Knee Kinematics Feature Selection for Surgical and Nonsurgical
Arthroplasty Candidate Characterization
M. A. Ben Arous
1,6
, M. Dunbar
2
, S. Arfaoui
3,6
, A. Mitiche
5
, Y. Ouakrim
4,6
, A. Fuentes
6
,
G. Richardson
2
and N. Mezghani
4,6
1
Collège Bois de Boulogne, Montreal, Quebec, Canada
2
Dalhousie University, Halifax, Nova Scotia, Canada
3
Collège Jean-de-Brébeuf, Montreal, Quebec, Canada
4
LICEF Research Center, TELUQ University, Montreal, Quebec, Canada
5
INRS Énergie, Matériaux et Télécommunications, Montreal, Quebec, Canada
6
Laboratoire de Recherche en Imagerie et Orthopédie (LIO), ETS/CRCHUM, Montreal, Quebec, Canada
Keywords:
Knee Kinematic, Biomechanical Data, Feature Selection, Complexity Measures, Arthroplasty.
Abstract:
The purpose of this study is to investigate a method to select a set of knee kinematic data features
to characterize surgical vs nonsurgical arthroplasty subjects. The kinematic features are generated from
3D knee kinematic data patterns, namely, rotations of flexion-extension, abduction-adduction, and tibial
internal-external recorded during a walking task on a dedicated treadmill. The discrimination features are
selected using three types of statistical complexity measures: the Fisher discriminant ratio, volume of overlap
region, and feature efficiency. The interclass distance measurements which the features thus selected induce
demonstrate their effectiveness to characterize surgical and nonsurgical subjects for arthroplasty.
1 INTRODUCTION
Knee kinematic data during locomotion, which
can be easily acquired in clinical settings (Lustig
et al., 2012), provide useful information about
knee function and can serve the development of
objective methods of computer aided diagnosis to
assist surgical decisions and treatment.
Preoperative knee conditions, prosthesis design,
and surgical techniques all influence knee kinematics
following an arthroplasty. However, kinematic
studies have primarily focused on postoperative
knee kinematics (Seon et al., 2011). Preoperative
investigations have been scarce (Casino et al., 2009;
Casino et al., 2008; Mihalko et al., 2007) in great part
due to knee kinematic data complexity (Mezghani
et al., 2008), which are high-dimensional vectors and
of high variability. The studies in (Casino et al.,
2009; Casino et al., 2008; Mihalko et al., 2007)
investigated knee kinematic data of osteoarthritis
patients and (Mezghani et al., 2016) specifically
addressed surgical vs nonsurgical discrimination of
candidates for arthroplasty.
High kinematic data variability and
dimensionality are illustrated in Figure 1, which
shows the graph of a sample of one hundred
fifty-three (153) participants curves and their
average curves. The intra-class high variability and
inter-class proximity, which are evident in the figure,
make discriminating feature extraction notoriously
difficult. In spite of the importance of this problem,
there has been no investigation of feature extraction
in terms of objective metrics. By reducing the
dimension of the data representation vector, feature
selection affords a means of escape from the curse of
dimensionality while maintaining a good description
of the data. The feature selection methods are usually
evaluated using the classification rate of a chosen
classifier. However, these methods are classifier
dependent. Our goal is to investigate measures for
feature selection independent of classifiers design.
In this study, we propose a knee kinematics
feature selection method based on statistical
complexity measures, namely, the Fisher
discriminant ratio, volume of overlap region,
and feature efficiency. The purpose is to select the
most discriminant features from a feature set of
interest in a classification task.
176
Arous, M., Dunbar, M., Arfaoui, S., Mitiche, A., Ouakrim, Y., Fuentes, A., Richardson, G. and Mezghani, N.
Knee Kinematics Feature Selection for Surgical and Nonsurgical Arthroplasty Candidate Characterization.
DOI: 10.5220/0006586601760181
In Proceedings of the 11th International Joint Conference on Biomedical Engineering Systems and Technologies (BIOSTEC 2018) - Volume 4: BIOSIGNALS, pages 176-181
ISBN: 978-989-758-279-0
Copyright © 2018 by SCITEPRESS Science and Technology Publications, Lda. All rights reserved
Figure 1: (a) Kinematic gait signals (of the database) during a gait cycle: Abduction-adduction (line1), Flexion-extension
(line 2), and Internal-external rotation (line3). The signals were interpolated and resampled from 1% to 100% (100 points)
of the gait cycle. Each red curve represents a surgical participant (S) and each blue one represent a Non-Surgical (Non-S)
participant (b) The mean and standard deviation of the kinematic gait signals. The blue and red lines represent respectively
the S and Non-S group average patterns.
2 METHODS
2.1 Database
The database was provided by the Division of
Orthopedic Surgery in Halifax QEII Health Sciences
Center (Nova Scotia, Canada). The one hundred
fifty-three (153) participants enrolled for the research
had a diagnosis of knee osteoarthritis ranging from
moderate to severe condition and were all scheduled
for an arthroplasty consult. All participants also
went through an orthopedic physical assessment
by one of two experienced orthopedic surgeon
and were consequently assigned to surgical (S) or
nonsurgical (Non-S) groups. Table 1 summarizes
the principal demographic characteristics of the
participants. A t-test was performed to examine the
general participant characteristic differences between
the two groups. The statistical analysis was conducted
using SPSS 20.0 (Statistical Package for Social
Sciences). The P-value of 0.05 was set as level of
statistical significance.
All participants underwent physiotherapy
assessment and patients reported outcome
questionnaires. Three-dimensional (3D) knee
Table 1: Demographic characteristics of S and Non-S
groups (BMI design the mean body mass index).
Groupe S Groupe Non-S
N =80 N = 73
Age (year) 64, 7 ± 9, 3 64.2 ± 9.2
Height(m) 1.67 ± 0.1 1.69 ± 0.1
Weight (kg) 92.8 ± 23.7 90.9 ± 19.3
BMI (kg / m
2
) 33.13 ± 7.0 31.5 ± 6, 0
Proportion of
men / group
37% 50%
kinematics data, namely, rotation measurements
for flexion-extension, abduction-adduction, and
tibial internal-external, in the sagittal, frontal,
and transverse planes, respectively, were recorded
while each participant walked on a treadmill at a
self-selected, comfortable speed. A validated knee
marker attachment system, the KneeKG system
(Emovi Inc, Montreal, Canada) (Figure. 2), was
installed on the participant’s knee to record the 3D
kinematics data during gait trials of 45 sec on an
instrumented treadmill at a comfortable self-speed.
This motion capture device is composed of a
harness and a tibial plate fixed quasi rigidly onto
Knee Kinematics Feature Selection for Surgical and Nonsurgical Arthroplasty Candidate Characterization
177
the femoral condyles and tibial crest, and provides
accurate, repeatable, and reliable measurements
(Lustig et al., 2012). A number of representative
gait cycles, generally 15, were averaged to obtain
a means pattern per subject. This was followed by
interpolation and resampling from 1% to 100% of the
gait cycle, therefore giving 100 measurement points
for each participant (Figure. 1).
Figure 2: Knee kinematic acquisition system.
2.2 Kinematic Feature Extraction
Sixty-nine (69) biomechanical parameters were
extracted from the 3D kinematic signals. These were
chosen from the common variable in clinical
biomechanical studies of knee osteoarthritis
populations (Astephen et al., 2011; Bytyqi et al.,
2014; Mezghani et al., 2017), such as maxima,
minima, varus and valgus thrusts, angles at initial
contact, mean value and range of motion (ROM)
throughout gait cycles, and sub-phases (stance phase,
swing phase) as illustrated in Figure 3.
Figure 3: Gait cycle phases and sub-phases.
2.3 Kinematic Feature Selection using
Statistical Measures of Complexity
Statistical measures of complexity, which evaluates
class ambiguity, were used to afford an evaluation
of the discriminant power of the class representation
features, i.e., the features capacity to distinguish data
samples from distinct classes. For each individual
feature, the complexity measure examines the range
and spread of the values of instances of different
classes and verify the discriminant power of a single
feature.
Let D = {x
1
, x
2
, ....., x
n
} a data set containing
n elements, each belonging to one of two distinct
classes c
1
and c
2
. In our case, c1 corresponds to
the surgical group (S) and c
2
to nonsurgical group
(Non-S). Each element x is characterized by a feature
vector ( f
1
, f
2
, ... f
p
), where p is the dimension of the
feature space (p = 69 biomechanical parameters).
The overlap is evaluated according to the
following measures:
2.3.1 Fisher Discriminant Ratio (F1)
This measure computes the maximum discriminative
power of each feature. For a two-class data set, the
Fisher discriminant ratio F1(i) of a feature f
i
, (i =
1, ..., p), is defined as:
F1(i) =
(µ
i1
µ
i2
)
2
(σ
2
i1
+ σ
2
i2
)
, (1)
where µ
i1
, µ
i2
, σ
i1
, σ
i2
are the means and variances
of the two classes, respectively, according to the i
th
feature, (i = 1, 2, . . . , p).
A high value of the Fisher’s discriminant ratio
indicates that the feature enables to separate the data
set of different classes with partitions that are parallel
to an axis of the feature space.
2.3.2 Volume of Overlap Region (F2)
This measure estimates the amount of relative overlap
of the bounding regions of two classes (Lorena and
de Souto, 2015). For each feature f
i
, (i = 1, ..., p),
where p is the dimension of the feature space, the
Volume of overlap region (F2) is defined as:
F2(i) =
MinMax(i) MaxMin(i)
MaxMax(i) MinMin(i)
(2)
MinMax(i) = min(max( f
i
, c
1
), max( f
i
, c
2
))
MaxMin(i) = max(min( f
i
, c
1
), min( f
i
, c
2
))
MaxMax(i) = max(max( f
i
, c
1
), max( f
i
, c
2
))
MinMin(i) = min(min( f
i
, c
1
), min( f
i
, c
2
))
where f
i
is the i-th feature. c
1
and c
2
refer to
the two classes and max( f
i
, c
i
) and min( f
i
, c
i
) are,
respectively, the maximum and minimum values of
the feature f
i
for class c
i
. In other words, the volume
BIOSIGNALS 2018 - 11th International Conference on Bio-inspired Systems and Signal Processing
178
of overlap is evaluated using the ratio of the width of
the overlap interval MinMax(i) MaxMin(i) to the
width of the entire interval MaxMax(i) MinMin(i).
A low value of the volume of overlap region
means that the feature can discriminate the examples
of different classes.
2.3.3 Feature Efficiency (F3)
The feature efficiency measure is particularly relevant
when dealing with high-dimensional data. It
informs on how much each feature contributes to
the separation of the classes. The contribution is
called efficiency. For each feature, the ambiguous
(overlapping) regions are removed so that only
non-overlapping regions remain.
Let MinMax
i
= min(max( f
i
, c
1
), max( f
i
, c
2
)) and
MaxMin
i
= max(min( f
i
, c
1
), min( f
i
, c
2
)). For each
feature f
i
, the feature efficiency F3(i) is given by the
following ratio:
F3(i) =
| f
i
[MinMax
i
, MaxMin
i
]|
n
, (3)
where | | denotes the number of non-overlapping
elements and n is the total number of elements in both
classes.
2.3.4 Thresholds of Class Ambiguity Measures
To be used to select the discriminant feature, the class
ambiguity measures require, for each measure, the
estimation of a threshold to decide if a specific feature
is whether discriminant or not.
We investigated thresholds estimation using
the probability distribution of the class ambiguity
measures. For each measure, i.e., the Fisher
discriminant ratio F1(i), the volume of overlap region
F2(i) and the feature efficiency F3(i), a probability
distribution has been determined. The thresholds are
estimated using the 95th quantile of the probability
distribution.
2.4 Evaluation of the Selected Features
Several studies have addressed feature selection
evaluation. The methods of evaluation can be divided
in two major groups: individual feature evaluation
and feature subset evaluation. A subset evaluation is
relevant in our case. We evaluated the efficiency of
the selected feature subset using interclass distance.
This measure was compared to the interclass distance
using the original set of all features (consisting of
69 biomechanical features). A high value of the
interclass distance indicates that the features are
relevant.
3 RESULTS AND DISCUSSION
The class ambiguity measures of each feature taken
individually and the corresponding thresholds are
represented in Figure. 4. The thresholds are estimated
using the 95th quantile of the probability distribution
of each complexity measure as explained in the
Section 2.3.4.
Table 2: Selected features.
Selected features
f
12
: Minimum frontal plan angle during
mid-stance, where abduction is negative and
adduction is positive
f
18
: Maximum axial plane angle, where internal
rotation is negative and external rotation is
positive
f
21
: Maximum flexion angle during the loading
phase
f
26
: Mean adduction/adduction angle during the
stance phase
f
28
: Maximum flexion angle
f
29
: % of GC where the maximum angle of
flexion occurs
f
38
: Maximum frontal plan angle, where
abduction is negative and adduction is positive
f
46
: Frontal plane angle at 54 % of the GC
f
54
: Mean transverse plane rotation during the
swing phase
f
61
: Transverse plane rotation angle at the end of
the terminal swing
f
62
: ROM of the internal/external rotation
f
63
: Maximum flexion angle (absolute value)
during loading
Figure 4 (a) represents the discriminant ratio
F1(i) for each feature f
i
(i = 1, 2, ..., 69) computed
according to Eq. 1. The threshold was set to 0.08.
The selected feature set contains { f
21
, f
26
}. In Figure
4(b), we represented the ratio of the width of the
overlap interval F2(i) of each feature. The threshold
here was set to 0.57 and we were interested in low
values of F2(i). The only retained feature is { f
12
}.
Finally, in Figure 4(c), we represented the individual
feature efficiency which describes the ratio of the
number of samples that are not in the overlapping
region to the total number of samples. The threshold
was set to 0.38. The combination of the features
identified as a result of the complexity analysis
forms the following set of the selected features are:
{ f
18
, f
26
, f
28
, f
29
, f
38
, f
46
, f
54
, f
61
, f
62
, f
63
}. Table 2
Knee Kinematics Feature Selection for Surgical and Nonsurgical Arthroplasty Candidate Characterization
179
0
0.05
0.1
0.15
0.2
(a) Fisher discriniminant ratio F1
f
1
f
3
f
5
f
7
f
9
f
11
f
13
f
15
f
17
f
19
f
21
f
23
f
25
f
27
f
29
f
31
f
33
f
35
f
37
f
39
f
41
f
43
f
45
f
47
f
49
f
51
f
53
f
55
f
57
f
59
f
61
f
63
f
65
f
67
f
69
0
0.2
0.4
0.6
0.8
1
(b) Volume of overlap region F2
f
1
f
3
f
5
f
7
f
9
f
11
f
13
f
15
f
17
f
19
f
21
f
23
f
25
f
27
f
29
f
31
f
33
f
35
f
37
f
39
f
41
f
43
f
45
f
47
f
49
f
51
f
53
f
55
f
57
f
59
f
61
f
63
f
65
f
67
f
69
0
0.02
0.04
0.06
0.08
(b) Feature efficiency F3
f
1
f
3
f
5
f
7
f
9
f
11
f
13
f
15
f
17
f
19
f
21
f
23
f
25
f
27
f
29
f
31
f
33
f
35
f
37
f
39
f
41
f
43
f
45
f
47
f
49
f
51
f
53
f
55
f
57
f
59
f
61
f
63
f
65
f
67
f
69
Knee Kinematic feature
Figure 4: Measures of class ambiguity for each feature f
i
(i = 1, 2, ..., 69): (a) The Fisher discriminant Ratio F1(i); a high
value of F1(i) indicates that the feature is discriminant. (b) The ratio of the width of the overlap interval F2(i); a low value of
F2(i) measure means that the feature can discriminate the samples of different classes. (c) The individual feature efficiency
F3(i); a high value of F3(i) indicates a good efficiency. The horizontal dashed black lines correspond to the threshold values
and the retained features are in red.
summarizes the selected features and their clinical
meaning.
This result supports previous studies on
biomechanical data and their association with
knee pathologies. Indeed f
62
, which corresponds
to the ROM of the Internal-external rotation, has
been identified as a characteristic of improvement
following a total knee replacement surgery (Jones
et al., 2006). Also, f
26
, which is the mean of
abduction-adduction angle during the stance
phase, has been identified discriminant for knee
osteoarthritis severity assessment.
The efficiency of the subset of selected features
have been measured using the interclass distance
measure (Table 3). This measure is higher when
compared to interclass distance using the whole
feature data set (1832.2 and 987.8 respectively) which
show that the selected features discriminate better the
two classes.
The statistical analysis reveals no differences in
the general characteristics between the two groups
(as described in Table 1), which means that these
characteristics are not involved in the characterization
of surgical and nonsurgical arthroplasty candidates.
Table 3: Surgical and nonsurgical interclass distances.
Data set Inter class distance
Feature data set (69
biomechanical features)
987.8
Selected feature data set
(12 retained biomechanical
features)
1832.2
4 CONCLUSION
In this study, we developed a feature selection method
for 3D knee kinematic data using statistical measures
of class ambiguity. We investigated each feature
taken individually using the Fisher discriminant ratio,
volume of overlap region, feature efficiency. Within
the original 69 biomechanical features extracted
from the 3D kinematic signals, 12 features have
been selected that contain pertinent information
to characterize surgical vs nonsurgical arthroplasty
subjects. This set of discriminant features can also
help in future clinical studies to identify biomarkers
for knee surgical arthroplasty candidate treatment.
BIOSIGNALS 2018 - 11th International Conference on Bio-inspired Systems and Signal Processing
180
In a subsequent study, the selected features will
serve as input to build classification models to help
discriminate automatically surgical from nonsurgical
arthroplasty subjects.
ACKNOWLEDGEMENTS
This research was supported in part by the Natural
Sciences and Engineering Research Council Grant
(RGPIN-2015-03853) and the Canada Research Chair
on Biomedical Data Mining (950-231214). The
authors would like to thank Hilary Mac Donald and
Tim Parlee for the kinematic data collection.
REFERENCES
Astephen, J., Deluzio, K., Dunbar, M., Caldwell, G., and
Hubley-Kozey, C. (2011). The association between
knee joint biomechanics and neuromuscular control
and moderate knee osteoarthritis radiographic
and pain severity. Osteoarthritis Cartilage,
26(3):186–193.
Bytyqi, D., Shabani, B., Lustig, S., Cheze, L.,
Karahoda Gjurgjeala, N., and Neyret, P. (2014). Gait
knee kinematic alterations in medial osteoarthritis:
three dimensional assessment. Int. Orthop.,
38(6):1191–1198.
Casino, D., Martelli, S., and Zaffagnini, S. (2009). Knee
stability before and after total and unicondylar knee
replacement: In vivo kinematic evaluation utilizing
navigation. Journal of Orthopaedic Research,
27(2):202–207.
Casino, D., Zaffagnini, S., and Martelli, S. (2008).
Intraoperative evaluation of total knee replacement:
kinematic assessment with a navigation system.
Knee Surgery, Sports Traumatology, Arthroscopy,
17(4):369–373.
Jones, L., Beynon, M., Holt, C., and Roy, S. (2006). An
application of the dempster-shafer theory of evidence
to the classification of knee function and detection of
improvement due to total knee replacement surgery. J
Biomechanics, 39(13):2512–2520.
Lorena, A. C. and de Souto, M. C. P. (2015). On
Measuring the Complexity of Classification Problems,
pages 158–167. Springer International Publishing,
Cham.
Lustig, S., Magnussen, R., Cheze, L., and Neyret, P. (2012).
The kneekg system: a review of the literature. Knee
Surg. Sport. Traumatol. Arthrosc., 20(4):633–638.
Mezghani, N., Husse, S., Boivin, K., Turcot, K., Aissaoui,
R., Hagemeister, N., and de Guise, J. (2008).
Identification of knee frontal plane kinematic patterns
in normal gait by principal component analysis.
Journal of Mechanics in Medicine and Biology,
13(3):r1230–1232.
Mezghani, N., Ouakrim, Y., Fuentes, A., Mitiche, A.,
Whynot, S., Richardson, G., and M, D. (2016).
Biomechanical signal classification of surgical and
non-surgical candidates for knee arthroplasty. The
IEEE International Symposium on signal, Image,
Video and Communication (ISIVC).
Mezghani, N., Ouakrim, Y., Fuentes, A., Mitiche, A.,
Whynot, S., Richardson, G., and M, D. (2017).
Mechanical biomarkers of medial compartment knee
osteoarthritis diagnosis and severity grading:
Discovery phase. Journal of biomechanics,
52(1):106–112.
Mihalko, W., Ali, M., Phillips, M., Bayers-Thering, M.,
and KA, K. (2007). Passive knee kinematics before
and after total knee arthroplasty. The Journal of
Arthroplasty, 23(1):57–60.
Seon, J., Park, J., Jeong, M., Jung, W., Park, K., Yoon, T.,
and EK, S. (2011). Correlation between preoperative
and postoperative knee kinematics in total knee
arthroplasty using cruciate retaining designs. Int
Orthopedic, 35(4):515–520.
Knee Kinematics Feature Selection for Surgical and Nonsurgical Arthroplasty Candidate Characterization
181