Delayed Mutual Information to Develop Functional Analysis on Epileptic

Signals

Victor Hugo Batista Tsukahara

1 a

, Pedro Virgilio Basilio Jeronymo

1 b

, Jasiara Carla de Oliveira

2 c

Vinicius Rosa Cota

2 d

and Carlos Dias Maciel

1 e

Signal Processing Laboratory, Dept. of Electrical Engineering, University of S

ao Paulo, S

ao Carlos, Brazil

Laboratory of Neuroengineering and Neuroscience, Dept. of Electrical Engineering,

Federal University of S

ao Jo

ao Del-Rei, S

ao Jo

ao Del-Rei, Brazil

Keywords:

Epilepsy, Entropy, Delayed Mutual Information, Channel Capacity, Transmission Rate.

Abstract:

Epilepsy is the second most prevalent brain disorder affecting approximately 70 million people worldwide. A

modern approach to develop the brain study is to model it as a system of systems, represented by a network

of oscillators, in which the emergent property of synchronisation occurs. Based on this perspective, epileptic

seizures can be understood as a process of hyper-synchronisation between brain areas. To investigate such

process, a case study was conducted applying Delayed Mutual Information (DMI) to perform functional con-

nectivity analysis, investigating the channel capacity (C) and transmission rate (R) between brain areas —

cortex, hippocampus and thalamus — during basal and infusion intervals, before the beginning of generalised

tonic-clonic behaviour (TCG). The main contribution of this paper is the study of channel capacity and trans-

mission rate between brain areas. A case study performed using 5 LFP signals from rodents showed that the

applied methodology represents an another appropriate alternative to existing methods for functional analysis

such as Granger Causality, Partial Directed Coherence, Transfer Entropy, providing insights on epileptic brain

communication.

1 INTRODUCTION

Epilepsy is the second most common neurological

disease (Organization et al., 2017) and affects ap-

proximately 70 million people worldwide (Spiciarich

et al., 2019) representing a public health concern

(Niriayo et al., 2019). It is a chronic disease of the

central nervous system (CNS) that reaches people of

all ages in which it is commonly associated with so-

cial difﬁculties (Beghi, 2019) and can cause health

loss such as premature mortality and residual disabil-

ity (Beghi et al., 2019).

Epilepsy-based studies usually uses electroen-

cephalography (EEG) (Ibrahim et al., 2019) or local

ﬁeld potentials (LFP) (Biasiucci et al., 2019) to check

brain electrical activity, although the use of electrodes

directly in brain tissue is an important option to map

https://orcid.org/0000-0003-0713-9067

https://orcid.org/0000-0002-1468-9051

https://orcid.org/0000-0002-5170-1072

https://orcid.org/0000-0002-2338-5949

https://orcid.org/0000-0003-0137-6678

electrical activity of the brain with better spatial reso-

lution (Bartolomei et al., 2017).

The latest approach to study epilepsy is the analy-

sis of hyper-synchronisation of brain frequencies os-

cillations as a feature (Yu et al., 2019). (Olamat and

Akan, 2017) performed a nonlinear synchronisation

analysis in LFP epileptic data introducing this new

perspective. (Weiss et al., 2019) used the concept

to understand seizure genesis and spreading in hu-

man limbic areas and (Devinsky et al., 2018) reported

hyper-synchronisation to discuss epilepsy epidemiol-

ogy and pathophysiology. The brain is modelled as a

complex system where each region represents a sub-

system and synchronization is an emergent property

(Andrea Avena-Koenigsberger, 2017). Changes in

this feature during the occurrence of epileptic seizures

are an important aspect to understand the epilep-

tic brain network and synchronization (Mei et al.,

2019). The pathologic hyper-synchronisation of fre-

quencies oscillations give rise to seizures (Berglind

et al., 2018).

There is a hypothesis that high-frequencies oscil-

lations are related with the cortical local brain in-

Tsukahara, V., Jeronymo, P., Carla de Oliveira, J., Cota, V. and Maciel, C.

Delayed Mutual Information to Develop Functional Analysis on Epileptic Signals.

DOI: 10.5220/0008974900890097

In Proceedings of the 13th International Joint Conference on Biomedical Engineering Systems and Technologies (BIOSTEC 2020) - Volume 4: BIOSIGNALS, pages 89-97

ISBN: 978-989-758-398-8; ISSN: 2184-4305

formation processing whereas low-frequencies have

connection with larger cortical networks (Anastasi-

adou et al., 2019). Consequently, the brain interac-

tions through these areas can become complex be-

cause of interactions between oscillations at differ-

ent frequency bands (Anastasiadou et al., 2019). In

this situation, functional connectivity may be per-

formed to detect dependencies among neurophysio-

logical signals (Andrea Avena-Koenigsberger, 2017).

It can be assessed through different methods with

the aim to infer patterns of direct inﬂuences (Andrea

Avena-Koenigsberger, 2017).

To estimate the dependency between time series

there are several methods (Gribkova et al., 2018) and

Mutual Information is one of them. It is an Informa-

tion Theoretic and nonparametric approach that mea-

sures generalized, both linear and nonlinear, interde-

pendence between two variables (Akbarian and Erfa-

nian, 2017). This meets the accepted vision that real

world time series usually are nonlinear and non sta-

tionary (Wan and Xu, 2018).

Usually, the Information Theoretic approaches do

not make any hypothesis about the dependency be-

tween time series (Nichols et al., 2005). The use

of time Delayed Mutual Information (DMI) seeks to

quantify the information shared between time series

taking into account the previous information content

as function of time (Endo et al., 2015). (Li et al.,

2018) demonstrated that DMI is a suitable option to

develop analysis of nonlinear systems as in the case

of neuroscience data. (Kim et al., 2018) used DMI to

analyse information transmission of an EEG set from

groups of people with mild Alzheimer disease. (Li

et al., 2017) applied DMI to characterise hippocam-

pal theta-driving neurons. (Chapeton et al., 2017) per-

formed a study using intracranial EEG to identify ef-

fective connections in the brain that exhibit consistent

timing across multiple temporal scales.

The objective of this paper is, in performing a case

study using Delayed Mutual Information, to develop

functional connectivity analysis in rodents LFP sig-

nals, investigating the channel capacity (C) and the

transmission rate between brain areas. In addition,

Surrogate method is used to evaluate the DMI mea-

sures. In section 2, it is presented the theory related

to DMI and Surrogate. Section 3 describes the LFP

data used and the applied methodology. Section 4

presents the achieved results, and in Section 5 the re-

sults are discussed. Finally Section 6 brings forward

paper conclusions.

2 THEORY

This section presents the main theory required to de-

velop this paper. First it is introduced Mutual In-

formation explaining the main concepts of channel

capacity and transmission rate. Then the Surrogate

method, used to assess statistical signiﬁcance of the

performed analysis, is deﬁned.

2.1 Delayed Mutual Information

The measure of how deterministic is a given variable

can be determined through its entropy (H), deﬁned by

(Cover and Thomas, 2012):

H(X) = −

∑

x∈χ

p(x)log

p(x) (1)

where X is a discrete random variable, p(x) = P{X =

x} is the probability of X equal to x, x ∈ χ, i.e. the

probability mass function of X, and a is the logarithm

base that provides the entropy measure in bits in the

case of a = 2. Given a signal X and another signal

Y , the Mutual Information may quantify the informa-

tion shared between this signals, which means how

much it is possible to reduce the uncertainty of sig-

nal X given the knowledge of signal Y (Cover and

Thomas, 2012).

The Delayed Mutual Information (DMI) accord-

ing to (Nichols et al., 2005) is the quantiﬁcation of

information shared between X and Y

where Y

is the

signal displaced by a lag τ. It is mathematically de-

ﬁned as:

I(X;Y

) =

∑

∈χ

∑

∈γ

p(x

, y

y−τ

)log

p(x

, y

n−τ

)

p(x

)p(y

n−τ

)

(2)

According to (Cover and Thomas, 2012) the chan-

nel capacity (C) represents the maximum measure of

Mutual Information:

C = maxI(X, Y ) (3)

and according to (Proakis and Salehi, 2001) the chan-

nel capacity for DMI is quantiﬁed by its peak value.

Also according to (Proakis and Salehi, 2001), the

transmission rate estimation (R) can be written as a

function of channel capacity and signal bandwidth

(BW) in Hertz:

R = 2.BW.C (4)

If the entropy is measured in bits, the transmission

rate is going to be measured as bits/s.

BIOSIGNALS 2020 - 13th International Conference on Bio-inspired Systems and Signal Processing

2.2 Surrogate for Hypothesis Test

The investigation of information sharing between

brain regions sometimes require the assertion of sta-

tistical signiﬁcance for conﬁdence in the functional

analysis performed. In this case Surrogate may be

useful (Lancaster et al., 2018).

One of the techniques to apply this method is

the IAAFT technique, proposed by (Schreiber and

Schmitz, 1996). It consists of generating a surro-

gate data from the original signal, keeping the same

power spectrum and randomizing Fourier phases, cre-

ating uncorrelated signals. Applying DMI on surro-

gate data represents the measures that are expected

when signals do not share any connectivity. There-

fore, when comparing the statistics from original sig-

nals and the surrogate data statistics, the null hypothe-

sis can be accepted or rejected. Some literature can be

reviewed in neuroscience related to the use of Surro-

gate to assist the type of interdependency among elec-

troencephalographic signals (Pereda et al., 2005; Faes

et al., 2010; Subramaniyam and Hyttinen, 2015; Ad-

kinson et al., 2019).

Related with the number of surrogate data to be

created, there is a well established rank-order test,

proposed by (Theiler et al., 1992), that can be used

(Schreiber and Schmitz, 2000). First, assume Ψ is the

probability of false rejection, then, deﬁne the level of

signiﬁcance (S) as:

S = (1 − Ψ) · 100% (5)

The number of surrogate data to be created (M) is

deﬁned as follows:

M =

− 1 (6)

where K is an integer number deﬁned by the type

of test - 1 if it is one-sided and 2 in the case of a two-

sided test. Usually, K = 1 is adopted due to compu-

tational effort to generate surrogates (Schreiber and

Schmitz, 2000).

3 METHODOLOGY

The section details the methodology used to analyse

the local ﬁeld potential signals, in order to assess mu-

tual information, channel capacity and transmission

rate between brain areas. Furthermore, it describes

the methodology employed to acquire the LFP signals

and the computational environment.

3.1 Applied Methodology

The diagram presented in Figure 1 depicts the applied

methodology. The ﬁrst step — blue box in Figure 1

— is to calculate the LFP signals entropy for cortex

(Cx), hippocampus (Hp) and thalamus (Th).

Then, in the second step, the optimal number of

bins to apply Mutual Information is determined — or-

ange box in Figure 1 — as follows: The rodents LFP

signals are discretized with different number of bins

— 2, 4, 8, 16, 32, 64 and 128 where used — and DMI

is applied among brain areas. Next, the DMI mea-

sures are compared to ﬁnd the best number of bins

- the DMI curve for a given number of bins that is

closest to highest DMI curve. Figure 2 explain better

the method. Another important measure performed is

the Kolmogorov-Smirnov test to compare the group

of rodents to check if there is a statistical difference

between groups.

The third step is to apply Delayed Mutual Infor-

mation to understand the information sharing and de-

pict the lag where there the maximum value occurs,

therefore determining the channel capacity. In the

fourth step, surrogate data is created with Iterative

Amplitude Adjusted Fourier Transform (IAAFT) al-

gorithm for cortex, hippocampus and thalamus sig-

nals. In this case study, 35 signals for 97% signiﬁ-

cance level were generated. In the ﬁfth step, each sur-

rogate is combined with other two original signals to

perform DMI analysis, investigating the connectivity

signiﬁcance between brain areas.

The surrogate data is compared with the origi-

nal DMI measures by means of Kolmogorov-Smirnov

(KS) test. In this paper, p-value = 5% was chosen to

evaluate the maximum mutual information and its val-

ues. The last step is to apply Fast Fourier Transform

to verify the signal’s bandwidth and, ﬁnally, calculate

the transmission rate between brain areas.

The applied methodology described was used to

investigate two periods of LFP signals: basal and con-

vulsant drug infusion, until generalized tonic-clonic

(TCG) behaviour. The analysis was performed in the

recordings of ﬁve rats.

Simulations were developed in Python language,

using the packages: Matplotlib, Nolitsa, Numpy, Pan-

das, Scipy, Seaborn and Time. The code was exe-

cuted on a computer with an Intel i7 processor, 8GB

of RAM, running MAC OS 10.14.6 operational sys-

tem.

3.2 Database for Case Study

We used LFP signals database from Interventional

Laboratory of Neuroengineering and Neuroscience

Delayed Mutual Information to Develop Functional Analysis on Epileptic Signals

LFP discretization

and entropy

calculation

DMI

Different bins

Transmission

Rate

FFT

LFP signals

Channel

Capacity (C)

Figure 1: Summary of applied methodology: First, the LFP signals are discretized and their entropy are calculated. Then,

DMI with different bin sizes are computed to determine the value that best ﬁts the dataset. After the optimal number of bins

is identiﬁed, DMI is calculated among all rodent brain signals (Cx, Hp and Th) and channel capacities are determined. To

calculate the transmission rate between brain areas, Fast Fourier Transform (FFT) is applied to all LFP signals to check the

signal’s bandwidth. Finally, the channel capacity and signal’s bandwidth are used to ﬁnd the transmission rate between brain

areas.

Figure 2: Delayed Mutual Information performed with dif-

ferent number of bins between two brain areas (τ is given

in samples). As can be observed the highest curve is pre-

sented for 256 bins. In this case the better resolution for

DMI is 256 bins. However, if the 256 bins curve would

not exist, only the other curves, it is possible to check three

curves with almost same values (32, 64 and 128 bins). In

that case it could be possible to choose 32 bits to perform

analysis because the results are similar to 128 bins curve

and the computational processing would be smaller.

(LINNce) from Federal University of S

ao Jo

ao Del

Rei. The laboratory employs male Wistar rats weigh-

ing between 250 and 350 grams coming from the Uni-

versity Central Biotherm to acquire data and evaluate

methods of electrical stimulation. All described pro-

cedures are in according to ethics committee under-

protocol 31/2014.

The signal recording is conducted with the aid of

electrodes (monopolar type and stainless steel cov-

ered by teﬂon) placed directly inside the right tha-

lamus and hippocampus of the rat’s brain through

stereotactic surgery (Cota et al., 2016). In addition,

two microsurgical screws were implanted (length 4.7

mm, diameter 1.17 mm, Fine Science Tools, Inc.,

North Vancouver, Canada) aiming the cortical regis-

tration of right hemisphere and to operate as reference

in frontal bone. The electrodes and screws were po-

sitioned with assistance of neuroanatomic atlas (Pax-

inos and Watson, 2013).

The LFP signals for each rodent was registered

while the subject was simultaneously ﬁlmed, to per-

form behavioural analysis (observe classic seizure

features such as facial automatisms, myoclonic con-

cussion, head myoclonus, anterior and posterior limbs

myoclonus, elevation and fall, generalized tonic-

clonic seizure) to allow their correlation with the elec-

trophysiological events observed during LFP record-

ing. For all rodents the time of recording was the same

with ten minutes of duration.

LFP recording was performed using 1 kHz sam-

pling rate. Signals were ampliﬁed 2000 V/V through

A-M Systems (model 3500) ampliﬁcation system and

digitalized on National Instruments (PCI 6023E) A/D

converter controlled by developed LINNce Virtual In-

strument from LabView platform. Sequentially, they

were ﬁltered using a second-order Butterworth ﬁlter

(0.3 to 300 Hz band).The power grid noise at 60 Hz

frequency was mitigated with use of shielded cables

and Faraday cage.

4 RESULTS

During basal and infusion intervals, stationarity was

observed, allowing the calculation of Shannon en-

tropy during each part of the signal. The Tables 1 and

2 display the entropy values (in bits) for all rodents

BIOSIGNALS 2020 - 13th International Conference on Bio-inspired Systems and Signal Processing

used in the case study during basal and infusion inter-

vals respectively. To ﬁnd the optimal number of bins

for Delayed Mutual Information different numbers of

bins were tested on the LFP signals and it provided

the number of 256.

The Kolmogorov-Smirnov test performed with ro-

dents groups indicated that there is no difference be-

tween the groups at the level of p value equals 10%.

Next, Surrogate method was applied. Figure 3 depicts

an example of the power spectrum of original signal

in comparison to the power spectrum of the surrogate

data.

DMI was calculated for surrogate data and origi-

nal signals. An example result of DMI(Cx,Hp) for ro-

dent R048 can be seen in Figure 4. The lag with max-

imum mutual information can be also observed: τ = 0

for all rodents used in this case study. The Tables 5

and 6 exhibit the signals bandwidths for each rodent

during basal and infusion intervals respectively.

Tables 3 and 7 show, respectively, all channel

capacities and transmission rates, simulated during

basal interval. The similar results during infusion in-

terval can be veriﬁed in Tables 4 and 8. Boxplots in

Figures 5 and 6 depict the mean and standard devia-

tion of transmission rate between each brain area con-

sidering all the ﬁve rodents used to develop the case

study.

The computational time to perform this case study

was approximately 3 hours for each DMI. Three DMI

between each pair of brain areas were computed, re-

sulting in a total of 9 hours. Therefore, for each inter-

val, basal and infusion, it was spent 27 hours, reach-

ing 54 hours total.

Table 1: Entropy calculated for all rodents used in the case

study during basal interval. DMI is given in bits.

Rodent Cx Entropy Hp Entropy Th Entropy

R048 15.36 15.36 15.36

R052 13.28 13.28 13.28

R064 14.96 14.97 14.97

R065 15.05 15.05 15.05

R072 15.05 15.05 15.05

Table 2: Entropy calculated for all rodents used in the case

study during infusion interval. DMI is given in bits.

Rodent Cx Entropy Hp Entropy Th Entropy

R048 17.39 17.39 17.39

R052 17.02 17.02 17.02

R064 16.62 16.62 16.62

R065 17.14 17.14 17.14

R072 17.29 17.29 17.29

Table 3: Channel capacity in bits for each rodent during

basal interval.

Rodent Cx → Hp Cx → Th Hp → Th

R048 1.28 1.42 1.75

R052 3.00 2.93 3.72

R064 0.61 0.65 1.48

R065 1.53 1.51 1.25

R072 2.45 2.40 2.15

Table 4: Channel capacity in bits for each rodent during

infusion interval.

Rodent Cx → Hp Cx → Th Hp → Th

R048 0.91 1.26 1.10

R052 1.42 1.51 2.81

R064 0.70 0.71 1.47

R065 1.29 1.42 1.09

R072 2.61 2.72 2.29

Table 5: Bandwidth (BW) in Hertz for each rodent during

basal interval.

Rodent BW Cx BW Hp BW Th

R048 1.30 1.49 1.23

R052 1.73 1.71 1.71

R064 9.00 10.50 8.71

R065 10.00 10.00 10.00

R072 2.77 2.75 2.74

Table 6: Bandwidth (BW) in Hertz for each rodent during

infusion interval.

Rodent BW Cx BW Hp BW Th

R048 30.00 20.00 20.00

R052 20.00 13.95 10.43

R064 26.00 33.00 36.00

R065 30.00 27.00 30.00

R072 20.26 15.00 20.48

Figure 3: Power spectrum of original cortex signal and sur-

rogate data of cortex area for rodent R048. The power

density spectrum of the synthetic data is approximately the

same of the original signal.

Delayed Mutual Information to Develop Functional Analysis on Epileptic Signals

Table 7: Transmission rate (R) for each rodent during basal interval. Base 2 was used for DMI logarithm. Frequency was

measured in Hertz, resulting in C being provided in bits and R in bits/s.

Rodent Cx → Hp Cx → Th Hp → Th Hp → Cx Th → Cx Th → Hp

R048 3.33 3.69 5.22 3.81 3.49 4.31

R052 10.38 10.14 12.72 10.26 10.02 12.72

R064 10.98 11.71 31.08 12.81 11.32 25.78

R065 38.70 30.2 25.00 30.6 30.2 25.00

R072 6.79 6.65 5.91 6.74 6.58 5.89

Table 8: Transmission rate (R) for each rodent during infusion interval. Base 2 was used for DMI logarithm. Frequency was

measured in Hertz, resulting in C being provided in bits and R in bits/s.

Rodent Cx → Hp Cx → Th Hp → Th Hp → Cx Th → Cx Th → Hp

R048 54.60 75.60 44.40 36.40 50.40 44.40

R052 56.80 60.40 78.40 39.62 31.50 58.62

R064 36.40 36.90 97.68 46.20 51.12 105.80

R065 38.70 30.20 29.43 34.83 42.60 32.70

R072 52.88 55.10 34.35 39.15 55.70 46.90

Figure 4: Delayed mutual information between cortex and

hippocampus for rodent R048 using 256 bins. The blue line

is the DMI performed with original signals and the red lines

are the DMI with surrogate. Due to the difference between

the surrogate DMI it is not possible to distinguish the dif-

ference among surrogate data DMI because it was approx-

imately the same. It is important to note that the lag for

maximum mutual information is zero, the same found for

another rodents used to perform the case study.

5 DISCUSSION

The entropy for all rodents used in this case study

during basal interval were similar with exception of

rodent R052 which was slightly lower. During in-

fusion interval, the entropy was more uniform and

higher then calculated for basal interval. This in-

dicates that LFP signals become more probabilistic

during infusion, meeting the hypothesis of increase

Figure 5: Boxplot denoting the transmission rate in bits/s

between each brain areas, for all the 5 rodents used to per-

form the case study, during basal interval (black dots rep-

resent the rodents measures). It is important to observe

that the highest standard deviation is veriﬁed in transmis-

sion rate between hippocampus and thalamus. The black

dots represent the rodents in the boxplot.

of information rate, which in turn is compliant with

the perspective of understanding epileptic seizure as a

hyper-synchronisation phenomena.

It is possible to check that signal bandwidth during

infusion interval is bigger then the bandwidth during

basal interval. This indicates initially larger informa-

tion for each brain area during infusion, again indi-

cating the increasing communication among cortex,

hippocampus and thalamus.

The lag with maximum MI was zero, found for

all rodents in this case study. Probably, this result

is related with the low sampling rate of LFP sig-

nals. All surrogate data created for this case study

maintained the power spectrum and randomized the

Fourier phases, as expected for IAAFT algorithm, as

BIOSIGNALS 2020 - 13th International Conference on Bio-inspired Systems and Signal Processing

Figure 6: Boxplot denoting the transmission rate in bits/s

between each brain areas, for all the 5 rodents used to per-

form case study, during infusion interval (black dots rep-

resent the rodents measures). The values during infusion

interval are higher when compared with values measured

during basal interval. A possible reason for that difference

is a larger signal’s bandwidth. The DMI is approximately

the same among brain areas for both intervals, see Tables 3

and 4. The black dot represent the rodents in boxplot.

illustrated in Figure 3. This created uncorrelated sig-

nals, with whose measures, it was possible to vali-

date the DMI measures for original signals. For all

rodents, it was possible to observe that the measures

of the original signals were higher than surrogate data

measures.

DMI revealed different measures for each rodent

even Kolmogorov-Smirnov test indicated statistical

equality among groups for 10% signiﬁcance. Yet,

during basal and interval the values for each rodent

was approximately the same, indicating that the chan-

nel capacity did not change during basal and infu-

sion intervals. Nonetheless, the bandwidth was differ-

ent between them, resulting in different transmission

rates as can be observed in Tables 7 and 8.

It is important to make clear that surrogate anal-

ysis assured 5% p-value using Kolmogorov-Smirnov

test indicating that signifcance level of comparison

between original signals DMI and surrogates DMI for

each rodent. When the results are compared between

rodents the results presented 10% p-value signifcance

level when Kolmogorov-Smirnov test was applied.

That is the reason for different Kolmogorov-Smirnov

p-values presented in this paper.

The increase of transmission rate, observed for all

rodents during infusion interval — in Figures 5, 6

and Tables 7, 8 — is an important result, meeting the

concept of hyper-synchronization phenomena that ap-

pears during epileptic seizures. DMI was able to cap-

ture the increase of communication among brain ar-

eas. Since there is more volume of information mov-

ing between brain areas during infusion, the uncer-

tainty (entropy) accordingly grows, as expected. The

channel capacity practically do not change between

intervals, pointing that the main reason for hyper-

synchronization is the growth of information sharing

between cortex, hippocampus and thalamus.

Delayed Mutual Information represented an an-

other appropriate alternative to existing methods be-

cause it was able to provide insights about the func-

tional connectivity among brain areas. It is a non lin-

ear method supporting the real world condition that

is not linear, do not require a large volume of data

when compared to another methods such as Transfer

Entropy and it is non parametric which means more

ﬂexibility to data analysis.

6 CONCLUSIONS

The use of DMI to perform a case study with ro-

dents LFP presented insights about the communica-

tion among brain areas before the occurrence of an

epileptic seizure. It was observed that entropy during

infusion interval was higher than during basal inter-

val, being the ﬁrst indicator that the communication

was increasing during infusion. The uncertainty about

signals was becoming higher. The second indicator

was the growth of LFP bandwidth for all signals. It

was also observed a consistent lag of zero for DMI

for all rodents. This last result may have being in-

ﬂuenced by the relatively low sampling rate used to

record the LFP signals. The veriﬁed channel capac-

ity was different for each rodent, however, exhibited

the same behaviour of staying approximately equal

during basal and infusion intervals. Consequently,

the transmission rate was different between periods

mainly due to the change of signal’s bandwidth. It in-

dicates that communication is increasing essentially

due to the growth of information sharing among brain

areas. This is the last indicator, which is in agreement

with the idea of hyper-synchronisation phenomena as-

sociated with epileptic seizure. Therefore, DMI rep-

resented a helpful method to perform functional anal-

ysis on LFP signals.

ACKNOWLEDGEMENT

This work was supported by the Fundac¸

ao de Am-

paro

a Pesquisa de Minas Gerais (FAPEMIG) [grant

number APQ 02485-15] and ﬁnanced in part by

the Coordenac¸

ao de Aperfeic¸oamento de Pessoal de

ıvel Superior - Brasil (CAPES) - Finance Code 001.

Delayed Mutual Information to Develop Functional Analysis on Epileptic Signals

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