HEALTH, 20 09, 1, 35-38
Published Online June 2009 in SciRes. http://www.scirp.org/journal/health
Lempel-Ziv complexity changes and physiological mental
fatigue level during different mental fatigue state with
spontaneous EEG*
Lian-Yi Zhang1, Chong-Xun Zheng2
1Electronic Information School of Shanghai Dianji University, Shanghai, 200240, China; 2The Key Laboratory of Biomedical Infor-
mation Engineering of Ministry of Education, Xi’an Jiaotong University, Xi’an, 710049, China
Received 6 April 2009; revised 11 May 2009; accepted 15 May 2009.
ABSTRACT
The objective was to study changes in EEG
time-domain Kolmogorov complexity under
different mental fatigue state and to evaluate
mental fatigue using Lempel-Ziv complexity
analysis of spontaneous EEG in healthy human
subjects. EEG data for healthy subjects were
acquired using a net of 2 electrodes (Fp1 and
Fp2) at PM 4:00, AM 12:00 and AM 3:00 in the 24
hours sleep-deprived mental fatigue experiments.
It was presented that initial results for eight
subjects examined in three different mental fa-
tigue state with 2-channel EEG time-domain
Lempel-Ziv complexity computations. It was
found that the value of mean Lempel-Ziv com-
plexity corresponding to a special mental state
fluctuates within the special range and the value
of C(n) increases with mental fatigue increasing
for the total frequency spectrum. The result in-
dicates that the value of C(n) is strongly cor-
relative with the mental fatigue state. These re-
sults suggest that it may be possible to nonin-
vasively differentiate different mental fatigue
level according to the value of C(n) for particular
mental state from scalp spontaneous EEG data.
This method may be useful in further research
and efforts to evaluate mental fatigue level ob-
jectively. It may also provide a basis for the
study of effects of mental fatigue on central
neural system.
Keywor ds: Lempel-Ziv complexity; mental fatigue;
spontaneous EEG; circadiac rhythm
1. INTRODUCTION
Fatigue has been a recurrent topic in medicine and psy-
chology and has recently been attracting much attention.
Mental fatigue has been a recurrent topic in medicine
and psychology and has recently been attracting much
attention. Mental fatigue is a term to cover the deteriora-
tion of mental performance due to the proceeding exer-
cise of, mental or physical, activity [1]. Working on cog-
nitively demanding tasks for a considerable time often
leads to mental fatigue, which can impact task perform-
ance [2]. But the concept of fatigue does not have a clear
definition. Thus, prevalence data are always dependent
on the particular definition used in the particular paper
[3]. Edwards [4] defined fatigue as a “failure to maintain
the required or expected force”, whereas others [5] have
defined it as an inability to “continue working at a given
exercise intensity”. Gandevia [6] defined fatigue as an
exercise-induced loss of power-or force-generating ca-
pacity. The physiological definition of fatigue, which is
the inability to sustain a specified force output or work
rate during exercise, has often been termed “objective
fatigue” [7]. D. van der Linden et al [2] defined mental
fatigue as a change in psychophysiological state due to
sustained performance. This change in psychophysi-
ological state has subjective and objective manifestation,
which include an increased resistance against further
effort, an increased propensity towards less analytic in-
formation processing, and changes in mood. Sustained
performance, in this definition, does not necessarily in-
volve the same task but can extend over different tasks
that require mental effort, such as fatigue because of a
day in the office. Working on cognitive demanding tasks
for a considerable time often leads to mental fatigue,
which can impact behavior of mental task. In industry,
many incidents and accidents have been related to men-
tal fatigue. Therefore, in order to prevent or deal with
fatigue related errors it is important to understand the
nature of mental fatigue and its specific effects on be-
havior. The study was conducted to provide some addi-
tional insights into mental fatigue and its underlying
processes.
The work is supported by National Natural Science Foundation of China unde
r
grant No. 30670534.

36 L. Y. Zhang et al. / HEALTH 1 (2009) 35-38
SciRes Copyright © 2009 HEALTH
One of the interesting questions in mental fatigue re-
search is in what way cognitive control of behavior
changes under fatigue. Lorist [8] used behavioural and
EEG-data to study the effects of time-on-task (i.e., men-
tal fatigue) on planning and task switching. The EEG-
data of their study showed that with increasing time-
on-task there was a reduced involvement of those brain
areas that are associated with the exertion of executive
control (the frontal lobes). It was reported that subjects
protected their performance by spending more effort in
the unfavorable conditions: after several hours of work
and after continuous work without short rest breaks [1].
The most important change in performance reported by
many authors in relation to fatigue is the deterioration of
the organization of behavior [9,10]. But the ways of
evaluating mental fatigue now are based on a subjective
sensation rather than on an objective assessment of
changes in psychophysiological state, and it does not
allow for a clear discrimination between different levels
of mental fatigue.
The human brain is one of the most complex systems
encountered in nature. Electroencephalogram (EEG)
reflects the electrical activity of the central neural system
(CNS). Even when the EEGs are analyzed from healthy
individuals, they manifest chaos in the nervous systems
[2,8,9,10]. Although the EEG has limitations with re-
spect to its use as a method for three dimensional ana-
tomical localization of neurofunctional system, it has
clear advantages relative to other neuroimaging tech-
niques as a method for continuous monitoring of brain
function. It is known that the non-linear dynamic method
can explore the specific properties of a system. So there
may be some advantages to analyze EEG signals with
the nonlinear dynamic method.
Kolmogorov complexity is one of the nonlinear dy-
namic methods. Intuitively, the complexity of a symbolic
sequence reflects an ability to represent a sequence in a
compact form based on some structural features of this
sequence. To evaluate textual complexity, modifications
of the complexity measure by Lempel and Ziv [11,12,13]
have been developed. The general approach to estimat-
ing the complexity of symbolic sequences (texts) was
suggested by A. N. Kolmogorov [14]. He proved that
there exists an optimal algorithm or program for the text
generation. Lempel-Ziv complexity is the length of the
shortest code generating a given sequence. Lempel-Ziv
complexity is not a recursive function (i.e. it is not incor-
porated in a computational scheme). However, for a se-
quence of finite length, various constructive realizations
of non-optimal coding have been developed [14], includ-
ing applications for DNA analysis [11,12,13]. In this paper,
the relationship between Lempel-Ziv complexity and dif-
ferent mental fatigue states was investigated.
The aim of this paper was to establish an EEG-based,
noninvasive mental fatigue test and to investigate
whether mental fatigue could be assessed using Lem-
pel-Ziv complexity measure. Here we present initial re-
sults for eight subjects examined in three different men-
tal fatigue state with 2-channel EEG time-domain Lem-
pel-Ziv complexity computations. It was found that the
value of mean Lempel-Ziv complexity corresponding to
a special mental state fluctuates within the special range
and the value of C(n) increases with mental fatigue in-
creasing for the total frequency spectrum.
The rest of the paper is organized as follows. Section 2
explains the methods and algoriyhms proposed in this
paper. Mental fatigue experiments are given in Section 3.
Section 4 is the results. Discussions and conclusiona are
given in Section 5.
2. METHODS AND ALGORITHM
Lempel and Ziv proposed measuring the complexity of a
sequence by the number of steps in the generating proc-
ess [14]. The permitted operations here are generation of
a new symbol (this operation is necessary at least to
synthesize the alphabet symbols) and direct copying of a
fragment from the already generated part of the text.
Copying implies the search for a prototype (i.e. repeat in
a common sense) in the text and extension of the text by
attaching the ‘prepared’ block. c(n) and C(n) both are
Lempel-Ziv complexity. The C(n) is the normalized
Lempel-Ziv complexity which does not depend on the
length of the sequence when n is large.
The properties of C(n) for different types of dynamics
are: C(n)=0 implies an ordered system, C(n)=1 corre-
sponds to a totally stochastic situation. The higher the
C(n), the closer to a stochastic the system is. So the
small value of C(n) corresponds to the light mental fa-
tigue.
3. MENTAL FATIGUE EXPERIMENTS
EEG data were acquired during the task using a net of 26
electrodes. The electrodes were placed at Fp1, Fp2 ref-
erence to the 10-20 system to record the EEG data in the
experiments. Recordings were made with reference elec-
trode that was pasted to the skin just above the tuber of
the clavicle at the right bottom of the Adam's apple by
using a high-pass filter of 0.1 Hz and a low-pass fillter of
100 Hz. Figure 1 shows the placement of electrodes.
The impedances of all electrodes were kept below 5 KΩ.
The EEG was acquired using a PL-EEG Wavepoint sys-
tem and were sampled at about 6 ms’ interval. The sig-
nals were recorded for 5 minutes during the task.
Eight subjects were chosen for the 24 hours sleep- de-
prived mental fatigue experiments. They were both male
and right-handed college students. The work time periods
of the college are am 9:00~12:00 and pm 1:00~5:00. All
subjects had their normal studing life before the 24 hour
experient and the subject was isolated in the experiment.
All subjects did not sleep in the afternoon usually.

L. Y. Zhang et al. / HEALTH 1 (2009) 35-38 37
SciRes Copyright © 2009
HEALTH
Figure 1. Electrode placement.
The experimental environment was quiet and the tem-
perature of it was around 20C°. The subjects were seated
in a comfortable chair throughout the experiment. The
subjects were asked to simply relax and try to think of
nothing in particular.
The light was on during the experiment. The duration
of each state was about 5 minutes and the subject’s eyes
were closed.
State 1: The duration of the experiment time: PM
4:00-4:05.
State 2: The duration of the experiment time: AM
12:00-12:05.
State 3: The duration of the experiment time: AM
3:00-3:05.
Alterations in a person’s state of mind are associated
with physiological alterations at the neuronal level and
sometimes also at the regional brain level [2]. Function-
ally, central neural system circuitry is complex, consist-
ing of a number of afferent connections, efferent con-
nections and loop (‘feedback’) connections [8]. Two
distinct loops, a motor loop and an association or com-
plex loop, connect basal ganglia with neocortex [9]. The
second loop (the association or complex loop) connected
caudate with inputs from the cortical association areas and
the final output from basal ganglia is projected to the pre-
frontal cortex. Recent findings have provided considerable
evidence that cortex, basal ganglia and thalamus are all
linked by the re-entrant circuits [10]. Prefrontal cortex was
chosen to place the electrodes. FP1 and FP2 two channels
were chosen to record the EEG data. Electrode placement
was shown as Figure 1.
4. RESULTS
In order to obtain the data of spontaneous EEG signals, a
FIR filter with bandpass 0.5-30 Hz was used. For dif-
ferent sleep-deprived states, the data of two channels
(Fp1 and Fp2) corresponding period during experiment
was analyzed randomly. The time length of data to be
analyzed was 15 seconds. Kolmogorov complexities of
14 continuous but not overlapped period were calculated
respectively. The average Kolmogorov complexity under
three different fatigue states was shown in Table 1. The
results of multiple comparisons were shown in Table 2.
Table 1. Average Kolmogorov complexity under three differ-
ent fatigue states.
State 1 State 2 State 3
Fatigue statePM 4:00-4:05AM 12:00-12:05 AM 3:00-3:05
average C(n)0.1895 0.2569 0.2168
Fp1 Fp2
Table 2. q test of multiple comparisons.
CZ
Compare group q (q test) P (probability)
State 1 and State 2 q(26,2)=8.44 P<0.01
State 1 and State 3 q(26,3)=14.18 P<0.01
State 2 and State 3 q(26,2)=5.74 P<0.01
The results of statistical analysis show that the three
state of mental fatigue have significant differences (F2,
26=50.8927, P<0.01) in general and each state is sig-
nificantly different from the others. The multiple com-
parisons showed that sleep may have important influ-
ence on Lempel-Ziv complexity or physiologic mental
fatigue.
The average of Fp1 and Fp2 channels corresponding
to different mental fatigue states changed over time and
it was shown in Figure 2. From Figure 2, it can also be
seen that the value of mean Lempel-Ziv complexity cor-
responding to a special sleep-deprived state fluctuates
within the special range.
5. DISCUSSIONS AND CONCLUSIONS
Human brain is not a stochastic system. C(n)=1 corre-
sponds to a totally stochastic situation. The higher the
C(n), the closer to a stochastic the system is. So the
small value of C(n) corresponds to the light mental fa-
tigue. The work time periods of the college being AM
9:00~12:00 and PM 1:00~5:00, so the cardiac rhythm of
the college students corresponds with the work time in
day. For most college students, their circadiac rhythms
are almost the same.
C(n)
Time: second(1:15)
Figure 2. Change of KC over time under different mental
fatigue states.

38 L. Y. Zhang et al. / HEALTH 1 (2009) 35-38
SciRes Copyright © 2009
In Figure 2, the value of C(n) under state 2 (AM.
12:00~PM. 12:05) was the largest and the one under
state 1 was the smallest. It indicates that, compared with
AM. 12:00 or Am. 3:00, college students are more vig-
orous at PM. 4:00. This is consistent with the fact. At
PM 4:00, being in work time of college, study effi-
ciency is higher than in night. It is a normal state that
the value of C(n) under state 1 (PM. 4:00~PM. 4:05)
was the smallest during all 3 different states. Generally,
college students become sober in night and it is well-
known that one is deadly sleepy at midnight and at
dawn. Therefore, the value of C(n) under state 2 (AM.
12:00~AM. 12:05) was larger than the one under state 3
(AM. 3:00~3:05).
HEALTH
In this experiment, the statistical analysis in Section 4
show that the three state of mental fatigue have signifi-
cant differences (F2,26=50.8927, P<0.01) in general and
each state is significantly different from the others.
Therefore, the following conclusions can be educed:
1) The value of C(n) is strongly correlative with the
mental fatigue state. The value of mean Lempel-Ziv
complexity corresponding to a special mental state fluc-
tuates within the special range.
2) The value of C(n) increases with mental fatigue in-
creasing.
3) It may be possible to differentiate different mental
fatigue level according to the value of KC. This method
may be useful in further research and efforts to evaluate
mental fatigue level objectively. It may also provide a
basis for the study of effects of mental fatigue on central
neural system.
Fatigue is likely to be an integrated phenomenon with
complex interaction among central and peripheral factors,
physiological and psychological factors, and so on. All
factors appear to mutually influence each other. The
method proposed in this paper includes only two EEG
channels of one cortical region and one parameter. For
those that mental states are very close according to time
or mental fatigue level, it may be difficult to differentiate
them by the method proposed in this paper.
Our results suggest that the value of mean Lempel-Ziv
complexity corresponding to a special mental state fluc-
tuates within the special range and the value of KC in-
creases with mental fatigue increasing. The results re-
ported here do not replace the results obtained with the
traditional test and other techniques, but supplement
them. In summary, these results suggest that it may be
possible to noninvasively detect, and even eventually
distinguish different level of mental fatigue from scalp
EEG data. This could be very helpful for safety in pro-
duction. These findings are preliminary and need to be
further studied in a large population base.
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