Mutual Information between EDA and EEG in Multiple Cognitive Tasks and Sleep Deprivation Conditions

Abstract

Sleep deprivation, a widespread phenomenon that affects one-third of normal American adults, induces adverse changes in physical and cognitive performance, which in turn increases the occurrence of accidents. Sleep deprivation is known to increase resting blood pressure and decrease muscle sympathetic nerve activity. Monitoring changes in the interplay between the central and autonomic sympathetic nervous system can be a potential indicator of human’s readiness to perform tasks that involve a certain level of cognitive load (e.g., driving). The electroencephalogram (EEG) is the standard to assess the brain’s activity. The electrodermal activity (EDA) is a reflection of the general state of arousal regulated by the activation of the sympathetic nervous system through sweat gland stimulation. In this work, we calculated the mutual information between EDA and EEG recordings in order to consider linear and non-linear interactions and provide an insight of the relationship between brain activity and peripheral autonomic sympathetic activity. We analyzed EEG and EDA data from ten participants performing four cognitive tasks every two hours during 24 h (12 trials). We decomposed EEG data into delta, theta, alpha, beta, and gamma spectral components, and EDA into tonic and phasic components. The results demonstrate high values of mutual information between the EDA and delta component of EEG, mainly in working memory tasks. Additionally, we found an increase in the theta component of EEG in the presence of fatigue caused by sleep deprivation, the alpha component in tasks demanding inhibition and attention, and the delta component in working memory tasks. In terms of the location of brain activity, most of the tasks report high mutual information in frontal regions in the initial trials, with a trend to decrease and become uniform for all the nine analyzed EEG channels as a consequence of the sleep deprivation effect. Our results evidence the interplay between central and sympathetic nervous activity and can be used to mitigate the consequences of sleep deprivation.

Full text

Citation: Martínez Vásquez, D.A.;
Posada-Quintero, H.F.; Rivera Pinzón,
D.M. Mutual Information between
EDA and EEG in Multiple Cognitive
Tasks and Sleep Deprivation
Conditions. Behav. Sci. 2023,13, 707.
https://doi.org/10.3390/bs13090707
Academic Editors: Paul E Rapp and
Michele Roccella
Received: 30 June 2023
Revised: 5 August 2023
Accepted: 22 August 2023
Published: 25 August 2023
Copyright: © 2023 by the authors.
Licensee MDPI, Basel, Switzerland.
This article is an open access article
distributed under the terms and
conditions of the Creative Commons
Attribution (CC BY) license (https://
creativecommons.org/licenses/by/
4.0/).
behavioral
sciences
Article
Mutual Information between EDA and EEG in Multiple
Cognitive Tasks and Sleep Deprivation Conditions
David Alejandro Martínez Vásquez 1,2, * , Hugo F. Posada-Quintero 3and Diego Mauricio Rivera Pinzón 2
1Electronic Engineering Faculty, Universidad Santo Tomás, Bogotá 110231, Colombia
2Department of Technology, Universidad Pedagógica Nacional, Bogotá 110221, Colombia;
dmrivera@pedagogica.edu.co
3Department of Biomedical Engineering, Connecticut University, Storrs, CT 06269, USA;
hugo.posada-quintero@uconn.edu
*Correspondence: damartinezv@upn.edu.co or davidmartinez@usta.edu.co
Abstract:
Sleep deprivation, a widespread phenomenon that affects one-third of normal American
adults, induces adverse changes in physical and cognitive performance, which in turn increases the
occurrence of accidents. Sleep deprivation is known to increase resting blood pressure and decrease
muscle sympathetic nerve activity. Monitoring changes in the interplay between the central and
autonomic sympathetic nervous system can be a potential indicator of human’s readiness to perform
tasks that involve a certain level of cognitive load (e.g., driving). The electroencephalogram (EEG)
is the standard to assess the brain’s activity. The electrodermal activity (EDA) is a reflection of
the general state of arousal regulated by the activation of the sympathetic nervous system through
sweat gland stimulation. In this work, we calculated the mutual information between EDA and
EEG recordings in order to consider linear and non-linear interactions and provide an insight of the
relationship between brain activity and peripheral autonomic sympathetic activity. We analyzed
EEG and EDA data from ten participants performing four cognitive tasks every two hours during
24 h (12 trials). We decomposed EEG data into delta, theta, alpha, beta, and gamma spectral
components, and EDA into tonic and phasic components. The results demonstrate high values of
mutual information between the EDA and delta component of EEG, mainly in working memory
tasks. Additionally, we found an increase in the theta component of EEG in the presence of fatigue
caused by sleep deprivation, the alpha component in tasks demanding inhibition and attention, and
the delta component in working memory tasks. In terms of the location of brain activity, most of the
tasks report high mutual information in frontal regions in the initial trials, with a trend to decrease
and become uniform for all the nine analyzed EEG channels as a consequence of the sleep deprivation
effect. Our results evidence the interplay between central and sympathetic nervous activity and can
be used to mitigate the consequences of sleep deprivation.
Keywords:
EEG (electroencephalography); EDA (electrodermal activity); ECG (electrocardiography);
HRV (heart rate variability); information theory; mutual information; sleep deprivation
1. Introduction
Human brain activity has been widely studied through the effects that determine
cognitive tasks produced in electroencephalography (EEG) signals, specifically in alpha,
beta, delta, theta and gamma oscillations. In this regard, tasks requiring the storing and ma-
nipulation of information, commonly known as working memory tasks, have demonstrated
an increase in delta oscillations associated to the concentration that individuals require to
perform them [
1
]. On the other hand, tasks demanding timing and inhibition, in which
individuals perceive visual or auditory stimuli and react in an inhibitory or encouraged
form, have been associated to the power increase in alpha waves [
2
], which, according
to [
3
], tend to diminish with drowsiness and sleep. In contrast, the power increase in theta
Behav. Sci. 2023,13, 707. https://doi.org/10.3390/bs13090707 https://www.mdpi.com/journal/behavsci

Behav. Sci. 2023,13, 707 2 of 18
waves has been related to the fatigue increment caused by sleep deprivation when tasks
requiring attention and reaction times are performed [
4
,
5
], which demonstrates that these
kinds of oscillations are useful to determine tiredness conditions that could be dangerous
in occupational contexts demanding rapid response times such as military, health care, and
others that in addition, require long periods of concentration or nocturnal activity. The
effects of sleep deprivation have also been studied through many approaches that use, in
most of the cases, tasks involving attention and vigilance to analyze the EEG components
directly [
6
,
7
]. In addition, the relationship between EEG bands and EDA components
is studied in some approaches to find correlations between phasic and theta waves and
determine connections between brain activity and sympathetic arousal [
8
]. The relation-
ship between EDA and HRV is also considered to find correlations between peripheral
sympathetic arousal and deterioration in cognitive abilities [
9
], or to identify risks due to
attention failure in individuals [
10
]. Signals’ interaction has not only been used for sleep
deprivation analysis, but also in other medical contexts such as the adolescent attention
deficit hyperactivity disorder described in [
11
], where a negative correlation between theta
and EDA, particularly for non-specific skin conductance responses (NS.SCRs), is identified
in attention deficit hyperactivity disorder patients. A high correlation between EDA, specif-
ically the skin conductance level (SCL, also known as tonic component) and the EEG alpha
and beta bands, is found in [
12
]. This result is introduced in a substantive relationship
between cerebral function and autonomic arousal. A similar study, but this time including
a combination of ECG, EDA and EEG signals, was conducted in [
13
], providing some
evidence on the benefits of Tibetan Singing Bowls in metastatic cancer patients. The previ-
ously mentioned works have put special interest in the EDA signal, considered an index of
autonomic sympathetic activity [
8
], and its relationship with brain and heart activities in
order to identify cognition stress and emotional or mental states when individuals cannot
self-report them [14].
Statistically, these signal relationships are commonly measured using tools such as
ANOVA, Pearson’s correlation coefficient, Friedman test and Spearman correlation, among
others that, in spite of their relevance, are limited to the linear scope, i.e., they are focused on
determining how a variable increases or decreases in the function of the other, which could
lead us to ignore relevant information hidden in the non-linearities. An important tool to
face this problem is the information theory, which, through the mutual information concept,
can identify how much information a signal provides about another, considering both
linear and non-linear interactions [
15
]. In this regard, we calculate the mutual information
between EEG and EDA to provide new insights about the connection between brain activity
and the autonomic sympathetic activity in different cognitive contexts that, to the best of
our knowledge, have been widely studied in only linear interaction analyses.
This paper is divided as follows. Section 2.1 describes the main concepts related to
information theory, EDA and EEG signals and the tasks used in this analysis. Section 2
describes the implemented methods to collect the EDA and EEG information, and the form
in which mutual information is calculated. Section 3describes the simulation results that
we finally analyze in Sections 4and 6.
2. Materials and Methods
In this study, whose protocol was approved by the Institutional Review Board of
The University of Connecticut, ten healthy (without sleep disorders) volunteers (7 male)
between the ages of 25–35 were involved. The participants had to perform the tasks
described in Section 2.2 every two hours during a 25 h time period.
Data acquisition started at 10 a.m., with EAT being the first executed task, followed
by the ship search, N-Back, and PVT tasks. The analyzed data for each case included the
EEG signals, covering the five frequency bands, as well as the EDA signal and including its
phasic and tonic components. Additionally, ECG signals were collected during each trial
to analyze the effect of sleep deprivation in HRV. More details in this regard are given in
Section 2.3. All participants were requested to reach the experimental site within two hours

Behav. Sci. 2023,13, 707 3 of 18
after waking up, and they had to fill a questionnaire to confirm the quality and amount of
the sleep they had before the experiment. During the study, an HP 78354A ECG monitor
manufactured by Hewlett–Packard, Palo Alto, CA, USA, was employed to gather ECG data,
while a galvanic skin response amplifier, specifically the FE116 model from ADinstruments,
Colorado Springs, CO, USA, was utilized to collect EDA (Electrodermal Activity) data.
Prior to each EDA recording trial, the device was calibrated to zero. To gather the EEG
signal, we used an actiCHamp amplifier (Brain Products GmbH, Gilching, Germany) with
an EasyCap electrode system (EasyCap GmbH, Herrsching-Breitbrunn, Germany).
2.1. Preliminaries
2.1.1. Information Theory
One of the essential concepts in information theory is the entropy, which determines
the uncertainty level of a random variable
X
from its probability distribution
p(x)
. Mathe-
matically, entropy is given by
H(X) = −∑
x∈X
p(x)log p(x) [bits], (1)
where
p(x) = Pr{X=x}
,
x∈ X
, with
X
as the alphabet of
X
. The maximum entropy of
X
occurs when each
x∈ X
has the same probability, and it is reduced when prior probability
information is given [16].
The entropy concept can be extended to multiple random variables, which let us
define joint entropy and conditional entropy for dependent variables. In this sense, the
joint entropy of Xand Yis described as
H(X,Y) = −∑
x∈X
∑
y∈Y
p(x,y)log p(x,y)
=H(X) + H(Y|X).
(2)
An explicit relationship between the entropy measures is shown in the Venn diagram
of Figure 1. Observe how, in addition to the joint, conditional and independent entropies,
we have a new measure given by the intersection between
H(X)
and
H(Y)
, which is known
as the mutual information and represents the information that any random variable has
about the other, in other words, it describes the uncertainty reduction about a random
variable for having information about the other. This is described by the expression
I(X;Y) = ∑
x∈X
∑
y∈Y
p(x,y)p(x)log p(x,y)
p(x)p(y)
=H(X)−H(X|Y).
(3)
Mutual information has gained special attention in recent years in areas such as
multi-agent systems [
17
], coverage control [
18
,
19
], distributed control in micro-grids [
20
],
and neuroscience [
15
,
21
] due to its capability to analyze relationships between data from
different contexts (e.g., voltage values, stimulus light position, animal position), the ability
to detect linear and nonlinear interactions, and its usage in multivariate systems.
2.1.2. Electrodermal Activity (EDA)
Electrodermal Activity (EDA) is the acronym used to describe the change in skin
conductance that reflects the sympathetic nerve activity on sweat glands. This is composed
mainly by the tonic component (also known as Skin Conductance Level: SCL) and the
phasic component (also known as Skin Conductance Response: SCR). The tonic component
(SCL) refers to the long-term fluctuations in the EDA signal that are not related to partic-
ular external stimulus, but to particular individual emotions, thoughts or electro-dermal
instability. On the other hand, the phasic component (SCR) is associated to the response
of particular external stimulus such as complex cognitive tasks, association between loud

Behav. Sci. 2023,13, 707 4 of 18
tones, images or shapes with threatening events, among others, that are applied to indi-
viduals at determined time intervals within 1–5 s [
22
,
23
]. The responses associated to this
kind of stimulus are commonly known as Event-Related SCR (ER-SCR), whereas those
responses without any determined cause are known as Non-Specific SCR (NS-SCR) [
24
]. In
this study, the phasic component has a special importance due to its high relationship with
the EEG signals, in particular with the delta component, as we will show in Section 3.
H(X,Y)
H(X)H(Y)
H(X|Y)H(Y|X)
I(X;Y)
Figure 1. Information theory measures.
2.1.3. EEG Signals
Electroencephalography (EEG) reflects the electrical activity of the brain caused by
the synchronized activity of thousands of neurons. Typically, the EEG signal is divided
in
alpha (α),
beta (
β
), theta (
θ
), gamma (
γ
), and delta (
δ
) waves, which have different
frequencies and amplitudes. Commonly, high frequency and low amplitude waves
(>7 Hz)
such as alpha, beta and gamma are related to the high brain activity or awake state of a
person. Alpha waves, with the lowest frequency range (7–12 Hz) for an awake person,
are associated to relaxation states, presenting amplitude increments when the eyes are
closed. Beta waves (12–30 Hz) have the highest frequency and lowest amplitude in awake
state. The beta amplitudes increase when a person plans or execute movements in any
body part or when the person observes someone doing any movement (mirror neuron
system) [
25
,
26
]. Gamma waves are related to rapid eye movements (micro-saccades) which
have been associated to information uptake [
27
], learning, and memory. On the other
hand, we find theta and delta waves, which commonly are classified as low frequency EEG
waves (
<
7 Hz). Theta waves (4–7 Hz) with high amplitudes are correlated with difficult
cognitive tasks and memorization, whereas those with low amplitudes are associated to
a lack of alertness and presence of drowsiness [
5
]. Delta waves (1–4 Hz) have typically
been correlated to deep sleep conditions. However, some results have demonstrated that
these kinds of waves are also associated to memory tasks requiring high concentration
levels [1,28].
2.2. Performed Tasks
2.2.1. EAT (Error Awareness Task)
This task takes 5 min. During this time, a sequence of images with the name of colors
written in colored letters are presented. Each image is visible during 900 ms and the interval
between two different images is 600 ms. Participants have to press a button
(‘Go’ trials)
when the color of the letters and the word match (e.g., the word Green appears with
green letters). On the other hand, when the color of the letters does not match with the
word or when the same word appears in two consecutive trials, the participant avoids
pressing the button (‘No Go’ trials) [
9
,
29
]. The two ‘No Go’ trials allow the participants to
be more attentive than repetitive, especially in the second case, in which, according to [
30
],
individuals are submitted to a stressful situation that increases the alertness condition.
2.2.2. N-Back
This is a memory task that takes 10 min. In this case, tones with different frequencies
and duration, normally separated by 3 s, are played through two speakers located in front

Behav. Sci. 2023,13, 707 5 of 18
of the participant. Using pre-determined keyboard computer keys, the user has to identify
whether a tone is identical to the n-previous one or not. The number of the n different tones
between two similar ones is incremented or decremented depending on the participant
performance. The use of tones (auditory stimulus) can be combined with visual stimuli,
which are presented simultaneously to increase the complexity [
31
]. This task is considered
as a highly demanding working memory task [32].
2.2.3. Ship Search
This is a task with 20 min of duration in which the participants are asked to identify the
moment (using the space bar) and position (specifying the coordinates verbally) of a ship’s
appearance in an interactive screen that simulates the water view from a periscope [
31
].
This kind of task is used to analyze the spatial and temporal awareness of individuals.
2.2.4. PVT (Psycho-Motor Vigilance Task)
In this task, which takes 10 min, participants are asked to click, as soon as possible,
the left mouse button when they observe a number on the screen that appears in intervals
between 2 and 10 s. The PVT task is performed by every participant in the same computer
and using the freely available software proposed in [
33
,
34
]. This task has been widely used
to analyze the degradation of attention under sleep deprivation, measuring the reaction
time (RT) to repetitive stimuli.
2.3. EEG and EDA Data Processing
EEG and EDA devices were connected to each participant five minutes before the test.
For the EEG case, a cap with ten electrodes was attached to the individual’s head, two
used as reference and located on the ears, and the other nine in frontal (F), frontal-polar
(Fp), temporal (T), parietal (P), and occipital (O) positions to capture the EEG channels
Fp2
,
F7
,
F8
,
O1
,
Oz
,
Pz
,
O2
,
T7
and
T8
, as shown in Figure 2. EEG signals were sampled to
200 Hz and filtered between 0.5 and 50 Hz. For the EEG electrodes, their impedance is
assured to be lower than 5 K
Ω
for a good contact with the scalp, and their conductance is
increased by means of an electrode gel.
Figure 2. EEG channels.
The five EEG bands shown in Figure 3were obtained using FIR filters designed using
the Parks–McClellan optimal equiripple approach.
Figure 3. EEG signals.

Behav. Sci. 2023,13, 707 6 of 18
On the other hand, the EDA signal was obtained using stainless steel electrodes placed
on the middle and index fingers of each individual’s non-dominant hand. This signal was
decomposed in tonic and phasic components using the convex optimization approach
proposed in [35]. The results for an individual executing EAT are shown in Figure 4.
0 50 100 150 200 250 300 350
-5
0
5
S
EDA
0 50 100 150 200 250 300 350
-5
0
5
S
Tonic component
0 50 100 150 200 250 300 350
Time (s)
-1
0
1
S
Phasic component
Figure 4. EDA and its components, Tonic and Phasic.
2.4. Mutual Information Between EDA and EEG
In order to obtain the probability distributions required for the information theory
analysis, we discretized the EDA and EEG signals using a uniform count binning process
to maximize the entropy and therefore the available information between the studied
signals (e.g., the mutual information between the EEG and phasic EDA component), avoid-
ing probability distribution assumptions. In this sense, by means of the Neuroscience
Information Theory Toolbox proposed in [
15
], we defined 12 uniform count bins or states
within which the continuous signal values for EDA and EGG were assigned (the value
of 12 for the uniform count bins was experimentally chosen between multiple tests. This
value offers the best trade between computational requirements (especially simulation
time) and acceptable values of entropy and mutual information). This process is described
in Figure 5for the phasic and delta components of EDA and EEG signals, respectively.
Observe how, due to the data density differences, some bins were narrower than others
in spite of having the same number of observations (2000 observations for each bin). The
entropy maximization generates a uniform probability distribution for each state, which is
calculated with the expression
p(s) = N(s)
Nobs
, (4)
where
N(s)
is the number of observations classified in a specific bin, and
Nobs
is the total
number of observations. In our case, the probability for each state belonging to any EDA
or EEG component is
=2000
12(2000)=
0.0833. The joint probability distribution, necessary
to calculate the mutual information, was obtained through the cumulative number of
times that data within two bins of two different signals appear at the same time. This
is described in Tables 1and 2for the case of the phasic component of the EDA signal
and the delta component of the EEG signal. Table 1shows the cumulative number of
times that data belonging to any bin of the phasic component and data belonging to
any bin of the delta component appear together. On the other hand, Table 2shows the
corresponding joint probability distribution calculated from the cumulative data. Observe
how the highest probability values corresponded to the highest cumulative values. Once
the joint distribution was obtained, we could apply (3) to obtain the mutual information
between all the EEG components and the phasic and tonic EDA components. The results,
shown in Section 3, demonstrate that the highest level of mutual information occurs
between the EDA signal and delta EEG component.

Behav. Sci. 2023,13, 707 7 of 18
Table 1. Cumulative number for δand phasic bins.
δBins
1 2 3 4 5 . 12
Phasic bins
1 64 118 322 254 407 . 97
2 98 416 201 84 169 . 282
3 99 250 105 132 177 . 139
4 81 224 102 32 97 . 94
5 0 60 119 117 216 . 114
........
12 1219 250 116 105 75 . 0
Table 2. Joint probability distribution between phasic and δbins.
δBins
1 2 3 4 5 . 12
Phasic bins
1 0.0027 0.0049 0.0134 0.0106 0.0170 . 0.0040
2 0.0041 0.0173 0.0084 0.0035 0.0070 . 0.0117
3 0.0041 0.0104 0.0044 0.0055 0.0074 . 0.0058
4 0.0034 0.0093 0.0042 0.0013 0.0040 . 0.0039
5 0 0.0025 0.0050 0.0049 0.0090 . 0.0047
........
12 0.0508 0.0104 0.0048 0.0044 0.0031 . 0
0.004 0.114 0.257 0.729 1.095
(a) Phasic component.
-79.1 -44.4 -16.5 1 14.5 35.6 50.1
(b) δcomponent.
Figure 5.
Binning process for phasic (
a
) and
δ
(
b
) components. Above are the 12 bins with their
corresponding sizes and value limits. Below is the data (2000 observations) distribution within
each bin.
3. Results
As we have mentioned, the mutual information was calculated between the EDA
components (phasic and tonic), and all the five components of EEG (
α
,
β
,
θ
,
δ
,
γ
). Addi-
tionally, we calculated this measure for all the EEG channels considered in this study
(
Fp2
,
F7
,
F8
,
O1
,
Oz
,
Pz
,
O2
,
T7
,
T8
), and for all the tasks described in Section 2.2. Initially,
we calculated the mutual information between EDA signal and EEG components, whose
results are shown in Table 3. In this case, the cumulative mutual information value was
taken for the 12 trials of participant 10 executing the N-Back task. Notice that the EDA
signal exhibited the highest mutual information value with respect to the delta component,
whereas it was at the minimum for the gamma component. This result was the same when
we decomposed the EDA signal in phasic and tonic components, as depicted in Figure 6. In
this case, the delta wave was still producing the highest mutual information, with a higher
value for the phasic than for the tonic component.
In the case of the EEG channels, as shown in Table 4, the mutual information tended
to be higher in frontal regions (Fp2,F7,F8) than in the occipital ones (O1,Oz).

Behav. Sci. 2023,13, 707 8 of 18
Table 3.
Mutual information between EEG components and EDA (N-Back task, participant 10,
12 trials, and all EEG bands).
EEG Component MI with EDA [bits]
α7.5386
β4.6661
θ8.9486
δ63.0043
γ3.3007
EEG components
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0.5
Mutual Information [bits]
Phasic
Tonic
Figure 6. Mutual information between tonic and phasic EDA components vs. EEG signals.
Table 4.
Mutual information between EEG components and EDA (N-Back task, participant 10,
12 trials, and all EEG channels).
EEG Channel MI with EDA [bits]
FP2 11.5861
F7 10.5022
F8 9.8471
O1 8.9789
OZ 9.0073
Pz 9.3320
O2 9.1991
T7 9.3958
T8 9.6097
In Figure 7, we present the results of the mutual information between EDA and EEG
signals for the four tasks described in Section 2.2. These results consider the averaged data
of the ten participants, the nine EEG channels (
Fp2
,
F7
,
F8
,
O1
,
Oz
,
Pz
,
O2
,
T7
,
T8
), and the five
EEG components (
α
,
β
,
θ
,
δ
and
γ
). It is noticeable that the mutual information exhibited
the highest values for the delta component, and the lowest values for beta and gamma
components for all the tasks; in other words, the lower the EEG component frequency,
the higher its mutual information with EDA. Additionally, the task presenting the highest
mutual information between EDA and EEG is the N-Back, whereas PVT and EAT have
the lowest values. The theta component presented the second highest mutual information
values with EDA, with low variations for most of the EEG channels in all trials, especially
for EAT and PVT. The alpha component was also present with low mutual information
values in some tasks such as the EAT and ship search, especially in the last trials, when
the sleep deprivation began to affect the participants’ reaction capability. A considerable
reduction in the mutual information was present in the last trials for most of the tasks,
especially in the ship search and EAT. In terms of EEG channels, the mutual information
presented more activity in frontal regions for the initial trials, and begins to distribute
between occipital, frontal and temporal zones as the number of trials increases.

Behav. Sci. 2023,13, 707 9 of 18
Trial 2
FP2 F7 F8 O1 OZ Pz O2 T7 T8
Trial 4
FP2 F7 F8 O1 OZ Pz O2 T7 T8
Trial 6
FP2 F7 F8 O1 OZ Pz O2 T7 T8
Trial 8
FP2 F7 F8 O1 OZ Pz O2 T7 T8
Trial 10
FP2 F7 F8 O1 OZ Pz O2 T7 T8
Trial 12
FP2 F7 F8 O1 OZ Pz O2 T7 T8
0.2
0.4
0.6
0.8
1
Mutual information [bits]
(a) N-Back.
Trial 2
FP2 F7 F8 O1 OZ Pz O2 T7 T8
Trial 4
FP2 F7 F8 O1 OZ Pz O2 T7 T8
Trial 6
FP2 F7 F8 O1 OZ Pz O2 T7 T8
Trial 8
FP2 F7 F8 O1 OZ Pz O2 T7 T8
Trial 10
FP2 F7 F8 O1 OZ Pz O2 T7 T8
Trial 12
FP2 F7 F8 O1 OZ Pz O2 T7 T8
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
Mutual information [bits]
(b) Ship search.
Trial 2
FP2 F7 F8 O1 OZ Pz O2 T7 T8
Trial 4
FP2 F7 F8 O1 OZ Pz O2 T7 T8
Trial 6
FP2 F7 F8 O1 OZ Pz O2 T7 T8
Trial 8
FP2 F7 F8 O1 OZ Pz O2 T7 T8
Trial 10
FP2 F7 F8 O1 OZ Pz O2 T7 T8
Trial 12
FP2 F7 F8 O1 OZ Pz O2 T7 T8
0.05
0.1
0.15
0.2
0.25
0.3
0.35
Mutual information [bits]
(c) EAT.
Trial 2
FP2 F7 F8 O1 OZ Pz O2 T7 T8
Trial 4
FP2 F7 F8 O1 OZ Pz O2 T7 T8
Trial 6
FP2 F7 F8 O1 OZ Pz O2 T7 T8
Trial 8
FP2 F7 F8 O1 OZ Pz O2 T7 T8
Trial 10
FP2 F7 F8 O1 OZ Pz O2 T7 T8
Trial 12
FP2 F7 F8 O1 OZ Pz O2 T7 T8
0.05
0.1
0.15
0.2
0.25
0.3
0.35
Mutual information [bits]
(d) PVT.
Figure 7.
Mutual information between EDA and EEG components (
α
,
δ
,
θ
,
β
,
γ
) for all the EEG
channels, and all the analyzed tasks. (
a
) N-Back. (
b
) Ship search. (
c
) EAT and (
d
) PVT. Results were
averaged for all participants. In order to avoid redundancy, only even trials are shown. The mutual
information is the highest for N-Back (greater than 1 bit) and the lowest for PVT (lower than 0.35 bits).

Behav. Sci. 2023,13, 707 10 of 18
In order to highlight the the brain activity during the trials, Figure 8shows the
normalized mutual information between EEG waves and EDA on each EEG channel and
for all the analyzed tasks. If we consider the low frequency EEG waves, we can observe
that for the initial trials,
FP2
is the channel with the highest mutual information for almost
all the tasks. On the other hand, channels
F7
,
F8
,
O1
,
O2
and
OZ
have considerable values
for the last trials, i.e., the mutual information propagates from frontal to occipital, and in
some cases to parietal and temporal regions when the sleepiness is present. For the high
frequency EEG waves (beta and gamma), mutual information values are less common
in frontal regions and more frequent in channels
T7
,
T8
,
O1
and
O2
; in other words, the
temporal activity is greater in higher EEG frequencies vs. lower frequencies.
(a) N-Back. (b) Ship search.
(c) EAT. (d) PVT.
Figure 8.
Scalp topographies of normalized mutual information between EDA and EEG components
(α,δ,θ,β,γ) for all the analyzed tasks. Results were averaged for all participants.

Behav. Sci. 2023,13, 707 11 of 18
Finally, in Figure 9, we show the mutual information on each EEG channel in all the
tasks considering the contribution of the whole set of trials. In Figure 9a, which shows
the results for the phasic component of EDA, we can observe that for the lowest EEG
frequencies, the mutual information value is higher for
Fp2
and
F7
in almost all the tasks,
especially for EAT. In contrast, for the highest EEG frequencies (beta and gamma), channels
T8
,
O1
and
O2
have considerable mutual information values, whereas channel
PZ
presents
the lowest values, particularly in the ship search task. In the case of the tonic component,
which is shown in Figure 9b, in spite of the fact that mutual information values are lower,
the behavior is quite similar to that described in the phasic case, except for the remarked
low participation of PZchannel in the ship search task.
(a) All phasic.
(b) All tonic.
Figure 9.
Scalp topographies of normalized mutual information between EDA and EEG components
(
α
,
δ
,
θ
,
β
,
γ
) for all the analyzed tasks. (
a
) Phasic component. (
b
) Tonic component. Results were
averaged for all trials and participants.

Behav. Sci. 2023,13, 707 12 of 18
4. Discussion
Results illustrated in Figure 7demonstrate that the mutual information was the highest
between the EDA and delta EEG component for all the tasks, especially in initial trials
and for frontal brain region. However, this measure tends to decrease with the number of
trials and to propagate from the frontal to other brain zones such as occipital, parietal and
temporal zones, which can be attributed to the sleep deprivation effect.
In the case of the N-Back task (Figure 7a), the mutual information values (
more than 1 bit
)
were higher than in the other evaluated tasks. This supposes a strong relationship between
the EDA signal and delta component when individuals perform demanding working
memory tasks. This result can be contrasted with results described in [
1
], where a working
memory task such as the Sternberg task, demonstrated an increase in delta activity, mainly
in frontal lobes. This last aspect, which has also been proposed in [
32
,
36
–
39
], is equally
visible in Figure 7a, where the mutual information in channels
Fp2
and
F7
is higher for
the initial trials, and tends to be uniform for the nine EEG channels as the number of
trials progresses.
Figure 7b shows the results for the ship search task, which had the second highest
levels of mutual information between EDA and EEG (around 0.5 bits). As described in [
1
],
this value can be attributed to the increase in delta oscillations when sensory afferences
are inhibited in activities requiring concentration. In terms of the EEG channels, the ship
search exhibited a similar behavior as N-Back, with high mutual information in frontal
lobes through channels
Fp2
,
F7
and
F8
in the initial trials, with an increasing participation of
occipital and temporal lobes as the number of trials increases. Additionally, an increase in
mutual information between the alpha component and EDA signal for the last trials is no-
ticeable, which can be associated with the inhibition and attention roles that, as mentioned
in [2,40], were present in cognitive tasks involving spatial and temporal orientation.
The mutual information between alpha component and EDA signal is also relevant
for EAT (Figure 7c). In this case, the inhibitory effect is given by the ‘No-Go’ trials. In
terms of the mutual information range, EAT has the lowest values in comparison with
the other tasks (less than 0.35 bits), which supposes a weak relationship between the EDA
signal and delta component when individuals are facing stressful situations as given by the
‘Go’ and ’No-Go’ trials. The theta component also has a considerable mutual information
with EDA for this task in the last trials, when the sleep deprivation begins to affect the
participants. This result can be contrasted with the results in [
5
], where, through a spectral
analysis, an association between the individual’s voluntary repression (No-Go trial) and
the power amplitude of the theta component is found in a sleep deprivation condition.
In relation to the mutual information values for the nine EEG channels, this task exhibits
higher values for
Fp2
and
F7
at the beginning, when individuals are not facing the effects of
sleep deprivation.
For the PVT case (Figure 7d), the mutual information values for occipital, parietal, and
temporal lobes are higher for the last trials than in the other tasks, especially in channels
Pz
,
O2
,
T7
and
T8
, which can be associated with the results in [
7
,
10
], where the delta and
theta power increases in occipital areas when the response time (RT) of PVT task begins to
increase as a consequence of sleep deprivation. Again, we can observe in
Figure 7d
that
the mutual information becomes more uniform with the number of trials for all the EEG
channels, although, in relation to the other tasks, it does not decrease. This case corresponds
with the results found through the power spectral analysis in [
6
,
7
], where the presence
of alpha, delta, and theta components increases with sleep deprivation and loss of the
vigilance ability.
In Figure 8, we show the normalized mutual information in order to highlight the
EEG channels’ behavior during the 12 trials and the 4 analyzed tasks. For the N-Back task
case, described in Figure 8a, we can observe a prominent mutual information in frontal
zones for low EEG frequencies (delta, theta and alpha) that diminishes and translates to the
occipital regions (
O1
,
O2
) in the last trials. In the high frequency cases (beta and gamma),
parietal and temporal regions have considerable values, which also decrease with the

Behav. Sci. 2023,13, 707 13 of 18
number of trials. These results are similar to the results shown in [
41
–
43
], where, through a
power spectral analysis, authors demonstrate that the frontal theta power increases and
parietal beta power decreases with working memory complexity, which can be comparable
with the difficulty to perform the task in sleepiness conditions. The ship search task
results are shown in
Figure 8b
. In this case, the frontal activity does not attenuate for theta
and alpha components as in the N-Back task case, which, as we have mentioned before,
can be attributed to the inhibitory and attentive roles involved in spatial and temporal
activities described in [
2
,
40
]. In addition, an important activity is distinguishable in the
right temporal lobe for beta and gamma waves, which can reflect the spatial awareness
required in these types of tasks [
44
]. In the EAT case (Figure 8c), the frontal activity is
the most common for all the EEG waves. This effect can be associated to the theta and
alpha power increase in this brain region due to the voluntary repression (No-Go trial) or
the inhibitory effect that these kinds of tasks imply in sleep deprivation conditions [
2
,
5
].
In Figure 8d, we reaffirm that PVT presents relevant activity in the occipital region as a
consequence of the response time increase caused by sleepiness, which can be contrasted
with results in [7,10].
Finally, in Figure 9, we have decomposed the EDA signal in phasic and tonic compo-
nents to find their normalized mutual information with each EEG component and each
EEG channel for all the analyzed tasks. In this case, not only the mutual information values
obtained for the 10 participants were averaged, but also the values obtained during the
12 trials. It is evident that the frontal region is the most relevant for all the studied tasks
in terms of mutual information between EDA (tonic and phasic) and low frequency EEG
waves (delta, theta and alpha). Beta and gamma also have frontal activity, especially for
the N-Back (working memory task). Again, we can observe right temporal activity for the
ship search task, and relevant mutual information in the occipital region for PVT, which
corresponds with the previous analysis. A comparison between phasic and tonic results
shows that the tonic analysis can provide additional information for high EEG frequencies.
5. Limitations and Future Directions
Power Analysis. We run a power analysis using as the effect size the Pearson’s
correlation to obtain the p-values shown in Table 5. Although these p-values are low
enough to consider a statistical relationship between the EEG and EDA measures (null-
hypothesis rejection), especially for the phasic case, the lowest sample size (theta-phasic
case) required to obtain a considerable statistical power was of 219 individuals. However,
due to the rigorous 25-h sleep deprivation experiment with demanding protocols both for
the conductors and subjects, and the lack of individuals disposed to face sleep deprivation
for such an extended period, this study was focused on a narrow group of 10 young and
healthy subjects, as we have mentioned before. In this sense, the limited sample size and
the specific characteristics of the subjects make the observations restricted to this particular
group. To reach broader conclusions, further data collection is necessary.
Table 5. Correlation Coefficients and p-values.
EEG-Band EDA-Component Pearson’s Correlation p-Value
Alpha Phasic −0.188 3.80−189
Beta Phasic 0.086 5.16−41
Theta Phasic 0.268 0.00
Delta Phasic 0.238 6.62−306
Gamma Phasic 0.004 5.19−1
Alpha Tonic −0.070 1.17−27
Beta Tonic 0.031 1.69−6
Theta Tonic 0.100 3.33−54
Delta Tonic −0.301 0.00
Gamma Tonic 0.003 6.88−1

Behav. Sci. 2023,13, 707 14 of 18
Heart Rate Variability (HRV). In order to assess variations in parasympathetic activity
throughout the experiment, we employed the RMSSD measure to calculate HRV. The results
are presented in Figures 10 and 11. Figure 10a demonstrates short RR-intervals (around
700 ms) after 10 h from the start of the experiment, indicating reduced parasympathetic
activity during the night hours caused by sleep deprivation. In contrast, Figure 10b reveals
an increase in RR-intervals (around 950 ms) during the final trials conducted during the
early morning hours, a result that we plan to investigate in future studies. On the other
hand, Figure 11 displays the overall HRV variations across all analyzed tasks. Notably, a
reduction in this parameter is observed for trials 5 to 8 in all cases, coinciding with the
night hours (from 20 h to 24 h).
84.0 84.5 85.0 85.5 86.0 86.5 87.0 87.5
Time (s)
0.0
0.2
0.4
0.6
0.8
1.0
(mV)
652.50 ms
630.00 ms
640.00 ms
625.00 ms
625.00 ms
615.00 ms
627.50 ms
617.50 ms
637.50 ms
627.50 ms
627.50 ms
640.00 ms
657.50 ms 662.50 ms
652.50 ms
655.00 ms
650.00 ms
640.00 ms
632.50 ms
632.50 ms
642.50 ms
642.50 ms 640.00 ms 642.50 ms
655.00 ms
687.50 ms 695.00 ms
697.50 ms
705.00 ms
702.50 ms
700.00 ms
665.00 ms
662.50 ms
690.00 ms
687.50 ms
700.00 ms
665.00 ms
670.00 ms
662.50 ms
655.00 ms
665.00 ms
657.50 ms
677.50 ms
685.00 ms
670.00 ms
670.00 ms
682.50 ms
655.00 ms
642.50 ms
662.50 ms
672.50 ms
667.50 ms
665.00 ms
672.50 ms
672.50 ms
690.00 ms
667.50 ms
657.50 ms
662.50 ms
662.50 ms
672.50 ms
687.50 ms
690.00 ms
687.50 ms
685.00 ms
697.50 ms 657.50 ms
652.50 ms
642.50 ms
665.00 ms
665.00 ms
677.50 ms
665.00 ms
685.00 ms 700.00 ms
722.50 ms
697.50 ms
697.50 ms
690.00 ms
670.00 ms 662.50 ms
660.00 ms 652.50 ms
660.00 ms
632.50 ms
660.00 ms
650.00 ms
662.50 ms
645.00 ms
635.00 ms
650.00 ms
650.00 ms
642.50 ms
645.00 ms
645.00 ms
652.50 ms
655.00 ms
622.50 ms
625.00 ms
635.00 ms
655.00 ms
645.00 ms
645.00 ms
665.00 ms
672.50 ms
685.00 ms
690.00 ms
657.50 ms
652.50 ms
645.00 ms
637.50 ms 622.50 ms
617.50 ms
642.50 ms
665.00 ms
722.50 ms
735.00 ms
722.50 ms 690.00 ms
675.00 ms
682.50 ms
672.50 ms
652.50 ms
667.50 ms
655.00 ms
655.00 ms
650.00 ms
655.00 ms
680.00 ms
717.50 ms
712.50 ms
710.00 ms
692.50 ms
697.50 ms 662.50 ms
660.00 ms
657.50 ms
650.00 ms
652.50 ms
630.00 ms
640.00 ms
647.50 ms
670.00 ms
665.00 ms
667.50 ms
685.00 ms
677.50 ms
680.00 ms
657.50 ms
665.00 ms
655.00 ms
660.00 ms
630.00 ms
637.50 ms
637.50 ms
662.50 ms
680.00 ms
657.50 ms
645.00 ms
672.50 ms
655.00 ms
687.50 ms
677.50 ms
690.00 ms
697.50 ms
717.50 ms
677.50 ms
685.00 ms
697.50 ms
707.50 ms
675.00 ms
662.50 ms
660.00 ms
652.50 ms
667.50 ms
665.00 ms
647.50 ms
660.00 ms
(a) R-R intervals for trial 5 (After 10 h).
84 85 86 87 88
Time (s)
0.0
0.2
0.4
0.6
0.8
1.0
(mV)
1055.00 ms
1085.00 ms
1022.50 ms
1010.00 ms 975.00 ms 922.50 ms
912.50 ms
932.50 ms
907.50 ms
915.00 ms
1015.00 ms
1060.00 ms
1020.00 ms
997.50 ms
1005.00 ms
1027.50 ms
1005.00 ms
1000.00 ms
1017.50 ms
1002.50 ms
960.00 ms
980.00 ms
1030.00 ms
1017.50 ms
1000.00 ms
1060.00 ms
1092.50 ms
1057.50 ms
1007.50 ms
1042.50 ms
1015.00 ms
1002.50 ms
1042.50 ms
1110.00 ms
1027.50 ms
982.50 ms
982.50 ms 935.00 ms
877.50 ms
830.00 ms
865.00 ms
1037.50 ms
1132.50 ms
1082.50 ms
1032.50 ms
1062.50 ms
1045.00 ms
1005.00 ms
977.50 ms
990.00 ms
1017.50 ms
1010.00 ms
1055.00 ms
1112.50 ms
1065.00 ms
1057.50 ms
1045.00 ms
992.50 ms
985.00 ms
1010.00 ms
1010.00 ms
980.00 ms
1017.50 ms
962.50 ms
935.00 ms
895.00 ms
927.50 ms
965.00 ms
957.50 ms
905.00 ms
937.50 ms
990.00 ms
1032.50 ms
970.00 ms
1007.50 ms
1072.50 ms
1047.50 ms
900.00 ms
855.00 ms
792.50 ms
800.00 ms
797.50 ms
835.00 ms
887.50 ms
950.00 ms
1027.50 ms
997.50 ms
997.50 ms
990.00 ms
857.50 ms
817.50 ms
785.00 ms
780.00 ms
825.00 ms
940.00 ms
980.00 ms
925.00 ms
937.50 ms
980.00 ms
957.50 ms
965.00 ms
982.50 ms
992.50 ms
967.50 ms
987.50 ms
960.00 ms
972.50 ms
1045.00 ms
1027.50 ms
995.00 ms
982.50 ms
1007.50 ms
945.00 ms
892.50 ms
915.00 ms
920.00 ms
882.50 ms
822.50 ms
810.00 ms
857.50 ms
930.00 ms
(b) R-R intervals for trial 11 (After 22 h of activity).
Figure 10.
RR-intervals after 5 trials (taken around 20:00 h) (
a
), and RR-intervals for early morning
hours of the second day (trial 12) (
b
). A decrease in RR-intervals is exhibited around 20:00 h,
which can be associated to parasympathetic activity reduction because of the beginning of normal
sleeping hours.

Behav. Sci. 2023,13, 707 15 of 18
1 2 3 4 5 6 7 8 9 10 11 12
Trial
30
40
50
60
70
HRV (ms)
EAT
Ship Search
N-Back
PVT
Figure 11.
Average HRVs for the analyzed tasks. HRV values decrease from trials 5 to 8 for all
activities (from 20 h to 24 h).
6. Conclusions
In this work, we have found the mutual information between EDA and EEG in order
to include linear and non-linear interactions. The signals were taken from ten participants
developing four cognitive tasks (EAT, ship search, PVT, and N-Back) during 12 trials
developed in 24 h. The results demonstrate that this measure is higher between the delta
EEG component and EDA, especially with its phasic component, and lower, in the same
order, for theta, alpha, gamma and beta, i.e., the lower the EEG wave frequency, the
higher its mutual information with EDA. For the four analyzed tasks, this measure is
higher for N-Back and lower, in the same order, for the ship search, PVT and EAT. This
means that the EDA signal can be especially used to analyze the performance in working
memory tasks, where delta oscillations are significative. On the other hand, the mutual
information between the EDA (particularly for tonic component) and alpha EEG component
demonstrates an important increase in the number of trials in tasks requiring inhibition and
attention behaviors, especially in the ship search and EAT, which can be associated with
other results found in literature that use a spectral analysis and other statistical methods,
such as ANOVA. Additionally, an increase in the mutual information between the EDA
and theta component is also visible with the number of trials, which can be associated
with the fatigue caused by sleep deprivation and response time delays described in other
approaches using different techniques [40,45–47].
In terms of the nine EEG analyzed channels, the mutual information values, for the
initial trials, are high for channels
Fp2
,
F7
and
F8
, and tend to be uniform and reduced for all
the tasks, because the number of trials increases, in other words, as the sleepiness appears.
These results can be contrasted with results found in some approaches using different
techniques, in which a relevant role of frontal lobes in cognitive functions such as attention,
working memory, decision making and inhibitory control is described. For the PVT case,
there is also a relationship with the findings of other approaches, where an increment
in delta and theta power is demonstrated for occipital areas as a consequence of sleep
deprivation. For the case of ship search, a particular behavior for the mutual information is
described in the right temporal region and for the gamma wave, which can be related to
the spatial awareness involved in this task.
In general, the mutual information between EDA and EEG signals, and its corre-
spondence with important results found in the literature based exclusively on the EEG

Behav. Sci. 2023,13, 707 16 of 18
signal, suggests that exploring EDA could be an intriguing alternative for investigating
brain behavior.
Author Contributions:
Conceptualization, H.F.P.-Q.; Methodology, D.A.M.V.; Formal analysis,
D.A.M.V.; Investigation, D.A.M.V. and H.F.P.-Q.; Resources, H.F.P.-Q. and D.M.R.P.; Writing—original
draft, D.A.M.V.; Project administration, H.F.P.-Q.; Funding acquisition, D.M.R.P. All authors have
read and agreed to the published version of the manuscript.
Funding:
This research was funded by Universidad Pedagógica Nacional, which provided financial
resources necessary for the completion of this study through the project number DTE-562-21.
Institutional Review Board Statement:
The study was conducted in accordance with the Declaration
of Helsinki, and approved by the Institutional Review Board of UConn (protocol code: H16-034 and
date of approval: 10 May 2016).
Informed Consent Statement: Informed consent was obtained from all subjects involved in the study.
Acknowledgments:
We would like to acknowledge the support of Universidad Pedagógica Nacional,
which provided financial resources necessary for the completion of this study through the project
number DTE-562-21. We also acknowledge the support of Universidad Santo Tomás and Connecticut
University for the equipment and facilities for data collection and processing.
Conflicts of Interest: The authors declare no conflict of interest.
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