Predicting Functional Recovery of Stroke Patients using Age Dependent

Model

Aleksandar Jeremic

, Milan Savic

, Ljubica Nikcevic

, Dejan Nikolic

and Natasa Kovacevic-Kostic

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

Special Hospital for Cerebrovascular Diseases, ”Sveti Sava”, Belgrade, Serbia

Physical Medicine and Rehabilitation, University Childrens Hospital, Faculty of Medicine, University of Belgrade,

Belgrade, Serbia

Clinical Centre of Serbia, Faculty of Medicine, University of Belgrade, Belgrade, Serbia

Keywords:

Functional Recovery, Stroke, Recovery Prediction.

Abstract:

Predicting functional recovery of stroke patients is important from both clinical and academic points of view.

From the clinical point of view it is important to patients, families and clinical workers. Most importantly, an

accurate prediction enables us to provide more accurate prognoses, set goals, manage therapies and improve

management of healthcare resources through optimal discharge procedures. For example, being able to predict

recovery of particular limbs we could potentially improve advanced planning of safe transfer in an optimally

determined time frame. Functional recovery is usually evaluated using various functional indices that evaluate

patients’ ability to perform daily living tasks. In this paper we propose to predict functional recovery using

two well established functional indices: functional independence measure and Barthels index. We model

those indices as a age dependent polynomial functions with unknown coefﬁcients and estimate the unknown

parameters. In order to demonstrate applicability of the propose technique we compare the performance of

our non-linear polynomial model with the performance on linear MANOVA model.

1 INTRODUCTION

Stroke is a leading cause of a long-term disability and

consequently can signiﬁcantly deteriorate quality of

life of the recovery patients. According to The Heart

and Stroke foundation report half of the patients re-

covering from stroke need help with daily activities.

Accordingly it would be beneﬁcial to predict func-

tional recovery as it would allow health professionals

to provide patients with prognoses, set goals, select

therapies and plan discharge. Achieving these goals

would make possible to optimize utilization of health

care resources in order to reach maximum attainable

recovery level.

In recent years there has been considerable re-

search interest in predicting stroke recovery of par-

ticular limbs (arms, legs) (Houwink et al., 2013),

(Craig et al., 2011) or functional independence re-

covery i.e. patient ability to perform particular tasks

(Veerbeek et al., 2011). Due to inherent patient-to-

patient variability most of the proposed models (tech-

niques) require certain experiment based adjustments

in order to account for that variability. In (Brown

et al., 2015), (Kimura et al., 2017) the authors demon-

strated that functional independence measure (FIM)

can be potentially used to predict functional recov-

ery of the stroke patients. In addition to FIM, an-

other generic disability measure Barthel index (BI),

has been widely used in order to evaluate patients

ability to perform daily tasks. In recent reviews multi-

ple authors identiﬁed that different variables can work

as somewhat successful predictors of various indi-

cators (ability to walk, arm recovery, etc.) (Chum-

ney et al., 2010), (Putten et al., 1999), (Govan et al.,

2009). As we have stated earlier in addition to pre-

dicting limb recovery it may be equally important to

predict patients’ functional recovery as it can poten-

tially be used for efﬁcient healthcare management.

In this paper we propose to predict functional in-

dependence recoveryusing coupled parametric model

based on functional independence measure (FIM)

and Barthel index (BI) measurements. As a pre-

liminary approach we evaluate applicability of the

growth curve model (generalized multivariate analy-

sis of variance model) in which the weighting coefﬁ-

cients are calculated optimally based on patient age.

Jeremic, A., Savic, M., Nikcevic, L., Nikolic, D. and Kovacevic-Kostic, N.

Predicting Functional Recovery of Stroke Patients using Age Dependent Model.

DOI: 10.5220/0007577702410245

In Proceedings of the 12th International Joint Conference on Biomedical Engineering Systems and Technologies (BIOSTEC 2019), pages 241-245

ISBN: 978-989-758-353-7

241

We ﬁrst propose parametric model in which the age is

accounted for by using parametric exponential func-

tions (known up to a parameter). We then estimate

the unknown parameters using part of the data set as

training set. We then evaluate the performance of the

proposed model by comparing it to the MANOVA

model and apply both models to the remaining pa-

tients. In future work we expect to include multivari-

ate dependence based on additional parameters such

as height, weight, body mass index, habits before the

stroke, etc.

The paper is organized as follows. In Section II we

describe the data set and the proposed estimation al-

gorithms. In Section III we evaluate the applicability

of the proposed algorithm using a real data set. Fi-

nally, in Section IV we discuss the results and future

work.

2 SIGNAL PROCESSING

MODELS

2.1 Data Set

We have evaluated 187 eligible participants that were

referred to the rehabilitation facility after stroke for

inclusion into rehabilitation program and follow-up.

To assess eligibility for the inclusion in the study the

patients were evaluated by board certiﬁed physiatrist

and specialist of internal medicine. Prior to the in-

clusion, all the participants were informed about the

study protocol and informed consent was obtained.

The study was approved by the Institutional Review

Board and was carried out according to the principles

of good clinical practice. The eventual onset of early

complications was indication for the termination of

the rehabilitation program for deﬁned period of time.

The exclusion criteria for the study were recurrent hip

fractures and inability to completely ﬁnish the reha-

bilitation program or follow-up that was deﬁned by

the study. Therefore, the initial group on admission

consisted of 217 patients, where 11 did not complete

rehabilitation program due to the worsening of health

condition and thus transferred to specialized referring

hospitals, while 19 subjects dropped out from dis-

charge period to the planned follow-up after 3 months

post-discharge.

Functional Independence Measure (FIM) was

used to evaluate patient’s functional status on 3 occa-

sions: at admission (Admission), on discharge from

the rehabilitation facility (Discharge) and 1 and 3

months after discharge (Follow-ups). After discharge,

patients were not included into any kind of rehabil-

itation program and were referred to home of resi-

dence. FIM presents valid and reliable test in the

estimation of aggregated changes in functional status

that appears in the deﬁned period of the study eval-

uation (Young et al., 2009)-(Dodds et al., 1993). It

is composed of 18 categories that are scaled from 1-7

each (Young et al., 2009) We organize the data set in a

database consisting of 187 rows corresponding to the

patients and 9 columns of (age, FIM at the admission,

FIM at the discharge, FIM after 1 month, FIM after 3

months, BI at the admission, etc.)

2.2 Parameter Estimation

In order to be able to predict the functional recov-

ery we ﬁrst propose standardized MANOVA model

in which the data is modelled as

Y = AX + E

where X is n × 5 matrix consisting of age and FIM

and Barthel indices at the admission and discharge,

A is a matrix of unknown parameters, and Y is an

n × 4 matrix consisting of FIM and Barthel indices

at 1 and 3 months after discharge respectively, and

E is the matrix of residual errors. This technique is

commonly used as a preliminary approach in order to

obtain goodness-of-ﬁt assuming that the data can be

modelled using linear model.

In the second approach we propose to model the

the indices values after the discharge using a new non-

linear polynomial approach in which the indices val-

ues are modelled as polynomial functions of the input

parameters. Note that originally this approach was

used to model time dependent growth change and is

commonly used technique if prior knowledge is not

available. In this paper we propose to use hierarchical

polynomials in order to account for patient-to-patient

variability. In this paper we use polynomial model

given by

i, j

∑

k=1

∗ age

k−1

)+αFIM

admission

+βBI

admisson

i,1

where q is the polynomial order, a are unknown pa-

rameters modelling age dependence, α and β are un-

known linear index parameters, and e

i, j

are residual

error (modelling noise).

To evaluate the applicability of the proposed algo-

rithms we ﬁnd the normalized mean-square error and

likelihood ratio test. Note that the above models can

be easily extended to include larger number of param-

eters and this will be discussed further in Section 3.

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242

3 RESULTS

The total number of patients admitted was 187 with

age and indices characteristics being given in Figures

1-4.

50 55 60 65 70 75 80 85 90

Age

Figure 1: Histogram of patients’ age at the admission.

0 10 20 30 40 50 60 70

Barthel - admission

Figure 2: Histogram of Barthel index distribution at the ad-

mission.

20 24 28 32 36 40 44 48 52 56

FIM - admission

Figure 3: Histogram of FIM index distribution at the admis-

sion.

Additionally in Table 1 we show the correlation

coefﬁcient of all the FIM and BI with respect to the

age. Due to existing inverse correlation relationship

the age dependent model can improve our ability to

100

Age

FIM 3mths

Barthel 3mths

100

120

140

Figure 4: 3D scatter plot of age, FIM and Barthel indices.

predict recovery. In addition the increase in corre-

lation between indices at the discharge indicate that

their values at the admission should be used simulta-

neously in order to improve the performance.

Table 1: Correlation coefﬁcients.

Age FIMa FIM3 BIa BI3

Age 1.00 -0.05 -0.15 -0.17 -0.13

FIMa -0.05 1.000 0.69 0.87 0.64

FIM3 -0.15 0.69 1.00 0.66 0.92

BIa -0.17 0.87 0.66 1.00 0.59

BI3 -0.13 0.64 0.92 0.59 1.00

To illustrate the statistical properties of the data

sample we present two scatter plots. In Figure 5

we present the FIM change between admission and

3 months after discharge and in Figure 6 we present

similar results for BI.

50 55 60 65 70 75 80 85 90

FIM change

-10

Figure 5: Two-dimensional scatter of age and FIM change.

In Figure 7 we present the prediction result in

terms of mean-square error (MSE) for nonlinear

model as a function of number of parameters i.e poly-

nomial order. As expected after initial decay the MSE

slope decreases signiﬁcantly which means that the

Predicting Functional Recovery of Stroke Patients using Age Dependent Model

243

50 55 60 65 70 75 80 85 90

BI change

Figure 6: Two-dimensional scatter of age and BI change.

1 1.5 2 2.5 3 3.5 4

Polynomial order

0.03

0.04

0.05

0.06

0.07

0.08

0.09

0.1

0.11

0.12

MSE

Figure 7: MSE of nonlinear model.

beneﬁts of introducing additional parameters should

be examined in more details as they may lead to in-

crease in the computational complexity as well as

Cramer-Rao bound.

−4 −3 −2 −1 0 1 2 3

x 10

−3

MSE

Count

Figure 8: Two group clustering.

The likelihood ratio for two parameters models is

given in Table 2. From the results it seems that the

nonlinear model provides better ﬁt in terms of the

likelihood function for the older patients. However

it should be noted that the sample size for the older

patients is slightly larger. In addition the nonlinear-

ity may play more important role at younger due to

more complex recovery processes and hence may not

be captured well by the proposed nonlinear model.

Table 2: Likelihood-ratio.

Likelihood-ratio nonlinear vs. linear

Age ≥ 65 0.35

Age ≤ 65 0.64

Finally in order to evaluate applicability of our al-

gorithm from the clinical point of view we classify

patients based on joint FIM and BI measurements in

the following way: if either FIM is larger than 36 or

BI is larger than 4 the recovery is labelled as sufﬁ-

cient otherwise the recovery of a particular patient is

labelled as insufﬁcient. We estimate the unknown pa-

rameters using half of the data set and evaluate its per-

formance using the other half. We repeat selection of

the training data set randomly 1000 times. The results

of the classiﬁcation using predicted values are given

in Table 3.

Table 3: Classiﬁcation error.

Error percentage

Insufﬁcient recovery error 2%

Sufﬁcient recovery error 1%

4 CONCLUSIONS

The importance of early inclusion in rehabilitation

program and exercise of older people after the stroke

could be explained by the fact that physical activity

inﬂuences the muscle strength and neural function re-

covery (Sipila et al., 2011). Such determinants are

very important particularly for individual’s quality of

life. It has been often hypothesized that the success

of recovery is extremely dependent on the timeliness

and adequacy of the treatment. While it is desirable to

provide the best possible care as soon as possible the

actual limitations that may exist in health-care sys-

tems due to a limited number of medical staff as well

as limited capacity in rehabilitation programs may

create need for appropriate planning and/or schedul-

ing.

To this purpose in this paper we proposed an al-

gorithm which can potentially be used to predict the

functional recovery which is one of the most impor-

tant factors that indicate ability for self-functioning of

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244

the patients and return to daily activities. As a pre-

liminary approach we proposed and compared two

parameters linear and nonlinear models using mean

square error and likelihood-ratio. In addition the

residual vector may not be Gaussian distributed es-

pecially in which case an effort should be made to

investigate different estimation techniques that may

be more suitable for non-Gaussian models. Finally, a

clinically study with a larger number of patients and

additional types of observation should be performed

is it may provide better insight and improve quality of

the prediction models.

REFERENCES

Brown, A., Therneau, T., Schultz, B., Niewczyk, P., and

Granger, C. (2015). Measure of functional indepen-

dence dominates discharge outcome prediction after

inpatient rehabilitation for stroke. Stroke, 46(4):1038–

1044.

Chumney, D., Nollinger, K., Shesko, K., Skop, K., Spencer,

M., and Newton, R. (2010). Ability of functional in-

dependence measure to accurately predict functional

outcome of stroke-speciﬁc population: Systematic re-

view. J Rehabil Res Dev, 47(1):17–29.

Craig, L., Wu, O., Bernhardt, J., and Langhorne, P. (2011).

Predictors of poststroke mobility: Systematic review.

Int. J. Stroke, 6:321–327.

Dodds, T., Martin, D., Stolov, W., and R, D. (1993). A val-

idation of the functional independence measurement

and its performance among rehabilitation inpatients.

Arch Phys Med Rehabil, 74:531–536.

Govan, L., Langhorne, P., and Weir, C. (2009). Categorizing

stroke prognosis using different stroke scales. Stroke,

40(10):3396–3399.

Houwink, A., Nijland, R., Geurts, A., and Kwakkel, G.

(2013). Functional recovery of the paretic upper limb

after stroke: Who regains hand capacity? Arch. Phys.

Med. Rehabil., 94(94):839–844.

Kimura, Y., Yamada, M., Hamanaka, K., Tanaka, N.,

and Muroh, Y. (2017). Usefulness of the prediction

method based on a logarithmic model for functional

recovery in stroke patients: in case of using the motor-

functional independence measure score. Int. J Rehabil

Res, 40(2):134–137.

Putten, J., Hobart, J., Freeman, J., and Thompson, A.

(1999). Measuring change in disability after inpa-

tient rehabilitation: comparison of the responsiveness

of the barthel index and the functional independence

measure. J Neurol Neurosurg Psychiatry, 66(4):480–

484.

Sipila, S., Salpakoski, A., Edgren, J., Heinonen, A., Kaup-

pinen, M., and M, A.-K. (2011). Promoting mobility

after hip fracture (promo): study protocol and selected

baseline results of a year-long randomized controlled

trial among community-dwelling older people. BMC

Musculoskelet Disord, 27:277.

Veerbeek, J., Kwakkel, G., van Wegen, E., Ket, J., and Hey-

mans, M. (2011). Early prediction of outcome of ac-

tivities of daily living after stroke: A systematic re-

view. Stroke, 42:1482–1488.

Young, Y., Fan, M., Hebel, J., and Boult, C. (2009). Con-

current validity of administering the functional inde-

pendence measure (ﬁm) instrument by interview. Am

J Phys Med Rehabil, 88:766–770.

Predicting Functional Recovery of Stroke Patients using Age Dependent Model

245