Vol.2, No.1, 38-44 (2010) Health
SciRes Copyright © 2010 Openly accessible at http://www.scirp.org/journal/HEALTH/
Gait spectral index (GSI): a new quantification method
for assessing human gait
Rodolphe Héliot1, Christine Azevedo-Coste2, Laszlo Schwirtlich3, Bernard Espiau4
1Inria, Montbonnot, France; rodolphe.heliot@gmail.com
Demar Inria/Lirmm, Montpellier, France; azevedo@lirmm.fr
Institute for Rehabilitation Dr Miroslav Zotovic, Belgrade, Serbia; laslo@bitsyu.net
Inria, Montbonnot, France; espiau@inrialpes.fr
Received 25 November 2009; revised 7 December 2009; accepted 12 December 2009.
This paper introduces a simple, quantitative as-
sessment tool to follow up the recovery of gait.
Today, micro-electro-mechanical systems (MEMS)
technology provides with small, simple, low-pow-
er consuming and easy to don and doff sensors.
In our approach we have selected an accelerome-
ter and introduced a new quantity that charac-
terizes the gait pattern in the frequency domain,
we term it Gait Spectral Index (GSI). GSI allows
assessing gait quality and closely relates to the
speed and cadence of gait (dynamics). We have
tested the GSI approach to quantify the quality
of the gait of healthy young and elderly, and post-
stroke hemiplegic individuals. We investigated
the repeatability and coherence of GSI in healthy
individuals (young and elderly) and contrasted
this to the post-stroke hemiplegic individuals.
We found that high correlation of the GSI with
conventional gait parameters. This suggests that
GSI, which needs only data from one acceler-
ometer, could be an objective quantitative mea-
sure of the quality of the walking thereby a sim-
ple yet reliable measure of the recovery of func-
tion during neuronrehabilitation.
Keywords: Gait Evaluation; Walk Training;
Accelerometer; Spectral Analysis
Clinical methods for gait evaluation consist in standard-
ized functional tests (Barthel Index, Rivermead Mobility
Index (Bohannon et al. 1987), Functional Ambulation
Category (FAC)) are qualitative; thereby, somewhat sub-
jective because they depend on individual observation
skills of the rater. We developed a simple instrument that
after appropriate processing provides objective quantita-
tive measure of the gait performance. This new instru-
ment is of great importance for clinical use for assessing
the gait pattern in all, including elderly and individuals
with disabilities (Sekine et al., 2002). The heart of the
instrument is the accelerometer that is being mounted on
the leg, does not need calibration and provides data that is
highly reproducible.
The development of this instrument follows the fast
growth of the filed of Micro-electro-mechanical systems
(MEMS). The MEMS sensors have been applied for the
assessment of physical activities using body-mounted
systems (Jasiewicz et al., 2006; Luinge and Veltink, 2004 ;
Pappas et al., 2002). MEMS based accelerometers pro-
vide a good representation of movement dynamics (Ja-
siewicz et al., 2006; Hester et al., 2006; Brandes et al.,
2005; Luinge and Veltink, 2004). The typical application
of multiple accelerometers is for reconstruction of the
kinematics of the gait (Wagenaar et al., 1992; Bussmann
et al., 2000). Reconstruction of gait kinematics is difficult
since the integration of data captured by accelerometers
results with drift and substantial errors. The alternative is
to use the acceleration data directly as a measure of the
quality of gait. Acceleration patterns of trunk have ex-
tensively been employed since they have been shown to
comprise low intra-variability; thereby suitable for de-
tection of phases of the gait cycle (Ziljstra et al., 2003;
Brandes et al., 2006). The reproducibility of trunk ac-
celerations declined as gait speed decreases which is the
case when analyzing the gait of elderly and even more of
subjects with gait disabilities (Saremi et al., 2006).
Acceleration can be analyzed in the frequency domain.
The fundamental frequency is equivalent to the stride
frequency, and the harmonics amplitudes vary depending
on the gait pattern. It is important to notice that the posi-
tion of the accelerometer on a body segment does not
affect the frequency content of the signal. One of the best
confirmations was presented by Waarsing et al. (1996)
showing that the power contained in the peaks is in-
versely proportional to stability performance.
Here, we show that only one accelerometer can be used
R. Héliot et al. / HEALTH 2 (2010) 38-44
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as a good source of data for gait characterization. One of
the features of this gait assessment system is that it does
not need to be calibrated to each individual, and provides
with easy donning and doffing. The major novelty that
allows the use of this simple hardware is the Gait Spectral
Index (GSI). The GSI is the new measure that character-
izes the gait pattern in the frequency domain. We hy-
pothesized that the GSI is highly correlated with the
conventional gait parameters. Based on proved hypothe-
sis we performed the experiments in which we compared
the GSI determined from analysis of the gait of healthy
young and elderly subjects with the GSI determined for
the gait of individuals of hemiplegia.
2.1. Subjects
Six healthy young (HY) (age 31. 8 years ± 7. 2), and ten
healthy elderly (HE) (age 67 years ± 6. 9) individuals
participated in the study to confirm the high correlation of
the GSI and conventional gait parameters. 19 post-stroke
hemiplegic individuals (SP) (age 58. 6 years ± 10.18) also
participated in the study in order to analyze the differ-
ences between healthy and pathological gait. Basic tada
on study the subjects is summarized in Tables 1-4.
The HY group was formed from volunteers from our
laboratory in LIRMM, France. Two subjects, out of ten, in
the HE group were recruited in an elderly cultural asso-
ciation while the other eight from a local waling club.
Hemiplegic individuals were recruited from the inpa-
tient population of the Institute for Rehabilitation Dr
Miroslav Zotovic in Belgrade. The hemiplegic gait abili-
ties were assessed by using the Functional Ambulation
Category scale (Holden et al, 1984). The FAC scale has
five grades: 1 - person needs to be physically supported
for any ambulation (the worst), and 5 - the person can
walk independently anywhere (the best). All hemiplegic
individuals could walk with their usual walking aid (13
patients used cane or tripod, 4 patients had also an ankle
or foot orthosis) as shown in Tables 3 and 4.
The (SP) group was divided into two sub-groups: (SP1)
includes the eight individuals with a 5 FAC rank and (SP2)
with the 11 remaining individuals.
This study was approved by the local ethics Committee,
and all study participants signed the informed consent.
2.2. Equipment
We used a uniaxial-accelerometer (ADXL-203, Analog
Devices) positioned on the shank close to the ankle. The
accelerometer axis was directed along the shank with the
positive direction pointing upwards (Figure 1). The alig-
nment was performed visually, except from this con-
straint, no specific care was needed for the positioning of
the accelerometer. In the case of hemiplegic individuals
the accelerometer was positioned on the non-paretic leg.
In order to determine the correlation with the conven-
tional gait parameters subjects were also equipped with
two 3-contact point insoles used to detect gait phases, gait
cadence and assess the averaged stride length when as-
sociated to chronometric recordings. The sampling rate
was 100 samples per second based on known low fre-
quency content of the signal.
2.3. Protocol
Subjects were asked to walk 10 meters at their normal
self-paced speed. Depending on the individual ability to
Table 1. Healthy young subject group (HY) gait description.
# Age Cadence
6 30 0.90
1 46 0.96
2 28 0.78
3 32 1.05
5 26 0.99
4 29 0.84
Mean 31.8 0.92
Std 7.2 0.1
Table 2. Healthy elderly subject group (HE) gait description.
# Age Walking
speed Cadence Stride
5 73 1.39 1.02 1.36
1 67 1.49 0.93 1.61
8 65 1.35 0.97 1.39
7 63 1.24 0.92 1.36
6 61 1.19 0.9 1.31
2 63 1.06 0.92 1.53
3 60 1.23 0.91 1.36
4 62 1.22 0.86 1.4
10 79 1.36 1.05 1.29
9 77 1.24 1.09 1.14
Mean 67 1.27 0.96 1.38
Std 6.87 0.12 0.07 0.13
R. Héliot et al. / HEALTH 2 (2010) 38-44
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Table 3. Stroke patient group 1 (SP1) gait description.
# Age FAC Walking aid Walking
speed Cadence Stride
length SI
4 54 4 Cane 0.3 0.44 0.68 15.47
3 69 4 Cane 0.38 0.56 0.68 27.61
6 71 3 Tripod 0.13 0.29 0.46 27.47
13 53 4 AFO+tripod+physio 0.1 0.22 0.48 16.99
5 67 1 AFO+tripod 0.12 0.32 0.4 9.83
16 77 3 Tripod 0.17 0.33 0.51 17.06
17 59 2 Tripod+physio 0.11 0.2 0.58 22.18
8 47 3 Tripod 0.29 0.39 0.75 66.57
11 46 3 Cane 0.07 0.33 0.24 3.71
7 77 4 AFO+tripod 0.2 0.54 0.72 6.54
9 58 4 Tripod 0.17 0.28 0.6 11.65
Mean 61.64 3.18 0.19 0.35 0.55 20.46
Std 11.20 0.98 0.10 0.12 0.15 17.15
Table 4. Stroke patient group 2 (SP2) gait description.
6 1.57
1 1.46
2 1.42
3 1.40
5 1.28
4 0.92
Mean 1.34
Std 0.23
walk for extended period of time, the data between four
and eight trials were collected for each subject.
2.4. Symmetry Index
The symmetry index (SI) can be calculated for swing and
stance phases using the following formula (Robinson et
al., 1987):
SI[%]=200(Tnonparetic-Tparetic)/(Tparetic+Tnonparetic) (2)
Tparetic and Tnonparetic are the durations of stance or swing
phases for paretic and non paretic legs. SI can be positive
or negative and the perfect symmetry index is SI=0.
2.5. Spectral Analysis and Gait Spectral
The recorded acceleration was transformed using the Fast
Fourier transform (FFT) to obtain the frequency spectrum
of the signal. There was no averaging; the spectrums were
computed over the whole trial duration (10 meters). The
gait spectral index (GSI) was defined as a ratio between
the power of the second harmonic component with re-
spect the power of the fundamental component.
GSI =Power_of_second_harmonic/
Power_of_fundamental (1)
Figure 1. Protocol description.
3. Results
In Tables 1-4 we reported the gait characteristics (walking
speed, cadence, stride length, symmetry index) measured
for each of the four groups.
Figure 2 shows the spectrums corresponding to one
individual of each population. Spectrums from a given
subject are highly reproducible from a trial to another and
spectrums for each of the groups are significant in terms
of harmonic repartitions (Tables 7 and 8). The computed
GSI for the three groups are reported in tables 5 to 8. The
aim of healthy group individuals was to compute GSI,
therefore we did not analyze all the gait characteristics for
these two populations.
3.1. Patients
In patient group GSI index varies from 0.52 to 1.69 (ta-
bles 7 and 8) with a low intra variation (average standard
deviation 0.16). The spectrum reproducibility is good as
R. Héliot et al. / HEALTH 2 (2010) 38-44
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stated by the low intra variability associated to funda-
mental and 2nd harmonic amplitudes (tables 7 and 8). For
each individual, we have also estimated the correlation
between each trial spectrum and the average spectrum for
this given individual. The good correlation (r=0.78) vali-
dates the hypothesis of the spectrum reproducibility. There
is a moderate correlation between GSI and FAC rank (r=
0.66). In figure 3 we plotted the GSI values obtained for
the two patient groups in function of FAC rank. In table 7,
the patients are classified in terms of GSI index values.
The higher GSI values correspond to best walkers in FAC
quotation (level 5-group SP1), they vary from 1.22 to
1.69. The mean value is 1.21. In SP2 group, GSI varies
from 0.52 to 0.89 (table 8). For lower levels, the GSI does
not seem to allow to discriminate between the different
levels. The mean value is 0.71.
There is a good correlation between GSI and gait speed
(r=0.81) and gait cadence (r=0.74). Correlation between
GSI and stride length is moderate (r=0.66). Correlation
with symmetry index is not significant. The mean value
of symmetry index is 21%.
It is interesting to notice that FAC rank and symmetry
index are not correlated (r=0.03). FAC rank is correlated
with gait speed (r=0.7), gait cadence (r=0.72) and stride
length (r=0.66).
3.2. Elderly
In elderly subject group GSI index varies from 0.4 to 1.3
(table 5). The mean value is 1.02. In healthy elderly group,
only stride length appeared to be significant in terms of
correlation with GSI (r= 0.72). The two older subjects (77
and 79) have the lower GSI scores.
3.3. Young
In young subject group GSI index varies from 0.92 to
1.57 (table 6). The mean value is 1.34.
4. Discussion
The results presented document that the spectrum of the
shank acceleration is highly reproducible from trial to
trial in the same subject and can be considered as an
individual signature pattern. We noticed the presence of
strong high frequencies components in the spectrums of
healthy and patient best walkers. High frequencies
components are likely present due to the richer dynamics
of healthy gait compared to the gait of hemiplegic and
poor walkers.
The proposed GSI ratio compares fundamental am-
plitude with second harmonic amplitude; it correlates
with gait speed which is classically considered as an
indirect measurement of gait quality. It is important to
notice that to be valuable speed should be evaluated
through distances long enough to assess adaptation and
gait efficiency.
The low correlation between FAC score and GSI
should be counterbalanced by the fact that the higher GSI
values correspond to best classification in FAC. But. FAC
classes are not varying linearly with gait quality and the
number of patients in each of the categories is not similar
enough to conclude.
The GSI scores in elderly population are higher com-
pared to our expectations. We suggest that this is due to
the fact that the population included in the study was
mainly recruited in a gait club. Hence, they are not rep-
resentative for typical aged walkers with limited sen-
sory-motor capacity.
Nor GSI, nor FAC are correlated with symmetry of gait
in patients. This should be an improvement of GSI in
The spectral analysis of the shank acceleration, in the
direction aligned with the shank can characterize the gait.
Two main observations can be made: 1) dealing with a
given subject: high reproducibility of spectrums from
trial to trial, and 2) presence of strong high frequencies
components in the spectrums of healthy and patients who
are good walkers.
We found out that placing one accelerometer on the
healthy leg of post-stroke hemiplegic patient allows
assessing the effects of gait reeducation. The instrumen-
tation and processing that we described are simple and
they comprise light and non expensive setup, including
wireless communication of sensory output to computer.
At this point the GSI index is mainly correlated with
gait speed and gait cadence and better than what FAC
rank. This is an interesting result as our approach is
technically less constraining than classical methods to
Figure 1. Hemiparetic stroke GSI.
R. Héliot et al. / HEALTH 2 (2010) 38-44
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Figure 2. Accelerometer signals spectrums examples for all 4 groups. The values on the vertical axis are normalized relatively to the
amplitude of the fundamental amplitude. The value of the 2nd harmonic therefore corresponds to GSI.
Table 5. Healthy young subject group (HY) mean value of the
GSI index over different trials for each subject for comparison
6 1.57
1 1.46
2 1.42
3 1.40
5 1.28
4 0.92
Mean 1.34
Std 0.23
assess the gait speed and cadence (chronometer, insoles).
The GSI could be applied not only for the individuals
who participated in this study, but in many other types of
pathological gait. The GSI needs then to be improved and
adapted to meet the specific pathologies and give object-
Table 6. Healthy elderly subject group (HE) mean value of the
GSI index over different trials for each subject for comparison
5 1.3
1 1.29
8 1.2
7 1.19
6 1.12
2 1.11
3 0.98
4 0.88
10 0.78
9 0.4
Mean 1.025
Std 0.28
tive measures of the improvement.
Healthy young control subject (HY) Healthy elderly control subject(HE)
Hemiparetic stroke patient subject - FAC 5 (SP1) Hemiparetic stroke patient subject FAC=3 (SP2)
R. Héliot et al. / HEALTH 2 (2010) 38-44
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Table 7. Stroke patient group 1 (SP1) GSI indexes and spectral analysis results.
GSI Fundamental
amplitude 2nd harmonic
amplitude Spectrum
std mean std mean std
2 1.69 0.10 0.85
0.07 1.46 0.20 0.79
1 1.36 0.20
0.70 0.25 0.93 .027 0.81
20 1.31 0.22
0.82 0.16 1.09 0.27 0.79
15 1.22 0.21 0.94 0.05 1.15 0.19 0.51
14 1.16 0.09
0.89 0.13 1.03 0.21 0.77
19 1.02 0.09 0.93 0.08 0.96 0.14 0.67
10 1.01 0.09 0.89 0.08 0.90 0.11 0.79
18 0.95 0.14 0.93 0.03 0.89 0.16 0.79
Mean 1.22 0.14 0.87 0.11 1.05 0.19 0.74
Std 0.24 0.05 0.08 0.07 0.18 0.05 0.10
Table 8. Stroke patient group 2 (SP2) GSI indexes and spectral analysis results.
GSI Fundamental
amplitude 2nd harmonic
amplitude Spectrum
std mean mean std
4 0.89 0.15
0.90 0.06 0.80 0.16 0.80
3 0.87 0.10 0.92 0.05 0.81 0.13 0.85
6 0.75 0.25 0.71 0.31 0.47 0.14 0.92
13 0.75 0.45 0.61 0.42 0.35 0.15 0.63
5 0.75 0.12 0.85 0.07 0.64 0.14 0.89
16 0.72 0.13 0.91 0.07 0.66 0.10 0.94
17 0.69 0.24 0.53 0.40 0.32 0.14 0.49
8 0.68 0.19 0.75 0.19 0.51 0.16 0.80
11 0.63 0.12 0.64 0.37 0.37 0.18 0.65
7 0.59 0.14 0.75 0.25 0.43 0.14 0.95
9 0.52 0.04
0.88 0.11 0.46 0.07 0.96
Mean 0.71
0.17 0.77 0.21 0.53 0.14 0.81
Std 0.11 0.10 0.13 0.14 0.17 0.03 0.15
Figure 3. Hemiparetic stroke GSI.
In the future, we propose to improve GSI in order to
include gait symmetry parameter. It would also be possi-
ble to give different weights to different gait quality cri-
teria within GSI.
Figure 4. GSI / subject ages.
The low intra variability of this spectral analysis could
easily be employed to assess the gait improvement of
each individual patient. A low GSI score could alert the
therapist on possible pathological problems.
R. Héliot et al. / HEALTH 2 (2010) 38-44
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