The influence of limb alignment on the gait of above-knee amputees

J. Bionuchanics Vol. 24. No. II, PP. 981-997, 1991. Prisfd

m21-9290/w

in Great Britain

s3.oo+m

Pergmoa Rcu pk

THE INFLUENCE

OF LIMB ALIGNMENT ON THE GAIT OF ABOVE-KNEE AMPUTEES

L. YANG,S.E. !&LOMONIDIS,* W. D. SPENCE and J. P. PAUL Bioengineering Unit, University of Strathclyde, Glasgow G4 ONW, U.K. Aketrac$-Biomechanical gait tceb on above-knee amputeea were conducted in which the alignment of the urosthesis was chantted evstcmaticull~. An cittbt-#nment biomechanicll model of the above-knee amnutec of alignment changes on the above-knee amputeea’gait were studied iu terms of the anguhu displacements of the lower limbs, ground reactiona and intersegmental momenta It was found that following the a@ment

amp;ta. l-be &ound r&&on force WM&n&e

to ali&uent chanw and in par&u& t& chaugu k the

antero-posterior interaegmental moments at the prosthetic ankle and knee jointa we&evidently i&enced

by alignment.

gAgyuyo :-

NOMENCXATURE FOX

peak. values of the push-off (accefemting) and brek&g @=htrating) forced =pectrvelY (=

TCP,

Tx0 XG

xK.

yK

time at which the centre of predsure of the grouud reaction force entera the toe area, i.e. the end of the tran&ion period of the progression of the Ctntre of pressure (see Fig 9) time at which the centre of pressure of the ground reaction force leaves the heel area, i.e. the start of the tramrition period of the progression ofthecentreofpremure(eeeFig9) inotaut of time at which the fore-aft component of the ground reaction force change8 from negative to positive (tee Fig 9) x-c@udmate of the ceutre of PFUre of the ground reaction force with respect to the ground coordinate ‘8~tur.l X-coordinate of the centre of prcmure of the ground reaction force with respect to the posterior corner of the heel X- and Yuxxdinates of the knee joint ccntre with rapect to the ground coordinate system X- and Y-coordinated of the knee joint centn with rcepect to the posterior corner of the heel X-coordinate of the posterior corner of the heel at heel strike with reupectto the ground coordinate ryatem A/p angular changes of the prosthetic anklrin the FAGS (-a’, -39 O”, 3”, 6”) (positive in plantar &xi00 direction) A/P angular changes of the prosthetic ankle in the PSACS: (6’, 39 o”, -33 -67 (positive in plantar fiexion direction) static orientation angle of the prosthetic foot (with #optimalalignment) in the AjP plane with rapecttothegroundframeofr&rence dyuamic orientation angle of the prosthetic foot (withoptimalahgnment)intheA/Pplanewith respect to the ground frame of mfemnce

Rec&ed inJburfJbrm 25 February 1991. l Author to whom corrupondence ahould be addremed. 8~ 24:11-A

in the

,6)(poatttveinfkxion

direction) A/I’angularchangeaofthesocketintheSACS (-6”, - 3”, O”,3”, 6”) (positive in Sexion direo tion) static orientation angle of the Eocket(with optimalaligmnent)intlieA/rJplanewithrespectto thegroundframeofmfemnce dvnamic orientation annk of the socket (with

for+aft component of the ground reaction force (positive is the aqekrating force) vertical component of the ground reaction force

xpE

chyu= &the +d ,-3,0”,3

the ground frame of &a static orientation angle of the prosthetic shank (with optimal alignment) in the m plane with respect to the ground frame of reference dynamic orientation angle of the pro&he& 8hank(withoptimalaligmnent)intheA/Ppiane with raqcct to the ground frame of reference

Successful rehabilitation of amputees requires that the prostheses fitted to them fulf3l the needs of each individual amputee with respect to three most important criteria: comfort, function and cosmesis. In order to satisfy the requircments, the socket must be fitted accurately and comfortably around the stump, and the various prosthetic components should be correctly chosen, assembled and aligned to provide maximum restoration of function and minimum gait deviation. The alignment of the prosthesis. defined as the relative position and orientation of the prosthetic components, affects all three criteria. Improper alignment would result in undcsirabk pressure distribution at the socket/stump interface giving rise to discomfort, pain and even tissue breakdown. Incorrect alignment could also inlluencc the function of the prosthesis. For example, an exccsai~e knee set-back would make knee flexion at the time of push-off di5cult. Finally, apart from the direct inffwnce ofthe alignment on the standing appeamncc ofthe amputeq the amputee would change his/her normal manner of walking in an attempt to compensate for any problems 981

982

L. YANG

comfort and function of the prosthesis, resulting in greater gait deviations. In current prosthetic practice, the final alignment of the prosthesis is arrived at by utilizing the prosthetist’s skill and experience and the patient’s comments. During the phase of dynamic alignment, the prosthetist observes the walking amputee from all angles, listens to his/her comments and makes adjustments, based on subjective judgement, aiming to satisfy the patient and to achieve minimum gait deviation. This !inal alignment, which ideally should be optimal and unique, is commonly referred to as the ‘optimal alignment’. However, the present subjective techniques of assessing the amputee’s gait have been stated to be inadequate. Saleh (1985)reported that visual observation is neither reliable nor sensitive enough to detect small gait deviations and the amputee’s comments are not always helpful, particularly in the case of geriatric patients. Therefore, modem gait analysis techniques have been adopted in an attempt to increase efficiency in obtaining prosthetic alignment. Several papers (e.g. Pearson er al., 1973; Winarski and Pearson, 1984) reported the effects of the alignment on the socket/ stump pressure distribution. Due to technical difficulties, only the normal pressure at selected sites was monitored. These investigations more or less concentrated on the aspect of comfort and the whole picture of the gait pattern was missed. Some other investigators (e.g. Hannah et al., 1984, Mizrahi et al., 1986) refer to the symmetry of the gait between the prosthetic and una&cted limbs. These researchers believe that correct alignment should reduce the asymmetry in the movement of the lower limbs. This concept is questionable however, since, as Winter and Sienko (1988)rightly pointed out, an amputee suffers a major asymmetry in the neuromuscular skeletal system; his/her function caenot be optimal when the gait is symmetrical. Instead, the amputee probably adopts a new asymmetrical optimum within the constraints of his/her residual system and prosthesis. Then is a need to study the amputee’s gait represented by variables such as joint moments and power. However, few detailed reports dealing with this subject have ap peared in the literature (Bresler et al., 1957;Cappozzo et ai., 1976; Lewallen et al., 1985;Winter and Sienko, 1988),and only three (Zahedi et al., 1985;Saleh, 1985; Morimoto et al., 1987)reported studies relating joint moments to alignment, the latter two of them dealing with below knee (BK) amputees. Since the 19708,investigations into the alignment of lower limb prosthhave been carried out at the Bioengineering Unit, University of Strathclyde. During an evaluation programme of the current modular limbs (Solomonidis, 1975,1980), the method of defining the alignment parameters and the technique for measuring the parameters were developed, making it possible to compare the diErent alignments quantitatively. In that programme, the alignment of the BK and above-knee (AK) prostheses was one of the-factors studied. It was found that the prosthetist aligning any in the

et 01.

one amputee with several limbs could come to a different final alignment for each limb, thus throwing the idea of a unique alignment for each amputee into doubt. Zahedi et al. (1986) conducted an extensive study on the alignment of BK and AK prostheses and the results confirmed that an amputee could tolerate several alignments. In another report (Zahedi et al., 1985),they presented the effects of alignment on the amputee’s gait and suggested that it was possible to select biomechanically the most suitable alignment from the range of acceptable alignments for any one amputee. However, it was recognized that the biomechanical aspects of the process were not fully established. This paper reports a recent study of the biomechanits of the AK amputee’s locomotion in relation to the prosthetic alignment. It is the goal of this paper to discuss how the AK amputees altered their gait, in terms of the angular displacements and joint moments, as a result of the alignment changes of the prostheses. Mlmi0Do~Y

The well-known method of inverse dynamics pioneered by Bresler and Frankel(l950) was used in this study. Briefly, for any body segment as shown in Fig. 1, if the following quantities are known: F,, M1 = the force and moment vectors acting at the distal joint of a body segment, respectively. Ifthe body segment concerned is the foot, the two quantities represent the ground reaction force and moment acting at the centre of F,, W

Pt.=?CR = the inertia (including

gravity) force and moment acting at or about the centre of gravity (CC) of the segment;

Fig. 1. The biomcchanical model of a body segment witb the vectors of resultant foras and moments. In the figure, {X, Y, Z} and {X,, Y,,Z,} are the fucd laboratory axes 8y8tcm and local segmental axes system respectively.

Limb alignment in above-knee amputees rt , rl, rc = the position vectors of the distal joint

centre, proximal joint centre and the centre of gravity of the body segment. The force and moment vectors acting at the proximal joint antre can be found as F,= -FI-Fi M,=-MI-M,-(r,-r,)xF,-(r,-r,)xF,.

(1)

The Cartesian coordinate system {X, Y, Z) shown in Fig. 1 was adopted as the laboratory axis system with positive directions being forward (in the direction of walking), upward and from left to right respectively. Fora components are taken as positive when acting along the positive direction of the corresponding axis. For moment components, the right-hand rule applies, i.e. positive if acting clockwise when viewed along the positive direction of the axis. To acquire the kinematic data of body segments during level wJking, reflective markers were fixed by double-sided tape onto the subjects at various anatomical landmarks (shown in Table 1) and, using i.r. stroboscopic ilhunination, their positions during locomotion were tracked as two-dimensional images on the frontal and sagittal planes by the Strathclyde Television Computer system operated at 50 Hz Details of the TV/computer system may be obtained by referring to Jarrett (1976). Andrews et al. (1981) and Andrews (1982). The three-dimensional spatial coordinates of the body markers were then generated through the DLT (Direct Linear Transformation method, developed by Abdel-&ix and Karara, 1971) from their two-dimensional images and the time sequences of the three-dimensional spatial coordinates of each body marker were digitally filtered with a cutoff frequency of 5 Hz to eliminate the noise by a fourth order Butter-worth low-pass digital filter. The joint centres and the centres of gravity of various body segments were subsequently determined from their fixed relation ta the body markers and their velocities and accelerations calculated by a numerical differentiation procedure.

983

The ground-foot reaction forces measured by two Kistler forceplates were also sampled at 50 Hz and synchronized with the TV data. To evaluate the inertia forces and moments, the mass properties of the body segment have to be estimated. For the sound lower limbs, segment masses were estimated using the stepwise equations derived by Clauser et al. (1969), and their antre of gravity and second moment of inertia were evaluated using Dempster’s data (Dempster, 1955). The prosthetic segments were directly weighed and the centre of gravity and second moment of inertia were determined from pendulum tests. Using equation (1) and proceeding from the foot segment upwards, the inter-segmental moments of the ankle, knee and hip joints were calculated. The derived moments were then transformed to the local coordinate system of the segment {X,, YL,ZL}, and their positive directions redefined, namely, a positive moment is generated by the loads applied below the joint concerned that tends to: for A/P moment: do&flex the ankle, extend the knee or flex the hip; for M/L moment: invert the ankle, adduct the knee or hip; for axial torque: internally rotate the ankle, knee or hip. From the induction of three-dimensional spatial coordinates of body markers to final gait variables presented in this paper, all the necessary calculations were performed on the University’s mainframe computer using a suite of FORTRAN programs. Subjects and prostheses A total of four AK amputees participated in the work presented in this paper and their general particulars are shown in Table 2. All the patients were in good health and their stumps were in good condition with a full range of motion available at the hip joint. Two different types of prostheses were worn by the subjects, illustrated in Fig. 2. The two amputees

Table 1. Positions of the body markers Marker locations

Segment Upper torso Pelvis

Left acromial process, sternum, right acromial process Left anterior superior iliac spine, sacral flat, right anterior superior iliac spine Prosthetic side

Contralateral side

Socket

Point at distal l/3 of anterior wall Point at proximal l/4 of lateral wag

Shank

Point on distal l/4 of lateral surface Point on proximal l/3 of medio-anterior surface Lateral knee joint axis

S-10 cm above lateral mafleohts Point on proximal l/3 of tibia1 flat 5-10 cm below tibia3 plateau

Foot

Equivalent 5th metatarsal base Mid-keel

5th metatarsal base. Toe of shoe Counter of shoe

984

L.

YANGet cd.

Table 2. Subject profiles Subject code

Sex

Age (Yr)

Mass (kg)

Height (ml

Prosthesis

Group

ALA ALD

Male Male

56 52

18.6 78.0

1.78 1.71

Otto Bock Otto Bock

1 1

ALB ARC

Male M&

62 53

88.4 72.0

1.80 1.73

Endolite Endolite

2 2

Explanation of the subject code: First letter: A-above knee amputee Second letter L-leB leg amputation; R-right Third letter A, B, . . . , subject identity code.

leg amputation.

Aligmt

change sequence(RCA’)

For an AK prosthesis, a total of 14 parameters is used to define its alignment, as shown in Fig. 3. It should be noted that in this definition, the prosthetic foot is taken as a rcfercncc. Three alignment change sequence% were designed in this study for analysiag their effects on the amputees’ gait and they were all in the A/P plane, as shown in Fig. 4. (1) The foot alignment change sequence (FACS): relative to the original inclination, the prosthetic foot was adjusted from 6” dorsiflcxion to 6” plantar &xion in increments of 3”. If the changes in ankle angle from the optimal alignment are denoted as @,*a and plantar flexion direction is taken as positive, the FACS may be written as Q,fAC9=(-60, -39 O”,3”, 6’). (a) !l’hs Otto eyetern

Bock

(b) The Endolite

eyetern

Fig 2. The above-knee prostlmw used in the study showing the sites on which the alignmeat changes were made.

wearing the Otto Bock system (Otto Bock Orthopadische GmbH & Co., Duderstadt, Germany) were each fitted with a quadrilateral suction socket, uniaxial knee with extension bias and a SACH (solid ankle cushion heel) foot which does not have an ankle joint. All components in the Otto Bock system can be angularly adjusted relative to each other in the anteroposterior (A/P) and mcdlo-lateral (M/L) planes and the foot also can be rotated in the transverse plane. The other two amputees wearing the EndoliteTY systcm (Chas A. Blat&ford & Sons Ltd, Basingstoke, U.K.) had a metal socket with rigid pelvic band suspension, an Endolite Stabilized Knee with uniaxial knee joint and pneumatic swing phase control, and a flexible ankle-foot assembly (MultiflexTy foot) which allows threedimensional rotation at the ankle joint. The foot angle can be adjusted in the A/P plane via foot serrations and the socket can be shifted in the transverse plane and/or rotated in three dimensions via a hole in the socket base.

(2-I)

It can be seen from Fig. 4 that the FACS changed all the angular and linear alignment parameters in the A/P plane. Due to the distance from the ankle joint centre (AJC) to the knee joint ccntre (KJC), and the greater distance to the socket, considerable shifts (linear displacements) occurred even with small angular changes at the foot. For patient ‘ALA’(Table 2) with 40.8 cm knee height and 70.5 cm socket height, 1” of foot plantar flexion would result in 0.7 cm backward shift of the knee joint centre and 1.2cm backward shift of the socket relative to the foot. (2) The socket alignment change sequence (SACS): using the original inclination of the socket as a basis, the socket was sequentially extended by 6” and 3” and then flexed by 3” and 6”. If the socket A/P tilt angle changes are denoted as YWcsand fiction direction is taken as positive, the SACS may bc expressed as Y SA*l={-60, -3”, O”,3”, 6’).

(2.2)

Referringto Fig. 4, as the adjustments were performed through the alignment mechanism above the knee joint centre, only the alignment parameters of the socket changed, that is, socket A/P tilt and A/P shift. (3) The foot and socket alignment change sequence (FSACS):relative to the original inclination of the foot and socket, the prosthetic foot was adjusted,

Limb alignment in above-knee amputees

_,m

985

eda

eocket *z-axis

Fig. 3. Definitions of alignment parameters for above-knee prostheses (refer to zahsdi et aI., 1986).

--.................

--.. .. ........... ..

--. ........ .... ... .

------_-

-__-_---

-

Dor*6d# Dard3cLg OptAl. -3M -Qw

-

-_-e-m-

=6

6.6

-3&a op+N. *3dDu *ed#

KJcBldc Man Kx: Buk 0.7an mu wcwdo.6an KJcfwd 1.Qan

Fig. 4. Alignment change sequences with the prosthetic foot 89 a reference.(1) The foot alignment change squcna(FACS); (2) the socket alignment change sequeaa(SACS);(3) the foot and socket alignment change sequence (FSACS).

by increments of Y, from 6” plantar to 6” dorsiflexion coupled with the socket angular changes from extension to flexion, by the same angle as that performed on the foot. Similarly, the FSACS may be mathematically expressed as FSACS =

Y FsAcs--Y sAcX @FSACS’-%a

(2.3)

Since the adjustments made at the foot and the socket were equal in magnitude but opposite in direction, the FSACS did not change the angular parameters of the prosthesis but altered the linear parsmeters. This alignment change sequence e&tively displaces the KJC from its optimum position sequentially by 1.4 cm and 0.7 cm posteriorly (backk 0.5 cm and 1.0 cm anteriorly (Fwd), as shown in Fig. 4.

L. YANG et al.

986

The definitions of alignment parameters in Fig. 4 are based on a reference system established on the prosthetic foot since the reference system of the foot is easily determined. However, when relating the prosthesis to the amputee, the socket seems to be a better choice since it is the socket that is directly connected to the patient. As will be shown in later discussion, choosing the socket as a reference can throw some light on the underlying biomechanics of the amputees’ gait in relation to the ACSs. Figure 5 shows the three ACSs with the socket as a reference. To describe the configuration of the prosthesis, three orientation angles were defined. If the alignment configuration of the prosthesis at optimal alignment is denoted by the subscript ‘Opt.‘, the configuration at the FACS could be written as

(3.3) that the foot orientation angles are the same for the AFACS and the ASACS and that the shank orientations are the same for the ASACS and the AFSACS. Experimental procedure

Only one alignment change sequence (i.e. FACS, SACS or FSACS) was performed in an amputee’s single visit to the locomotion laboratory. This restriction was imposed as each sequence normally took 34 h to complete, and it was desirable that the patient was neither allowed to tire, nor his interest in the study permitted to deteriorate, by prolonged testing. For each alignment setting several walking trials were performed in order to ensure the collection of sufficient data to allow the analysis of three test walks per setting. AFACS={‘I’,,,&,,,., @W.-%,cs} (3.1) The amputees wearing the Otto Bock system underwhere the letter ‘A’is included to denote ‘alignment’ went three full ACSs and altogether 45 test walks were analysed for each amputee. The amputees fitted with configuration. For example, the first alignment co>he Endolite” system underwent a full FACS, part of uration in the FACS is the SACS with three alignment changes made, and a AFACS= {‘I’or,,.,eo,,,., ‘I’*. +a’}. total of 24 teat walks were analysed for each amputee. As the aim of the project was to obtain data relating Similarly, the alignment configuration of the SACS to the change in the alignment configuration from a and FSACS may be expressed as: previously determined ‘optimal’ alignment by simuASACS= {‘I’,,., 6,,. -‘I‘wx, %,,,.-‘I’s,,& (3.2) lating the dynamic alignment process as closely as was practical, the following procedure was adopted. After AFSACS= (‘I’,., eo,. - ‘I’FSACV @opt.1 each alignment change was ma&, the amputee was (3.3) asked to walk while under close observation to ensure ={yo,., e,,.-ys,,, mm.). It can be seen clearly from equation (3.1) to equation safety of the alignment setting. The amputee was then

............ ..... --_-m-m-

-ebg oad3~ WCJ. -3w -6-B

Fig. 5. Alignment change sequences with the socket as a nferencc. (1) The foot alignmmt change sequence (FACS); (2) the socket alignment change sequence (SACS);(3) the foot and wxket alignment change sequence (FSACS).

Limb alignment in above-knee amputees given sufficient time to feel secure and confident on the prosthesis and to be able to comment on the effects of the alignment changes on his gait and socket comfort. All the amputees participating in the investigation demonstrated that they had the ability to accommodate the prosthetic changes within several minutes. Testing did not commence until the patient declared that he was able to control the prosthesis. It is possible that, had the patients been asked to walk for a much longer time in order to become more accustomed to the prosthesis, or indeed taken delivery of it to use for several days or weeks or months, the results of the gait analysis might have been different from those obtained from this investigation. Such a study, however, is considered to be beyond the aims of the present project. Also, the practice of delivering a prosthesis with deliberate malalignment is thought to be ethically unacceptable. RESULTSANDDlSCUSlON Most results presented here are shown in the form of the mean values of three test runs for each alignment setting rather than any one particular run. There is a considerable step-to-step variation for any gait variable, as shown by Zahedi et al. (1987). Several methods (Widter and Sienko, 1988, for example) were suggested to establish the criteria by which the differences in gait variables between the normal and disabled populatlion could be defined, but they were not applicable in the situation where the relatively minor differences were to be analysed within the same category of disabled population. We felt that the step-tostep variation.is random in nature and averaging data of several test,runs will reveal the trend along which a gait variable changes although it is often statistically significant only at a restricted confidence limit. In order to, take the body build of the subject into account, the kinetic gait variables were normalized to be of dimensionless form as suggested by Andriacchi and Stricklaod (1985), that is, the ground reaction forces were normalized by the body weight (BW) whereas the intersegmental moments by both the body weight and height (H) of the subject. As previously stated, moments at the joints are taken as positive if, generated by loads applied from a distal to a proximal segment, they tend to dorsiflex the ankle, extend the knee and flex the hip. Although a three-dimensional analysis was performed, only A/P moments are shown since the alignment changes in this study were confined to this plane. There were effects in the coronal plane which may be presented in a subsequent paper. Sagittal plane angular displacements of the lower limbs

Figure 6 shows the sag&al plane angular displacements at the sound side due to the alignment change sequence FAGS. In the figures, the definitions of the angular displacement of the ankle joint, knee joint and

0’06

0’06

0’06

0’0

0’068

988

L. YANGet al.

the thigh are also shown. No consistent trends of change were observed in the figure, and the results from other ACSs show a similar picture. At the prosthetic side and during prosthetic stance phase, the ankle joint angle was found to be affected by the FACS and FSACS, and the knee joint angle influenced by the SACSand FSACS. However it was recognized that, since the amputees had no voluntary control of their ankle and knee, and the prosthetic knee was in full extension during the prosthetic single stance, the changes observed were the alignment changes made to the prosthesis and did not provide any further information. The hip joint at the prosthetic side, on the other hand, is functionally intact and the amputee can voluntarily alter his hip joint angle to compensate for the aligmnent changes. Figure 7 shows the angular displacements of the prosthetic thigh for three alignment change sequences. The curves display a consistent pattern of change during stance phase with the SACS and the FSACS, that is, the thighhpexed more compared with that at the optimal alignment as the socket tilt angle was changed along the Pexion direction, and vice versa. The effects of the changes in the prosthetic thigh angles can be seen more clearly as the angular displacements of the prosthetic lower limb are expressed with respect to the laboratory system, as shown in Fig. 8. If the time functions of the dynamic orientation of the prosthetic foot, shank and thigh are denoted as cP(t),e(t) and Y(f) and those at optimal alignment are denoted as @&,,., e(t),,. and ‘I’(&,,, respectively, and the incremental changes of the thigh angle are assumed to be uniform, the dynamic configuration of the prosthesis with the SACS and FSACS can be expressed as

I

0

O’OC

0’02

O’OL-

0’0

l-

o-w8

E

CI

3 ;; ‘s

2 z

e a

DSACS = {‘I’(tb. +O.SY,, Wop&-0.5YsAcW Wopl.-0.5YLKa);

(4.1)

O’W

0’02

o*oi-

0’0

O’W8

E-

DFSACS = {Y(t)opt.+0.5YMcs,

. 7 i

e(t&. -0.5YFM,,

1

WopL + 0.5YFsAcs~ = {Y(t&.

+0.5Y&$cs,

Wo@. -0.5YsAcW Wopl. + 0.5YsAcs)

(4.2)

in which the letter ‘D’ denotes ‘dynamic’ contiguration. In equations (4.1) and (4.2) a factor of 0.5 was included based on the observation that the range of the changes (about 6”) in the thigh angle was approximately half of the changes in the socket alignment changes of 12”. By comparing the above expressions with those in equations (3.1)-(3.3), it can be clearly seen that through changes in thigh orientation made by the patient: (1) in the DSACS, the inclination of the shank and foot approached the dynamic ccmfiguration of the leg at optimal alignment; (2) in the FSACS,

\

O’OC

0’02

O’OZ0’0 < '6,P) ~WV

0’04-

t

g

989

Limb alignment in above-knee amputees

the shank inclination was closer to that obtained with the optimal alignment, but the foot orientation deviated. It therefore appeared that the amputees tried to maintain similar orientations of the prosthetic shank to those in optimal alignment. This compensation action for alimment changes is not known to have been reported in the literature on AK amputees and indeed, such a systematic approach to changing the prosthetic aliigriment and observing various gait parameters has not been attempted before by other investigators on AK amputees. Morimoto et al. (1987) conducted a similar study on BK amputees and the results they obtained also showed some compensatory actions. The dynamiu configuration of the prosthetic lower limb in the FACS, designated as DFACS, can also be similarly expressed as DFACS = {‘IV),. , WA,,,,., Wh,,t. - %,,).

(4.3)

It should be noted that as the positive direction of @FACS is opposite to that of cP(t), a negative sign precedes the term mFAa of equation (4.3). Ground reaction forces To quantitatively characterize the effects of limb alignment on the ground reaction forces, a one-way

analysis of variance was conducted on some parameters of the ground reaction forces (the definitions of the parameters are shown in Fig. 9), similar to that reported by Chao et al. (1983), for each alignment setting of the ACS. The results are shown in Tables 3,4 and 5. In the tables, the parameters Fx( +) and Fx(-) are peak push-off and braking forces (in % BW) respectively, the parameter TX, is the instant of time (in % stance phase) at which the A/P ground force component changes from negative to positive (referred to as change-over time), and the parameters TCP, and TCP, represent the instant of time (in % stance phase) at which the centre of pressure of the ground reaction force leaves the heel area and enters the toe area respectively, that is, the start and end points of the transition period of the centre of pressure (CP). These parameters are illustrated in Fig. 9. The alignment changes which affect the peak values of the fomaft force most are not always apparent. One may think that the prosthetic push-off force could be increased by plantar tlexing the prosthetic foot, but the results obtained in this study did not show this effect conclusively: the prosthetic push-off force did not increase significantly with the FACS. The orientation angle of the prosthetic foot relative to the ground @(t) did not appear to be a dominant factor to

- - - - - DYrmmic cmfiomltiul

DFACS

Optimal

Alim’nent

D8ACS

-_-_______ Akvnent

Ccrtflglstion

DF8AC8

Fig. 8. Effect of the compensatory action of the prosthetic thigh on the dynamic configuration of the prosthetic lower limb.

%dUllO9~

%-Fb-

Fig. 9. Typical graphs of Fo, and Xo showing the parameters used in the analysis (see Tables 3.4 and 5).

990

L. YANOet al.

influence the peak values of the prosthetic forcaft force: 0(t) was decmased with the SACS and increased with the FSACS, but the trend of change in the fore-aft force components was the same with both the SACS and FSACS. In an attempt to identify the alignment changes which have a dominant effect on the peak values of the foroaft shear force, it was noted that (1) at the prosthetic side, the push-off forces increased while the braking forces decreased with both the SACS and FSACS, and vice versa for the sound side; (2) the dynamic orientation angles of the prosthetic thigh Y(t) increased while the dynamic orientation angles of the prosthetic shank e(t) decreased with both the SACS and FSACS. This similarity in the trend of change suggests that Y(t) and e(t) akt the peak values of the foroaft force component most. As discussed in the previous section, the compensatory changes in the prosthetic thigh angle Y(t) reduced the deviation of the prosthetic shank orientation e(t) from that in the optimal alignment, but not enough to completely cancel the effects of the alignment changes made, and as a result the e(t) decreased with both the SACS and FSACS. The decrease in the dynamic orientation angle of the prosthetic shank has two effects (referring to Fig. 8):(1) during early stance phase, the inclination angle of the shank will be decreased (i.e. the shank is in a more vertical orientation relative to that in optimal alignment) and the heel tends to contact the ground at a point nearer the standing contralateral foot (i.e.with shorter step length). At such an inclination, the shank is likely to be able to transmit a lower braking force and a higher vertical force; (2) at late stance phase, decreasing the shank dynamic orientation angle results in the increase of the inclination angle of the prosthetic shank and higher push-off forces could be transmitted through the shank. Since the changes in the dynamic orientation angle of the shank e(t) cmrcspond to the socket A/P tilt angle, it may be deduced that the socket A/P tilt angle has a marked influence on the peak values of the for+aft shear, that is, extending the socket increases the braking force and decreases the push-off, while flexing the socket improves push-off force but reduces the brakiig effect. As far as the transition period of the CP is concerned, it is mostly influenced by the dynamic orientation angle of the prosthetic foot @(t)relative to the ground: as Q(t) is incmased, the CP of the ground reaction forces dwells at the heel area for a longer period of time, and thus the transition period of the CP occurs later. This effect is evident in Tables 3, 4 and 5. It is interesting to note that, for group 1 amputees, due to the compensatory changes in the prosthetic thigh angles, the ranges of change in (D(t)with the SACS and the FSACS are about half of those with the FACS (i-3” for the SACS and FSACS and &6” for the FACS), the ranges of change in the transition period of the CP with the SACSand FSACS are also about half of those with the FACS (i-8% for the SACS and FSACS and f20% for the FACS). This finding

991

Limb alignment in above-knee amputees

Table 4. Effect of the socket alignment change sequence (SACS) on the values of parameters of the ground reaction forces Group 1 amputees 0” -3” 3” Flexion Extension +I--),

-6 Prosthetic side 9.4& 1.7 7.8f 1.1 34k3 39*4 66&3

Fx(+)* FM-)* T T?Pf TCP;

9.6kO.6 7.9* 1.0 38*7 36*4 6255

6”

-3” Extension

Group 2 amputees 0” 3” Flexion *I-*

10.7&0.8 6.4& 1.3 41*9 30*5 54*6

12.9kO.4 5.4f 1.2 39f8 28&4 52&6

13.3kO.9 4.8kO.7 44stlO 24+4 48&B

RX(+) RX(-)* T,, TCPf TCP:

122f 1.0 20.0f2.1 34*4 50f4 65f4

12.0* 1.2 12.7fl.O 33*4 41*5 52*5

14.1 f 1.4 9.71to.9 29f5 36*4 Mf3

22.5k3.1 15.1k3.8

21.Okl.7 17.1k2.4

20.11tO.8 16.5f1.8

Fn(+)* Fr(-)*

28.8kl.O 16.5k3.1

27.0f2.1 17.2k2.4

23.5k1.2 21.8k2.1

Contralateral side W+) Fr(-)

21.4kl.l 13.4k3.0

22.7k1.4 13.1k2.1

See Fi8.9 for the definition of the parameters. The values in the tabk are mean f SD. Unit for peak force is % body weight and for temporal parameter is % stance phase. Parameters tiith (0) are significantly a&ted by the alignment changes (p dO.05). Setting Y)“’corresponds to the optimal alignment setting.

Table 5. Effect of the foot and socket alignment change sequence @‘SACS) on the values of parameters of the ground reaction forces

Variations of KJC (mm)

-14

Group-l amputees -7 0 5 KJC forward KJC backward +I*

10

Prosthetic side W+)* Fx( -)+ TIo TCP: TCPE

8.5 f 0.6 7.0&-1.2 51*2 25&2 461t2

10.45 1.6 6.6* 1.1 43*9 28&4 52f5

11.9k1.8 5.8 f 2.0 43*8 33*2 56&4

12.0f0.8 5.2 f 0.4 32&2 36&3 61*2

13.0f 1.6 4.OkO.8 28k4 37k2 63rt3

20.4k3.1 10.5* 1.8

21.4k3.8 17.9*4.1

19.5i2.8 17.6kO.8

16.4 f 3.4 20.1 f3.0

Contralateral side W+)* M-Y

22.4k3.3 9.2kO.6

See Fig. 9 for the definition of the parameters. The values in the table are mean&SD. Unit for peak force is % body weight and for temporal parameter is % stance phase. Parameters with (*) are significantly a&ted by the alignment changes @
confirms the above argument. It should be pointed out that the changes in CD(r) with the FSACS were not the direct result of the alignment changes ma&, but rather the consequences of the compensatory changes in the prosthetic thigh Y(z). It is noted from Tables 3 and 5 that the trends of the changes in the change-over time of the forc+aft shear forces TX, are opposite to those in the orientation angle of the prosthetic foot q(t) and from this, one can deduce that (p(r)is the factor which affects TX0mostly. However, the qechanism in which cp(r)influences TX, is not apparent, One may reason that as Q(t) increases, the CP would dwell at the prosthetic heel, the braking force would be ~appliedon the heel for a longer period of time, thus TX,, would be increased. This effect is contrary to what the results show. Therefore, another explanation h+ to be found and a possible one may be as follows: as q(t) increases, the amputee pivots over

the prosthetic heel for a longer period of time and moves forward at an enhanced speed. As a result, the trunk of the amputee enters a forward accekation phase earlier. This is reflected by the decmaae in the values of TX,. Since Q(z) changes in all three AC&, the alignment adjustment performed at the proa&e& foot or the socket or both will change the change-over time of the fore-& shear force. In summary, a correlation between the alignment parameters and the characteristics of the ground reaction forces emerges. Changes of aligmnent angles at the prosthetic foot (FACS) alTect& the -ion of the CP, whereas changes of the argbs at the socket (SACS) or the position of the pr~thctic lu# joint centre (FSACS) a&cted, apart from the progmmion of the CP, the peak values of the fore-aft shear force. Mizrahi et al. (1986) demonstrated a procedure to reach optimal alignment by improving the smooth-

L. YANG et d

992

ness of the for+aft shear curve vs time. Incorporating

this correlation into their procedure would certainly enhance its efficiency. Ankle joint moments The typical dorsi/plantar flexing moment pattern about the contralateral ankle joint with three different ACSs is shown in Fig. 10. The basic pattern of the curves obtained was similar to that reported in the literature for normal subjects (Andriacchi and Strickland, 1985).No significant or consistent trends of change with the ACSs were observed. The typical effectsof the ACSs on the dorsi/plantar flexing moment at the prosthetic ankle joint are shown in Fig. 11. Results from other amputees showed similar trends although to different extents. The alignment changes did not have significant effects on the magnitude of the dorsiflexing moment about the prosthetic ankle joint; the magnitude is limited by the length of the foot. However, the instant at which the plantar flexing moment changes into dorsifiexing moment is sensitive to alignment changes and is closely dependent on the orientation angle of the foot cP(t) relative to the ground. Referring to equations (4.1)-(4.3),as the inclination angles of the prosthetic foot decmased with the FACS and SACS, the ground reaction force would be applied on the heel area for a shorter period of time, thus reducing the duration of the plantar flexing moment at the prosthetic ankle joint; increasing the angle O(t) had the opposite effect.

Knee joint moments Figure 12 shows typical extending/flexing moment patterns for the contralateral knee joint with the AC%. No consistent trends of change were obscrvcd with the ACSs. Typical prosthetic knee joint moment patterns about the knee axis are shown in Fig. 13. Other amputees tested displayed similar patterns of change but with variable magnitudes. Since the extending moment at the prosthetic knee joint, M,, during prosthetic stance phase indicates the stability of the knee joint, it deserves detailed discussion. Considering that the moments due to the inertial and gravitational forces of the prosthetic shank and foot are small during stana phase, they can be neglected and M, may be determined by the following equation: Wu- -~t3u~c&-&l+~c3,~ YK in which the terms Fox and FGu are the fore-aft and vertical components of the ground reaction forces respectively; X, is the Xcoordinate of the CP of the ground reaction forces, Xx and Yxare the coordinates of the KJC in the sag&al plane. The above equation is not particularly useful in assessing the effect of its terms on MxZ sina Xo and Xx are dependent on the position of the foot on the foraplate. The X-coordinates of the CP and KJC may be related to the

OE’O

02’0

01’0

00’0

OL’O-

CODE:

ALA FACS SUBJECT

CODE:

ALA

8.

8 i

0

8.

d

0) 0

d

n

PHS 0

]

I

SUBJECT

1

CODE:

ALA

,

PHS

20

z drib

bath

40

60

ALA

60

(all3 sad Hcd strlb)

CODE:

1ooy

0

z *klc

20

40

Fe;

T-

Ext. Ext.

SACS

CODE:

60

ALA

60

durothn ME: samdICC1Strike)

-------------------

SUBJECT

1ooy

.

8 0’

0

w

0

40

CODE:

60

ALA

60

%strldc drdlrn tsHs: swd Ned strike)

20

SUBJECT

100

Fig. 12. Etiect of the alignment change sequence on the normalized extending/flexing moment at the contralateral knee joint. Positive moments due to loads applied distal to the joint tend to extend the shank.

c:O

SUBJECT

too 40 00 60 20 z skids titian MlS: Rarurcic Hcsl strllu) %drib fhtlal (Pl6: RaN*tIc wrcl strike) Fig 11. Effect of the alignment change sequence on the normalized dorsi/plantarflexing moment at the prosthetic ankle joint. Positive moments due to loads applied distal to the joint tend to dorsiflex the foot.

SUBJECT

L. YANGet d.

posterior comer of the heel of the shoe, i.e. M I(z=~ou’{CXo-Xsl-CX,-Xsl}+~ox’

YK

=FOY.[r~-X;]+FOX* Yw (5) where Xs is the X-coordinate of the posterior comer of

21'0 (u

fig)

80’0

40’0

00’0

?uawm th;xalj/bu;pua?xa

to* oawn

the heel at heel strike. The term XL is influenced by the orientation angle of the prosthetic foot a(t): for a given instant of time during stance phase, as the dynamic orientation of the prosthetic foot O(t) is increased, the transition period of the CP occurs later in the stance phase and X& decreases, and vice versa. The term X; is a5ected by the orientation angle of the shank e(t): increase in e(t) results in the KIC being positioned more posteriorly, thus decreasing Xi. The term F,, is character&d by its peak value Fx( +) and Fx(-), as well as by T’x,: a smaller value of TX, indicates longer duration of push-off force, and vice versa. The terms FGu and Yx may be regarded as constants since they undergo small changes for different alignment settings during stance phase, hence making small contribution to the change in Mxx. Equation (5) thus can be used to assess qualitatively the contribution of various terms and to explain the effect of the alignment changes on the pattern of Max. It was observed that the instant at which the extending moment reaches its full value occurs progressively earlier with the FACS, although the peak values do not change markedly. The changes in the pattern of the Mu may be caused by the FACS in the following way: with the FACS, the dynamic orientation angle of the prosthetic foot decmases [see equation (4.3)] and the transition period occurs earlier (see Table 3), resulting in the increase of Xo and causing the first term of equation (5) to increase. On the other hand, the change-over time TX, is delayed, tending to reduce the second term of equation (5). From the fact that the Mxx reaches its full value at progressively earlier times with the FACS, it may therefore be deduced that the first term in equation (5) dominates the pattern of the Mu, and further, that the dynamic orientation angle of the prosthetic foot is a major factor in intluencing the changes in the patterns of the M,. With the SACS, the knee extending moment Mm showed similar patterns to that at optimal alignment, but the magnitudes decrea& with the SACS. With the SACS, XL in equation (5) increases as Q(t) decreases [see equation (4.1)] and earlier occurreoce of the transition period of the CP (see Table 4) takes place, but X; also increases as the shank orientation angle e(t) decreases [see equation (4.1)], thus the change in the fhst term of equation (5) depends on the relative magnitudes of XL and Xi. The term Fax increases with the SACS as a result of higher Fx(f) and lower Fx(-) (see Table 4), suggesting that the second term in equation (5) increases and so does the M,. However, the Mm was actually found to decrease with the SACS,implying that Xx or the orieotation angle of the shank is the controlling factor of the Mwz.

995

Limb alignment in above-knee amputees The MKZ underwent consistent changes with the FSACS, that is, it decreased. With the FSACS, Xo in equation (5) is demased as a result of increased @(t) [see equation (4,2)] and the later occurrence of the transition period of the CP (see Table S), and X, is increased due to the decrease in the shank orientation angle [see equation (4.2)], both tending to decrease the value of the fjrst term in equation (5). The value of the term Fxo in equation (5) is increased as a result of the higher Fx( + ) and lower Fx( -) and the advance of the change-over time of the fore-aft ground force (see Table 5), tending to increase the extending moment. From the fact that the extending moment is decreased with the FSACS, it can be deduced that the first term in equation (5) is dominant. In summary, the three alignment change sequences have consistent effects on the extending/flexing moment about the prosthetic knee joint, that is, on the stability of the prosthetic knee during stance phase. However, the manner in which they affect the Mxa is different: the chunges in the A/P tilt angle of the prosthetic foot a&ct the time at which the extending moment reaches its peak value; the alignment changes in the socket A/1, tilt angle affect the peak value of the extending moment; the alignment changes in both the foot and socket a&& both aspects of the extending moment.

with ACSs. However, the results from the present investigation show that they did not exhibit any sign&ant or consistent changes in the patterns with the ACS for the amputees tested. Figure 14 shows such an example in which all the curves are seen to be fairly close to each other. In an attempt to understand the underlying biomechanics, the following comments may be made. The possibility may exist that, sina the prosthetic hip joint moments are closely correlated to the pressure distribution in the stumeet interface, it might be the amputees’ objective to maintain similar hip joint moments or the stumpsocket Pressure distribution in different alignments by changing other gait variables, for example, position of thigh or the trunk. Another factor relates to the force distribution in a quadrilateral socket. Several years ago, an investigation into the forces acting on the is&al seat during walking was carried out at the University of Strathclyde &awes, 1982). It was found that approximately 50-60% of the external longitudinal load by-passed the hip joint for the two subjects tested. It was estimated that the effect of ischial bearing could reduce the total muscle fora at the hip joint by between 25 and 50%. This uncertain fora distribution could have affected the estimation of the true hip moment. Energy consumption

Hip joint moments The muscles acting over the hip joint on the prosthetic side are the only power soura available to the amputee to manipulate and control the prosthesis during the various phases of the gait cycle. We therefore expected the hip joint moments to be important parameters in the understanding of the walking mechanism and that they would show significant changes

0

SUBJECT

Id

CODE:

ALA FACS

The changes in gait may alfect the amputee’s energy consumption. The energy transmitted between limb segments is only part of the overall energy consumption and does not take account of the energy cost of isometric muscle fora development. In future studies it may be possible to use respired gas analysis to determine the changes in energy cost due to such alignment changes.

$. 1 0 8.

SUBJECT

CODE:

ALA

51

0

8. 0

::. ‘: $. 20

YO Z

40 60 00 stridedrrtim (!a?~bandHmlstrike)

loop

0

20 40 60 x stride&Mm wHsI-1c

80 Hnl steiiu)

Fig. 14. F$ect of the ahgnmeutchaage sequence on the normahxedtkxin@xtending moment at the hip jomt. Positive moments due to loads applied distal to the joint tend to tkx the thigh.

100

L.

996

YANc3 et al.

CONCLUSION The angular displacement of the prosthetic thigh was found to be an important factor in prosthetic gait analysis: it illustrates the compensatory action which the amputee adopts to cope with the alignment changes. It was found that an aligmnent change at the foot did not affect the angular movement of the prosthetic thigh, suggesting that the amputee did not change his way of using the prosthesis. It was noted, however, that as the alignment of the socket or of both the socket and the foot was changed, the angular movement of the prosthetic thigh was modified so that contact with the ground occurred with the prosthetic shank being in an almost constant angle of orientation relative to the ground. Plantar/dorsiflexing the prosthetic foot had sign&ant effects on the ground reaction forces and the joint moments at the prosthetic side, namely: (1) shortcning/extending the duration in which the CP is within the heel B~CB; (2) shortening/extending the duration of the push-off force phase, (3) extending/shortening the duration of the dorsiflexing ankle moment; (4) incrcasing/decreasing the duration of the peak extending moment about the KJC, that is, increasing/decreasing the knee stability. Flexing/extending the socket had sign&ant e%cts on the ground reaction forces and the joint moments at the prosthetic side. These were as follows: (1) shortening/extending the duration in which the CP is within the heel are8; (2) increasing/decreasing the maximum value of push-off force; (3) decreasing/increasing the maximum value of braking force; (4) extending/shortening the duration of the dorsiflexing ankle moment; (5) decreasing/increasing the maximum value of extending moment about the IUC, that is, decreasing/increasing the knee stability. Dorsi/plantarflexing the foot coupled with flex&/extending the socket had significant effects on the ground reaction forces and the joint moments at the prosthetic side. These were as follows: (1) extending/shortening the duration in which the CP is within the heel area; (2) extending/shortening the duration of the push-off force; (3) increasing/decreasing the maximum value of push-off force; (4) decreasing/increasing the maximum value of braking force; (5) shortening/extending the duration of the dorsiflexing ankle moment; (6)decreasing/increasing both the peak value of extending moment and the duration of the peak extending moment about the KJC, that is, decreasing/increasing the knee stability.

REFERENCE8 Abdel-Az4 Y. I. and Karara, H. M. (1971) Direct linear transformation from comparator coordinates into object space coordinates in close-range pbotogramtnetry. ASP Sump. Close Range Photogrammetry. Urbana, Illinois, pp. l-18. American Society of Photogrammetry, Falls Cburcb, ,I* .I%

Andrews, B. J. (1982) On-line locomotion analysis using television techniques. Ph.D. thesis, University of Stratbclyde, Glasgow, Scotland. Andrews, B. J.. Nicol, S. M., Thynne, G. and Beale. A. Q. (1981) The Stratbclydc TV system for human motion analysis. In Computing in Medicine (Edited by Paul, J. P, Smith, E. M. and McCall, M. IL), Macmillan, U.K. Andriaccbi, T. P. and Strickland, A. B. (1985) Gait analysis as a tool to assess joint kinetics. In BiomechanicsofNorma and PathologicalAritictdatingJoints(Fkiied by Betme, N, Engin, A. E. and Correia de Silva, K. M.), pp. 83402. Martinus Nijbofl, Dordrccbt. Bresler, B. and Frankel, J. P. (1950) The forces and moments in the leg during level walking nuns. Am. Sot. Mech. Engng. 72,27-K Breslcr, B., RadclitTe, C. W. and Berry, F. R. (1957) Energy and power in the legs of above-knee amputees during normal level walking, Report Series 11, Issue 31. Univcrsity of California, Berkeley. Cappozzo, A., Figura, F, Leo, T. and March& M. (1976) Biomcchanical evaluation of above knee prostheses. In Bkmwchanics V-A (Edited by Komi, P. V.), pp. 366-372. University Park Press, Baltimore. Theo, E. Y., Laughman, R K., Schneider, E. and Stat&r, R. N. (1983) Normative data of knee joint motion and ground reaction forces in adult level walking, J. Biomechanics16, 219-233. Clauaer, C. E., McConvilk, J. T. and Young, J. W. (1969) Weight, volume and ccntre of mass of segments of tbe human body. Aerospace Medical Research Laboratory Technical Report 69-70, Wright-Patterson Air Force Base, Ohio. Dempster, W. T. (1955) Space requirements of the seated operator. USAF, WA%, Technical Report 55-159, Wright-Patterson Air Force Base. Ohio. Hannah, R E., Morrison, J. B. and’Cbapman. A. E. (1984) Prosthetic alignment: effect on gait of persons with bclowknee amputations. Arch. Phys. Med. Rehabil.65,159-162. Jarrett, M. 0. (1976) A television/computer system for human locomotion analysis. Ph.D. thesis, University of Strathclyde, Glasgow, Scotland. Lawes, P. (1982) Alignment kinetics in patient-prosthesis matching. Ph.D. thesis, University of Stratbclyde, Glasgow, Scotland. Lewalkm, R., Quanbury, A. C.. Ross, K. and Let@ R. M. (1985) A biomecbanical study of normal and amputee gait. In Biomechanks IX-A (Editedby Winter, D. A., Norman, R. W., Wells, R. P., Hayes, K. C. and Patla, A. E.), pp. 587-592. Human Kinetics Publishers, champaign, IL. Mizrahi, J., Susak, Z., S&tar. R. and Najenson, T. (1986) Alignment procedure for the optimal fitting of lower limb prostheses. J. Biomed. Engng 8,229-234. Morimoto, S., Aoyama, T. and Tsuchiya, K. (1987) Dynamic evaluation of prosthetic alignment usinn instrumented pylon and flexible ekxtrogo&ometer. P& 9th Int. Symp. ECHE, 31 August-5 Scotember. Dubrovnik_ Yuaoslavia Pearson, J. R.. H&qren, &, Mar&, L. and O&r& k.(1973) Pressure in critical regions of below-knee patellar tendon bearing prosthesis. Bull. Pros&t. Res. Spring 1973.52-76. Web M. (1985) Alignment and gait opt&is&on in lower limb amputees. In AmputationSurgery and Lower Limb Prosthetics(Edited by Murdoch, G. and Donovan, R. G.), pp. 357-367. Blackwell, Oxford. Solomonidis, S. E. (1975) (Ed.) ModularArtijicialLimbs.First report on a continuing programme of clinical and laboratory evaluation, below-knee systems. H.M.S.O., London. Solomonidis, S. E. (1980) (Ed.) Modular Artlfcial Limbs. Second report on a continuing programme of clinical and laboratory evaluation, above knee systems. S.H.H.D.. Edinburgh, RE72105 MO 3/80 TCL. Winarski, D. J. and Pearson, J. R. (1984) Least-squares matrix correlations between stump stress and prosthesis loads for below-knee amputees. ASME Trans. 109, 238-246.

Limb alignment in above-knee prostheses Winter, D. A. and Sienko, S. E. (1968) Biomechamcs of below-knee amputee Sait. J. Biomechanics 21, 361-367. Zahedi, M. S., Spence, W. D. and Solomonidis, S. E. (1985) The influence of alignmmt on prosthetic gait. In Amputation Surgery and Lower J&b Prosthetics (Edited by Murdoch, G. and Donovan, R. G.), pp. 367-379. Blackwell, Oxford.

B"

24:11-8

991

Zahedi, M. S., Spence, W. D., Solomon&s, S. E. and Paul, J. P. (1986) Alignment of lower-limb prostheses. J. Rehab. Res. Devel. 23, 2-19. Zahcdi, M. S., Spence, W. D, Solomonidis, S. E. and Paul, J. P. (1987) Repeatability of kinetic and kinematic measure ments in gait studies of the lower limb amputee. Pro&et. Orthot. ht. 11, %X4.