Modulation of limb dynamics in the swing phase of locomotion

Modulation of limb dynamics in the swing phase of locomotion

MODULATION OF LIMB DYNAMICS IN THE SWING PHASE OF LOCOMOTION MELISSA Department of G. HOY Kinesiology, and Umversity RONALD of California, F...

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MODULATION

OF LIMB DYNAMICS IN THE SWING PHASE OF LOCOMOTION

MELISSA Department

of

G. HOY

Kinesiology,

and

Umversity

RONALD

of California,

F. ZERNICKE Los Angeles. CA 90024. U.S.A.

Abstract-A

method was presented for quantifying cat (F&s cotus) hind limb dynamics during swing phase rigid body model of!eg and paw, which highlighted the dynamic interactions between segments. Comprehensive determination was made of cat segment parameters necessary for dynamic analysis, and regression equations were formula:ed to predict the inertial parameters of any comparable cat. Modulations in muscle and non-muscle components of knee and ankle joint moments were examined at two treadmill speeds using three gaits: (a) pace-like walk and trot-like walk, at 1.0 ms- ‘, and lb) gallop. at 2.1 m s- ‘. Results showed that muscle and segment interactive moments significantly effected limb trajectories during swing. Some moment components were greater in galloping than in walking, but net Joint maxima were not signiticantly different between speeds. Moment magnitudes typically were greater for pace-like ualking than for trot-like walking at the same speed. Generally, across gaits, the net and muscle moments were in phase with the direction ofdistal joint motion, and these same moments were out of phase \rlth proximal joint motion. Intersegmental dynamics were not modulated exclusively by speed of locomotion. but interactive moments were also influenced significantly by gait mode.

oflocomotionusing a two-link

ISTRODlJCTlON

; (I, + rjm,)U, i knee joint net [MI I knee generalized muscle

Limb motion during the swing phase of locomotion is determined by muscular forces and dynamic mechanical interactions among segments. Moments associated with gravity, joint contact forces and forces arising from the deformation of passive viscoelastic tissues also modulate the resultant motion. The relative contribution of each moment component to the total joint moment is important to understand the control of limb trajectories during swing and how kinetic parameters vary with such locomotor variables as speed of locomotion and gait mode. The dynamic substrate of limb motion, comprising both muscle and non-muscle components of joint moments, is explained by rigid body dynamics. Dynamicanalysiscouples the trajectory (position-time series) of a rigid body system with the forces and moments causing motion. Using the inverse dynamics approach, in which joint moments are calculated from known limb trajectories, muscle, inertial and gravitational components of total joint moments can be parcelled out, and the relative contribution of each can be quantified. The relative contributions of muscular and motion-dependent components of segment dynamics have been investigated for the swing phase of human walking (Mena et al., 1981). running (Phillips et al., 1983), and kicking (Putnam, 1983), but comparable data do not exist for locomotion of any other vertebrate. The purpose of this study was to develop and implement techniques of rigid body mechanics to: (I) explain hind limb dynamics during the swing phase of locomation in the cat, and (2) examine modulations of limb dynamics with speed of locomotion and gait mode. Rigid body mechanics have not been applied routinely to studies of cat locomotion, potentially,

moment moment ( - (r*m,l, cos$ +m,l:) 0,) knee moment due to leg angular acceleration { -r2m211sin$di{ knee moment due to leg angular vrlocity knee mo[ - (rp21, cos$+ rim, + l,)ii,i ment due to paw angular acceleration [r,mzl, sindd :: knee moment due to paw angular vrloc~ty I(r,mI sin0, +m,/, CosV, +r,m2 sinV,).i: -(r,m, cosV, +m>i, COsV, +r,m, cosV,)i: knee moment due to linear acceleration of knee (-(r,m, cosU, +m,l, CosV, +r,ml cosV,)g) knee momect due to gravity II, + rimz)O,) ankle joint net moment

{ hl,: ankle gen,eralized muscle moment : - r2mzi, cos&?, ] ankle moment due to

leg angular acceleration [ -rlm,/, sin#, Vi) ankle moment due to leg angular velocity (rzm2 sinVz .f --rlmz COSV, j:) ankle moment due to knee linear acceleration [ - rrm2 cosV,gi ankle moment due to gravity masses of leg and paw distances from the proximal joint to center of mass of leg and paw lengths of leg and paw moments of inertia at center of mass of leg and paw weights of leg and paw generalized joint forces at knee and ankle orientation angles of leg and paw from the right horizontal IV, - tl, : difference between orientation angles

Rrcricrd

Januarl

1984; in wl-rsrdjorm

16 July

1984. 49

50 because

MELISSA G. HOY and RONALD F. ZERNICKE

convenient

parameters

were

estimates not

of

segmental

available.

inertial

Such parameters include the masses, centers of mass, and moments of inertia of the individual body segments of the animal. Grand (1977) measured segment masses for several species, including three cats, but reported neither moments of inertia nor center of mass locations for limb segments. In Manter’s classic study of cat locomotion (1938), selected mass parameters for one cat are reported, however, the data have limited utility for more extensive kinetic analyses. Detailed segmental parameters of the adult cat (Fe/is catus) are presented in this study. Physical constants are presented as percentages or functions of external measurements, thus eliminating the need for animal sacrifice for future biomechanical studies. The compiled data allow modeling the cat as a system of 23 individual segments, nine of which are point masses (PM). The 23 segments are: head (PM), neck (PM), thoracic trunk (PM), lumbosacral trunk (PM), scapulae (2). arms (2). forearms (2), carpals (2), fore digits (PM, 2) thighs (2), legs (2). tarsals (2), hind digits (PM 2). and tail (PM). Fore limbs and hind limbs were characterized in more detail because of their importance in cat locomotion. In this study, analytical techniques were developed and segmental parameters were obtained to investigate the intersegmental dynamics of cat hind limb during the swing phase of locomotion. Specifically, knee and ankle joint kinetics were examined at two speeds of treadmill locomotion. Two different gait modes (pace-

like walk and trot-like walk) were used at a lower speed, and a third gait mode (transverse gallop) was used at a higher speed. Muscle moments and dynamic mechanical interactions between leg and paw segments contributed significantly to joint moments. Increased speed of locomotion was associated with greater magnitudes of some moment components, but net joint moments did not increase significantly from walking to galloping. Typically, moment magnitudes were greater for pace-like walking than for trot-like walking at the same speed. Results showed that intersegmental dynamics were not modulated exclusively by speed of locomotion, but interactive moments were also intluenced significantly by type of gait. MATERIALS AND METHODS Drrrrminotion

segmenr parameters

HIND DIGITS

FOREDIGITS THORACIC 43.6%

o/cat

Nine cats (2561.2f411.4g) were sacrificed (Nembutal), weighed, and joint centers of rotation marked by drilling needle markers into palpated centers of the joints of the fore limbs and hind limbs (Stewart, 1980). Joint centers marked on the fore limb were: the spinous process of the scapula at the superior border, posterior border of the greater tuberosity of the humerus, lateral epicondyle of the humerus, styloid process of the ulna, and the metacarpophalangeal joint. For the hind limb, joint centers were: the greater trochanter and lateral epicondyle of the femur, the lateral malleolus, and the metatarsophalangeal joint. Measurementsofsegment lengths ( f 0.5 mm) were made using an anthropometer. Cadavers were maintained in a position approximating standing posture (Fig. I) as body temperatures were lowered to - 80°C. Hind limbs and fore limbs were removed with a

LUMBOSACRAL 56.4%

Fig. I. Segmental sections of the cat (top); renter of mass locations (x) of head, lumbosacral trunk segments (bottom).

neck and

thoracic and

Limb dynamics

scalpel when the ammal was partially congealed. to permit limb removal without fluid loss. The hind limbs were detached at the hip joint; hip and thigh musculature remained with the hand limb. Forelimbs were removed by cutting along the perimeter of the scapula. retaining m. subscapularis with the scapula. The frozen torsos and limbs rvere sectioned with a saw. The thigh was cut distally through the center of the knee joint, bisecting theangle between femur and tibia (Fig I). The leg was sectioned at the ankle joint center, bisecting the angle between the leg and the tarsals. The tarsal segment contained the metatarsal and the tarsal bones, and the hind digits contained the phalanges. The fore limb was divided into five sections: scapula, arm, forearm, carpals. and fore digits. The scapula was separated from the arm at the glenohumeral joint with a transverse cut (Fig. I ). The arm contained the humerus and was removed from the forearm at the elbow joint center. Thr forearm section contained ulna, radius, and muscles of the forearm. The carpal section comprised metacarpals and carpals, and the fore digits contained the phalanges. The head was severed at the base of the skull. The neck section. containing all cervical vertebrae, was separated from the torso after removal of the limbs. The rostra1 border of the scapula overlapped the neck section and some of the skin on the ntck was removed with the scapula. but none of the ribs wascontained in the neck section. The trunk was sectioned in dorsoventral planes at each vertebral marker. The tail was stationed at its base. Head. neck and thigh segment masses were determined with + 0.5 g scale accuracy, while the remaining segments were measured to 52.5 mg. The centers of mass for all segments except the tail were determined via suspension technique (Halliday and Resnick, 1974); tails were balanced on a knife edge to locate the centers of mass. Each frozen segment was hung from a silk suture and photographed (I6 mm Bell 8~ Howell D-70); the segment was subsequently re-hung from an alternate attachment site and rephotographed. Segmental moments of inerna were determined via pen-

51

in swing phase

dulum techmque (Manter. 1938). Using the parallel axis theorem, an average moment of inertia at the mass center for each segment was found from the oscillations about the proximal axis and the distal axis. A stitf steel wire (1 mm diameter) was inserted through transverse axes drrlled proximally and distally in each frozen segment. Periods of oscillation ( + 50 ps) uere determined when swinging limb segments interrupted a hght beam connected to a timer. One period of oscillation was sampled from each of nine trials. and the average was used as the final estimate of the period. Fore and hind digits were so small that ii uas not feasible to drill multiple holes through the specimen. and these were modeled as point masses. Serial 16 mm photographs were projected (X 29) with a pin-registered projection system (Vanguard Ml6C). onto a digitizer (HP 9830/9864), and measurements ( + 127 pm) were taken ofcoordinates ofjoint centers, proximal and distal points of rotation. and lmes of suspension. Descriptive statistics uere calculated for segment mass, center of mass location. and moment of inertia. Best fit. linear or logarithmic, regression equations estimated segment mass from the mass of the cat and segment length or estimated the segment moment of inertia from segment mass. cat mass and segment length. Intrrsrymrnlal

segment,

rigid

as a planar,

body system. Anatomical

paw

(Fig. 2. Segmenf 2). Although

occurs

at the metatarsophalangeal

swing

phase

modeled

(Goslow

as a single

metatarsophalangeal

et

al.,

rigid joint

the

paw

was

the

body,

since the effect

of

on paw center

of

mass location

was negligible to occur

-F2-

motion

during

motion

was assumed moments

of

I), and the

limited joint

1973).

two-

correlates

the rigid links were the leg (Fig. 2. Segment

(< 6’)b). Limb

in a single

plane

acted about an axis (Z) normal

-M2

Fig. 2. Orientation

dynamic~s

The cat leg and paw were modeled

and

to that plane.

Wl

I

angles of leg (0,) and paw (0,) segments, 4 = ez -8, (left). Forces and moments on the leg (segment 1) and paw (segment ?) (right).

motion

(XI),

acting

52

MELISSA G. HOY and RONALD F. ZERWKE

Forces and moments acting on the rigid body segment are given in Fig. 2. The applied moments M, and M2 are generalized muscle moments resulting from active and passive flexor and extensor muscle forces, and the restraining effects of periarticular tissues. The equations of motion were formulated using Newtonian mechanics to highlight the dynamic interaction between segments (Putnam, 1983)

+ r2m2 sin O,)d - (r,ml - ((r,m,

(I, +r:n*&

cos 0, +m,/,

cos 0, + r2m2 cos O,)jj

cos 0, + m,l,

cos 0, + rzmz cos 02)g)

= Mz - {r2mJ, cos&

) - fr2mJ,

sin#tit

(1)

1

+ {rzmz sin O,,? - r2m2 cos O,j;) - (r,m,

cos O,gj.

(2)

Net joint moments at the knee and ankle are given by the expressions on the left side of equations (1) and (2), respectively. The first term on the right side of each equation represents the influence of generalized muscle moments on knee and ankle joint net moments. Terms which include segmental angular accelerations (ii,, d,) or segmental angular velocities (u,, &) indicate the infiuences of leg and paw motions on joint moments. The influence of knee linear acceleration on knee and ankle joint moments is represented in termscontaining i and j;. Component segmental moments which are functions of knee linear accelerations, segmental angular accelerations, or segmental angular velocities represent motion-dependent or inertial moments. Du(u ucyuisilion

and analysis

Food and affection rewards were used as positive reinforcement to train a cat (2.3 kg) to locomote on a motorized treadmill (1.5 m long, 0.5 m wide). After training was completed, locomotion was examined on separate occasions at I.0 and 2.1 ms-‘. Prior to filming, the right hind limb was shaved, and black and white contrasting markers (12mm diameter) were placed on the skin overlying the iliac crest, and the hip, ankle and metatarsophalangeal joint centers. Cat mass and hind limb segment lengths were measured. Locomotion was filmed using a pin-registered 16 mm camera (Photosonics 1PL) positioned 2-3 m from the treadmill with optical axis perpendicular to the hind limb. Camera speed, nominally set at 100 fps, was verified by internal timing lights (Photosonics TLC). Rectangular coordinates of iliac crest and hip, ankle, and metatarsophalangeal joint centers were obtained from serial film frames projected (Vanguard M16C) onto a rear projection screen mounted with a digitizer (Graf/Pen) and interfaced to a minicomputer (DEC

PDP/ 1 l-23). Because independent movements of the over the knee prevent an accurate determination of the knee joint center from a skin marker, knee joint location was determined analytically (Goslow et (II.. 1973). Limb position-time data were calculated from the digitized coordinates. Kinematic data were smoothed and derivatives were computed according to the techniques descrihd by Hatze (1981). The sequence of limb contacts with the tread was determined by film inspection. Gait pattern was defined according to Hildebrand (1976); a minimum of three consecutive step cycles were analyzed for each gait. Only step cycles in which the speed of the cat matched treadmill velocity were selected for analysis. Step cycle duration, relative and absolute durations of swing and stance phases, and interlimb coordination were described for each step cycle. Two sets of parameters were computed for the swing phase: (I) hip, knee and ankle angular data and (2) leg and paw angular data, and knee translational data, required as input for the kinetic analysis. Hip, knee and ankle joint angles were defined as the included angle at each joint; paw and leg segment angles were defined as a counterclockwise rotation of each segment about the proximal joint from the right horizontal axis. During the swing phase, knee and ankle motions were each divided into two phases (Grillner, 1981): (I) a flexion phase (F) from paw off to peak joint flexion, and (2)an extension phase (El) from peak joint flexion to paw contact. The period between the knee joint maximum flexion and the ankle joint maximum Rexion was termed: F-El transition. Segmental moments were computed for each swing phase using equations (I ) and (2). Segmental centers of mass and moments of inertia were calculated with the appropriate regression equations. Tarsal and hind digit masses were summed to yield paw mass. Paw center of mass location was determined from component 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. Analysis of variance was used to detect significant differences among gait variables, and Tukey’s HSD post hoc pairwise comparisons were used to locate differences between means. A significance level of p < 0.05 was used for all tests. skin

RESULTS Cut body segment

parameters

Summary statistics (Table 1) show that segmentation and measurement errors were negligible, as evidenced by the summed percent mass estimates (99.1%). Moments of inertia were calculated at proximal and distal axes and subsequently translated to the center of mass (Table 1) by the parallel axis theorem. These two estimates of moment of inertia about the

53

Limb dynamics in swing phase Table I. Body segment parameters of cat Percent mass

Center of mass

Moment of inertia

( 7:)

( %V

(gcm2):

Segment Scapula Arm Forearm Carpals Fore digits Thigh Leg Tar&s Hind digits Head Neck Thoracic trunk Lumbosacral trunk Tail

18 18 18 10 18 18 18 18 18 4 5

2.52 (0.42). 2.37 (0.40) 1.30 (0.15) 0.30 (0.05) 0.29 (0.06) 5.02 (0.50) 2.41 (0.33) 0.67 (0.10) 0.34 (0.07) 7.93 (0.53) 4.88 (1.21)

5

23.40 (4.90)

5 5

31.30 (3.20) 1.12 (0.19)

47.62 48.82 45.43 52.27 50.00 44.30 42.30 48.61 50.00

(6.33) (2.39) (6.04)

399.41 (133.01) 391.81 (159.28) 233.34 ( 84.06) 7.51 ( 1.96) 8 1130.70 (302.60) 562.40 (192.57) 73.94 ( 27.99)

II

-

-

(5.13) (3.37) (2.39) (17.15)

32.25 (2.02)

99.1% 7 *Mean (standard deviation). fPercent length from proximal joint. SMoment of inertia at center of mass. BSegrnents represented as point masses. I/See text for description of the center of mass location. TSum of mass segments.

center of mass were averaged, and the mean difference

for all segments was 7.9% (*8.3x). A statistical comparison of right and left sides revealed no significant differences for any parameter, and hence, limb data were combined. Regression equations predicted segment masses as a function of cat mass and segment length (Table 2). The equations predicted the moment of inertia of a segment as a function of segment mass, segment length and cat mass (Table 3). Each trunk segment was assigned to either the thoracic or lumbosacral group (Fig. 1). The division between these two groups occurred at a point 43.6 % of the distance from the first thoracic vertebra (Tl) to the base of the tail (dorsal aspect) as depicted in Fig. 1. The centers

of mass

of the lumbosacral

and

thoracic

sections were located on a sagittal reference system with respect to a rostral-caudal line (Tl to base of tail) and a ventral-dorsal line (Fig. 1, line A-B). The head center of mass position was located on the lateral aspect of the head halfway between the lateral corner of the eye and the anterior edge of the ear and centered cephalocaudally (Fig. 1). The center of mass of the neck was 36 y0 of the distance from Cl to C7 and centered dorso-ventrally. Kinematics

The step sequences used during locomotion are illustrated in Fig. 3. Two different walking gaits, lateral couplets (a) and diagonal couplets (b), were used at 1.0 m s- ‘, and the transverse gallop (c) was used at 2.1 m s-‘. Hind limbs alternated in both walking gaits,

Table 2. Regression equations to predict segment masses Regression equation*

Segment Scapula Arm Forearm Carpals Fore digits Thigh Leg Tarsals Hind digits

(SlW)= log (SM) = log (SAf) = log (SM) = (SM) = (SM) = log (SM) = log (SM) = (SM) =

0.012 (CM)+4.50 (g- I.25 0.36 log (CM) + 1.64 log (L) -0.94 0.75 log (CM) + 0.39 log (L) - 1.39 0.78 log (CM) + 0.89 log (L) - 2.23 O.OCMl4 (CM)+ 1.57 (L)-0.18 0.052 (CM) - 12.46 (Q+ 102.13 0.29 log (CM)+ 1.37 log (L) -0.60 0.73 log (CM) + 0.66 log (L) - 1.78 0.0006 (CM) + 3.24 (L) -4.02

Multiple R

Standard error of estimate

0.61 0.92 0.78 0.94 0.50 0.86 0.85 0.82 0.73

8.78 0.05 0.05 0.04 1.29 5.23 0.05 0.06 0.95

*All calculations are based on n = 18 except for carpals where n = 6. Values of the individual segment masses (SM) and cat mass (CM) are in g, and the lengths (L) are in cm. The best fit, linear or logarithmic, regression equations are provided.

MELISSA

54

Table 3.

G.

HOY and RONALD F. ZERNICKE

Regression equations to predict moment of inertia at center of mass Multiple

Segment Scapula Arm Forearm Carpals Fore digits Thigh Leg Tarsals Hind digits

R

Regression equation

Standard error of estimate

log (/cm) = -0.27 log (CM) + 1.43 log (SM) + 0.02 (L) + 0.80 0.97 log ([cm) = -0.44 log (CM) + 1.59 log (shf) + 0.04 (~1 +0.91 0.99 log (Icm) = -0.06 log (CM)+ 1.01 iog (SM)+0.09 (L) + 0.27 0.94 log (I cm) = -2.29 log (CM) + 3.59 log (SM) -0.28 (L) + 6.39 3.99 Point mass (lent) = -0.31 (CM)+ 20.54 (SM)+ 38.78 (L) - 1041.96 0.93 log (fcm) = -0.19 log (CM)+ 1.55 log (SM)+0.02 (y + 0.44 0.98 log (Icm) = -0.23log(CM)+l.l2log(SM)+0.07(L) + 0.79 0.91 Point mass

0.04 0.04 0.06 0.03 48.85 0.03 0.07

‘All calculations based on n = 18 except for carpals where n = 6. Values of segmental moment of inertia (/cm) are in g (cm)*. Cat masses (CM) and segments masses (SM)are in g. Segment lengths (t) are in cm. Pest fit. linear or logarithmic, regression equations are provided.

::;.

“cl4 10

20

30

-/ /

40 PERCENT

50 OF STEP

60 CYCLE

70

80

90

100 I

Fig. 3. Footfall sequences used in pace-like walk (a), trot-like walk (b),and transversegallop (c). From top to bottom. bars indicate average contact interval for right hind limb (RH), right fore limb (RF), left hind limb (LH). and left fore limb (LF).

but fore and hind limb coordination was different; in the lateral couplets gait (pace-like walk), ipsilateral limbs were coupled in time, and in diagonal couplets gait (trot-like walk), contralateral limbs were paired (Hiidebrand, 1976). The gallop was characterized by coupling of fore limb pairs and hind limb pairs. The trailing foot of a limb couplet was termed the lead, and the transverse gallop was distinguished by contralateral fore and hind limb leads (Hildebrand. 1977). During walking, the mean percent delay between right and left hind limb contact was 49.6 + 1.0%. Coordination of ipsilateral limbs was significantly different for the two walking gaits; the percent delay

between placement of right hind and fore limbs was 11.O+ 1.6 % for the pace-like walk and 39.2 + 3.2 % for the trot-like walk. Step cycle duration was significantly shorter in the gallop (350 + 33 ms) than in the two slower speed gaits (464 + 14 ms). Swing phase duration was not different among gaits (173 &-14 ms), thus duration of swing relative to cycle time was significantly greater in the gallop (47 f 2 %) than in the walking gaits (38 + 2 %). Times of maximum knee and ankle joint flexion were not coincident, and a 32 f 7 ms delay between onset of knee and ankle extension was observed in all gaits. The percent of swing spent in flexion was significantly

Limb dynamics in

swing phase

cantly different for the trot-like walk, pace-like walk and gallop at: (1) onset of swing, (2) end of swing, (3) time of peak knee flexion, and (4) time of peak ankle flexion. Joint angles at these four key times are illustrated as stick figures for each gait in Figs 4 and 5.

different for all gaits Knee flexion occurred during 37 + 4 % of the swing for the pace-like walk, 43 k 3 9: for the gallop, and SOkO% for the trot-like walk. Duration of ankle Aexion during swing was greater for the trot-like walk and gallop (6.5 + 4%) than for the pace-like walk (54 f 5 %). Speed of locomotion affected joint angular excursions of the hip and knee during swing, but ankle range of motion was not significantly different among gaits (42 + 5’). Hip range of motion was less in the gallop (32 k 5’) than in the lower speed gaits (41 k 2”), and knee excursion was greater in the gallop (51 +6”) than in either walking gait (32 k 4’). Joint angles were signili-

Kinetics Ankle joint. Mean ankle joint moments and component segmental moments for the pace-like walk, trot-like walk, and gallop are illustrated in Fig. 4a-c. respectively. Maximum mean flexor and extensor ankle moments are listed in Table 4. In all gaits, ankle flexion was paired with a flexor ankle joint net moment ANKLE

\

25

55

MOMENT

AMI

a 1.0 m/s

0%

25% PERCENT

50% OF SWING

75%

100%

PHASE

b 1.0 m/s

0%

25% PERCENT

50% OF SWING

75%

100%

PHASE

c 2.0

I-

F

‘F-El

25%

50%

E,

m/s

-

-50 0%

PERCENT

OF SWING

75%

100%

PHASE

Fig. 4. Averageanklejoint net moment and component segment moments in the pace-like walk (a), trot-like walk (b), and transverse gallop (c). Times of maximum knee and ankle flexion are indicated with vertical lines; stipled regions indicate standard deviations. Average hind limb orientation at times ofswing onset, maximum knee flexion, maximum ankle flexion, and swing end are illustrated at top for each gait. See Nomenclature for moment definitions.

MELISSAG. HOY and RONALDF.

56

ZERNICKE

KNEE MOMENT

a 1.0 m/s

25%

0%

PERCENT

-15&Y___. 0%

50%

F. 25%

PERCENT

75%

OF SWING

-t

F-El

f:

50% OF SWING

100%

PHASE

El

\

75%

L2 100%

PHASE

C 2.0

PERCENT

OF

SWING

m/s

PHASE

Fig. 5. Average knee joint net moment and component segment moments in the pace-like walk (a), trot-like walk (b), and transversegallop (c). Times of maximum knee and ankle flexion are indicated with vertical lines; stipled regions indicate standard deviations. Average hind limb orientation at times ofswing onset, maximum knee flexion, maximum ankle Rexion. and swing end are illustrated at top for each gait. See Nomenclature for moment detinitions.

(AM (C));

the flexor net moment decreased as the ankle maximum flexion. Prior to peak ankle flexion, the ankle net moment reversed direction and tended to extend the ankle joint. The ankle net moment remained extensor until the end of swing. Maximum flexor net moment was significantly lower for the trot-like walk than for the pace-like walk or gallop but the peak extensor net moment was not significantly different among gaits. The generalized ankle muscle moment (AM (M2)) approached

tended to cause ankle flexion during F and ankle extension during El in all gaits. Magnitude of the flexor ankle muscle moment was gait-dependent; maximum values increased significantly from the trot-like walk, to the pace-like walk, to the gallop. Extensor ankle muscle moment was sustained for a longer portion of the swing, and the maximum value was significantly greater in the gallop than in the walking gaits. The influence of leg motion on ankle net moment

Limb dynamics in

swing phase

57

Table 4. Ankle moment maxima Pace-like walk Flexor Extensor (mNm) (mNm) ‘4 .%I(X 1

36.0 (6.9)’

-32.1

cl,lf Ihl,)

34.5

-21.1

Nlii,)

17.8 (2.0)

15.6)

Ahf ldf)

-

rlM I.i.:f)

8.8

(7.11 (3.6) - IO.4 (1.3)

(1.7) AShI(y)

6.7 (0.4)

*Standard

gallop

Extensor (mh’m)

Flexor (mNm)

(0.9)

_ 22.1 (2.1)

34.2 (13.41

Il.7 (4.2)

- 22.0 (11.4)

56.2 (17.91

-42.3

7.9 (4.2)

- 9.2

38.9 (16.91

- 27.3

13.1

(1.0) - 17.1 (1.1)

16.3 (7.8)

- 10.0 (0.2)

7.6 (0.4)

- 7.6 (0.4) - 9.2 (0.1)

-

Extensor (mNm)

_ 29.2 (6.81 (4.3) (7.9) -31.1 (1.3)

38.0 (6.7) 7.9 (0.8)

- 28.0 (18.2) - 10.3 (0.1)

deviation.

qualitatively similar for all gaits, but moment magnitudes were gait-dependent. The leg angular .. acceleration moment (AM (0,)) extensor maximum during ankle flexion and flexor maximum during ankle extension were greater in the gallop than in the walking gaits. Theanklecomponent moment due to legangular velocity (AM (of)) tended to extend the ankle during the entire swing; maximum values were significantly different for the trot-like walk, pace-like walk, and gallop. The pattern and magnitude of the ankle moment due to knee linear acceleration (AM(2.j;)) were different for each gait. In the pace-like walk, the knee linear acceleration moment tended to flex the ankle joint throughout swing; in the trot-like walk and gallop, knee linear acceleration tended to extend the ankle during the initial phase of the swing. Maximum flexor knee linear acceleration moments occurred during knee extension for all gaits, and were significantly greater in the gallop than in the lower speed gaits. In all gaits, the ankle gravitational moment (AM(g)) exerted similar moments. The relative contribution of ankle muscle and inertial moments to ankle net moment differed in each swing component phase. The large, flexor ankle muscle moment during early F counteracted the tendency of the inertial moments, especially leg angular acceleration and knee linear acceleration moments, to extend the ankle. Similarly, in late El, the extensor ankle muscle moment opposed the tendency of inertial moments to flex the ankle joint. In mid-swing, as the magnitude of ankle muscle moment approached zero, the turning effect of leg angular velocity moment was important in determining the ankle net moment. During F-El transition in the gallop, an extensor ankle muscle moment compensated for the large, flexor knee linear acceleration moment. was

Flexor ImNm)

- 25.3 (3.51 -

Transverse

Trot-like walk

Knee joint

Mean knee joint moments and component segmental moments for the pace-like walk, trot-like walk, and gallop are illustrated in Fig. 5a-c, respectively. Maximum mean flexor and extensor knee moments are listed in Table 5. During the swing phase of all three gaits, the knee joint net moment (KM(E)) tended to resist knee motion; knee net moment was extensor during knee flexion and initial extension, and was flexor during the remainder of knee extension. Both maximum extensor and flexor knee net moments were significantly greater for thegallop than for the trot-like walk. Values for the pace-like walk were intermediate to the trot-like walk and gallop. The magnitude and direction of the knee muscle moment (KM (M,)) were gait-dependent during knee flexion, while during knee extension, the maximum magnitude of knee muscle moment was large, flexor, and gait independent. During knee flexion, the knee muscle moment tended to extend the knee in the pacelike walk and gallop, and to flex the knee in the trotlike walk. Peak knee muscle moments during knee flexion were significantly different for all gaits. The influence of knee angular motion-dependent moments on knee net moment was qualitatively similar across gaits. The inertial moments at the knee due torleg and paw angular accelerations (KM (8,) and KM (0,)) tended to flex the knee during F and to extend the knee during El. The maximum flexor leg angular acceleration moment was greater in the gallop than in the walking gaits. The maximum extensor leg angular acceleration moment, and the maximum flexor and extensor magnitudes of paw angular acceleration moment were significantly greater in the gallop than in the trot-like walk; values for the pace-like walk were intermediate to trot-like walk and gallop. The knee

58

MELISSA

G.

HOY and RONALD F. ZERXICKE

Table 5. Knee moment Pace-like walk Flexor Extensor (mNm) (mNm) h’hf (1) KICf(hf,l KM (6,) KM (if,

- 242.4 (34.3)

51.1 (13.3)

- 160.1 (61.7)

- 75.9 (7.9) - 25.3

116.5 (127) -

-59.1 (3.9) - 17.1

-

KM (0;)

- 66.8 (14.8) -

36.0 (8.0) 41.1 (4.8)

KM(i.~)

-

44.1 (13.4) 60.0 (2.5)

KM(g) *Standard

Flexor (mNm)

- 35.0

(3.5) KM (f&)

Trot-like walk

47.1 (4.7)

- 68.5 ( 7.8)*

maxima

(10.2)

(1.1) - 22.9 (1.3) -

Extensor (mNm)

Transverse gallop Flexor Extensor (mtiml (mNm)

35.5 (2.0)

-88.7 (35.4)

63.0 (21.0)

1

- 268.9 (71.8)

148.3 (34.8~

- 118.0 (36.9) - 32.5

168.4 (69.21 -

58.0 (19.1) -

(3.0)

-

-76.1 (33.9) -

-

26.6 (2.7) 26.5 (2.1)

-

74.4 (24.0)

- 110.3 (120.5)

88.0 (14.9)

1

61.5 (0.41

- 13.0 (4.4)

59.2 (1.0)

-

45.0 (4.2) 45.3 (16.9)

deviation.

moment due to paw angular velocity (KM (di)) tended to extend the knee, and the knee moment due to leg angular velocity (KM (0:)) tended to flex the knee throughout swing. Peak values for leg angular velocity moments were significantly different for all gaits. The pattern of the knee moment associated with knee linear acceleration (KM (.;i,j)) depended on gait. The knee linear acceleration moment was extensor throughout swing for the lower speed gaits, but in the gallop, the knee linear acceleration was flexor at swing onset. Peak extensor knee linear acceleration moments were significantly greater in the gallop than in the pacelike walk. The knee gravitational moment (KM (9)) tended to extend the knee during swing in the walking gaits, but in the gallop, gravitational moment exerted flexor torque at the end of swing. Maximum extensor gravitational moment occurred at swing onset and was similar for all gaits. The contribution of the gravitational moment to knee net moment was especially marked during F in the slower speed gaits; there, the absolute magnitude of the gravitational moment exceeded any other component segment moment. The interaction between knee muscle and inertial moments depended on gait. During knee flexion in all gaits, leg and paw angular acceleration exerted flexor moments. During trot-like walking, additional flexor moment was provided by the knee muscle moment. In the pace-like walk and gallop, knee muscle and knee linear acceleration moments opposed the angular acceleration moments. In all gaits, as the knee started to extend during F-El transition, flexor knee moments arising from knee muscle forces and leg and paw angular accelerations acted together to oppose the dominant extensor inertial moments. During El, a

large, flexor knee muscle moment counteracted the tendency of the inertial moments to extend the knee at the end of swing. DISCUSSION

Techniques of rigid body mechanics were used to examine the mechanical influences on cat hind limb trajectory during the swing phase of locomotion. Cat segmental parameters determined in this study provided the inertial constants necessary for dynamic analysis, and regression equations extended these data by allowing prediction of inertial parameters of any comparable cat. Formulation of the equations of motion highlighted dynamic interaction between linked limb segments by parcelling out the separate contributions of muscle, inertial and gravitational components of net joint moments. Quantification of the relative influences of muscle and non-muscle moments was important for understanding neural control mechanisms, since only muscle moments reflected the active participation of the central nervous system in control of limb trajectory during locomotion. Hind limb dynamics during swing were markedly different for pace-like walking and trot-like walking at the same speed; results suggested that, as speed of walking increased, the kinetic demands of swing were reduced by shifting to the trot form of interlimb coordination. Double support was provided by an ipsilateral bipod in the pace and a contralateral bipod in the trot, but the ipsilateral bipod was less stable statically than the contralateral bipod (Hildebrand, 1980). The relative instability of the pace mode of interlimb coordination, preferred by the adult cat at

59

Limb dynamics in swing phase lower velocities (Peters, 1983; Wetzef et al., 1975; Miffer er al., 1975). was afforded by minimizing time of double support. Accordingly, as velocity increased, double support time increased and the trot was preferred (Peters, 1983; English, 1979; Miller ef al., 1975: Wetzel er of., 1975). although the pace was occasionally observed during treadmill locomotion. The walking gaits in this study were intermediate in double support time between values observed for pacelike walk (preferred at lower velocities) and the trot (preferred at higher velocites). The relative instability of the ipsilateral double support during swing may have contributed to the increased moment magnitudes in pace-like walking. Locomotor speed doubled from walking to galfoping. but knee and ankle moments during swing were not increased proportionately. Time of swing was constant between treadmill speeds. Thus, modulation of hind limb dynamics with locomotor speed reflected changes in hind limb trajectories that were functions of gait mode and overall speed of locomotion rather than of movement time. However, relative motions of the leg and paw were sufliciently similar across speeds that profiles of the angular motion-dependent moments were qualitatively similar. The stereotypic limb motion during swing was achieved by generating appropriate muscle moments to compensate for large, phasic inertial moments. For example, at the start and end of swing, muscle moments at both the ankle and knee joints countered large, interactive moments in all gaits. Thus, the counter moments to which muscle moments acted were substantially increased due to dynamic interaction between segments. Further, the net inertial loads on limb segments were gait-dependent, and accomodating muscle moments varied both qualitatively and quantitatively among gaits. Muscle moments functioned differently at proximal and distal joints. Generally, across gaits, muscle moments were in phase with the direction of distal joint motion, and were out of phase with the direction of proximal joint motion. At the knee, inertial moments dominated the net joint moment, and the tendency of the knee muscle moment to oppose limb motion was derived from eccentric contraction and/or passive lengthening of knee musculature. Conversely, at the distal joint, concentric contraction of ankle musculature dominated ankle joint dynamics. Knee and ankle muscle moments were consistent with known muscle activity during swing. During F, ankle flexors (tibialis anterior, extensor digitorum longus) actively shorten, yielding the flexor muscle moment observed at the ankle (Goslow er a/., 1973; Rasmussen et al., 1978; Engberg and Lundberg, 1969). Although knee flexor muscles (semitendinosus, semimembranosus posterior) are active during F (Goslow PI al., 1973; Engberg and Lundberg, 1969), the net extensor knee muscle moment was dominated by active (sartorius, rectus femoris) and passive (vastus lateralis) knee extensor muscles in the pace-like walk

and gallop (Halbertsman, 1983; Gosfow PI a~., 1973: Rasmussen et al., 1978). During El, the extensor muscle moment at the ankle is associated with active shortening of ankle extensors (gastrocnemius, soleus, plantaris) (Goslow er al., 1973; Rasmussen er al., 1978; Engberg and Lundberg, 1969; Halbertsma, 1983). Knee joint extension was associated with a large flexor muscle moment in all gaits. Both knee flexor and extensor muscles are active during El (Engberg and Lundberg, 1969; Goslow et al., 1973), and co-activity is particularly evident just prior to foot placement (Wetzef er al., 1976). The dominant flexor muscle activity was required to decelerate the leg prior to contact. while activity in knee extensor muscles may have prepared muscles for loadbearing during stance. CONCLUSIONS 1. The inertial parameters found provide constants required for dynamicanalyses of the moving cat. Using techniques of rigid body mechanics, the relative influence of muscle and dynamic interactions between linked segments in control of limb motion during swing phase of cat locomotion were quantified. 2. Muscle and segmental interactive moments significantly affected limb trajectories during swing. Muscle moments functioned differently at proximal and distal joints. Generally, muscle moments were in phase with ankle motion and were out of phase with knee joint motion. 3. Intersegmental dynamics were modulated by gait mode and speed of locomotion. Most segmental moment magnitudes were greater in galloping than in walking, but net joint moments were not significantly different between speeds. At the same speed of locomotion, moment magnitudes typically were greater for pace-like walking than for trot-like walking. 4. Intersegmental dynamic analysis produced important, quantitative information about the mechanical demands and constraints upon the cat*s neuromuscular system. Comprehensive determination of cat segmental parameters allows expansion of rigid body analyses to multi-link models to increase sophistication of experimental investigations into control and energetics of cat locomotion. authors thank Holly Stewart and Mary Carter for assistance in data collection and Douglas Peller for programming expertise. This work was supported by Public Health Service Grant NSlO423 and Biomedical Support Grant. UCLA.

Acl;nowMgemmzs-The

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MELISSA G. HOY and RONALD F. ZERNICKE

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