Determination of Directional Inﬂuences of Kinematic Data in the Stance

Period During Running

Giovana Yuko Nakashima

1,4

, Theresa Helissa Nakagawa

, Ana Fl´avia dos Santos

F´abio Viadanna Serr˜ao

and Carlos Dias Maciel

Federal Institute of Education, Science and Technology of S˜ao Paulo, Campus Salto, Rua Rio Branco,

1780, Salto, SP, 13321-271, Brazil

Uninorte Laureate International Universities, Avenida Joaquim Nabuco, 1232, Manaus, AM, 69020-031, Brazil

Laboratory of Assessment and Intervation in Orthopaedics and Traumatology (LAIOT), Physiotherapy Department,

Federal University of S˜ao Carlos, Rodovia Washington Luiz, km 235, S˜ao Carlos, SP, 13565-905, Brazil

Laboratory of Signal Processing (LPS), Electrical and Computer Engineering Department, University of S˜ao Paulo,

Avenida Trabalhador S˜ao-carlense, 400, S˜ao Carlos, SP, 13566-590, Brazil

Keywords:

Partial Directed Coherence, Kinematics, Knee.

Abstract:

The study of the interactions among elements of a system is decisive to understanding their behavior patterns.

The knowledge of the details of human motion allows physiotherapists to propose prevention and rehabilitation

programs, as well as to identify movements that could lead to an injury. This work examines Partial Directed

Coherence measures to determine the direction of the inﬂuences, throughout the stance phase only, among

kinematic joints data acquired during the running activity. Five channels of the ankle, knee, hip, pelvis and

trunk kinematic data were processed in each of the three anatomical planes, sagittal, frontal and transverse.

These analysis suggested that the ankle joint receives a intense proximal to distal inﬂuence, whereas the knee,

hip, pelvis and trunk joints presents a predominance of distal to proximal interaction.

1 INTRODUCTION

In many biomedical systems, the knowledge of the in-

teractions among the structural elements plays a key

role to understand their connectivity architecture. In

this way, the direction of the information ﬂow is an as-

pect of great interest, since it could improve the inter-

pretation of the dynamics present (Blinowska, 2011).

Physical therapists deal with human motion and

are especially concerned with movement disorders

that could lead to injuries. This study focused on

running, a commom physical activity which involves

more than 38 million Americans (NSGA, 2011). This

sport presents potential risk to injury that comes with

the exponential growth. It is estimated an incidence

higher than 70% of musculoskeletal injury each year

among runners (Ferber et al., 2009). The knee is the

most affected site (Ferber et al., 2009).

The interactions of the joint kinematic during run-

ning are complex and not yet fully understood (Pandy

and Andriacchi, 2010). There is a hypothesis that

proximal segments (i.e, trunk, pelvis and hip) could

inﬂuence the distal’s ones (i.e knee) and vice-versa

(Powers, 2003); (Hewett and Myer, 2011). A better

comprehension of the interjoint movement coordina-

tion could improve knee injury treatment and preven-

tion programs.

In this study, multi-joints recordings of 3D joint

kinematics generated a huge amount of biomedical

data of thirty subjects. Although (Nakashima et al.,

2014) analyzed kinematic data with Partial Directed

Coherence (PDC) covering all the running trial, in-

cluding stance and swing phases, most running in-

juries occurs during the ground contact when the lo-

comotor system must dissipate the ground reaction

force (Cavanagh and Lafortune, 1980). The impact

peak during each step is equivalent to 2-3 times of the

body weight (Lieberman et al., 2010). So our aim was

to examine directional inﬂuences of the 3D joint kine-

matics data of the trunk, pelvis, hip, knee and ankle

acquired during a usual running, with the PDC ap-

proach considering only the stance phase events, that

is, the target of the analysis are the parts of the signal

when ground contact occurred.

PDC is a frequency domain approach of the

Granger-Geweke Causality (GGC) method (Jo-

Nakashima G., Nakagawa T., dos Santos A., SerrÃ

co F. and Maciel C.

Determination of Directional Inﬂuences of Kinematic Data in the Stance Period During Running.

DOI: 10.5220/0006167701930197

In Proceedings of the 10th International Joint Conference on Biomedical Engineering Systems and Technologies (BIOSTEC 2017), pages 193-197

ISBN: 978-989-758-212-7

193

vanovi´c et al., 2013). PDC determines the direct con-

nection strength between two distinct signals (Fasoula

et al., 2013). According to (Baccala et al., 2016),

PDC proposes a direct path of inﬂuence, indicating

the structures that are adjacents. Many of the PDC

studies is in neural structures, where the aim is to de-

termine the brain connectivity patterns (G¨urkan et al.,

2014); (Jovanovi´c et al., 2013); (Varotto et al., 2012).

This work follows this description. The Theory

Section introduces the framework of pairwise PDC

approach. The Material and Methods Section de-

scribes the participants of the study, 3D joint kine-

matic data acquisition process details and their pro-

cessing procedures. In Result Section, three distinct

graphs present the PDC values computed, one for

each of the three anatomical planes: sagittal, frontal

and transverse. The Discussion and Conclusion Sec-

tion compares the results with interpretations of the

literature.

2 THEORY

Granger Causality (GC) method applies the linear re-

gression model in a pairwise analysis of two station-

ary stochastic processes. The main idea of GC is that

if the prediction of a time series x

could be improved

by including the past terms of a time series x

, then

is said to cause x

(Blinowska, 2011). Speciﬁcally,

is estimated using only previous values of the se-

ries x

, and then x

is estimated including previous

values of the series x

. In both estimations, two ma-

trices are computed: the autoregressive (AR) coefﬁ-

cients matrix and the covariance matrix of the noise

terms. Thus, comparing the variances of the AR pre-

diction error of x

before and after including the series

, the improvement of the prediction is determined

by the decrease of the variance with past values of x

(Blinowska, 2011).

Multivariate formulation and spectral form of GC

were stated by GGC (Jovanovi´c et al., 2013), where

the multivariate autoregressive(MVAR) model is esti-

mated and the causal inﬂuence between two channels

is computed from the spectral density matrix (Fasoula

et al., 2013).

As an adaptation of GGC, Directed TransferFunc-

tion (DTF) is a causality measure in frequency do-

main (Jovanovi´c et al., 2013) that describes direct and

cascade inﬂuences (Blinowska, 2011), that is, DTF

describes the inﬂuence direction including indirect

propagation, when the interaction ﬂows through inter-

mediate elements (Baccala et al., 2016). Thus, if there

is a propagation from 1 to 2 and from 2 to 3, DTF

presents inﬂuence from 1 to 3 (Blinowska, 2011).

PDC was introduced by (Baccal´a and Sameshima,

2001) as a normalized measure (Jovanovi´c et al.,

2013) and sets a pairwise analysis of directional inter-

actions in an n-dimensional random process X(t) =

(t), x

(t), ..., x

(t)]

(T denotes matrix transposi-

tion). Assume that the Eq. 1 is the MVAR represen-

tation of the process X(t), where p is the model or-

der, A(r) are the MVAR estimative coefﬁcient matri-

ces and E(t) = [e

(t), e

(t), ..., e

(t)]

is a zero mean

white noise vector.

X(t) =

∑

r=1

A(r)X(t − r) + E(t) (1)

Each A(r) matrix is formed by a

(r) elements that

represent the lagged effect of the j − th on the i− th

series.

Applying Fourier transform in Eq. 1,

′

( f)X( f) = E( f) (2)

where A

′

( f) (Eq. 4) is calculated from A( f), the fre-

quency domain representation of A(r), given by

A( f) =

∑

r=1

A(r)e

−ir2π f

(3)

′

( f) = I − A( f) (4)

(Baccal´a and Sameshima, 2001) denotes PDC, di-

rect inﬂuence from x

to x

at frequency f as in the

Eq. 5, where a

′

( f) is the k

column of A

′

( f). In the

Eq. 4, I is the identity matrix and in Eq. 5, H denotes

Hermitian matrix.

( f) =

′

( f)

′

( f)a

′

( f)

(5)

3 MATERIAL AND METHODS

3.1 Subjects

In this study, thirty recreational runners participated

(mean (SD); age 27.67 (5.43) years, mass 72.05

(13.61) kg, height 1.73 (0.09) m, average running dis-

tance 35.70 (18.25) km/week and running experience

4.13 (4.02) years). They were familiar with treadmill

running and ran a minimum of 20km/week at least 3

months prior to study enrollment. The presence of

bone, joint, and ligament injury for at least 3 months

prior the assessment, lower limb surgery, pain in the

ankle, knee, hip or trunk while running or wearing or-

thotics that could interfere with their running pattern

BIOSIGNALS 2017 - 10th International Conference on Bio-inspired Systems and Signal Processing

194

were the exclusion criteria. The subjects were evalu-

ated by a licensed physical therapist to screen for the

inclusion and exclusion criteria. The testing protocol

was approved by the Federal University of S˜ao Car-

los Ethics Committee for Human Investigations, and

the subjects signed a written informed consent form

to participate in this study.

3.2 Data Acquisition Procedure

The session started with a 5-minute warm-up on a

treadmill (model LX 160 GIII, Movement, Manaus,

Brazil) at 1.38 m/s. Next, the subjects were instructed

to start running at a comfortable speed, determined by

the volunteer and adjusted by the assessor for 2 min-

utes. A neutral running shoe (Asics Gel-Equation 5,

ASICS, Kobe, Japan) wasprovidedfor all the runners.

The kinematic data of the dominant lower limb

and trunk were recorded at 240 Hz during running

with a six-camera Qualisys motion analysis system

(Qualisys Inc., Gothenburg, Sweden). Twenty re-

ﬂective markers located on anatomical landmarks and

ﬁve cluster tracking markers were placed on each sub-

ject. Each running trial was performed for 1 minute

and 30-s and samplings of data were collected without

informing subjects about the exact moment of sam-

pling or the variables studied.

The Cardan angles were calculated using the joint

coordinate system deﬁnitions recommended by the

International Society of Biomechanics (Wu et al.,

2002) relative to the static standing trial using the Vi-

sual 3D software (C-Motion Inc, Rockville, MD). The

kinematic data were ﬁltered with the Visual 3D soft-

ware using a fourth order, zero lag, low-pass Butter-

worth ﬁlter at 12 Hz. For each plane (X - sagittal, Y -

frontal and Z - transverse), ﬁve joints were collected:

ankle, knee, hip, pelvis and trunk.

3.3 Data Processing

As the ﬁrst step, data from all the 30 volunteers were

processed in order to separate their stance phases,

and, from these periods, PDC values were computed.

3.3.1 Stance Phases

Stance phases of the kinematic data were deﬁned

based on heel strike and toe-off. Heel strike was iden-

tiﬁed as the velocity inversion (positive to negative)

of heel marker in frontal plane (Y) (Zeni et al., 2008).

Toe-off was determined by the second peak knee ex-

tension (sagittal plane) (Fellin et al., 2010). Thus, for

each stance phase, there were two points identiﬁed,

one for the beginning (heel strike) and another for the

ending (toe-off) of the period.

3.3.2 PDC

The kinematic data were processed by an app de-

veloped in Python 2.7.4 (Python Software Founda-

tion, USA), running on Intel Core i5 (Intel Corpora-

tion, USA) CPU at 1.70GHz, 4 GB RAM and Ubuntu

13.04 operating system (Canonical Ltd., UK). As a

preprocessing step, each data channel was normalized

by its root mean square (RMS).

The estimation of the AR coefﬁcients matrix used

the periods of stance already established as different

observations of the system. Thus, from the heel strike

point until the toe-offpoint of one stance event, a time

window was set. The values of the 15 channels in

that time window was included to determine the best

Bayesian Information Criterion (BIC) value and then

the AR model estimative. A visual selection by reg-

ularity in data was done to analyze the stationarity of

the signals.

The function developed to identifying the best

BIC value took into account values from 1 to the min-

imum number of points of the stance phases of the

individual running trial. Therefore the number of or-

der tests was diversiﬁed among the subjects, because

each one had different points number.

PDC values were computed taking the channels in

pairs. The highest one was used to represent the inter-

action between two channels of a subject. The inﬂu-

ence of the thirty subjects was evaluated by the mean

value of the group. Distal to proximal and proximal to

distal inﬂuences were analyzed by anatomical plane

between each pair of joints. To determine whether the

inﬂuence was distal to proximal or proximal to distal,

the T-Test was applied with 5% of signiﬁcance under

the null hypothesis that the means of that two types of

inﬂuences were equal.

At each relevant step, intermediate ﬁles were

saved, such as the stance phases, the orders analyzed

to determinate the best BIC value, the PDC values

themselves, including the resumed ones and the di-

rected graphs.

4 RESULTS

The process of dividing the entire running trial in

stance phases generated 35 periods and 73 points per

period, on average, both for the entire group. There-

fore, an average of more than 30 observations were

used to compute the PDC values.

The best BIC order accepted was between 1 and

5, depending on the number of points of the stance

phases of the subject, since the procedure tested val-

ues from 1 to the minimum of that number of points.

Determination of Directional Inﬂuences of Kinematic Data in the Stance Period During Running

195

In average, the routine for determining the best BIC

order computed the AR estimative up to order 77, the

mean of the minimum number of points.

The resumed PDC values were presented in three

directed graphs, for each anatomical plane. Thus, in

one graph, there are ﬁve nodes, representing the kine-

matic joints in that plane. The interactions are be-

ing illustrated by edges where thicker stubs are the

arrows. Moreover, the thickness of the edges denotes

the strength of the inﬂuence. Therefore, in Fig. 1,

the edge between nodes ”Ankle” and ”Trunk” shows

an inﬂuence from ”Trunk” to ”Ankle”, and its PDC

value is higher than between ”Hip” to ”Pelvis”. There

is only one direction between two nodes, the higher

value chosen from the distal to proximal or proximal

to distal inﬂuences mean values, when there was a sta-

tistical difference indicated by the T-Test.

In the sagittal plane, ankle received the strongest

inﬂuences. Also, Fig. 1 shows that pelvis and trunk

are highly inﬂuenced too. Instead, knee and hip are

sources of inﬂuences.

Figure 1: Directional inﬂuences of the 3D kinematic data

during running, in sagittal plane. Nodes are the kinematic

joints (ankle, knee, hip, pelvis and trunk). Each edge rep-

resents the mean value from the thirty subjects computed

from the individual maximum PDC, and its thickness is the

strength of the inﬂuence. Thicker stubs represent arrows.

In frontal plane, ankle remains as the most inﬂu-

enced channel. As Fig. 2 presents, pelvis still receives

a substantial inﬂuence from hip and less strong inter-

actions from knee and trunk. Hip stays as a source of

inﬂuences.

Transverse plane (Fig. 3) presents ankle and trunk

as the receivers with the highest PDC. Pelvis is des-

tination of intermediate inﬂuence, and hip persists as

an essential source of interactions.

5 DISCUSSION AND

CONCLUSION

The aim of this work was the analysis of the direc-

tion of inﬂuence of the kinematic data, considering

Figure 2: Mean values computed from individual maximum

PDC, in frontal plane, during running. As in Fig. 1, nodes

are the kinematic joints of ankle, knee, hip, pelvis and trunk.

Thicker stubs represent arrows.

Figure 3: Mean values computed from individual maximum

PDC, during running, in transverse plane. Also, nodes are

the kinematic joints of ankle, knee, hip, pelvis and trunk.

Thicker stubs represent arrows.

only the stance phase, during running, by the PDC

approach.

To the best of the authors knowledge, no study as-

sessed the direction of interaction ﬂow of 3D kine-

matics of the ankle, knee, hip, pelvis and trunk cov-

ering stance phases during running. In (Nakashima

et al., 2014), the kinematic channels of one subject

were analyzed during the entire running cycle, with-

out any stance phase separation.

In fact, the hypothesis that there was a marked

proximal to distal inﬂuence to ankle motion indicated

in (Nakashima et al., 2014) was conﬁrmed in this

study with a larger sample size, even analyzing specif-

ically the stance phase. Our data is also supported by

(Mackinnon and Winter, 1993) that hypothesized that

the trunk and hip motion could inﬂuence the ankle

motion during walking.

Interestingly, the hip inﬂuenced the most proxi-

mal (pelvis and trunk) and distal joints (ankle and

knee), supporting the importance of the core stabil-

ity to control de movements of the extremities (Peters

and Tyson, 2013); (Noehren et al., 2013). The trunk

joint was especially inﬂuenced in the sagittal and the

transverse planes. The pelvis joint received impor-

tant inﬂuences in sagittal and frontal planes. In frontal

plane, (Mackinnon and Winter, 1993) indicated an in-

ﬂuence from the hip and (Powers, 2003) suggested an

effect from the knee.

BIOSIGNALS 2017 - 10th International Conference on Bio-inspired Systems and Signal Processing

196

The next step is to analyze results from general-

ized PDC (gPDC), a variation of PDC that deal with

time series with different variances (Taxidis et al.,

2010).

These analyses can expose the directional inﬂu-

ence patterns that may help physiotherapists to dis-

tinguish normal movements from altered ones during

running and to propose treatment running techniques,

prevention and rehabilitation programs.

ACKNOWLEDGEMENTS

This work was supported by CNPq project

475064/2013-5.

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