KNEE JOIhpT TORQUE DURING THE SWING PHASE OF NORMAL TREADMILL WALKING* PETER R. CAVASAGHand ROBERTJ. GREGOR Biomrchanics Laborator). College of Hcslth. Physical Education and Recrerttion. The Pennsylvania
State Cni\srsity.
University
Park. Pennsylvania
16802. CL-!.
;tbstract--Net torques due to muscular action at the knee joint have been calculated in five normal male subjects during the swing phase of treadmill walking at speeds ranging from I.5 to 5 mph. Surface clectromjograms were also recorded from selected muscle groups in the thigh. The results indicate that in a given subject the variations in peak torque can be explained on the basis of walking speed. The EblG’s also show modifications which are speed dependent. From an examination of torques in all ti\r subjects. it is su ggested that consideration of the relevant body segment parameter is necessary to account for the between subject variations that are encountered at a given speed of walking. The versatility of the normal knee joint is emphasized in a discussion of the calculated power characteristlcs and the implications of these findings for prosthetic replacement of the knee are discussed.
IVTRODLCTIOS It is to be svpccted that changes in the speed of walking and the inertia of the limb segments will affect the muscular torques acting about the joints of the lower limb during normal human locomotion. It is well kno\vn that a wide (eight-fold) range of speeds is possible (Grieve. 1969) and that a three-fold range of moments of inertia of the shank and foot was found in a group of only eight cadavers (Dempster. 1955). In this paper a systematic study of both of these factors in the development of muscular torques during the swing phase ofwalking has been made and the net torques about the knee joint habe been compared to the patterns of electromyographic activity recorded from certain thigh muscles. The majority of studies in n-hich joint moments throughout the walking cycle have been presented (Bartholemew. 1951: Bresler and Frankel. 1950; Paul. 1971: tilorrison. 1970a) have shown data from undisclosed speeds of walking which were probably not the same in different subjects. All these -results were expressed in srandard derived units which were not related to the anthropometric dimensions of the subjects. Bresler et n[. (1957) indicated that speed had a considerable effect upon the hip and knee torques of unilateral above knee amputees although the variations on both sides uith different prostheses were also large. Gage (1964) presented angular accelerograms from the swing phase which varied considerably with cadencs in both normal and amputee gaits. Paul (1970) has also shown that the mean values of hip and knee torques increase with the body weight of the individual and with stride length and therefore with speed. In experiments on a single subject Cavanagh (1971) showed an approximate sis fold increase in the peak knee flexor torque before heel strike as well as considerable changes of torque shortly after toe off as the speed of walking increased. hlay ( 1971) has also presented idea* R~r’il.cd
19 .4prii 1971.
lized knee moment curves indicating an approximate 50 per cent increase in the Aesor moment before heel strike with an increased cadence from 80 to 100 steps per min. Although Paul (1971) and Morrison (l97Oa. b) recorded simultaneous electromyograms from lower limb and trunk muscles during walking, no indication of the variation in the EMG which accompanied variations in torque was presented. It is the purpose of this paper to examine the effect of both ths speed of walking and variations in individual body segment parameters upon the net muscular torque at the knee joint during the swing phase of normal treadmill walking. In addition. quantified surface EMG’s from various muscles acting across the knee joint are presented for comparison at different speeds of walking.
METHODS a. Anthroponterric
model
and body
segtttettt parameters
The shank and foot were assumed to be a single rigid body attached to the thigh by a frictionless pin joint. The free body diagram for the model is shown in Fig. 1. Since only the saving phase was investigated there were no external forces acting on the limb. All symbols shown on the diagram and in the subsequent equations are defined at the end of the paper. Resolving
vertically: R,
_
by=
5, 9
Resolving horizontally:
Summing moments gravit!
about the shank and foot center of
: - R,r cos 0 - R,r sin 0 - l,,C? = 0.
(1)
33s
P. R. CAVASACHand R. J.
GRECOR
Substituting for R,. R, and replacing
RI
e L L t
The weight of the shank and foot were estimated by a water displacement technique assuming a density of 1.08 (Dempster. 1955). The moment of inertia of the shank and foot about the knee joint was at first estimated by the quick release method. but a systematic investigation of the technique (Cavanagh and Gregor. 1974) cast doubt on its validity. The moment of inertia about the center of gravity was estimated from the value of 30.3 per cent (Drillis and Contini. 1966) for the radius of gyration as a percentage of shank segment length. The center of gravity of the combined shank and foot was assumed to be located 41.6 per cent of segment length distal to the center of rotation of the knee joint (Dempster, 1955; Drillis and Contini. 1966).
Five healthy male subjects whose heights. weights and ages are shown together with body segment parameter data in Table 1. underwent a habituation period of 100 min treadmill walking consisting of periods of 5 min at speeds of 1.5. 2.0. 3.0, 4.0 and 5.0 mph on each of 4 days prior to the experimental day. The subjects walked without shoes and wore minimal clothing. Following the habituation period, the subjects were filmed with a LoCam tine camera at a frame rate of 97 frames per set while they walked at each of the five speeds presented in random manner. White adhesive markers. 0.25 in’, were applied to darkened areas of the skin overlying the superior border of the greater trochanter. the approximate center of rotation of the knee joint. the lateral malleolus and two points on the lateral surface of the foot. The approximate plane of movement of the left lower limb was calibrated using a grid of 6 in squares filmed prior to the walk. A plumb line provided an external vertical reference. and a 100 Hz signal on timing lights within the camera gave precise time calibration. Four pairs of silver-silver chloride surface electrodes were applied to the limb 5cm apart over the medial and lateral hamstring groups.
Ive.
Fig. I. Free body diagram of shank and foot during the swing phase ofwalking. Sign conventions are also indicated.
and at sites overlying rectus femoris and vastus medialis. To standardize the placement of electrodes. lines were constructed on the anterior and posterior surfaces of the thigh. The anterior line was drawn betvveen the center of the superior border of the patella and the anterior superior illiac spine: the posterior line was drawn between the midpoint of the horizontal distance between the superior border of the greater trochanter and the natal cleft and the center of the popliteal crease. The rectus femoris electrodes were placed along the anterior line. 2.5 cm on either side of its midpoint, and the electrodes over vastus medidlis were parallel to the anterior line but 7.5 cm medial to it with the distal electrode 7.5 cm above the patella. Both pairs of hamstring electrodes u’ere placed parallel to the posterior line, 5 cm medial and lateral to it with the distal electrode in each pair at a height of 12.5cm above the popliteal fossa. The electromyograms were amplified using differential amplifiers with a band width of 1~5-500 Hz and recorded on FM magnetic tape together with a synchronization pulse which was also present on the film. Part of the experimental situation is shown in Fig. 2. c. Data ard_vsis A Vanguard Motion Analyzer with a potentiometric readout was used to obtain the X-Ycoordinates of the body markers for every frame of a single swing phase during each trial. Data were collected from ten frames
Table I. Body dimensions of subjects Units Age
Height Weight Shank and foot weight Shank length Shank and foot moment of inertia about knee joint
v in. Ibf. Ibf. in.
Ibf. ft. se?
Subject A
Subject B
Subject C
Subject D
Subject E
29 69 IX
41 69 176
3 71 152
25 72 160
3-I 70 213
9.5 16.1
@I572
11.5 I64
0.1930
1o-4
17.3
O-1963
LO.5 17.6
0.205 I
13.2 174
0.2506
Fig. 2. The experimental
(Frxi/z: p. 338)
situation showing subject E during data collection.
Knez joint torque
before observed toe ofl’ until ten frames after he4 strike. The coordinates were input to a Fortrnn computer program on an IBM 370 165 which calculated the positions. angles and their derivatives required for the solution of equation (2) at each frame. Second derivatives were calculated from the follovving formula described b> Lnnczos (1957):
vvhere (I;, _ n)represents the value of Yat a point kt set before the time at which the second derivative of I-is required. The hea\> filtering effect that this procedure has on the second derivative is discussed elsewhere (Cnvnnagh. 1972). No additional smoothing was performed on an! of the data. The EMG’s were digitized off-line at a rate of 5 kHz per channel using a Hewlett-Packard 21ljA computer. Tht sqchronization p~dsr enabled the parts of the signal corresponding to the swing phase for which coordinJte data was available to be identified. These sections of the EXIG records were digitally full wave rectified and integrated in periods of 50 msec in a manner similar to that described by Grieve and Cavanagh (1973). The 50 msec period containing the greatest amount of activity vvhen all speeds were considered \vas called 100 per cent and all other periods were expressed relative to this maximum. An integral number of 50 msec periods xere alvvays extluated and the last period. containing heel strike. is shown at its complete value but in a reduced time period representing the actual duration of the swing phase. Simultaneous estimates for torque and EMG were thus available throughout the svving phase.
RESCLTS
The torque-time curves for one subject (subject B) at all speeds of walking are shown in Fig. 3. The considerable modifications that appear in these curves as the speed of walking increases can be seen. A torque tending to extend the knee during early swing develops at speeds greater than 2 mph replacing a torque that tended to flea the knee at slower speeds. During late saving at all speeds. a torque tending to Hex the knee is developed falling away rapidly as heel strike approaches. The peak value of this negative torque increases in magnitude steadily as the speed of walking increases. The results for all subjects have been grouped according to the speed of walking and are shovvn in Fig. 4. Similar changes to those described above are seen in all subjects despite differences in the magnitude of the torques. The peak values of torque tending to Hex the knee before heel strike have been plotted for all subjects as a function of speed in Fig. 5. There is a considerable intersubject range of peak torques at any speed. but apart from the lower speeds of walking where subject
Fiv2’ _. ;
ualking.
Torqtle-time cur\es for subject B a~ .dI speeds of All curves begin at observed toe of and exl at observed heel strike.
B had high values. it is clear that the same rank order exists at every speed with subject A having the smallest values and subject E always showing the largest peak at any speed. A fairly linear increase in peak torque with speed is also apparent. During the Inter stages 01‘ swing where these peak values occurred. the posi’tion of the kneejoint in space will tend to be relatively tised and the expression for the value r n,ill. to a tirst approximation. be: I,$ + Cfi sin0. Also 0 is never greater than +25‘ and thus the term It? sin0 rsprssents a maximum negative moment of 29 and 43 Ibf. in. for smallest and largest subjects respectiveI!. The remaining term. 1,s. therefore accounts for most of the variation in torques calculated during the late stages of swing. Variations in the peak angular acceleration. 8. during swing represent the adaption of the individual to the constraints of stride length, speed and linear dimensions of his lower limb segments. .A consistent bias to the torque \vill be from individual differences in I,. and it would appear reasonable to attempt to normalize the results shown in Fig. 5 on the basis of the moment of inertia of the shank and foot about the knee. The data for subjects A. D and E have been extracted from Fig. 5 and presented in a three dimcnsional plot in Fig. 6. The plots representing the peak flexor torque against the speed of walking have been separated in the third dimension according to the value for the moment of inertia. I,. It is clear from this figure that peak torque during’late swing increases vvith both the speed of walking and the moment of inertia I,. To obtain a mean all speeds profile of the torqutime curves which might be applicable to any subject regardless of the value of I,. all the curves shown in Fig. 1 uere normalized by_multiplying each discrete value of T by (7,. I,). where I, uc’as0.20 Ibf. ft. se?. the mean value of the moment of inertia from all five subjects. A mean normalized pattern at each speed was then calculated and the results are shown in Fig. 7. The differences in swing time between subjects at a given speed have been accounted for by using percentage
310
P. R. CAVAXAGH
and R. J. GREGOR
200 r
>... ,.... .., -v
$ :
-200
-300
F
- 4001
0.1
0.2
0.3
Time,
5: 2
“2
‘>_
0
\ -
s
P
:
-100
-400
o’,
I 0.3
’ 0.2
.
Ttme, 200
I
I 0.6
1
1 O.,
ii/ j
1
0:3
0.2
0’4
Time,
I
I
0.5
0.6
curves for all subjects grouped according
swing time as a basis for the calculation of each mean curve while maintaining the proportionate relationships between mean swing times at different speeds of walking.
I z
o-3
O-4
0.6
set
SK
Fig. 3. Torque-time
0,
0.5
i 1 :., ‘_ :: : i .:
T ~me.
set
,,
(e)
r
-400
I 0.5
0.4
; ,,: ;
.?\i
\
i,
- 300
I
0.6
!.
\
‘; ,
-200
0.5
‘.s.
=..,
‘,
co 8
0.4
set
I 3
Speed,
I 4
I 5
mvh
Fig. 5. The peak flexor torque before heel strike plotted against the spsed of walking for all subjects.
to
the speed of walking
The power characteristics of the knee joint at different speeds of walking were obtained from the product of net torque and knee joint angular velocity. The definitions of Bresler and Berry (1951) which differentiate between power output and dissipation were adopted: power output was said to occur when the net muscular torque and the angular velocity were in the same direction, power dissipation whsn torque and angular velocity were in opposite directions. The results for subjects A and Eat I.5 and 5 mph are shown in Fig. 8. These represent the extremes of the results obtained and show at 1.5 mph a continuous low level dissipation of power throughout most of the swing phase which is similar in both subjects. At 5 mph there is a radically different situation and thr22 identifiable phases are apparent in both subjects. At toe off, the knee continues to flex and a net positive torque is devzloped to halt and sventually reverse this flexion. Thus there is a dissipation of power in this tirst phase which. in subjzct D, ends with power output
Knee joint
torque
Fig. 7. blean normalized torque-time curves from all subjects at five speeds of walking. The dotted Itncs join the value of torque at observed toe off and heel strike to the time axes.
? Fig. 6. A three dimensional Calcomp representation of the peak Hexor torque plotted against the speed of walking (as in Fig. 5) but separated in the third dimension on the basis of the moment of Inertia of the shank and foot about the knee joint. Data from subjects A. D and E are shown.
as knee extension begins. The second phase is the major dissipation phase in both subjects as negative torques tend to resist the extension that is underway. the peak power dissipated reaching 65 and 160 ft. lb. set- I in subjects A and E. respectively. The final phase of the power characteristic is one of power output as the knee Hexes slightly prior to heel strike and a net negative torque persists.
The integrated EMG’s from rectus femoris and the lateral hamstring group for subject B at all speeds of walking are shown in Fig. 9. These results correspond to the torque-time curves for this subject shown in Fig. 3. The increase in torque tending to flex the knee immediately before heel strike which was noted preciously is seen to be accompanied by a steady increase
output
I
in the lateral hamstring activity as the speed of walking increases. However. it is clear from Fig. 9 that there is some co-contraction of flexors and extensors during late swing, with rectus femoris activity developing during the final 100 msec before heel strike. At the highest speed. the high level of activity in the rectus femoris in the region of toe-off is also prominent. suggesting that it is being used partly to produce the torque tending to extend the knee which is seen in Fig. 3 at this speed of walking. Similar patterns of electromyograms were noted in all five subjects and Fig. 10 represents a mean picture of the electrical activity of the 4 muscles investigated in all 5 subjects.
DISCL’SSIOS The accuracy of results from experiments of this nature are limited by tvvo important factors: the validity of the anthropometric model used and the methods used to obtain acceleration from displacement-time data. The model assumed in the present
I.5 mph
5.0 mph
150 t IO0
:
L I
c
I
Phase 2
I
:
50
50
\ P
t
z
0 \.-
/ i
Phase 3
r\
.I \
1
‘.
-
.. to be diKerent and only limited data under isometric conditions are available for the value of this dela! (Inman CJ~(II.. 192). Also. the co-contraction of flexors and estcnsors whjch was observed would complicatc the establishment of a simple relationship het\veen the EMG from any one muscle group and the net torque about the joint. The changes in the power characteristics of the normal knee joint as the speed ofkvalking increases, shown in Fig. 8. are particularly relevant considerations in delining the performance criteria of prosthetic knee mechanisms designed to provide external power or restraint during the swing phase (Wallach and Saibel. 19701. !Vhiie being a relatively passive component at lower speeds of walking, the function of the knee joint at higher speeds becomes increasingly that of dissipation of pobver. This versatility of the human knee joint is clearI> an important factor in the wide range of speeds that the normal person has at his disposal. Despitc the fact that the mass and intertial properties of :I prosthetic replacement will be different from those of the normal subject and that the anatomy of the thigh G ill be considerably changed by an aboLe knee amputatlon it is likeI> that similar changes in the power characteristics of the prosthetic knee will be required. The considerable amounts of power dissipated at the knee during the siving phase at higher speeds of walking indicates that possibilities for energ! storage exist during this phase of the cycle. However. it must be emphasized that both dissipation and output of power at the knee joint are greater during the stance phase than during samg (Bresler and Berry. 1951) and it is important that the bvhole walking cycle be considered in this respect.
T\\o main conclusions are to be drawn from the results of the present study. Firstly. both the torque and EXIG results show a dependence upon speed lo hich emphasizes the importance of considering the speed of ivalking as a major variable in locomotion
studies. Secondly. the results indicate that the variations in the magnitude of torque due to muscular activity produced at the knee can be rationalized between subjects if the r&vent bodb segment parameter-in this case the moment of inertia of the shank and foot about the knee-is considered. The large variations in peak torques Lvere obtained during the swing phase of normal walking. and it is likely that other activities in the daily life of the normai person and the amputee will demand much greater restraining torques. .~ckJlo~~~rtiyr,nr,lcs--This work was supported in part by a grant from the Faculty Research Fund. College of HPER. PSU. The authors are grateful to Dr. D. W. Grieve for his comments on the manuscript. to Xlessrs. Ken Petak. John Palmgren and Chuck Kuhn for their technical assistance. REFERESCES
Bartholemew. S. H. (1952) Determination
of knee mornents during the swing phase of walking and physical constants of the human shank. Prosth. Dev. Res. Proj. Institute of Eng. Research. Cnlv. Calif.. Berkeley. Series Il. Issur 19. Bigland. B. and Lippold. 0. C. J. (193) The relation betbvesn force. velocity and integrated electrical actibitk in human muscles. J. Phrsiol. 113, 211-22-L Brooks. C. M. i 19731 Validation of the gamma mass scanner for determination of center of gravity and moment of inertia of biological tissue. (Unpublished blasters Thesis) Pennsylvania State University. Bresler. B. and Berry. F. R.. Jr. (I95 I) Energy and power in the leg during normal level ivalking. Prosth. Dev. Rrs. Proj. Institute of Eng. Research. Univ. Calif.. Berkele>. Series I I. ISSlIt 15. Bresler. B. and Frankel. J. (1950) The forces and moments in the leg during level walking. 7ix~s. .4.S..LI.E. 72, Paper No. 1%.A-62. pp. 27-36. Bresler. B.. Radcliffe. C. W. and Berry. F. R.. Jr. (1957) Energy and power in the legs of above-knee amputees during normal 15~21 walking. Lower Evtremitv Amputee Research Project. Institute of Eng. Research. ogram to muscular tension. EEG c/it!. .Yruroph~siol. 4. 187-191.
344
P. R. C.-\VI\NAGH and R. J.
Lanczos. C. (1957) Applied .kzl,vsis. Pitmans. Sew York. Lindholm. L. E. (1974) An optoelectronic instrument for remote on-line movement monitorina. Biomrchanics IV. (Edited by Nelson. R. C. and MorehoLse, C. A.). University Park Press. Baltimore. May. D. R. W. (1971) The development of a comprehensive external prosthetic knee control. Confrrence on Human Locomotor Engineering, pp. 179-195. Inst. &tech. Engnrs. London. Morris. J. R. W. (1973) Accelerometry-A technique for the measurement of Human Body Movements. J. Biomrchnnics
Mai.
63, 200.
Paul, J. P. (1971) Comparison of EMG signals from leg muscles with the corresponding force actions calculated from walkpath measurements. Cor$rrncr on Human Locomoror E:rzgiwering, pp. 13-X Inst. Mech. Engnrs., London.
Wallach, J. and Saibel. E. (1970) Control mechanism performance criteria for an above-knee leg prosthesis. J. Biomechanics
3, 87-97.
SOSlESCL.ATURE
6, 729-736.
Morrison. J. B. (197Oa) The mechanics of the knee joint in relation to normal walking. J. Biomechnuics 3, 5 l-61. Morrison. J. B. (1970b) The mechanics of muscle function in locomotion. J. Biomechdcs 3, 43 I-45 I. Paul. J. P. (1970) The effect of walking speed on the force actions transmitted at the hip and knee joint. Proc. R. Sot.
GRECOR
r
vertical component of reaction at the knee joint horizontal component of reaction at the knee joint weight of shank and foot acceleration due to gravity vertical component of acceleration of shank and foot center of gravity horizontal component of acceleration of shank and foot center of gravity net torque due to muscular action at the knee joint knee joint center to shank and foot center of gravrity distance shank angle to vertical moment of inertia of shank and foot through center of gravity in sagittal plane moment of inertia of shank and foot through knee joint center in sagittal plane the mean value for I, calculated for the 5 subjects.
State Cni\srsity.
University
Park. Pennsylvania
16802. CL-!.
;tbstract--Net torques due to muscular action at the knee joint have been calculated in five normal male subjects during the swing phase of treadmill walking at speeds ranging from I.5 to 5 mph. Surface clectromjograms were also recorded from selected muscle groups in the thigh. The results indicate that in a given subject the variations in peak torque can be explained on the basis of walking speed. The EblG’s also show modifications which are speed dependent. From an examination of torques in all ti\r subjects. it is su ggested that consideration of the relevant body segment parameter is necessary to account for the between subject variations that are encountered at a given speed of walking. The versatility of the normal knee joint is emphasized in a discussion of the calculated power characteristlcs and the implications of these findings for prosthetic replacement of the knee are discussed.
IVTRODLCTIOS It is to be svpccted that changes in the speed of walking and the inertia of the limb segments will affect the muscular torques acting about the joints of the lower limb during normal human locomotion. It is well kno\vn that a wide (eight-fold) range of speeds is possible (Grieve. 1969) and that a three-fold range of moments of inertia of the shank and foot was found in a group of only eight cadavers (Dempster. 1955). In this paper a systematic study of both of these factors in the development of muscular torques during the swing phase ofwalking has been made and the net torques about the knee joint habe been compared to the patterns of electromyographic activity recorded from certain thigh muscles. The majority of studies in n-hich joint moments throughout the walking cycle have been presented (Bartholemew. 1951: Bresler and Frankel. 1950; Paul. 1971: tilorrison. 1970a) have shown data from undisclosed speeds of walking which were probably not the same in different subjects. All these -results were expressed in srandard derived units which were not related to the anthropometric dimensions of the subjects. Bresler et n[. (1957) indicated that speed had a considerable effect upon the hip and knee torques of unilateral above knee amputees although the variations on both sides uith different prostheses were also large. Gage (1964) presented angular accelerograms from the swing phase which varied considerably with cadencs in both normal and amputee gaits. Paul (1970) has also shown that the mean values of hip and knee torques increase with the body weight of the individual and with stride length and therefore with speed. In experiments on a single subject Cavanagh (1971) showed an approximate sis fold increase in the peak knee flexor torque before heel strike as well as considerable changes of torque shortly after toe off as the speed of walking increased. hlay ( 1971) has also presented idea* R~r’il.cd
19 .4prii 1971.
lized knee moment curves indicating an approximate 50 per cent increase in the Aesor moment before heel strike with an increased cadence from 80 to 100 steps per min. Although Paul (1971) and Morrison (l97Oa. b) recorded simultaneous electromyograms from lower limb and trunk muscles during walking, no indication of the variation in the EMG which accompanied variations in torque was presented. It is the purpose of this paper to examine the effect of both ths speed of walking and variations in individual body segment parameters upon the net muscular torque at the knee joint during the swing phase of normal treadmill walking. In addition. quantified surface EMG’s from various muscles acting across the knee joint are presented for comparison at different speeds of walking.
METHODS a. Anthroponterric
model
and body
segtttettt parameters
The shank and foot were assumed to be a single rigid body attached to the thigh by a frictionless pin joint. The free body diagram for the model is shown in Fig. 1. Since only the saving phase was investigated there were no external forces acting on the limb. All symbols shown on the diagram and in the subsequent equations are defined at the end of the paper. Resolving
vertically: R,
_
by=
5, 9
Resolving horizontally:
Summing moments gravit!
about the shank and foot center of
: - R,r cos 0 - R,r sin 0 - l,,C? = 0.
(1)
33s
P. R. CAVASACHand R. J.
GRECOR
Substituting for R,. R, and replacing
RI
e L L t
The weight of the shank and foot were estimated by a water displacement technique assuming a density of 1.08 (Dempster. 1955). The moment of inertia of the shank and foot about the knee joint was at first estimated by the quick release method. but a systematic investigation of the technique (Cavanagh and Gregor. 1974) cast doubt on its validity. The moment of inertia about the center of gravity was estimated from the value of 30.3 per cent (Drillis and Contini. 1966) for the radius of gyration as a percentage of shank segment length. The center of gravity of the combined shank and foot was assumed to be located 41.6 per cent of segment length distal to the center of rotation of the knee joint (Dempster, 1955; Drillis and Contini. 1966).
Five healthy male subjects whose heights. weights and ages are shown together with body segment parameter data in Table 1. underwent a habituation period of 100 min treadmill walking consisting of periods of 5 min at speeds of 1.5. 2.0. 3.0, 4.0 and 5.0 mph on each of 4 days prior to the experimental day. The subjects walked without shoes and wore minimal clothing. Following the habituation period, the subjects were filmed with a LoCam tine camera at a frame rate of 97 frames per set while they walked at each of the five speeds presented in random manner. White adhesive markers. 0.25 in’, were applied to darkened areas of the skin overlying the superior border of the greater trochanter. the approximate center of rotation of the knee joint. the lateral malleolus and two points on the lateral surface of the foot. The approximate plane of movement of the left lower limb was calibrated using a grid of 6 in squares filmed prior to the walk. A plumb line provided an external vertical reference. and a 100 Hz signal on timing lights within the camera gave precise time calibration. Four pairs of silver-silver chloride surface electrodes were applied to the limb 5cm apart over the medial and lateral hamstring groups.
Ive.
Fig. I. Free body diagram of shank and foot during the swing phase ofwalking. Sign conventions are also indicated.
and at sites overlying rectus femoris and vastus medialis. To standardize the placement of electrodes. lines were constructed on the anterior and posterior surfaces of the thigh. The anterior line was drawn betvveen the center of the superior border of the patella and the anterior superior illiac spine: the posterior line was drawn between the midpoint of the horizontal distance between the superior border of the greater trochanter and the natal cleft and the center of the popliteal crease. The rectus femoris electrodes were placed along the anterior line. 2.5 cm on either side of its midpoint, and the electrodes over vastus medidlis were parallel to the anterior line but 7.5 cm medial to it with the distal electrode 7.5 cm above the patella. Both pairs of hamstring electrodes u’ere placed parallel to the posterior line, 5 cm medial and lateral to it with the distal electrode in each pair at a height of 12.5cm above the popliteal fossa. The electromyograms were amplified using differential amplifiers with a band width of 1~5-500 Hz and recorded on FM magnetic tape together with a synchronization pulse which was also present on the film. Part of the experimental situation is shown in Fig. 2. c. Data ard_vsis A Vanguard Motion Analyzer with a potentiometric readout was used to obtain the X-Ycoordinates of the body markers for every frame of a single swing phase during each trial. Data were collected from ten frames
Table I. Body dimensions of subjects Units Age
Height Weight Shank and foot weight Shank length Shank and foot moment of inertia about knee joint
v in. Ibf. Ibf. in.
Ibf. ft. se?
Subject A
Subject B
Subject C
Subject D
Subject E
29 69 IX
41 69 176
3 71 152
25 72 160
3-I 70 213
9.5 16.1
@I572
11.5 I64
0.1930
1o-4
17.3
O-1963
LO.5 17.6
0.205 I
13.2 174
0.2506
Fig. 2. The experimental
(Frxi/z: p. 338)
situation showing subject E during data collection.
Knez joint torque
before observed toe ofl’ until ten frames after he4 strike. The coordinates were input to a Fortrnn computer program on an IBM 370 165 which calculated the positions. angles and their derivatives required for the solution of equation (2) at each frame. Second derivatives were calculated from the follovving formula described b> Lnnczos (1957):
vvhere (I;, _ n)represents the value of Yat a point kt set before the time at which the second derivative of I-is required. The hea\> filtering effect that this procedure has on the second derivative is discussed elsewhere (Cnvnnagh. 1972). No additional smoothing was performed on an! of the data. The EMG’s were digitized off-line at a rate of 5 kHz per channel using a Hewlett-Packard 21ljA computer. Tht sqchronization p~dsr enabled the parts of the signal corresponding to the swing phase for which coordinJte data was available to be identified. These sections of the EXIG records were digitally full wave rectified and integrated in periods of 50 msec in a manner similar to that described by Grieve and Cavanagh (1973). The 50 msec period containing the greatest amount of activity vvhen all speeds were considered \vas called 100 per cent and all other periods were expressed relative to this maximum. An integral number of 50 msec periods xere alvvays extluated and the last period. containing heel strike. is shown at its complete value but in a reduced time period representing the actual duration of the swing phase. Simultaneous estimates for torque and EMG were thus available throughout the svving phase.
RESCLTS
The torque-time curves for one subject (subject B) at all speeds of walking are shown in Fig. 3. The considerable modifications that appear in these curves as the speed of walking increases can be seen. A torque tending to extend the knee during early swing develops at speeds greater than 2 mph replacing a torque that tended to flea the knee at slower speeds. During late saving at all speeds. a torque tending to Hex the knee is developed falling away rapidly as heel strike approaches. The peak value of this negative torque increases in magnitude steadily as the speed of walking increases. The results for all subjects have been grouped according to the speed of walking and are shovvn in Fig. 4. Similar changes to those described above are seen in all subjects despite differences in the magnitude of the torques. The peak values of torque tending to Hex the knee before heel strike have been plotted for all subjects as a function of speed in Fig. 5. There is a considerable intersubject range of peak torques at any speed. but apart from the lower speeds of walking where subject
Fiv2’ _. ;
ualking.
Torqtle-time cur\es for subject B a~ .dI speeds of All curves begin at observed toe of and exl at observed heel strike.
B had high values. it is clear that the same rank order exists at every speed with subject A having the smallest values and subject E always showing the largest peak at any speed. A fairly linear increase in peak torque with speed is also apparent. During the Inter stages 01‘ swing where these peak values occurred. the posi’tion of the kneejoint in space will tend to be relatively tised and the expression for the value r n,ill. to a tirst approximation. be: I,$ + Cfi sin0. Also 0 is never greater than +25‘ and thus the term It? sin0 rsprssents a maximum negative moment of 29 and 43 Ibf. in. for smallest and largest subjects respectiveI!. The remaining term. 1,s. therefore accounts for most of the variation in torques calculated during the late stages of swing. Variations in the peak angular acceleration. 8. during swing represent the adaption of the individual to the constraints of stride length, speed and linear dimensions of his lower limb segments. .A consistent bias to the torque \vill be from individual differences in I,. and it would appear reasonable to attempt to normalize the results shown in Fig. 5 on the basis of the moment of inertia of the shank and foot about the knee. The data for subjects A. D and E have been extracted from Fig. 5 and presented in a three dimcnsional plot in Fig. 6. The plots representing the peak flexor torque against the speed of walking have been separated in the third dimension according to the value for the moment of inertia. I,. It is clear from this figure that peak torque during’late swing increases vvith both the speed of walking and the moment of inertia I,. To obtain a mean all speeds profile of the torqutime curves which might be applicable to any subject regardless of the value of I,. all the curves shown in Fig. 1 uere normalized by_multiplying each discrete value of T by (7,. I,). where I, uc’as0.20 Ibf. ft. se?. the mean value of the moment of inertia from all five subjects. A mean normalized pattern at each speed was then calculated and the results are shown in Fig. 7. The differences in swing time between subjects at a given speed have been accounted for by using percentage
310
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The power characteristics of the knee joint at different speeds of walking were obtained from the product of net torque and knee joint angular velocity. The definitions of Bresler and Berry (1951) which differentiate between power output and dissipation were adopted: power output was said to occur when the net muscular torque and the angular velocity were in the same direction, power dissipation whsn torque and angular velocity were in opposite directions. The results for subjects A and Eat I.5 and 5 mph are shown in Fig. 8. These represent the extremes of the results obtained and show at 1.5 mph a continuous low level dissipation of power throughout most of the swing phase which is similar in both subjects. At 5 mph there is a radically different situation and thr22 identifiable phases are apparent in both subjects. At toe off, the knee continues to flex and a net positive torque is devzloped to halt and sventually reverse this flexion. Thus there is a dissipation of power in this tirst phase which. in subjzct D, ends with power output
Knee joint
torque
Fig. 7. blean normalized torque-time curves from all subjects at five speeds of walking. The dotted Itncs join the value of torque at observed toe off and heel strike to the time axes.
? Fig. 6. A three dimensional Calcomp representation of the peak Hexor torque plotted against the speed of walking (as in Fig. 5) but separated in the third dimension on the basis of the moment of Inertia of the shank and foot about the knee joint. Data from subjects A. D and E are shown.
as knee extension begins. The second phase is the major dissipation phase in both subjects as negative torques tend to resist the extension that is underway. the peak power dissipated reaching 65 and 160 ft. lb. set- I in subjects A and E. respectively. The final phase of the power characteristic is one of power output as the knee Hexes slightly prior to heel strike and a net negative torque persists.
The integrated EMG’s from rectus femoris and the lateral hamstring group for subject B at all speeds of walking are shown in Fig. 9. These results correspond to the torque-time curves for this subject shown in Fig. 3. The increase in torque tending to flex the knee immediately before heel strike which was noted preciously is seen to be accompanied by a steady increase
output
I
in the lateral hamstring activity as the speed of walking increases. However. it is clear from Fig. 9 that there is some co-contraction of flexors and extensors during late swing, with rectus femoris activity developing during the final 100 msec before heel strike. At the highest speed. the high level of activity in the rectus femoris in the region of toe-off is also prominent. suggesting that it is being used partly to produce the torque tending to extend the knee which is seen in Fig. 3 at this speed of walking. Similar patterns of electromyograms were noted in all five subjects and Fig. 10 represents a mean picture of the electrical activity of the 4 muscles investigated in all 5 subjects.
DISCL’SSIOS The accuracy of results from experiments of this nature are limited by tvvo important factors: the validity of the anthropometric model used and the methods used to obtain acceleration from displacement-time data. The model assumed in the present
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.. to be diKerent and only limited data under isometric conditions are available for the value of this dela! (Inman CJ~(II.. 192). Also. the co-contraction of flexors and estcnsors whjch was observed would complicatc the establishment of a simple relationship het\veen the EMG from any one muscle group and the net torque about the joint. The changes in the power characteristics of the normal knee joint as the speed ofkvalking increases, shown in Fig. 8. are particularly relevant considerations in delining the performance criteria of prosthetic knee mechanisms designed to provide external power or restraint during the swing phase (Wallach and Saibel. 19701. !Vhiie being a relatively passive component at lower speeds of walking, the function of the knee joint at higher speeds becomes increasingly that of dissipation of pobver. This versatility of the human knee joint is clearI> an important factor in the wide range of speeds that the normal person has at his disposal. Despitc the fact that the mass and intertial properties of :I prosthetic replacement will be different from those of the normal subject and that the anatomy of the thigh G ill be considerably changed by an aboLe knee amputatlon it is likeI> that similar changes in the power characteristics of the prosthetic knee will be required. The considerable amounts of power dissipated at the knee during the siving phase at higher speeds of walking indicates that possibilities for energ! storage exist during this phase of the cycle. However. it must be emphasized that both dissipation and output of power at the knee joint are greater during the stance phase than during samg (Bresler and Berry. 1951) and it is important that the bvhole walking cycle be considered in this respect.
T\\o main conclusions are to be drawn from the results of the present study. Firstly. both the torque and EXIG results show a dependence upon speed lo hich emphasizes the importance of considering the speed of ivalking as a major variable in locomotion
studies. Secondly. the results indicate that the variations in the magnitude of torque due to muscular activity produced at the knee can be rationalized between subjects if the r&vent bodb segment parameter-in this case the moment of inertia of the shank and foot about the knee-is considered. The large variations in peak torques Lvere obtained during the swing phase of normal walking. and it is likely that other activities in the daily life of the normai person and the amputee will demand much greater restraining torques. .~ckJlo~~~rtiyr,nr,lcs--This work was supported in part by a grant from the Faculty Research Fund. College of HPER. PSU. The authors are grateful to Dr. D. W. Grieve for his comments on the manuscript. to Xlessrs. Ken Petak. John Palmgren and Chuck Kuhn for their technical assistance. REFERESCES
Bartholemew. S. H. (1952) Determination
of knee mornents during the swing phase of walking and physical constants of the human shank. Prosth. Dev. Res. Proj. Institute of Eng. Research. Cnlv. Calif.. Berkeley. Series Il. Issur 19. Bigland. B. and Lippold. 0. C. J. (193) The relation betbvesn force. velocity and integrated electrical actibitk in human muscles. J. Phrsiol. 113, 211-22-L Brooks. C. M. i 19731 Validation of the gamma mass scanner for determination of center of gravity and moment of inertia of biological tissue. (Unpublished blasters Thesis) Pennsylvania State University. Bresler. B. and Berry. F. R.. Jr. (I95 I) Energy and power in the leg during normal level ivalking. Prosth. Dev. Rrs. Proj. Institute of Eng. Research. Univ. Calif.. Berkele>. Series I I. ISSlIt 15. Bresler. B. and Frankel. J. (1950) The forces and moments in the leg during level walking. 7ix~s. .4.S..LI.E. 72, Paper No. 1%.A-62. pp. 27-36. Bresler. B.. Radcliffe. C. W. and Berry. F. R.. Jr. (1957) Energy and power in the legs of above-knee amputees during normal 15~21 walking. Lower Evtremitv Amputee Research Project. Institute of Eng. Research. ogram to muscular tension. EEG c/it!. .Yruroph~siol. 4. 187-191.
344
P. R. C.-\VI\NAGH and R. J.
Lanczos. C. (1957) Applied .kzl,vsis. Pitmans. Sew York. Lindholm. L. E. (1974) An optoelectronic instrument for remote on-line movement monitorina. Biomrchanics IV. (Edited by Nelson. R. C. and MorehoLse, C. A.). University Park Press. Baltimore. May. D. R. W. (1971) The development of a comprehensive external prosthetic knee control. Confrrence on Human Locomotor Engineering, pp. 179-195. Inst. &tech. Engnrs. London. Morris. J. R. W. (1973) Accelerometry-A technique for the measurement of Human Body Movements. J. Biomrchnnics
Mai.
63, 200.
Paul, J. P. (1971) Comparison of EMG signals from leg muscles with the corresponding force actions calculated from walkpath measurements. Cor$rrncr on Human Locomoror E:rzgiwering, pp. 13-X Inst. Mech. Engnrs., London.
Wallach, J. and Saibel. E. (1970) Control mechanism performance criteria for an above-knee leg prosthesis. J. Biomechanics
3, 87-97.
SOSlESCL.ATURE
6, 729-736.
Morrison. J. B. (197Oa) The mechanics of the knee joint in relation to normal walking. J. Biomechnuics 3, 5 l-61. Morrison. J. B. (1970b) The mechanics of muscle function in locomotion. J. Biomechdcs 3, 43 I-45 I. Paul. J. P. (1970) The effect of walking speed on the force actions transmitted at the hip and knee joint. Proc. R. Sot.
GRECOR
r
vertical component of reaction at the knee joint horizontal component of reaction at the knee joint weight of shank and foot acceleration due to gravity vertical component of acceleration of shank and foot center of gravity horizontal component of acceleration of shank and foot center of gravity net torque due to muscular action at the knee joint knee joint center to shank and foot center of gravrity distance shank angle to vertical moment of inertia of shank and foot through center of gravity in sagittal plane moment of inertia of shank and foot through knee joint center in sagittal plane the mean value for I, calculated for the 5 subjects.
