between the intersec- each muscle. A standard deviation above and tion of two lines t o the hip pivot, one from the below the mean on-off time is shown by the knee pivot and the other from the tuberosity superimposed lines at the ends of the bars. The of the ischium. This angle thus increases as arrowhead above the bar indicates the point of the femur moves forward in hip flexion. For all foot contact in the strides. The point of foot speeds, figure 1 reveals movements of the contact presented for each muscle is an averknee and ankle joints that are in phase age value of foot contact for the strides studthroughout the cycle. The hip joint is largely ied for that muscle. The points of foot contact out of phase with the knee and ankle during are expressed as a percentage (*S.D.) of total stride time. El and E2, all three joints being in phase in F The data for the walking gait are presented and E3. E2 is characterized by flexion of the knee and ankle (the “yield”), which becomes in figure 2. The forward velocities a t this gait progressively more extensive from walking to ranged from 0.57 mhec to 1.25 m/sec. Data for galloping. In galloping the two hindlimbs semimembranosus anterior, semimembranomove with sufficient synchrony to reveal sub- sus posterior, and tensor fascia latae muscles stantial movements of the lower spine. The are not presented because there was no detec-

posterior curvature of the toes on the metatarsals a t the metatarsophalangeal joints. The frame of contact was taken as that frame where the animal first started to support its body weight. The criteria were that the plantar surface of the animal’s paw was clearly in contact with the supporting surface or that compression of the foot had occurred. The frame of contact designated simultaneously the end of the swing phase of a stride and the beginning of the stance phase. The stance phase was considered terminated a t lift-off of that limb, and the step cycle was then complete. A diagram of the phases of the step cycle relative to joint angle change during locomotion is presented in figure 1. The EMG data were converted from a n absolute time base t o a relative or percentage value so that the activity patterns of each of the discrete muscles during strides of variable duration could be collated. To do this, the total number of film frames in each stride was divided into the numerical value of the frame in that stride sequence when the muscle of concern either turned on or off. These fractions were then converted to percentages for presentation of data in figures 2, 3 and 4.

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' The data here are the numerical values (mean 2 S.D) for the EMG data presented graphically in figures 2, 3, and 4. This table should he used in conjunction with those figures. Absolute times were converted to relative or percentage values for each stride and then collated (METHODS). The number of strides analyzed is given for each muscle a t each gait in figures 2,3, and 4. Walking speeds ranged from 0.57 to 1.25m/s; trotting speeds, from 0.89 to 3.3 m/s; and galloping speeds, from 2.1 to 4.2 mis.

Hip Gluteus maximus Gluteus medius Gluteus minimus Adductor femoris Caudofemoralis Biceps femoris anterior Biceps femoris posterior Gracilis Semimembranosus anterior Iliopsoas Sartorius Tensor fasciae latae

Knee Vastus intermedius VI Active Vastus lateralis VL Active Vastus medialis VM Active Rectus femoris RF Active Semimembranosus posterior SMp Inactive Semitendinosus St Inactive

Ankle Flexor digitorum longus Flexor hallucis longus Lateral gastrocnemius Medial gastrocnemius Plantaris Soleus Extensor digitorum longus Tihialilis anterior Peroneus brevis Peroneus longus Peroneus tertius

Musculature

TABLE 1

4 7 2 7 -802 7

4 4 2 8 882 5 392 8 7928 35' 4 802 4 412 6 8325 382 8 8226 432 6 8729 402 5 7529 432 6 782 5 4 1 2 8 - 7 2 2 10

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Electromyographic activitypatterns of select cat hindlimb muscles duringposture and unrestrained locomotion

258

S. RASMUSSEN, A. K. CHAN AND G. E. GOSLOW, JR.

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Fig. 2 EMG activity patterns of cat hindlimb musculature during unrestrained walking. Data are from seven cats walking a t speeds ranging from 0.57 m/s to 1.25m/s. The three joints of major concern are the ankle, knee, and hip. Where appropriate in this figure, and figures 3 and 4, muscles are categorized as extensors and flexors about each joint. Muscles whose actions are not so stereotyped a t e delimited by horizontal lines. Those muscles spanning two or more joints are so indicated ( +). Muscle abbreviations are as in table 1. In order to collate the activity patterns of each of the discrete muscles during strides of variable duration, the EMG data were converted from a n absolute time base to a relative or percentage value. The number of strides analysed for each muscle is indicated on the right of the figure. The arrowhead above the bar indicates the point of foot contact in the strides. This is the average value for each muscle, and i t is expressed as a percentage point ( 2 S.D.) of total stride time. The large bar represents the average activity interval for each muscle. One standard deviation above and below the mean on-off time is given. There appears to be a general pattern of activity for t h e extensor muscles, regardless of which joint their primary action affects. These muscles are active during the stance phase and almost universally become active prior to foot contact. The general activity pattern for the flexors occurs during the early swing phase, but they all become active prior to foot lift-off a t the end of the stance phase.

259

HINDLIMB ELECTROMYOGRAPHY

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PERCENTAGE Fig. 3 EMG activity patterns of cat hindlimb musculature during unrestrained trotting. Data are from seven cats trotting a t speeds ranging from 0.89 m/s to 3.3 m/s. This figure is organized similar to figure 2. At increasing forward speed the total stride time is reduced, a t greatest expense to the stance phase. The relative percentage of extensor muscle activity prior to foot contact increases.

table electrical activity from these muscles during the walking gait. There appears to be a general pattern of activity for the extensor muscles of the ankle, the knee, and the hip. These extensor muscles are active during the stance phase and typically become active prior to foot contact. The general activity pattern

for the flexor muscles occurs during the early swing phase, but these muscles all become active prior to foot lift-off a t the end of the stance phase. The data in figure 3 for the trotting gait come from strides ranging in velocity from 0.89 m/sec to 3.3 m/sec. This gait appeared to

260

S. RASMUSSEN, A. K. CHAN AND G. E. GOSLOW, J R

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Fig. 4 EMG activity patterns of cat hindlimb musculature during unrestrained galloping. Data are from seven cats galloping a t speeds ranging from 2.1 m/s to 4.2 m/s. Activity patterns were taken from the lead leg of transverse and rotatory gallops. This figure is organized similar to figure 3.

be the preferred fast gait for the cats, and all of the muscles studied were utilized in this gait. Data for the galloping gait are presented in figure 4.Data are not easily obtained a t this gait as the cats, not forced to gallop as they might be on a treadmill, usually choose a fast trot rather than a galloping gait. The situation is also complicated by the possibility that the actions of specific hindlimb muscles may differ depending upon whether the limb is the lead or trailing limb (Tokuriki, '74). The criteria for a lead or trailing limb of a pair during galloping depend upon which limb strikes ahead of the other; the lead foot strikes more anteriorly, the trailing foot more posteriorly.

The data in figure 4 come from the lead foot for both the transverse gallop (lead foot of forelimbs the same as hindlimbs) and the rotatory gallop (lead foot of forelimbs opposite to lead foot of hindlimbs). The animals moved along the curved track from right to left with reference to the camera's view of the locomotion, and thus the animals turned slightly to their left as they galloped. This filming arrangement favored a left lead. Apparently, however, the implantation of certain limb muscles hindered this favored pattern, and the cats refused to lead with the implanted limb. Thus lead limb data for the peroneals, semitendinosus, caudofemoralis, and the gluteals are not available.

HINDLIMB ELECTROMYOGRAPHY

26 1

Perhaps this need to choose a lead for the gallop also influenced the cats to prefer the trotting gait. The velocities for the gallops, ranging from 2.1 m/sec to 4.2 m/sec, were not much greater than the velocities of the trot. This study recognizes the small sample of gallop strides and the limitations on interpretation that result. General comparisons of the muscular activity patterns during the three gaits of walk, trot, and gallop show that the duration of activity of the extensor muscles spanning each of the three studied joints decreases relative t o total stride time as the speed of locomotion increases and as the gaits change. The general pattern of onset of muscular activity during E' prior t o foot contact and continuation of activity during E2 and on into E3 remains the same in all three gaits, as does the pattern of cessation of activity prior to foot lift-off a t the end of the stance phase. Similar comparisons of the activity patterns during the three gaits of the flexor musculature spanning the respective three joints shows that the duration of flexor musculature activity relative to total stride time actually increases. Note especially that the hip flexor musculature, iliopsoas, sartorius, and tensor fasciae latae, shows appreciably greater periods of activity relative to total trotting or galloping strides than during walking strides. This relative increase is so great that the hip flexor muscles become active during almost all or all of the stance phase in the trot or gallop as compared to the walk. The hip flexor musculature even becomes active in the trot and gallop before the beginning of the stance phase, as designated by foot contact, and then the musculature remains active during the subsequent entire stance phase. More specific discussion of these observations and possible explanations or reasons for their occurence follow in the next section of this paper.

be remembered that the EMG patterns recorded during treadmill locomotion differ from overground locomotion, particularly for the muscles controlling the hip. Wetzel et al. ('75) studied cats walking and trotting on a treadmill and found that even though the total swing phase was similar in duration to that of the swing phase in overground locomotion, that F was relatively longer and that El was about 20%shorter. They also found that the knee began its extension earlier than the ankle a t the F.E1 junction; and that the stance phase was shortened, presumably a t the expense of E3. Their final conclusion was that the cats tended to crouch as they moved on the treadmill. There are limitations in the use of EMGs that must be recognized. Electrical activity in muscles indicates only that some fibers are active, but there is no direct relationship between the amplitude of the EMG and the force produced. Thus, i t is not possible to tell directly from EMG recordings what skeletal movements result from an associated muscular contraction. The interpretation of skeletal movements from t h e study of anatomy, kinematics, and EMGs is still a matter of judgment . An extensive baseline study of the EMGs for the unrestrained cat is not a t present available in any other one source. In an effort to increase the usefulness of these data for others, our discussion of the patterns of activity for each muscle and muscle group is detailed. I t is, however, acknowledged that this approach may lead to some repetition. The discussion following has been organized into three divisions centered on the activity patterns of the muscles that span the ankle, knee, and hip joints. Comparisons have been made among the EMG activities of the various muscles acting on the respective joints during the three gaits of walk, trot, and gallop.

DISCUSSION

Ankle The ankle extensors, flexor digitorum longus, flexor hallucis longus, lateral gastrocnemius, medial gastrocnemius, plantaris and soleus, exhibit EMGs in keeping with the traditional view of the action of these muscles during stepping (Engberg, '64; Engberg and Lundberg, '69; Gambaryan et al., '71; Tokuriki, '73a,b, '74).That is, these muscles become active prior to foot placement. This muscular activity corresponds t o the first extension phase (El) a s the animal reaches forward with

The EMG data presented here are considered from two viewpoints: (1) the relationship of the muscle activity patterns to movements of the hindlimb as events in the step cycle; and (2) a comparison of such data for unrestrained cats to similar studies of dogs moving on treadmills (Tokuriki, '73a,b, '74; Wentink, '76) and to studies of decerebrate cats moving on a treadmill (Gambaryan e t al., '71). For the purposes of this discussion, i t should

262

S. RASMUSSEN, A. K. CHAN AND G. E. GOSLOW, J R

the hindlimb in preparation for foot contact and the ensuing supportive and propulsive actions of the stance phase. The ankle extensors continue their activity during the yielding portion of the stance phase (E'),when the animal is supporting part of its body weight on t h a t limb. The ankle joint angle decreases somewhat (fig. 11, but the joint must not collapse if the animal is to support and prepare himself for t h e third and final propulsive extension of the limb. The yielding action, however, elicits elongating or eccentric contractions from the extensor musculature. As such, some of the energy from these eccentric contractions is stored in t h e elastic component of the muscles and tendons of the system. Subsequent use of this energy has been discussed and reviewed by Cavagna e t al. ('77). The extensor muscles undoubtedly produce propulsive force during t h e remainder of their contraction. The electrical activities of the extensor muscles cease, though, before the foot is actually lifted from t h e supporting surface. This suggests t h a t , at least for the slower gaits, the limb must be unloaded in preparation for recovery, and continued contact with the supporting surface is due largely to momentum of t h e limb in t h e direction of extension. The ankle flexor muscles become active in E3, and this activity continues through F of the swing. This suggests t h a t the flexor muscles slow the extension movement of the ankle and then continue to contract in order to change the direction of motion of the foot. During the walk, flexor activity begins slightly after the extensor muscles cease to contract. At faster forward speeds, however, there is increased activity overlap in E3 of the ankle flexors and extensors. It is apparent t h a t the relative duration of activity of the ankle extensor muscles decreases as the speed of locomotion and gait change from walk, to trot, to gallop. The most striking comparison, of course, is between walking and galloping. The ankle extensor muscles contract during almost half of the step cycle in the walking gait. During the gallop, however, these muscles are contracting during only a third or so of the duration of the step cycle. This is due perhaps to t h e greater decrease in the duration of the stance phase, with which extensor musculature activity is associated, relative to the duration of the swing phase as t h e speed of locomotion in-

creases and the gait changes from walk, to trot, to gallop (Arshovskii e t al., '65; Goslow et al., '73). The activities of t h e extensor muscles are associated with the stance phase. Gambaryan e t al. ('71) have reported similar observations from mesencephalic cats. Tokuriki ('73a,b, '74) does not speak directly to this point, but extrapolation from the data in his figures and tables for gastrocnemius and flexor digitorum supports this concept. In the trot and gallop there is overlap in the EMGs of the extensor and flexor muscles of the ankle in E3. There could be several reasons for this. The change in the direction of motion of t h e limb must be accomplished more abruptly in these gaits, because the step cycle frequency increases and the step cycle duration decreases (Howell, '44; Gray '68). Thus the flexor musculature activity in E3 represents eccentric contractions which load the muscles with elastic energy to facilitate the rapid flexion of t h e ankle during the subsequent F phase. The limbs also move with greater velocities and possess more inertia a t the trot and gallop than a t the walk. Therefore, t h e muscular contractions necessary to supply t h e decelerating a n d accelerating forces requisite to changes in direction of motion of t h e limb would have to anticipate t h e kinematic changes more a t these gaits t h a n at the slower walk. The mechanical factors of limb motion, such as velocity and inertia, when coupled with intricate coordinations of the applied forces, have the effect of smoothing out the transition from stance to swing phases. The supporting limbs have to be kept in a more rigid state because there are only two limbs supporting the animal much of the time in these two gaits. This creates problems of motion control which may demand more precise limb positioning. During quiet standing, flexor digitorum longus is always active, while the activity of flexor hallucis longus is variable. In addition to ankle extension, these muscles serve as the primary physiological extensors of the digits. Flexor hallucis longus is t h e stronger of the pair (Goslow et al., '72). During standing, the soleus muscle shows marked activity. Activity is also consistently recorded a t this posture from the other two primary ankle extensors, lateral gastrocnemius and plantaris. Medial gastrocnemius may or may not be active during standing. This may be determined by t h e position of the center of gravity in various postures, or it may be

HINDLIMB ELECTROMYOGRAPHY

due t o the degree of stability of the animal in various standing positions. During walking, soleus begins its activity much earlier and anticipates foot placement more than the other ankle extensors. A t the two faster gaits, however, the gastrocnemius pair preempts soleus' activity. These findings are consistent with our knowledge of the motor unit populations for these three muscles in which soleus appears to be primarily designed for postural and slow gaits and the gastrocnemius muscles for phasic events (Betts et al., '76; Burke and Edgerton, '75). The activity patterns presented here for these ankle extensors contrast with those of Gambaryan et al. ('71) for the mesencephalic preparation. His data reveal simultaneous activation of the four muscles during walking and galloping and simultaneous cessation of activity, with the exception of soleus which turns off sooner a t both gaits. Our data for the unrestrained animal reveals activity patterns which are much more variable, one muscle to the other, particularly a t the faster gaits. Unlike Prochazka et al. ('741, we did not see soleus activity during F of the walk. EMG data for the peroneal muscles, peroneus brevis, longus and tertius, were available in this study for standing, walking, and trotting. All these muscles are active during standing. During locomotion, the peroneals appear to follow a pattern of activity like that of the extensors. This requires some explanation, since this is contradictory to the traditional function ascribed to these muscles. The peroneus brevis and tertius tendons of insertion pass through a canal formed by a groove posterior on the lateral malleolus of the fibula and a ligament that transversely spans that groove. This canal acts as a pulley to change the direction of pull of the contracting muscles. Since this canal and, therefore, the line of pull of the two peroneal muscles lies caudal to the axis of the ankle joint, i t would appear that the muscles would have an extension action on the ankle joint. This role is not always the role proposed for the muscles in anatomy texts. Crouch ('691,for example, indicates that peroneus brevis is a n extensor of the foot, while peroneus longus and peroneus tertius muscles are flexors of the foot. Our view, however, is that the functional anatomy of the passage of peroneus brevis and tertius tendons of insertion through the canal would cause these two muscles to extend the foot. This point was studied by separate, direct

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stimulation of the three peroneal muscles which were exposed by dissection of a n anesthetized cat. This direct stimulation, where there could be no doubt that the stimulated muscles were in fact the peroneal muscles, elicited a weak foot extension response from peroneus brevis and an almost negligible foot extension response from peroneus tertius. Peroneus longus was a fairly strong foot flexor. These observations lead us to conclude that the peroneus brevis and tertius muscles are active during the stance phase to serve as synergists to the other ankle extensor muscles. The peroneal muscles may also help to stabilize the ankle, as they all are in a functional position lateral to the flexion-extension axis of the ankle joint. This stabilizing action is especially plausible for peroneus longus, where the action is foot flexion but where the EMG activity during the step cycle fits an extensor pattern. It should be noted that Engberg ('64) describes an ankle flexor pattern for peroneus longus in contrast t o the extensor pattern seen here. The ankle flexor muscles, tibialis anterior and extensor digitorum longus, are not active during standing and exhibit EMG activity during locomotion that is antagonistic to the extensor muscles. These muscles become active before foot lift-off in E3. As discussed in the preceding paragraphs, this action presumably slows the limb's excursion in extension and changes the direction of ankle movement to one of flexion after the foot has been lifted from the supporting surface. Further, these muscles are associated with the swing phase of a step cycle, when the limb is recovered and the ankle flexed to clear the terrain and to protract the limb forward leading into the next stride. Since the major decrease in step cycle duration as the animal progresses to faster gaits comes from a reduction in the stance phase, it follows that the flexor muscles active during the swing phase would assume a greater proportion of total stride duration. The extensor digitorum longus muscle shows two bursts of activity during galloping. One of these bursts begins during the end of E3 and is carried on through F. This activity occurs as the ankle flexes in protraction of the limb and as physiological flexion of the digits is initiated to allow clearance of the supporting surface. This first burst stops early in the swing phase, and then a second burst occurs.

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The knee extensor muscles cease their activities before the foot is lifted from the supporting surface a t the end of the stance phase. This occurs in all knee extensor muscles at all gaits, except rectus femoris during the gallop. The general view of cessation of activity before foot lift-off is t o allow unloading of the limb prior t o initiation of the swing phase. The knee flexors, semitendinosus and semimembranosus posterior (caudal), show variable activity depending on the gait and forward speed. Thus no "typical" pattern can be described. The vastus complex of muscles shows strong activity during standing, while rectus femoris is only moderately active during this posture. During the gallop, rectus femoris shows an activity pattern which continues through the entire stance phase and on into the swing phase. This contrasts with the general knee extensor pattern described above. Rectus femoris spans two joints, the hip and the knee, while the other muscles categorized as knee extensors in this study cross only the knee. The knee extension action of rectus femoris might be a necessary synergistic action t o the other knee extensor muscles a t all gaits, but the hip flexion action may be unnecessary a t walking and trotting gaits. During galloping, however, the animal may find i t necessary to supplement the actions of other hip flexors by soliciting continued use of rectus femoris from the E3 of the stance phase into F of the subsequent swing phase. That the knee was going Knee through a flexion movement as the rectus The knee extensors studied included rectus femoris was active would not necessarily profemoris, vastus intermedius, vastus lateralis, hibit a hip flexion action for the muscle. Flexand vastus medialis muscles. Their EMG ac- ion of the knee would elongate the muscle, but tivity patterns showed that they are active flexion of the hip would shorten the muscle. during the step cycle a t the same time as the The net result would be that the muscle conankle extensor muscles. The knee and ankle tinues to operate a t nearly the same length, joint movements as depicted by changes in which would be close perhaps to its physiologijoint angles are very much in phase through- cal optimum length (Goslow et al., '73). No apparent differences exist among the out the entire step cycle in the walk, trot and gallop (Engberg and Lundberg, '69; Goslow et EMG patterns described here for the vastus al., '73). The activities of the knee extensors muscles and those of the other EMG studies. would be expected, therefore, to be in phase In contrast to our typical knee extensor patwith the actions of the ankle extensors tern for rectus femoris during the walk and trot, however, Tokuriki ('73a,b) and Wentink throughout the step cycle in the three gaits. The knee extensor muscles become active ('76) described a concentration of activity a t just before the animal puts his foot down a t the F aEl junction in the swing and again in E3 the beginning of the stance phase. They con- of the stance. Recall that, for the treadmill tinue to be active during the yielding stage of walk and trot, knee extension occurs earlier the stance phase for the same reasons that than ankle extension a t the F.E' junction. were presented in the discussion of the actions The isolated burst of rectus femoris a t this junction is probably responsible for this moveof the ankle extensor muscles.

That this sequence of actions for extensor digitorum longus muscle occurs only during the gallop might be related to the increased power of muscular action a t this gait. The action of extensor digitorum longus during walking and trotting may not be so powerful that i t would pull the digits into a pronounced extension; therefore, the activity can continue through the entire swing phase. In the gallop, however, the action of extensor digitorum longus during the initial flexion of the ankle may be so powerful that, were i t to continue, the digits would be drawn in to a pronounced extension. The second burst of activity occurs in E' and, as in the walk and trot, is simultaneous with activity of flexor digitorum longus and flexor hallucis longus to stabilize the digits prior t o foot placement. Data presented here for extensor digitorum longus and tibialis anterior are similar to that of Engberg ('64). The data from Tokuriki's ('73a,b, '74) and Wentink's ('76) work with dogs as they walked and trotted on a treadmill showed no late E3 activity. In their kinematic comparison of overground versus treadmill locomotion in cats, Wetzel et al. ('75) found a reduced stance phase during walking and trotting for the treadmill animals. The stance phase on a treadmill may, therefore, be over before the EMG activity of the ankle flexors is initiated. For the mesencephalic preparation ankle flexor activity does not continue through El in either the walk or the gallop.

HINDLIMB ELECTROMYOGRAPHY

ment in dogs, but t h e necessity for early knee extension is not clear. For the gallop, Tokuriki ('74) describes a hip flexion pattern, where we see a pattern suggesting a combination of hip flexion-knee extension. For t h e mesencephalic preparation Gambaryan e t al. ('71) also described late E3 activity for both the walk and gallop and described early F activity in t h e walk suggestive of hip flexion. The late E3 early F burst seen by these investigators may relate to t h e lengthening of rectus femoris during E3 (Gambaryan e t al., '71) and t h e dynamics of treadmill locomotion. In contrast to Engberg and Lundberg ('691, we found no differences between the proximal and the distal portions of rectus femoris for any of the studied gaits. Semimembranosus posterior and semitendinosus a r e t h e only two muscles whose EMG activities fit a knee flexor pattern. Neither of these muscles is active during standing. There are several other two-joint muscles, biceps femoris posterior is a n example, whose anatomical position would suggest a knee flexion action (Crouch, '69). The data in the present study do not show t h a t these other muscles are active during t h e time period in t h e step cycle when knee flexion is occurring. Semimembranosus posterior was essentially inactive during t h e walking gait. Activity for this muscle during the trot shows two bursts: one during t h e swing phase and one during the stance phase. The activity during the swing phase can be associated with knee flexion. That the muscle would be active at this time in t h e trot, and not in the walk, could be explained by t h e relative momentums of the shank in the two gaits. The shank would develop very little momentum in a caudal direction during t h e stance phase of a walking step. I t would carry on to a position only slightly caudal to the terminal stance position before t h e hip would begin a flexion movement to recover the limb forward in swing phase. This hip flexion action would draw the shank forward with very little effort required from the knee flexor musculature to maintain adequate clearance of t h e supporting surface. In t h e trot, however, t h e shank possesses more backward momentum at the beginning of t h e swing phase. This backward momentum carries t h e knee through a few more degrees of flexion than is t h e case in the walk (Goslow et al., '73). The shank is now in a position where aid is required from knee flexor musculature in order to hold the shank up against the force

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of gravity while the limb is brought forward in preparation for extension into the next stance phase. The second burst of EMG activity for semimembranosus posterior observed a t the trotting gait occurs during the stance phase. This activity is associated with hip extension. The muscle thus performs two actions, knee flexion and hip extension, but at different time periods in the trotting step cycle. The EMG during the gallop from semimembranosus posterior is continuous as one period of activity, from the last part of t h e swing phase overlapping into t h e stance phase. This continuous activity may be due in part to t h e addition of lower spinal movements to the locomotor sequence of limb movements at the galloping gait (Peters and Rick, '77). The cat, when i t gallops, utilizes a lower spinal movement t h a t draws t h e pelvic girdle forward in the swing phase. This spinal flexion allows t h e hindlimbs to advance a greater distance before foot strike t h a n would be the case were t h e spine held straight (Hildebrand, '59). At foot strike and on through the propulsive stance phase, t h e lower spine extends until the animal leaps into the airborne portion of a galloping stride. The semimembranosus posterior muscle may aid in the spinal flexion portion of t h e swing phase. If the semimembranosus posterior muscle is contracted as the hindlimb is brought forward in swing phase by t h e hip flexors, semimembranosus will hold the femur to the pelvic girdle and cause the femur and the pelvis to operate as one unit. The abdominal musculature will actually flex t h e lower spine while t h e hip extensor muscles, like semimembranosus, bring t h e posterior pelvic girdle forward by anchoring i t to t h e moving femur. The continuous activity of semimembranosus posterior muscle through t h e initial portion of the stance phase during the gallop conforms to the more conventional function of hip extension. This is a powerful action, as t h e animal literally launches himself with his hindlimbs into t h e airborne portion of a galloping stride. Semitendinosus muscle exhibits two EMG activities during both the walking and the trotting gaits. One of these periods of activity begins during t h e last part of t h e stance phase and continues into the first part of t h e swing phase. This is t h e conventional pattern of flexor activity, and i t appears t h a t semitendinosus is active a t this time as a knee flexor. This action from semitendinosus appears to be

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unaided by other muscles in the walk and would be of continued importance in the trot, even though semimembranosus posterior acts synergistically. The second EMG activity pattern for semitendinosus occurs during the last part of the swing phase and continues into the first part of the stance phase a t both the walking and trotting gaits. This action generates hip extension, but semitendinosus does not appear t o continue to be active through as much of the stance phase as other hip extensor muscles. Perhaps this is due to the two joint actions of semitendinosus. Tension from semitendinosus might be necessary synergistically as a hip extensor in preparation for foot strike and in the early stance phase, when the animal's hindlimb yields under the load of part of its body weight; but continued action of semitendinosus during more of the stance phase could be undesirable because i t might cause knee flexion. Other hip extensor musculature, such as adductor femoris, caudofemoralis, and biceps femoris, may be more ideally situated to continue hip extension during the latter portions of the stance phase. Data were not available in this study for semitendinosus of the lead leg during the gallop. Data for the trailing leg, however, reveal an E'-E2 period of activity, as in the trot, in addition to a late E3 period of activity. If the EMG patterns of the lead and trailing leg do not differ to a marked degree (Tokuriki, '741, the function of semimembranosus is consistent for the three gaits. Evidently, neither Tokuriki ('73a,b, '74) nor Gambaryan et al. ('71) recorded activity from semimembranosus posterior. Engberg's and Lundberg's recordings from this muscle a t any given gait reflect variability between cats (fig. 7: Engberg and Lundberg, '69). The gallop profiles from Engberg's work agree with ours, as do some strides for the trotting gait. Relative to semitendinosus, Wentink's ('76) data resemble ours for the walk, whereas Tokuriki ('73a,b) sees a flexor pattern only a t the walking and trotting gaits. Our data for this muscle a t all gaits are similar to that of Gambaryan et al. ('71) and Engberg ('64). Hip The gluteal muscles, gluteus maximus, gluteus medius, and gluteus minimus, are grouped in figures 2 and 3. These muscles run from the ilium to the greater trochanter of the femur and are viewed traditionally as hip ex-

tensors, with the exception of gluteus minimus, which is usually considered a lateral rotator of the femur. During standing, gluteus maximus and medius show moderate activity, while gluteus minimus shows no activity. Data for these muscles during the gallop were not available. The EMGs of the gluteal muscles all fit the extensor pattern. The muscles are active during the support phase in both walk and trot. The gluteal muscles are ideally situated to function as hip joint stabilizers. During the stance phase, the animal's weight carried on the supporting limb would cause the pelvic girdle to sag away from the supporting limbs. This tendency could be counteracted by contraction of the gluteal muscles, which would then hold the pelvic girdle and the supporting limb in a more rigid alignment. The gluteal muscles are anatomically positioned to offer thigh abduction, or they generate pelvic girdle lateral rotation if the thigh is fixed and immovable in abduction, as it is when the limb is supporting the animal's body. This stabilizing action during the walk would not have t o be very powerful nor of very long duration, since the animal supports himself simultaneously on three limbs so much of the time and moderate muscular actions appear adequate. Electrical activity of the gluteal muscles begins well before foot contact in the trot. This may be due to the need for powerful thigh extension and hip joint stabilization in the trot, and the gluteal muscles are solicited t o aid in these functions. Since the animal supports himself on only two limbs a t a time in the trot, the stabilizing action would need to be more extensive than in the walk in order to counteract the more pronounced loading of each limb. The muscles of this complex studied by Tokuriki ('73a,b, '74) are gluteus medius and apparently gluteus maximus, while Wentink ('76) studied gluteus medius. Their data for all three gaits reflect a typical extensor pattern similar to ours. The data from the study by Gambaryan et al. ('71) on gluteus medius show a flexor pattern a t both the walk and gallop. This contrasts with the results of the previously cited studies and ours, but no explanation, beyond the possible influences of the mesencephalic preparation, can be offered. The hip extensor muscles studied included adductor femoris, biceps femoris anterior, biceps femoris posterior, caudofemoralis, gra-

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cilis, and semimembranosus anterior. These tional hip extensor pattern where contraction muscles, for the most part, behaved in all gaits of the muscle during El and EZhelps to extend according to a common extensor activity pat- the hip as the animal propels itself forward. It tern. They generally became active near the might be expected that the anterior portion of end of the swing phase, when the first exten- the muscle would be active only as a hip extension of the limb occurs in preparation for foot sor because of its separate insertion on the femoral epicondyle. The burst of activity by contact. The muscles remain active during E' as the animal supports part of his body weight semimembranosus anterior during F, howon that limb. Like the ankle and knee exten- ever, is puzzling. Perhaps the insertions of the sors, the hip extensor muscles cease their ac- anterior and posterior heads of semimemtivity prior to foot lift-off. branosus are not as functionally distinct as The hip flexor muscles studied include ilio- has been proposed. If the insertions coalesce, psoas, sartorius, and tensor fascia latae. In then tension from the anterior head could aid general, these muscles are active during F the knee flexion action of the posterior head and E3 of the step cycle. As forward speed in- by drawing the tendon of insertion more creases, however, additional activity during toward the femur, using the femoral epiconE' and E2 is evident. As the cat converts from dyle attachment as a fulcrum. The other two single joint hip extensors, the walk, to trot, to gallop, the relative extent of activity overlap during the stance phase be- adductor femoris and caudofemoralis, are intween the hip extensors and hip flexors in- active during standing. Lead leg data for creases. This may be necessary to keep the caudofemoralis during the gallop are unavaillimbs in a more rigid state because there are able; however, data from the trailing leg periods in trotting and galloping where only reveal a typical hip extensor pattern. This pattwo limbs support the animal. A second tern is consistent for both muscles a t all forreason may be that the change in the di- ward speeds. The hip flexor, iliopsoas, shows no activity rection of motion of the limb must be quicker a t increasing speeds. Since the kinetics of the during standing. In walking, this muscle is muscular actions involved in these directional active during F and late E3. In the gallop, this changes must deal with greater velocities and muscle becomes active sooner in the extension inertias a t the faster gaits, an anticipatory of the limb. The activity in late El and E2 may coactivation may be necessary. The marked relate to hip and leg stabilization explained overlap of extensor and flexor activity in the above. No activity of the two-joint hip flexors, sargallop may reflect the need for hip joint stability a t this gait when lower spine action torius and tensor fascia latae, is seen during standing. Further, tensor fascia latae is inaccontributes t o locomotion. Biceps femoris anterior, biceps femoris pos- tive during walking. Sartorius and tensor terior, and gracilis are inactive during quiet fascia latae can be considered two joint musstanding. During locomotion, the activity pat- cles because both of them arise from the ilium tern differences between the anterior and pos- and eventually insert on the patella and tibia. terior heads of the biceps are negligible. This The insertion of the sartorius muscle is rather was determined by both simultaneous and direct; but the insertion of the tensor fascia independent recordings from the two heads. In latae muscle is more indirect, in that i t inserts the walk, we could see a slight burst of activ- on the fascia latae of the thigh, which in turn ity in the late E3 and early F for biceps femoris extends to the patella. The result is that both posterior, but these data are not presented in muscles could have action on both the hip and the figures because their signal to noise ratio the knee. The sartorius, like iliopsoas, shows a was not adequate. This activity could relate to typical hip flexor pattern in the walk and inknee flexion, but, in our view, by far the domi- creased activity during the stance phase of the nant activity pattern for both heads reflects a trot and gallop. Tensor fascia latae shows hip extension function. Gracilis also shows a slight variation from the other hip flexors in hip extensor pattern a t all gaits, being active that two periods of activity are seen during the stance phase of the trot. in El and the stance. The increased activity of sartorius and tenSemimembranosus anterior is inactive during standing as well as walking. During the sor fascia latae during the stance phase of the trot two bursts of activity are seen. The second trot and gallop may relate to their knee extenburst, according to our data, fits the tradi- sion function. The time in the step cycle when

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these two muscles become active approaches the time when the more conventional knee extensors, like rectus femoris and the vastus muscles, become active. Sartorius and tensor fascia latae may be recruited in response to a need for more knee extension power in t h e trot and gallop, but this would be a n intricate maneuver because of the possibility of also eliciting a n unwanted hip flexion action. Special note of the inactivity of hip extensors and hip flexors, except gluteus maximus and gluteus medius, during quiet standing should be made. This reflects the balance achieved in positioning the axial skeleton over the four limbs at this posture. Our data show t h a t the hindlimb is held rigid at the metatarsophalangeal, ankle, and knee joints during standing. If a similar situation exists for the forelimb, though i t is recognized t h a t t h e skeletal structures are not the same, then t h e four limbs would exist as rigid appendages over which the axial portion of the body is bridged. Whatever stabilizing action of the hips is necessary to hold this position must be offered by joint structures other t h a n muscle or by smaller muscles of the hip t h a t were not investigated in this study. In contrast to our and Wentink's ('76) El-E' activity for adductor femoris in the walk, Tokuriki ('73a) reports only El activity. For the other two gaits, however, our data are in agreement for this muscle. Tokuriki ('73a,b, '74) does not clarify whether his biceps femoris data are from t h e anterior or posterior head; but, with the exception of a small burst in F of his data for the gallop, our data a r e in agreement. Wentink ('76) and Gambaryan e t al. ('71) looked at the activity of the two heads separately. Their p a t t e r n for t h e biceps femoris anterior is like ours, but they show a knee flexor pattern for the posterior head during the walk and gallop. Apparently t h e gracilis turns on and turns off slightly earlier in the treadmill dogs than in t h e overground cats studied here. Differences exist between Tokuriki's ('73a,b, '74) activity patterns for semimembranosus and our patterns for t h e anterior and posterior heads. Whereas he shows a n El and early E' burst for t h e trot, we show two bursts, a n F and a n E'-EZ. His data for t h e gallop show two bursts of activity, one at the E3.F junction and one a t t h e El. E2 junction. We see a single burst during El and early E2 suggestive of his walk and trot pattern. Within the hip extensors, then, major differences between Tokuriki's data and our own relate to

t h e activity patterns of semimembranosus. Gambaryan's e t al. ('71) data for the hip extensors are in agreement with our own, with the exception of a knee flexor pattern seen for biceps femoris posterior and gracilis during the walk. Engberg ('64) reports a pure hip extensor pattern for semimembranosus anterior during t h e walk and trot and a knee flexor activity pattern for biceps femoris (head not specified: Engberg and Lundberg, '69). Differences between Tokuriki's ('73a,b, '74) iliopsoas data and our own are in the gallop. He reports almost continuous activity with the exception of brief periods a t the F. E' and E2.E3 junctions. This contrasts with our general pattern of activity during early F and late El, E', and E3. His data for sartorius during the walk and gallop reflect a flexor pattern with t h e muscle active in late E3 through F. In the trot, sartorius is active continuously in F and El. Gambaryan's e t al. ('71) data for the iliopsoas and tensor fascia latae differ from ours only in t h e gallop. For this gait, the two muscles do not show the E' and E2 activity seen in our figures. His data and ours for sartorius are in agreement. No differences between the data presented by Engberg ('64) for iliopsoas and sartorius and ours are apparent. I t is evident that, within the muscles controlling the hip, t h e activity patterns seen a r e quite variable among t h e experimental situations compared. The hip muscles are responsible for directly tying the mechanical function of the limb to the trunk and, as such, their activity patterns a r e subject to a variety of postural subtleties. Specific reasons for the variation in these muscles from preparation to preparation are not readily apparent, but i t does serve to emphasize the dynamics of muscle interaction during locomotion. I t should be noted t h a t within our own series of measurements, as well as those of others (Engberg and Lundberg, '69; Prochazka e t al., '74), activity pattern differences were frequently seen from stride to stride. Though our data treatment tends to smooth these differences out, we must not forget their existence. I t becomes apparent t h a t the most tightly controlled experimental situation for stepping (Gambaryan e t al., '71) results in t h e most sharply defined patterns of flexion and extension in the hindlimb. In the unrestrained animal, however, the "facultative" nature of limb movement and stepping (Wetzel and Stuart, '76) is manifest most sharply by those complex muscles associated with t h e knee and hip.

HINDLIMB ELECTROMYOGRAPHY ACKNOWLEDGEMENTS

This work was supported by the Organized Research Committee, Northern Arizona University. We would like to thank L. Coss and D. Wright for their technical assistance. We would also like to thank E. C. Frederick, R. Hardwick, J. Hermanson, J. Larsen, and R . Gallagher for their useful suggestions for improvement of t h e manuscript. LITERATURE CITED Arshavskii, Y. I., Y. M. Kots, G. N. Orlovskii, I. M. Rodionov and M. L. Shik 1965 Investigation of the biomechanics of running by the dog. Biofizika, 10: 737-746. Betts, B., J.L. Smith, V. R. EdgertonandT. C. Collatos 1976 Telemetered EMG of fast and slow muscles in cats. Brain Res., 11 7: 529-533. Burke, R. E., and V. R. Edgerton 1975 Motor unit properties and selective involvement in movement. In: Exercise and Sports Science Reviews. Vol. 111. J.H. Wilmore and J. F. Keogh, eds. Academic, New York, pp. 33-81. Cavagna, G. A., N. C. Heglund and C. R. Taylor 1977 Walking, running and galloping: mechanical similarities between different animals. In: Scale Effects in Animal Locomotion. T. J.Pedley, ed. Academic, London. Chan, A. K., S. Rasmussen and G. E. Goslow, Jr. 1977 A simple technique for correlating EMG signals with film for locomotion studies. Behav. Res. Meth. Instrumen., 9: 377-378. Crouch, J. E. 1969 Text-Atlas of Cat Anatomy. Lea and Fehiger, Philadelphia Engberg, I. 1964 Reflexes to foot muscles in the cat. Acta Physiol. Scand., 62 (Suppl.): 235. Engherg, I., and A. Lundberg 1969 An electromyographic analysis of muscular activity in the hind limb of the cat during unrestrained locomotion. Acta Physiol. Scand., 75: 614-6330, Gamharyan, P. P., G. N. Orlovskii, T. G. Protopopova, F. V. Severin and M. L. Shik 1971 The activity of muscles during different forms of locomotion in the cat and adaptative changes of the locomotor organs in family Felidae. Trudy Zool. Inst. Akad. Nauk., (USSR),48: 220-239. (In Russian). Gans, C. 1966 An inexpensive arrangement of movie

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The cat step cycle: electromyographic patterns for hindlimb muscles during posture and unrestrained locomotion.

The Cat Step Cycle: Electromyographic Patterns for Hindlimb Muscles during Posture and Unrestrained Locomotion S. RASMUSSEN,' A. K. CHAN2.4AND G. E. G...
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