JOURNALOF NEUROPHYSIOLOGY Vol. 54, No. 5, November 1985. Prinwd
in U.S.A.
Contrasting Roles of Inertial and Muscle Moments at Knee and Ankle During Paw-Shake Response M. CT. HOY,
R. F. ZERNICKE,
AND
J. L. SMITH
Laboratory of NeurmnotorControl, Departmentof Kinesidogy, University of Cal$ornia, Los Angeles, CaZ$ornia90024
SUMMARY
AND
CONCLUSIONS
1. Intralimb kinetics of the paw-shake response(PSR) were studied in four spinal, adult cats. Using rigid body equations of motion to determine the dynamic interactions between limb segments,knee and ankle joint kinetics were calculated for the steady-state cycles as defined in the preceding paper (22). Hindlimb motion was filmed (200 frames/s) to obtain knee and ankle kinematics. Responsesof flexors and extensors at both joints were recorded synchronously with cinefilm. 2. Ankle and knee joint kinematics were determined from 5 1 steady-state cycles of 16 PSRs. Average maximum displacements, velocities, and accelerations were substantially greater for the ankle than for the knee joint. Knee and ankle motions were out of phasein the first part of the cycle; knee extension occurred simultaneously with ankle flexion. In the second part of the cycle, motions at the two joints were sequential; rapid knee flexion, accompanied by negligible ankle displacement, preceded rapid ankle extension with minimal knee displacement. 3. At the ankle joint, peak net moments tending to cause flexion and extension were similar in magnitude and determined primarily by muscle moments. Moments due to leg angular acceleration contributed significantly to an extensor peak in the net moment near the end of the cycle. Other inertial and gravitational moments were small. 4. At the knee joint, net moments tending to cause flexion and extension were also similar, but smaller than those at the ankle. The knee muscle moments, however, were large and counteracted large inertial moments due to paw angular acceleration. Also, moments 1282
due to leg angular acceleration and knee linear acceleration were substantial and opposite in effect. Other inertial and the gravitational moments were negligible. 5. Muscle moments slowed and reversed joint motions, and active muscle force components of muscle moments were derived from lengthening of active musculotendinous units. Segmental interactions, in which proximal segment motion augmented distal segment velocity, increased the effectiveness of PSR steady-state cycles by facilitating the generation of extremely large paw linear accelerations. 6. Limb oscillations during PSR steadystate result from interactions between muscle synergies and motion-dependent limb dynamics. At the ankle, muscle activity functioned to control paw acceleration, whereasat the knee, muscle activity functioned to control leg and paw inertial interactions. Data from our kinetic analyses are compatible with the notion that for PSR steady-state, the output from the pattern generator to ankle muscles may be programmed without regard to limb dynamics, whereas at the knee, motion-dependent feedback may assumea high priority in the recruitment of knee extensors, since muscle moments at the knee are necessaryto counteract large segmental interactive moments, INTRODUCTION
In the preceding paper (22), we show that the paw-shakeresponse(PSR), a behavior that functions to remove an irritant from a cat’s paw, is characterized by unique, mixed (flexorextensor) muscle synergiesand corresponding hindlimb displacements.In PSRselicited from
0022-3077/85 $1 SO Copyright 0 1985 The American Physiological Society
DIFFERENTIAL
CONTROL
spinal cats held with hindlimbs pendent, a region of “steady-state” or constant-amplitude hindlimb oscillations typically emerges during the middle four to five cycles of the response (see Fig. 6 of Ref. 22). Hindlimb trajectories during steady-state are determined not only by forces resulting from muscle contractions but also by motion-dependent (inertial) and gravitational forces acting on limb segments. It is not known how muscular and nonmuscular determinants of limb dynamics contribute to hindlimb trajectories during steady-state oscillations. Therefore, the purpose of our present study was to detail the interaction between muscle and inertial moments at the knee and ankle joints. Dynamics of the cat hindlimb, a multilinked, rigid body system, are interactive, and the motion of one limb segment (e.g., the paw) influences the motion of the leg, while at the same time the leg influences the motion of the paw. Inertial moments can be significant in determining the motion of non-weight-bearing, multisegmented limbs (6, 7, 17, 20), and during high-velocity limb movements such as PSR, the influence of motion-dependent moments may be especially pronounced. Previous studies have demonstrated that muscle activity patterns are related to interactive, inertial moments generated during reaching tasks in humans (12) and in the swing phase of locomotion in cat (7). Using Newtonian methods that are common to inverse dynamics (7,20), we quantified the joint moments for knee and ankle during steady-state cycles. Net moments were partitioned into three categories (muscle, motiondependent, and gravity) and were related to the joint kinematics and muscle activities. We show that muscle moments dominate at the ankle, whereas at the knee, muscle moments counteract large inertial moments produced particularly by paw acceleration. This knowledge of intralimb kinetics during PSR steadystate cycles suggests different roles for motiondependent feedback at the two joints. A brief account of this study has been published (9). METHODS
Preparation
and testing
Subjects were four spinal, adult cats (3.2 * 0.6 kg) that achieved PSR steady-state oscillations as determined from kinematic records (22). The cordotomy (T12) procedure and care of spinal cats are
OF
KNEE
AND
ANKLE
described in previous reports (2 1, 23). Testing was conducted 3-6 mo after spinalization. To assess muscle activity at the ankle and knee, tibialis anterior (TA), lateral gastrocnemius (LG), and vastus lateralis (VL), in all cats, and biceps femoris (BF) in two cats, were recorded and analyzed according to techniques reported in the preceding paper (22). Before each filming session, the implanted hindlimb was shaved, and black-and-white markers (12 mm diam) were glued on the skin overlying the iliac crest of the pelvis, greater trochanter of the femur (hip), lateral malleolus of the fibula (ankle), and the fifth metatarsophalangeal joint. Cat weight and hindlimb segment lengths were measured. PSRs were tested with the trunk of the spinal cat held vertically with hindlimbs pendent (see Fig. 3). Responses were filmed using a pin-registered 16 mm camera (Photosonics 1PL) positioned with optical axis perpendicular to the movement plane of the hindlimb. Camera speed (200 frames/s) was verified by a pulse-generating microprocessor that activated interna timing lights of the camera. EMG and pulse data were recorded synchronously onto FM tape.
Assessment of limb kinematics Cartesian coordinates of iliac crest and hip, ankle, and metatarsophalangeal joint centers were obtained by digitizing serial film frames projected onto a rear projection screen mounted with a sonic digitizer (Graf Pen GP-3), which was interfaced to a minicomputer (DEC i l/23). Knee joint location was determined analytically (4) because motion of the skin overlying the knee prevents accurate determination of the knee joint center from a skin marker. Limb position-time data were calculated from the digitized coordinates. Kinematic data were smoothed, and derivatives were computed by use of the optimally filtered Fourier series method described by Hatze (5). Only trials in which limb motions remained reasonably parallel to the film plane were analyzed. Planarity was calculated from the difference between the directly measured paw length and that same length calculated from film data; a maximum of 10% discrepancy was permitted. Knee and ankle angles were computed for each PSR. Leg and paw angular data, and knee translational data, required as input for the kinetic analysis, were computed for all steady-state cycles.
Assessment of limb kinetics Relevant details of the dynamics formulation used in the present study of paw-shake response are provided in the APPENDIX. The following section briefly summarizes the methods we used for the kinetic analysis of the PSR. The cat’s leg and paw were modeled as a planar, two-segment, rigid body system, with the ankle modeled as a hinge joint (Fig. 1). The paw was modeled as a single rigid body because the motion
1284
HOY, ZERNICKE, AND SMITH LIN ACC). At the knee joint, the inertial moment components arise from leg angular acceleration (LEG ANG ACC), leg angular velocity (LEG ANG VEL), paw angular acceleration (PAW ANG ACC), paw angular velocity (PAW ANG VEL), and knee linear acceleration (KNEE LIN ACC). 3) Gravitational moment.This final component is a result of gravitational forces (GRAVITY) acting on each of the segments at its respective center of mass.
Statistical procedures To detect significant differences between flexor and extensor motions and moments at each joint and between joints, multivariate analysis of variance was used. Univariate analysis of variance was used for post hoc tests. A significance level of P < 0.01 was accepted. RESULTS
Kinematics and muscle activity Knee and ankle joint kinematics for 5 1 steady-state cycles from 16 PSRs were averaged, and displacements for both joints are illustrated by four steady-state cycles in Fig. 2. The average cycle period was 81 t 3 ms, FIG. 1. Anatomical correIates of the 2-segment cat hindlimb model. Leg (0,) and paw (0,) segmental angles were calculated with respect to the right horizontal from the proximal joint center. The difference between segmental angles is 4 ($ = BP- 0,).
of the phalanges has a negligible effect on the center of mass location of the combined tarsometatarsal and phalangeal unit. Segmental masses, centers of mass, and moments of inertia were calculated with regression equations that used cat mass and segment lengths as predictor variables (7). Equations of rigid body motion were formulated by use of Newtonian mechanics to determine the mechanical interactions between leg and paw segments during PSR. Because of the form of the equations that we used, netjoint moments(NET) were partitioned into three categories of moment components (moment components are mathematically defined in the APPENDIX):
STEADY-STATE El 57 Y L
60
(\ 80
E
r \ \ \ \ V
Y
’
KNEE
I I I I I I I
140 9 5 160
m
I) Muscle moment. This moment
component is a “generalized” muscle moment (MUSCLE) that includes active muscle forces, passive musculotendinous forces, and forces arising from the deformation of passive periarticular tissues. 2) Inertial moments.These motion-dependent moments arise from mechanical interactions between limb segments. At the ankle, the inertial moment components arise from leg angular acceleration (LEG ANG ACC), leg angular velocity (LEG ANG VEL), and knee linear acceleration (KNEE
0
ANKLE 180
TIME’
150
ms ’
FIG. 2. Exemplar knee and ankle excursions during 4 steady-state cycles of PSR. Dashed linesindicate motion just before and just after steady-state. A representative sample of a complete PSR with start-up, steady-state,and slow-down is illustrated in, the preceding paper (see Fig, 6 of Ref. 22).
DIFFERENTIAL
CONTROL
with consecutive peak ankle extensions defining the cycle. Ankle joint excursions averaged 38”, with peak flexion at 122 t 4” and peak extension at 160 t 9”, whereas knee excursions were less, averaging 24”, with peak displacements of 57 t 6O (flexion) and 8 1 t 7” (extension). Knee oscillations were symmetric, but ankle oscillations were usually asymmetric. This asymmetry was due to a slight hesitation or pause in motion when the ankle was near peak flexion; this pause was more pronounced in some kinematic records than in others (cf. Fig. 6 in Ref. 22). A
I
130
Coordination of ankle and knee motions is illustrated by the angle-angle plot in Fig. 3. At cycle onset, motions between the two joints were out of phase, i.e., ankle flexion was paired with knee extension (diagonal line from A to B). From peak ankle flexion to the end of the cycle, ankle and knee actions were sequential. Knee flexion, represented by the vertical line (B to C, Fig. 3), was accompanied by negligible ankle displacement. Ankle extension with minimal knee displacement followed (horizontal line from C to A, Fig. 3). Relationships between ankle and knee ve-
8
I
140
1285
OF KNEE AND ANKLE
C
I
t
I
1
160
150 ANKLE
ANGLE
I
1
170
I
180
(deg)
FIG. 3. Angle-angle plot illustrating knee and ankle coordination during a typical PSR steady-state cycle. Cat hindlimb positions A, B, and C are marked on the angle-angle plot. The cycle begins at peak ankle extension (A) and continues in a counterclockwise direction. B marks peak knee extension, which just precedes peak ankle flexion (not labeled). C marks the slowing of knee flexion and the onset of ankle extension. Intervals between dots are 5 ms. Shaded bar indicates knee extensor activity; unshaded bar indicates ankle flexor activity; stippled bar indicates knee flexor and ankle extensor activity.
1286
HOY, ZERNICKE, AND SMITH A
B
C 2
24
r
60 18 F\ \ \ \
/
\ ’ kd
/’
/ R-1
/
12 \
-
ANKLE
---
KNEE
160
N
a7 -X
6
-18
180
-ANKLE KNEE ---
-3
\
-24 L 0
20
40 TIME Ims)
60
80
I 0
I
I 1 b 20 40
1
1 60
TIME (ms)
1 I 80
0
20
40
60
80
TIME (ms)
FIG. 4, Typical knee and ankle joint displacements (A), velocities (B), and accelerations (C) during a steady-state cycle. All records begin and end at peak ankle extension. Note that joint actions reverse as velocity curves pass through zero.
locities during a single representative cycle are eration peaks coincided, respectively, with shown in Fig. 4B. Positive velocities corre- maximum knee flexion and extension. Peak spond to extension (increasing angle), whereas positive and negative accelerations at the knee negative velocities are associated with flexion joint were significantly less than corresponding (decreasing angle). Maximum velocities at the values at the ankle. The extremely large anankle (1,940 t 323 deg/s) were twice as large gular accelerations of the ankle resulted in as those at the knee (95 1 t 193 deg/s). At both comparably large linear accelerations of the joints, peak extensor velocities had about the paw. For example, it was not uncommon for same magnitudes as peak flexor velocities. At resultant linear accelerations of the paw to apthe ankle, flexor velocity peaked before (14 & proach values of 265 m/s2 (27 G) during PSR 4 ms) maximum ankle flexion, and extensor steady-state. The relationship between muscle activity velocity peaked before (20 t 14 ms) maximum ankle extension (cf. Fig. 4, A and B). and joint displacement is shown in Fig. 3. At Relationships between ankle and knee angular accelerations are illustrated in Fig. 4C. Average peak positive and negative accelera- TABLE 1. Ankle moment maxima for tions were not significantly different; however, substantial differences existed in some cycles steady-state cycles such as those shown for the ankle in Fig. 4C. Flexor, Extensor, Peak ankle negative acceleration occurred Component mNm mNm within 5 ms of peak ankle extension. Two positive acceleration peaks occurred: The first -437 (78) NET 449 (101) MUSCLE 458 (85) -393 (83) occurred within 6 ms of peak ankle flexion -168 (33) LEG ANG ACC 136 (43) (Fig. 4C, 35 ms), and the second, associated LEG ANG VEL none -24 (13) with the pause in ankle extension, occurred -88 (26) KNEE LIN ACC 63 (19) approximately midway between peak ankle GRAVITY none -14 (1) flexion and peak ankle extension (Fig. 4C, 65 * n = 4; SD, average, within subjects. ms). At the knee, positive and negative accel-
DIFFERENTIAL
CONTROL
OF KNEE AND ANKLE
the ankle, TA activity began soon (17 t 6 ms) after peak ankle flexion, continued throughout extension, and terminated at peak ankle exANKLE
A
600
E 21 i
r
,PEAK
ANKLE
1287
tension. Onset of LG activity coincided with peak ankle extension and initiation of rapid knee extension. The LG activity was coinci-
MOMENT
EXTENSION
/
PEAK
ANKLE
FLEXION MUSCLE NET
400
t
r
I
Eb EXTENSOR
0
10
20
30
40 TIME
8 PEAK
600
ANKLE
EXTENSION
50
60
ANKLE
FLEXION
FLEXOR
70
I
80
90
(ms)
PEAK
MUSCLE NET
m4
“N
KNEE
n
/LEG
LIN ACC ANG VEL
LEG ANG ACC
IO
I
10
20
30
40 TIME
50
60
70
80
90
(ms)
FIG. 5. Ankle joint dynamics during a typical steady-state cycle. Both records are referenced to peak ankle extension. In A, NET and MUSCLE moments have been isolated from the other components. Bars represent the timing of extensor and flexor muscle activities at the ankle joint. In B, the NET, MUSCLE, and GRWITY moments are shown with the three inertial moments: LEG ANG ACC, LEG ANG VEL, and KNEE LIN ACC. Also, the relationship of these ankle moments to peak ankle and knee displacements is illustrated.
1288
HoY,ZERNICKE,ANDSMITH
dent with ankle flexion and knee extension, terminating before (7 t 5 ms) maximum ankle flexion and before (10 f- 0 ms) peak knee extension. The BF was active synergistically with LG; burst onsetsoccurred within 3 t 2 ms of LG onsets, The VL was active during knee flexion, and VL onset followed (13 -t 8 ms) peak knee extension, Coactivity of VL and TA occurred during the terminal phase of rapid knee flexion. Typically, VL activity preceded TA activity by 5-f 5 ms, There were no steadystate cycles analyzed in this study in which TA activity preceded the onset of VL activity (cf. Fig. 6, Ref, 22).
ankle flexion (Fig. 5A, O-40 ms), the net moment decreasedits tendency to flex the ankle and subsequently achieved a maximum extensor effect just before peak ankle flexion. While the ankle extended (Fig. SA, 40-85 ms), the net moment approached zero, but then developed a second extensor peak before rapidly increasing to achieve a maximum flexor effect just before peak ankle extension. Magnitude of the extensor net moment peak during ankle flexion tended to be larger, although not significantly, than the extensor net moment peak during ankle extension. Throughout most of the cycle, the muscle moment dominated ankle joint dynamics (Fig. 5A), and the net effect of inertial moments was minimal. During ankle flexion, the knee linear acceleration moment effectively counteracted the leg angular acceleration moment, and net and muscle moments were very closely associated(Fig. 5B). Leg angular velocity and gravitational moments contributed very small extensor moments during the entire PSR cycle.
Kinet its DYNAMICS. The net moment and component moments acting on the paw during a typical steady-state cycle are shown in Fig. 5, A and B. Average maxima of ankle moments are given in Table 1. Net moment achieved maximum magnitudes near peak ankle joint displacements (Fig. 5A). During ANKLEJOINT
-
PEAK
ANKLE
EXTENSION
PEAK
ANKLE
FLEXION
/ MUSCLE
LEG
PEAK
KNEE
EXTENSION
PEAK
KNEE
t
I
40 TIME
I
50
ACC
FLEXION
I 30
ANG
I
I
60
FLEXOR I
I f
70
I
80
90
{ms)
FIG. 6. The alternate pattern of ankle joint dynamics during a steady-state cycle. Contribution of MUSCLE to extensor NET peak during ankle extension (65 ms) is flexor rather than extensor (cf. Fig. 5B, 65 ms). The cycle is referenced to peak ankle extension. NET, MUSCLE, and LEG ANG ACC moments have been isolated from the other component moments. Bars represent the timing of extensor and flexor muscle activities at the ankle joint. Also, the relationship of these ankle moments to peak ankle and knee displacements is illustrated.
DIFFERENTIAL
CONTROL
KNEE
A
15oor
c
\
PEAK
KNEE
OF
KNEE
AND
ANKLE
1289
MOMENT
EXTENSION
PEAK
KNEE
FLEXlON
f\
MUSCLE v
/
\-NET
‘i
’
I 0
I
I 10
f
I 20
I
I 30
I
I
I 50
40 TIME
I
I 60
1
I
I 70
PAW ANG
I
80
ACC
1 90
(ms)
B
-
1500
s 5
PEAK
\( \
1000
ANKLE
; 5
\
\\
FLEXION
- sa -MM
/ I
ir\ \
KNEE
LIN ACC
\
\
-500
------\ \ \ \ \ \‘A
PAW ANG
VEL
LEG ANG
ACC
--m-m. I
/
/ ’ \
: Y IL
ANKlE
/‘,-MUSCLE
500
0
PEAK
/
s ul s E 5
EXTENSION
/ I
:: -1000
“PAW
ANG
ACC
-1500 PEAK
KNEE
EXTENSION
PEAK
KNEE
FLEXION \
4 0
10
20
30
40 TIME
50
60
70
I 80
I
1 90
(ms)
FIG. 7. Knee joint dynamics during a typical steady-state cycle. Both records are referenced to peak ankle extension. In A, the NET moment is isolated along with the counteracting MUSCLE and PAW ANG ACC moments, Bars represent the timing of extensor and flexor muscle activities at the knee joint. In B, the NET, MUSCLE, and GRAVITY moments are shown with the 5 inertial moments: LEG ANG ACC, LEG ANG VEL, PAW ANG ACC, PAW ANG VEL, and KNEE LIN ACC. Also, the relationship of these knee moments to peak ankle and knee displacements is illustrated.
1290
HOY,
ZERNICKE,
During ankle extension, two net moment patterns were observed. In most steady-state cycles, muscle and leg angular acceleration moments added to produce the second extensor peak in the net moment (Fig. 5B, 65 ms). In two cats an alternate pattern occurred in which the muscle moment first approached zero (Fig. 6, 35-50 ms), but then contributed a small flexor rather than extensor moment to the second extensor net moment peak (Fig. 6, 50-85 ms). Thus, the leg angular acceleration moment was especially important in generating the extensor peak in the net moment during ankle extension in these steady-state cycles (Fig. 6, 65 ms). JOINT DYNAMICS. The net moment and component moments acting on the leg during a representative steady-state cycle are shown in Fig. 7, A and B. Average maxima of knee moments are given in Table 2. Maximum flexor net moment occurred near peak knee extension (Fig. 7A), and maximum extensor net moment occurred just before peak knee flexion. Peak muscle moments were over three times larger than peak net moments, Peak flexor muscle moments coincided with peak knee extension, but extensor muscle moments peaked after maximum knee flexion. Inertial interactions between limb segments were significant in determining knee joint dynamics (Fig. 7B). Moments generated by paw angular acceleration dominated inertial contributions to the net moment. Although paw angular acceleration moments were large, the influence on net moment was mitigated by large, counteracting muscle moments (Fig. 7A). Leg angular acceleration and knee linear acceleration were effective maximally at peak knee displacements,but in opposite directions. Paw angular velocity contributed an extensor moment during the entire PSR cycle, while very small flexor moments resulted from the leg angular velocity and gravity.
AND
SMITH
2. Knee moment maxima for steady-state cycles
TABLE
Component NET MUSCLE LEG ANG ACC LEG ANG VEL PAW ANG ACC PAW ANG VEL KNEE LIN ACC GRAVITY
FIexor, mNm
Extensor, mNm
-290 (89) -96 1 (228) -643 (I 36) -24 (13) -1,115 (270) none -426 (96) -45 (11)
312 (67) 1,178 (222) 582 (179) none 800 (152) 200 (35) 329 (110) none
* yt = 4; SD, average, within subjects.
KNEE
RELATIONSHIP OF MUSCLE EMG. Muscle moment
MOMENTS
AND
and corresponding EMG activity are shown for ankle joint in Fig. 5A and for knee joint in Fig. 7A. At the ankle, the flexor muscle moment coincided with the activity of ankle flexors, representedby the TA. Flexor activity began asthe ankle muscle moment approached zero, and ceased as the muscle moment achieved a flexor maximum.
At the knee, VL activity began asthe extensor
muscle moment increased from zero, and terminated at the time of peak extensor muscle moment. At the ankle, LG activity began when the flexor muscle moment was large, and ceasedjust before peak extensor muscle moment was achieved. At the knee, LG and BF were active as the extensor muscle moment decreased and flexor muscle moment began to increase. The delay between EMG onsets and initiation of muscle moment and between EMG offsets and peak muscle moments (Figs. 5B and 7B) indicated a phaselag between timing of muscle activity and development of muscle moments. DISCUSSION
Interplay intralimb
between muscle function and dynamics
The paw-shake response serves to remove irritants from the paw by generating large accelerations at the most distal segment. The high-frequency, large-amplitude joint motions characteristic of PSR are unique in the cat’s movement repertoire, and joint moments during PSR may exceed those of most other limb movements of the cat. For example, knee and ankle muscle moments during PSR steady-state cycles are larger than reported values for swing phase (7) and stance phase ( 14) of locomotion or elbow moments during landing from jump down (16). Muscle activity corresponds with muscle moments and joint acceleration, rather than with joint displacement. Characteristically, as
DIFFERENTIAL
CONTROI
with sinusoidal oscillations, the angular displacements during PSR steady-state cycles are out of phase with accelerations. This fundamental relationship for sinusoidal displacement and its derivatives is illustrated in Fig. 84 and the analogous relationship is shown (Fig. 8B) for paw angular displacement, velocity, and acceleration during PSR oscillations. For sinusoidal motion, angular velocity is 90° out of phase with angular displacement, and the angular acceleration is 180* out of phase with angular displacement. Net moments are proportional to angular acceleration; therefore, the net joint moments are out
OF KNEE AND
ANKLE
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of phase with angular displacement during PSR steady-state cycles. Since muscle moments would act in phase with net joint moments during sinusoidal movement (see Eqs. 1 and 2 in APPENDIX), muscle moments during PSR steady-state cycles control limb dynamics by slowing and reversing joint motions. Consequently, active muscle forces contributing to muscle moments are derived from lengthening of active musculotendinous units. Potentially, such lengthening action facilitates force production in musculotendinous units (1, 10, 11). Muscle moments at the knee and ankle play
A ACCELERATION
ACCELERATION
VELOCITY
DISPLACEMENT
VELOCITY
FIG. 8. Analogy of PSR kinematics to sinusoidal motion. In A, sinusoidal angular displacement is shown with corresponding angular velocity and angular acceleration. In B, paw angular displacement, paw angular velocity, and paw angular acceleration are shown for 2 steady-state cycles.
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HOY,
ZERNICKE,
different roles in control of limb dynamics during PSR steady-state cycles. At the ankle, muscle moment dominates ankle joint dynamics, and ankle muscle activity functions to control paw acceleration. In contrast to the limited effect at the ankle, inertial moments have a substantial influence at the knee joint. Large muscle moments are generated to counteract large inertial moments, and knee muscle activity functions to control intersegmental dynamics between leg and paw. Thus, peak knee muscle moments are significantly greater than ankle moments (Tables 1 and 2), although peak net moments at the knee are significantly smaller than peak net moments at the ankle. Within a steady-state cycle the exquisite interplay between muscle moments and intersegmental dynamics at the knee and ankle is readily apparent, as well as the unique mechanical function of biarticular muscles (i.e., LG) in contrast to uniarticular muscles (i.e., VL and TA). From the outset of the cycle (see Fig. 34, the conjoined motions at the knee and ankle stretch the active biarticular LG. The LG activity contributes simultaneously to development of flexor muscle moment during knee extension and to extensor muscle moment during ankle flexion, effectively coupling the out-of-phase joint motions. Following the simultaneous motion of ankle and knee, the knee flexes rapidly (Fig. 3, B to C), and it is probable that LG force dissipates quickly as the muscle shortens rapidly. The rapid stretching of active knee extensors (VL) slows knee flexion, and as knee flexion stops, extensor leg angular acceleration and net moments peak at the ankle (Figs. 5B and 6,65 ms). Thus, the very large ankle extensor velocities subsequent to the extensor peak in net moment are not due exclusively to activity of ankle extensor muscles, but are a consequence of an effective dynamic interaction between segments in which acceleratory motion of the leg augments velocity of the paw. The sequential pattern of joint displacement during PSR steady-state cycles is consistent with transfer of angular momentum from the proximal segment to the distal segment; however, the specific relationship between angular momentum and joint kinetics during PSR is the subject of a future analysis.
AND
SMITH
D$wential control of knee and ankle The principal results of the kinetic analysis of PSR steady-state cycles are that ankle muscles produce moments to control paw acceleration, whereas knee muscles produce moments to control intersegmental dynamics between the paw and leg. Such biomechanical results provide unique insights about the requirements for the neural control of PSR, For example, since knee muscle moments counteract moments created by paw angular acceleration, do spinal circuits receive and use information about paw motion to produce compensatory moments by recruitment of knee muscles? Detection of paw angular acceleration during the PSR cycle may be of particular importance to controlling circuits within the lumbosacral cord. Output from muscle spindles, especially Ia afferents with cLaccleration responsiveness” ( 15), may be important in detecting the rate of muscle lengthening and consequently ankle joint angular acceleration. Except for two brief accounts (13, 19), however, there is little information about Ia discharge during PSR. Prochazka et al. (19) show that Ia gastrocnemius discharge coincides with the muscle’s lengthening contraction (see Fig. 9 of Ref. 19); thus, Ia discharge from ankle extensors during PSR is maximal just before knee extensor activity. Ia discharge from ankle extensors may influence excitation of knee extensors by facilitating interneurons that regulate pattern generation or by facilitating motoneurons via intersegmental branches (3). In contrast, there appears to be little need for the spinal circuits that control ankle muscle recruitment to account for intersegmental dynamics. Although motions at proximal hindlimb joints are appreciable, the inertial moments generated by these movements have only limited influence on the net ankle moment, and muscle moments predominate at the ankle during steady-state cycles (Fig. 5). These kinetic results imply that perturbations of limb dynamics during PSR should have a greater influence on recruitment of knee muscles than on ankle muscles. Indeed, published data, heretofore unexplained, are consistent with this prediction. For example, Sabin and Smith (2 1) and Phillips and Smith ( 18) report that PSRs can be elicited with knee and ankle joints immobilized by plaster cast.
DIFFERENTIAL
CONTROL
Activity patterns of ankle muscles (LG, TA) during these motion-restricted PSRs are not changed; however, knee extensor (VL) recruitment is altered. Often VL bursts are missing or are substantially reduced. Similar irregular patterns are observed when limb dynamics are perturbed by adding weights (28 and 46 g) to the hindpaw of the shaking limb (2). In the previous study (22), we show that knee extensor EMG and knee motions during PSR in spinal cats can be disrupted in the absence of applied limb perturbations (cf. Fig. 8, Ref. 22). We have not examined the kinetics of disrupted paw shakesand do not know the nature of the intersegmental feedback during theseresponses.If motion-dependent feedback during PSR is important in determining muscle recruitment during steady-state cycles, particularly at the knee, it may not be necessary to preplan the compensatory muscular responseto the complex limb kinetics. Rather, motion-dependent feedback allows neural adaptation to the emergent limb dynamics (8). APPENDIX
mL, mp TL, rP Ir. IL,
IP
OL,
flP
4 2, y g
Masses of leg and paw Distances from proximal joint to center of mass of leg and paw Length of leg segment Moments of inertia at center of mass of leg and paw Leg and paw angles from the right horizontal { Op - 0,) Difference between leg and paw angles Knee joint linear acceleration Gravitational constant
Dynamics formulation The cat leg and paw were modeled as a planar, two-segment rigid body system, with the ankle modeled as a frictionless hinge joint (Fig. 1). Limb motion was assumed to occur in a single plane (xy>, and moments to occur about an axis (z) normal to that plane. The equations of motion were formulated using Newtonian mechanics to highlight the dynamic interactions between segments (7, 20) .. (Ip + rp2mp)Op = MA - { rpm& cos &} - { rpmpZLsin &‘} + { Ypmpsin BpX
- rpmpcosOpy}- { rpmpcosBpg} (I)
1293
OF KNEE AND ANKLE (IL + rL2mL)& - { rpmpZL
=
MK - { (rpmpZL cos 6 + mpZL2)&}
sin $gL2} - { (rpmpZL cos 4
+ rp2mp + I,)$,}
+ { rpmpZL
sin #bp2}
+ { (rLmL sin & + mpZL sin 8L + y pmp sin 0,)X - (rLmt
cos OL + mpZL cos OL + rPmP cos 8p)j;)
- { (rLmL cos BL + mpZL cos Or + rpmp cos Op)g}
(2)
Ankle and knee joint moments were computed for each paw-shake response using Eqs. I and 2, respectively. Segmental centers of mass and moments of inertia were calculated using regression equations developed previously in our laboratory (7) for the leg, tarsal, and hind-digit segments. Tarsal and hind-digit masses were summed to yield paw mass. Paw center of mass location was determined from tarsal and hind-digit segment masses and their respective centers of mass locations. Tarsal and hind-digit regression equations and the parallel axis theorem were used to determine the moment of inertia of the paw about its center of mass.
Mument
abbreviations
Moment component abbreviations used in the text correspond to terms in Eqs. 1 and 2 according to the following scheme: ANKLE MOMENT COMPONENTS NET {UP + r,2mp)gp} MUSCLE IMd LEG ANG ACC { -TpmpZL cos &} LEG ANG VEL { -rpmpZL sin #bL2} KNEE LIN ACC { rpmp sin 0,X - rpmP cos Opj} GRAVITY { -rPmP cos ePg> KNEE MOMENT COMPONENTS NET { (1~ + t2mdk} MUSCLE Pw LEG ANG ACC { -(rpmpZL cos 4 + mpZL2)e,} LEG ANG VEL { -rpmpZL sin &‘} PAW ANG ACC { -( rpmpZL cos # + rp2mp + Ip)Bp} PAW ANG VEL { rpmpZLsin 4bp2} KNEE LIN ACC { (rLrnL sin 0~ + m& sin & + rpmp sin 8,)2 - (rLmL cos OL GRAVITY
+ mpZL cos 6~ + rpmp cos Sp)i;) { -(rLmL cos BL + mpZL cos OL + rPmP
cos
BPk}
ACKNOWLEDGMENTS
The authors thank Nina Bradley, Mary Carter, Carol Giuliani, Gail Koshland, and Dorothy Phillips for their assistance in data collection. We also thank Steve Gibson for verifying the dynamics formulation and Robert Gregor and Tim Poston for their helpful comments on an earlier draft of this manuscript. This work was supported by National Institutes of Health Grant NS- 19864 and UCLA Academic Senate Research Grant. Received 24 August 1984; accepted in final form 5 June 1985.
1294
HOY,
ZERNICKE,
AND
SMITH
REFERENCES
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