J. Biomedical Science and Engineering, 2010, 3, 322-326
doi:10.4236/jbise.2010.33044 Published Online March 2010 (http://www.SciRP.org/journal/jbise/
Published Online March 2010 in SciRes. http://www.scirp.org/journal/jbise
Cyclogram and cross correlation: A comparative study to
quantify gait coordination in mental state
Deepak Joshi1,2, Sneh Anand1,2
1Center for Biomedical Engineering, IIT Delhi, India;
2Center for Biomedical Unit, AIIMS, New Delhi, India.
Email: joshideepak2004@yahoo.co.in
Received 19 December 2009; revised 28 December 2009; accepted 4 January 2010.
The purpose of this study to evaluate the effect of
mental task on gait coordination. The comparison
between two techniques Crosscorrelation and Cyclo-
gram has been performed. A set of gait experiments
was developed and conducted to evaluate the effect of
mental task on gait coordination. The perimeter derived
from the geometric figure, cyclogram perimeter (CP),
of the knee-knee cyclogram is the main descriptor
considered in this study. For crosscorrelation it is the
peak value of cross correlation coefficient (CCC) that
has been taken for comparison. The sensitivity of
both the techniques in terms of percentage has been
calculated. Crosscorrelation is highly sensitive
(mean=20.4 S.D.=2.3), towards the change in gait
coordination with mental task, in comparison to
cyclogram perimeter (mean=2.2 S.D.=1.2). The re-
sults have strength to assess the progress of rehabili-
tation among Parkinson patients.
Keywords: Gait Coordination; Cyclogram; Crosscorre-
lation; Mental Task
It is no longer sufficient to consider gait as a mostly au-
tomatic motor activity, but rather one that requires the
integration of motor function with cognitive processes
such as attention, memory and planning. The evidence of
improvement in gait disturbance in Parkinson’s disease
patients after giving training in mental singing also sup-
ports this concept. A focus on high level gait performance
therefore requires a focus on cognition [1,2].
1.1. Dual Task Interference
Walking, Running, Swimming and other similar locomo-
tive activities involve gross motor skills and the coordi-
nation to perform this is gross motor coordination. Gross
motor coordination is left-right coordination, which re-
fers to the alternating left and right limb movement. The
basic neuronal circuits that generate this type of coordi-
nated activity are located in the spinal cord. Similar to
the lower limb there is left-right coordination in upper
limb as well e.g., playing piano, drumming. In walking
humans, arm to leg coordination is a well established
phenomenon. It could be derived from the intrinsic or-
ganization of the human CNS (central Nervous System),
but it could also consist of a movement induced epiphe-
nomenon [3]. Arm and hand movements are mainly con-
trolled by the motor cortical regions, whereas locomo-
tion is thought to be regulated mainly at brain-stem, spi-
nal, and cerebellar regions, with descending input from
the cortex. Gait consists of highly preprogrammed
movements, whereas some upper-extremity movements
are more novel and thought to require attention, visual
guidance, and somatosensory feedback to control their
performance [4]. Interference between cognitive tasks
and motor control activities such as gait is a problem in
neurological rehabilitation settings. Interference between
cognition and locomotor tasks may be important in as-
sessing a neurological patients’ ability to function inde-
pendently, and in designing therapies for both cognitive
and motor rehabilitation.
Figure 1. Cognitive aspects that affect knee joint motion.
D. Joshi et al. / J. Biomedical Science and Engineering 3 (2010) 322-326
Copyright © 2010 SciRes
Quantification of the extent of interference between
gait and cognitive tasks after brain injury has been re-
ported. The walking speed of Alzheimer’s disease pa-
tients slowed more than that of elderly subjects during
the dual task. This may contribute to the risk of falls [5,
6]. People with chronic stroke incidence cope well with
the challenges of varied environments and can maintain
their gait speed while performing a secondary task. De-
spite moderate levels of gait impairment, gait automatic-
ity may be restored over time to a functional level [7].
So many gait parameters has been studied for assessment
of dual task interference. A recent research shows the
gait parameters velocity, step time, swing time, and
stance time have a significant interaction between com-
plexity of mental task and articulation, with articulation
having a greater effect at higher levels of complexity [8].
Very few researchers have taken the kinematic variables
for the assessment of same. Knee joint has its leading
role in most of the locomotion like walking, running
squatting and sitting crossed leg (SCL). So knee angle
can be the most affected parameter while monitoring
dual task assessment. Figure 1 shows the knee joint
cognition aspects. Time histories of neuromuscular and
mechanical variables of human motion are often com-
pared by using discrete timing events (onset, offset, time
to peak, zero crossing, etc.). The determination of these
discrete timing points is often subjective and their inter-
pretation can cause confusion when attempting to com-
pare patterns [9].
1.2. Crosscorrelation
Keeping in mind the matching of pattern of knee angle
trajectories for various locomotion tasks has been moni-
tored to assess the effect on mental task on locomotion
activity. Crosscorrelation is a well-known and elegant
method of detecting common periodicities between two
signals of interest. Crosscorrelation is a measure of
similarity of two waveforms as a function of a time-lag
applied to one of them. For discrete functions, the
crosscorrelation is defined as:
 
m (1)
where f and g are two time series, having m samples
each. The n variable corresponds to the lag (in number
of samples) by which the time series is shifted. The
crosscorrelation gives an indication of pattern similarity
between the two sets of data. In that sense Crosscorrelation
is an objective means of pattern recognition and com-
parison. Crosscorrelation has been used to quantify co-
ordination between joints of the same and different limbs
during spontaneous kicking in 7 to 8 week old infants
[10]. Study has been conducted to compare EMG signals
from different walking trails, different test sessions, and
different individuals in able-bodies adults. The results
shows that crosscorrelation may be useful for evaluating
changes in an individual patient’s muscle activation pat-
terns [11]. Another potential application of crosscorrela-
tion was in monitoring the adaptations in interlimb and
intralimb coordination to asymmetric loading in human
walking. Changes in coordinative patterns were quanti-
fied utilization both crosscorrelation and root-mean-
square difference (RMS) measures. Crosscorrelation
measures were utilized to assess differences in the tem-
poral evolution between coordination patterns [12].
1.3. Cyclogram
A cyclogram is formed by ignoring the time axis angle
and directly plotting knee angle of one leg VS knee an-
gle of other leg (Figure 3). Cyclograms reflect the gait
kinematics during the total gait cycle which is different
from having other discrete measures such as the step
length, or walking speed, which are more common in
literature. The geometrical features of cyclogram have
been used to study the human walking in slope surface
[13]. Simple iterative algorithm has been proposed for
the computation of moments from a polygon approxima-
tion of the boundary, like in cyclogram. A discrete ver-
sion of Green’s theorem, which evaluates a double sum
over a two dimensional discrete object by a simple
summation along the discrete boundary of the object,
was implemented [14,15]. The cyclograms are readily
adaptable to clinical purposes by overlay of normal and
abnormal gait traces. In human the pattern is speed de-
pendent, highly predictable, and dramatically affected in
the case of gait abnormalities. Comparison between bi-
pedal and quadrupedal locomotion has been done by
cyclogram [16]. Neural network approach was used to
classify three gait patterns using the features of hip-knee
cyclogram. Three gait patterns were generated from
normal gait, a simulation of leg length difference, and a
simulation of leg weight difference [17]. Cyclogram is
also used for gait signature. If it is use as the signature in
gait recognition and verification, it could lead to an
automatic person recognition system using video footage
from security cameras. To compare the signatures be-
tween two gaits, the difference of shape and phase of the
cyclograms were calculated using the point projection
method and extreme points of curves [18].Hip range,
knee range, ratio of hip range/knee range, ratio of knee
range/hip range, area of cyclogram, circularity, eccen-
tricity, orientation, and cusp orientation [19]. No litera-
ture is available that reports use of cyclogram for as-
sessing the dual task interference. Authors used the pe-
rimeter of knee-knee cyclogram to see the eefect of
mental task on gait coordination. Further the results are
compared with the previous work of authors in which
the crosscorrelation between knee angles was used to
assess the effect of mental task on gait coordination [20].
324 D. Joshi et al. / J. Biomedical Science and Engineering 3 (2010) 322-326
Copyright © 2010 SciRes
ole in walking.
To compare the performance of both techniques the sen-
sitivity of both, for gait with mental task is calculated as
% sensitivity (CC) = {CCC (NW)-CCC (MT)}/CCC (NW)
% sensitivity (CP)) = {CP (NW)-CP (MT)}/CP (NW)} (3)
Where CCC- peak of crosscorrelation coefficient, CP-
Cyclogram Perimeter, NW-Normal Walk, MT-walking
with mental task, CC-Crosscorrelation.
Besides Crosscorrelation and Cyclogram, Artifical Neu-
ral Network (ANN) can be most powerful tool to evalu-
ate the coordination in different gait patterns [21,22].
Though ANN needs more computational power and is
quite complex to be calculated in comparision of Cross-
correlation and Cyclogram, in real time. So authors
compared the sensitivity of Crosscorrelation and cyclo-
gram for this study.
Six male healthy subjects (mean age=26 years, S.D.
=4.6years) without any history of lower extremity injury
participated voluntarily for the experiment. All of them
provided written consent to participate. Subjects were
educated enough to carry out the mental task exercise.
Data was collected in a 3 D motion analysis system us-
ing six CCD Cameras. EVA 7.0 and Orhtotrak 6.2 soft-
ware were used for data recording and gait analysis re-
spectively. Twenty five Cleveland markers were placed
on the subjects.
2.1. Experiment Protocol
Subjects were introduced to the various locomotive tasks
initially, except walking with a mental task. This was
done to avoid any biasing to the mental state while only
walking. Data recording began 2-3 minutes after the
subjects began walking. This was done to habituate the
subjects to maintain constant speed. This speed was pre-
ferred speed. Seven to eight trials were performed for
each locomotive task to get sufficient amount of data for
comparison and analysis. After completing all locomo-
tive tasks, they were asked to perform a mental task ex-
ercise along with walking. The mental task assigned to
them was naming of months from December to January.
Subjects were instructed not to skip any month in be-
tween and if they commit any mistake they should im-
prove it. Thus difficulty level of the task was maintained.
2.2. Data Collection
Data was collected at the sampling frequency of 120 Hz.
The time duration to record the data for every trial was 3
seconds, except walking with mental task. Therefore the
total sample for a trial was 360. While having mental
task the subjects was instructed to walk until they com-
plete it. Some of the trials were not included for analysis
as they were corrupted due to incomplete information or
noise. A low pass Butterworth filter with cut off of 6.0
Hz was used to remove the noise from data. The
Orthotrak software produced output in Excel format. The
data from Orthotrak was imported to Matlab 7.0 for
analysis. Out of 360 samples, data which completes a
gait cycle was taken for analysis i.e. heel strike to heel
strike. The data in different planes was analyzed. The
CCC between the knee angles was observed for every
trial in all the planes. The knee angle was considered
because the knee plays a leading r
2.3. Data Analysis
The maximum of CCC was calculated and noted down
for each trail. The CCC in the other two planes Frontal
and Transversal were also calculated. Figure 2.1 shows
the crosscorrelation coefficient profile for walking and
walking with mental task. The CCC in these planes var-
ied irregularly and was low too, thus, it was not possible
to reach a conclusion. Therefore their values were ig-
Figure 2 NW denotes Normal Walk and MT denotes walking
with mental task.
D. Joshi et al. / J. Biomedical Science and Engineering 3 (2010) 322-326
Copyright © 2010 SciRes
nored. The CCC was calculated using Eq. 1 where f and g
are left and right knee angle time series, respectively.
Cyclogram was drawn as right knee angle vs. left knee
angle. Figure 3 shows the cyclogram for while walking
and walking with mental task. There was a possibility to
synchronize both lower limb gait events, using the lag
where peak CCC exists, to draw cyclogram. This
was avoided to get any bias of CCC in cyclogram. Cyc-
logram perimeter is calculated from following Equation:
Li ={ (Ølk(i+1)- Ølk(i))2 + (Ørk(i+1)- Ørk(i))2}1/2 (4)
where Ølk represents the angle of left knee and Ørk
represents the angle of right knee. i represents a particu-
lar instant of time. gives the value of cyclo-
gram perimeter.
The cyclogram perimeter is the total distance travelled
in their respective joint spaces. Cyclogram area was not
taken into consideration as it is more sensitive to noise
comparative to perimeter.
010 20 3040 50 60 7080
Right Knee Angle
Left Knee Angle
010 20 30 40 50 60 70
Right Knee Angle
Left Knee Angle
Figure 3 NW denotes Normal Walk and MT denotes
walking with mental task.
3.1. Crosscorrelation
The CCC with walking is 0.78 (mean) SD = 0.03 which
significantly decreases to 0.62(mean) SD = 0.01. The
CCC in the other two planes Frontal and Transversal
were also calculated. The CCC in these planes varied
irregularly and was low too, thus, it was not possible to
reach a conclusion. Therefore their values were ignored.
3.2. Cyclogram Perimeter
Cyclogram perimeter decreases with mental task. The
normal walk knee-knee cyclogram perimeter matches
with the range of hip-knee cyclogram (212.8 degree) cal-
culated at 0 degree slope of walking [13]. The Cyclogram
perimeter with walking is 268.2 (mean) SD = 13.2 which
significantly decreases to 261.9 (mean) SD = 16.9.
In contrast to cyclogram perimeter, Crosscorrelation
shows higher sensitivity (mean=21.5 S.D. =2.8) towards
the mental task along with gait. The sensitivity calcu-
lated for cyclogram perimeter was mean=2.9 S.D. =1.5.
Methods have been proposed to assess mental task while
locomotion. CCC analysis in this research work shows
CCC as a good marker to assess mental state. CCC
decreases significantly as the walking goes along with
the mental task. The results also shows that CCC is
highly subjective but it follows the same decreases
pattern with mental task. Using Knee angle is more
direct measurement in comparision to EMG. Cross cor-
relation and Cyclogram are independent techniques.
Though both of them are well established technique to
quantify coordination, this study shows CCC is highly
sensitive to quantify the change in coordination of limbs,
while with mental task. This may be due to the fact that
in Crosscorrelation it is the strength of matching of sig-
nals to each other with respect to time irrespective of the
range the signal (knee angle) covers while in cyclogram
it is the sum of range covered by the knee angles trajec-
tories. In terms of implementation in real time in hard-
ware both are equal in terms of complexity. Finally, this
study involved a limited number of healthy subjects and
the level of education, of subjects, is not taken into
account. This work was performed in the 3 D motion
analysis lab, a portable , low cost embedded system can
be design to calculate CCC and cyclograms of knee
angles in the saggittal plane while walking and then can be
dedicated for the assesment/toughness of mental task only.
The authors highly acknowledge Director, Defence Institute of Physio-
logy and Allied Sciences (DIPAS) New Delhi for allowing the authors
to collect data. A sincere acknowledgement to both the subjects for
participating voluntarily.
326 D. Joshi et al. / J. Biomedical Science and Engineering 3 (2010) 322-326
Copyright © 2010 SciRes
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