Estimation of Postoperative Knee Flexion at Initial Contact of Cerebral

Palsy Children using Neural Networks

Omar A. Galarraga C.

1,2

, Vincent Vigneron

, Bernadette Dorizzi

, Néjib Khouri

1,4

and Eric Desailly

UNAM, Pôle Recherche & Innovation, Fondation Ellen Poidatz, 1 rue Ellen Poidatz, Saint-Fargeau-Ponthierry, France

IBISC EA 4526, Université d’Evry Val d’Essonne, 40 rue du Pelvoux, Courcouronnes, France

Institut Mines-Télécom, Télécom SudParis, UMR 5157 SAMOVAR, 9 rue Charles Fourier, Evry, France

Hôpital Universitaire Necker-Enfants malades, 149 rue de Sèvres, Paris, France

Keywords:

Clinical Gait Analysis, Nonlinear Data Fitting, Neural Networks, Cerebral Palsy, Biomechanics.

Abstract:

Cerebral Palsy (CP) affects walking and often produces excessive knee ﬂexion at initial contact (KFIC). Ham-

string lengthening surgery (HL) is applied to decrease KFIC. The objective of this work is to design a simulator

of the effect of HL on KFIC that could be used as a decision-making tool. The postoperative KFIC is esti-

mated given the preoperative gait, physical examination and the type of surgery. Nonlinear data ﬁtting is

performed by feedforward neural networks. The mean regression error on test is 9.25

◦

and 63.21% of subjects

are estimated within an error range of 10

◦

. The simulator is able to give good estimations independently of

the preoperative gait parameters and the type of surgery. This system predicts the outcomes of orthopaedic

surgery on CP children with real gait parameters, and not with qualitative characteristics.

1 INTRODUCTION

Cerebral Palsy (CP) is an umbrella term that refers

to a group of neurological disorders from brain dam-

age that affect human movement, balance and posture.

These disorders frequently entail muscle and bone de-

formities. Two typical CP gait troubles are crouch

gait and equinus gait (Gage et al., 2009): crouch gait

is principally characterized by excessive knee ﬂexion

during walking, while equinus gait refers to ground

contact ﬁrst done by the toes instead of the heel.

In order to lessen these pathological gait patterns,

orthopaedic surgery is usually performed on CP pa-

tients. Multiple bone and soft tissue deformities can

be corrected during a single-event multilevel surgery

(SEMLS) which combines several surgical gestures

according to the functional objective, the technique

applied, the body parts that are affected, etc. For in-

stance, the most common treatment for crouch gait

is hamstring lengthening. Its purpose is to decrease

knee ﬂexion at ground contact by increasing ham-

strings length surgically. This surgery has reportedly

given good results (Ma et al., 2006), however its in-

dication is not always straightforward. First because

this surgery may have side effects on pelvic tilt. Sec-

ond because at this time there is currently no method

or simulation tool, other than the surgeon experience,

that is able to predict hamstring lengthening effect on

knee ﬂexion at initial contact. Physical examination

and clinical gait analysis (CGA) (Gage et al., 2009)

are performed on patients to improve diagnosis and

assert suitable treatments. Speciﬁcally for the ﬁrst

point, most of the useful results are related to muscu-

loskeletal simulations (Arnold et al., 2006; Desailly,

2008; Sebsadji et al., 2012).

On the other hand, simulation studies for predict-

ing effect of treatment on CP gait are rare, e.g. on

equinus gait (Armand et al., 2007) or on effect of rec-

tus femoris transfer surgery (Reinbolt et al., 2009). In

both studies, the estimations are qualitative, i.e. they

can only predict "good" or "bad" outcomes, but not

values of gait parameters. In addition, there is no re-

ported study about simulation of the effects of ham-

string lengthening on CP gait.

In this paper the effect of SEMLS on gait is evalu-

ated, in particular the effect of hamstring lengthening

on knee gait ﬂexion at initial contact. Initial contact

is the stage of gait cycle when foot strikes the ﬂoor, as

338

Galarraga C. O., Vigneron V., Dorizzi B., Khouri N. and Desailly E..

Estimation of Postoperative Knee Flexion at Initial Contact of Cerebral Palsy Children using Neural Networks.

DOI: 10.5220/0005286503380342

In Proceedings of the International Conference on Pattern Recognition Applications and Methods (ICPRAM-2015), pages 338-342

ISBN: 978-989-758-077-2

 2015 SCITEPRESS (Science and Technology Publications, Lda.)

can be seen in ﬁgure 1.

The objective of this work is to design a simulator

that could be applied as a decision-making tool for

including or not the hamstring lengthening procedure

in a SEMLS context.

Figure 1: Gait cycle stages (gai, 2014 ).

To achieve the objective, supervised learning tech-

niques are applied on data of CP children that under-

went SEMLS (section 3). Post-surgical knee ﬂexion

at initial contact is estimated knowing pre-surgical

gait and physical examination, given a surgery. The

nonlinear regression is performed by multi-layer

feedforward neural networks.

2 DATA DESCRIPTION

All the patients in the database have undergone

surgery and have had at least a CGA before and af-

ter the surgery. To simplify the problem, both sides

lower limbs are considered independently. In total

there are N = 193 limbs corresponding to N

pat

= 100

patients (7 limbs are not valid due to lack of informa-

tion whether on CGA or the physical exam). Male

subjects represent 61% of the population and 39% are

female. The mean ages and standard deviation of the

patients at the three different stages considered (Pre-

operative CGA, surgery and Postoperative CGA) can

be seen in table 1.

Table 1: Distribution of patients ages at CGAs and surgery.

µ σ

Preoperative CGA 11.80 3.30

Surgery 12.60 3.24

Postoperative CGA 14.76 3.32

For each CGA, we consider ﬁfteen gait angles at

initial contact, as shown in ﬁgure 2. The mean of

each of these angles is computed when several gait

cycles are available (multiple initial contacts). Phys-

ical examinations provide preoperative popliteal an-

gles (PoplA).

We collect n = 714 walk cycles (n  193 because

we record several walk cycles per patient) and denote

our observation set by (x

, y

), . . . , (x

, y

) that may

be regarded as a ﬁnite realization of a multivariate

Figure 2: Considered gait angles. Example for the right

lower limb signals. The left lower limbs signals are also

considered at both sides initial contacts.

stochastic data collection. The parameters used for

the computation are deﬁned as:

PTIC Pelvis Tilt

POIC Pelvis Obliquity

PRIC Pelvis Rotation

HFIC Hip Flexion

HAIC Hip Abduction

HRIC Hip Rotation

KFIC Knee Flexion

AFIC Ankle DorsiFlexion

FFIC Foot-Ground Flexion

cont

IC Contralateral Hip Flexion

cont

IC Contralateral Hip Abduction

cont

IC Contralateral Hip Rotation

cont

IC Contralateral Knee Flexion

cont

IC Contralateral Ankle Flexion

cont

IC Contralateral Foot Flexion

The above angles are in degrees and are measured at

initial contact (see ﬁgure 1).

3 METHOD

First, input variables are selected from all available

data. Second, a nonlinear regression of the post-

surgical knee ﬂexion angle during gait is done by a

feedforward neural network. Leave-one-out cross-

validation (Bishop, 2006) is performed in order to

have a measure of the regression error for each patient

in the database.

The variable selection is done by a ranking tech-

nique adding a prone variable (Guyon and Elisseeff,

2003). The variables ranked higher than the prone are

selected as inputs for the neural network. Variables

ranked lower than the prone are rejected as entries.

EstimationofPostoperativeKneeFlexionatInitialContactofCerebralPalsyChildrenusingNeuralNetworks

339

The prone is a completely random variable unrelated

to the target output.

The ranking technique consists on a Gram-

Schmidt orthogonalization (Dreyfus et al., 2008;

Guyon and Elisseeff, 2003). If P

, . . . , P

are the k

vectors corresponding to the candidate variables, R is

the prone and Y is the target output vector, this it-

erative procedure is described by algorithm 1, where

hhA, Bii is the inner product of vectors A and B.

Algorithm 1: Gram-Schmidt variable ranking with prone.

1: P

k+1

← R

2: for i = 1 to k + 1 do

3: Z

← argmax

, j=1,...,k+1

Cov(P

,Y )

4: for j = 1 to k + 1 do

5: P

← P

−

hhP

hhZ

6: end for

7: Y ← Y −

hhY,Z

hhZ

8: end for

At the ﬁrst iteration in algorithm 1, the candidate

variable that is most correlated with the target output

is selected. Then all the candidate variables and the

target output are projected into the orthogonal space

of the selected variable. In this new space, again the

variable which is the most correlated to the target is

chosen. This process is repeated until all variables are

ranked.

The candidate variables are the ﬁfteen preopera-

tive mean gait angles at foot strike and the preopera-

tive popliteal angle.

The selected variables are the input of the neural

network plus a binary input corresponding to the in-

clusion of hamstrings lengthening surgery. HL = 1

means that the hamstrings lengthening was performed

and HL = 0 means that another kind of surgery was

applied. The target output is the postoperative knee

ﬂexion angle at initial contact (KFIC

post

The neural network architecture consists of a

multi-layer perceptron with one hidden layer. The

number of hidden units is optimized using the val-

idation error rates. The learning method is the

Levenberg-Marquardt algorithm (Bishop, 2006). Pre-

processing consists on centering and normalizing

data.

In order to have a measure of the error for all the

patients in the database, a neural network is trained

for each subject, then tested only for the subject in

question. For each neural network, the training set is

composed of all the available gait cycles, except for

those belonging to the patient that will be tested. Test

is performed only over the mean cycle angles per pa-

tient. The architecture of the neural networks is al-

ways identical.

The leave-one-out cross-validation (Duda et al.,

2001) is performed M = 10 and then the mean errors

per patients are calculated, as shown in algorithm 2.

The error measure considered for each patient i is the

root mean-square error (RMSE) computed as in equa-

tion 1.

Algorithm 2: Leave-one-out cross-validation.

1: for i = 1 to M do

2: for j = 1 to N

pat

3: Initialize NN

4: Train NN without patient j

5: Test patient j

6: end for

7: end for

8: Compute mean errors

RMSE

− g(X

))

= |Y

− g(X

)| (1)

4 RESULTS

From the list of variables in section 2, the selected

inputs ordered by relevance are: KFIC, FF

cont

IC,

PoplA, HR

cont

IC, AFIC, HA

cont

IC and PTIC.

Best results were obtained for m = 10 hidden

units. Figure 3 shows the estimated KFIC with re-

spect to the real KFIC

post

for one of the multiple

leave-one-out procedures (see section 3). The black

line corresponds to the ideal estimation and points

between the two red lines stay within a 10

◦

RMSE

range.

0 10 20 30 40 50 60

KFICpost

Estimated KFIC

Figure 3: Estimated vs. real post-surgical knee ﬂexion.

ICPRAM2015-InternationalConferenceonPatternRecognitionApplicationsandMethods

340

Table 2: Test results per patient and given the type of

surgery.

RMSE

Subjects µ

RMSE

± σ

RMSE

≤ 10

◦

≤ 15

◦

All 9.25

◦

± 5.45

◦

63.21% 86.53%

HL = 1 9.36

◦

± 5.68

◦

62.61% 85.22%

HL = 0 9.09

◦

± 5.13

◦

64.10% 88.46%

In table 2, mean RMSE and the corresponding

standard deviations can be observed for all patients,

those who underwent hamstring lengthening (HL =

1) and those who had another type of surgery. In

addition, percentages of subjects within 10

◦

and 15

◦

RMSE range are also given.

To show the relation between the outputs (target,

estimated and errors), ﬁgure 4 shows these three out-

puts with respect to the preoperative knee ﬂexion at

initial contact. In 4(a) and 4(b), points over the black

line correspond to patients where the KFIC increased.

On the other hand, in ﬁgure 4(c), the black line rep-

resents the mean of the difference between estimated

KFIC and KFIC

post

. The red lines correspond to plus

and minus one and two standard deviation respec-

tively. In all the images previous mentioned, blue

crosses represent subjects that underwent hamstring

lengthening and red circles correspond to subjects that

had another kind of surgery.

5 DISCUSSION

The variable selection applied allows to decrease the

dimension of the problem from 16 to 7, which is

less than the half. This also decreases complexity of

the nonlinear regression. Moreover, with the Gram-

Schmidt orthogonolization, we maximize the corre-

lation of the input with the target output and, at the

same time, we reduce redundancy between the entry

variables.

Since surgical treatment implies various risks and

potential complications, a threshold for the difference

between estimated and measured postoperative knee

ﬂexion has to be deﬁned in order to determine wether

or not an estimation is acceptable. If we consider that

intrasubject gait variability is higher in CP children

than in normal children (Steinwender et al., 2000),

that the interlaboratory gait variabilty for knee ﬂexion

is 13

◦

in (Noonan et al., 2003) and that there are un-

certainties associated to CGA (Charlton et al., 2004;

Groen et al., 2012) and surgery, we deﬁne as accept-

able an estimation with maximum 10

◦

of error. The

system estimates 63.21% of patients within this er-

ror range (see table 2). The error rates are almost the

same for both groups of patients: those who under-

0 10 20 30 40 50 60 70 80

KFICpost

HL=1

HL=0

(a)

0 10 20 30 40 50 60 70 80

Estimated KFIC

(b)

0 10 20 30 40 50 60 70 80

−40

−30

−20

−10

Estimated KFIC − KFICpost

KFICpre

(c)

Figure 4: Target, estimation and error with respect KFIC

pre

(a) KFIC

post

vs. KFIC

pre

. (b) Estimated KFIC vs. KFIC

pre

post

vs.

KFIC

pre

went hamstring lengthening and those who had an-

other surgery.

On the other hand, the distribution of points in ﬁg-

ures 4(a) and 4(c) are similar, and they have the same

proportion of data above and below the black line.

This means that the system can forecast bad (above

the black line) and good outcomes. In ﬁgure 4(c), we

can observe that the systems overestimates and un-

derestimates uniformly with respect to preoperative

knee ﬂexion at initial contact. Additionally, errors

are equally distributed in function of the KFIC

pre

in-

put independently if the subjects had or not hamstring

lengthening.

EstimationofPostoperativeKneeFlexionatInitialContactofCerebralPalsyChildrenusingNeuralNetworks

341

6 CONCLUSIONS

The proposed simulator can estimate the postopera-

tive knee ﬂexion at initial contact, given the preopera-

tive gait, physical examination and a surgery. On test,

63.21% of the N = 193 limbs are estimated with an

acceptable regression error (see section 5). In addi-

tion, the mean RMSE is 9.25

◦

, which means that the

expected error of regression is also acceptable (infe-

rior to 10

◦

The developed system is able to give good estima-

tions independently of the preoperative gait parame-

ters and the type of surgery. However, around a third

of the patients are not well estimated. For the applica-

tion, it is important to apply surgery only if a good re-

sult can be asserted. Conversely, it is crucial to avoid

a surgery plan if a bad outcome is most likely. For

this reason, it would be interesting to detect a priori

patients that will be badly estimated. With this strat-

egy, patients more likely to be badly estimated, could

be rejected by the simulator. For example, if a new

patient is too far from the training patients in the in-

put space, no estimation will be given.

In order to improve estimation, a prior cluster-

ing of the patients could be applied, so the regression

method would be able to adapt to the type of subject.

Finally, this study predicts the outcomes of or-

thopaedic surgery with real gait parameters, and not

with qualitative parameters that are too relative and

ambiguous for such a sensitive application.

Further work will focus on estimating the whole

postoperative knee ﬂexion gait cycle signal and not

only the initial contact point.

ACKNOWLEDGEMENTS

This work is part of a project funded by the Fondation

Ellen Poidatz, the Fondation Bettencourt Schueller

and the Region Ile de France. The authors would like

to thank the UNAM medical and technical team of the

Fondation Ellen Poidatz, who recorded all data used

in this work.

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