Vector (Butterfly ) Diagrams for Osteoarthritic Gait a Preliminary Report_Khodadadeh

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Journal of Medical Engineering & Technology,Volume 12 , Number 1 (January/February 19881,pages 15-19

Vector (butterfly) diagrams for 0 s eoarthri ticgait: a preliminary reportSoussan KhodadadehOrthotic Research C5 Locomotor Assessment Unit , Robert Jones & Agnes HuntOrthopaedic Hospital , Oswcshy, Shropshire SYlO 7AG, OKTh is pape r describes brieJy a simple three-dimensional vectordiagram displ ay combining a ll the forc e components o gait in onediagram. The locus o f the centre o pressure of thefeet on hegroundis J;lb illustrated. Th is provides a us eful reference for theconsideration of th e position of th e centre o body mass over one oo tor the other. In the case of some pathological ga its, the lateraldisplacement can be substantial. The traditional two-dimensionaldiagram fa ils to show some of thes e effects.

IntroductionThe traditional form of displaying gait measurementsincludes the plotting, on a time basis, of the vertical,horizontal and lateral components of the force betweenthe feet and the ground.An alternative form of visual display of force platereadings is the well-known display due to Pedotti [ l] inwhich the vertical (2 ) and horizontal (Y) orce com-ponents are combined into a resultant polar vector (R) tan angle (0 ) o the vertical acting at the centre ofthrust onthe foot. As the locus of the centre ofpres sure moves alongthe ground so radial vectors emanate, producing thecharacteristic fan-shaped diagrams shown in figure 1.In some cases the vertical-horizontal vector combinationalone fully indicates the condition of the pathological gait ,so these diagrams are adequate. However, Khodadadeh[2] has shown that in many instances ofosteoarthritic gaitthe lateral ( X ) component of the gait force is mostsignificant, and in a few cases all three components aresignificant. It is therefore essential at least in an initialinvestigation of pathological gait that all relevant forcecomponents are measured and displayed. This will beprovided by a three -dimensional display. W e believe amore comprehensive assessment can be obtained with athree dimensional representation of the data.

This is a brief preliminary report on a relatively simplemethod of displaying all three force components, and onits value.

Three-dimensionaldiagramsIsometric drawings (Abbo tt [3]) are used to display thethree-dimensional dat a so that measurements or estima-tions of the length of the resultant force vector may bemade.The force components arc measured by means of Kistlerforce plates; the co-ordinates of the centr e of pressure in

-0.0 0.Right

o .6 Lef t 1 . 2 m

Post-op. r e su l t sPatient no. B 2

6 mFigure I . Vector (butterJy) diagrams , f i r osteoarthritic gait .the plate(s) are calculated from the forces and momentsby the method described by Khodadadeh [4].In the case of single (on e leg) suppo rt, if the co-ordinatesof the centre of pressure a re (Xo, Yo, 0) and the tota l forceis ( X I , 1 ,Z I )kN(figure 2 [ a ] ) , he resul tant force vectorisrepresented in the butterfly diagram by a straight-linejoining points (Xo , Yo,0) and (X, XI, o + YI , 2 , ) .In the double support case there are force vectors fromboth feet, F R [= ( X R , YR , ZR)] rom the right leg and Fl,[= ( X L , Y,-, Z L ) ] rom the left leg. The resultant forcevector I = ( XR+ X L , Y R+ YL,ZR + Z,) acts at an angledefined by the a ppro pria te direction cosines (figure 2[b]).Hence to plot t he resu ltant vector all that is needed is thepoint of application, at plate level, of the resultant. Theresul tant vector will pass through the point of intersectionof the forces FR an d F L. The resultant centre of pressurefor the double support case is determined by projectingthe force I through this common point to the intersectionwith the horizontal plane at plate level.Patients studiedTh e technique has been used to assess 42 patients, withan average age of 65 years ( 2 7 female and 15 male) beforeand approximately six months after a Charnley total hipreplacement operation. When the patient was walkingwithout hesitation the Kistler plate recording was star-ted. Three specimen walks were recorded. All patientscould walk independently without walking aids.


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S. Khodadadeh Vr c to r (huttrrfl!) diag rams for osteoarthrit ic gait

2

P r o j e c t i o n o ff o r c e o n t oc o o r d i n a t e s( X , Y , 2 )

F o r c e vec to r

R esu lForce

\\\I n t e r s e c t i o n o f/ i n g l e f or ces

t a n t\ \


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S . Khodadadeh \ cctor (bu t ter f ly ) d iaqram s fix- ostcoar thr i t ic gai t

1 4 -

1 2 -

1 0 -

0 . 8 -0 6 -

0 L -

0 2 -

kN

IIlil

--7/

Figure 3. Three-dimensional vector (bu tl erj y) d iag rams for osteoarthritic gail (wi lh unilaleral hi p disease). Direction oJwalking right tol e f i . Full lines = single support; dotled lines = double support.

kN1. 41 . 2 f

I

k N1 .L -1. 2 -1. 0 -0.8

0 . 6 -0 4 -0.2 - .rk I 7/

-.-JPatient no. A 2Pre-op walk 2Figure 4. Three-dimensional cector (butterJy) dia gram sfor osteoarthritic gait ( x) it hunilateral hip disease). Direction ofirtalking ri


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1 . 2 4 I / I

kN o .81.6 IJ

- . -. Patient no. B 3.-.> Post-op walk 1- - - - _ _ _->

7-.

Figuw 5. %r-ee-dinirnriorial m l o r (butlerJv) dia\qrcinis f o r osleoarlhrilic g ai t fu7irh bihteral h ip di.rease). Direction (jzr,alking r igh l loIefi. Ful l l i n r r = ting le support: dotted lines = doub le .support.

kN

1 . 2 & 1k N L 7

-.-

l o

0. 8

0 6

0.i

0.2

Patient no. C 1

7-.


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S . Khodadadeh \.ci.tor ( Ix i t t c r t l y )d ia g ra m s for ostcoarthritic gait

The patients were divided into three groups:Group A - Patients with unilatrral hip disease (23Group 3 - Patients with bilatrral hip disease ( 1 1

Group C - Patients with the first of two total hip

patients).

patients).

replacements (8 patients).A selection of these cases have been chosen to illustratethe value of the techniques.

Results and discussionFigure 3 shows, for the pre-operative condition of theright foot, motion of the centre of pressure which is socomplex that i t would be totally obscured in theconventional two-dimensional diagram. Th e centreadvances, retreats in the same line, and finally proceedsin a different path to completion. For the left foot, theprogression is smooth, but the shorter vector length andoutline indicate the defective leg as clearly as in thesimple two-dimensional butterfly d iagram . The post-operative results show smoother movement of the centreof pressure, clearly tracing the non-linear motion,together with an adequately-deve loped butterfly outline.Both diag rams of figure 3 show two common characteris-tics of the double support vectors. Firstly the smoothtransition from the single supports (full line), to doublesupport (do tted lines), despite the known unreliability ofthe individual vectors near the heel-strike and toe-off.Secondly, the combined centr e of pressure always movessteadily across from right leg to left, whereas i t might beexpected, at least for paticnts with a severe condition, thatthere would be a sha rp sideways movement correspond-ing to the transfer of weight from one leg to the other.In figure 4, two further points are exhibited. Thedifference between the left leg and the diseased right legpreoperatively is obvious but i t is noticeable that thetransient vectors are well separated laterally from thesteady-state principal group. This suggests strongly thatthey arise from calculations based on insufficientlyaccurate Kistlcr plate output, whereas the two-dimen-sional representation often shows the transients as beingclose to heel-strike and toe-off, which would indicate apossible genuine significance. Pre-operatively , he doublesupport vectors are very widely spaced near the right foottoe-off illustrating a lurch towards the healthy leg. Thecorrection of this condition is shown by the much moreeven spacing post-operatively.Figure 5 shows a very slow walk, with tight bunching ofall vectors pre-operatively and an erratic trace for the

centre of pressure. The post-operativc diagram shows aclear improvement, with smooth curves for hoth centresof pressure. Hcre it can be seen also that bunching in thehorizontal direction is typically accompanied by somelateral displacement, so that therc is, in fact, continuingmotion of the foot, even though inspection of the plot ofhorizontal against vertical factors would indicate stasis.Figure 6 illustrates an obvious factor, namely a walk withone foot badly splayed out. Again, the horizontalprojection would show slower motion than the actualspeed at the plate. The right foot, pre-operatively, and theleft foot, post-operatively, also show the typical bunchingof vectors near a lateral shift in the motion of the centre ofpressure.

ConclusionsPolar vector butterfly diagrams provide a useful visualmeans of representing gait force data which in conjunc-tion with the temporal plottings of vertical, horizontaland lateral force components enable assessment to bemade of the gait of patients before and after hipreplacement operations. Although butterfly diagrams intwo-dimensional form are well known, we belicve thethree-dimensional diagrams presented here are moreadvantageous in that all force components are rcpresen-ted. In particular, the movement of the centre ofpressureacross the plates during double support gives a usefulreference for the considera tion ofthe position of the centreof mass over one foot or the other . Thi s aspect of gait isnot revealed by temporal plottings. However, it is notpossible to es timate from some of the resultan t vectors themagnitude of the lateral and horizontal force com-ponents.

AcknowledgementsI would like to thank Mr J . D. Harris, Director of theOxford Orthopaedic Engineering Centre, and theDepartment of Health and Social Security and theOxford University Computing Centre for providing thefacilities for this study.

References1. PEDOTTI, . (1977) Simple equipm ent used in clinicalpractice for evaluation of locomotion. IEEE Tran.mcfionson

Biomedical Engineering, BME-24, 5.2. K H O D A D A D E H ,. (1987) Quantitative approach to osteo-arthritic gait assessment. Engineering in ,bfedzcine, 16, 1.3. ABBOTT,LV. (1944) Machine Drawing and Design. Part I(Blackie & Sons L t d, U K ) , p p. 24-48.4 . KHODADADEH,. (1981) The use of th e force plates inthe clinical examination of locomotor disabilities (M.Sc.lhesis, University of Oxford).

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Vector (Butterfly ) Diagrams for Osteoarthritic Gait a Preliminary Report_Khodadadeh