Identification of Pronation-supination Patterns on Runners

An Aplication of Functional Principal Component Analysis

E. Medina

, H. De Rosario

, J. Olaso

, A. Ballester

, J. Navarro

and A. Page

2,3

Instituto de Biomecánica de Valencia, Valencia, Spain

Departmento de física Aplicada,Universidad de Politécnica Valencia, Valencia, Spain

Grupo de Tecnología Sanitaria del IBV

CIBER de Bioingeniería, Biomateriales y Nanomedicina (CIBER-BBN), Zaragoza, Spain

Keywords: Running, Pronator, Functional Data Analysis, Functional Principal Component Analysis.

Abstract: The correct classification of runners according to their gait patterns is a relevant issue for the design of

sports footwear. Specifically, the classification of runners as neutral, pronators, and supinators is a problem

that is not yet fully solved, and requires expert observation, since current models based on the automatic

processing of kinematic measures are very limited. This work proposes a method based on Functional Data

Analysis (FDA) for automatically describing the morphology of the curves that represent ankle movement

patterns. By Functional Analysis of Principal Components, the information contained in each data stream is

reduced to a small set of variables, that allows an efficient classification of subjects.

1 INTRODUCTION

In recent years, there has been an increment in the

practice of running. In spite of the evident

advantages of sports practice, running has some

health risks, as any other physical activity. One of

the risk factors is the inadequacy of footwear to the

runner’s characteristics. Specifically, the excess of

pronation or supination has been described as one of

the most frequent causes of injury in urban races

(Hintermann and Nigg, 1998; Nester et al, 2003;

Branthwaite et al., 2004).

Classifying a runner as normal, pronator, or

supinator , currently requires the expert judgment of

a professional, and it is not easy to do automatically.

Most specialists use qualitative methods based on

observing the orientation of body parts during the

support stance (Kapandji, 1987; Stell and Buckley,

1998). Many research studies use video-

photogrammetry in order to measure pronation and

supination as the maximal inversion-eversion angle

during the support phase (Perry and Lafortune,

1995; McClay, 1998).

However, the attempts to develop automatic

systems for such a classification have not led to

good results. First, inversion-eversion measures

show a relevant dispersion, and it is difficult to

establish clear limits (Stacoff et al., 2000). Besides,

multivariate classification requires using many

variables, and such systems usually have robustness

issues (Stefanyshyn et al., 2003). Moreover,

defining the variables that characterize the gesture is

not a trivial task, since it is highly dependent on the

shape of the motion curves, which do not always

show easily identifiable patterns. Finally, the

parameterization of the curves implies a loss of

information, since any limited set of parameters

cannot convey the whole continuous information of

a function recorded over time.

One possibility to overcome those limitations is

Functional Data Analysis (FDA). Instead of

extracting scalar parameters from a curve (such as

maxima, minima, phase durations, etc.), this

statistical technique works with time functions that

consider each curve as a single datum (Ramsay and

Silverman, 2005). FDA has been used to generalize

many classic statistical techniques, such as principal

component analysis (FPCA) (Ramsay and Dalzell,

1991). FPCA allows describing the variability

associated to a set of curves, in order to reduce

continuous information into a small set of

independent variables, while maintaining all the

information of original curves (Epifanio et al.,

2008).

The goal of this study was to define a procedure

for classifying runners in three groups: neutral,

294

Medina E., de Rosario H., Olaso J., Ballester A., Navarro J. and Page A..

Identiﬁcation of Pronation-supination Patterns on Runners - An Aplication of Functional Principal Component Analysis.

DOI: 10.5220/0004215102940297

In Proceedings of the International Conference on Bio-inspired Systems and Signal Processing (BIOSIGNALS-2013), pages 294-297

ISBN: 978-989-8565-36-5

 2013 SCITEPRESS (Science and Technology Publications, Lda.)

pronators and supinators by using video-

photogrammetry three-dimensional records of

continuous motion. The method uses Functional

Principal Component Analysis (FPCA) to obtain a

reduced set of principal factors as data, which are

used for characterizing the subject groups and for

defining a classification model of individuals.

2 METHODS

2.1 Sample of Study

The study sample consisted on 14 assiduous male

runners aged from 21 to 50. The runners were

selected from the competitors of the 32nd Valencia

marathon, and a Sports Society in Valencia called

‘Correcaminos’ (Road Runner), specialized in

athletics and trekking. These were all heel strikers,

and did not suffer any current injury.

2.2 Clinical Assessment

A footcare specialist performed a clinical evaluation

of the users’ lower limb, carrying out an anamnesis,

as well as a static assessment of the characteristics

and morphology of their legs, including ankles and

feet, using exploration techniques and a podoscope

for recording the shape of the foot’s plant. This

information was used to classify the runners into

three groups: normal, pronator and supinator

runners.

2.3 Biomechanical Analysis

Each runner performed four trials with two footwear

models, so that there were 112 observations in total.

During the study, subjects were asked to run at a

fixed and controlled speed of 5 minutes/km, that is,

12 km/h. In addition, the testing order of the

footwear models was randomized, so learning

effects were eliminated.

Motion of lower limb and footwear were

recorded by using videophotogrammetry

(Kinescan/IBV, Page et al 2009). A set of reflective

markers were placed at anatomical places according

to the protocol described in (Wu et al., 2002). The

gestures were recorded at 250 fps. The movement of

markers was analyzed to measure flexion-extension,

axial rotation, and inversion-eversion angles, using

the algorithm of kinematical analysis described in

Page et al. (2009). Three curves were taken for each

record, corresponding to the time functions of those

angles.

2.4 Data Processing and Statistical

Analysis

The support phase of each record was extracted by

trimming the original signal. The data streams were

smoothed by a base of B-splines, as described in

Ramsay et al. (2005), and time scales were linearly

adjusted in order to express the evolution of the

movement as a percentage of the support time.

FPCA was applied separately to the three angles

(flexion, rotation and inversion-eversion) using the

whole set of 112 observations for each angle. This

technique defines a base of independent functions

that can be combined some way to explain all the

observed variability. Thus, for the observed i-th

function f

(t),

(t) = F(t) + a

(t) + a

(t) +...

...a

(t)

(1)

where F(t) is the functional average of f

(t) for all

observations, PC

(t) are the functional principal

components, and a

are the scores of the i-th

observation for component PC

(t). The full

calculation procedure is described by Epifanio et al,

(2008).

These data were used to define a classification

model by linear discriminant analysis. The

independent variables were the a

scores, whereas

the model was trained by the classification in three

levels (neutral, pronator, or supinator) of the

participants, according to the opinion of an expert.

All calculations were performed in MATLAB.

Figure 1: Movement patterns for each group.

IdentificationofPronation-supinationPatternsonRunners-AnAplicationofFunctionalPrincipalComponentAnalysis

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Figure 2: Results of FPCA for the eversion angle. Each graphics represents the functional mean (solid black line) and the

mean plus or minus the sd(a

)  PC

(t).

3 RESULTS AND DISCUSSION

Figure 1 show the averages and standard deviations

of the three angles measured for each group. As can

be seen in the graphs, there are qualitative

differences between groups, although it is not easy

to quantify them, since each group has a different

number of local maxima and minima.

Figure 2 shows the results of the FPCA for the

eversion angle (EVE). This analysis was also

applied to the other angles, rotation (ROT) and

flexion (FE) but only the case of eversion is shown

because it is the most relevant one for the attempted

classification. Each plot represents the functional

mean (solid black line) and the mean plus or minus

the sd(a

)  PC

(t). This representation allows

assigning an intuitive meaning to each component.

Thus, PC1-EVE is an “offset” factor, related to

the general position of the whole curve in the Y-

axis. PC2-EVE is related to the range of the first

support phase, and the moment where maximal

eversion is seen. PC3-EVE indicates the differences

in the signal shape, so that high scores are associated

to lower ranges and two local minima, whereas

negative scores are related to broader ranges and just

one minimum. Finally, PC4-EVE is mainly related

to the final value of eversion before taking off.

The first four principal components explained

97.3% of the observed variance. Likewise, 4 factors

explained 97.5% of variance in flexion-extension

angles, and further 4 factors explained 96.2% of

axial rotation variance. Thus, FPCA allows

representing the whole information contained in the

curves with just 4 variables. This is an important

improvement with respect to classical methods,

which require identifying specific landmarks and use

many variables (Stacoff et al, 2000; Cheung and Ng,

2007)

Table 1 shows the coefficients of the two

discriminant functions (LD1, LD2) that were

obtained in the discriminant analysis, using PCj. as

independent variables. Figure 3 shows a scatter plot

of these functions for the observed values.

Table 1: Classification results.

1FE

3EVE

2ROT

2FE

1EVE

3FE

4ROT

LD1 0.61 0.60 -0.37 -0.41 0.24 0.10 -0.12

LD2 -0.13 0.013 -0.48 0.09 0.07 -0.53 0.61

As can be seen in Figure 3, LD1 clearly separates

between pronators (high values) from the rest of

subjects; and this function specially depends on the

first and third components of eversion, (PC1-EVE,

PC3-EVE) the first component of flexion-extension

(PC1-FE), and the second component of axial

rotation (

PC2-ROT) (see Table 1).

The distinction between supinators and neutrals

is less clear, and it depends on a combination of LD1

and LD2. This function is associated to the fourth

and second component of axial rotation angle, and to

the third component of flexion-extension.

Figure 3: Scatterplot of observations for discriminant

function coefficients.

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Finally, Table 2 shows the results of the

classification obtained by a “leave-one-out” cross-

validation. The classification is fairly good for

pronators, who are clearly discriminated from the

rest, but not that good for the supinators.

These results show that it is possible to classify

runners from kinematical variables by means of

FDA, in contrast with the lack of correspondence

between clinical and biomechanical criteria that has

been reported in previous works (Stefanyshyn,

2003).

Table 2: Classification results.

Prediction

Group P N S Success

P (24) 21 2 1 88%

N (64) 1 57 6 89%

S (24) 0 9 15 63%

4 CONCLUSIONS

Using functional data is advantageous for the

statistical treatment of time functions. FPCA in

particular allows reducing the information of a

family of curves to a small set of scalar variables,

automatically and without loss of the original

information that is contained in the raw signals.

This technique has been applied to the

classification of runners as neutral, pronators, or

supinators. The scores of the principal components

allowed to distinguish clearly between pronators and

the result of population, whereas the separation

between neutrals and supinators will require further

data processing, like analyzing the movement of the

distal part of the foot.

This technique has clear advantages for the

extraction of scalar variables form curve

characteristics: it does not require a pre-processing

of the function, and it allows using curves of

different morphologies, since that information is

already included in the principal components.

ACKNOWLEDGEMENTS

This research has been partially supported by

Seventh Framework Program of the EC (Project

Fit4U, NMP2-SE-2009-229336), and by the

Spanish Government with co-financiation of UE

FEDER funds (Grant DPI2009-138030-C02 01 and

02 and IMPIVA IMDEEA/2011/93 and

IMDEEA/2011/50).

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