Source-based Multifractal Detrended Fluctuation Analysis for

Discrimination of ADHD Children in a Time Reproduction Paradigm

Shiva Khoshnoud

1,3

, Mohammad Ali Nazari

and Mousa Shamsi

Institute for Frontier Areas of Psychology and Mental Health, Freiburg, Germany

Faculty of Advanced Technologies in Medicine, Iran University of Medical Sciences, Tehran, Iran

Biomedical Engineering Faculty, Sahand University of Technology, Tabriz, Iran

Keywords: Multifractal Detrended Fluctuation Analysis, ADHD, Time Perception, EEG.

Abstract: Electroencephalography recordings have a scale-invariant structure and multifractal detrended fluctuation

analysis (MF-DFA) could quantify the fluctuation dynamics of these recordings in different brain states.

However, the channel-based electrical activity of the brain has low spatial resolution and considering the

source-level activity patterns is a good answer for this restriction. In this work, the multifractal spectrum

parameters of the channel-based EEG, as well as the corresponding source-based independent components

in children with Attention Deficit Hyperactivity Disorder (ADHD) and the age-matched control group, has

been investigated. Considering the perceptual timing deficit in children with ADHD, for the analysis of the

multifractality, two brain states including the eyes-open rest and the time reproduction condition have been

considered. The results obtained showed that switching from rest to the time reproduction condition

increases the degree of multifractality and so the complexity and non-uniformity of the signal. While the

channel-based multifractal properties could not significantly distinguish two groups, the results for the

source-based multifractal analysis showed a significantly decreased degree of multifractality for children

with ADHD in prefrontal, mid-frontal and right frontal source clusters suggesting reduced activation of

these clusters in this group. Utilizing support vector machine (SVM) classifier it is found that, the source-

based multifractal features provide a significantly higher accuracy rate of 86.67% in comparison to the

channel-based measures.

1 INTRODUCTION

Electroencephalography (EEG) recordings as a

nonstationary time series possess a scale-invariant

structure which indicates that signal repeats its

structure on different sub-intervals (Eke, Herman,

Kocsis, & Kozak, 2002; Ihlen, 2012; Zorick &

Mandelkern, 2013). Time series with a complex

structure like EEG are multifractal and the

multifractal detrended fluctuation analysis (MF-

DFA) has been proposed for evaluation of their

fractal properties (Kantelhardt et al., 2002). Several

reports suggest that changes in the scale-invariant

structure of the biomedical signals reflect changes in

the adaptability of physiological processes and

successful treatment of pathological conditions

might changes the fractal structure and improve

health (Goldberger et al., 2002). Multifractal

properties of the sleep stage EEG signals have been

assessed in several studies representing that these

measures

correlated with the sleep depth, exhibiting

different values for deeper sleep stages (Ma, Ning,

Wang, & Bian, 2006; Weiss, Clemens, Bódizs, &

Halász, 2011; Weiss, Clemens, Bódizs, Vágó, &

Halász, 2009; Zorick & Mandelkern, 2013). Zorick

& Mandelkern (2013) revealed that even short EEG

tracings represent significant dissimilarities in the

width of the multifractal spectrum for the different

sleep stages. Assessing the height of the multifractal

spectrum, Weiss et al. (2011, 2009) indicated that

EEG signals tend to be less multifractal during

NREM4 compared to NREM2 and REM sleep

stages. Moreover, the predictive power of

multifractal parameters in epilepsy research was also

examined in order to detect and predict focal

seizures (Dick & Svyatogor, 2012; Dutta, Ghosh,

Samanta, & Dey, 2014; Easwaramoorthy &

Uthayakumar, 2010; Figliola, Serrano, & Rosso,

2007). Fractal parameters have also been utilized to

study the scaling behavior of the fluctuations of the

EEG while listening to musical stimuli (Maity et al.,

2015; Natarajan, Acharya U, Alias, Tiboleng, &

Khoshnoud, S., Nazari, M. and Shamsi, M.

Source-based Multifractal Detrended Fluctuation Analysis for Discrimination of ADHD Children in a Time Reproduction Paradigm.

DOI: 10.5220/0008876700380048

In Proceedings of the 13th International Joint Conference on Biomedical Engineering Systems and Technologies (BIOSTEC 2020) - Volume 4: BIOSIGNALS, pages 38-48

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

Puthusserypady, 2004). Despite this consistent

evidence for the brain-state related adaptability of

the multifractal structure, a few studies have been

conducted in the area of neurodevelopmental

disorders. Attention-deficit hyperactivity disorder

(ADHD) is a common neurodevelopmental disorder

in school-aged children which exhibit varying levels

of hyperactivity, inattention, and impulsivity, and

substantially affect their cognitive performance

(American Psychiatric Association, 2013; Sadock &

Sadock, 2011).

In our previous study, the multifractal spectrum

alterations of the resting-state EEG in children with

ADHD have been identified (Khoshnoud, Nazari, &

Shamsi, 2018). More precisely, during rest

condition, over frontal and right parietal scalp

channels, the multifractal spectrum was higher in

children with ADHD compared to the age-matched

control group. This elevated multifractal structure

suggests more complex EEG patterns in children

with ADHD compared to the healthy subjects during

rest. Considering this outcome, an investigation of

the multifractal structure of the EEG signals during

different paradigms in this group would have a great

impact on understanding their disorder. Several

studies have demonstrated that children with ADHD

have deficits in perceptual timing (Barkley, 1997;

Barkley, Edwards, Laneri, Fletcher, & Metevia,

2001; Barkley, Koplowitz, Anderson, & McMurray,

1997; Noreika, Falter, & Rubia, 2013; Rubia, Halari,

Christakou, & Taylor, 2009; Toplak & Tannock,

2005; Toplak, Dockstader, & Tannock, 2006).

Taking into account the different cortical activity

patterns of these children during time reproduction

(Khoshnoud, Shamsi, Nazari, & Makeig, 2017), one

could expect to see distinct multifractal structures

for these cortical sources during the time

reproduction condition.

To address this issue, we conducted an EEG

study in children with ADHD and age-matched

control subjects during two EEG recording sessions:

eye-open rest and time reproduction condition. We

used both the channel-based and the source-based

multifractal spectrum analysis in order to visualize

distinguished patterns of activity in both groups.

Finally, two groups were classified based on these

distinct multifractal patterns utilizing a support

vector machine (SVM) classifier. Our main

hypothesis was that children with ADHD would

exhibit distinct multifractal structure during both

EEG recording sessions and this pattern would be

more distinguishable in the source-based level

analysis.

2 MATERIALS AND METHODS

2.1 Participants and the Experimental

Design

The EEG data used here is the authors’ previously

recorded dataset consisting of EEG time series of 15

ADHD and 19 controls, 7-11 years of age in the

eyes-open rest and time reproduction conditions.

Details about the diagnosis criteria and inclusion

procedures could be found in Khoshnoud et al.

(2017). EEG recording starts with the eyes-open

resting period for 3 min followed by a visual time

reproduction task for approximately 10 min. In each

trial, following a trial start cue, a target white disk is

displayed on the screen center indicating the start of

a target interval of 1000 or 2200 ms (short and long

encoding phase). Participants are requested to keep

this interval in mind and reproduce it after a waiting

period of 1500 ms as indicated by a red disk

displayed at the screen center.

2.2 Data Processing

EEG data collection was accomplished using the

Mitsar® amplifier with 21 channels and WinEEG®

software. The reference electrodes were linked ear

lobes, with the ground electrode placed on AFZ. The

sampling frequency was 250 Hz. For this study, we

were particularly interested in the MF-DFA analysis

of the channel-based EEG signals as well as the

source-based components of the signals during both

recording sessions. Therefore each analysis was

followed by a specific processing procedure. The

EEG data were processed using EEGLAB functions

(version 13) (Delorme & Makeig, 2004) running on

Matlab (MATLAB2013a, The Mathworks, Inc.).

At first, the raw EEG signals were high-pass

filtered above 1 Hz and were low-pass filtered below

50 Hz using a windowed FIR sync filter to remove

line noise and other artifacts. After re-referencing to

a common average reference, the EEG time series

were visually inspected to reject periods with

abnormally high artifact levels. After this general

pre-processing step, the channel-based study was

continued with the MF-DFA analysis (section 2.3).

For the source-based study, additional processing

steps have been performed. The schematic overview

of these steps has been illustrated in Figure 1. At

first, the raw EEG signals were high-pass filtered

above 1 Hz and were low-pass filtered below 50 Hz

using a windowed FIR sync filter to remove line

noise and other artifacts.

Source-based Multifractal Detrended Fluctuation Analysis for Discrimination of ADHD Children in a Time Reproduction Paradigm

Figure 1: Overview of the EEG data processing steps for the source-based MF-DFA analysis after pre-processing of the

data. 1) Single-subject EEG data are decomposed by AMICA into a set of ICs and then nonbrain ICs are identified and

removed from further processing. 2) Equivalent current dipole positions for resumed ICs are estimated. 3) Based on the

dipole position and mean log spectra, the ICs are clustered across subjects into 7 clusters.

After re-referencing to a common average reference,

the EEG time series were visually inspected to reject

periods with abnormally high artifact levels. After

this general pre-processing step, the channel-based

study was continued with the MF-DFA analysis

(section 2.3). For the source-based study, additional

processing steps have been performed. The

schematic overview of these steps has been

illustrated in Figure 1.

ICA Decomposition- In order to decompose the

pre-processed EEG data to a corresponding set of

statistically independent source components, the

Adaptive Mixture Independent Component Analysis

(AMICA) algorithm (Palmer, Kreutz-Delgado, &

Makeig, 2006, 2011; Palmer, Makeig, Kreutz-

Delgado, & Rao, 2008) was used. AMICA has been

shown to have superior performance among blind

source separation algorithms for EEG decomposition

(Delorme, Palmer, Onton, Oostenveld, & Makeig,

2012). After identifying and removing the eye and

muscle activity-related components based on their

spectra, scalp maps, and time courses, the brain-

related independent components (ICs) were

selectedfor further analysis (Makeig et al., 2002).

Equivalent Current Dipole Position Estimation-

Subsequently, equivalent source distribution of the

brain-related ICs were computed using the DIPFIT

toolbox within EEGLAB

(http://sccn.ucsd.edu/wiki/A08:_DIPFIT). Scalp

electrode positions were co-registered to an MNI

template brain (Montreal Neurological Institute,

MNI, and Quebec) using nonlinear warping. Then, a

best-fitting equivalent current dipole was matched to

each IC using a template three-shell boundary

element method (BEM) head model based on the

MNI brain template. ICs with the equivalent dipole

model located within the brain which explained

more than 90% of the variance of the IC scalp map

were retained for further analysis.

IC Clustering- ICs across subjects were classified

based on similarities in IC dipole locations and mean

log spectra using K-means algorithm and totally

seven clusters were computed (Makeig et al., 2002;

Onton & Makeig, 2006). ICs whose distance to any

cluster centroid was more than three standard

deviations from the cluster mean distance were

considered outliers.

⋮

IC3

IC1

IC2

IC4

IC5

IC6

Vertical eye movements

Horizontal eye movements

Muscle activity

Noise

3. Clustering ICs based on dipole location and

mean-log spectra

2. Equivalent current dipole position

estimation

1. ICA decomposition and non-brain IC rejection

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

2.3 Multi-fractal Detrended

Fluctuation Analysis

There are two distinct types of multifractality in time

series: multifractality due to a broad probability

density function and multifractality due to long-

range correlations of the small and large fluctuations

in time series. While the former cannot be removed

by shuffling the data, the corresponding shuffled

series of the latter one will exhibit no- or weaker

multifractality scaling behavior (Kantelhardt et al.,

2002). The complete procedure for Mf-DFA is

divided into the following steps:

Step 1: The noise-like structure of the time series 



with length N was converted into a random walk:



















, 1,…,





)

Step 2: The integrated time series are divided into 



number of non-overlapping segments with equal

lengths s as follows:















)

Step 3: For each segment, the root mean square

(RMS) variance is calculated by Equation (3), in

which 



1,...,2



and 



 is the fitting

polynomial in segment ν:





,≡

























)

Step 4: Subsequently, to obtain the qth-order

fluctuation function, the mean RMS value over all

segments is calculated:





≡

2







,

/









/

)

Step 5: Because of spatial and temporal variations in

the scale-invariant structure of the multifractal time

series, the procedure is repeated for several time

scales (s). Finally, the scaling behavior of the

fluctuation functions is determined by analyzing the

log-log plots of 









versus s for each value of q:









(5)

The q-order Hurst exponent is related to the scaling

exponents 







by Equation (6):

1

(6)

Thereafter, scaling exponents could be converted

into the q-order singularity exponent (α) and the q-

order singularity dimension () by the following

equations to obtain the multifractal singularity

spectrum:



′

 and 





)

The width and shape of the multifractal spectrum

are valuable factors for distinguishing different

multifractal structures. In this study, we used the

width (maxmin) and the height of the

spectrum (















) as well

as mean (α) and mean  to evaluate the

multifractal spectrum.

2.4 Classification

The distinguishability of the extracted fractal

features was examined using a support vector

machine algorithm. The aim of the SVM is to

compute an optimal separating hyperplane to which

the distance from each nearest data sample in each

class is maximized (Vapnik & Lerner, 1963). SVM

offers a solution for non-separable cases, using

kernel mapping with projecting the data into a

higher-dimensional feature space using a nonlinear

function (ϕ(·)). Given a weight vector W and a bias

term b, the formulation of the hyperplane is as

follows:





.0

)

To find such an optimum hyperplane, the

optimization problem is as follows:













‖



‖



 







1

)

The above-mentioned problem is solved using the

Lagrangian optimization theory. Here, we tested

linear, polynomial and RBF kernel functions and

RBF kernel led to a better discrimination accuracy.

Source-based Multifractal Detrended Fluctuation Analysis for Discrimination of ADHD Children in a Time Reproduction Paradigm

Figure 2: a) Average values of the width (d) and height () of the channel-based multifractal spectrum in children

with ADHD and age-matched controls during rest (R) and time reproduction (Tp). b) Mean d for all scalp electrodes

during rest and time reproduction. c) Mean  for all scalp electrodes during rest and time reproduction.

3 RESULTS

3.1 Group Differences in the

Channel-based MF-DFA

As mentioned in the previous section, the EEG time

series have multifractal structures that contain both

types of multifractality. The important intellectual

question here is how this multifractality changes

through different brain states. In order to assess

variations in the degree of multifractality in

transition from the rest to time reproduction, average

MF spectra for each EEG signal in both conditions

(rest and time reproduction) were computed. A

comparison of the multifractal structures in the two

brain states was made by evaluating four features

extracted from MF spectra in each time series for all

subjects. These features are as follows: the width

(dα) and the height ( ) of the spectrum, mean

q-order singularity exponent (mean_

 ), and mean

q-order singularity dimension (mean_ 

 ).

Repeated measures analysis of variance (ANOVA)

was conducted separately on each feature with the

condition (rest vs. time reproduction) and electrode

positions as the within-subject factors and group

(ADHD vs. control) as the between-subject factor.

For the width and the height features, ANOVA

revealed a significant main effect of condition [(F (1,

32) = 9.15; p= .005), (F (1, 32) = 8.45; p =.007)],

demonstrating that for both groups, the shape of the

multifractal spectrum in the two conditions differ

significantly. In transition from the rest to time

reproduction, the width increased and the height

decreased. Figure 2 (a) shows the averaged values of

these two extracted features along with the standard

deviations of them in each condition for both groups.

Also, the electrode × condition interaction effect was

significant. Figure 2(b) and 2(c) demonstrate the

significant rise in the width and significant decline

in the height of the multifractal spectrum during

time reproduction in most of the scalp electrodes.

For mean_

, there was a significant effect of

condition (F (1, 32) = 8.52; p = .006) showing lower

values for time reproduction than rest state (Figure

3(a)). The effect of the group just for the mean_



was near significant (F (1, 32) = 8.45; p =0.07) with

controls showing higher values than ADHD subjects

regardless of the paradigm (Figure 3(b) and 3(c)).

This lower mean q-order singularity exponent value

in individuals with ADHD shows that the degree of

multifractality in signals of this group is marginally

lower than control subjects.

0.48

0.5

0.52

0.54

0.56

0.58

0.6

R_ADHD Tp_ADHD R_Control Tp_Control

dα

df(α)

(c)

(b)

(a)

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

Figure 3: a) Average values of the q-order singularity exponent (mean_) and q-order singularity dimension (mean_)

of the channel-based multifractal spectrum in children with ADHD and age-matched controls during rest (R) and time

reproduction (Tp). b) Mean_ for children with ADHD and control in transition from rest to time reproduction. c) Mean_

for all scalp electrodes during rest and time reproduction.

3.2 Group Differences in the

Source-based MF-DFA

The channel-based multifractal features showed

significant alterations between two conditions, failed

to clearly distinguish two groups. Concerning better

spatial resolution of the source-based analysis, one

could expect to see a more significant trend in the

source components. However, unlike scalp channels,

a pair of independent components from two subjects

might resemble or differ from each other in many

ways. Even with one subject in a different paradigm,

the results could be different as each paradigm leads

to specific source components. Therefore making

direct comparisons about the transition from rest to

the time reproduction for ICs would not be logical.

Notwithstanding, it is possible to assess ICs’

multifractal properties for two groups during one

paradigm. To achieve this, the multifractal spectrum

of 349 ICs from 34 subjects in 7 clusters were

calculated and averaged for each group and each

cluster. Figure 4(a) represents the clusters including

two occipital, one occipital-temporal, three frontal,

and one prefrontal cluster. The averaged multifractal

spectrums of each cluster for both groups during the

encoding phase of the time reproduction task has

been shown in figure 4(b). According to the figure

4(b), in the prefrontal, mid-frontal and right frontal

clusters, the multifractal spectrum of subjects with

ADHD in both durations exhibited a leftward shift

reflecting a lower degree of multifractality for these

individuals in these clusters. Similar to the previous

section, for the purpose of statistical analysis four

features of these spectrums (dα, 







,mean_

, and

mean_

 ) were assessed utilizing independent t-

test. The results showed that mean_

 for the

prefrontal, mid-frontal and right frontal source

clusters in the ADHD group were significantly lower

than that of the control group for both durations (p-

values < 0.02). Moreover, mean_

 for the right

occipital cluster in individuals with ADHD was

significantly higher than that for control subjects (p-

value < 0.019). Multifractal spectrum width in the

prefrontal cluster also displayed a significant

difference between two groups with the lower value

for the ADHD group than controls.

(c)

(b)

0.35

0.4

0.45

0.5

0.55

0.6

0.65

0.7

0.75

0.8

R_ADHD Tp_ADHD R_Control Tp_Control

mean_α

mean_f(α)

(a)

Source-based Multifractal Detrended Fluctuation Analysis for Discrimination of ADHD Children in a Time Reproduction Paradigm

Figure 4: a) 7 IC source clusters including two occipital, one occipital-temporal, three frontal, and one prefrontal cluster. b)

Averaged multifractal spectrums of each source cluster for each group (ADHD vs. control) during two interval reproduction

(short vs. long).

3.3 Classification Results for the Both

Channel-based and Source-based

Features

The multifractal features ability to distinguish

between two groups was furthermore evaluated

by passing them to the SVM classifier. For

both the channel-based and the source-based

measures, SVM with three types of kernel

functions (linear, polynomial, and radial basis

functions (RBF)) were tested. Here, the results

for the RBFSVM are mentioned as it yielded

better results. Using the holdout cross-

validation method, 80% of the data were used

to train the classifiers; the other 20% were kept

for testing and the results were reported as an

average accuracy after 20 repetitions.

Channel-based Classification- In favor of data

reduction, the 76 channel-based multifractal features

(19 electrode * 4 features) were reduced to the 15

principle components using the principle component

analysis preserving 90% of the signal variance.

Afterward, these principal components were fed into

the SVM classifier. Table 1 summarizes the results

of applying multifractal features to the SVM. Using

channel-based multifractal features showed 73.5%

and 77.78% accuracy during rest and time

reproduction, respectively. This outcome revealed an

increase in the accuracy of the classification of two

groups applying the time reproduction paradigm.

Source-based Classification- as reflected by the

group discrepancy results in section C, mean_

and mean_ 

 parameters yielded significant

differences across the two groups. Hence, these two

features were chosen for the classification with the

SVM. Considering the ICA algorithm, some subjects

might not have an IC in a cluster. In this case, the

nearest dipole to the central dipole of that cluster

was identified and the above mentioned multifractal

features from the corresponding IC were considered

as the features of that cluster for that subject.

Fourteen features (7 clusters * 2 features) for each

subject were passed to the SVM classifier with the

holdout cross-validation method described above.

The results have been reported in Table 1. The

mean_

 and the mean_  presented high

accuracy values of 86.67% and 81.67%,

respectively. It is in accordance with the previous

results in section C that mean_

 showed the most

distinguishing feature between the two groups.

4 DISCUSSION

In the current study, we used multifractal properties

to describe the dynamics of brain electrical activity

during two different brain states, the eyes-open rest

and the time reproduction condition. Furthermore,

multifractal features were assessed in the channel-

based as well as the source-based level to discover

(a)

(b)

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

group discrepancies between ADHD and age-

matched control participants. We found evidence of

multifractal structures as well as the presence of

both types of multifractality in the EEG signals. This

confirmed the presence of the scale-invariant

structure in the brain activity as stated in the

previous studies (Ihlen, 2012; Zorick & Mandelkern,

2013). Interestingly, the channel-based assessment

revealed that the shape of the multifractal spectrum

exhibited a significant alteration from rest to the

time reproduction condition. According to our

statistical results, in transition from the rest to time

reproduction, the width of the multifractal spectrum

increased and its height decreased significantly for

both groups. This indicates that switching from rest

state to the time reproduction state increased the

degree of multifractality of the EEG signals in both

groups. As represented in Figure 2(b-c), this trend

has been seen in almost all studied scalp electrode

sites.

The rise of the width of the singularity spectrum

during the time reproduction demonstrates an

increase of the non-uniformity and the complexity of

the signal and, hence, a climb in the degree of the

multifractality. An increase in brain complexity can

be regarded to be a measure for the brain reaching

an active state (Maity et al., 2015). According to the

MF-DFA, this increase is due to the rise in the

values of the q-order singularity exponents, hence

increase in the weak variations of the signal (h > 0

for q < 0) since at large variations (q<0) signals

behavior become more monofractal (Kantelhardt et

al., 2002). This can be interpreted in the light of

more beta activity during time perception. Beta

oscillations have been reported to correlate with time

perception (Ghaderi et al., 2018; Kononowicz &

Rijn, 2015).

Similarly, a decline in the q-order singularity

dimension variation and mean (  and

mean_  ) reflected a higher degree of

multifractality for EEG time series during time

reproduction. This outcome confirmed the previous

studies arguing the applicability of the scale-

invariant or multifractal structures to reflect changes

in the brain states (Dick, Svyatogor, Ishinova, &

Nozdrachev, 2012; Dutta et al., 2014; Figliola et al.,

2007; Ma et al., 2006; Maity et al., 2015; Natarajan

et al., 2004; Weiss et al., 2011, 2009; Zorick &

Mandelkern, 2013). Maity et al. (2015) reported a

considerable increase in alpha and theta multifractal

spectrum width and hence complexity of these

particular brain waves when subjects listen to the

Tanpura drone. Although channel-based multifractal

features provide significant measures for

distinguishing between the rest and the time

reproduction brain states, they showed weak results

for differentiating the two groups. Among the

multifractal properties, just the mean q-order

singularity exponent displayed near significant lower

values for ADHD subjects compared with controls.

In both conditions the mean_ , hence the degree of

multifractality of EEG signals for ADHD group was

lower than that for healthy control subjects.

It is well known that EEG has a limited spatial

resolution and the channel-level analysis can only

provide limited information about the cortical

regions involved in the generation and the

perturbation of these cortical regions activity

(Makeig, Bell, Jung, & Sejnowski, 1996). One

possible solution for improving the spatial resolution

of EEG is to perform source analysis by means of

source localization methods. To our knowledge, this

is the first time that MF-DFA is performed on the

source ICs of the EEG signals. Our main hypothesis

was that children with ADHD would exhibit distinct

multifractal structure during both EEG recording

conditions and this pattern is more distinguishable in

the source-based analysis. Our source-based

multifractal analysis in the time reproduction task

revealed significant differences between two groups

reaching better spatial resolution. As stated in the

results section, the prefrontal, mid-frontal and right

frontal clusters displayed a significantly different

multifractal spectrum shape for both short and long

duration reproduction conditions for both groups. To

be more precise, the multifractal spectrum of

individuals with ADHD exhibited a leftward shift

which reflects lower degree of multifractality,

consequently, less complexity and more uniformity

of ICs in these individuals compared to the control

subjects. The central tendency of the multifractal

spectrum is closely related to the monofractal Hurst

exponent.

Table 1: Classification accuracy for the channel-based and the source-based multifractal features.

Features

The channel-based

features

The source-based features

Mean-  Mean_





Rest

73.5% ----- -----

Time reproduction

77.78% 86.67% 81.67%

Source-based Multifractal Detrended Fluctuation Analysis for Discrimination of ADHD Children in a Time Reproduction Paradigm

The central tendency between 0.5-1 reflects a time

series with long-range correlations and below 0.5

would be an index of anti-correlated structure

(Kantelhardt et al., 2002). Therefore the leftward

shift in the multifractal spectrum of participants with

ADHD indicates less long-range correlations in their

EEG signals. This suggests that IC time series in

participants with ADHD in prefrontal, mid-frontal,

and right frontal regions are more uniform and

regular than in the control group. Similarly, it might

be because of fewer small and large variations on the

time series in these areas. These results are in line

with the previous studies reporting reduced

activation in the right dorsolateral prefrontal cortex

(DLPFC) and supplementary motor area (SMA) in

individuals with ADHD during a time discrimination

task (Rubia et al., 2009; Smith, Taylor, Brammer,

Halari, & Rubia, 2008). Correspondingly, in our

previous study, the higher amplitude of the mid-

frontal P300 evoked by the onset of the encoding

phase of time reproduction for ADHD individuals

has been linked to inappropriate and insufficient

allocation of attentional resources for the encoding

of the target interval (Khoshnoud et al. 2017).

Both groups of features were separately

exploited for the classification with SVM. While the

best accuracy for the 4 channel-based multifractal

features was during time reproduction condition

with 77.78%, the source-based mean_α displayed a

significantly higher accuracy with 86.67%. Using

the source-based multifractal features not only

increased the accuracy rate but also reduced the

number of features from 76 (19 * 4) to 14 (7 * 2) for

each participant. Our results confirmed our main

hypothesis by showing greater distinguishability of

the source-based multifractal features. Nevertheless,

the present study has some limitations that should be

considered. First and foremost is that this study

utilized a clinical EEG recording system with 19

electrodes, which resulted in a limited set of ICs and

therefore restricted source clusters. We believed that

using high-resolution EEG signals will lead to more

accurate source localization and subsequently more

ICs which would lead to better classification

accuracy. The second shortcoming of this work is

the small sample size (15 ADHD and 19 controls)

which might be the main source of low statistical

power for discrepancies between the two groups.

5 CONCLUSIONS

This study conducted a multifractal detrended

fluctuation analysis on the neural activities of the

brain in individuals with ADHD and age-matched

healthy children during the eyes-open rest and time

reproduction conditions. It was found that

multifractality could quantify the fluctuation

dynamics from two different pathological EEGs

taken at these two conditions. The results showed

that the sensor-level and the source-level

multifractal features provide different information

about the brain state. According to the results, in

transition from the rest to the time reproduction, the

degree of multifractality of the EEG signals for both

groups displayed a significant increase indicating

more complex and non-uniform activity during time

reproduction. Also, the prefrontal, mid-frontal and

right frontal clusters displayed significantly different

multifractal spectrum shapes for both groups.

Independent components in these clusters for

participants with ADHD exhibited less long-range

correlations suggesting reduced activation in these

source regions.

ACKNOWLEDGEMENTS

The first author would like to thank Dr. Marc

Wittmann and Dr. Scott Makeig for their support

and their great comments on this project.

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