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Engineering, 2012, 5, 11-15
doi:10.4236/eng.2012.410B004 Published Online October 2012 (http://www.SciRP.org/journal/eng)
Copyright © 2012 SciRes. ENG
Case Study on Assessment of Mild Traumatic Brain Injury
Using G ranular Computi ng
Melaku A. Bogale1, Huiying Yu1, Thompson Sarkodie-Gyan1, Murad Alaqtash1,
James Moody2, Richard Brower3
1Department of Electri cal an d Compu ter Engineering, Univ er sity of Texas at El Paso, El Paso, Texas, USA
2Men t is NeuroRehabili t atio n, El Paso , Texas, US A
3Department of Medi cal Educa tion, Texas Tech U niv ersity Health Sciences Cen ter, El Paso , Texas, US A
Patients with mild traumatic brain injury complain about having balance and stability problems despite normal clinical examination.
The objective of this study is to investigate the stride-to-stride gait variability of mTBI subjects while walking on treadmill under
dual-task gait protocols. Fuzzy-granular computing algorithm is used to objectively quantify the stride-to-stride variability of tem-
poral gait parameter s. The degrees o f similarity (DS) o f temporal gait p arameters in the dual tasks were det ermined from th e corres-
ponding granulated time-series. The mTBI grou p sho wed rel ativel y smaller d egree o f similari t y for all wind ow sizes un der th e cogni-
tive (dual) task walking, showing pronounced stride-to-stride variability. Different levels of DS among the mTBI subjects were ob-
served. Individually, both healthy and mTBI group showed different DS under the two dual-tasks, reflecting t he chall engin g level o f
the co gnit ive tasks whil e walkin g. The mean val ues of th e te mporal par ameters for t he mTBI gro u p wer e di fferen t fro m th e averaged
normal refer ence. On the o ther hand , the individual variance analysis sho ws no sign ificant d ifferen ces between the no rmal and dual
task values for some mTBI subjects. The granular approach however is able to reveal very fine differences and exhibited similar
trends for all mTBI subjects. Different DS values among mTBI group could be indicative for the different severity level or the un-
derg one re ha bilita t ion proc e s s.
Keywords: Fuzzy Granular Algorithms; Fuzzy-similarity; Stride-to-stride Variability ; Temporal Gait Variables; Dual-task Gait
Protocol; Mild Traumatic Brain Injury
Mild traumatic brain injury (mTBI) is one of the most common
neurological disorders . According to the Center for Dis-
ease Control (CDC) , 75 % of head injuries are mild trau-
matic brain injuries. Th e C D C acknowledged mTBI as a seri ous
public health problem in the United States in its 2003 report 
to the US congress. This report pointed out, mTBI is underes-
timated by the cu rrent “surveil lance metho ds” and some people
with mTBI show no sign of abnormalities under the clinical
diagnosis techniques and made recommendation for further
research and studies . Furthermore, research findings in two
studies [10,11] indicated that mTBI could be misdiagnosed and
altered cognitive and behavioral functions may still exist even
years after mTBI. Many peop le with mTBI su ffer from balan ce
and stability problems even though the clinical neuropsycho-
logical examinations show no sign of abnormality . Failure
of the clinical evaluation of mTBI in showing any clear mor-
phological brain effects was reported in  despite patients’
complaints about cognitive and emotional difficulties after they
were discharged from the hospital. Gaetz et al. reported the
insensitivity of the standard clinical EEG technique to most
brain functions change after mTBI .
Research studies [2,3,5,8,13,14,17,27,28] investigated into
possible gait alterations of people after mTBI. Body sway
measurements, under different visual inputs, while the subject
is standing, gathered from force plate were used to quantifying
balance and stability changes [2,14]. Motion capture systems
[3,8,13,14,27,28] were used to study gait dynamics among the
general TBI population.
Li-Shan et al  studied dynamic instability using obstacle
crossin g as a secondary task among the general traumatic brain
injury patients. Gait stability after concussion was investigated
using divided attention [27,28] among college athletes who
sustained Grade 2 concussion. In  10 college-age men and
women who suffered a concussion and 10 uninjured matched
control group performed dual task walking that consisted of
two trials of walking: Normal walking (undivided attention)
and walking while performing “mental-task”. These “mental-
tasks” were randomly selected from a set of three dual-tasks
comprising the spelling of a 5-letter word in reverse, subtrac-
tion by seven and reciting the month of the year in reverse or-
ders. The result of this study with respect to the spatial-temp o -
ral gait p arameters showed that a significant slower gait veloci-
ty, shorter stride-length, and longer stride-time during the
dual-task walking trials in both healthy and the concussed
group. However, the variation in stride-length and gait velocity
did not show significant difference between the concussed and
matched control group . In an effort to study the effect of
cognitive task on gait stability after concussion, Catena et al. 
performed single task level walking and walking while per-
forming cognitive tasks. They used the same cognitive tasks
M. A. BOGALE ET AL.
Copyright © 2012 SciRes. ENG
(recitin g th e mont hs o f th e year in r everse, su b tracti n g b y se ven
and spelling a five letter word in reverse) as Parker et al., 
in the first dual-task walking. The second dual-task walking
was reaction-time (RT) test, where subjects responded by
pressing a button when they heard an audible cue . A differ-
ence in spatial-temporal variables was reported in both healthy
and concussed groups. Both groups exhibited slower speed in
both dual tasks compared with the normal level walking. Long-
er stride-time was observed among the concussed group. A
significantly shorter stride-length and increased step width were
observed during the cognitive task walking compared to the
reaction-time test walking.
Differen t d ual -task gai t protocols were shown to discriminate
between able-bodied and mTBI groups [4,15,24,27,28]. How-
ever, the current research of mTBI in dual-task paradigm is
mostly focused on comparing the mean values of the spatial-
temporal parameters of normal group with mTB I gr oup [27,28 ].
For people with neurological disorders, gait analysis is used
to provide diagnosis, evaluation and treatment planning infor-
mation. The benefit of gait analysis is so well established that
it has now become a part of routine process in many rehabili ta-
tion centers [16,25]. Recognition and understanding of “nor-
mal” gait patterns and behavior are very important in the clini-
cal gait analysis process for the purposes of identification of
pathological gait. The observed or measured “normal” gait
patterns or parameters serve as a reference or standard against
which a p atholo gi cal gait can be compared.
Studying gait parameters over a gait cycle, particularly,
comparison of established reference patterns with that of the
neurological impaired subject’s data over a cycle [19,23] is a
common way of assessment and evaluation. However, wave-
form anal ysis and comparis on of averaged gait par ameters over
a gait cycle may not be sensitive enough to detect any subtle
variation or irregularity in mTBI subjects’ gait parameters.
We present a case s tudy for a possible application of granul ar
computing to accomplish the required local comparisons and
analysis. The purpose of this study is therefore to investigate
the effect o f a secondar y cognit ive task on stab ility of temporal
gait parameters using fuzzy information granulation. We spe-
cifically aim to compute the similarity of temporal gait para-
meters in the dual-task walking with that of the undivided at-
tention walking, individually by calculating degree of similarity
of each variable. A statistical variance analysis will also be
presented for comparison purposes. We hypothesize that mTBI
subjects would show more pronounced stride-to-stride vari abil-
ity under the dual task walking conditions, and hence smaller
degree of similarity and significantly different values from
normal walki ng parameters.
2. Fuzzy Granulation Algorithm
2.1. Information Granulation
Information granulation is an essential activity of human cogni-
tion, information processing and communication [18 - 20]. The
goal of information granulation is to better understand the
problem and transform it into more tractable smaller parts, so
that we have smaller sub problems with smaller computational
complexity . Information granules are established using set
theory, rough sets, fuzzy sets, and shadow sets, etc., . There
are essential two steps in the granulation process, namely, seg-
mentation and granular representation . In the first phase
we divide the original data into segments that retain the expe-
rimental nature of the data. In the second phase we create a
granular representation of each segment . These two phases
has competi ng goals, since we are t rying to acco mmodate more
informatio n fo r experi ment al rel evance an d at the same ti me we
de ma nd to be more specific in each information granule. Algo-
rithmic optimization  approach aims to compromise these
two conflicting goals.
2.2. Fuzzy-granulation Applied to Temporal Gait
Given the original 100-point stride-time, stance-time and
swi ng -ti me, ti me series dat a, th e goal of granu lat io n i s to divide
the given original data points into smaller segments and
represent each segment with a fuzzy membership function.
Before doing any granulation, normalization was performed to
min imize the effect of speed of walking  and individual dif-
ferences in temporal gait variables .The data were normalized
max( )min( )
where T0 is the original time-series d ata, max is maxi mu m, and
min is mi nimum.
We then divided the 100 cycles’ ti me series data in to several
equal parts of different window sizes. Window sizes (w = 2, 4,
5) were used so that the original time-series is divided into
segmen ts (gran ule) o f equal data po ints. Fi nally, a fuzzy tri angular
membership function was designed based on the methods outlined
[6,7] t o repr esent each gran ule. For each segment in the inter val
[a, b], the triangular membership function is established as
where m is the modal or core of the respective fuzzy set. The
median of each segment is taken as the modal value . To
obtain the parameters, a and b of each fuzzy set, the optimiza-
tion equation (3) was solved for each segment [1,6].
2.3. Granular Matrix and Calculation of Degree of
Next, we form the granular matrix,
information granule represented by
where p is the
number of segments . The degree of similarity (DS)  be-
tween two granulated time series
was calculated by
M. A. BOGALE ET AL.
Copyright © 2012 SciRes. E NG
DS G Hgh
and max(, )
gh isgh∨. The
DS is within a range between 0 and 1. DS value of zero signi-
fies no similarity at all and 1 represents 100 % similarity. A DS
value closer to 1 indicates higher degree of similarity and DS
values close to zero show little or no similarity.
3. Experimental Design and Methods
The institutional review board (IRB) of The University of Tex-
as at El Paso approved this study. Subjects obtained explana-
tions about the study and are asked to sign informed consent
prior to participation. Fifteen healthy male control subjects with
no history of gait abnormalities are recruited from the El Paso
community. Four male mTBI s ubjects are recr uited from a l ocal
NeuroRehabilitation center in El Paso. Reported loss of con-
sciousness for less than 30 minutes, post-traumatic amnesia les s
than 24 hours and post-concussive symptoms (dizziness, mem-
ory loss, headache, confusion) were used to diagnosis subjects
with mild traumatic brain injury.
3.2. Experimental Protocol
Both normal control and mTBI subjects performed treadmill
walking at their comfortable speed for three minutes under
three different conditions: 1) Undivided attention (refer as
Normal walking), 2) Walking while reciting the months of the
year in reverse order start ing from December (ref er as Dual task
1), and 3) Walking while subtracting by two starting from 299
(refer as Dual task 2.). These protocols are the standard in
mental status examinations [26,27].
3.3. Data Proc e ssing and Feature Extraction
A dual-belt instrumented treadmill (Bertec®, USA) was used to
measure th e groun d react ion forces (GR Fs) in three-d i me nsions.
The speed of the treadmill is controllable and can be set at the
subject’s comfortable speed. The force plates measure the
ground reaction forces in 3D at 100Hz sampling frequency.
Vertical GRF was filtered using a second order Butterworth
low pass filter with cut-off frequency of 20 Hz. The vertical
ground reaction force (vGRF) was used to define the gait cycles.
A gait cycle begins at the instant one-foot strikes or contacts the
ground and the instant when the same foot strikes the ground
again marks the end of the gait cycle. The stance phase covers
the duration from initial contact to toe-off and swing phase is
Figure 1. Sample granulated time-series.
defined from toe off to the next initial contact. The stride-time,
stance-time and swing-time for 100 gait cycles were extracted
for the three walking trial. The three walking trials temporal
variable were segmented into different window sizes. A trian-
gular fuzzy membership function was used to represent each
segment as described ab ove in equations 2a and 2b . The granu-
lar matrix for each walking set was then established from the
respective values o f a, m, and b d etermined from the optimiza-
tion equation. To study the effect of the cognitive task on
stride-to-stride variability of the temporal gait parameters we
calculat ed the degree of similari ty between th e granular matric-
es built from the data in the normal walking, with that of the
two dual tasks walking using equation (4). The reference degree
of similarity was built from the average of the 15 able-bodied
subj ects’ degree of similarities.
Figure 2 represents a sample granulated plot of stride time
shown for window size w =5, we have twenty segments of the
stride data each being represented by the respective triangular
fuzzy-m ember s hips f unc ti on pa r a m e t e rs a, m and b.
Table 1 shows th e calculated degrees of similarities of able-
bodied (reference) and the four-mTBI subjects (PM01, PM02,
PM03, PM04) for the three temporal variables (stride-time,
stance-time and swing-time). DS (N, D1) represents the DS of
normal walking temporal variable with that of walking with
dual task 1 (reciting month of the year backwards). Similarly,
DS (N, D2) stands for DS of normal walking temporal variable
with dual task 2 (counting backwards) walking. The DS values
for the three temporal parameters are relatively smaller than
unity in the two dual task walking for both able-bodied and
mTBI subj ects.
Figure 2. Original swing-time for mTBI subject PM03.
Tabl e 1. Mean values of temporal parameters.
M. A. BOGALE ET AL.
Copyright © 2012 SciRes. ENG
*No significant difference (p > 0.05) from the corresponding averaged control
group; †No significance difference (p > 0.05) from their respective individual
nor mal w alking val ues ; ††No significance difference (p > 0.1) from their respective
individual normal wa lking va lues.
Table 2. DS values for reference and mTBI subjects.
The calculated DS for stride-time, stance-time and swing-
time of the four-mTBI subjects are smaller than the DS of the
reference gro up for all window size consi dered. The t wo-mTBI
subjects (PM01 & PM04) relatively have a higher DS among
the mTBI group though smaller than the normal group for all
the tree temporal parameters (stride-time, stance-time and
swi ng -time). The one-way ANOVA comparison between nor-
mal walking and the two dual tasks for PM01 have p > 0.05
(Table 1), showing no difference at all. Also, the dual task 2
values of PM02 for stride-time and stance-time display no sig-
nificance d ifference fro m the cor responding normal values (p >
0.05), but the DS values are quite different form the reference
values. In this regard, the granular approach is shown to reveal
very small differences, that otherwise would have been im-
possible to pick up.
Both the reference and mTBI group have a higher degree o f
similarity in dual task 2 walking. The DS of swing-time for
PM02 and PM03 suffered a si gnificant d ecrease in th e two dual
task walking. These notable deviations are expected because
looking back at the original swing-time series data of PM03 in
the three trials (Figure 2), we observer different values and
hence little similarity.
In this research study dual-task gait (with cognitive tasks) pro-
tocols are proved to be able to discriminate able-bodied and
neurologically challenged mTBI group in agreement with pre-
vious research findings [15,27,28]. The proposed granular
computing approach was shown to provide a simple parameter
(DS) th at is capable o f revealing very fine individual differenc-
es that otherwise would have been very difficult to pick up
using the usual statistical variance analysis. This approach has a
greater advantage over the statistical averaging methods pre-
sented [4,15,27,28] because it furnishes a single individual
parameter that can be used to individually follow and evaluate
recovery process and outcome of an intervention. Our approach
can easily be integrated into a clinical setting with real-time
data processing. Particularly, this can be applied in sports
where ind ivid u al baselin e perfo rmances of ath let es on an y dual-
task gait protocol before a game could be collected and com-
pared with post-game performance. Likewise we can extend
this application to army soldiers where individual evaluation
can be do ne before and after dep loyment .
The authors would like to acknowledge the Computational
Science program of University of Texas at El Paso and the
Stern foundation for their financial support. These funds were
used to support a graduate student in this project. The authors
also would like to thank all subjects who participated in this
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