What does delta band tell us about
cognitive processes: A mental
calculation study
Stavros I. Dimitriadis,Nikolaos A. Laskaris, Vasso Tsirka,
Michael Vourkas, Sifis Micheloyannis
Electronics Laboratory, Department of Physics, University of Patras, Patras 26500,
Greece
Artificial Intelligence & Information Analysis Laboratory, Department of Informatics,
Aristotle University, Thessaloniki, Greece
Medical Division (Laboratory L.Widιn), University of Crete, 71409 Iraklion/Crete,
Greece
Technical High School of Crete, Estavromenos, Iraklion, Crete, Greece
http://users.auth.gr/~stdimitr
1
Outline
Introduction
-Multichannels EEG recordings
-math calculations (comparison and multiplication)
-delta activity (cognition and relation to the difficulty of the task
-DMN (default mode network)
Methodology
sub-bands (0.78 – 3.96 Hz)
-Signal Power (SP) (derived via squaring and averaging the
filtered EEG data)
-network analysis (clustering coefficient (C) + path length (L))
-Small-World theory (γ,λ,σ)
-four delta
2
Outline
Results
Conclusions
3
Intro
Method
Results
Conclusion
s
Mathematical thinking, as a cognitive process, activates local and
spatially distributed cortical networks
Exact calculations are correlated with language function activating
language specific regions located in the left hemisphere
During mental calculations different processes are necessary, such as
the
-recognition of the numbers in their Arabic form,
-the comprehension of verbal representation of numbers,
-the assignment of magnitudes to numerical quantities,
-attention, memory, and other more specialized processes
During difficult math calculations, additional cortical regions,
particularly of the left hemisphere, show increased activation.
These calculations demand retrieval of simple mathematical fact
4
Intro
Method
Results
Conclusion
s
Motivation
Most widely studied bands are theta, alpha, beta and lower gamma
Delta and higher gamma activity have been examined less due to
artifact contamination
We intended not only to replicate the previous findings but also to
promote the understanding about the significance of this slow band
in math calculation
An increase of delta activity has been reported (Dolce &
Waldeier,1974,Harmony et al., 1996)
5
Intro
Method
Results
Conclusion
s
Outline of our methodology
The employment of narrow subbands gave us the opportunity to
distinquish the actual brain activity from eye movement related
activity, which is equally visible in all frequency range
Calculation of SP for each recording site
Based on EEG activity and the network of electrodes
the notion of functional connectivity graph (FCG) topology ,
is utilized to identify different modes of brain’s self organization.
Network analysis is performed for each subject/task and the intertask comparison reveals significant differences between the two
6
cognitive tasks
Intro
Method
Data acquisition: Math
Experiment
3 Conditions:
Control
Comparison
Multiplication
Results
Conclusion
s
18 subjects
30 EEG electrodes
Horizontal and Vertical EOG
Trial duration: 3 x 8 seconds
Single trial analysis
The recording was terminated when at least an EEG-trace
without visible artifacts had been recorded for each condition7
Intro
Filtering
Method
Results
Conclusion
s
Using a zero-phase band-pass filter (3rd order Butterworth filter),
signals were extracted within four different narrow bands (0.78-3.9 Hz
was divided into non-overlapping subbands, each of 0.78 Hz width)
Artifact Correction
Working individually for each subband and using EEGLAB (Delorme
& Makeig,2004), artifact reduction was performed using ICA
-Components related to eye movement were identified based on their
scalp topography which included frontal sites and their temporal course
which followed the EOG signals.
-Components reflecting cardiac activity were recognized
from the regular rythmic pattern in their time course widespread
8
in the corresponding ICA component.
Intro
Method
Results
Signal Power (SP)
Conclusion
s
Calculation of SP for each recording site
The SP values corresponding to each single electrode were
contrasted for every subband and additionally the whole
delta-band. Significant changes were captured via one-tailed
paired t-tests (p < 0.001).
Τhe functional connectivity graph (FCG) describes
coordinated brain activity
In order to setup the FCG, we have to establish connections
between the nodes (i.e. the 30 EEG electrodes).
Phase synchronization, is a mode of neural synchronization,
that can be easily quantified through EEG signals
9
Intro
Method
Results
Conclusion
s
Phase-locking Value (PLV)
PLV quantifies the frequency-specific synchronization between two
neuroelectric signals (Mormann et al., 2000 ; Lachaux et. al. 1999).
We obtain the phase of each signal using the Hilbert transform.
(t, n) is the phase difference φ1(t, n) - φ2(t, n) between the
signals.
PLV measures the inter-trial variability of this phase
difference at t.
If the phase difference varies little across the trials,
PLV is close to 1; otherwise is close to 0
10
Intro
Method
Results
Conclusion
s
PLV procedure for a pair of
electrodes
Adopted from Lachaux et
al,1999
11
Intro
Method
Results
Building the FCG
Conclusion
s
Establishing links
for a single electrode
0.9
0.6
The process is repeated for every electrode,
creating a complete graph.
12
Intro
Surrogate Analysis
Method
Results
Conclusion
s
-To detect significant connections, we utilized surrogate data to form
a distribution of PLI values, for each electrode-pair separately, that
corresponds to the case in which there is no functional coupling
- Functional connections that showed significant differences,
with respect to the distribution of PLI values generated
by a randomization procedure corresponding to each electrode
pair,were only considered.
-Since our analysis was based on a single sweep, we shuffled the time
series of the second electrode for each pair (in contrast to the case of
multiple trials where one shuffles the trials of the second electrode as
described in Lachaux et al., 2000).
13
Intro
Method
Surrogate Analysis
Results
Conclusion
s
-Finally, the original PLI values were compared against the
emerged baseline distribution (surrogate data) and this
comparison was expressed via a p-value which was set at p <
0.001.
-Graph
edges where the above criterion was not met, were
assigned a zero-weighted link.
5%
Nonparametric Null Distribution
14
Intro
Method
Results
Conclusion
s
Network Analysis
The clustering coefficient C of network is defined as :
C
1

N iN
 ( wij w jh wih )1 / 3
j , hGi , j , h  i
ki ( ki 1)
in which ki is the degree of the current node
The characteristic path length L is defined (through integration
across all nodes) as:
C
1

N iN
 ( wij w jh wih )1 / 3
j , hGi , j , h  i
ki ( ki 1)
15
Intro
Method
Results
Small – World network measures
Conclusion
s
-We rewired each network 1000 times using the algorithm
proposed in (Maslov & Sneppen, 2002)
-Derived Cr and Lr as the averages corresponding
to the ensemble of randomized graphs. The two (normalized)
ratios γ= C/Cr and λ= L/Lr were used in the summarizing measure
of “small-worldness”, defined as σ= γ/λ, which becomes greater
than 1 in the case of networks with small-world topology
-The above described computations were performed for
each subject separately
- Results were employed to detect systematic trends, via statistical
comparison among different tasks (comparison–control,
multiplication–control,comparison–multiplication), across subjects.
16
Intro
Method
Results
Small – World network measures
Conclusion
s
The three graph metrics (γ,λ and σ ) were contrasted, for every
subband, in a similar manner via paired t-test.
Recording Montage
-The selected data had been originally recorded based on a montage
using a common reference electrode.
-Since, this selection could influence significantly the subsequent
computations of SP and phase-synchrony we additionally rereference the data.
-Using average-reference, we repeated the above described calculations.
- We mention the observed differences and commonalities.
17
Intro
Signal Power (SP)
Method
Results
Conclusion
s
Bi-color (black and grey) circles denote the sites where significant
increase is observed before, but not after average re-referencing
Αll subbands show widespread SP-increase during math
Higher SP values of delta rhythm are seen over regions of the
left hemisphere during multiplication in contrast to the number
comparison
18
Intro
Method
Results
Conclusion
s
Network Analysis
Simultaneously, all subbands show small-world network characteristics i.e. optimum
organization.
The (normalized) clustering coefficient and the (normalized) path length are higher
during multiplication, for networks corresponding to those subbands which showed
significant inter-task SP-differences.
These findings could be considered as the result of increased nodal (local) activity
and less efficient remote connections within the corresponding brain
networks.
19
Intro
Method
Results
Conclusions
Conclusion
s
We investigate brain activity in four sub-bands during math
calculation.
We characterize EEG recorded brain activity
(Related to any particular cognitive task and the four sub-bands)
Based on functional connectivity graphs
Artifact contamination (occulographic and myographic activity)
can be overcomed using sub-bands + ICA.
Our methodology offers novel knowledge about delta activity during
math calculation and the nodal organization of the related FCGs.
The changes in SP and network organization related to
delta rhythm could be possibly explained as the results of inhibitory
20
mechanisms reflecting the deactivation of the default network.
21