Prediction of the Impact of Physical Exercise on Knee OsteoarthritisPatients using Kinematic Signal Analysis and Decision Trees

M. Mezghani1,2, N. Hagemeister2, M. Kouki1, Y. Ouakrim2,4, A. Fuentes3 and N. Mezghani2,41Ecole Superieure de la Statistique et de l’Analyse de l’Information, Universite de Carthage, Tunisia

2Laboratoire de Recherche en Imagerie et Orthopedie (LIO), Centre de Recherche du CHUM, Montreal, Canada3 EMOVI Inc, Quebec, Canada

4LICEF Reserach Center, TELUQ University, Montreal, Canadaneila.mezghani@teluq.ca, marwamezghani96@gmail.com

Keywords: 3D Kinematics, Decision Trees, Knee Osteoarthritis, Physical Exercise, Knee Kinesiography.

Abstract: The evaluation of knee biomechanics provides valuable clinical information. This can be done by means of aknee kinesiography exam which measures the three-dimensional rotation angles during walking, thus provid-ing objective knowledge about knee function (3D kinematics). 3D kinematic data is quantifiable informationthat provides opportunities to develop automatic and objective methods for personalized computer-aided treat-ment systems. The purpose of this study is to explore a decision tree based method for predicting the impact ofphysical exercise on a knee osteoarthritis population. The prediction is based on 3D kinematic data i.e., flex-ion/extension, abduction/adduction and internal/external rotation of the knee. Experiments were conducted ona dataset of 309 patients who have engaged in physical exercise for 6 months and have been grouped into twoclasses, Improved state (I) and not-Improved state (nI) based on their state before (t0) and after the exercise(t6). The method developed was able to predict I and nI patien with knee osteoarthritis using 3D kinematicdata with an accuracy of 82%. Results show the effectiveness of 3D kinematic signal analysis and the decisiontree technique for predicting the impact of physical exercise based on patient knee osteoarthritis pain level.

1 INTRODUCTION

The knee is a joint of great anatomical and biome-chanical complexity, and is the basis for the mobilityand stability of the human body. This joint under-goes various static and dynamic stresses that makeit subject to several degenerative diseases, includingknee osteoarthritis (OA). The World Health Organi-zation estimates that 10% of the adult population indeveloped countries suffers from osteoarthritis, 6.1%of which affects the knee (Woolf and Pfleger, 2003).In Canada, hundreds of thousands of people sufferfrom osteoarthritis of the knee, which affects theirfunctional abilities and undermines their quality oflife. The prevalence of osteoarthritis is increasing asthe population ages. Indeed, professionals estimatethat it will have doubled by the year 2020 (Creamerand Hochberg, 1997). Knee osteoarthritis is also oneof the most important chronic diseases in terms ofthe use of health services (Health Council of Canada,2007).

Although there are protocol and practice guide-lines for better management of osteoarthritis, several

studies show that the treatment of this pathology isfar from optimal and that significant deficiencies ex-ist both for the diagnosis and for the therapeutic man-agement of knee osteoarthritis.The diagnosis of os-teoarthritis can be made either by a family doctor(general practitioner) or by an orthopedic surgeon af-ter a musculoskeletal evaluation that can be combinedwith an imaging examination (X-ray). However, be-cause radiological examinations are performed in astatic state, they collect data on the integrity of kneestructures but do not describe the functional aspectsof the knee. While such examinations allow us to de-termine the impact of an injury on knee function, theyare not sensitive enough to allow clinicians to make aninformed choice about the treatment to be prescribed,particularly when it comes to prescribing physical ex-ercise. Properly formulated exercises are very im-portant because they aim to delay the progression ofthe disease while improving symptoms and joint func-tion. In addition, exercise is among the non-surgicaltreatments that have the most scientific evidence tosupport their effectiveness (Fransen et al., 2015). De-spite this, no studies have investigated the effect of

exercises to predict their impact on the osteoarthritisand thus examine whether they could improve state ofthe knee.

In this context, functional evaluation of the kneeprovides valuable clinical information. It can bedone by means of a knee kinesiography exam whichmeasures the three-dimensional rotation angles (3Dkinematics) of the knee during walking, thus mak-ing it possible to identify mechanical biomarkers di-rectly related to the progression of the disease andthe patient’s symptoms. This type of evaluation caneasily be performed in a clinical setting using theKneeKGT M system (EMOVI Inc, Montreal, Canada).

Figure 1: Knee kinematic acquisition system.

Several studies have demonstrated the accuracy,validity and reproducibility of 3D knee movementsmeasured by this technology (Lustig et al., 2011). Forthe first time, then, the use of this system allows toassess a valid and accurate functional evaluation ofthe knee in a clinical setting. This evaluation is non-invasive and reliable allows the biomechanical func-tion of the knee to be evaluated and analyzed in 3D,in real time, in motion and under load. 3D kine-matic data, which is quantifiable information aboutknee function, provides an opportunity to objectivelystudy the impact of a physical exercise program onknee function.

2 METHODOLOGY

To achieve our objective, we adopted the methodol-ogy described in the block diagram of Figure 2 whichis based on the following main steps. The first stepwas to establish a database of knee OA patients whohad completed a 6-month exercise program. The stateof the patient was assessed before starting and aftersix months of exercise. This assessment was basedon the Knee Injury and Osteoarthritis Outcome Score(KOOS) questionnaire, which assesses the patient’sknee pain (9 items), other symptoms (7 items), func-tion and daily life (17 items), sport and recreation

(5 items) and knee related quality of life (4 items).These scores range from 0 to 100 with a score of 0 in-dicating the worst possible knee symptoms and 100indicating no symptoms of knee pathology. Basedon the questionnaire responses, the participants weregrouped into two classes: a class of patients whosecondition has been improved (I) and a class whosecondition has not been improved (nI). The second stepwas to develop a classification system to predict theimpact of physical exercise, using knee 3D kinematicdata as input. The predicted state is displayed via aninteractive platform in order to better serve clinicians.

2.1 Data-base

A total of 309 participants with knee osteoarthritistook part in this study. All had completed an exerciseprogram. Participants are described by their demo-graphic characteristics (age, gender and Body MassIndex(BMI)) and one clinical characteristic, the ra-diographic severity grade of their osteoarthritis mea-sured by the Kellgren-Lawrence scale (grade 2: mild;grade 3: moderate; grade 4: severe). These character-istics were measured at the beginning of the project(t0) and after 6 months (t6). All participants also com-pleted the KOOS questionnaires before (t0) and af-ter the exercise program (t6), to assess whether or notthere was an improvement in the patient’s condition(as described in section 2.2).

Table 1: Demographic characteristics of I (improved) andnI (not-improved) classes (BMI designates the mean bodymass index).

Class I Class nIN = 141 N = 168

Age (years) 62.9±9.51 63.66±8.44BMI (kg / m2) 30.2±6.54 29.89±6.0Proportion ofmen / group

36% 40%

2.2 Identification of Patients Accordingto their Improvement Status

Patient improvement was determined based on theKOOS. This questionnaire provided us with a globalevaluation of the knee as well as five specific evalua-tions of particular aspects (pain, symptoms, functionand daily life, sport and leisure and quality of life).The score values measured before (at time t0) andafter the physical exercise (at time t6) were used todeduce whether the patient’s condition had improved(Class I) or not (Class nI). Indeed, according to theliterature , a condition can be considered improved

Biomechanical feature

extraction

0 10 20 30 40 50 60 70 80 90 100

-50

0

50

An

gle

in d

eg

(°)

Flexion/Extension

0 10 20 30 40 50 60 70 80 90 100-40

-20

0

20

40

An

gle

in d

eg

(°)

Adduction/Abduction

0 10 20 30 40 50 60 70 80 90 100

Gait Cycle %

-20

0

20

40

An

gle

in d

eg

(°)

Internal/External rotation

Decision tree classifier

State prediction

I / nI

KOOS evaluation before and after

the physical exercices

Identification of the

improvement state

Figure 2: Block diagram of the methodology adopted.

if the end state assessment exceeds that of the ini-tial state by a threshold of 10 % (Roos and Lohman-der, 2003). This threshold can be applied to the sixvariables (the five KOOS subscales and the overallKOOS), which may introduce several sources of vari-ability in the identification of patients based on theirimprovement state. Preliminary research (Bensalmaet al., 2019) suggests that the KOOSpain is the mostrepresentative score. In the discussion below, states Iand nI are therefore determined using KOOSpain. Inother words, for each patient, the variable η is com-puted as follows:

η =KOOSpain(t6)−KOOSpain(t0)

KOOSpain(t0)

and, the assigned state (class) is then:{I, if η ≥ 10%nI, otherwise

(1)

2.3 Kinematic Factor Extraction

Kinematic data describes the joint angles between thetibia and femur in the three-dimensional space (3D).These are in the form of 3D curves correspondingto flexion-extension in the sagittal plane, abduction-adduction in the frontal plane and internal-externalrotation in the transverse plane. These curves arenormalized to a range from 1% to 100% where 1corresponds to the beginning and 100 to the endof the cycle. From these curves, parameters of in-terest are then extracted to characterize the patternof each participant. The parameters in our case,are 11 kinematic factors extracted from the flexion-extension, abduction-adduction and internal-externalrotation curves.

2.4 Classification System

In order to predict the patient’s improvement status (Ior nI), we have developed a supervised classification

Figure 3: Kinematic curves of the 309 subjects in thedatabase (I: improved state and nI: not improved state).

system based on decision trees. The decision treeswere built using the Classification And RegressionTree (CART) algorithm and allows to reach the endof each path from the root to a leaf, a description ofone of the classes.

The algorithm for building a binary decision treeusing CART operates node by node, running throughthe M attributes (x1,x2, ...,xM) one by one, startingwith x1 and continuing until xM . For each attribute,it explores all possible tests (splits) and chooses thebest split, i.e., the one that maximizes impurity (un-certainty) reduction. Then, it compares the M bestsplits to choose the best one. The function that mea-sures impurity will necessarily reach its maximumwhen the instances are equitably distributed amongthe different classes and its minimum when one classcontains all the examples (the node is pure). In order

to build the nodes of the tree, ”most discriminating”questions are chosen by the Gini index (Girard, 2007).

This index measures the frequency with which arandom element of the set would be misclassified ifits label were randomly selected based on the distribu-tion of labels in the sub-set. The index ranges between0 and 1 and reaches its minimum value (zero) whenall the elements of the set are in the same class of thetarget variable. The Gini diversity index used by theCART algorithm can be calculated by the followingformula: on a node t with a probability distribution ofthe classes on this node P( j|t), j = 1, ...,J, we have(Hawarah, 2008):

G(t) = i(t) = ϕ(p(1/t), p(2/t), ..., p(J/t))

= 1−∑j(P( j|t))2

where p( j/t) is the proportion of individuals belong-ing to class j and ϕ is the proportion function to mea-sure the impurity i(t).

It should be noted that the decision trees werepruned by the post-pruning method to avoid over-learning. This approach proceeds as follows: aftercompleting the decision tree building process, the treeis pruned. To this end, classification errors are esti-mated at each node. The subset is replaced by a leaf(class) or by the most frequent branch. We then startat the bottom of the tree and examine each of the sub-trees (non-folio) to see whether replacing the sub-treeby a leaf or its most frequent branch would result into a lower error rate. If so, we trim the sub-tree byperforming the replacement(Hawarah, 2008).

2.5 Evaluation of Classification System

The evaluation of the classification system was car-ried out by dividing the database into two sub-databases: a training database and a test database.This division allows the model to be developed andtested on different data to verify its relevance. In ourcase, we opted for a division allocating 2/3 of the datafor training and the remaining 1/3 for testing. Thisgave us 206 participants for the learning process and103 participants for the validation of the model.

Following training, we considered the classifica-tion rate as an evaluation criterion. This rate is theratio of the total number of well classified data pointsto the total number of data points.

Classification rate =Well classified observations

Total number of observations

The confusion matrix can also be presented for abetter interpretation of the results. This is a matrix

representation that determines the classification errorfrom a set of test data. The confusion matrix is asquare matrix of size [C×C] where C is the number ofclasses. The columns of this matrix correspond to thenumber of occurrences of an estimated class, whilethe rows correspond to the number of occurrences ofan actual class. The following table shows an exampleof a confusion matrix with two classes. The precisionof the classifier is calculated by formula (2), and thesensitivity and specificity by formulas (4) and (5), re-spectively.

Predicted classReal class C1 C2

C1 True Positive False NegativeC2 False Positive True Negative

True Positive (TP) = C1 group participant correctlyclassified.True Negative (TN) = C2 group participant correctlyclassified.False Positive (FP) = C2 group participant classifiedas C1.False Negative (FN) = C1 group participant classifiedas C2.The mathematical formulas for the evaluation param-eters of a classifier are as follows:

Accuracy =T P + T N

Total number o f observations(2)

Precision =T P

T P + FP(3)

Sensitivity =T P

T P + FN(4)

Speci f icity =T N

T N + FP(5)

To be considered accurate, a classifier must beboth highly sensitive and highly specific.

3 RESULTS: CLASSIFICATIONBASED ON DECISION TREES

We developed the classification system using theCART algorithm and an input vector of 13 variables,i.e., 9 kinematic factors, 2 demographic variables(BMI and Age) and the KOOSpain score at t0. Train-ing was performed using both the hold out approach(2/3 of the data for training and 1/3 for testing) andleave-one out cross validation. Table 2 shows that theclassification rate reaches 82% for leave-one out cross

Koos pain at t0

< 76

Koos pain at t0nI

48 / 54

< 76

Maximum of flexion

during swingBMI

Flexion Amplitude

during the stance

nI

27 / 30

I

4 / 5

< 15 >= 15

Maximum of flexion

during swing

Flexion amplitude

at stance phase

nI

7 / 7Age

nI

34 / 55BMI

>= 7 < 7

< 67 >= 67

nI

5 / 7

I

16 / 20

>= 25 < 25

>= 54 < 54

>= 55 < 55

< 56 >= 56

I

13 / 16

Flexium initial at

contact

Flexion excursion

at loading

< 37 >= 37

>= 8.1

I

21 / 22

Internal rotation

at loading

< 8.1

nI

14 / 17

I

4 / 4

>= 20 < 20

Internal rotation

at loading

nI

8 / 9

>= -0.52

Varus thrust

at loading

< -0.52

I

6 / 6

< 1.1

Varus thrust

at loading

>= 1.1

nI

5 / 5

I

7 / 10

>= 2 < 2

I

34 / 42

>= 0.25 < 0.25

Figure 4: The KOOSpain decision tree.

validation and 75% for hold out approach based onthe 1/3 testing data.

Table 2: Classification rates using the CART algorithm.

Training and testing Classification rate2/3 of the database for training 75%and 1/3 for testingLeave-one-out cross validation 82%(309 patients)

Figure 4 illustrates the decision tree obtained. Ofthe 13 input variables used, 9 were retained by theCART algorithm. The KOOSpain score at t0 was iden-tified as the most important variables ranked by impu-rity.

Table 3: Confusion matrix for the training based on leave-one-out cross validation.

Predicted classReal class I nI

I 105 36nI 20 148

4 CONCLUSION

To our knowledge, this study is the first to explore,the use of machine learning techniques to predict theimpact (improvement or not) of physical exercise onthe knee in a gonarthrotic population. To this end, wefirst developed a large database composed of subjectswho had completed a personalized physical exerciseprogram, whose condition was measured at the begin-ning of the project (time t0) and after 6 months (timet6). In a second step, we developed a classificationsystem based on decision trees. This classificationsystem uses 3D knee kinematic data as input to per-form an objective, evidence-based decision. The deci-sion trees achieved a classification rate of 82% basedon KOOSpain using a leave-one-out procedure (75%based on KOOSpain on test data only). Unlike manyclassification methods, decision trees are intuitive andprovide a graphic, meaningful and easy-to-read repre-sentation. This advantage has been exploited by im-plementing a user-friendly graphical interface that al-lows clinicians to query patient characteristics for a

better understanding of the classification system’s de-cision.

ACKNOWLEDGMENTS

This research was supported in part by the NaturalSciences and Engineering Research Council Grant(RGPIN-2015-03853) and the Canada Research Chairon Biomedical Data Mining (950-231214).

REFERENCES

Bensalma, F., Mezghani, N., Ouakrim, Y., Fuentes, A.,Choiniere, M., Bureau, N., Durand, M., and Hage-meister, N. (2019). A multivariate relationship be-tween the kinematic and clinical parameters of kneeosteoarthritis population. Applied Bionics and Biome-chanics, 2019:14.

Creamer, P. and Hochberg, M. (1997). Osteoarthritis.Lancet, 350:503–8.

Fransen, M., McConnell, S., Harmer, A., der Esch, M. V.,Simic, M., and Bennell, K. (2015). Exercise for os-teoarthritis of the knee: a cochrane systematic review.British Journal of Sports Medicine.

Girard, A. (2007). Exploration d’un algorithme genetiqueet d’un arbre de decision a des fins de categorisa-tion. Master’s thesis, Universite du Quebec a Trois-Rivieres.

Hawarah, L. (2008). Une approche probabiliste pour leclassement d’objets incompletement connus dans unarbre de decision. Master’s thesis, Ecole DoctoraleMSTII.

Lustig, S., Magnussen, R., Cheze, L., and Neyret, P. (2011).The kneekg system: A review of the literature. KneeSurgery, Sport. Traumatol. Arthrosc.

Roos, E. M. and Lohmander, L. S. (2003). The knee injuryand osteoarthritis outcome score (koos): from joint in-jury to osteoarthritis. Health Qual Life Outcomes.

Woolf, A. and Pfleger, B. (2003). Burden of major mus-culoskeletal conditions. Bulletin of the World HealthOrganisation, 81(9):646–56.