Cyclogram and cross correlation: A comparative study to quantify gait coordination in mental state

doi:10.4236/jbise.2010.33044

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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/

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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: [email protected]

Received 19 December 2009; revised 28 December 2009; accepted 4 January 2010.

ABSTRACT

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

1. INTRODUCTION

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

323

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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:



 

**n

gfmgn









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

ole in walking.

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To compare the performance of both techniques the sen-

sitivity of both, for gait with mental task is calculated as

follows:

% sensitivity (CC) = {CCC (NW)-CCC (MT)}/CCC (NW)

(2)

% 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.

2. EXPERIMENTAL METHOD

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

325

)

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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.

L(Li





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. RESULTS

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.

4. DISCUSSION AND CONCLUSIONS

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.

(NW)

(MT)

5. ACKNOWLEDGEMENTS

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

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