ANALYSIS OF BERG BALANCE SCALE IN HIP FRACTURE

PATIENTS USING FUZZY CLUSTERING

Aleksandar Jeremic

, Natasa Radosavljevic

, Dejan Nikolic

and Milica Lazovic

Department of Electrical and Computer Engineering, McMaster University, Hamilton, ON, Canada

Institute for Rehabilitation, Belgrade, Serbia

Physical Medicine and Rehabilitation, University Childrens Hospital, Belgrade, Serbia

Faculty of Medicine, University of Belgrade, Belgrade, Serbia

Keywords:

Fuzzy clustering, Hip fracture, Clinical decision making.

Abstract:

Hip fractures are most frequent cause of hospitalization after the fall in older population and consequently

have been subject of great interest in medicine and biomedical engineering. It has been observed that the

incidence of hip fractures is rising at the approximate rate of 1-3% per year, with subsequent mortality rates

at approximately 33% in ﬁrst year after the fracture. In this paper we propose to classify patients at the time

of admission into several clusters with respect to their ability for successful recovery. To this purpose we ﬁrst

evaluate the efﬁcacy of rehabilitation program based on the balance function improvement measured by Berg

Balance Scale (BBS) in elderly (in the remainder of the paper deﬁned as above 65 years of life) after hip

fractures, and evaluate inﬂuence of gender, age and comorbidity on balance function improvement in these

patients. Then we design clustering procedure in which the patients are clustered according to BBS improve-

ment using statistically most signiﬁcant parameters. We then evaluate the proposed clustering procedure on

a data sample consisting of 203 patients that have been admitted to the Institute for Rehabilitation, Belgrade,

Serbia.

1 INTRODUCTION

Hip fractures are most frequent cause of hospitaliza-

tion after the fall in older population (Roudsari et al.,

2005) and consequently has been subject of great in-

terest in medicine and biomedical engineering. It has

been observed that the incidence of hip fractures is

rising at the approximate rate of 1-3% per year, with

subsequent mortality rates at approximately 33% in

ﬁrst year after the fracture (Johnell and Kanis, 2004;

Roche et al., 2005). Consequently because of the in-

creasingly large number of elderly patients with these

fractures signiﬁcant advances have been made with

respect to surgical procedures, post-surgical rehabili-

tation procedures as well as social support services. It

is often emphasized that management and allocation

of resources is of utmost importance in patient care.

In practical situations the amount of resources is lim-

ited and thus proper assignment of priorities may play

crucial role in recovery. As an example certain pa-

tients experiencing hip fracture may show signiﬁcant

progress if surgeries and rehabilitation programs are

allocated in timely manner thus leading to more efﬁ-

cient health care.

One of the most important aspects of rehabilita-

tion in these patients is habilitation for independent

walking which has been strongly correlated with the

balance establishment and/or improvement in these

individuals. Furthermore it has been reported that the

balance improvement has demonstrated strong nega-

tive correlation with probability of further falls and

hip fractures in elderly (Berry et al., 2007). One of

the commonly used techniques (measures) for bal-

ance evaluation is Berg Balance Scale (BBS) and it

has been demonstrated that it is of particular interest

in elderly population (Santos et al., 2011). In this pa-

per we propose to classify patients at the time of ad-

mission into several clusters with respect to their abil-

ity for successful recovery. To this purpose we ﬁrst

evaluate the efﬁcacy of rehabilitation program based

on the balance function improvement measured by

Berg Balance Scale (BBS) in elderly (in the remain-

der of the paper deﬁned as above 65 years of life) af-

ter hip fractures, and evaluate inﬂuence of gender, age

and comorbidity on balance function improvement in

these patients. Then we design clustering procedure

466

Jeremic A., Radosavljevic N., Nikolic D. and Lazovic M..

ANALYSIS OF BERG BALANCE SCALE IN HIP FRACTURE PATIENTS USING FUZZY CLUSTERING.

DOI: 10.5220/0003875504660469

In Proceedings of the International Conference on Bio-inspired Systems and Signal Processing (BIOSIGNALS-2012), pages 466-469

ISBN: 978-989-8425-89-8

 2012 SCITEPRESS (Science and Technology Publications, Lda.)

in which the patients are clustered according to BBS

improvement using statistically most signiﬁcant pa-

rameters. It is often argued that proper administration

of intrahospital as well as post-recovery procedures

can signiﬁcantly improve the recovery of patients. To

this purpose it would be extremely beneﬁcial to prop-

erly triage (cluster) patients at the admission stage in

order to ensure optimal distribution of resources. We

then evaluate the proposed clustering procedure on a

data sample consisting of 203 patients that have been

admitted to the Institute for Rehabilitation, Belgrade,

Serbia.

The paper is organized as follows. In Section II we

describe the data set and the proposed classiﬁcation

models. In Section III we evaluate the applicability of

the proposed algorithm using a real data set. Finally,

in Section IV we discuss the results and future work.

2 SIGNAL PROCESSING

MODELS

2.1 Data Set

The prospective study included 203 patients with hip

fractures that were referred into the specialized re-

habilitation institution for the rehabilitation program

and admitted from january 2011 until June 2011.

Prior to the inclusion into the study, eligible partici-

pants were informed about the study protocol and re-

habilitation program with possible contraindications

that might arise over the course of treatment. The

informed consent was obtained prior to the inclu-

sion. The study was approved by the Institutional

Review Board. Implementation of rehabilitation pro-

gram was individually prescribed with respect to the

patients functional status and continuously monitored

for early identiﬁcation of possible complications that

could arise during the treatment. Functional status of

every individual in the program was evaluated by the

Berg Balance Scale test on 3 occasions: at the ad-

mission (Group 1), at discharge from the rehabilita-

tion facility (Group 2) and 3 months after discharge

(Group 3). Berg Balance Scale test evaluated 14 tasks

(5 static and 9 dynamic) that are graded as 5 points

scale with the range from 0 to 4, to the maximal value

for the summarized scores of 56 (Stevenson et al.,

2010). Ability to predict falls in elderly population

suggests the validity of BBS test (9). The BBS is

used to measure functional balance that is composed

of 3 dimensions: position maintaining, postural ad-

justment to voluntary movements and reaction to ex-

ternal disturbance (Berg et al., 1995).

2.2 Preprocessing

We organize the data set in a database consisting

of 203 rows corresponding to the patients and 33

columns of different features (age, height, weight,

respiratory conditions, heart conditions, BBS at the

admission, BBS at the discharge, BBS three months

after discharge, etc.) Then we analyze cross-

correlation between all the features and extract sta-

tistically signiﬁcant ones using Pearson coefﬁcient.

In order to study dynamics of rehabilitation we use

log-values of BBS score ratios. The rationale behind

this approach is that we expect exponential change in

balance improvement and thus log (semi-log) models

may represent better ﬁt.

2.3 Clustering Algorithm

Once statistically signiﬁcant features have been se-

lected the problem reduces to clustering of m-

dimensional vectors into a set of pre-determined clus-

ters. In order to determine appropriate use of clinical

resources as a preliminary approach we proposeto de-

termine which patients have largest/smallest capacity

for recovery. We propose to determine the signiﬁcant

parameters using Spearman correlation coefﬁcient

which is commonly used technique in cases/models

where nonlinearity is expected. We then propose to

cluster all the patients into several clusters. We inves-

tigate two possible scenarios in this paper: a) two-

cluster scenario consisting with high rate recovery

and low rate recovery patients, and b) three-cluster

scenario - low, medium, and high rates of recovery.

Note that the number of clusters can be arbitrarily set

and is usually controlled by the overall error of clas-

siﬁcation. In addition, the quality of health care and

resource management can be relatively robust to the

overall error of classiﬁcation and thus the overall re-

sults in treatments may not change signiﬁcantly for

small variations in number of clusters.

In order to cluster the data set we propose to use

fuzzy clustering based on Gath-Geva (Gath and Geva,

1989) clustering which uses Gaussian distance and

consequently assumes that the data set arises from

mixture of Gaussian distributions. A general outline

of the algorithms is as follows: a) arbitrarily assign

each patient to a cluster i.e. arbitrarily pick if the pa-

tient is high or low rate recovery. Note also that the

preliminaryclustering can be either done arbitrarily or

using a hard clustering algorithms such as K-means,

b) update cluster centers, c) reassign objects to the

clusters to which the objects are most similar, d) re-

peat until no change by reassignment. The update of

clustering matrix is done using the following approa-

ANALYSIS OF BERG BALANCE SCALE IN HIP FRACTURE PATIENTS USING FUZZY CLUSTERING

467

Table 1: General characteristics of patient population with

respect to the age and severity index of fracture.

Age Severity Index

Total N=203 77± 6.11 1.74± 0.49

Female N=149 78.28± 5.86 1.74± 0.43

Male N =54 76.19± 6.56 1.76± 0.64

Group1 N=65 70.48± 3.14 1.72± 0.65

Group 2 N=114 79.92 ± 2.88 1.75± 0.41

Group 3 N=25 86.56± 1.39 1.73± 0.37

ch: if there is any distance greater than zero then

membership grade is the weighted average of the dis-

tances to all the centers else the patient belongs to this

cluster and no other clusters. Note that in GG al-

gorithm the distance calculated is Gaussian distance

given by

detA

exp



− ν

)

−1

− ν

)



where ν

is the cluster center, P

is the probability

that patient x

belongs to the ith cluster and A

the weighted sample covariance matrix the ith cluster

with membership values being the weighting coefﬁ-

cients.

3 RESULTS

In order to evaluate the performance of our techniques

we should ideally have the possibility to validate use-

fulness of classiﬁcation in terms of recovery. How-

ever since in this paper we present only proof of con-

cept that classiﬁcation is possible we propose to eval-

uate efﬁcacy of classiﬁcation in two ways: a) by com-

paring variance of each cluster to the quantization

error calculated using empirical histogram of recov-

ery rate distributions and b) by evaluating probabil-

ity of misclassiﬁcation where we assume that an er-

ror occurs at every instance of discrepancy between

our clusters and histogram deﬁned clusters. The to-

tal number of patients admitted was 203 with general

characteristics being described in Table 1.

In order to illustrate statistical properties of BBS

value for all the patients in Figures 1-3 we illus-

trate histograms at the admission, at the discharge and

three months after discharge. As expected we can ob-

serve shift towards higher values which is expected as

a consequence of rehabilitation. After we performed

correlation analysis using Spearman coefﬁcients we

decided to reduce the number of features for cluster-

ing. To simplify the procedurewe decided to use three

most signiﬁcant features: age, rate of BBS change

during rehabilitation and severity index.

5 10 15 20 25 30 35 40

Figure 1: Empirical probability density function of BBS at

the admission.

10 15 20 25 30 35 40 45 50

Figure 2: Empirical probability density function of BBS at

the discharge.

In Figure 4 we present the result of the cluster-

ing assuming there are only two groups. The centers

of the clusters are marked with letter x. As expected

fuzzy clustering represents an adequate choice due to

the arbitrarily shaped cluster regions. In Figure 5 we

present the same results when three clusters are used.

Observe that the separation of the clusters in the latter

case is less visible but this is in general true when the

number of clusters is increasing.

The error analysis results are summarized in Ta-

ble 2. In ﬁrst column we calculate the mean square

5 10 15 20 25 30 35 40 45 50 55

Figure 3: Empirical probability density function of BBS

three months after rehabilitation.

BIOSIGNALS 2012 - International Conference on Bio-inspired Systems and Signal Processing

468

Age

Rate gradient during rehabilitation

Severity Index

Figure 4: Two group clustering.

Age

Rate gradient during rehabilitation

Severity Index

Figure 5: Three group clustering.

error of the cluster relative to the expected quantiza-

tion error for a given data set. In the second column

we calculate the probability of misclassiﬁcation as ex-

plained above. As expected we observe slightly larger

error for three-clusters scenario which is expected. It

is important to reiterate that in order to truly evaluate

performance we need a clinical study in which the re-

sults of this clustering are applied in clinical decision

making in terms of treatment timelines and rehabili-

tation techniques.

4 CONCLUSIONS

In this paper we demonstrated ability to classify hip

fracture recovery patients admitted to the rehabilita-

tion program. We classiﬁed the patients with respect

to the dynamics of their recovery that was inferred

from gradients of Berg Balance Scale which is com-

Table 2: Mean square error and probability of error.

MSE / QE Probability of error

Two clusters 1.21 0.15

Three clusters 1.13 0.23

monly used technique for evaluating balance of the

patients and hence is one of the indicators of the re-

covery degree. Our ultimate goal is to develop clus-

tering algorithms for triage purposes which would al-

low clinical staff and administration to properly plan

treatment program based on the available resources.

As such this approach requires further study in which

the success of recovery between two groups (with and

without clustering based triage) would be monitored.

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