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Runner Up of the ESMAC 2008 Best Paper Award

The Gait Profile Score and Movement Analysis Profile

Richard Bakera,b,c,d, Jennifer L. McGinleya,c,*, Michael H. Schwartze,f,g, Sarah Beynona,

Adam Rozumalskie,g, H. Kerr Grahama,h, Oren Tirosha

aMurdoch Childrens Research Institute, Royal Children’s Hospital, Melbourne, Australia

bDepartment of Mechanical and Manufacturing Engineering, The University of Melbourne, Australia

cSchool of Physiotherapy, The University of Melbourne, Australia

dSchool of Physiotherapy and National Centre for Prosthetics and Orthotics, La Trobe University, Australia

eGillette Children’s Speciality Healthcare, St Paul, MN, USA

fDepartment of Orthopaedic Surgery, University of Minnesota, USA

gDepartment of Biomedical Engineering, University of Minnesota, USA

hDepartment of Orthopaedics, The Royal Children’s Hospital, Melbourne, Australia

This paper was selected by an ESMAC Reading Committee headed by Professor Maria Grazia Benedetti. The present paper was edited by Dr. Tim Theologis.

1. Introduction

Instrumented three-dimensional gait analysis generates kine-

matic measurements of a wide range of variables across the gait

cycle. These span different joints and different planes. Clinical

decisions are generally based on an interpretation of the complex

information contained in these highly interdependent data. It can

oftenbeuseful,however,tohaveasinglemeasureofthe‘quality’of

a particular gait pattern. Such a measure can quantify the overall

severity of a condition affecting walking, monitor progress, or

evaluate the outcome of an intervention prescribed to improve the

gait pattern.

Although other measures have been proposed, the only one to

have widespread clinical acceptance is the Gillette Gait Index [1]

(GGI, originally referred to as the Normalcy Index), which

quantifies the difference between data from one gait cycle for a

particular individual and the average of a reference dataset from

people exhibiting no gait pathology. The GGI, however, has several

shortcomings. These have been well documented and largely

overcome in a recent paper proposing an alternative, the Gait

Deviation Index [2] (GDI). The GGI incorporates temporal spatial as

well as kinematic parameters. The GDI uses only kinematic

variables, and might thus be taken as a cleaner reflection of gait

quality. The entire variability in kinematic variables across the gait

cycle is used, rather than a small number of discrete parameters,

thereby removing much of the subjectivity in choosing those

parameters. Selection of the parameters for the GGI was specific to

children with cerebral palsy whereas the GDI would appear to be a

more general measure of gait pathology.

Gait & Posture 30 (2009) 265–269

A R T I C L EI N F O

Article history:

Received 15 March 2009

Received in revised form 28 April 2009

Accepted 18 May 2009

Keywords:

Gait pathology

Outcome

Gait Profile Score

Gait Deviation Index

Movement Analysis Profile

A B S T R A C T

TheGaitDeviationIndex(GDI)hasbeenproposedasanindexofoverallgaitpathology.Thisstudyproposes

an interpretation of the difference measure upon which the GDI is based, which naturally leads to the

definition of a similar index, the Gait Profile Score (GPS). The GPS can be calculated independently of the

feature analysis upon which the GDI is based. Understanding what the underlying difference measure

represents also suggests that reporting a raw score, as the GPS does, may have advantages over the

logarithmic transformation and z-scaling incorporated in the GDI. It also leads to the concept of a

MovementAnalysisProfile(MAP)tosummarisemuchoftheinformationcontainedwithinkinematicdata.

A validation study on all children attending a paediatric gait analysis service over 3 years (407

children) provides evidence to support the use of the GPS through analysis of its frequency distribution

across different Gross Motor Function Classification System (GMFCS)and Gillette Functional Assessment

Questionnaire(FAQ)categories, investigationofintra-sessionvariability,andcorrelationwiththesquare

root of GGI. Correlation with GDI confirms the strong relationship between the two measures.

The study concludes that GDI and GPS are alternative and closely related measures. The GDI has prior

art and is particularly useful in applications arising out of feature analysis such as cluster analysis or

subject matching. The GPS will be easier to calculate for new models where a large reference dataset is

not available and in association with applications using the MAP.

? 2009 Elsevier B.V. All rights reserved.

* Corresponding author at: Murdoch Childrens Research Institute, Hugh

Williamson Gait Laboratory, Flemington Road, Parkville, Victoria 3052, Australia.

E-mail address: jennifer.mcginley@mcri.edu.au (J.L. McGinley).

Contents lists available at ScienceDirect

Gait & Posture

journal homepage: www.elsevier.com/locate/gaitpost

0966-6362/$ – see front matter ? 2009 Elsevier B.V. All rights reserved.

doi:10.1016/j.gaitpost.2009.05.020

Page 2

It has been shown that the GGI requires a reasonably large

number of people in the reference dataset [3], and that values can

vary significantly between different reference datasets [4]. In

contrast, values of the GDI appear much less sensitive to

differences in the reference data [5]. The GDI proceeds naturally

from the gait feature analysis, which provides considerable data

compression and provides a framework for other analytical

techniques such as cluster analysis for gait classification [6].

Finally, the GDI has been demonstrated to correlate well with GGI

and the Functional Assessment Questionnaire (FAQ) in a compre-

hensive validation study [2].

As with any other measure, the GDI does have some limitations.

The technique depends on the preliminary analysis of a large

dataset containing examples of all likely gait deviations (3351

subjects were used in the original study [2]). Although the authors

have made the gait features derived from this analysis available for

use, this does limit the potential for this technique to be expanded

to other applications. Deriving a similar index for a new

biomechanical model based on a different marker set, incorporat-

ing functional calibration, or including more complex modelling of

the foot, for example, would be a considerable undertaking.

The GDI is a scaled version of the Euclidean distance of a

subject’s kinematics from the average of a reference dataset

calculated ina basis comprised of 15gait features.At first sight this

appears a somewhat abstract quantity and the clinical interpreta-

tion of the measure is based upon its scaling relative to the

reference dataset. That scaling has been chosen to ensure a

measure with good statistical properties.

This paper proposes a simpler interpretation of the distance

measure underlying the GDI, which leads to the proposal of a

modified measure that can be calculated independently of the

feature analysis. This adds to our understanding of how it can be

interpreted clinically, and suggests that there may be advantages

in using a raw score (as opposed to a scaled index). The paper thus

presents data to validate such a raw score, and uses the new

understanding of the distance measure as a basis for considering

the relative advantages and disadvantages of raw scores or scaled

indices.

2. Method

2.1. Interpreting the difference measure of the GDI

Thekey tounderstand the differencemeasureused inthe GDIis torecognise that

the feature analysis is based on projecting the original gait data onto the gait

features usingan orthonormal transformation. By definition, theEuclidean distance

–andthereforetheRMSdifference–betweenanytwogaitvectorswillbepreserved

by any such transformation. Thus, if all 459 gait features were used in the GDI

(rather than just the first 15), the difference measure used in the GDI would be the

RMS difference between the patient’s data and the average from the reference dataset

taken over all relevant kinematic variables, for the entire gait cycle. For reasons which

willemergebelow,thisquantitywillbereferredtoastheGaitProfileScore(GPS).As

only the first 15 features are used in the GDI (because this represents a close

approximation to the original gait data), the actual distance measure will be a close

approximation to the GPS. A more formal proof of this is attached as an electronic

appendix.

2.2. Definition of Gait Variable Scores (GVS), the Movement Analysis Profile (MAP) and

the Gait Profile Score (GPS)

Appreciating that the fundamental quantity on which the GDI is based is the

RMSdifferencebetweenthegaitvectorandtheaveragegaitvectorforpeoplewith

no gait pathology suggests that there may be value in considering the RMS

difference between a similar quantity calculated for a single gait variable rather

than the entire gait vector. This will be referred to as a Gait Variable Score (GVS).

The GVS for nine key relevant kinematic variables for the right and left legs can be

combined to form a Movement Analysis Profile (MAP, Fig. 1). The RMS average of

all the variable scores for a particular side will then equal the GPS calculated from

the entire gait vector. It is also possible to calculate an overall GPS from the

variable scoresfromboth sides. Given that the pelvis is common to both segments

it is sensible to include pelvic kinematics from one side only (the left is used by

convention in this paper).

2.3. Validation of the Gait Profile Score

The GPS already has high face validity. The formal validation focuses on its

statistical properties, how it is distributed, its intra-session reliability, and its

concurrent validity compared to the FAQ, Gross Motor Function Classification

System (GMFCS), GDI, and GGI. The data upon which this is based came from all

patients under the age of 18 attending for an instrumentedgait analysis at a tertiary

paediatric hospital during the years 2005–2007. If patients attended more than

once during this period, then only data from their first visit were included. Data

from a sample of convenience of 38 children under 18 years of age with no known

gait pathology were used to form the reference dataset.

All data had been captured using a VICON 512 or MX system and processed with

the PluginGait component for Workstation software (Vicon, Oxford, UK) based on

the required marker set with the use of knee alignment devices during a static trial.

Two AMTI force plates were used to capture force plate data. Trials were processed

sequentially.Ifvalidforce platedatawere availablethen thefirstthreeleft andright

gait cycles identified as having valid kinematic and kinetic data for each patient

were included in the analysis (although no reference was made to kinetic data in

this particular study). If valid force plate data was not available then the first three

left and right gait cycles identified as having valid kinematic data for each patient

were included. Data was uploaded into Gaitabase (http://gaitabase.rch.org.au)

which includes modules for calculating the GGI, GDI and GPS from gait data.

Examination of the distribution of the GPS follows the method of Schwartz and

Rozumalski [2] in assessing concurrent validity with the FAQ, GMFCS, GGI and GDI.

The FAQ is a ten-point scale rating gait function which is not specific to a particular

pathology [7]. The five-level GMFCS is now the standard classification of severity of

cerebral palsy [8]. The frequency distributions of the first recorded GPS score for

each side of all children in each FAQ category and each GMFCS category were

plotted, as were those of the reference dataset of children with no gait pathology.

A Euclidean distance such as the GPS is likely to have a chi-distribution so results

are reported in terms of the median value and inter-quartile ranges (IQR). The GDI,

which involves a logarithmic transformation, was found to be normally distributed

by Schwartz and Rozumalski, and thus both the raw GPS and its logarithmic

transform were assessed for normality using the Kolmogorov–Smirnov test.

Intra-session variability was calculated as the IQR of the GPS for each child

estimated from the three trials.1The median of this was estimated similarly for all

patients and for each category of GMFCS and FAQ.

Concurrent validity was examined by comparing the GPS against other measures

of gait pathology. The GGI is the only widely accepted continuous measure of gait

pathology [2]. Following Schwartz’s observation that the derivation of the GGI

suggests that the metric actually represents the square of the deviation from

normal, the correlation between GPS and the square root of GGI ð

dimensional gait speed (normalised by dividing through by

length and g is the acceleration due to gravity) were examined using Spearman’s

rank correlation and with GDI using exponential regression. As these correlations

are essentially between two measurements made on a single gait cycle, all gait

cycles (i.e. threerightand threeleftforeachchild)areincluded.Analysis ofvariance

(of the logarithmic transform of the GPS to ensure a normal distribution) was used

to determine whether it distinguished between levels of the GMFCS and FAQ. Post

hoc tests were used to identify where the differences occurred.

ffiffiffiffiffiffiffiffiffi

GGI

p

Þ and non-

ffiffiffiffiffi

gL

p

, where L is the leg

Fig. 1. The Movement Analysis Profile. Each column corresponds to one of the

kinematic variables. Its height represents the (RMS) average difference across time

between a specific gait cycle and the average gait cycle from people with no gait

pathology. The black area at the foot of the columns represents the average value of

this for people with no gait pathology. The GPS for left side, right side and overall

gait pattern are displayed in the rightmost column.

1Medians and inter-quartile ranges were estimated on the assumption that the

logarithmic transform of the GPS is normally distributed. Thus the mean (m) and

standard deviation (sd) of ln(GPS) were calculated and exp(m), exp(m ? 0.67sd),

and exp(m + 0.67sd) taken as estimating the median, and lower and upper quartiles

of the GPS.

R. Baker et al./Gait & Posture 30 (2009) 265–269

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The final part of the analysis was to investigate the properties of the individual

GVSs which comprise the MAP, and to determine the relationship of the individual

GVS scores with each other and with the GPS. A Spearman’s rank correlation was

performed between each GVS and the GPS and for each pair of GVSs.

3. Results

Data from the 407 children were used. 271 had cerebral palsy,

88 had general orthopaedic conditions (such as Perthes disease,

slipped upper femoral epiphysis and rotational malalignment), 43

had other neurological conditions (such as spina bifida, hereditary

spastic paraplegia and acquired brain injuries) and five were

idiopathic toe walkers (Table 1).

The frequency distributions of the GPS for the categories of the

FAQ (levels 6–10) and GMFCS (I–III) and also for the children with

no gait pathology (there were too few children in other categories

for meaningful analysis) exhibit skewed distributions as expected

(Fig. 2). Kolmogorov–Smirnov tests showed significant differences

from a normal distribution in the raw GPS scores for all categories

(all p values < 0.05) but no such evidence for any category of the

log transformed data (all p values > 0.05).

For intra-session variability, the median IQR was 0.678. Only 6%

of all patients showed an IQR of greater than 2.08.

A moderate correlation (r = .79) between GPS and

found, suggesting that the two measures are similar (Fig. 3a). The

correlation between GPS and walking speed is weak (r = ?.28,

Fig. 3b) suggesting that the overall effect of walking speed is only

weakly reflected in the kinematics. This suggests that the GPS and

speed may serve as complementary outcome measures reflecting

differentdomains ofgait quality.Thereisa very strongexponential

correlationbetweenGPS andGDI (r = 0.995, Fig.4),confirmingthat

the strong mathematical relationship between them. The one-way

ANOVA confirmedGPSdiffers with bothFAQ (p < .001)and GMFCS

(p < .001) and post hoc tests showed differences between all levels

of the FAQ and GMFCS (p < .02), except for between FAQ levels 7

and 8.

Table 2 shows the Spearman rank correlations of the GVSs with

GPS and with each other. It can be seen that none of the GVSs

correlates particularly strongly with the GPS (knee flexion shows

the highest correlation, r = .72) and that none of the GVS pairs

ffiffiffiffiffiffiffiffiffi

GGI

p

was

correlate particularly strongly (pelvic tilt and hip flexion showing

the strongest correlation, r = .66).

4. Discussion

The GPS has strong face validity being based on the RMS

difference between gait data for an individual child and the

average data from children with no gait pathology. Analysis of

intra-session variability suggests that it is also a reliable measure

(within a single session). The moderate correlation with

the significant differences in GPS between both FAQ and GMFCS

levels provide further evidence of validity.

The extremely strong correlation between the GPS and the GDI

confirms the theoretical conclusion that the two are based on

essentially similar measures of difference. A consequence of this is

that any evidence validating one will automatically stand as a

validation of the other. Indeed, in this context this paper can be

read as independently replicating the study of Schwartz and

Rozumalski [2] in a different laboratory and population, and

strengthening the conclusion that both the GDI and the GPS are

valid and largely equivalent measures of gait pathology. Reporting

of a raw score for GPS and a transformed and scaled index for GDI,

however, results in them having quite different properties. The

decision as to whether one or other is preferable thus rests on a

consideration of these differences.

TheGDI isderivedfromgaitfeature analysiswhichisbasedona

very large dataset of subjects with a wide range of gait pathologies.

Schwartz and Rozumalski [2] have made their gait features

publicly available so that this makes little practical difference to

calculating either measure for data derived from the conventional

gait model. It does, however, impose a considerable barrier to

extending similar techniques to data derived from different gait

models or different activities (running, stair climbing, etc.). The

GPS is independent of the feature analysis and can be calculated

directly from the data of an individual and the averaged data of

people with no gait pathology. On the other hand, Schwartz and

Rozumalski [2] have outlined several interesting properties of

feature analysis and having a measure of gait pathology that

derives directly from the analysis has its attractions.

Another potential advantage of the GPS is the decomposition

referred to here as the MAP. The MAP provides useful insights into

which variables are contributing to an elevated GPS. The lack of

strong correlations of the individual GVSs with the GPS and with

each other suggests that there is considerably more information

contained within the MAP than in the GPS alone. There is a simple

mathematical relationship between the GPS and GVSs as the GPS is

the RMS average of the GVSs. Whilst it is possible to conceive of a

similar decomposition of the GDI it does not have the same

elegance. The extension of logarithmic transform and z-scoring to

the constituent gait variables, in particular, would lead to a

complex relationship between component scores and the GDI.

The other major difference between the two scores is that the

GPS is defined as a raw score whereas the GDI is transformed and

ffiffiffiffiffiffiffiffiffi

GGI

p

and

Table 1

Characteristics of study cohort and reference subjects. Mean and standard

deviations are quoted where an assumption of normally distributed data seems

reasonable, median and inter-quartile range are quoted otherwise.

Summary statisticsCohortReference

Number

Age (years)

BMI (kg/m2)

Non-dimensional walking speed

GPS (8)

GGI (no units)

GDI (no units)

407

12 (3)

20 (5)

1.1 (0.3)

9.7 (4.9)

105 (164)

78 (13)

38

11 (3)

19 (5)

1.3 (0.2)

5.2 (1.9)

17 (11)

100 (10)

Mean (sd)

Mean (sd)

Median (IQR)

Median (IQR)

Median (IQR)

Mean (sd)

Table 2

Correlations between GPS and GVS and between the different pairings of GVS expressed in terms of Spearman’s rank correlations (r).

Pel Tilt Hip FlexKnee Flex Ank Dors Pel OblHip Abd Pel RotHip Rot Foot Prog

GPS

Pel Tilt

Hip Flex

Knee Flex

Ank Dorsi

Pel Obl

Hip Abd

Pel Rot

Hip Rot

.47 .63

.66

.72

.34

.54

.60

.26

.36

.56

.44

.29

.30

.36

.31

.44

.24

.26

.35

.32

.61

.47

.19

.21

.34

.31

.28

.36

.44

.09

.15

.10

.09

.14

.18

.17

.57

.10

.15

.31

.23

.24

.18

.22

.12

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Fig. 2. Frequency distribution of the GPS across different levels of the GMFCS (left column), FAQ (right column) and from children with no gait pathology (bottom left).

R. Baker et al./Gait & Posture 30 (2009) 265–269

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scaled. The GPS is reported in the same units (degrees) as the

kinematic variables and its interpretation is based upon this. The

interpretation of the GDI is based on the scaling which has an

average score of 100 for people without gait pathology and ?10

units for every standard deviation away from this. Choice of which

is more appropriate may be dependent on the purpose for which

such scales are being used and also on personal preference.

ThelogarithmictransformationusedtoderivetheGDIresultsin

it having better behaved statistical properties than the GPS. The

normal distribution of the GDI within different categories of the

FAQ does provide a basis for using parametric statistics directly. To

be rigorous it makes sense to perform parametric statistics on the

logarithmic transform of the GPS or non-parametric statistics on

the raw scores. On the other hand the linear relationship between

the GDI and difference from the average data for people with no

gait pathology is lost. A person whose data is twice as different

from that of people with no gait pathology than another person’s

will have twice the GPS.

5. Conclusion

The study concludes that GDI and GPS are alternative and

closely related measures. The GDI has prior art and is particularly

useful in applications arising out of feature analysis such as cluster

analysis or subject matching. The GPS will be easier to calculate for

new models where a large reference dataset is not available and in

association with applications using the MAP.

Acknowledgements

The authors acknowledge funding support from the National

Health and Medical Research Council of Australia [Centre for

Clinical Research Excellence in Gait Analysis and Gait Rehabilita-

tion Grant No 264597].

Conflict of interest

Authors Richard Baker, Jennifer L. McGinley, and Oren Tirosh

have filed a patent through their employers for an invention

making use of some of the ideas described in this paper. Otherwise

none of the authors have any financial and personal relationships

with other people or organisations that could inappropriately

influence (bias) their work.

Appendix A. Supplementary data

Supplementarydataassociatedwiththisarticlecanbe found,in

the online version, at doi:10.1016/j.gaitpost.2009.05.020.

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Fig. 3. Correlations of GPS with ð

ffiffiffiffiffiffiffiffiffi

GGI

p

Þ and non-dimensional walking speed displaying linear regression line.

Fig. 4. Correlation of GPS with GDI displaying exponential regression line.

R. Baker et al./Gait & Posture 30 (2009) 265–269

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