The Velocity Effect on GEDEM Measurements

Nikos Papadakis

, George Tzagarakis

1,2

, N. Kampanis

, Savakis K.

P. Katonis

, K. Stergiopoulos

2,1

and D. G. Christakis

TEI of Crete,Biomechcanics Laboratory, School of Mechanical Engineering

TEI of Crete, Estavromenos, Greece

Department of Orthopaedics, University of Crete School of Medicine

University Hospital of Heraklion, Crete, Greece

Foundation of Research and Technology Hellas, Institute of Applied and Computational

Mathematics, PO Box 1385, 71110 Heraklion, Crete, Greece

Abstract. Gait Evaluation Differential Entropy Measure (GEDEM) [1] is a new

quantitative approach to evaluating the condition of a subject by monitoring the

acceleration [2][3]. The approach is capable to identify medical conditions [2,

3] and is also not dependent on age, weight, height or BMI. The initial studies

[4][5][6] required the walking on the ground along a straight line for 20-30 sec-

onds. Due to the promising results of the method, work is currently carried out

on a treadmill. The treadmill alleviates the constraint of long corridors, and ad-

ditionally offers better control on the gait velocity, minimum deviation in the

coronal plane, and less variability in the GEDEM values [7, 8]. This work in-

vestigates the relationship between the gait velocity and the GEDEM. The gait

velocity is a measurement parameter that influences the gait acceleration spec-

trum and therefore it is expected to influence GEDEM values.

1 Introduction

Human walking patterns are different. Each person’s ideal gait is a combination of

periodic movements determined by the body characteristics and the personal ability to

control the gait. In the case of neuromuscular and musculoskeletal pathologies or

injuries, these movements are not periodic and provide random variability. The walk-

ing pattern variability reflects the quality of the individual neuromuscular control and

increases in cases of neuromuscular and musculoskeletal pathologies or injuries [9]

Accelerometer methods have proved appropriate and reliable for gathering gait da-

ta. Human body motion acceleration measurements have been analyzed with the use

of entropy, as a measure of randomness, during the last two decades. Accelerometer

sensors are low cost, small, light and easy to be adopted into portable measuring

systems.

Shannon introduced the term entropy in order to quantify the information on a sig-

nal [10]. The concept of entropy was proposed as a general measure for both the

randomness and harmony by Christakis [11]. The entropy is correlated, by definition,

to the variability and the randomness while harmony is defined as the property of

Papadakis N., Tzagarakis G., Kampanis N., K. S., Katonis P., Stergiopoulos K. and Christakis D. (2009).

The Velocity Effect on GEDEM Measurements.

In Proceedings of the 1st International Workshop on Mobilizing Health Information to Support Healthcare-related Knowledge Work, pages 3-12

DOI: 10.5220/0001811900030012

 SciTePress

systems to match each other. Systems in harmony provide periodic, repeatable and

identical behaviour and thus they are easy to be recognized and serve for definite,

prescribed purposes, able to be matched to related systems. Christakis [12, 13] distin-

guished between harmony and the randomness proposing appropriate models for each

concept. The current physics and mathematics do not provide a coherent general

background for the study of harmony while the entropy stands as a basic concept to

measure the randomness of systems. Entropy reduction is considered as an indication

but not a measure of harmony. Randomness is a different concept than harmony.

Because of the relationship between entropy and harmony and the existence of rele-

vant mathematical formulations, entropy was introduced as a measure to evaluate the

quality of the human gait and, therefore, to detect injuries and pathologies.

In 1991, Pincus introduced the approximate entropy technique [14]. ApEn is a

technique that can be used to quantify the irregularity or variability of short finite

time series based on the statistics. ApEn is a measure of likelihood of predicting fu-

ture behaviour of a time series based on past values of the signal.

Arif et al. [15, 16, 9] and other authors proposed accelerometers and Approximate

Entropy for studying the effect of fatigue on walking stability and the walking stabil-

ity of young and elderly subjects. Kavanagh et al. [17] used Approximate Entropy for

studying the effect of ageing on the pattern and structure of head and trunk accelera-

tions during walking.

Gait Evaluation Differential Entropy Measure (GEDEM) [1] is a new quantitative

approach to evaluating the condition of a subject by monitoring the accelera-

tion[2][3]. The approach is capable to identify medical conditions [2, 3] and is also

not dependent on age, weight, height or BMI. A device records the gait acceleration.

Through spectral analysis is possible to estimate and quantify the level of uncertainty

in the movement and summarize it in the GEDEM index. The principle is that patho-

logical or mental conditions will increase the movement uncertainty and non perio-

dicity of the movement. The initial studies required the walking on the ground along a

straight line for 20-30 seconds. This work investigates the relationship between the

walking velocity and the GEDEM. The gait velocity is a measurement parameter that

influences the gait acceleration spectrum and therefore it is expected to influence

GEDEM values.

2 Measurement Protocol

2.1 General Overview of GEDEM Method

The GEDEM Method consists of the following steps. The measurement of the gait

acceleration signal is the first step. The measurement device consists of a tri-axial

accelerometer device connected appropriately to a data logger. The device is attached

on the subject’s body near the O5 (Figure 1). The human body Centre of Gravity

(COG) is considered to be near the O5 [18, 19]. The COG is reflects body movements

and has an important role in maintaining the dynamic stability during walking [15,

16, 9, 20]. The measurement devise is designed to achieve the minimum disturbance

on the subjects’ walking. The subject executes a usual walking pattern; e.g. walk for

15 meters or walk for more than 15 seconds on treadmill.

In the second step, the gait acceleration signal is analysed by the differential Entropy

method developed by Papadakis and Christakis [1]. Differential entropy values are

obtained for each axis. In this study only the Z-axis results will be presented.

2.2 Equipment

The Gait acceleration measurement device consists of an accelerometer sensor, a

microcontroller, a voltage regulator, a memory, a transceiver and a battery. Acceler-

ometer sensor is a tri-axial 12-bit accelerometer, capable to measure accelerations up

to 2 g. The measurement device is based on an 8-bit microcontroller, ΑΤΤΙΝΥ2313.

The device dimensions are 125x65x25 mm weight 150 g (including the battery). Low

weight is important to minimise the effect on the measurement. The data is trans-

ferred to PC via an RS232 port. The data is stored in a PC in ASCCI Format. An

example of a typical raw accelerometer signal is presented in Figure 2. In this study

only z-axis acceleration is was used.

Fig. 1. Accelerometry Device on the body.

3 Measurement Procedure

Acceleration data was collected whilst the participant walks across a distance of sev-

eral metres on the treadmill. All measurements were performed in the afternoon. All

subjects were asked to walk on the treadmill for at least 2 minutes before the meas-

urements were obtained. The subject was not alerted with regard to the commence-

ment of the measurement. The measurement duration was 30 sec. Subjects wore light

clothes and thin shoes. The subjects were calm and not nervous.

3.1 Exercise Protocol

During the measurement, the treadmill inclination was zero. Five 5 repetitions for

each velocity level were performed. The order of the velocity is random to avoid any

systematic error.

The subjects are wearing light clothes and casual walking shoes. During the meas-

urement, the subjects were asked to focus on a point on the wall positioned 140 cm

above the floor lying directly in front of their walking path. This was to avoid distrac-

tions. In general, every possible measure was taken to avoid outside stimuli on the

subject during the measurement.

The following treadmill speeds were selected:2.5 [km/h], 4.0 [km/h], 5.5 [km/h],

7.0 [km/h].

3.2 Subjects

The subjects’ were interviewed. The surname, name, father name, gender, occupa-

tion, address, telephone, height, weight, age and medical history was recorded. All

subjects signed an informed consent according to the University Institutional Review

Board. The measurements were performed in the premises of the TEI of Crete in an

airconditioned room. Care was taken to minimise distraction on the subjects during

the measurements. All subjects are healthy individual. The names of the subjects are

not presented.

Table 1.

No ID Gender Age Height Weight BMI

1 ZA Male 26 172 70 23.6

2 MS Male 23 165 65 23.8

3 MI Male 23 177 60 19.1

PP Male 26 170 75 25.9

AS Male 24 180 89 27.4

4 Analysis/Discussion

4.1 X-axis Distribution GEDEM

This index represents the dispersion of the acceleration values in the axis of the

movement. It is expected that increased velocity will lead to an increased dispersion.

Fig. 2 presents the X-axis Distribution GEDEM values vs the gait velocity. It is obvi-

ous that as velocity increased the X-axis Distribution GEDEM values increase. It

appears that the gradient of the increase is similar. In all the subjects, a gradient be-

tween 0.2 and 0.21 was exhibited. Only one subject has a higher value.

Table 2. X-Axis Distribution GEDEM Value vs Velocity Linear Model Coefficients.



X-Axis Dist GEDEM Y-Axis Dist GEDEM Z-Axis Dist GEDEM

Name Intercept Gradient Intercept Gradient Intercept Gradient

AS -1.511 0.277 -1.076 0.2401 -1.434 0.317

MI -1.48 0.2105 -1.42 0.1861 -1.677 0.3127

MS -1.295 0.2027 -1.521 0.2444 -1.865 0.3246

PP -1.309 0.2145 -1.352 0.1769 -1.578 0.3167

ZA -1.279 0.2106 -1.411 0.2172 -1.861 0.3632

34567

-1.0 -0.5 0.0 0.5

Velocity [km/h]

Distribution GEDEM X Axis [Nats]

(2.5,3.14] (4.43,5.07] (6.36,7]

-1.0 -0.5 0.0 0.5

Velocity [km/h]

Distribution GEDEM X Axis [Nats]

Fig. 2. X-Axis Distribution GEDEM vs Gait Velocity scatter plot (left) and whisker plot

(right).

4.2 Y-Axis Distribution GEDEM

This index represents the dispersion of the acceleration values in the lateral axis (y-

axis) (on the transverse plane perpendicular to the axis of movement). Since the total

displacement on the Y-axis is zero, the uncertainty is calculated from oscillations

around the zero acceleration value. As the velocity increases, the movement in the y-

axis needs to be more pronounced. Therefore, it is expected that increased velocity

will lead to an increased dispersion.

Fig. 3 presents the Y-axis Distribution GEDEM values vs the gait velocity. It is ob-

vious that as velocity increased the Y-axis Distribution GEDEM values increase.

Table 2 present the gradients of a linear model. It appears that the gradient of the in-

crease range from 1.7 to 2.5.

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-1.0 -0.5 0.0 0.5

Velocity [km/h]

Distribution GEDEM Y Axis [Nats]

(2.5,3.14] (4.43,5.07] (6.36,7]

-1.0 -0.5 0.0 0.5

Velocity [km/h]

Distribution GEDEM Y Axis [Nats]

Fig. 3. Y-Axis Distribution GEDEM vs Gait Velocity scatter plot (left) and whisker plot

(right).

4.3 Z-Axis Distribution GEDEM

This index represents the dispersion of the acceleration values in the vertical axis (z-

axis). Similarly to the Y-axis It is expected that increased velocity will lead to an

increased dispersion and therefore increased GEDEM index.

Fig. 4 presents the Z-axis Distribution GEDEM values vs the gait velocity. It is obvi-

ous that as velocity increased the Z-axis Distribution GEDEM values increase.

Table 2

presents the gradients of a linear model. It appears that the gradient of the increase

range from 3.1 to 3.6.

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-1.0 -0.5 0.0 0.5

Velocity [km/h]

Distribution GEDEM Z Axis [Nats]

(2.5,3.14] (4.43,5.07] (6.36,7]

-1.0 -0.5 0.0 0.5

Velocity [km/h]

Distribution GEDEM Z Axis [Nats]

Fig. 4. Z-Axis Distribution GEDEM vs Gait Velocity scatter plot (left) and whisker plot (right).

4.4 X axis Spectral GEDEM

This index represents the dispersion of the power spectrum in the axis along the

movement nt (x-axis). This index is lower if the number of frequency components

which are important is less (i.e. when the movement is constant and at a certain

rhythm). If there are significant changes in the rhythm then the index will increase.

Fig. 5 presents the X-axis Spectral GEDEM values vs the gait velocity. The figure

initially appear not to be consistent. Because there is high dispersion during the initial

values, a decrease around 5.5[km/h], and a further increase at 7.0[km/h]. This is at-

tributed to the fact that at low velocities during the measurement on the treadmill, it

was observed that the subjects were finding the velocity to low. As a result the lim-

ited length of the treadmill resulted in accelerations and decelerations trying to com-

pensate for the movement; thus having a significant effect on the movement. The

effect was different among the subjects (i.e. some performed better at 4.0[km/h],

some better at 5.5[km/h]). Beyond 5.5.[km/h] the dispersion of the values increased.

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-1.0 -0.5 0.0 0.5 1.0 1.5

Velocity [km/h]

Spectral GEDEM X Axis [Nats]

(2.5,3.14] (4.43,5.07] (6.36,7]

-1.0 -0.5 0.0 0.5 1.0 1.5

Velocity [km/h]

Spectral GEDEM X Axis [Nats]

Fig. 5. X -Axis Spectral GEDEM vs Gait Velocity scatter plot (left) and whisker plot (right).

Table 3. X,Y,Z -Axis Spectral GEDEM Value vs Velocity Linear Model Coefficients.



X-Axis Spectral GEDEM Y-Axis Spectral GEDEM Z-Axis Spectral GEDEM

Name Intercept Gradient Intercept Gradient Intercept Gradient

AS 0.1709 0.06568 1.733 -0.243 1.681 -0.371

MI -0.4487 0.07911 1.059 0.008 1.609 -0.444

MS -1.0123 0.1318 1.09 -0.092 1.244 -0.411

PP -0.9658 0.15675 1.36 -0.096 1.356 -0.387

ZA -0.4489 0.15491 1.171 0.092 1.336 -0.293

Table 3 presents the gradients of a linear model for each subject. This index could be

used to determine a velocity that the subject is comfortable with.

4.5 Y axis Spectral GEDEM

This index represents the dispersion of the power spectrum in the lateral movement

axis (y-axis) – on the transverse plane perpendicular to the movement. This index is

lower if the number of frequency components which are important is less (i.e. when

the movement is constant and at a certain rhythm). If there are significant changes in

the rhythm then the index will increase.

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0.0 0.5 1.0 1.5 2.0

Velocity [km/h]

Spectral GEDEM Y Axis [Nats]

(2.5,3.14] (4.43,5.07] (6.36,7]

0.0 0.5 1.0 1.5 2.0

Velocity [km/h]

Spectral GEDEM Y Axis [Nats]

Fig. 6. Y-Axis Spectral GEDEM vs Gait Velocity scatter plot (left) and whisker plot (right).

Fig. 6 presents the Y-axis Spectral GEDEM values vs the gait velocity. There appear

to be totally different trends in this graph between subjects. Others appear to increase

and other to decrease. Due to the limited number of samples it was not possible to

investigate a relationship, with other characteristics. This will be the subject of a

further study.

Table 3 presents the gradients of a linear model for each subject. One is almost

constant, two appear to increase and two to decrease.

4.6 Z axis Spectral GEDEM

This index represents the dispersion of the power spectrum in the vertical movement

axis (z-axis) – intersection of Coronar and Sagittal planes. This index is lower if the

number of frequency components which are important is less (i.e. when the move-

ment is constant and at a certain rhythm). If there are significant changes in the

rhythm then the index will increase.

Fig. 7 presents the Z-axis Spectral GEDEM values vs the gait velocity. Up to 5.5.

[km/h], all subjects exhibit lower Z-axis Spectral GEDEM values with increasing

velocity. Beyond 5.5. [km/h] the metric appears to level or increase in some subjects.

It appeared that the movement on the treadmill beyond 4.0[km/h] was more regular

than the vertical movement below 4.0[km/h]. This metric could be used to identify a

velocity that the subject is comfortable with.

Table 3 presents the linear model gradients of Z-axis Spectral GEEM for each sub-

ject. The gradient values appear to be decreasing with values between -.29 and -.45.

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-1.5 -1.0 -0.5 0.0 0.5 1.0

Velocity [km/h]

Spectral GEDEM Z Axis [Nats]

(2.5,3.14] (4.43,5.07] (6.36,7]

-1.5 -1.0 -0.5 0.0 0.5 1.0

Velocity [km/h]

Spectral GEDEM Z Axis [Nats]

Fig. 7. Z -Axis Spectral GEDEM vs Gait Velocity scatter plot (left) and whisker plot (right).

4.7 Implications

Until now there was no understanding of the velocity effect on the GEDEM meas-

urements. Through this work, the effect has been clarified. Also it was identified that

a linear model between the measurements can be a good approximation in certain

cases. Therefore a method for translating measurements to other velocities and com-

paring is possible.

Also some of the indexes with respect to the velocity exhibited inflection points.

This is attributed to velocities that corresponded to measurements that the subject

appeared to be more comfortable. As a result these indexes could be used to develop

a methodology for identifying the normal gait velocity. However this is beyond the

scope of this work.

5 Conclusions

This work presents the effect of gait velocity on GEDEM values. One of the problems

until now was that it was not possible to compare measurements at different veloci-

ties.

Five subjects were measured. The subjects walked on a treadmill at 4 different ve-

locity levels (2.5, 4 and 5.5 and 7km/h) and the accelerations were obtained. There

was statistically significant evidence that the gait velocity influences the GEDEM

values. In all cases a point of inflection appeared. The gradient of GEDEM index vs

velocity appeared to be consistent and is possible to use the results for comparing

GEDEM measurements at different velocity rates. Also this work maybe used to

standardise a measurement protocol.

Acknowledgements

The authors of that paper would like to acknowledge the financial help from the

medical company Ygiea and the PENED project 03ED966 of GSRT under Measure

8.3 of the Operational Program "Competitiveness" of 3

CSF

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