Fuzzy clustering of temporal-distance and kinematic parameters for cerebral palsy children

92

Gait & Posture PREDICTING CEREBRAL

Karen

1995; 3: No 2

THE OUTCOME PALSY USING

OF SURGERY PRE-OPERATIVE

FOR CHILDREN WlTH GAIT ANALYSIS

Sullivan,

M.S:, James Richards. Ph.D.*. Freeman Miller. Patrick Castagno, MS:‘. Nancy Lennon. P.T.” *University of Delaware, Newark. DE 19716 **Alfred I. duPont Institute. Wilmington, DE 19899

equations case.

on future

rectus

transfer

patients

will

determine

if this

1s the

M.D.** Knee

Introduction Surgeries are performed on pediatric cerebral palsy patients in order to improve the ef5dency of their gait patterns. The resulting gait patterns rarely resemble those of ‘normal’ children, and consequently. visualization of the changes in the gait pattern prior to surgical intervention is verv difllcult for professionals and family members alike. The goal of this study was to-evaluate a methodology to enable the visualization of expected post-operative gait patterns based on parameters obtained from the pre-operative gait analysis.

Flexion/Extension Pre-surgery Post-surgery

-

Predicted

-

-

-

-20 0

25

50 % of Gait

75

100

Cycle

Methodology Subjects consisted of 15 patients who had pre-operative gait analyses followed by post-operative gait analyses at least one year after rectus femoris transfers on 25 knees. Rigid criteria for performing the rectus femoris transfer included decreased or late peak knee flexion in swing phase with the presence of rectus femoris activity on EMG in the middle 3/5 of swing phase. Gait analysis was performed utilizing Motion Analysis hardware and OrthoTrak software for kinematic evaluation of the lower extremities in three dimensions. Discrepancies between preoperative and post-operative Joint position/time curves for each axis and each lower extremity joint were quantified by means of four parameters: range shift. maxima scale, minima scale, and phase shift. The four criteria were then entered as dependent variables into a regression analysis. Kinemauc variables from the preoperative gait analysis were used as independent variables in the regression analysis. Predicted postoperative curves were then used to regenerate marker positions and subsequently to render and animate a skeletal image on a Silicon Graphics workstation. The animation allowed visualization of an individual’s pre-operative gait pattern alongside of their predicted postoperative gait pattern.

Discussion A forward based model for predicting the functional effects of specific surgical procedures on the gait patterns of cerebral palsy patients based on pre-operative kinematic data will require the development of a large. data base because of the many different patterns of involvement. Baaed on our evaluation of this small group. however, the predicted outcome was good. This type of program should be an excellent mechanism to communicate to parents and professionals alike what the expected outcome of surgical procedures would be in an individual child.

Results Preliminary results on the limited sample of patients used in this study produced imperfect but encouraging results. Regression equations were produced for 30 out of 40 wave form parameters. Predicted wave forms clearly approached the actual post-surgical wave forms [see figure). and tolerance values generated in the regression analysis indicated that the equations should be stable across samples. Cross validation of the

Ounpuu, Palsy,

FUZZY

CLUSTERING PARAMETERS

OF TEMPORAL -DISTANCE FOR CEREBRAL PALSY

AND KINEMATIC CHILDREN

Mark J. O’MaUey’, Mark Abel* and Die Dam&m* 1 Dept. of Electmnic and Electrical Enguxering, University College, Dublin 4, Ireland. 2 Depa~~mnts of Orthopaedics, University of Virginia, CbarIotresviUe. Virginia, 22903, USA.

lntmduction palsy (Gage, 1991) and subjective attempts have been made to classify them (Wiiters et al, 1987). This study employs an objective pattern recognition paradigm fuzzy clustering (Be&k, 1981). to cluster temporal distance and kinerwtic parzuxters for cerebral palsy (CP) chikire~~ The fuzzy paradigm was employed because this method separates subjects into clusters and qua&es a membership value for each subject in each cluster. The clustering is done in an unsupervised mde and duster validity techniques (Be&k et al., 1992) are used to identify the most natural clusters. The objective is to diicrimmate sub groups of CP children into well defmed clusters. Once defined these clusters would then form the basis for more precise pre and post intervention comparisons. The clusters themselves provide clinical insight into which features distinguish one cluster from another. The purpose of this study was to assess the fuzzy clustering technique as a tool for defining groups of CP patients.

References DeLuca. P., Gait Analysis in the ‘lYeatment of the Ambulatory Child Cerebral Palsy. Clint Orth and Related Res. 264:65-74. 1990. Gage, J., et. al., Rectus Femorls Children with Cerebral Palsy. 1987.

Transfer to Improve Deu Med and Child

with

Knee Function New. 29:159-166.

of

Gage, J., et. al.. Pre- and Post-operative Gait Analysis in Patients with SpasUc Diplegia: A Preliminary Report, J of Ped Orth 4:715-724. 1984. S., et.al., Rectus Femoris Surgery in Children Parts I and 11, JofPed Orth. 13:325-335, 1993.

Perry, J.. Distal Rectus 29:153-158. 19487

Femoris

Transfer,

Deu

Med

with and

Sutherland, D.. et& Treatment of Stiff Knee Gait in Cerebral Comparlson by Gait Analysis of Distal Rectus Femoris Versus Proximal Rectus Release. J ofPed Orth, l&433-441.

Cerebral

Child

New.

Palsy: A Transfer 1990.

and those wth higher nornukzed atnde length It \hould be noted that the gap 1%not evident before normdmtion emphasiring the importance of normaliiarion. From Figure 1 it IS evident that the difiaence between Cluster I and Cluster 2 is cadence. Rgure 2 mdlcates that hip exurs~on distinguishes Cluster 3 from Cluster 4 but it should also be noted from Figure 1 that cadence also plays a part. Cluster I has eight subjects, all limed community ambulators. Clwter 2 has one nod two community ambulators and two limed community ambulators. Cluster 3 consists of 12 subjects, nine nom& and three of the community ambulators Cluster 4 consists of 7 of the communitv ambulators and two of the limited commumtv ambulators.

Gait patterns vary in cerehal

^

*“,........................

,70~...............x.........

Methodology Gait analysis was perfortxd on 24 children with spastic diplegic CP and ID, age matched, normals usiig a three dimensional kinematic gait analysis system For comparison purposes the children wth CP wae split into two groups based on a subjective judgment of ambulatory status; 12 community ambulators and 12 limited community ambulators (Hoff. er al., 1973). As in any pattern recognition problem the selection of features is crucial to the outcome (Duda et al., 1973). In this case feature extraction was based on clinical judgment. The features used were stride length cm), cadence (lhin.), stance tii (%) and kuwnatics (hip, knee, and ankle excursion (degrees) in the saglttal plane). Due to the differences in age and leg length, nomalization for both stride length and cadence was considered. Smde length was nowith respect to age and leg length simultaneously by removing hear mends. Cadence varies with age in a reciprocal manner (Sutherland er al., 1988) and therefore removing linear trends is not suitable. The fuzzy c-means algorithm generalized by Be&k (1981) was used and cluster validity was tested by using several methods (Be&k et ni. 1992).

ReSUlfS Initial results using alI six fearures and assuming three clusters produces results whtch largely agree with clinical judgment i.e. normal, conunmity ambulator and linxted community ambulator. However after performing cluster validity tests, four clusters emerged as a more natural choice. Consideration must also be given to the dimension of the feature space as a ratio of the number of subjects. With a six dimensional feature space and with only 34 subjects [here is a danger that the subjects will be “lost” within the feature space. Therefore the number of features was reduced subsequently to three: nonn&ed snide length, cadence and hip excursion. These three were chosen because they were deemed to lx fundamental parameters and could be measured accurately and reliably. Cluster validity again suggested four clusters and the results are illustrated in Flgure I and Figure 2 where the fuzzy clusters are transformed (for the purpose of illusrration) into had clusters by taking each subject to be a member of the cluster for which they have highest membership value. FromFigure 1 and Figure 2, an &dent gap exists between subjects with low nomallzcd stride length

Conclusion Wide variability and heterogeneity in CP has been recognized clmically, and LS problemas in evaluation of intervention in this population. The fuzzy clustering of temporal-distance and kinenntx parameters as described above results in groups which are nore natural than subjective techmques and ifused in a prc and post intervalon study will emphasize intra group changes. Tbc number of features which can be used is limited by the number of subjects bang clustered xnd the whole issue of which features to use from the almost infinite number produced during gait analysis is an open question. As illustrated above by stride length, normalization is cnrc~al to the outcome of any clustering procedure. Cadence 1s not normalized here as it exhibits a non linear relationship with age and the removal of linear trends is not suitable. This work examines the use of unsupavised fuzzy cluster anaIysls to discrinunate among cluklren with and without CP in a seal sample. Currently the analysis is being expanded to a much larger sample in an attempt to distinguish ctical subgroups in the general population of children with cerebral palsy. These groupmgs may indicate some underl$ng similarity, structure and/or cause m the cerebral palay population a, a whole. References Be&k, I. C. et al. Fuzzy Models for Pattern recognition. IEEE Press, 1992. Be&k, J. C., Pattern Recognition with Fuzzy Objectwe Function Algorithmi, Plenum Press, 1981. Duda, R. 0. er al. Pattern Classification and Scene Analysis, John Wiley. 1973. Hoffer, M. M. a al. Journal of Bone and Iomt Surgery, 55. 137.148, 1973. Gage, I. R. Gait Analysis m Cerebral Palsy, Mac Keith Press. 1991. Sutherland D H. et ai. TbcDevelopnrxn of Mature Walking, Mac Keith Pras, 1988. Winters, T.F. etul. The Joumnl of Bone and Joixt Surgeiy, h9A: 437.441, 1987