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Brain connectivity in epilepsy

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Brain connectivity in epilepsy

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BRAIN CONNECTIVITY IN EPILEPSY

by

Hossein Shahabi

A Dissertation Presented to the
FACULTY OF THE USC GRADUATE SCHOOL
UNIVERSITY OF SOUTHERN CALIFORNIA
In Partial Fulfillment of the
Requirements for the Degree
DOCTOR OF PHILOSOPHY
(ELECTRICAL ENGINEERING)

August 2022

ii

To Mom and Dad

iii

Acknowledgment

I would like to express my deepest gratitude to my advisor, Dr. Richard Leahy, whose sincerity,
and encouragement I will never forget. Dr. Leahy has been an inspiration for me through my PhD
study. He is the true definition of a leader and the ultimate role model. This dissertation would not
have been possible without Dr. Dileep Nair, whose guidance from the initial step in research
enabled me to develop an understanding of the subject. I am thankful for the extraordinary
experiences he arranged for me and for providing opportunities for me to grow professionally. It
is an honor to learn from Dr. Leahy and Dr. Nair. I would also like to thank my committee members
for their efforts and contributions to this work: Dr. Vasilis Marmarelis and Dr. Justin Haldar.

I am grateful for my parents whose constant love and support keep me motivated and confident.
My accomplishments and success are because they believed in me. Deepest thanks to my sisters,
who keep me grounded, remind me of what is important in life, and are always supportive of my
adventures.

iv

Table of Contents

Dedication ............................................................................................................................. ii
Acknowledgment ................................................................................................................. iii
List of Tables ....................................................................................................................... vii
List of Figures .................................................................................................................... viii
Abstract .............................................................................................................................. xiii
1 Introduction & Background ............................................................................................ 1
1.1 Concepts .................................................................................................................. 2
1.1.1 Seizure and epilepsy .................................................................................................................2
1.1.2 Seizure types .............................................................................................................................2
1.1.3 The epileptogenic zon ...............................................................................................................3
1.1.4 Treatments for epilepsy ............................................................................................................4
1.1.5 Cortico-cortical evoked potentials ............................................................................................5
1.1.6 Graph analysis of brain connectivity ........................................................................................6
1.2 Motivation ............................................................................................................... 7
1.2.1 Seizure dynamics ......................................................................................................................7
1.2.2 EZ localization ..........................................................................................................................7
1.2.3 Brain connectivity atlas ............................................................................................................8
1.3 Contributions .......................................................................................................... 8
1.3.1 Developing a new measure of graph centrality for brain networks ..........................................8
1.3.2 Defining a network-based biomarker for the epileptogenic zone ............................................9
1.3.3 Comparing brain connectivity dynamics between seizures ......................................................9
1.3.4 Spatiotemporal analysis of CCEPs in focal cortical dysplasia .................................................9
1.3.5 Constructing an atlas for effective connectivity using CCEPs ...............................................10
1.3.6 Employing graph filtering techniques for estimating the epileptogenicity ............................10
1.3.7 Implementing brain connectivity Algorithms for public research and clinical purposes .......11
2 Ictal brain network ........................................................................................................ 12
2.1 Introduction ........................................................................................................... 12
2.1.1 Functional brain connectivity during seizures ........................................................................12
2.1.2 Multiunit recording .................................................................................................................13
2.1.3 High frequency oscillations (HFOs) .......................................................................................13
v

2.1.4 Epileptogenic networks ..........................................................................................................14
2.1.5 Modeling brain connectivity by multilayer networks ............................................................15
2.1.6 Brain networks in different frequency bands .........................................................................15
2.2 Methods................................................................................................................. 16
2.2.1 Patients and recordings ...........................................................................................................16
2.2.2 High-frequency ictal networks ...............................................................................................18
2.2.3 Eigenvector centrality .............................................................................................................18
2.2.4 Multilayer eigenvector centrality (mlEVC) ............................................................................19
2.2.5 Quantization and decomposition of mlEVC ...........................................................................20
2.2.6 Unsupervised clustering for EZ localization using left singular vectors of mlEVC ..............21
2.2.7 Evaluating the clustering performance ...................................................................................22
2.2.8 Weighted consensus clustering ...............................................................................................23
2.2.9 Brain state clustering by right singular vectors of mlEVC .....................................................24
2.2.10 Statistical analysis of functional connectivity in high-frequency ...........................................25
2.2.11 Computing low-frequency propagation networks ..................................................................26
2.3 Results ................................................................................................................... 27
2.3.1 Multilayer modeling of ictal networks discerns the epileptogenic zone ................................27
2.3.2 Seizures evolve with divergent network topologies ...............................................................32
2.3.3 EZ desynchronization occurs in the ictal period ....................................................................36
2.3.4 The EZ becomes isolated by aging and the duration of epilepsy ...........................................40
2.3.5 Expansive connectivity in low-frequency emerges before seizure termination .....................41
2.3.6 Pre-termination connectivity predicts post-ictal synchronization ..........................................44
2.4 Discussion ............................................................................................................. 45
2.4.1 The virtue of multilayer modeling of brain networks ............................................................46
2.4.2 Comparing results with Fingerprint approach ........................................................................46
2.4.3 Brain network alterations in epilepsy .....................................................................................47
2.4.4 Correlation between neural activity and patient’s demographics ...........................................48
2.4.5 High frequency synchronization in epilepsy ..........................................................................48
2.4.6 Dissimilar brain dynamics among seizures ............................................................................49
2.4.7 Brain network dynamics in seizure generation, evolution, and termination ..........................50
2.4.8 Final notes ..............................................................................................................................51
3 Effective connectivity in focal cortical dysplasia ......................................................... 52
3.1 Introduction ........................................................................................................... 52
3.2 Materials and methods .......................................................................................... 54
3.2.1 Demographic and SEEG data of participants .........................................................................54
3.2.2 Recording and anatomical labeling ........................................................................................56
3.2.3 CCEPs analysis .......................................................................................................................57
3.2.4 Assessing the significance of CCEPs responses by permutation test .....................................57
3.2.5 Comparing RMS of CCEPs between two FCD types using percentile bootstrap ..................58
3.2.6 Latency Analysis using between-by-within test .....................................................................58
3.3 Results ................................................................................................................... 59
3.3.1 RMS of CCEPs in FCD types I and II ....................................................................................59
3.3.2 Focal to bilateral tonic-clonic seizures and epilepsy localization ..........................................61
3.3.3 Latency periods ......................................................................................................................62
3.3.4 Electrode implantation ............................................................................................................64
3.3.5 Surgery Outcomes ..................................................................................................................65
3.4 Discussion ............................................................................................................. 67
4 Effective connectome .................................................................................................... 71
4.1 Introduction ........................................................................................................... 71
4.1.1 Brain stimulation and epileptogenicity ...................................................................................72
4.1.2 Current challenges in Stereoelectroencephalography ............................................................72
4.1.3 Hypotheses and goals .............................................................................................................73
vi

4.2 Methods................................................................................................................. 74
4.2.1 Patients and recordings ...........................................................................................................74
4.2.2 Effective connectome .............................................................................................................74
4.2.3 Graph Signal Processing .........................................................................................................82
4.2.4 Graph Filters ...........................................................................................................................82
4.2.5 Multi-input multi-output (MIMO) system identification. ......................................................84
4.2.6 Simulation of node variant graph filters .................................................................................86
4.3 Results ................................................................................................................... 89
4.3.1 Calculating the effective connectome ....................................................................................89
4.3.2 Distributions of normal and abnormal connections ................................................................91
4.3.3 Investigating the abnormal connections .................................................................................92
4.3.4 Estimating the epileptogenicity of brain ROIs in patients ......................................................96
4.4 Discussion ........................................................................................................... 100
4.4.1 Conclusion ............................................................................................................................100
4.4.2 Limitations and future work .................................................................................................101
References ......................................................................................................................... 102

vii

List of Tables
Table 2-1 Clinical characteristics of patients
Table 2-2 Comparing SEEG channels identified as true positives between two methods. for mlEVC in this work vs.
those identified using the Fingerprint
63
.
Table 2-3 Test statistics for network measures in high-frequency
Table 2-4 Test statistics for network measures in low-frequency
Table 3-1 Clinical characteristics of patients
Table 4-1 Top 10 ROIs with largest connectivity in normal brain
Table 4-2 Top 10 ROIs with highest chance of abnormality in outward connections
Table 4-3 Clinical characteristics of eight patients
Table 4-4 Epileptogenicity scores for eight patients

viii

List of Figures
Figure 1-1 Implanted SEEG electrodes from scalp view and skull X-ray. Pictures are obtained from Cleveland Clinic
website.
Figure 1-2 MRI images after surgery depicts the resected region of the brain. Pictures are obtained from Cleveland
Clinic website
Figure 2-1 Schematic of a multilayer network and measure of mlEVC. Four consecutive layers (time-points) of a
simulated network with intralayer (solid lines) and interlayer (dashed lines) edges. Nodes in each layer represent the
set of SEEG contacts and are colored and categorized into two clusters (red and blue). Interlayer edges (couplings)
were included between the same contacts at adjacent time points. The diameter of each node represents the relative
value of mlEVC, in which larger nodes are the most connected nodes and smaller nodes are more isolated
Figure 2-2 Identification of epileptogenic zone based on mlEVC (Patient 17). (a) SEEG signals during ictal period.
The red signals are a sample of contacts inside the EZ as identified by our method, and blue signals depict non-EZ
contacts outside the resection zone. (b) The multi-layer eigenvector centrality (mlEVC) during the ictal period. Each
row represents a channel (contact). Contacts are categorized and organized into two groups: resected and non-
resected as indicated on the right. They are also classified into two groups based on the proposed clustering
algorithm: target and non-target. The blue elements of mlEVC describe the isolated nodes of the super-graph (brain
network) while red values describe highly connected contacts. (c) The first three left singular vectors of the mlEVC.
The mlEVC spectra of different seizures were first quantized and concatenated before performing singular value
decomposition. The red nodes are those identified as predicted EZ based on unsupervised clustering.
ix

Figure 2-3 EZ localization for 16 patients. The predicted EZ (red circles) was computed as described in Methods.
Blue squares show non resected contacts and green triangles demonstrate the resected electrodes. The axes are the
top three left singular vectors of mlEVC.
Figure 2-4 Seizure evolution and state transition in three patients. Seizure evolution and brain states were extracted
using right singular vectors of mlEVC (see Methods). Capital letters show the center of each state. 𝒗𝑎,𝒗𝑏,𝒗𝑐, and
𝒗𝑑 are the best features extracted from singular vectors to cluster seizure evolution into brain states. (a) Patient 1.
All recorded seizures are scattered in same places. (b) Patient 3. The 𝒗𝑎−𝒗𝑏 plot portrays states that are unique for
seizures 1 and 2, but not observed in seizure 3. (c) Patient 15. The 𝒗𝑐−𝒗𝑑 plot depicts a distinctive area for seizure
1, which was not traversed in two other reordered seizures.
Figure 2-5 Seizure evolution and state transition in three patients. Seizure evolution and brain states were extracted
using right singular vectors of mlEVC (see Methods). Capital letters show the center of each state. 𝒗𝑎,𝒗𝑏,𝒗𝑐, and
𝒗𝑑 are the best features extracted from singular vectors to cluster seizure evolution into brain states. (a) Patient 1.
All recorded seizures are scattered in same places. (b) Patient 3. The 𝒗𝑎−𝒗𝑏 plot portrays states that are unique for
seizures 1 and 2, but not observed in seizure 3. (c) Patient 15. The 𝒗𝑐−𝒗𝑑 plot depicts a distinctive area for seizure
1, which was not traversed in two other reordered seizures.
Figure 2-6 High-frequency synchrony during ictal period. (a) time-varying high-frequency synchrony values for
three defined measures. The ictal period is normalized to a zero to one scale. The solid lines represent the median
and shaded plots display the normalized median absolute deviation (MAD), based on 10-4 bootstrap tests. The gray
rectangles display the periods of special interest. Note that EZ-nR connectivity drops substantially towards mid-
seizure and increases to match nR-nR and RnEZ-nR at seizure termination and post-ictally. (b) Connectivity
measures in pre-ictal, mid-seizure, and post-ictal. The centers of error bars show the median of all seizures in two
frequency bands and lines depict the MAD. Scatter circles exhibit the actual values (n=78 for each group). P-values
were computed for pairwise comparison between and within the three measures at each of the three periods.
Asterisks display corrected P-values; *P<0.05, **P<0.01, ***P<0.001. Only the mid-seizure interval shows
significant differences between EZ-nR and other measures. All measures are considerably higher in post-ictal than
their corresponding values in mid-seizure and pre-ictal periods. EZ-nR drops significantly in mid-seizure from pre-
ictal.
x

Figure 2-7 Connectivity measures in pre-ictal, mid-seizure, and post-ictal. The centers of error bars show the
median of all seizures (n=39) in two high-frequency bands (80-140 Hz and 140-200 Hz) and lines depict the scaled
median absolute deviation. Scatter circles exhibit the actual values (n=78 for each group). Visually, the
epileptogenic zone (EZ) is strongly desynchronized with resected non-EZ.
Figure 2-8 Correlation between normalized EZ-nR values and patients’ history. (a) Correlation between patients’
age and normalized EZ-nR synchronization in high frequency. Each data point indicates the average of normalized
EZ-nR values in mid-seizure among all seizures and two high-frequency bands (n=39). (b) The same plot as (a)
except here the x-axis describes the duration of epilepsy among patients.
Figure 2-9 Low-frequency brain connectivity during ictal period. (a) time-varying low-frequency connectivity
values for three defined measures. The ictal period is normalized to a zero to one scale. The solid lines represent the
median and shaded plots display the normalized median absolute deviation (MAD) based on 10-4 bootstrap tests.
The gray rectangles display the periods of special interest. EZ-nR connectivity drops in early-seizure and a
widespread brain connectivity occurs in the pre-termination period. (b) Connectivity measures in pre-ictal, early-
seizure, and pre-termination. The centers of error bars show the median of all seizures in two frequency bands and
lines depict the MAD. Scatter circles exhibit the actual values (n=39 for each group). P-values were computed for
pairwise comparison between and within the three measures at each of the three periods. Asterisks display corrected
P-values; *P<0.05, **P<0.01, ***P<0.001. Only the early-seizure interval shows significant differences between
EZ-nR and two other measures. All measures are considerably higher in pre-termination than their corresponding
values in early-seizure and pre-ictal periods.
Figure 2-10 Correlation of overall pre-termination low-frequency connectivity and post-ictal high-frequency
synchrony during the critical transition. (outliers were removed using a covariance method)
Figure 3-1 Recording paradigm and CCEPs responses in two reference montages. (A) A schematic representation of
electrode implantation. Each electrode can include up to 16 contacts. (B) CCEPs responses by stimulating the L’6-
L’7 pair. Cyan highlighted waveforms indicate significant responses after the permutation test (see Methods). (C)
Significant RMS values of CCEPs (in referential montage) are depicted for 10-600ms latency period. Each point in
the scatter plot represents a unique recording contact from a stimulation site. Hypothesis testing was conducted
using contacts in near distances (<50mm). The box at the bottom left displays the trimmed mean and confidence
interval for each group and the p-value for their comparison. For illustration purposes, data points larger than four
xi

median absolute deviations above the median were Winsorized in each axis, independently. Marginal distributions
depict the increased connectivity for FCD type I in comparison to FCD type II. N denotes the number of patients in
each category. (D) The data displayed using a bipolar montage illustrates consistent findings between FCD types I &
II.
Figure 3-2 CCEPs response in two subcategories. (A) RMS values of CCEPs (in referential montage) in latency
period 10-600ms. Here, only patients with focal to bilateral tonic-clonic seizures (FBTCS) were considered. Each
point in the scatter plot represents a unique recording contact from a stimulation site. Hypothesis testing was
conducted using contacts in near distances (<50mm). The box at the bottom left displays the trimmed mean and
confidence interval for each group and the p-value for their comparison. For illustration purposes, data points larger
than four median absolute deviations above the median were Winsorized in each axis, independently. Marginal
distributions depict the increased connectivity for FCD type I in comparison to FCD type II. N represents the
number of patients in each category. (B) The equivalent plot for patients with temporal lobe epilepsy.
Figure 3-3 CCEPs responses in different latency intervals. (A) RMS values of CCEPs are computed in early,
middle, and late latencies in patients with focal to bilateral tonic-clonic seizures (FBTCS). The plot shows the
trimmed mean (20% trimming on each side) with 95% confidence interval based on the trimmed mean. A robust
between-by-within analysis presented a significant difference in factor A (FCD Type). Numerical p-values illustrate
the distinction for each latency. Comparing FCD types in early and middle latencies revealed a disordinal interaction
(p<10-4). N denotes the number of patients in each category. The variable NP represents the number of contacts that
passed the permutation test for each latency. All p-values are corrected. (B) The same approach is illustrated for
patients with temporal lobe epilepsy.
Figure 3-4 Electrode implantation. Probability distribution functions (PDFs) of distances between recording contacts
and the stimulation pairs. (A) This plot shows PDFs for type I and type II considering all implanted electrodes and
gray matter contacts. (B) This plot is restricted to contacts with significant CCEPs responses. A between-by-within
ANOVA based on ranks indicated an interaction among factors (FCD type and significant response) (p=5.4×10
-6
).
Additionally, the differences of variances in two cases imply a broader response for FCD type I.
Figure 3-5 CCEPs responses for different surgery outcomes. Variations of CCEPs responses in different latency
intervals for two Engel classes of surgery outcomes in patients with FCD type II. RMS values of CCEPs are
computed in early, middle, and late latencies. The plot shows the trimmed mean (20% trimming on each side) with
xii

95% confidence interval based on the trimmed mean. A robust between-by-within analysis presented a significant
difference in factor A (Engel Class). Numerical p-values illustrate the distinction between two Engel Classes for
each latency. N denotes the number of patients in each category. The variable NP represents the number of contacts
that passed the permutation test for each latency. All p-values are corrected.
Figure 4-1 Framework for estimating the effective connectome
Figure 4-2 Distribution of connectivity elements in all patients after normalization
Figure 4-3 Probability distributions for normal and abnormal connections in the simulated data
Figure 4-4 The accuracy of detecting abnormal elements and estimating the true connectivity value
Figure 4-5 Graph filtering framework
Figure 4-6 Ground truth for graph filters and their estimation
Figure 4-7 Normalized mean squared error in estimating node-variant graph filters in different combinations of
graph shift operator density and signal to noise ratio.
Figure 4-8 Effective connectome (S).
Figure 4-9 Number of patients for estimating brain connections
Figure 4-10 Probability distributions for identified normal and abnormal connections
Figure 4-11 Comparing brain connections between different patients. Red dots represent the connectivity values
identified as abnormal while the gray dots depict normal connections.
Figure 4-12 Epileptogenicity maps on cortical surfaces

xiii

Abstract
In epilepsy, investigating brain connectivity has attracted considerable attention since
multiple different networks are involved in this neurological disorder. Seizure generation,
propagation, and termination occur through spatiotemporal brain networks. Notably, researchers
have studied functional and effective connectivity among patients with epilepsy. Functional
networks are constructed by statistical dependency between time series, and effective connectivity
displays the flow of information in the brain, i.e., the causality of signals. In this work, we have
pursued three general goals. First, we examined the functional connectivity during seizures.
Second, we investigated effective connectivity in patients with focal cortical dysplasia (FCD) by
using cortical stimulation. Lastly, we have developed a framework for creating an effective
connectivity atlas (connectome). We used this connectome to estimate the epileptogenicity of brain
regions in different patients.
Chapter 2 demonstrates the significance of large-scale brain interactions in high-frequency
(80-200 Hz) for identifying the epileptogenic zone (EZ) and seizure evolution. We have modeled
brain connectivity constructed from stereoelectroencephalography (SEEG) data during seizures
using multilayer networks to incorporate the continuity of neural dynamics. After introducing a
new measure of brain connectivity for temporal networks, named multilayer eigenvector centrality
xiv

(mlEVC), we applied a consensus hierarchical clustering to the developed model to identify the
epileptogenic zone (EZ) as a cluster of nodes with distinctive brain connectivity in the ictal period.
Our algorithm could successfully predict electrodes inside the resected volume as EZ for 88% of
participants, who all were seizure-free for at least 12 months after surgery. Our findings illustrated
significant and unique desynchronization between EZ and the rest of the brain in early to mid-
seizure. We showed that aging and the duration of epilepsy intensify this desynchronization, which
can be the outcome of abnormal neuroplasticity. Additionally, we illustrated that seizures evolve
with various network topologies, confirming the existence of different epileptogenic networks in
each patient. Our findings suggest the importance of early intervention in epilepsy and the possible
factor that correlates with disease severity. Moreover, by analyzing the propagation patterns of
different seizures, we asserted the necessity of collecting sufficient data for identifying the
epileptogenic networks.
In chapter 3, we compared cortico-cortical evoked potentials (CCEPs) as measures of
effective brain connectivity in 25 FCD patients with drug-resistant focal epilepsy who underwent
intracranial evaluation with stereoelectroencephalography (SEEG). We analyzed the amplitude
and latency of CCEPs responses following ictal onset single-pulse electrical stimulation (iSPES).
Our findings showed that compared to FCD type II, patients with type I demonstrated significantly
larger responses in electrodes near the ictal onset zone (<50mm). These findings persisted when
controlling for the location of the epileptogenic zone, as noted in patients with temporal lobe
epilepsies, and controlling for seizure type, as indicated in patients with focal to bilateral tonic-
clonic seizures (FBTCS). In type II, the root mean square (RMS) of CCEPs responses dropped
substantially from the early segment (10-60ms) to the middle and late segments (60-600ms). The
middle and late CCEPs latency segments showed the most considerable differences between FCD
xv

types I and II. FCD type II displayed a more restrictive area of hyperexcitability in both temporal
and spatial domains. In patients with FBTCS and type I FCD, the increased amplitudes of RMS in
the middle and late CCEPs periods appear consistent with cortico-thalamo-cortical network
involvement of FBTCS. The degree and extent of hyperexcitability differences may contribute to
the different postsurgical seizure outcomes noted between these two pathological substrates.

In chapter 4, we first explained the current challenges in incorporating the data of different
patients. We first proposed a methodology to identify the abnormal elements of a vector. We
applied this technique to the CCEPs data of our patients to construct an effective connectivity atlas
(connectome). Furthermore, we used node-variant graph filters to identify the epileptogenic
regions of the brain using the estimated connectome. Results revealed that in most patients with
seizure freedom after surgery, the brain areas with the highest score are inside the resected region.
These findings suggest the applicability of this technique for identifying the epileptogenic zone.

1 Introduction & Background
1

1 Introduction & Background
The term “brain connectivity” or “brain network” describes the interaction and cooperation
of brain regions. Different neuroimaging studies, e.g. Electroencephalography (EEG) and
functional magnetic resonance imaging (fMRI), have been employed to explore brain networks in
resting-state or during various cognitive tasks. Researchers have classified brain networks into
three categories: structural connectivity such as synapses or fiber pathways
1
; functional networks
constructed by statistical dependency between time series
2
; and effective connectivity which
displays the flow of information in the brain, i.e. causality of signals. Recent work in the last
decades has investigated brain networks in both healthy individuals and those with neurological
diseases. These studies have laid out essential information regarding brain functions and abnormal
changes in brain connectivity among patients with a mental disorder
3
.
In epilepsy, investigating brain connectivity has also attracted considerable attention
4
since
multiple different networks are involved in this neurological disorder
5–7
. This includes microscopic
and macroscopic recordings in ictal and interictal states
8,9
. In this work, we explore functional and
effective brain networks in patients with epilepsy using stereoelectroencephalography (SEEG)
signals
10
. SEEG is an invasive neural recording technique used to pinpoint the location of epileptic
seizures. Clinicians implant electrodes in specific parts of the brain, which are then tracked to
1 Introduction & Background
2

identify the cause of the seizure. Figure 1-1 presents the location of SEEG electrodes inside the
brain. Here, we first introduce some neurological and mathematical concepts, then describe the
motivation of our study, and finally outline the main contributions of this work.
1.1 Concepts
1.1.1 Seizure and epilepsy
The international league against epilepsy (ILAE) has defined an epileptic seizure as “a
transient occurrence of signs and/or symptoms due to abnormal excessive or synchronous neuronal
activity in the brain”
11
. The conceptual definition of seizure was then stated as “a disorder of the
brain characterized by an enduring predisposition to generate epileptic seizures, and by the
neurobiological, cognitive, psychological, and social consequences of this condition. The
definition of epilepsy requires the occurrence of at least one epileptic seizure”
11
. Later in 2014,
ILAE proposed the practical definition of epilepsy in which it is characterized as a brain disease
when any of the following conditions exist: “(a) at least two unprovoked (or reflex) seizures
occurring more than 24 hours apart; (b) one unprovoked (or reflex) seizure and a probability of
further seizures similar to the general recurrence risk after two unprovoked seizures (at least 60%)
occurring over the next 10 years; and (c) diagnosis of an epilepsy syndrome”
12
.
1.1.2 Seizure types
Seizures can be classified into two categories: generalized and focal. According to ILAE,
“Generalized epileptic seizures are conceptualized as originating at some point within, and rapidly
engaging, bilaterally distributed networks”
13
. Although for each seizure the onset might be
localized, the lateralization and exact location vary among instances. Generalized seizures can be
1 Introduction & Background
3

subdivided into; clonic, tonic, atonic, myoclonic, absence, and tonic-clonic
13
. In contrast, focal
seizures initiate in one hemisphere with a consistent pattern of ictal onset and can propagate to the
contralateral hemisphere. Focal seizures are characterized according to one or more features
including aura, motor, autonomic, and awareness and responsiveness
14
. However, for some
patients, there is more than one seizure type and propagation pattern
15
. These concepts have been
expressed in the form of electroclinical semiology. Clinical semiology is the manifestation of
epilepsy
16
which depends on electrical activity.
1.1.3 The epileptogenic zon
In a simple definition, the epileptogenic zone (EZ) is the area of the brain whose removal
would result in seizure freedom. In SEEG, the epileptogenic zone (EZ) not only takes into account

1
https://consultqd.clevelandclinic.org/turning-to-seeg-for-pediatric-patients-with-refractory-epilepsy/

Figure 1-1 Implanted SEEG electrodes from scalp view and skull X-ray. Pictures are obtained from
Cleveland Clinic website
1
.
1 Introduction & Background
4

the earliest ictal EEG change, it emphasizes an anatomo-electroclinical analysis
17
. This concept
incorporates both the anatomic region that initiates the epileptic discharge as well as the “primary
organization” which leads to the manifestation of the clinical seizure itself
18
. The gold standard
method of confirming EZ localization is based on whether seizure freedom has been achieved by
resection or ablation. The actual ground truth for EZ location is unknown since in many cases the
resection volumes may extend well beyond the EZ. In recent work, the EZ has been considered as
part of a network
19
. These epileptogenic networks in focal epilepsy have been invoked in
explaining the underlying pathogenesis of epilepsy, seizure initiation, ictal propagation, and
disease progression as well as various associated comorbidities
20
. This perspective is utilized in
our work to analyze seizures in the context of a distributed network of interacting regions that
include the EZ.
1.1.4 Treatments for epilepsy
Overall, 60-70% of patients can achieve seizure-freedom with medication
21
. In contrast,
drug-resistant epilepsy is defined as “failure of adequate trials of two tolerated and appropriately
chosen and used AED [antiepileptic drug] schedules (whether as monotherapies or in combination)
to achieve sustained seizure freedom”
22
. Patients with drug-resistant epilepsy would be subject to
further assessments and criteria to be eligible for surgery. These assessments include neuroimaging
studies such as scalp and invasive EEG, Magnetoencephalography (MEG), MRI, positron
emission tomography (PET), and ictal single-photon emission computed tomography (SPECT).
Patients with focal seizures and well-localized epileptogenic zone are suitable candidates for
epilepsy surgery. Currently, up to 50% of those with surgical resections attain long-lasting seizure
freedom after the surgery
23
. As a result there is considerable room for improvement in outcomes
1 Introduction & Background
5

through improved localization of the EZ and the networks with which it is associated, which is one
of the goals of this work. Surgical treatment can be performed by resecting or ablation of the EZ,
or other approaches to disconnect the problematic tissue from the rest of the brain network.
Recently, responsive neurostimulation (RNS) therapy has been developed to modulate brain
regions for halting seizures. In all cases, identifying the epileptogenic zone is the critical step.
Figure 1-2 shows examples of resected areas of the brain in post-op MRIs.
1.1.5 Cortico-cortical evoked potentials
As mentioned earlier, effective connectivity aims to establish a causal or directed relationship
between separate brain regions
24
. One approach for measuring effective connectivity involves
recording cortico-cortical evoked potentials (CCEPs)
25
which can be performed in patients
undergoing intracranial electrode evaluation with either subdural electrodes or SEEG. CCEPs are
recorded by applying single pulse direct electrical cortical stimulation (SPES) to pairs of
intracranial electrodes and averaging the evoked potentials in the remaining. In this way, CCEPs
can directly study pathological and functional large-scale brain networks in-vivo with a high
degree of spatiotemporal resolution
25,26
in the regions of the implanted intracranial electrodes.
Using this paradigm, researchers have identified the language
25
and motor
27
networks.
Additionally, SPES and CCEPs have been employed to map the degree of epileptogenicity by
measuring the level of neuronal excitability
28,29
. In this work, we use CCEPs to differentiate
between two types of Focal Cortical Dysplasia (FCD). These studies suggested that either an
increased amplitude of the early response of CCEPs or the presence of a delayed response
following SPES can localize the epileptic cortex.

1 Introduction & Background
6

1.1.6 Graph analysis of brain connectivity
One of the main approaches for quantification of brain connectivity that we will use in this
work is graph analysis. various methods have been proposed during the last two decades which
assess the integration, segregation, and node centrality in single-layer brain networks
30
. Recently,
the concept of multilayer networks has been expanded to different aspects of science, engineering,
and sociology
31
. In brain connectivity studies, multiscale networks have emerged with several
capabilities, such as analysis of ordinal brain networks
32
. In this research, we employ knowledge
of multiscale brain networks to address one current shortcoming in epilepsy research. To be
precise, we use the term “multilayer networks” in this manuscript when referring to ordinal
samples of time-varying networks. Section 2.2.4 describes the mathematical formulation of
multilayer networks.

2
https://my.clevelandclinic.org/ccf/media/files/Epilepsy_Center/Transcript_Bingaman.pdf
Figure 1-2 MRI images after surgery depicts the resected region of the brain. Pictures are obtained from Cleveland
Clinic website
2

1 Introduction & Background
7

1.2 Motivation
In this section we mention our top three motivations for pursuing this research.
1.2.1 Seizure dynamics
Neural activity is highly time-varying and non-stationary. In order to study brain network
dynamics, researchers have commonly constructed time-varying networks by windowing and then
analyzing each window separately. One drawback of this technique is potential discontinuity of
the computed measures across time, in contrast to intrinsic continuity of neurological systems.
Also, separate analysis of temporal brain networks limits the timescale of the method to the sample
rate. There is growing evidence that neural processes occur in multiple timescales
33
. The use of
multilayer networks in brain connectivity studies, as we describe in 2.2.4, can facilitate the
modeling of brain dynamics across temporal scales during and between ictal periods.
1.2.2 EZ localization
Current methods for identifying the epileptogenic zone mostly evaluate the presumed
features of the ictal onset zone, like spiking and high frequency oscillations (HFOs) in each
electrode, independently. There are a couple issues limiting these approaches for EZ localization.
First, not all electrodes inside the EZ represent those features, and not all electrodes who display
that features belong to EZ. Second, as we discussed previously, the EZ has been recently
considered as part of an epileptogenic network with possibly distributed locations. Consequently,
it is rational to hypothesize that in a large-scale brain graph, a set of nodes with distinctive features
can better describe the EZ.
1 Introduction & Background
8

1.2.3 Brain connectivity atlas
Most of the research in CCEPs has been done at the subject level, as electrode implantations
are unique for each patient and do not cover the entire brain. Few studies have explored creating
an atlas of brain connectivity using CCEPs. However, those investigations require the clinical
labels of all regions and patients to remove connections related to the epileptogenic zone from the
analyses. In this work, we developed a methodology to estimate brain networks in a normal brain
(connectome), using the patients' data by automatically identifying the abnormal connections
without labels. We use this connectome to determine the epileptogenicity of brain areas.
1.3 Contributions
1.3.1 Developing a new measure of graph centrality for brain networks
Multilayer modeling of brain networks allows us to define new measures of brain
connectivity which mimics topological structure of neural interactions. In 2.2.3 we discuss the
basics of eigenvector centrality which can represent the importance of each node in a network.
Since we analyze brain connectivity during seizures as a multilayer network, the conventional
measure of EVC which is defined for single layer graphs cannot incorporates the non-stationary
characteristics of brain networks. As a result, we developed a new metric using the leading
eigenvectors of the adjacency matrix of the super-graph. This measure not only captures the
continuity of neurological signals but also processes data across multiple time scales.
1 Introduction & Background
9

1.3.2 Defining a network-based biomarker for the epileptogenic zone
In this research, we proposed a biomarker for EZ localization based on the centrality feature
of multilayer brain graphs. Unlike other biomarkers, this measure does not assume specific
characteristics for EZ, except a distinctive pattern of connectivity in spatiotemporal networks. To
implement this approach in an automatic framework, we used unsupervised hierarchical clustering
to identify a dense cluster of nodes in the feature space of all nodes extracted from left singular
vectors of mlEVC. This approach is described in 2.2.6.
1.3.3 Comparing brain connectivity dynamics between seizures
Neurologists are interested in classifying seizures, usually by semiology, or the way epileptic
seizures manifest themselves. This can be done through sensory, motor, autonomic and
consciousness related manifestations and their order of appearance before and during seizures
34
.
Another way to investigate semiology is by using electrical activity produced by epileptic seizures
and analyzed with respect to established neural pathways as the seizure progresses in time and
space. In this study, we analyzed and compared different seizures in each patient using the
temporal component of mlEVC. Our results indicate that seizures can have dissimilar patterns of
propagation within a single subject, suggesting several semiologies in each individual. In other
words, seizures can be generated by various and separate epileptogenic structures
15,35
.
1.3.4 Spatiotemporal analysis of CCEPs in focal cortical dysplasia
Focal cortical dysplasia (FCD) is a common pathological substrate in epilepsy surgery. In
chapter 3, we discuss different types of FCD and pathological differences among them. Similar to
other substrates of focal epilepsy, a notable challenge in FCD is to determine the extent of the
1 Introduction & Background
10

epileptogenic zone. Effective brain connectivity can be employed as a measure for identifying the
epileptogenic zone. We used CCEPs as a measure of hyperexcitability to compare responses
between the two common types of FCD. Our findings illustrated the wider and larger response for
FCD type I when compared with type II. We also found that a better surgical outcome is associated
with spatially and temporally limited CCEPs response.
1.3.5 Constructing an atlas for effective connectivity using CCEPs
CCEPs allow us to map effective connectivity from stimulated sites to other recording areas.
Since electrode implantation differs among patients and does not cover all cortical and subcortical
areas in each case, a full connectivity mapping cannot be gained by subject-level analysis. Instead,
by combining the networks of all patients, we can derive a group atlas, which we refer to as the
effective connectome. The challenge is to construct this atlas while also accounting for differences
in epileptic networks across subjects. Our goal then is to construct a nominally ‘normal’ atlas
without having the clinical labels for brain regions in each patient.
1.3.6 Employing graph filtering techniques for estimating the epileptogenicity
Once a group-level effective connectome is calculated, we can compare an individual’s brain
connectivity with the atlas and find the abnormalities for each patient. We employed node variant
graph filters to adjust the connectome among participants. The filter weights can indicate the
epileptogenicity of nodes in each subject. Our findings suggested that this measure pinpoints the
epileptogenic zone in majority of patients.
1 Introduction & Background
11

1.3.7 Implementing brain connectivity Algorithms for public research and clinical purposes
In the last two decades, our group, the BIG lab, has implemented signal and image
processing techniques used in neuroscience and neuroimaging research in two publicly available
software packages, namely Brainstorm
36
and Brainsuite. As a key collaborator in Brainstorm, I
have developed and updated several signal filtering and connectivity tools which are accessible
and useful to anyone interested in doing brain research. Using these techniques, we investigated
whether posterior regions of the default mode network (DMN), showed elevated connectivity with
the subgenual prefrontal cortex (sgPFC) in remitted major depressive disorder (rMDD) and
whether this connectivity was related to maladaptive rumination
37
. We examined this hypothesis
in 20 rMDD patients compared to 17 healthy controls. Also, we assessed whether this posterior
DMN–sgPFC connectivity positively correlates with rumination. Using minimum norm as the
source estimation method, we extracted current density maps from six regions of interest (ROIs)
within the posterior DMN. EEG source-space functional connectivity was calculated using the
Amplitude Envelope Correlation method. Relative to controls, rMDD showed increased posterior
cingulate cortex (PCC)–sgPFC connectivity in the beta-3 (25–30 Hz) band. As hypothesized,
PCC–sgPFC connectivity was positively associated with rumination for rMDD, even after
controlling for depression and anxiety. In conclusion, EEG resting state PCC–sgPFC functional
connectivity is significantly elevated in rMDD and is associated with rumination, suggesting that
EEG PCC–sgPFC connectivity may be useful as a neural marker to identify individuals at risk for
depression.

2 Ictal brain network
12

2 Ictal brain network

2.1 Introduction
2.1.1 Functional brain connectivity during seizures
Investigating brain connectivity in epilepsy has attracted considerable attention
4
since
multiple different networks are involved in this neurological disorder
5,6,38
. Large-scale
epileptogenic networks consist of cortical and subcortical areas that are involved in seizure
generation and propagation
35
. These networks can either represent an increase or decrease in brain
synchrony
5,39,40
or elucidate regions traversed by ictal propagation which is referred to as travelling
waves in studies with microscopic recordings
9,41–45
. This underlying association between brain
areas in epilepsy can describe the seizure spread and termination processes
4
, explain seizure
semiology
16
or assist in identifying the seizure onset zone (SOZ)
8
. Traditionally, seizures have
been considered to be characterized by a state of hypersynchrony. Yet recent work
4
describes an
early stage of desynchronization
5,46
followed by synchronization amid seizure termination
47,48
.
Constructing connectivity maps with various recording techniques and different computational
2 Ictal brain network
13

measures over a wide range of frequencies has given rise to different controversial perspectives on
how seizures should be characterized
49
. Few studies have examined the functional connectivity
between SOZ and other areas of the brain during ictal periods. Electrocorticographic (ECoG) data
suggested that for some patients the SOZ is isolated from the rest of the network early in the
seizures allowing for SOZ detection in this way
8
. It has also been suggested that ictal periods can
be delineated by a steady series of states
8
, although whether this is true in all patients remains
controversial. Others have shown a decreased synchrony between SOZ and normal brain regions
50
.
It remains unclear how the degree of desynchronization is correlated with physiological parameters
such as age and duration of epilepsy
7
.
2.1.2 Multiunit recording
Several studies have used multiunit recording to explore ictal propagation
networks
9,41,43,44,51
. At the microscopic spatial scale, the hypersynchronous ictal core with high
neural firing can be distinguished from penumbra with relatively small and sparse firings
44
. In the
early part of the seizure, the slow-moving ictal wavefront involves the core and surrounding areas.
After recruitment, the low-frequency travelling waves rapidly propagate to other cortical regions
43

in a two-dimensional spatial scale
9
. However, the mechanism in which ictal discharges spread in
the brain volume is still undetermined.
2.1.3 High frequency oscillations (HFOs)
The intense firing of neurons in the ictal core is characterized by high-frequency oscillations
(HFOs)
52
in local field potentials (LFPs)
41
. These oscillations, which span 80-500 Hz
53
, have been
analyzed for their value in SOZ localization
54,55
during ictal
41
and interictal
56,57
periods.
2 Ictal brain network
14

Nevertheless, manual HFO (ripple) detection is time consuming
56
and automatic approaches
produce a large number of false positives
58
. Moreover, some interictal analyses of slow-wave sleep
questioned the utility
59
and accuracy
60
of HFOs to serve as a biomarker for epileptogenic tissue
identification. These observations can be further supported by a resting-state
stereoelectroencephalography (SEEG) study which has delineated the long-range high-frequency
synchronization of physiological HFOs among the non-epileptogenic regions
61
. While HFOs have
been employed in analyzing functional
46
and propagation
6
networks, the spatiotemporal dynamics
of ictal high-frequency synchronization (HFS) at macroscopic scales remain largely unknown.
2.1.4 Epileptogenic networks
In this chapter we analyze SEEG recordings of cortical and subcortical regions. In SEEG,
the epileptogenic zone (EZ) not only takes into account the earliest ictal EEG change, it emphasizes
an anatomo-electroclinical analysis
17
. This concept incorporates both the anatomic region that
initiates the epileptic discharge as well as the “primary organization” which leads to the
manifestation of the clinical seizure itself
18
. The gold standard method of confirming EZ
localization is based on whether seizure freedom has been achieved by resection or ablation. The
actual ground truth for EZ location is unknown since in many cases the resection volumes may
extend well beyond the EZ. In recent work, the EZ has been considered as part of a network
19
.
These epileptogenic networks in focal epilepsy have been invoked in explaining the underlying
pathogenesis of epilepsy, seizure initiation, ictal propagation, and disease progression as well as
various associated comorbidities
20
. This perspective is utilized in our work to analyze seizures in
the context of a distributed network of interacting regions that include the EZ. Because of the
importance of HFOs in epilepsy and SOZ localization, we construct synchronization networks in
2 Ictal brain network
15

the 80-200 Hz range, to be in line with similar studies
46,54
. Fast rhythmic bursting neurons, which
have the highest tendency to initiate seizures, are largely responsible for generating ultra-fast
oscillations or ripples (80-200 Hz)
62
. We hypothesize that during seizures, the EZ has an abnormal
and unique pattern of connectivity with other brain areas.
2.1.5 Modeling brain connectivity by multilayer networks
Spatiotemporal high-frequency synchronization is modeled here using multilayer networks,
in which individual graphs in different times are linked together to construct a single super-graph.
The multilayer structure has considerable advantages over single-layer analysis
32
. First, the
interlayer coupling between neighboring time points in this model allows us to incorporate the
continuity in neural dynamics and dependency between seizure states. Second, by tuning the
coupling parameter, processes with different timescales can be distinguished. Third, the extracted
measures on these networks are less susceptible to noise in the data or spurious connectivity. We
explore the question of whether the EZ can be identified by unsupervised clustering of nodes
(representing SEEG contacts) in the feature space of these multilayer networks.
2.1.6 Brain networks in different frequency bands
Our connectivity-based EZ identification results show reasonable consistency with a
previous approach (described as the fingerprint of the epileptogenic zone)
63,64
which uses three
ictal features for EZ localization, namely: low-voltage fast activity (LFD), preictal spiking, and
suppression of lower frequencies. Understanding the connectivity dynamics of EZ and surrounding
areas with the rest of the brain can shed light on underlying processes including seizure
propagation and termination. We evaluate these interactions in different frequency bands. To use
2 Ictal brain network
16

consistent terminology, here the term “high-frequency synchrony” is mostly utilized to describe
brain networks at higher frequencies (80-200 Hz). On the other hand, the word “connectivity” has
been assigned to both propagation networks in low frequency (2-50 Hz) and synchronization
networks in high frequency (80-200 Hz). Our findings illustrate early high-frequency
desynchronization and late increase in brain connectivity during seizures. Although seizures
usually initiate with a loss of synchronization in a small area, their termination process demands
widespread brain connectivity across multiple scales. During seizure cessation, the brain
experiences a critical transition with a hysteresis behavior
65
, indicating the future state depends on
the current one. Accordingly, we hypothesize that post-termination high-frequency synchrony is
correlated with pre-termination connectivity in low frequency.
2.2 Methods
2.2.1 Patients and recordings
The full procedure for participant selection and data recording is described in our previous
work
63
. Briefly, we selected 16 patients who underwent SEEG implantation in the Epilepsy Center
at Cleveland Clinic. SEEG placement
66
used multi-lead depth electrodes (AdTech, Integra, or
PMT). Post-implanted 3D computed tomography (CT) images were aligned to T1-weighted MRI
for anatomical localization of electrode leads. Patients were monitored for up to two weeks and
their seizures recorded by the Nihon Kohden EEG system with a sampling rate of 500 Hz (before
2012) or 1000 Hz (after 2012). After a thorough evaluation, the identified epileptogenic zone was
resected or ablated. The contacts (electrode leads) inside the resection or ablated region were
determined by coregistration of the post-implant CT to a post-resection MRI 1-6 months after
2 Ictal brain network
17

surgery. Based on follow-up information, all patients were determined to be seizure-free (Table
2-1). Only contacts inside the gray matter were considered in our analyses.

Table 2-1 Clinical characteristics of patients
ID
Age
(years)
Epilepsy
duration
(years)
MRI lesion
Resection/ablation
details
Surgical pathology
Follow-
up
(months)
Anatomical
location of the
epileptogenic zone
1 43 37
FCD, insular/frontal
operculum
Anterior insular/ frontal
operculum
FCD type 2B 13
Insular/frontal
operculum
3 33 17 Hippocampal sclerosis Anterior temporal lobe Hippocampal sclerosis 48 Temporal
4 17 8 Negative
Laser ablation, superior
frontal gyrus
No pathology 19 Frontal
5 16 1
Benign neoplasm,
posterior para-
hippocampal gyrus
Posterior para-
hippocampus gyrus and
neoplasm
Low grade glial/
glioneuronal neoplasm
39
Basal posterior
temporal
6 46 41 FCD, mesial frontal Prefrontal lobe Non-specific 38 Frontal
7 5 1 Negative
Superior frontal gyrus,
superior frontal sulcus,
frontal pole
FCD type 2B 21
Superior frontal
gyrus/superior
frontal sulcus
8 63 14 Negative Orbitofrontal FCD type 1 44
Orbitofrontal/ pars
orbitalis
9 33 19
Gliotic postoperative
changes
Anterior temporal lobe FCD type 1B 40 Temporal
10 21 11 Negative Occipital lobe
Grey matter
heterotopia,
FCD type 1B
12 Cuneus
11 32 27 FCD, precentral gyrus Precentral gyrus Non conclusive 77 Precentral gyrus
12 22 3
FCD, superior frontal
sulcus
Superior and middle
frontal gyri, anterior
cingulate
FCD type 2B 78 Frontal
13 19 18 Negative Middle frontal gyrus FCD type 1 48
Inferior frontal
sulcus/middle
frontal gyrus
14 30 18 Negative Frontal operculum FCD type 2B 47
Frontal operculum/
subcentral region
15 20 11 Negative Frontal lobe FCD type 1 82
Superior frontal
gyrus/superior
frontal sulcus
16 65 25 Negative Anterior temporal lobe FCD type 1C 39 Temporal
17 65 9 Negative Anterior temporal lobe FCD type 1C 36 Temporal
2 Ictal brain network
18

2.2.2 High-frequency ictal networks
Intracranial EEG signals (N channels) were bandpass filtered in the 2-200 Hz range and
notch filtered at 60, 120, and 180 Hz. The time-varying brain networks were computed in two
frequency bands, 80-140Hz, and 140-200Hz. Briefly, we first applied the Hilbert transform to
compute analytical signals in each frequency band. Dynamic connectivity matrices were calculated
using pair-wise lagged-coherence
67
between signals in 2.5s windows with 80 percent overlaps.
Here, the term “synchrony” is employed interchangeably with brain connectivity in high-
frequency. Lagged-coherence removes spurious coherence values caused by volume conduction.
As a result, we have time-varying N×N networks in two frequency bands for each seizure. The
connectivity matrices were z-scored with respect to the pre-ictal period and their values mapped
into the interval (0 1] using an exponential transform
8
. Assuming a total of T overlapping 2.5s
windows during a seizure, in which T depends on the length of the seizure and window parameters,
results in a three-dimensional (N×N×T) matrix or network for each frequency band. Next, we
investigated the node centrality in these spatiotemporal networks, by multilayer modeling of
graphs. However, before introducing our method, we explain the mathematical background for
eigenvector centrality in single-layer graphs.
2.2.3 Eigenvector centrality
Consider graph G with adjacency matrix A and N vertices. For simplicity, we assume matrix
A is weighted and symmetric. Based on the concept of eigenvector centrality (EVC), the
importance of a vertex in a network is increased by having connections to other vertices that are
themselves important, so each node’s score is proportional to the sum of the scores of its
2 Ictal brain network
19

neighbors
68
. Assume we have an initial guess about EVC value for each node 𝑥
!
and we aim to
improve it for node i
69
,
𝑥
"
#
=#𝐴
"!
𝑥
!
!
(2−1)
It can happen several times and be written in a vector form as
𝒙(𝑡)=𝐀
$
𝒙(0) (2−2)
The initial condition 𝒙(0) can be expressed by a weighted (𝑐
"
) sum of the eigenvectors (𝒗
"
)
of matrix A. After substitution,
𝒙(𝑡)= 𝐀
$
#𝑐
"
𝒗
"
"
=𝜆
%
$
#𝑐
"
2
𝜆
"
𝜆
%
3
$
𝒗
"
"
(2−3)
where 𝜆
"
are the eigenvalues of matrix A. Since 𝜆
%
>𝜆
"
𝑓𝑜𝑟 𝑖 ≠1, all terms in the above
sum except the first one will converge to zero when 𝑡 →∞. As a result, the eigenvector centrality
will be proportional to the leading eigenvector of the matrix A. However, this simplification might
become problematic in case we have several structures (cliques) in our graph
68,69
, an issue that we
face in time-varying brain networks. Consequently, we introduce a new measure using multilayer
modeling of temporal network.
2.2.4 Multilayer eigenvector centrality (mlEVC)
Using the (N×N×T) matrix in 2.2.2, we constructed an NT×NT super-adjacency
(connectivity) matrix 𝒜 with coupling effects between layers
31
. The diagonal N×N blocks were
the adjacency matrices at different time points. Off-diagonal terms were identity matrices
multiplied by a coupling parameter c, in which 𝑐 ∈{1,2,…,10,15}. Matrix 𝒜 is irreducible for
any c>0. The weighted identity blocks represent ordinal interlayer links between nodes
2 Ictal brain network
20

corresponding to a particular contact (neighboring time points). One can consider the leading
eigenvector of matrix 𝒜 (𝝋
%
∈ℝ
&'
) as the eigenvector centrality (EVC) of this super-graph
70
.
However, in our work, this vector was focused on a few adjacent layers and did not visually capture
the centrality across all layers. This is because of the time-varying nature of ictal networks and the
relatively weak coupling across time in our model. We therefore defined a multilayer EVC
(mlEVC) that combines the eigenvectors corresponding to the largest eigenvalues. The effective
rank of 𝒜 was 𝑇 in most cases in which the eigenvectors 𝝋
%
,…,𝝋
'
were each restricted to
significant values across a few layers only. The Perron-Frobenius theorem asserts the positivity of
𝜎
%
(the largest eigenvalue) and 𝝋
%
but the elements of other eigenvectors will be non-positive
(𝝋
"
≼0 𝑓𝑜𝑟 2≤𝑖 ≤𝑇). Since EVC is a measure of ranking between nodes, we considered the
absolute values for all vectors. To extract the mlEVC for matrix 𝒜, the T largest eigenvalues were
multiplied by their corresponding eigenvectors and the absolute values of the results summed,
𝑚𝑙𝐸𝑉𝐶 =|𝜎
%
𝝋
%
|+|𝜎
(
𝝋
(
|+⋯+|𝜎
'
𝝋
'
| (2−4)
This vector was then reshaped to an N×T matrix, representing the variation in each node’s
centrality over time, which we refer to as the multilayer EVC (mlEVC). In the case where c=0,
mlEVC represents the concatenated EVC of the adjacency matrices computed separately for each
time point. Elements with the smallest or highest values show isolated or strongly connected
instances in time, respectively. Figure 2-1 displays schematic of a multilayer network and measure
of mlEVC for a network with four layers.
2.2.5 Quantization and decomposition of mlEVC
Since eigenvector centrality provides a connectivity ranking among nodes, the mlEVC of
each seizure was quantized based on a percentile thresholding (d). The top d/2-portion of elements
2 Ictal brain network
21

were assigned a value of ‘1’, the bottom d/2-portion a value of ‘-1’, and the remainder a value of
‘0’. We concatenated the quantized mlEVC matrices into an 𝑁×𝑇
$)$
matrix, in which 𝑇
$)$
=
∑ ∑ 𝑇
*+
(
+, %
-
*, %
, where Tsf denotes the number of samples in the network for the s
th
seizure and f
th

frequency band. This matrix contains the centrality measure for I ictal periods in two frequency
bands. The singular value decomposition (SVD) was applied to this matrix to find the left and right
singular vectors: 𝒖
"
∈ℝ
&
and 𝒗
"
∈ℝ
'
!"!
. The left singular vectors summarize each node’s
characteristics across all seizures in the context of centrality.
2.2.6 Unsupervised clustering for EZ localization using left singular vectors of mlEVC
To identify candidate contacts for the epileptogenic zone, weighted consensus clustering
71,72

was employed, using combinations of the first four left singular vectors. These vectors were z-
scored and used as features in a hierarchical clustering algorithm. This approach clusters the nodes

Figure 2-1 Schematic of a multilayer network and measure of mlEVC. Four consecutive layers (time-points) of a
simulated network with intralayer (solid lines) and interlayer (dashed lines) edges. Nodes in each layer represent
the set of SEEG contacts and are colored and categorized into two clusters (red and blue). Interlayer edges
(couplings) were included between the same contacts at adjacent time points. The diameter of each node represents
the relative value of mlEVC, in which larger nodes are the most connected nodes and smaller nodes are more
isolated
2 Ictal brain network
22

in a bottom-up agglomerative fashion. Based on our hypothesis, the EZ should have a distinctive
pattern of connectivity and so centrality. Our goal is therefore to find a dense target cluster of
nodes (X=1) whose feature vectors have a significant distance from the centroid of the feature
vectors of the other nodes (Y=0). As a result, we trace the dendrogram to the last step where the
final two groups merge. For a fixed coupling and threshold, c and d respectively, feature vectors
were selected from a pool of normalized singular vectors, consisting of the five combinations:
𝒦 ={{𝒖
%
,𝒖
(
},{𝒖
%
,𝒖
.
},{𝒖
(
,𝒖
.
},{𝒖
%
,𝒖
(
,𝒖
.
},{𝒖
%
,𝒖
(
,𝒖
.
,𝒖
/
}}
For each combination, 𝜅
0
∈𝒦,𝑟 ={1,…,5}, the feature vectors of dimensions 2 to 4 were
integrated into the MATLAB hierarchical clustering function linkage (centroid with Euclidean
distance). Nodes were divided into two groups before the last linkage. We assigned a binary label
“1” to nodes in the smaller cluster (presumptive target X) and “0” to other channels (presumptive
Y). Since hierarchical clustering is prone to outliers, we went one step back in the dendrogram if
the minor cluster consisted of less than 5% of the nodes. In other words, we divided the nodes into
three groups and selected the second minor group as the presumptive target.
2.2.7 Evaluating the clustering performance
Ideally, we would like to see a tight target cluster that is well separated. Consequently, one
can evaluate a clustering technique by computing the quotient
73
,
𝑝𝑒𝑟𝑓(𝑟)=
𝑠𝑒𝑝(𝑟)
𝑐𝑜𝑚𝑝(𝑟)
(2−5)
where the separation index for the r
th
combination is defined as the Euclidean distance:
𝑠𝑒𝑝(𝑟)=‖𝒴
_
0
−𝒳
a
0
‖
(
(
(2−6)
2 Ictal brain network
23

where 𝒳
a
0
and 𝒴
_
0
are the centroids of target and not-target clusters. Compactness is defined as the
product of two measures of intra-cluster distance in the target group,
𝑐𝑜𝑚𝑝(𝑟)= c
1
𝑀
# # e𝒙
"0
−𝒙
!0
e
(
!1" "
f(𝑚𝑎𝑥
"
‖𝒙
"0
−𝒳
a
0
‖
(
) (2−7)
in which 𝔁
"0
is the feature vector of the i
th
point in the target cluster and M is the total number of
pairs. The first term calculates distances between all nodes and the second term finds the farthest
distance of a point from the center of the cluster.
2.2.8 Weighted consensus clustering
We combined the hierarchical clustering results for all sets of feature vectors. The vector
𝒘∈ℝ
&
is calculated as the probability that each node is a candidate for EZ,
𝒘=
1
∑ 𝑝𝑒𝑟𝑓(𝑟)
2
0, %
#𝑝𝑒𝑟𝑓(𝑟)
2
0, %
𝓵
0
(2−8)
where 𝓵
0
∈ℝ
&
is the hierarchical labeling result for the r
th
case. The parameter n≤5 is defined as
the number of feature vector sets that lead to clustering where 𝑐𝑜𝑚𝑝(𝑟)≠0 which in turn requires
a minimum of 2 contacts in the EZ cluster. Since we need a EZ vs, non-EZ classification for each
node, the vector 𝒘 was binarized using a threshold 𝜃 =
23%
2
. For the specific case n = 1, 𝜃 =0.5.
We constructed the binary vector 𝓵∈ℝ
&
by thresholding 𝒘,
ℓ
"
=p
1 𝑤
"
>𝜃
0 𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒
(2−9)
We repeated the above procedure for a range of parameter values: 𝑐 ∈{1,2,…,10,15} and 𝑑 ∈
{0.1,0.2,…,0.8}. The final consensus vector 𝖜∈ℝ
&
was then computed to represent the overall
chance of a node being in the target (EZ) cluster as
2 Ictal brain network
24

𝖜=# # 𝑝𝑒𝑟𝑓(𝑐,𝑑)𝓵
45
5 4
(2−10)
The vector 𝖜 is continuous where larger values indicate increasingly likely candidates for the EZ.
We applied k-means clustering (k=3) on vector 𝖜 and took the cluster with the largest average
value as the final target (EZ) group of contacts. The mentioned processes are summarized in
Algorithm I. Results are available in Figure 2-3.
2.2.9 Brain state clustering by right singular vectors of mlEVC
The seizure evolution is captured by the right singular vectors (𝒗
"
∈ℝ
'
!"!
). To preprocess
the data, the singular vectors were separated into distinct seizures and frequency bands. For each
vector, the MATLAB outlier removal function hampel was then used to remove outliers, with 15
neighboring points and three scaled median absolute deviation (1.4826×MAD). These vectors
were then reconcatenated in two frequency bands (𝒗 v
"+
∈ℝ
'
!"!
/(
). Please consider that 𝑇
$)$
was
defined as two times the length of seizures. Afterward, we applied K-means clustering, separately
for each possible combination of four drawn from the six vectors corresponding to the first three
pre-processed singular vectors in each of two frequency bands. In other words, selecting from the
following set,
𝒮 ={𝒗 v
%%
,𝒗 v
%(
,𝒗 v
(%
,𝒗 v
((
,𝒗 v
.%
,𝒗 v
.(
}
We repeated the analysis for different numbers of clusters and used the MATLAB silhouette
function to determine the optimal number of clusters and best set of vectors. This metric compares
the distance of each point with other points in its cluster to the distances to other clusters.
The classification with the highest Silhouette value was selected to construct the transition matrices
and find the transitions among brain states (clusters) shown in Figure 2-4 and Figure 2-5. The final
four selected vectors from 𝒮 were named as 𝒗 a
7
,𝒗 a
8
,𝒗 a
4
, and 𝒗 a
5
.
2 Ictal brain network
25

2.2.10 Statistical analysis of functional connectivity in high-frequency
To quantify brain dynamics, time-varying connectivity measures were constructed for each
seizure and frequency band, based on the connectivity between brain regions as follows: EZ-nR,
RnEZ-nR, and nR-nR, where EZ, RnEZ, and nR represent respectively predicted EZ (identified
using the methodology described above), resection region not in the EZ, and non-resected areas.
Algorithm I
For 𝑐 =1,2,…,10,15
Construct super-graph 𝒜
#

Compute 𝑇 largest eigenvalues and corresponding eigenvectors {𝜎
$
,..,𝜎
%
} and {𝝋
$
,..,𝝋
%
}
𝒆=|𝜎
$
𝝋
$
|+|𝜎
&
𝝋
&
|+⋯+|𝜎
%
𝝋
%
|
𝑆
⏞
= [𝒆(1:𝑁) 𝒆(𝑁+1:𝑁∗2)…𝒆(𝑁∗(𝑇−1)+1:𝑁𝑇)]
For 𝑑 =0.1,0.2,…,0.8
Threshold 𝑆 =𝑔
'
(𝑆
⏞
)
Singular value decomposition 𝑆 =𝑈𝛴𝑉
Z-score 𝑢
$
,𝑢
&
,𝑢
(
,𝑢
)

Define 𝒦 ={{𝑢
$
,𝑢
&
},{𝑢
$
,𝑢
(
},{𝑢
&
,𝑢
(
},{𝑢
$
,𝑢
&
,𝑢
(
},{𝑢
$
,𝑢
&
,𝑢
(
,𝑢
)
}}
For 𝑟 =1,2,…,5
Select a set of features 𝜅
*
∈𝒦
Cluster nodes using function linkage in MATLAB
Label nodes 𝓵
*
∈ℝ
+
(X=1, target (smaller set), and Y=0, non-target)
Assume 𝔁
,*
feature vector of ith point in the target cluster
Define 𝒳
Q
*
and 𝒴
S
*
centers of target and not-target clusters
Compute separation 𝑠𝑒𝑝(𝑟)=‖𝒴
S
*
−𝒳
Q
*
‖
&
&

Compute compactness 𝑐𝑜𝑚𝑝(𝑟)= Z
$
-
∑ ∑ \𝒙
,*
−𝒙
.*
\
&
./, ,
^(𝑚𝑎𝑥
,
‖𝒙
,*
−𝒳
Q
*
‖
&
)
Evaluate clustering performance 𝑝𝑒𝑟𝑓(𝑟)=
012(*)
#562(*)

End 𝑟
Define 𝜃 =
78$
7
where 𝑛 ≤5 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑎𝑐𝑐𝑒𝑝𝑡𝑒𝑑 𝑐𝑙𝑢𝑠𝑡𝑒𝑟𝑖𝑛𝑔
Consensus index over 𝑛 𝒘=
$
∑ 21*:(*)
!
∑ 𝑝𝑒𝑟𝑓(𝑟)
*
𝓵
*

Label by majority vote for node 𝑖 ℓ
,
=i
1 𝑤
,
>𝜃
0 𝑜𝑡ℎ𝑒𝑟𝑠𝑖𝑠𝑒

Define final label 𝓵
#'
=[ℓ
$
ℓ
&
… ℓ
+
]
%

Compute 𝑝𝑒𝑟𝑓(𝑐,𝑑) based on 𝓵
#'

End 𝑑
End 𝑐
Define Epileptogenicity index 𝖜=∑ ∑ 𝑝𝑒𝑟𝑓(𝑐,𝑑)𝓵
#' ' #

Apply k-means clustering (k=3) on vector 𝖜∈ℝ
+

Label the largest group as predicted epileptogenic zone
2 Ictal brain network
26

Each measure was defined by averaging all connectivity values between nodes in the two regions.
As a result, we have three synchrony time-series vectors for each seizure/patient/frequency (s/p/f)
at 2 samples/sec.
We examined these time series over three sub-intervals: pre-ictal (-0.3, -0.1)L, mid-seizure
(0.3, 0.5)L, and post-ictal (1, 1.2)L. For each synchrony measure, we computed the average value
of connectivity in these intervals, resulting in nine values for each s/p/f (39 seizures in total and
two frequency bands). We employed a robust percentile bootstrap test
74
with a one-step M-
estimator to perform statistical tests for pairwise comparison between and within the three
measures at each of the three periods (function rmmcppb in WRS2 package
74
for R). Computed p-
values were corrected using Hochberg FDR correction for J=18 comparisons. The results are
shown in Figure 2-6. The EZ-nR connectivity in mid-seizure was the most remarkable
characteristic of the ictal period. Consequently, we used this to explore how the feature changes
among patients. For each participant, we averaged the value of EZ-nR among all seizures. We then
performed robust regression of these values using bootstrap sampling and the Theil-Sen
algorithm
74
against both patient age and duration of epilepsy as shown in Figure 2-8.
2.2.11 Computing low-frequency propagation networks
Data was filtered in the range of 2-50 Hz. Propagation networks were computed using the
phase lag index (PLI) over a moving window with 2.5s length and 80% overlap. Connectivity
matrices were computed from normalized PLI values using element-wise z-scoring with respect
to the pre-ictal period and their values mapped into the interval (0 1] using an exponential
transform
8
. We used the previously defined measures, EZ-nR, RnEZ-nR and nR-nR, to explore
interactions among brain regions at these lower frequencies. An analogous analysis to the last
2 Ictal brain network
27

section was performed except the selected time intervals were pre-ictal (-0.3,-0.1)L, early-seizure
(0,0.2)L, and pre-termination (0.8,1)L. These results are presented in Figure 2-9.

2.3 Results
2.3.1 Multilayer modeling of ictal networks discerns the epileptogenic zone
SEEG data were recorded using implanted intracranial electrodes in 16 patients who
underwent resective surgery and were seizure-free for at least 12 months post-resection (Table
2-1). We studied the dynamics of brain connectivity during seizures via multilayer networks
75

which captures continuity in neural interactions during the ictal period. A schematic of a multilayer
network with inter and intralayer edges is depicted in Figure 2-1. SEEG contacts were defined as
graph vertices while the lagged-coherence
67
was used to define edge strength in each layer as a
measure of the macroscopic HFS (see Methods). We investigated two broad bands of HFOs: 80-
140 Hz and 140-200 Hz, similar to related studies
41,61
.
The association of different brain regions within the epileptogenic network and their use for
EZ identification was evaluated using a novel approach based on multilayer eigenvector centrality
(mlEVC) and unsupervised clustering. The mlEVC represents the prominence of a node in
multiplex networks evolving over time (Figure 2-1). Nodes with high connectivity over time and
space in the multilayer network display larger values in mlEVC than isolated vertices. We
calculated this measure (Figure 2-2 b) for all seizures and patients. We assumed that the EZ can
be identified as the set of nodes in the graph that exhibit a characteristic and distinct pattern of
connectivity to other areas during the seizure. To explore this question, we applied hierarchical
unsupervised clustering to the left singular vectors (𝒖
"
∈ℝ
&
where 𝑁 is the number of nodes) of
2 Ictal brain network
28

the concatenated and quantized mlEVC (see Methods). Based on these features, SEEG contacts
were classified into two clusters; target and non-target. Following our initial hypothesis, the target
cluster that represents the EZ was identified as a dense and distinctive cluster in the feature space
with a significant distance from nodes in the non-target group (Figure 2-2 c). By comparing the
clustering results with information about which contacts were included in the resected volume
(Figure 2-2 b), we define three categories: ‘EZ’, ‘resected non-EZ’, and ‘non-resected’. The EZ
included the nodes in the target cluster, resected non-EZ consists of nodes in the non-target cluster
removed during surgery, and non-resected comprises the rest of the nodes, which were neither
resected nor classified in target cluster (Figure 2-3). Ideally, the predicted EZ or target cluster
should only contain nodes in the resected area for these participants since all patients were seizure-
free after surgery. However, the classification algorithm and proposed technique are not flawless
so there are a small number of electrodes outside the resection region selected as EZ, i.e. false
positives.
Our approach identified electrodes inside the resected volume as EZ for 88% of participants,
i.e. all but two (patients 8 and 11). For patient 11, two out of three available seizures were short
(25s and 12s) and the sampling rate was relatively low (500 Hz). Lack of sufficient samples might
be the source of miss identification for this patient and a limitation of our approach. The false-
positive rate (FPR) was calculated by dividing the number of predicted electrodes as EZ outside
the resection zone over the total number of electrodes in the non-resected region. Only four
participants had electrodes falsely identified as EZ and the FPR was 1.79% across all 16 patients.
The details of predicted electrodes for each patient are given in Table 2-2. We compared our results
with Fingerprint
63
analysis that employs time-frequency features of pre- and post-seizure onset, to
predict the EZ.
2 Ictal brain network
29

Although these two algorithms are fundamentally different in their assumptions,
contacts/nodes identified in our approach as EZ have 41% overlap (same contact labels) with those
found using the Fingerprint. Interestingly, the mlEVC algorithm could identify electrodes inside
the resection zone for two patients in which Fingerprint was not able to predict the EZ (participants
6 and 16). In contrast, the latter could localize EZ for two patients (8 and 11) on which our method
failed. For several patients, the two approaches identified different but adjacent areas inside the
resection region. Nonetheless, 67% of patients had common electrodes labelled as EZ in the
resected volume by both algorithms.

Figure 2-2 Identification of epileptogenic zone based on mlEVC (Patient 17). (a) SEEG signals during ictal period.
The red signals are a sample of contacts inside the EZ as identified by our method, and blue signals depict non-EZ
contacts outside the resection zone. (b) The multi-layer eigenvector centrality (mlEVC) during the ictal period.
Each row represents a channel (contact). Contacts are categorized and organized into two groups: resected and non-
resected as indicated on the right. They are also classified into two groups based on the proposed clustering
algorithm: target and non-target. The blue elements of mlEVC describe the isolated nodes of the super-graph (brain
network) while red values describe highly connected contacts. (c) The first three left singular vectors of the mlEVC.
The mlEVC spectra of different seizures were first quantized and concatenated before performing singular value
decomposition. The red nodes are those identified as predicted EZ based on unsupervised clustering.
2 Ictal brain network
30

Table 2-2 Comparing SEEG channels identified as true positives between two methods. for mlEVC in this
work vs. those identified using the Fingerprint
63
.
ID Predicted EZ by mlEVC Predicted EZ by Fingerprint
1 X01-X02, X02-X03, X03-X04, X05-X06
R01-R02, R02-R03, R03-R04, X01-X02, X02-X03,
X03-X04, X05-X06
2 Full seizure data was not available
3 C01-C02, C02-C03
B01-B02, B02-B03, B03-B04, B04-B05, B07-B08,
B08-B09, C02-C03, E01-E02, E02-E03, E06-E07
4 Lp01-Lp02, Lp02-Lp03, Lp03-Lp04, Lp04-Lp05 Lp01-Lp02, Lp03-Lp04, Lp05-Lp06
5 Lp01-Lp02, Lp02-Lp03 Lp01-Lp02
6 Op06-Op07, Op07-Op08

7 K01-K02, N01-N02, N02-N03 M03-M04, M05-M06, M07-M08
8

O07-O08
9
A01-A02, B01-B02, B02-B03, B03-B04, B04-B05, B05-
B06
A03-A04
10 O09-O10, O10-O11 V07-V08
11

L05-L06, L06-L07, L07-L08
12 K05-K06, K06-K07, K07-K08 K04-K05, K05-K06, K07-K08
13 Xp03-Xp04, Xp04-Xp05, Xp05-Xp06, Xp06-Xp07 Wp06-Wp07
14 R04-R05, R05-R06 R04-R05, R05-R06
15 L01-L02, L02-L03
L01-L02, L02-L03, L03-L04, L04-L05, L05-L06,
O03-O04, O05-O06, Q05-Q06
16 A06-A07, A08-A09

17
Tp01-Tp02, Tp02-Tp03, Tp03-Tp04, Tp04-Tp05, Tp05-
Tp06, Tp06-Tp07, Tp07-Tp08, Tp08-Tp09
Bp01-Bp02, Bp03-Bp04, Tp01-Tp02, Tp04-Tp05,
Tp05-Tp06, Tp07-Tp08, Tp08-Tp09
2 Ictal brain network
31

Since both analyses were retrospective and actual ground truth is unknown, these techniques can
perhaps be used to complement each other. (see Table 2-2 for a detailed comparison).
It was striking that for most of the patients the EZ was distinguishable based on the singular
vectors of mlEVC (Figure 2-3). Consistent with other studies, we found out that possibly only a
portion of the resected area is responsible for epileptogenicity. Figure 2-2 b captures the
Figure 2-3 EZ localization for 16 patients. The predicted EZ (red circles) was computed as described in Methods.
Blue squares show non resected contacts and green triangles demonstrate the resected electrodes. The axes are the
top three left singular vectors of mlEVC.

2 Ictal brain network
32

discrepancies between the EZ, resected non-EZ, and non-resected areas. Furthermore, it distinctly
displays various brain states (phases) during the ictal period. Nodes experience isolated and fully
connected phases with respect to the rest of the network. These results confirm the importance of
the entire ictal period for EZ identification. For the rest of this chapter, we utilize the categorization
of nodes introduced above with the following small modifications: removing false positives from
the EZ groups (defined as those contacts lying outside the resected volume) and discarding patients
8 and 11 in whom we were unable to observe any unique pattern of connectivity in electrodes
inside the resected area.
2.3.2 Seizures evolve with divergent network topologies
In our multilayer modeling of epileptogenic networks, the left singular vectors of mlEVC
were used to classify nodes into two categories, predicted EZ and non-EZ. Here, the associated
right singular vectors were employed to display seizure evolution. In clinical epileptology,
stereotypy in seizures is defined as similarities in both seizure semiology and ictal EEG recordings
over repeated seizures
44
. Multiunit recordings have shown that stereotypical firing patterns occur
when micro-electrodes are implanted in recruited areas
44
. To evaluate stereotypy in this study, we
clustered ictal dynamics into different states using the four features from a pool of six-dimensional
feature vectors, including the top three right singular vectors of mlEVC split into the two high-
frequency bands (see Methods).
Figure 2-4 compares different seizures for patient 16. Quantized mlEVC are depicted in
Figure 2-4b with corresponding state changes in part c. Results indicate that ictal brain activity
evolves through diverse phases during different seizures. In the first seizure, the EZ is mostly
isolated with respect to the other nodes and ictal activity advances through three states (F, E, D).
2 Ictal brain network
33

In contrast, the epileptogenic zone exhibits strong connectivity in the second seizure while the
centrality measure passes through four states (B, C, A, E). Figure 2-4d illustrates the ictal dynamics
using the four selected features extracted from the top three right singular vectors of mlEVC in
two frequency bands (see Methods). In this case, seizure 1 evolves quite differently from seizures
2 and 3 whose traces share similar ictal dynamics.
The same analysis was performed for all patients and results for several of these participants
are shown in Figure S2. We observed that stereotypy, here considered as similar state transitions
among all recorded seizures, does not necessarily occur, especially at high frequencies. In fact, the
brain experiences divergent topologies, which might be the result of dissimilar EEG recordings.
While previous studies suggested stereotypy in focal firing
44
and brain connectivity
8
, our
multilayer analysis of epileptogenic networks does not imply stereotypy in macroscopic HFS. Our
findings confirm the necessity of collecting adequate seizures and large-scale recordings for a
better understanding of seizure evolution.
2 Ictal brain network
34

Figure 2-4 Seizure evolution and state transition in three patients. Seizure evolution and brain states were extracted
using right singular vectors of mlEVC (see Methods). Capital letters show the center of each state. 𝒗 Q
;
,𝒗 Q
<
,𝒗 Q
#
, and
𝒗 Q
'
are the best features extracted from singular vectors to cluster seizure evolution into brain states. (a) Patient 1.
All recorded seizures are scattered in same places. (b) Patient 3. The 𝒗 Q
;
−𝒗 Q
<
plot portrays states that are unique
for seizures 1 and 2, but not observed in seizure 3. (c) Patient 15. The 𝒗 Q
#
−𝒗 Q
'
plot depicts a distinctive area for
seizure 1, which was not traversed in two other reordered seizures.
2 Ictal brain network
35

Figure 2-5 Seizure evolution and state transition in three patients. Seizure evolution and brain states were
extracted using right singular vectors of mlEVC (see Methods). Capital letters show the center of each state.
𝒗 Q
;
,𝒗 Q
<
,𝒗 Q
#
, and 𝒗 Q
'
are the best features extracted from singular vectors to cluster seizure evolution into brain
states. (a) Patient 1. All recorded seizures are scattered in same places. (b) Patient 3. The 𝒗 Q
;
−𝒗 Q
<
plot portrays
states that are unique for seizures 1 and 2, but not observed in seizure 3. (c) Patient 15. The 𝒗 Q
#
−𝒗 Q
'
plot
depicts a distinctive area for seizure 1, which was not traversed in two other reordered seizures.
2 Ictal brain network
36

2.3.3 EZ desynchronization occurs in the ictal period
We were interested in exploring the fundamental question of how HFS changes throughout
the seizures. To do this, three synchrony measures were computed. The first measure, EZ-nR,
quantifies the synchrony between EZ and non-resected (nR) areas. The second metric, RnEZ-nR,
computes the connectivity of resected nonEZ and nR. Lastly, we computed interactions between
non-resected regions, labeled nR-nR. Figure 2-6a presents the dynamics of these measures during
the ictal period. Collectively, 39 seizures and two frequency bands were analyzed. Seizures with
different durations were resampled/rescaled to a zero to one interval, where zero indicates the onset
and one indicates the termination time. In general, among the three measures, EZ-nR exhibited a
substantial decline in synchrony during early and mid-seizure while widespread synchronization
occurred during seizure termination (Figure 2-6a). Based on this observation we compared the
HFS in three time periods: pre-ictal, mid-seizure and post-ictal (Figure 2-6a). Data for all seizures
was extracted for statistical analysis in RStudio
76
. To handle possible outliers, the paired percentile
bootstrap with one-step M-estimator
74
was employed and p-values were computed for pairwise
comparison between and within the three measures at each of the three periods, corrected using
Hochberg’s algorithm (B=10
4
number of bootstraps, J=18 tests, see Methods). All tests and their
corresponding corrected p-values can be found in Table 2-3.
Figure 2-6b presents the extracted connectivity values for the above measures in the selected
periods. To give a pairwise visual comparison, we subtracted the average synchrony between all
pairs of contacts in the pre-ictal interval from nine connectivity measures (Figure 2-6b).
Unsurprisingly, there was no difference between measures in the pre-ictal period (p≈1 for all
pairwise comparisons). In mid-seizure, EZ-nR was significantly smaller than RnEZ-nR
2 Ictal brain network
37

(p=0.0108) and nR-nR (p<10
-4
), indicating that the epileptogenic zone is maximally
desynchronized from the rest of the brain.
Early-onset and late ictal HFOs have been considered biomarkers for seizure onset zone
identification
41
, with the latter found to be a more reliable metric
77
. Our EZ localization technique
considers both features. The substantial decrease in EZ connectivity with the entire network in
mid-seizure might be the result of these pathological HFOs in the epileptogenic zone. At a smaller
scale, EZ-nR desynchronization could be the result of heterogeneous neuronal spiking activity
during seizures
78
. Microelectrode recordings of the ictal core presented a dramatic rise in the Fano
factor, a statistical measure of spiking desynchronization (variance of spiking divided by the
mean), in early and mid-phases of seizures
44,78
. Theoretical modeling of neuronal assemblies has
shown that asynchrony is necessary to maintain a high firing rate
79
. We further studied the

Figure 2-6 High-frequency synchrony during ictal period. (a) time-varying high-frequency synchrony values for
three defined measures. The ictal period is normalized to a zero to one scale. The solid lines represent the median
and shaded plots display the normalized median absolute deviation (MAD), based on 10-4 bootstrap tests. The gray
rectangles display the periods of special interest. Note that EZ-nR connectivity drops substantially towards mid-
seizure and increases to match nR-nR and RnEZ-nR at seizure termination and post-ictally. (b) Connectivity measures
in pre-ictal, mid-seizure, and post-ictal. The centers of error bars show the median of all seizures in two frequency
bands and lines depict the MAD. Scatter circles exhibit the actual values (n=78 for each group). P-values were
computed for pairwise comparison between and within the three measures at each of the three periods. Asterisks
display corrected P-values; *P<0.05, **P<0.01, ***P<0.001. Only the mid-seizure interval shows significant
differences between EZ-nR and other measures. All measures are considerably higher in post-ictal than their
corresponding values in mid-seizure and pre-ictal periods. EZ-nR drops significantly in mid-seizure from pre-ictal.
2 Ictal brain network
38

variations of each measure among different periods. Between pre-ictal and mid-seizure, EZ-nR
connectivity declined considerably (p≈0.002), followed by a marginally significant fall for RnEZ-
nR (p=0.056). In contrast, all measures were substantially elevated during seizure termination and
the post-ictal period in comparison to mid-seizure and pre-ictal intervals (p<10
-4
for all tests). This
observation is well aligned with other studies, suggesting a widespread synchronization during
seizure termination
4
, especially in 80-200 Hz
46
.

Table 2-3 Test statistics for network measures in high-frequency
Post-hoc analysis Corrected p-values
Pre-ictal: EZ vs RnEZ ≈ 1
Pre-ictal: EZ vs nR ≈ 1
Pre-ictal: RnEZ vs nR ≈ 1
Mid-seizure: EZ vs RnEZ 0.0108
Mid-seizure: EZ vs nR < 10
-4
Mid-seizure: RnEZ vs nR < 10
-4

Post-ictal: EZ vs RnEZ 0.2664
Post-ictal: EZ vs nR 0.1680
Post-ictal: RnEZ vs nR ≈ 1
EZ: Pre-ictal vs Mid-seizure 0.0020
EZ: Pre-ictal vs Post-ictal < 10
-4

EZ: Mid-seizure vs Post-ictal < 10
-4

RnEZ: Pre-ictal vs Mid-seizure 0.0560
RnEZ: Pre-ictal vs Post-ictal < 10
-4

RnEZ: Mid-seizure vs Post < 10
-4

nR: Pre-ictal vs Mid-seizure ≈ 1
nR: Pre-ictal vs Post-ictal < 10
-4

nR: Mid-seizure vs Post-ictal < 10
-4

EZ: predicted epileptogenic zone, RnEZ: resected non-EZ, nR: non-resected
2 Ictal brain network
39

We do not include the connectivity between the EZ and RnEZ in Figure 2-6 for the following
reason. The three measures we do compute are all relative to the non-resected region which we
know to definitely be outside the EZ. Within the resection, there is some ambiguity as to which
contacts are within EZ and which are not.
Second, a measure between EZ and RnEZ would be more susceptible to noise as the number
of RnEZ electrodes is typically much smaller than the number in the non-resected region so that
establishing statistical significance is difficult. Nevertheless, this measure is computed for the
curious reader in Figure 2-7. It can be perceived by visual inspection that EZ-RnRZ has a pattern
similar to EZ-nR, suggesting again that the EZ is functionally disconnected from surrounding areas
up to mid-seizure
50
.

Figure 2-7 Connectivity measures in pre-ictal, mid-seizure, and post-ictal. The centers of error bars show the
median of all seizures (n=39) in two high-frequency bands (80-140 Hz and 140-200 Hz) and lines depict the
scaled median absolute deviation. Scatter circles exhibit the actual values (n=78 for each group). Visually, the
epileptogenic zone (EZ) is strongly desynchronized with resected non-EZ.
2 Ictal brain network
40

2.3.4 The EZ becomes isolated by aging and the duration of epilepsy
Although the epileptogenic zone exhibited a general pattern of desynchronization, it was not
the case for all patients. In mid-seizure, several participants showed larger EZ-nR values when
compared with the average connectivity in the entire network. This observation is expected since
patients have dissimilar seizure types, etiology, and electrode implantations. Consequently, we
postulated that a patient’s demographics might explain differences in EZ connectivity with the rest
of the brain. Patients’ age and duration of epilepsy were assessed as predictors for the EZ-nR
synchrony in the middle of seizures. For each seizure and patient, the average synchrony between
all pairs of contacts in mid-seizure was subtracted from the EZ-nR to reduce inter-subject and
inter-seizure variabilities. We constructed a three-dimensional vector consisting of EZ-nR
connectivity for each seizure (n=39) along with the corresponding age and duration of epilepsy.
We utilized a robust regression estimator based on bootstrap sampling and the Theil-Sen
algorithm
74
. The correlation between patients’ age and normalized EZ synchronization is shown
in Figure 2-8a. Results indicate a strong negative association, suggesting the ictal core becomes
increasingly desynchronized with age (p < 10
-4
, r = − 0.414). Similarly, we observed a reduction
in connectivity between the EZ and non-resected areas with a longer duration of epilepsy (Figure
2-8b, p = 0.032, r = − 0.254).
These findings suggest possible variables which can modify the epileptogenic networks
7
.
Recently, interictal ECoG recordings of patients with temporal lobe epilepsy (TLE) have shown a
negative
correlation between TLE duration and overall phase lag index at low frequencies
80
. A
resting-state fMRI study also found a negative correlation between epilepsy duration and
2 Ictal brain network
41

functional connectivity between two contralateral ROIs in inferior frontal gyrus
81
. However, our
findings delineate the correlation in a specific pathological pathway among patients with medically
intractable focal epilepsy with different SEEG electrode implantations. A decrease in functional
connectivity with age might also be observed in a control group. However, the fact that we
normalize by subtracting the overall synchronization in each patient from EZ-nR values weakens
the influence of that factor in our findings.
2.3.5 Expansive connectivity in low-frequency emerges before seizure termination
Low-frequency brain signals (2-50 Hz) are mainly shaped by rhythmic synaptic currents
44
,
which in many cases traverse to other regions. These travelling waves are involved in different
sensory processes and brain states
42,43
. In epilepsy, ictal discharges exhibit this activity during
seizures. Recently, two scenarios have been proposed for seizure spread and termination
9
. The first
a b

Figure 2-8 Correlation between normalized EZ-nR values and patients’ history. (a) Correlation between patients’
age and normalized EZ-nR synchronization in high frequency. Each data point indicates the average of
normalized EZ-nR values in mid-seizure among all seizures and two high-frequency bands (n=39). (b) The same
plot as (a) except here the x-axis describes the duration of epilepsy among patients.
2 Ictal brain network
42

theory postulates that ictal discharges emerge from a fixed cortical source in EZ, while the second
hypothesis asserts that the moving ictal wavefront generates travelling waves
43
. This process
dominates when the ictal wavefront recruits the seizure core and penumbra, i.e. the area around
the core in which low-voltage signals spread, roughly during the mid-seizure period. These
scenarios have contradictory explanations for how seizure termination occurs. The fixed source
theory assumes inactivation of a small region would end the seizure while the active
wavefront requires a mechanism which affects an expansive area.
We analyzed connectivity in low-frequency during seizures. Brain networks were
constructed using phase lag index (PLI) to minimize the confounding impact of volume conduction
and spurious interactions. Similarly to high-frequency networks, these connectivity matrices were
normalized to the pre-ictal period (see Methods). Previously defined measures were computed,

Figure 2-9 Low-frequency brain connectivity during ictal period. (a) time-varying low-frequency connectivity
values for three defined measures. The ictal period is normalized to a zero to one scale. The solid lines represent
the median and shaded plots display the normalized median absolute deviation (MAD) based on 10-4 bootstrap
tests. The gray rectangles display the periods of special interest. EZ-nR connectivity drops in early-seizure and
a widespread brain connectivity occurs in the pre-termination period. (b) Connectivity measures in pre-ictal,
early-seizure, and pre-termination. The centers of error bars show the median of all seizures in two frequency
bands and lines depict the MAD. Scatter circles exhibit the actual values (n=39 for each group). P-values were
computed for pairwise comparison between and within the three measures at each of the three periods. Asterisks
display corrected P-values; *P<0.05, **P<0.01, ***P<0.001. Only the early-seizure interval shows significant
differences between EZ-nR and two other measures. All measures are considerably higher in pre-termination
than their corresponding values in early-seizure and pre-ictal periods.
2 Ictal brain network
43

and their dynamics depicted in Figure 2-9. In comparison to HFS, we observed a stronger
resemblance in PLI among the three interaction measures (EZ-nR, RnEZ-nR and nR-nR) other
than in a short early-seizure period. Additionally, ictal discharges displayed an expanding coverage
after mid-seizure, which was maximized before seizure termination. As a result, early-seizure and
pre-termination along with pre-ictal were chosen for statistical analyses as analogues to HFS
(n=39, see Error! Reference source not found.).

Table 2-4 Test statistics for network measures in low-frequency
Post-hoc analysis Corrected p-values
Pre-ictal: EZ vs RnEZ 0.7820
Pre-ictal: EZ vs nR 0.7820
Pre-ictal: RnEZ vs nR 0.7820
Early-seizure: EZ vs RnEZ 0.0374
Early-seizure: EZ vs nR < 10
-4

Early-seizure: RnEZ vs nR 0.0540
Pre-termination: EZ vs RnEZ 0.7820
Pre-termination: EZ vs nR 0.7820
Pre-termination: RnEZ vs nR 0.7820
EZ: Pre-ictal vs Early 0.7820
EZ: Pre-ictal vs Pre-termination < 10
-4

EZ: Early vs Pre-termination < 10
-4

RnEZ: Pre-ictal vs Early 0.7820
RnEZ: Pre-ictal vs Pre-termination < 10
-4

RnEZ: Early vs Pre-termination < 10
-4

nR: Pre-ictal vs Early 0.7820
nR: Pre-ictal vs Pre-termination < 10
-4

nR: Early vs Pre-termination < 10
-4

EZ: predicted epileptogenic zone, RnEZ: resected non-EZ, nR: non-resected

2 Ictal brain network
44

We did not find any difference between measures in pre-ictal and pre-termination PLI
(p>0.05 for all cases). However, EZ-nR was distinguishable from RnEZ-nR (p=0.0374) and nR-
nR in early-seizure (p<10
-4
). This observation can be linked to early-onset suppression in low-
frequency, reported as a possible signature of the EZ
63
. Comparing with early-seizure and pre-ictal
periods, all measures were significantly elevated in pre-termination (p<10
-4
for all tests). Consistent
with our findings, a recent study showed that an increased temporal and spatial correlation along
with flickering, the condition when a system fluctuates between two attractors, are signatures of a
critical transition when seizures self-terminate
65
.
2.3.6 Pre-termination connectivity predicts post-ictal synchronization
It has been stated that the brain manifests hysteresis between the two states before and after
termination
65
. In other words, the post-ictal state is dependent on pre-termination. Consequently,
we were interested to examine how the brain changes between these two states. Pre-termination
connectivity in low-frequency and post-termination synchrony in high-frequency were among the
distinctive features of the results presented above. To test the hypothesis of possible dependency,
we computed overall brain connectivity for these two measures. Figure 2-10 illustrates the
correlation between pre-termination and post-ictal intervals. Each point in the graph belongs to
one seizure in which the two values for two high-frequency bands are averaged. There is a strong
association between the two states (p<0.02, r = 0.452, n = 34) after removing outliers using
projection method and MAD-median rule
82
), supporting the existence of hysteresis in the system.
In other words, the brain state in the post-ictal period can be predicted using its condition in pre-
termination.

2 Ictal brain network
45

2.4 Discussion
Our results investigate large-scale ictal brain connectivity as it relates to EZ localization and
seizure generation, propagation, and termination. We showed that the EZ exhibits differential
dynamics compared to other brain regions during seizures. This observation is independent of
seizure type, etiology, presence or absence of MRI lesion, and occurred in both temporal and extra-
temporal lobe epilepsy. High-frequency oscillations have been widely studied as a potential
biomarker in epilepsy
83
, including both early- and delayed-onset ictal HFOs
41
. However, there is
still some debate on their spatial specificity, timing, and appropriate detection algorithms. As an
alternative marker, we computed high-frequency synchrony (HFS) over the entire seizure period.
HFS was first modeled using a multilayer network and the potential EZ was identified using a

Figure 2-10 Correlation of overall pre-termination low-frequency connectivity and post-
ictal high-frequency synchrony during the critical transition. (outliers were removed using
a covariance method)

2 Ictal brain network
46

novel measure of centrality. Our approach to identifying the epileptogenic zone is complementary
to other approaches avoiding explicit assumptions regarding seizure patterns and dynamics.
2.4.1 The virtue of multilayer modeling of brain networks
The multilayer network approach used here for EZ prediction and identification of state
transitions allows us to explore seizure dynamics in a graph-theoretic context. Traditionally in
brain network studies, researchers explore graph measures like clustering and centrality, in single-
layer (non-dynamic) networks
3,84
. However, the multilayer framework with an adjustable coupling
parameter can reveal processes with different timescales and facilitate defining new measures
32
.
We used an unsupervised clustering algorithm to find a set of nodes among all channels, i.e. the
target cluster, as the predicted EZ. The presented method was based on hierarchical clustering and
a cost function that combines the separation of clusters and compactness of the target group. The
optimized coupling parameter varies substantially between patients (Figure 2-3), verifying the
necessity of analyzing multiple timescales.
2.4.2 Comparing results with Fingerprint approach
In some cases, this automatic unsupervised clustering may fail to find all nodes (contacts)
with features that would identify them as belonging to the EZ using other methods, such as the
fingerprint method that finds a distinctive combination of pre-ictal spiking, low-frequency
suppression, and low-voltage fast activity (LFD). This is reflected in the differences in contacts
identified as EZ between the two approaches, which is reported in Table 2-2. However, the
complementary dynamic-synchrony based approach described here also finds plausible EZ
contacts in cases where the fingerprint does not, as mentioned in the result section. Finally, based
2 Ictal brain network
47

on the predicted epileptogenic zone and information regarding the resection areas, the SEEG
electrodes were categorized into three groups; EZ, Resected non-EZ (RnEZ), and non-resected
(nR). We employed this classification to compute the dynamics of regional ictal connectivity in
low and high frequency bands.
2.4.3 Brain network alterations in epilepsy
There is substantial evidence of multiscale alterations in structural and functional brain
networks in epilepsy
85–87
. A meta-analysis of dozen interictal studies with variant imaging
methodologies showed increased clustering and path length
3
. Resting-state fMRI research has
revealed decreased inter-hemispheric functional connectivity in medial and lateral temporal
regions among patients with temporal lobe epilepsy
88,89
. Ictal SEEG recordings of focal cortical
dysplasia (FCD) type II have shown that nodes within the lesion have higher values of out-degree
and betweenness centrality in the gamma range (30-80Hz)
90
. These observations have created a
new field of research known as connectivity-based biomarkers in epilepsy
91
, which is mostly
performed by automatic approaches and machine learning algorithms. Applications include
estimating neurocognitive performance
92
, lesion detection in FCD type II
93
, lateralization of
seizure focus
94
, and ictal onset zone identification
95
. Although these measures have been extracted
using non-invasive resting-state imaging techniques, in many cases they are limited to specific
types of epilepsy, such as FCD type II or lesional patients. On the other hand, we demonstrated
that during seizures nodes belonging to the EZ share a unique pattern of centrality, which was
verified in the majority of our patients with different etiologies. Our results are consistent with
iEEG
50
and ECoG
8
studies that demonstrated the isolation of SOZ from the rest of the network.
2 Ictal brain network
48

2.4.4 Correlation between neural activity and patient’s demographics
More importantly, we investigated the relation between EZ-nR connectivity and patient’s
demographics. We observed a negative correlation between these parameters, in which the
epileptogenic zone and non-resected regions become more desynchronized by aging and the
duration of epilepsy (Figure 2-8). This finding can be explained by abnormal neuroplasticity,
where the continuous recruitment of epileptogenic networks intensifies their anomaly
86
. Related
work has shown a negative correlation between TLE duration and overall interictal phase lag index
at low frequencies (0.5-48 Hz)
80
. A resting-state fMRI research indicated that the connectivity
between two contralateral regions in the mesial temporal lobe is negatively correlated with the
duration of epilepsy
81
. Our results along with the mentioned studies suggest that network
abnormalities can portray the disease severity
86
. To further verify these findings, additional studies
should be performed on a larger dataset while considering other influencing factors, including sex,
handedness, and the side of epilepsy.
2.4.5 High frequency synchronization in epilepsy
The origin and frequency range of HFOs in ictal and interictal states are still
disputable
6,41,53,96,97
. Recent research has emphasized that narrow-band physiological HFOs, not
pathological HFOs or broad-band multi-unit activity (MUA), are responsible for long-range high-
frequency synchronization in interictal recordings
61
. Also, it has been suggested that widespread
HFO synchronization should be a characteristic of healthy brain activity
61
. In our findings, the ictal
HFS between the epileptogenic zone and non-resected areas was the most distinctive pattern
among others and showed a significant desynchronization in the early and middle parts of the
seizure (Figure 2-6). In this period, the exclusive presence of pathological HFOs inside the EZ
2 Ictal brain network
49

resulted in decreased EZ-nR synchrony while the nR-nR connectivity was left intact. Towards
seizure termination, this unique activity faded
43
and elevated the similarity of signals in the EZ
and non-resected areas, which is consistent with a previous study in the same frequency range
46
.
Once the seizure terminated and the brain resumed a healthy activity, we observed a widespread
HFS irrespective of pathology, a possible outcome of physiological HFOs.
2.4.6 Dissimilar brain dynamics among seizures
We used the right singular vectors in mlEVC decomposition to explore the network topology
during seizures (Figure 2-4). This feature demonstrated the reconfiguration of brain networks and
was later used for clustering these dynamics into brain states. The profound alterations of these
features revealed the extensive changes in network topology, even when the nR-nR connectivity
was relatively stable. Several studies have also displayed the presence of different brain states in
the ictal period
8,98
. However, our findings are distinctive in that they present dissimilar brain states
among different seizures of the same individual, suggesting variant structures for seizure
generation and propagation. It has been shown that TLE seizures can be divided into several
categories and in an overwhelming majority of patients they belong to more than one category
15
.
Consequently, in each individual, seizures can be generated by various and separate epileptogenic
structures
15,35
. Another study of temporal lobe epilepsy has identified patients with different
seizure semiologies
99
, a possible outcome of variations in propagation networks. Recently, the
Fingerprint features of the epileptogenic zone were employed for clustering the seizures of each
patient. In the presence of these variations in epileptogenic networks, it is essential to record
multiple seizures
100
and prolonged interictal
56
data. Also, seizure dissimilarities have been assessed
by brain network measures in a wide frequency range
33
. Here, we presented a new approach to
2 Ictal brain network
50

classify seizures based on the features of high-frequency synchronization networks. Additional
work can be done to associate these findings with patient’s semiology.
2.4.7 Brain network dynamics in seizure generation, evolution, and termination
While we mainly focused on the dynamics of high-frequency synchrony, the low-frequency
(2-50 Hz) propagation networks were also computed, to have a better understanding of large-scale
brain interactions during seizures. Here, the phase lag index was used to address delays between
ictal discharges in different channels. In early-seizure, the EZ-nR PLI was significantly smaller
than connectivity among non-resected areas. This finding can be related to early-onset suppression
of low frequencies in the epileptogenic zone, as demonstrated in recent studies
63,101
. The low-
frequency suppression can be described by rapid inhibitory synaptic currents which resist the
seizure spread, causing inhibitory restraint
44,102
. By mid-seizure, the ictal wavefront has recruited
more areas and ictal discharges are traversing farther regions
43
. Our results indicated an extensive
increase in brain connectivity approaching seizure termination (Figure 2-9). This observation is
consistent with multiscale recordings, reporting an increase in spatial and temporal correlation
before seizures cease
9,65
, as well as macroscopic cortical networks
5,48,49
. The underlying
mechanisms of seizure generation, evolution, and termination remain a matter of debate
9
. In
addition to studies based on microscopic recordings and modeling, macro-electrode studies and a
large-scale explanation of brain dynamics are necessary to develop a full understanding of this
issue. Our findings suggest that at seizure-onset, the EZ loses synchronization with the rest of the
network and the brain enters a desynchronized state. This condition continues through mid-seizure
until the ictal wavefront has recruited many areas, including core and penumbra
43
. Subsequently,
the brain connectivity increases temporally and spatially, indicating an upcoming critical
2 Ictal brain network
51

transition
65
. It has been shown theoretically and experimentally that brain networks require a
higher coupling strength to restore synchronization than to lose synchronization
103
. Our results
support this idea since considerably stronger connectivity was needed to terminate seizures in
comparison to that in the pre-ictal.
2.4.8 Final notes
It is important to remember that the recording techniques, signal processing approaches, and
frequencies of interest are crucial in any study of brain connectivity. These parameters can be the
reasons for current controversies
49
. Employing the bipolar montage and a robust measure of
synchrony, helped us to eliminate the effect of volume conduction and muscle artifacts (see
Methods). However, classic measures like coherence strikingly increase spurious connectivity.
Additionally, our findings do not simply reflect the distance among the electrodes. We normalized
the synchronization matrices with respect to the pre-ictal period based on an element-wise
approach, previously suggested in
8
. This process reduces the chance of distance alone affecting
the value of connectivity.

3 Effective connectivity in focal cortical dysplasia
52

3 Effective connectivity in focal
cortical dysplasia
3.1 Introduction
Focal cortical dysplasia (FCD) is a common pathological substrate in epilepsy surgery
104
.
FCD Type II is characterized by architectural disorganization as well as the presence of
dysmorphic neurons with (type IIB) or without (type IIA) balloon cells
105
. MRI abnormalities in
FCD type II include increased cortical thickness, increased signal on fluid-attenuated inversion
recovery (FLAIR), and gray-white matter blurring. The “transmantle” sign, a hallmark MRI
finding in FCD, suggests the presence of FCD IIB
106
. Type I, which is not as well-defined, is
mainly characterized by architectural columnar and/or laminar disorganization in the absence of
clear morphological cellular abnormalities. However, the MRI is often normal in the majority of
patients with FCD type I
105,106
. FCD type I can be associated with non-specific MRI differences
including reduced white matter volume and subtly increased signal on FLAIR and T2 images
107
.
As with other substrates of focal epilepsy, a notable challenge in FCD is to determine the
extent of the epileptogenic zone, even in MRI positive lesions. Intracranial electrode monitoring
3 Effective connectivity in focal cortical dysplasia
53

may reveal epileptogenicity that extends beyond the nidus of the MRI abnormality
108
. Due to this
characteristic of FCD, surgical failure can occur if only the MRI lesion is removed
109
. On the other
hand, MRI-negative or non-lesional epilepsy poses a significant challenge in surgical
management
110
often requiring the use of intracranial electrode monitoring
111
.
Recent studies of focal epilepsy analyzing brain imaging, electrophysiology, and modeling
techniques have shown evidence of multiple brain regions involved in epileptogenicity rather than
a discrete area of dysfunction
112,113
. One of the posited reasons for surgical failure is that the given
epileptic network is widely distributed
114
. This finding is supported by the observation that few
patients achieve good outcomes following a small surgical resection
115,116
. The concept of epilepsy
as a network-based disease has gained widespread acceptance from studies analyzing structural
connectivity
117
, functional connectivity
118
, and effective connectivity
26,119
.
Effective connectivity aims to establish a causal or directed relationship between separate
brain regions
24
. One approach to measuring effective connectivity involves recording cortico-
cortical evoked potentials (CCEPs)
25
which can be performed in patients undergoing intracranial
electrode evaluation with either subdural electrodes or stereoelectroencephalography (SEEG).
CCEPs are recorded by applying single pulse direct electrical cortical stimulation (SPES) to pairs
of intracranial electrodes and averaging the evoked potentials in the remaining. In this way, CCEPs
can directly study pathological and functional large-scale brain networks in-vivo with a high
degree of spatiotemporal resolution
25,26
in the regions of the implanted intracranial electrodes.
Additionally, SPES and CCEPs have been employed to map the degree of epileptogenicity by
measuring the level of neuronal excitability
28,29
. These studies suggested that either an increased
amplitude of the early response of CCEPs or the presence of a delayed response following SPES
can localize the epileptic cortex.
3 Effective connectivity in focal cortical dysplasia
54

Epilepsy surgery is more successful in FCD type II
120
, possibly due to its association with
MRI lesions. In contrast, there is a greater risk for epilepsy surgical failure in patients with FCD
type I
121
. One reason for failure may relate to the difference in the extent of epileptogenicity. We
hypothesize that the extent of epileptogenicity is greater in FCD type I and more restricted in type
II. We test our hypothesis using CCEPs, a marker of hyperexcitability, among patients who
underwent SEEG for epilepsy surgical localization. We expect the above differences between FCD
types to result in distinctive patterns of hyperexcitability that can be assessed by ictal onset single
pulse electrical stimulation (iSPES) of the suspected ictal onset zone This difference would be an
important consideration when planning epilepsy surgery guided by SEEG.
3.2 Materials and methods
3.2.1 Demographic and SEEG data of participants
Patients were recruited with approval from our institutional review board (IRB protocol #12-
857). Consecutive patients were identified from 2015 to 2018 who had undergone SEEG and had
FCD type II. A total of ten patients (age-range: 5-47, two females) were identified, including seven
type IIa and three type IIb. For each FCD type II patient, we matched at least one FCD type I, with
a similar epilepsy localization and age range. To ensure accurate comparison of epilepsy
localization, we chose FCD type I patients with the best seizure-free outcomes. As a result, fifteen
FCD type I patients (age-range: 5-69, eight females) were selected (Table 3-1). The iSPES was
performed in 58 pairs for type I and 32 pairs for type II. On average, each participant had 3.6
iSPES sites (type I: 3.9, type II: 3.2), 13 implanted electrodes (type I: 14, type II: 12), and 116
3 Effective connectivity in focal cortical dysplasia
55

Table 3-1 Clinical characteristics of patients
ID
Sex
Age (Years)
FCD
Implanted Electrodes
Gray matter contacts
Ictal Stim Pairs
SEEG Classification Resective Surgery
Outcomes Engel Class
Duration of epilepsy
(Years)
Focal to bilateral tonic-
clonic seizures
Region
M1977J4I M 37 Type IIA 8 69 4 Right Perirolandic (face)
Right Subcentral & Right
Caudal Precentral Gyrus
IA 32 + Extra
F1996J57 F 19 Type IIA 10 47 2
Right Precuneus and Post
Cingulate
Right Precuneus,
Ant/Mid/Post Cingulate
IIB 19 - Extra
M1968H92 M 47 Type IIB 11 73 2
Left Temporo-perisylvian
(posterior)
Redo – Left Posterior
Temporal
IA 43 + Temporal
M2000H77 M 16 Type IIA 15 113 4
Left Fronto-parietal
operculum
Left Fronto-parietal IA 10 + Extra
M1986H8I M 30 Type IIA 14 138 7 Left Baso-mesial Frontal Left Orbitofrontal IA 21 + Temporal
M1987I2S M 30 Type IIA 14 129 4 Left Lateral Temporal Left Temporal N/A 26 + Extra
M1992I2F M 25 Type IIA 14 156 2
Left Superior & Middle
Frontal Gyrus
Left Superior Frontal
Gyrus and Mid Cingulate
IIB 25 - Extra
M2000H8Q M 16 Type IIA 14 138 2 Left frontal epilepsy Left lateral frontal IIB 11 - Extra
M1979H8J M 38 Type IIB 10 87 4
Left neocortical temporal
epilepsy
Left posterior
lateral/basal temporal
IB 36 + Temporal
F2012H8C F 5 Type IIB 9 98 1
Left mesial frontal
epilepsy
Left mesial frontal
resection
N/A 3 - Extra
F1982I2H F 35 Type I 14 140 2
Left mesial frontal
epilepsy
Left superior frontal gyrus
as well as the motor
cingulate
IIB 24 + Extra
F1983I26 F 34 Type I 10 116 6
Right Precentral and
Inferoir Frontal Gyrus
Right Frontal IA 26 + Extra
M1960GAP M 56 Type I 10 74 10
Left Caudal Postcentral
Gyrus
Left Parietal IA 36 + Extra
M1997J5C M 18 Type I 15 113 3
Left Precuneus, Posterior
Cingulate, Occipital
Left Parieto-occipital IIA 18 + Extra
F1987I33 F 31 Type I 16 142 3
Left Superior Temporal
Gyrus & Heschl’s Gyrus
Left Superior Temporal
Gyrus & Heschl’s Gyrus
IA 25 - Temporal
F2005H33 F 11 Type I 14 132 1
Left Orbitofrontal &
Frontal Operculum
Left Orbito-frontal IA 10 - Extra
M1984J4H M 30 Type I 14 98 4
Right Basal Temporo-
Occipital
Right Extensive Temporal IA 12 + Temporal
M1984GBB M 32 Type I 15 125 5
Left Antero-lateral-basal
Temporal
Left Temporal IA 3 + Temporal
F1988H88 F 29 Type I 16 131 4
Right Temporal &
Collateral Sulcus
Right Temporal IA 16 + Temporal
M1990J42 M 24 Type I 16 133 2
Right Temporal Pole,
Inferior &
Middle Temporal Gyrus
Right Temporal IA 17 + Temporal
M1984I2P M 33 Type I 14 117 3
Right Superior Frontal
Gyrus
Right Superior & Middle
Frontal Gyrus
ID 32 + Extra
F1965HAA F 52 Type I 15 149 7 Right mesial frontal Right frontal IA 4 + Extra
F2005HC8 F 12 Type I 14 134 4
Right frontal (mesial and
lateral)
Right frontal IA 10 + Extra
M1999J4J M 16 Type I 15 139 1 Left temporal pole Left anterior temporal IA 4 + Temporal
F1949G4Q F 69 Type I 14 112 3 Right frontal Right frontal pole IA 50 + Extra
3 Effective connectivity in focal cortical dysplasia
56

contacts in gray matter (type I: 124, type II: 105). We performed t-tests to compare these
variables between FCD types I and II. However, no significant difference was observed in these
four features: age, iSPES sites, implanted electrodes, and contacts in the gray matter after
correcting for multiple comparisons (family-wise error (FWER) < α = 0.05 using the Hochberg
technique).
3.2.2 Recording and anatomical labeling
Our SEEG methodology has been previously reported
122
. Briefly, the electrodes were placed
for clinical purposes as a part of the epilepsy surgical evaluation. The depth electrodes (Adtech,
Integra, or PMT) were implanted using Talairach or stereotactic method in orthogonal or oblique
trajectories. Figure 3-1A portrays electrode implantation using this technique.
A detailed description of the CCEPs recording method was previously published
25,123,124
.
Typically, CCEPs recordings are performed towards the later stage of the SEEG evaluation when
the patients are on medications. Cortical stimulation was delivered by a Grass S88 stimulator
(Warwick, RI, USA) using Nikon-Kohden software. We utilized a square wave pulse (width of
300μs, frequency of 1Hz, and intensity of 4mA) with an alternating polarity between two adjacent
electrode pairs. The stimulating pair of electrodes were chosen for iSPES were those electrodes
representing ictal onsets in each patient as determined by the clinical team. Stimulation train was
discontinued in the uncommon event of afterdischarges or seizures. Postsurgical seizure outcomes
are tracked by an independent group at the Cleveland Clinic Epilepsy Center tasked with
maintaining objectivity.
3 Effective connectivity in focal cortical dysplasia
57

3.2.3 CCEPs analysis
In this chapter we considered only contacts in gray matter. The electrocorticography data
containing the SPES periods were processed using Brainstorm
36
. Trials were visually inspected
and those containing excessive noise were removed from further analysis. The remaining trials
were averaged to obtain the evoked potential from all other cortical SEEG electrodes for each
recording site. We analyzed these waveforms either in their entire response period (10-600ms after
the stimulation onset) or divided them into three intervals: early latency (10-60ms), middle latency
(60-250ms), and late latency (250-600ms).
3.2.4 Assessing the significance of CCEPs responses by permutation test
The early, middle and late latency periods of the averaged CCEPs responses were assessed
for statistical significance by employing a sign permutation test as described in our recent work
123
.
The test operates by randomly multiplying the responses of each trial by +1 or -1 and forming a
new average evoked response for each contact. Under the assumption that no response has been
recorded, there should be no effect on the distribution of the evoked response. When a latency
period is identified as significant using this method, the root mean square (RMS) of the response
can be calculated to represent the strength of connectivity. In this section, we employed SAS 9.3
software (SAS Institute, Cary, NC) to perform statistical analyses on a complete-case basis
(α=0.05). The averaged CCEPs responses and results of applying the sign permutation test are
depicted in Figure 3-1B. Similarly, the sign permutation test was also performed for the entire
period (10-600ms). We limited further analyses to statistically significant responses. Thereafter,
the CCEPs were divided into two groups based on the Euclidean distance from the mid-point of
3 Effective connectivity in focal cortical dysplasia
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the stimulating pair to the recorded contact. These groups were labeled as near (<50mm) and far
(>50mm).
3.2.5 Comparing RMS of CCEPs between two FCD types using percentile bootstrap
Statistical analysis between RMS responses of types I and II in the period of 10-600ms was
conducted by percentile bootstrap on trimmed means (B=10
4
number of bootstraps, with 20%
trimming on each side). This method can deal with possible non-normality and heteroscedasticity
of the sampled data
82
. The test was performed using the trimpb2 function in the WRS2 package
82

for R (R Foundation for Statistical Computing, Vienna, Austria). We contrasted the RMS values
between the two FCD types for near distances since FCD type II significant responses were seen
predominantly within 50mm of the stimulation site.
3.2.6 Latency Analysis using between-by-within test
We used a between-by-within test to assess the effects of two main factors: FCD type (Factor
A with two independent levels: types I and II) and latency (Factor B with three dependent levels:
early, middle, and late), and their possible interaction on CCEPs responses. This 2-by-3 design
was evaluated using a robust bootstrap-t method on trimmed means
82
(B=10
4
number of bootstraps,
with 20% trimming on each side using the bwmcp function in WRS2 package
82
). All p-values,
including the post hoc analysis, were collectively corrected using the Hochberg technique (FWER
<0.05).

3 Effective connectivity in focal cortical dysplasia
59

3.3 Results
3.3.1 RMS of CCEPs in FCD types I and II
We analyzed electrodes with significant RMS values of CCEPs responses based on the sign
permutation test following SPES of the ictal onset zone. Figure 3-1A illustrates the RMS of CCEPs
responses in the entire analysis period (10-600ms) for FCD types I and II, using a referential
montage (midline scalp reference). The x-axis represents the distance of each contact from the
stimulated pair. Five (two with type I and three with type II) out of 25 patients were discarded in
this section since none of their contacts showed a significant response. Comparing marginal
distributions, FCD type II displays more restricted RMS values than type I in both axes. This was
true when comparing absolute RMS values where FCD type I had greater values than FCD type II
as well as RMS values measured from distance to stimulation site where FCD type II had RMS
values that dropped off more drastically than FCD type I in contacts further away from the
stimulation site. Similar results were observed for the bipolar montage (Figure 3-1B).
Based on the above statistical analysis, type I demonstrated significantly larger RMS values
than type II, encompassing the entire analysis period (10-600ms) after the stimulation (p<10
-4
for
both referential and bipolar montages). The similarity of results in Figure 3-1 among referential
and bipolar montages argues against the possible influence of reference selection bias or far field
potentials. For the scatter plots, marginal distributions, and statistical tests, the selection of bipolar
or referential montage had no effect on our findings except that the bipolar montage showed a
faster drop in the spatial distribution in FCD type II. For simplicity, we represent our findings in
referential montage only after Figure 3-1.

3 Effective connectivity in focal cortical dysplasia
60

Figure 3-1 Recording paradigm and CCEPs responses in two reference montages. (A) A schematic representation
of electrode implantation. Each electrode can include up to 16 contacts. (B) CCEPs responses by stimulating the
L’6-L’7 pair. Cyan highlighted waveforms indicate significant responses after the permutation test (see Methods).
(C) Significant RMS values of CCEPs (in referential montage) are depicted for 10-600ms latency period. Each
point in the scatter plot represents a unique recording contact from a stimulation site. Hypothesis testing was
conducted using contacts in near distances (<50mm). The box at the bottom left displays the trimmed mean and
confidence interval for each group and the p-value for their comparison. For illustration purposes, data points larger
than four median absolute deviations above the median were Winsorized in each axis, independently. Marginal
distributions depict the increased connectivity for FCD type I in comparison to FCD type II. N denotes the number
of patients in each category. (D) The data displayed using a bipolar montage illustrates consistent findings between
FCD types I & II.
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3.3.2 Focal to bilateral tonic-clonic seizures and epilepsy localization
In the prior section we pooled all patients independent of their seizure type or epilepsy
localization. However, one can argue that these parameters might be influential on the amplitude
of CCEPs. To examine this hypothesis we categorized our data in two different ways. First, only
patients with FBTCS were compared. The result is depicted in Figure 3-2A, in which a similar
pattern to that noted in Figure 3-1 can be observed. For those patients with FBTCS, CCEPs
responses are significantly larger for FCD type I than type II (p<10
-4
for near contacts).
Additionally, we investigated temporal lobe epilepsy patients separately (this category includes
patients with temporo-perisylvian and lateral temporal SEEG hypotheses) as we had a large
number of patients in this category. Figure 3-2B shows that our previous finding holds in this
scenario as well: the trimmed mean for RMS of CCEPs is significantly larger for FCD type I than
type II (p<10
-4
for near contacts). Other epilepsy subtypes were not evaluated due to the smaller
number of patients in other categories.

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62

3.3.3 Latency periods
We divided CCEPs into three latency intervals: early (10-60ms), middle (60-250ms), and
late (250-600ms). Figure 3-3A compares these latency periods between FCD types I & II in
patients with FBTCS. Each bar depicts the mean and confidence interval of the corresponding
subgroup.
Consistent with our previous findings, the main effects analysis of the between-by-within
test indicated a larger RMS response for FCD Type I than type II (p<10
-4
). In the post hoc analysis,
middle and late latency periods of the CCEPs exhibited the same pattern (p<10
-4
for both),

Figure 3-2 CCEPs response in two subcategories. (A) RMS values of CCEPs (in referential montage) in latency
period 10-600ms. Here, only patients with focal to bilateral tonic-clonic seizures (FBTCS) were considered. Each
point in the scatter plot represents a unique recording contact from a stimulation site. Hypothesis testing was
conducted using contacts in near distances (<50mm). The box at the bottom left displays the trimmed mean and
confidence interval for each group and the p-value for their comparison. For illustration purposes, data points larger
than four median absolute deviations above the median were Winsorized in each axis, independently. Marginal
distributions depict the increased connectivity for FCD type I in comparison to FCD type II. N represents the
number of patients in each category. (B) The equivalent plot for patients with temporal lobe epilepsy.
3 Effective connectivity in focal cortical dysplasia
63

however, results revealed a slightly greater response in the early latency period (10-60ms) for type
II (p=0.0283 in Figure 3-3A for patients with FBTCS). Furthermore, we compared different
latency periods for each level of FCD type. Type I presented a substantial increase from early to
middle
and late latency intervals (p<10
-4
for both comparisons among patients with FBTCS). In type
II, when comparing early to other latency periods, we observed a decrease in amplitude of RMS
responses (p<10
-4
for early-middle and p<10
-2
early-late). Additionally, our statistical analysis
indicated an interaction between FCD types and latencies (p<10
-4
for early-middle). Lastly, FCD
type II showed a steeper falloff in significant electrodes, denoted as NP in Figure 3-3A, by the end
of the response, indicating its temporal restriction.

Figure 3-3 CCEPs responses in different latency intervals. (A) RMS values of CCEPs are computed in early,
middle, and late latencies in patients with focal to bilateral tonic-clonic seizures (FBTCS). The plot shows the
trimmed mean (20% trimming on each side) with 95% confidence interval based on the trimmed mean. A robust
between-by-within analysis presented a significant difference in factor A (FCD Type). Numerical p-values illustrate
the distinction for each latency. Comparing FCD types in early and middle latencies revealed a disordinal
interaction (p<10-4). N denotes the number of patients in each category. The variable NP represents the number of
contacts that passed the permutation test for each latency. All p-values are corrected. (B) The same approach is
illustrated for patients with temporal lobe epilepsy.
3 Effective connectivity in focal cortical dysplasia
64

A similar analysis was conducted when considering patients with temporal lobe epilepsy
(Figure 3-3B). Results are largely similar to the previous plot. FCD type I represents a larger
response in all latency periods (p<10
-4
) and FCD type II shows diminishing RMS values from
early to middle and late latency periods (p<10
-4
for both comparisons). We also find a decline for
type I when comparing early and late latency periods (p<10
-2
). In this case, the interactions were
detected in early-late and middle-late latency periods (p<10
-3
for both comparisons).
3.3.4 Electrode implantation
One question that may arise is whether observed differences between the two types of FCD
are due to the electrode implantations. In clinical practice, planning of the SEEG implantation
incorporates the results of multiple non-invasive tests. While the presence of a lesion on the MRI
may affect the position of one or two electrodes, suspicion of FCD type I over type II or vice-versa
does not alter the overall implantation targets. To demonstrate, we computed empirical probability
distribution functions (PDFs) of distances between contacts from the stimulation areas for type I
and type II in two scenarios. In the first scenario we considered all pairs of contacts and stimulation
sites. In the second we considered only pairs with significant responses in recording contacts based
on the permutation test (see Methods). These distributions are depicted in Figure 3-4. Visually, the
PDFs are similar when considering all electrodes (Figure 3-4A). However, when considering
electrodes that were deemed significant, the corresponding PDF for type II exhibits a more rapid
falloff (Figure 3-4B). This restrictive spatial response in type II can be verified by two analyses.
First, by comparing the differences between variances of each distribution in Figure 3-4A and 4B,
which changes from -105 to 187 when subtracting the variance of type II from type I. Second, the
interaction term of a between-by-within ANOVA test based on ranks
82
can contrast the effect of
3 Effective connectivity in focal cortical dysplasia
65

sign permutation test on distance distributions for two FCD types. We found that this interaction
is statistically significant (p=5.4×10
-6
), suggesting FCD type II has a more restricted distribution
of highly connected contacts with ictal onset zone than type I. These investigations indicate
that our findings were not impacted by initial electrode implantation.
3.3.5 Surgery Outcomes
In this study, the surgery outcomes of all but one of the patients with FCD type I were
classified as Engel I, i.e. seizure-free. For type II, we had a wider range of outcomes; five patients
with Engel class I versus three patients with Engel class II. This observation might seem
contradictory to our assumption that, in general, FCD type II would have a higher chance of

Figure 3-4 Electrode implantation. Probability distribution functions (PDFs) of distances between recording
contacts and the stimulation pairs. (A) This plot shows PDFs for type I and type II considering all implanted
electrodes and gray matter contacts. (B) This plot is restricted to contacts with significant CCEPs responses. A
between-by-within ANOVA based on ranks indicated an interaction among factors (FCD type and significant
response) (p=5.4×10
-6
). Additionally, the differences of variances in two cases imply a broader response for FCD
type I.
3 Effective connectivity in focal cortical dysplasia
66

seizure-freedom. However, it is important to note that the surgery outcomes in our data are the
result of the study design. We analyzed FCD type II patients who required SEEG which suggests
a less clear surgical hypothesis from just the noninvasive data (such as nonlesional MRI). FCD
type I patients on the other hand were matched to FCD type II and FCD type I cases with best
surgical outcomes were chosen to ensure adequate matching of epilepsy localization.
We compared the RMS of the CCEPs responses between two Engel classes in FCD type II
patients. Figure 3-5 illustrates these differences. We observe that patients with a better surgery
outcome (class I) have smaller and more restricted CCEPs responses than class II. A 2-by-3
between-by-within test (percentile bootstrap on trimmed means) was conducted in which Engel
class and latency were factors A and B, respectively. The main effects analysis of this test indicated
a larger RMS response for class II than class I (p<10
-4
for factor A). Post-hoc analysis for the three

Figure 3-5 CCEPs responses for different surgery outcomes. Variations of CCEPs responses in different latency
intervals for two Engel classes of surgery outcomes in patients with FCD type II. RMS values of CCEPs are
computed in early, middle, and late latencies. The plot shows the trimmed mean (20% trimming on each side) with
95% confidence interval based on the trimmed mean. A robust between-by-within analysis presented a significant
difference in factor A (Engel Class). Numerical p-values illustrate the distinction between two Engel Classes for
each latency. N denotes the number of patients in each category. The variable NP represents the number of contacts
that passed the permutation test for each latency. All p-values are corrected.
3 Effective connectivity in focal cortical dysplasia
67

latency intervals also revealed a similar pattern (p=2×10
-4
for early and

p<10
-4
for middle and late
periods).
3.4 Discussion
We used CCEPs, a measure of effective connectivity, to demonstrate that FCD type II shows
a more restricted pattern of connectivity compared to type I. We examined CCEPs responses that
were close to the ictal onset zone (distances within 50mm) for two reasons: 1) this distance has
previously been shown to be significantly modulated by CCEPs
125
, and 2) our analysis showed
that significant responses in FCD type II were seen predominantly within 50mm. In this study, we
showed increased hyperexcitability at the ictal onset zone in FCD type I compared to type II
(Figure 3-1C-D). We also observed a greater extent of hyperexcitability in FCD type I compared
with type II. In other words, FCD type I induces a higher degree of distal connectivity than type II
(Figure 3-1C and Figure 3-1B). These observations lend support to the notion of the formation of
a local epileptogenic network in FCD type II and a more extended epileptogenic network in type
I. This difference could explain the results of a previous study showing better seizure-free
outcomes following epilepsy surgery in patients with FCD type II
126
. Effective connectivity based
on clinical seizure types in FCD was also assessed in our study. We found the same difference in
the pattern of connectivity between FCD types I and II when considering the presence of FBTCS
(Figure 3-3A). Focal epilepsy with FBTCS has been noted to have a larger propagation network
than in focal epilepsy without FBTCS
127,128
. Therefore, the question could be raised of whether the
increase in RMS CCEPs both near and distant from ictal onset zone in FCD type I could be
attributable to a greater percentage of patients having FBTCS. Our analysis shows that this is not
the case in this study. When patients with FBTCS were analyzed separately, the difference between
3 Effective connectivity in focal cortical dysplasia
68

types I and II was more clearly seen in the middle and late periods of the CCEPs response than in
the early period (Figure 3-3A). In FCD type I, the middle and late components of CCEPs
significantly increased compared to the early component. The middle and late components of
CCEPs have been attributed to activation of cortico-thalamo-cortical networks in epilepsy whereas
the early latency component is believed to result from cortico-cortical activation
25,129
. The
thalamus has been implicated as one of the hubs that modulates propagation of FBTCS in focal
epilepsy
130
. The findings of the later components of CCEPs being accentuated in FBTCS in FCD
type I could represent activation of these cortico-thalamo-cortical pathways. In patients with
FBTCS and FCD type II the early component was larger than the earlier component in type I yet
still retained the same pattern of a dramatic fall-off in RMS values in middle and late components,
suggesting a restricted region of hyperexcitability. In FCD type II with FBTCS, the larger RMS
values in early latency may suggest that the mechanism of propagation relies on the cortico-cortical
pathways as opposed to the cortico-thalamo-cortical pathways as noted in FCD type I. Aberrant
functional connectivity profiles have been reported within and beyond FCD type II lesions as
determined by seed-based functional MRI combined with geodesic distance maps both within and
beyond the MRI visible lesion
126
.
In connectivity analysis of FCD, the degree and extent of abnormal synchronization may
also vary based on the pathology and location of the focus. We looked at whether the difference
in the pattern of synchronization between FCD types I and II would hold when controlling for the
location of epilepsy. In our cohort, we had an adequate number of patients with temporal lobe
epilepsy to perform this analysis. A similar difference of more restricted area of hyperexcitability
and synchronization was seen in FCD type II compared to type I in this localization (Figure 3-3B).
Therefore our findings held up when controlling for a specific epilepsy localization.
3 Effective connectivity in focal cortical dysplasia
69

In FCD type II we also found that patients with Engel class I outcome had an even more
restricted region of hyperexcitability than those with Engel class II (Figure 3-5). The more
restricted epileptogenicity may explain the reason for the improved postoperative seizure outcome.
In general, surgical management of FCD focuses on the assessment of epileptogenicity in relation
to an MRI lesion, if present
131
. For instance, the correlation of frequent rhythmic epileptogenic
discharges measured by electrocorticography in relation to the lesion can be used as a guide to
assess the required extent of surgical resection
131
. However, the margins of resection in cases of
nonlesional epilepsy are more difficult to assess as indicated by the lower postoperative seizure
freedom rates
132
. Our results suggest that CCEPS in patients with FCD type II and MRI negative
epilepsy who undergo SEEG may help predict postoperative seizure outcomes.
Our finding of more widespread excitability in FCD type I compared to type II may be
related to the following mechanisms: tangential migration of GABAergic inhibitory interneurons
which may be impaired in patients with FCD type I
133,134
; more extensive hyperexcitable network
as supported by nuclear imaging studies showing diffuse γ-aminobutyric acid type A receptors
135
;
and large-scale brain connectivity difference as noted in the subtypes of FCD type IIA versus type
IIB
136
. Although different patterns of connectivity could exist for the various subtypes of FCD type
II, we did not have sufficient numbers in our cohort to analyze any potential difference in CCEPs
connectivity.
In conclusion, FCD type I has a greater degree of excitability in cortices both near ictal zone
regions and regions of the brain distant from the ictal zone. Our finding of widespread
hyperexcitability and functional connectivity noted in FCD type I, a common pathological
substrate of nonlesional epilepsy, is supported by the observation of poor surgical outcomes after
a focal resection in this group
137,138
. FCD type II with Engel class I outcomes had the most
3 Effective connectivity in focal cortical dysplasia
70

restricted region of hyperexcitability. These differences in connectivity between types I and II were
maintained when controlling for epilepsy localization and seizure type. Some important limitations
of this study include the following: first, this is a single center study with a relatively small number
of FCD type II patients, and second, CCEPs methodology requires intracranial EEG analysis and
this is a retrospective study. A larger prospective study would be needed to assess whether our
findings can be replicated and also whether they would aid in epilepsy surgical planning for
patients with presumed FCD requiring SEEG evaluation.

4 Effective connectome
71

4 Effective connectome

4.1 Introduction
Chapter 2 explored the theory that functional connectivity in the ictal period has critical
information about the epileptogenic zone and brain states. This notion was confirmed by multilayer
modeling of brain networks and its corresponding measure of eigenvector centrality, accompanied
by an unsupervised consensus clustering. Furthermore, considerable time intervals and frequency
bands were identified, including the early to mid-seizure connectivity in high frequency. In chapter
3, we emphasized the importance of CCEPs as a measure of effective connectivity for brain
mapping. These recordings were employed to compare brain responses to stimulations between
types I and II of focal cortical dysplasia. Results indicated the effectiveness of this method in which
FCD type II displayed a more restrictive spatiotemporal response when compared with type I. In
the following chapter, we constructed a brain connectivity atlas (connectome) using CCEPs and
used this connectome to predict the degree of epileptogenicity in different brain areas.

4 Effective connectome
72

4.1.1 Brain stimulation and epileptogenicity
As discussed, CCEPs are induced by single-pulse electrical stimulation (SPES) and represent
excitatory postsynaptic potentials (EPSPs)
25
. Recent studies have revealed the significance of
CCEPs in the localization of the EZ
139
, mapping the language and motor networks
140
, and its
significant overlap with structural connectivity constructed by diffusion-weighted images
141
.
Importantly, CCEPs amplitude and outward connectivity were larger when the ictal onset zones
were stimulated
141,142
. These studies lend credence to the idea that the seizure onset zone is
hyperexcitable. Several factors might contribute to this hyperexcitability, such as changes in
excitatory and inhibitory circuits or the existence of a pathological tissue
143
. Understanding the
correlation between brain responses to low-frequency stimulation and its epileptogenicity, we aim
to build a connectivity atlas using CCEPs and use this mapping for identifying epileptogenic zone
in patients.
4.1.2 Current challenges in Stereoelectroencephalography
While SEEG recordings and in particular CCEPs provide valuable information about neural
interactions in epilepsy, the majority of research has been conducted at the subject-level and falls
short of group-level analysis. This limitation arises due to the following reasons:
• Electrode implantation and characteristics of the epileptogenic zone vary significantly
among patients.
• Depth electrodes only cover a portion of the brain volume so we cannot construct a full
network of brain connectivity in each individual.
4 Effective connectome
73

• Interpreting the CCEPs responses requires extensive knowledge regarding the physiology
of the stimulated site, epilepsy type, and pathology of the epileptogenic zone. Additionally,
for many patients, this information is either not available or not accurate.
4.1.3 Hypotheses and goals
In this chapter, we hypothesized that effective brain connectivity, constructed by CCEPs in
each patient, is a combination of the group-level effective connectome (with some deviation), for
non-epileptogenic regions, and abnormal (larger) connections for the epileptogenic areas. The
connectome portrays the connectivity in a normal brain and includes all cortical and several
subcortical regions. Since we could not measure this matrix directly in healthy individuals, we
were required to use CCEPs of patients for calculating this graph. Previous research has used
patients’ clinical labels to identify and discard connectivity values inside presumptive EZ and
compute a normal connectivity network by averaging among the remaining connections. Here, we
have employed a data-driven approach and an algorithm for detecting abnormal connections to
construct the effective connectome without using clinical labels. Thereafter, we hypothesized that
node-variant graph filters, with connectome as the graph shift operator matrix, can predict the
degree of epileptogenicity in different brain regions.

4 Effective connectome
74

4.2 Methods
4.2.1 Patients and recordings
We have used a new and developing database for this chapter that includes CCEPs, ictal
data, and brain images (MRI and CT) for each patient. This feature is essential for our multimodal
analysis of epileptogenic networks. The SEEG implantation and CCEPs recording are similar to
the process explained in 3.2.2. At this time, there are 44 patients in the database. Later in this
chapter, we have provided the clinical characteristics of eight of those patients.
4.2.2 Effective connectome
An effective connectome is a brain connectivity atlas, and it is the cornerstone of the analyses
we want to perform in this chapter. Figure 4-1 demonstrates the framework for calculating this
matrix.
4.2.2.1 Coregistration and parcellation
For each subject, the processing workflow was as follows. The individual electrodes were
identified manually by marking the tip and skull entry. The pre(surgical)-MRI was coregistered to
computed tomography (CT) image using Brainstorm. The patient's MRI is analyzed using
BrainSuite to generate a model of the brain that is labeled by USCBrain atlas
144
, a high-resolution
atlas built using both anatomical and functional information to guide the parcellation of the
cortex. Brainstorm was then used to automatically assign contact labels using the segmented cortex
and contact coordinate locations. This workflow performs the contact labeling process in a semi-
automated manner.
4 Effective connectome
75

4.2.2.2 CCEPs processing
Raw CCEPs were first bandpass filtered in the range 1-200Hz and power line noise (60,
120, 180Hz) was removed using notch filters. Filtered data was categorized for each stimulated
contact and reshaped into trials. We identified artifact trials using an outlier detection method
based on scaled median absolute deviation (MAD). A trial was considered artifact if its RMS
values in either of pre (150-25ms before the stimulation) or post (15-300ms after the stimulation)
periods, were four MADs above the median of all trials.
4.2.2.3 Subject-level connectivity matrix
Among non-artifact trials, we performed bootstrap in which half of the trials were randomly
selected and averaged to create the evoked response. We used the RMS value of the averaged
response (15-300ms) as the indicator of effective connectivity from the stimulated area to receiving
contacts. We conducted the same procedure for all stimulation regions to create the subject-level
effectivity connectivity matrix in contact space. The bootstrap was performed five times, resulting

Figure 4-1 Framework for estimating the effective connectome
4 Effective connectome
76

in five connectivity matrices for each patient. Since only a portion of contacts was stimulated in
each patient, this matrix is not entirely constructed.
We aimed to alleviate the inter-subject variability of CCEPs before integrating the adjacency
matrices of all patients. We first thresholded large values to the 95
th
percentile of all connections
in each participant. Next, we clustered connectivity values into three groups using k-means
clustering and chose the center of the first cluster as the baseline connectivity for that patient. As
a result, adjacency matrix elements were normalized to that baseline. Figure 4-2 depicts the
distribution of connectivity values after normalization in 38 patients. The following section
discusses the algorithm for estimating the effective connectome using the individuals’ connectivity
matrices.

Figure 4-2 Distribution of connectivity elements in all patients after normalization
4 Effective connectome
77

4.2.2.4 Proposed algorithm for estimating the effective connectome
Using the single-pulse electrical stimulations and induced evoked potentials, we computed
the effective connectivity matrix for each patient. Those matrices were defined in the contact space
of each participant. Since each patient might have a different level of response to electrical
stimulations, we normalized the connectivity values, to reduce inter-subject variability.
Additionally, we transferred each subject’s connectivity matrix in contact space to USCBrain atlas
with (𝑁 =208) ROIs.
The patients’ adjacency matrices include normal and abnormal connections. We aim to
compute the 𝑁×𝑁 matrix 𝐒, as the normal effective connectivity graph (connectome) using the
data of all patients. The measured connectivity matrix 𝐓
9
for the m-th patient can be expressed as,
𝐓
9
=(𝟏−𝐂
9
−𝐑
9
)∘(𝐒+𝐄
9
)+𝐂
9
∘(𝐙
9
+𝐕
9
) (4−1)
in which 𝟏 is the all-ones matrix and 𝐂
9
is the binary indicator matrix, showing the abnormal
connections in the m-th participant,
𝐂
9
(𝑖,𝑗)=p
1 (𝑖,𝑗) 𝑖𝑠 𝑎𝑏𝑛𝑜𝑟𝑚𝑎𝑙
0 𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒

Matrix 𝐑
9
identifies the connections in 𝐒 that do not exist for the m-th patient, due to incomplete
and heterogenous sampling of SEEG electrodes or lack of stimulation,
𝐑
9
(𝑖,𝑗)=p
1 (𝑖,𝑗) 𝑖𝑠 𝑛𝑜𝑡 𝑑𝑒𝑓𝑖𝑛𝑒𝑑
0 𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒

Notation ∘ represents the Hadamard product, and matrix 𝐄
9
models the deviation of normal
connections in each patient from the connectome. In other words, we assume a Gaussian
distribution for brain connectivity values in a healthy brain.
The second term in equation 4-1 applies to abnormal connections, in which 𝐙
9
models the
patient’s true abnormal connectivity and 𝐕
9
displays the deviation from the true abnormal
4 Effective connectome
78

connection. This deviation can be either because of averaging among different trials or stimulating
distinct parts of one ROI. Our goal is to estimate the connectome matrix 𝐒 and identify the
abnormal elements 𝐂
9
, so we have proposed the following cost function,
argmin
𝐒,𝐂
𝑚

'((𝟏−𝐂
𝑚
−𝐑
𝑚
)∘(𝐓
𝑚
−𝐒)(
𝐹
2
+ 𝜆‖𝐂
𝑚
‖
1
𝑀
𝑚=1
(4−2)
Subject to
𝐂
9
is binary
The first term only applies to available and normal connections of 𝐓
9
. To solve equation 4-2, we
first show that it can be formulated in an elementwise form. We define,
𝚪
9
=𝟏−𝐂
9
−𝐑
9

𝚫
9
=𝐓
9
−𝐒
The cost function in the equation 4-2 can be written as,
argmin
𝐒,𝐂
𝑚

'‖𝚪
𝑚
∘𝚫
𝑚
‖
𝐹
2
+ 𝜆‖𝐂
𝑚
‖
1
𝑀
𝑚=1
(4−3)
For simplicity, we assume a 2×2 connectivity matrix, then,
argmin
𝐒,𝐂
𝑚

' ,
-γ
11
.
𝑚
(δ
11
)
𝑚
-γ
12
.
𝑚
(δ
12
)
𝑚
-γ
21
.
𝑚
(δ
21
)
𝑚
-γ
22
.
𝑚
(δ
22
)
𝑚
,
𝐹
2
+ 𝜆/
(𝑐
11
)
𝑚
(𝑐
12
)
𝑚
(𝑐
21
)
𝑚
(𝑐
22
)
𝑚
/
1
𝑀
𝑚=1
(4−4)
which can be expanded as follows,
argmin
𝐒,𝐂
𝑚

' 0-γ
11
.
𝑚
(δ
11
)
𝑚
0
2
+
𝑀
𝑚=1
𝜆|(𝑐
11
)
𝑚
|+⋯ (4−5)
#|(γ
%(
)
9
(δ
%(
)
9
|
(
+
D
9, %
𝜆|(𝑐
%(
)
9
|+⋯
#|(γ
(%
)
9
(δ
(%
)
9
|
(
+
D
9, %
𝜆|(𝑐
(%
)
9
|+⋯
4 Effective connectome
79

#|(γ
((
)
9
(δ
((
)
9
|
(
+
D
9, %
𝜆|(𝑐
((
)
9
|
Since γ
"!

9
can be computed using 𝑐
"!

9
, and δ
"!

9
is a function of s
"!
, each row of the
equation 4-5 is a separable optimization problem, so the matrix form decouples for each
connection. As a result, we perform the optimization problem elementwise, for those connections
that exist. Equation 4-2 can be rewritten for the (i,j) element of graph,
argmin
s
𝑖𝑗
,!𝑐
𝑖𝑗
"
𝑚

' 021−-𝑐
𝑖𝑗
.
𝑚
3∗2-t
𝑖𝑗
.
𝑚
−s
𝑖𝑗
30
2
+ 𝜆0-𝑐
𝑖𝑗
.
𝑚
0
𝑀
′
𝑚=1
(4−6)
Subject to
𝑐
"!

9
is binary
in which 𝑀
#
is the set of connections/patients that t
"!

9
is defined. Since we performed
bootstrapping and projected connections from contact space to USCBrain atlas, there might be
more than one t
"!

9
realization for each pair of ROI in each patient. For a better estimation, we
included all values.
To solve the optimization problem in equation 4-6 we used a stepwise approach. In step
one, all connections were considered normal, so the second term was dropped, s
"!
was estimated
as the average of all t
"!

9
, and the cost function was computed. Next, the largest connection in
the set was labeled as abnormal, so it was removed from the s
"!
computation and its cost was added
as 𝜆. If the new cost was lower than the original one, these labels and s
"!
were accepted as the
recent estimate and we continued the process by labeling the top two largest values in the set as
abnormal. The algorithm stopped when labeling more abnormal connections could not lower the
overall cost anymore and the labels with the lowest cost were considered the final estimate.
4 Effective connectome
80

4.2.2.5 Evaluating the performance of the proposed method
To assess the performance of the proposed method, we run simulations over a range of
parameters for density of abnormal connections and the weight of the regularization term (𝜆). In
our simulations, we aimed to mimic the distribution of connectivity values in CCEPs. For normal
connections, we assumed a Gaussian distribution Ν(1, 0.1). The abnormal connections were
extracted from a uniform distribution U(1.5, 8). Figure 4-3 presents the probability distributions
for normal and abnormal connections in the simulated data.
We employed the algorithm in section 4.2.2.4 to estimate the true normal connectivity value
and abnormal connections. We performed 100 simulations for each set of parameters. Figure 4-4a
depicts the accuracy of identifying the abnormal values of the 𝑐
"!

9
for different values of 𝜆 and
density of abnormal elements. Figure 4-4b displays the normalized root mean square error
(NRMSE) in estimating the true connectivity for each case, considering (1) as the grand truth.

Figure 4-3 Probability distributions for normal and abnormal connections in the simulated data
4 Effective connectome
81

By increasing the 𝜆, the cost of labeling connections as abnormal was increased and less
connections were identified as abnormal. While that might be less problematic when the density
of abnormal elements is small, it becomes an issue when that density is high. However, the
NRMSE of estimation the true connectivity value is still low for several values of 𝜆. In general,
𝜆 =0.5 had the best performance. We compared the proposed technique with two MATLAB built-
in functions for outlier detection, gesd and one-class SVM. In both cases our method outperformed
with a wide margin.
Our findings demonstrated the applicability of the proposed algorithm to real data. Before
applying this technique to CCEPs, we have introduced the second part of our methodology. The
proposed optimization technique can help us to estimate the normal connectivity matrix (S).
However, we need an approach to compare the effective connectivity in each patient with matrix
S to identify the epileptogenic regions. We use graph filters for this purpose which are described
in the following sections.
a b

Figure 4-4 The accuracy of detecting abnormal elements and estimating the true connectivity value
4 Effective connectome
82

4.2.3 Graph Signal Processing
Graph analysis of complex systems provides new tools for better understanding of those
networks. The field graph signal processing (GSP) aims to advance our knowledge about different
aspects of complex networks and their interactions
145,146
. Here, we introduce some basic concepts
in GSP.
Consider directed graph 𝒢 with a set of nodes 𝒱 (with the cardinality of 𝑁) and set of edges
(links) ℰ, 𝒢 =(𝒱,ℰ), such that if node 𝑖 is connected to 𝑗 then (𝑖,𝑗)∈ℰ. Signal x can be defined
by a 𝑁×1 vector on 𝒢, displaying the values of each node. We define the 𝑁×𝑁 matrix S as the
graph-shift operator (GSO)
147,148
, which can be the graph Laplacian or adjacency matrix.
Assuming A as the adjacency matrix of graph 𝒢, 𝐀
"!
is non-zero if there is a link from node 𝑗 to 𝑖.
Thus, the outgoing neighborhood of node 𝑗 can be expressed, 𝒩
!
={ 𝑖|(𝑗,𝑖)∈ℰ}. When matrix S
is diagonalizable, we can write it as 𝐒=𝐕𝚲𝐕
3%
, in which matrix 𝐕
3%
acts as the frequency
(spectral) transform for signals in vertex domain and 𝚲 is a diagonal matrix where its elements are
eigenvalues of the graph-shift operator, i.e., 𝚲=diag({𝜆
%
,…,𝜆
&
}). As a result, we refer to 𝐱 =
𝐕
3%
𝐱 the frequency representation of signal x. Lastly, we define ℓ
I
norm of vector x as ‖𝐱‖
I
≔
|𝑠𝑢𝑝𝑝(𝐱)| in which 𝑠𝑢𝑝𝑝(𝐱)≔{𝑖|𝑥
"
≠0}, the number of non-zero elements in x.
4.2.4 Graph Filters
Graph filtering is considered a linear or nonlinear operation on signal x, resulting in the
output y
149
. This relationship can be described in the frequency domain using the eigen
decomposition of graph Laplacian matrix L to compute 𝐱 , applying a pointwise operator in the
spectral domain, and transforming the output to the vertex domain
145
. A general approach which
4 Effective connectome
83

is more suitable for directed graphs is using linear operators, 𝐲=𝐇𝐱 in which the 𝐇 is the filter.
A simple representation for 𝐇 is the expression based on a polynomial of matrix 𝐒 as follows
147
,
𝐇≔ #ℎ
J
𝐒
J
K3%
J, I
(4−7)
where 𝐡=[ℎ
I
,…,ℎ
K3%
]
'
and K is the order of the filter. To represent equation 4-7 in the
frequency domain, we first define the 𝑁×𝐾 Vandermonde matrix.
𝚿≔£
1
⋮
1

𝜆
%
⋮
𝜆
&

𝜆
%
K3%
⋮
𝜆
&
K3%
¥ (4−8)
Using Ψ, the 𝐡 can be transferred to the frequency domain, 𝐡
§
=𝚿𝐡.
4.2.4.1 Modified node-variant graph filters
The equation 4-7 does not have enough degrees of freedom and might come short in some
situations. As a result, several filters have been proposed, including the node-variant (NV) graph
filter
150
,
𝐇
2L
#
≔ #𝑑𝑖𝑎𝑔𝛟
(J)
𝐒
J
K3%
J, I
(4−9)
in which vector 𝛟
(J)
=[𝜙
%
(J)
,⋯,𝜙
&
(J)
]
'
contains the weight of each node for k-th shift. While
equation 4-9 is the common representation of node-variant graph filters, here we employ a slightly
different version of it. In (4-9) the weight 𝜙
"
(J)
is applied to incoming links of node i while in our
application in finding epileptogenicity of brain regions, we are mostly interested in the effect of
each region on its outgoing connections. Consequently, the following notation of NV filters have
been used for the rest of this work,
4 Effective connectome
84

𝐇
2L
≔ #𝐒
J
𝑑𝑖𝑎𝑔(𝛟
(J)
)
K3%
J, I
(4−10)
4.2.5 Multi-input multi-output (MIMO) system identification.
As stated previously, the brain response to a single pulse direct electrical cortical stimulation
(SPES) can be modeled by individually tailored brain networks based on group-level effective
connectome in atlas space. The modified version of node-variant graph filters can be a suitable
candidate in this regard. Figure 4-5 represents the suggested framework in our analysis, in which
the weighted directed GSO matrix 𝐒 is the effective connectome obtained by the process described
in 4.2.2.
The system identification problem is defined to estimate 𝛟
(J)
given inputs, outputs and the
GSO matrix. Assume we have access to a set of P input signals p𝐱
"
(O)
«
O, %
P
and their corresponding
outputs p𝐲
"
(O)
«
O, %
P
, in which P describes the number of realizations. The subscript 𝑖 in 𝐱
"
(O)

represents the stimulation of node 𝑖 for the p-th input, i.e., 𝐱
"
(O)
=[𝑥
",%
(O)
,…,𝑥
",&
(O)
]
'
is a 𝑁×1
canonical basis where the i-th element is non-zero. Since the GSO matrix is defined in atlas space,
and even in our clinical recording of CCEPs one pair of contacts can be stimulated in several set
of trials, we can have several inputs at the same region.
Suppose 𝐵
"
={𝛽
%
,…,𝛽
8
A
}⊆{1,…,𝑃} includes the indices of inputs where the node i is
stimulated, where 𝑏
"
is the cardinality of the subset 𝐵
"
. While input vectors in subset 𝐵
"
are
identical, this is not true for output signals, due to non-deterministic nature of neural signals and
varying physiological characteristics inside each ROI.
For a particular input 𝐱
"
(O)
, the output of the filter can be written as,
4 Effective connectome
85

𝐲
"
(O)
=𝐇
2L
𝐱
"
(O)
+ 𝒆
"
(O)
= #𝐒
J
𝑑𝑖𝑎𝑔(𝛟
(J)
)
K3%
J, I
𝐱
"
(O)
+𝒆
"
(O)
(4−11)
where vector 𝒆
"
(O)
is an i.i.d zero-mean Gaussian noise and included to model the response
variability for a constant input. The 𝑁×𝑁 matrix 𝐒
J
can be described by its columns 𝐬
"
(J)
, 𝐒
J
=
[𝐬
%
(J)
…𝐬
"
(J)
…𝐬
&
(J)
]. The input 𝐱
"
(O)
selects the i-th column of 𝐒
J
along with the i-th element of
𝛟
(J)
,
𝐲
"
(O)
=𝑥
","
(O)
#𝜙
"
(J)
𝐬
"
(J)
K3%
J, I
+𝒆
"
(O)
(4−12)
where 𝑥
","
(O)
is one and can be dropped. Equation 4-12 represents a system of maximally N linear
equations with K variables in which 𝑁 ≫𝐾. Please note that in practice the number of linear
equations will be reduced if,
∃ 𝑖 ∈{1,…,𝑁} 𝑠.𝑡.∀ 𝑘 ∈{0,…,𝐾−1},𝐬
"
(J)
=0
4.2.5.1 Least-squares estimation
We define vector 𝛟
"
=[𝜙
"
(I)
,…,𝜙
"
(K3%)
]
'
as the corresponding outdegree weights at node i
for 𝐾 shifts. Using (4-6), 𝛟
"
can be estimated singly, due to the way we have characterized the
inputs.
By defining the coefficient matrix,
Figure 4-5 Graph filtering framework
4 Effective connectome
86

𝚷
"
=·𝐬
"
(I)
… 𝐬
"
(K3%)
¸
&×K
(4−13)
in which 𝑟𝑎𝑛𝑘(𝚷
"
)≤𝐾. We can write the output as
𝐲
"
(O)
=𝚷
"
𝛟
"
+𝒆
"
(O)
(4−14)
To estimate 𝛟
"
using least-squares,
𝛟
¹
"
(O)
=(𝚷
"
'
𝚷
"
)
3%
𝚷
"
'
𝐲
"
(O)
(4−15)
Since same inputs at node i can have different outputs, we calculate 𝛟
¹
"
(O)
in each case to
form a distribution and assign the mean of that distribution as its final estimation.
Proposition I: ∀ 𝑖 ∈{1,…,𝑁} the vector 𝛟
"
can be estimated using least-squares if all
following conditions hold true:
a) The cardinality of 𝐵
"
is non-zero, i.e., 𝑏
"
≥1
b) 𝑟𝑎𝑛𝑘(𝚷
"
)= 𝐾
Proof: The weight 𝜙
"
(J)
for 𝑘 ∈ {0,…,𝐾−1} only appears in equations with 𝐱
"
(O)
as input,
so it is necessary to have at least one stimulation at node i. Since matrix 𝚷
"
is full rank skinny and
𝑁 ≫𝐾, we can neither have infinite solutions nor an exact solution, so we need least-squares (4-
15) for approximation. ∎
In our application, the condition b in Proposition I holds true almost invariably, so a single
stimulation at i-th region guarantees the estimation of 𝛟
"
.
4.2.6 Simulation of node variant graph filters
We performed a simulation to evaluate the algorithm in 4.2.5. A weighted directed network
with 64 nodes and 20% edge density was created. We generated the graph using “synthetic modular
small-world network” in Brain connectivity toolbox
30
. A node variant filter with two shifts
4 Effective connectome
87

operators, i.e. 𝐒
%
and 𝐒
(
, was considered while the zero-shift component was dropped. The first
filter was a Kaiser window centered on samples (32,33) and the second was a Gaussian window
circularly shifted 31 samples from the center of the first filter. Figure 4-6 depicts the ground truths
for these two filters in solid lines. For each node, the output signal was computed by applying a
single-entry input to that vertex, filtering and adding a random Gaussian noise. The noise power
was selected so that SNR = 6dB. Shaded lines in Figure 4-6 demonstrate the estimated graph filters
in different realizations (iterations) with presumed parameters.
To better understand the effect of noise and graph density on estimation error we performed
the simulation based on several values of these two parameters.
Figure 4-7 illustrates the normalized mean squared error (NMSE) for seven SNR and two
density values. As expected, non-sparse graphs would result in a lower NMSE, so by employing a
proper atlas and ample number of participants, the estimation can be improved. In conclusion, this
simulation gives us insights about authenticity of our method and the conditions for ideal
estimation.

Figure 4-6 Ground truth for graph filters and their estimation
4 Effective connectome
88

Figure 4-7 Normalized mean squared error in estimating node-variant graph filters in different combinations of
graph shift operator density and signal to noise ratio.
4 Effective connectome
89

4.3 Results
4.3.1 Calculating the effective connectome
As previously discussed, the subjects' evoked responses were normalized to reduce the inter-
subject variability. To improve the algorithm's performance by increasing the number of samples,
we created five networks for each patient, constructed by five bootstraps from a random sample of
trials. We randomly chose a subset of trials for each stimulation site, averaged among them to
create CCEPs, and computed the RMS. Employing the optimization algorithm in 4.2.2.2, we
calculated the effective connectome (S) based on CCEPs. Figure 4-8 presents the adjacency matrix
constructed by data from 38 patients. Each column shows outdegree connections from the
stimulated ROI. Following the simulations in 4.2.2.5, we chose 𝜆 =0.5. There are 208 ROIs (104
in each hemisphere), including cortical areas with some subcortical regions such as the
hippocampus and amygdala.

Figure 4-8 Effective connectome (S).
4 Effective connectome
90

Visually, intra-hemispheric connectivity is stronger than inter-hemispheric interactions. This
observation makes sense since, in most situations, the SEEG electrodes are implanted unilaterally.
Our analysis only estimated elements of the connectivity matrix with at least 20 realizations
(without bootstrap, 100 with bootstrap) to have a more reliable value. Additionally, we only
considered connections that are available in at least two patients. Consequently, the density of
matrix S was only 3.5%, suggesting substantially more samples are needed. Figure 4-9 displays
the number of patients included in estimating different elements of matrix S.
Previous studies have identified brain regions, such as the hippocampus and amygdala, as
the ROIs with higher than normal inward and outward connectivity strengths in the non-
epileptogenic brain
151
. Table 4-1 illustrates the top 10 ROIs with the largest outward connectivity
values, in which the hippocampus is ranked first.

Figure 4-9 Number of patients for estimating brain connections
4 Effective connectome
91

4.3.2 Distributions of normal and abnormal connections
In section 4.2.2.5 we analyzed the effect the lambda on the accuracy of the estimating the
abnormal elements and grand truth. Since the range of values in the connectivity networks is close
to the simulated data, we selected 𝜆 =0.5. Figure 4-10 depicts the distributions of identified
normal and abnormal elements. The overlap between these distributions was predictable since the
true connectivity value varies between different brain connections.
Table 4-1 Top 10 ROIs with largest connectivity in normal brain
ROI Outward connectivity Number of Samples
R. hippocampus 1.392 2010
L. transverse temporal gyrus 1.307 2630
R. middle frontal gyrus - posterior 1.205 10145
R. precentral gyrus - superior 1.195 5560
L. middle temporal gyrus - dorsoposterior 1.167 2155
R. pars opercularis - inferior 1.146 5365
R. cingulate gyrus - posterior 1.141 6750
R. inferior temporal gyrus - anterior 1.132 3455
R. postcentral gyrus - superior 1.120 4895
L. precentral gyrus - inferior 1.110 15930

Figure 4-10 Probability distributions for identified normal and abnormal connections
4 Effective connectome
92

4.3.3 Investigating the abnormal connections
We calculated the chance of one region being identified as abnormal using the optimization
results. For each element of the connectivity matrix, we computed the chance of being abnormal
using the predicted labels for that connection in all patients. Next, by computing the median of
those values among the available outward connections of that ROI, we estimated the chance of
abnormality in the population for that region. Table 4-2 presents the top 10 ROIs with highest
chance of abnormality. Results are consistent with our understanding of pathologies and
locations/classifications of epilepsy. For instance, abnormalities in superior and inferior temporal
gyrus and amygdala are common in many patients diagnosed with epilepsy
152
.
Additionally, we were interested in comparing patients’ characteristics and their surgery
information with connections identified as abnormal, i.e. 𝑐
"!

9
=1. Table 4-3 presents the
clinical characteristics of eight patients in this database, in which all except one have Engel Score
IA (completely seizure free since surgery). As a result, the resected region should include the
epileptogenic zone, and abnormal connections are most likely inside the resected area. Here, we
have investigated the connections that are available in at least 10 patients. Figure 4-11 displays all
connections with that feature.
Table 4-2 Top 10 ROIs with highest chance of abnormality in outward connections
ROI Chance of Abnormality Number of Samples
L. superior temporal gyrus - posterior 0.750 3140
L. paracentral lobule 0.727 1110
R. hippocampus 0.725 2010
R. inferior temporal gyrus - anterior 0.711 3455
R. amygdala 0.648 3605
L. supramarginal gyrus - anterior 0.636 5760
L. pars opercularis - superior 0.592 4540
L. middle temporal gyrus - dorsoposterior 0.585 2155
R. postcentral gyrus - superior 0.574 4895
L. superior temporal gyrus - middle 0.570 6570
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Table 4-3 Clinical characteristics of eight patients
Sub ID Age Gender Ictal Onset Zone
Epilepsy
Classification
Surgery Engel Score
F1983I26 34 F
Right Inferior Frontal
Gyrus, Pars orbitalis,
Orbitofrontal Gyrus, Middle
Frontal gyrus And Superior
Frontal gyrus
Right Frontal
Epilepsy
Right Frontal Excision
IA:
Completely
Seizure-Free
Since Surgery
M2010I2M 8 M
Inferior/Middle Temporal
Gyrus
Left Lateral
Frontal Epilepsy
Resection Dorsolateral
Aspect of The Left Frontal
Lobe
IA:
Completely
Seizure-Free
Since Surgery
F1993I32 24 F
Focal Left Temporal Pole,
Amygdala, Perirhinal
Left Mesial
Temporal
Epilepsy
Anterior Aspect of The Left
Temporal Lobe Including the
Amygdala
IA:
Completely
Seizure-Free
Since Surgery
F1987I33 31 F
Focal Left Temporal
operculum, Heschl's Gyrus
Left Temporal
Epilepsy
Awake Craniotomy Superior
Temporal Gyrus Part of
Heshl(U) With ECOG
IA:
Completely
Seizure-Free
Since Surgery
F2010I37 7 F
Superior Frontal
Sulcus/Lesion
Left Focal
Epilepsy
Superior And Middle Frontal
Gyrus Centering on The
Superior Frontal Sulcus
About 2/3 Posteriorly
IA:
Completely
Seizure-Free
Since Surgery
M1993I27 25 M
Focal Left Precuneus and
Posterior Cingulate
Left Mesial
Parietal Epilepsy
The Parietal Lobe with
Minimally Invasion Towards
Occipital and Respecting The
Posterior Ramus Of The
Cingulate Was Performe
IA:
Completely
Seizure-Free
Since Surgery
M1964I2J 53 M
Amygdala, Temporal pole,
Collateral sulcus
Hippocampus
Left Temporal
Epilepsy
Left Anterior Temporal
Lobectomy, Resecting
Temporal Pole Amygdala,
Sparing Hippocampus
IA:
Completely
Seizure-Free
Since Surgery
M1992I2F 25 M
Focal Left Middle Frontal
gyrus /Left Superior Frontal
sulcus
Left Focal
Epilepsy
Resection Of the Superior
Frontal Gyrus including the
Major Structures With
Preservation Of The
Cingulate
IIB: Rare
Disabling
Seizures Since
Surgery
4 Effective connectome
94

Each dot in each column in figure 4-11 depicts the connectivity strength between two ROIs
in one patient. Red dots indicate the situation in which that connection is labeled as abnormal, and
gray dots are showing the normal connections. We selected three patients from table 4-3 to further
analyze their results. These patients are highlighted in figure 4-11 with the first and last three letters
of their ID.
For patient F2010I37 (FI37), there were several large connections in which the posterior part
of the “left superior frontal gyrus” was stimulated. By looking at Table 4-3, we confirmed this
region was inside the resected area. Interestingly, when the anterior part of the “left superior frontal
gyrus” was stimulated, we did not observe an abnormal connection.

Figure 4-11 Comparing brain connections between different patients. Red dots represent the connectivity values
identified as abnormal while the gray dots depict normal connections.

4 Effective connectome
95

For patient M2010I2M (MI2M), the left dorsolateral frontal lobe is resected. Figure 4-11
shows that when left middle frontal gyrus was stimulated, we can see abnormal connections. In
contrast, stimulating areas outside the resection region, such as the left postcentral gyrus or left
cingulate gyrus did not result in a big response in CCEPs.
Patient M1992I2F (MI2F) was diagnosed with left focal epilepsy, where the left superior
frontal gyrus was resected. Results in figure 4-11 show abnormal connections mainly when left
superior frontal gyrus was stimulated. In this figure, for most cases when the middle frontal gyrus
was stimulated, we do not see an abnormal connection.
Our findings suggest that the proposed methodology for estimating the connectome and
identifying abnormal connections have clinical implications and it can be employed in presurgical
evaluations. However, we are interested in a framework that systematically predicts the
epileptogenicity scores of brain regions. In the next section, we used the previously introduced
graph filters for this application.

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96

4.3.4 Estimating the epileptogenicity of brain ROIs in patients
One of the main aims of this chapter's work was to develop a methodology for identifying
the epileptogenicity of brain regions in each patient. We constructed a normal brain connectivity
atlas (connectome) to then compare the individuals' brain responses to that network using node-
variant graph filters. By employing the calculated matrix S and data of each participant, we
estimated filter's weights, using the method in section 4.2.5. For simplicity, we only considered
one shift of the GSO matrix (order one) with no DC component.
By applying equation 4-15, we computed one coefficient per each stimulated area. Following
our hypothesis and the literature, this weight should be correlated with the epileptogenicity of that
region. We expected that nodes inside the epileptogenic zone have the largest weights, i.e., high
outdegree values due to the hyperexcitability of the EZ. Since all except one of the patients in table
4-3 are completely seizure-free (Engel class IA), the EZ should be inside the resected area. Table
4-4 displays the epileptogenicity scores, computed using graph filters, for each stimulated ROI.
Comparing tables 4-3 and 4-4, we observed that in most cases ROIs with large epileptogenicity
scores are inside the resected area. For majority of patients in this dataset, brain stimulations were
only conducted in presumptive epileptogenic zone, so we expect a significant portion of areas in
table 4-4 is associated with the EZ.
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97

Table 4-4 Epileptogenicity scores for eight patients
ROI Epileptogenicity Score
F1983I26
R. pars orbitalis 4.11
R. precentral gyrus - superior 2.87
R. postcentral gyrus - inferior 2.45
R. superior frontal gyrus - posterior 2.43
R. postcentral gyrus - superior 2.36
R. supramarginal gyrus - anterior 2.35
R. middle frontal gyrus - posterior 2.32
R. anterior orbito-frontal gyrus 2.10
R. precentral gyrus - inferior 1.93
R. middle frontal gyrus - anterior 1.85
M2010I2M
L. superior frontal gyrus - posterior 3.74
L. anterior orbito-frontal gyrus 3.73
L. middle frontal gyrus - posterior 3.54
L. middle frontal gyrus - anterior 3.37
L. temporal pole 3.10
L. gyrus rectus 2.87
L. pars triangularis - posterior 2.87
L. pars opercularis - superior 2.71
L. posterior orbito-frontal gyrus 2.41
L. middle orbito-frontal gyrus 2.31
L. lateral orbitofrontal gyrus - anterior 1.39
F1993I32
L. hippocampus 2.81
L. superior temporal gyrus - anterior 2.72
L. middle temporal gyrus - middle 2.30
L. amygdala 2.25
L. temporal pole 2.07
L. superior temporal gyrus - middle 1.52
F1987I33
L. superior temporal gyrus - posterior 6.35
L. superior temporal gyrus - middle 3.11
L. insula - posterior 2.43
L. fusiform gyrus - posterior 1.95
L. pars opercularis - inferior 1.75
L. insula - anterior 1.69
R. insula - posterior 1.45
L. middle temporal gyrus - ventroposterior 1.42
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98

R. precentral gyrus - inferior 1.39
R. transverse temporal gyrus 1.18
F2010I37
L. middle frontal gyrus - posterior 2.77
M1993I27
L. temporal pole 3.45
L. hippocampus 3.37
L. precuneus - superior 2.28
L. angular gyrus - anterior 2.10
L. cingulate gyrus - posterior 2.00
L. supramarginal gyrus - posterior 1.52
L. lingual gyrus - anterior 0.89
L. superior temporal gyrus - posterior 0.86
M1964I2J
L. amygdala 5.19
L. superior temporal gyrus - middle 3.53
L. middle temporal gyrus - anterior 3.01
L. gyrus rectus 2.89
L. temporal pole 2.43
L. superior temporal gyrus - anterior 2.17
M1992I2F
L. postcentral gyrus - superior 5.04
L. paracentral lobule 3.86
L. supramarginal gyrus - anterior 3.71
L. supramarginal gyrus - posterior 3.58
L. precuneus - superior 3.36
L. amygdala 2.76
L. superior frontal gyrus - posterior 2.46
L. superior parietal gyrus - anterior 2.45
L. superior temporal gyrus - middle 2.40
L. superior frontal gyrus - anterior 2.38
L. precentral gyrus - superior 2.32
L. middle frontal gyrus - posterior 2.12
L. precuneus - inferior 1.75
R. angular gyrus - middle 1.20

4 Effective connectome
99

To better visualize these results, we used cortical surfaces. Figure 4-12 demonstrates the
epileptogenicity scores computed by graph filters in four patients. In several cases, such as patients
“F1987I33” and “M2010I2M” the resected regions display the highest score. These findings
further support the two proposed algorithms in this chapter.

Figure 4-12 Epileptogenicity maps on cortical surfaces
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100

4.4 Discussion
4.4.1 Conclusion
This chapter started by mentioning the current challenges in using CCEPs. We first stated
our approach to address these issues. Next, we proposed two algorithms, one for estimating the
effective connectome and one for identifying the epileptogenic regions in each patient using the
connectome as the GSO matrix.
In our simulations, the algorithm for identifying the abnormal connections had an excellent
performance even with considerable overlap between normal and abnormal distributions and a
high density of abnormal connections. Significantly, it could vastly outperform the conventional
outlier detection techniques. When applied to the real data, the identified normal and abnormal
connections were consistent with our expectations about intrinsic brain connectivity and the
epileptogenic zone in each patient. For instance, a high percentage of outward connections in the
superior temporal gyrus were predicted as abnormal, related to the significant number of patients
with temporal lobe epilepsy.
Next, we used a modified version of node-variant graph filters to estimate the
epileptogenicity score of brain ROIs in several patients. In this paradigm, brain stimulation was
considered an input to our system, with the stimulated node having the value of 1 and the rest zero.
The GSO matrix was adapted from the estimated connectome, and the output was the RMS of
CCEPs in each electrode location. We then computed the filter weight for each ROI. Our findings
were consistent with identified regions as epileptogenic zones by clinicians.
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101

4.4.2 Limitations and future work
One of the limitations of this study was the number of patients and stimulations. We could
estimate only a small fraction of connections in effective connectome. CCEPs evaluation should
focus on more comprehensive brain stimulation than just stimulating the presumptive ictal onset
zone, so we will have a better estimate for normal brain connectivity. This issue will be solved
once we add the data of new patients to our dataset.
The USCBrain atlas that was used in our study includes regions with different sizes and
some ROIs are expansive. Since we map all connections inside that region into a single ROI, the
CCEP response might vary substantially, when stimulating different parts of an expansive ROI.
Once we increase the number of samples in the database, future work can address this issue using
atlases with finer scales.

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Abstract (if available)

Abstract In epilepsy, investigating brain connectivity has attracted considerable attention since multiple different networks are involved in this neurological disorder. Seizure generation, propagation, and termination occur through spatiotemporal brain networks. Notably, researchers have studied functional and effective connectivity among patients with epilepsy. Functional networks are constructed by statistical dependency between time series, and effective connectivity displays the flow of information in the brain, i.e., the causality of signals. In this work, we have pursued three general goals. First, we examined the functional connectivity during seizures. Second, we investigated effective connectivity in patients with focal cortical dysplasia (FCD) by using cortical stimulation. Lastly, we have developed a framework for creating an effective connectivity atlas (connectome). We used this connectome to estimate the epileptogenicity of brain regions in different patients.
Chapter 2 demonstrates the significance of large-scale brain interactions in high-frequency (80-200 Hz) for identifying the epileptogenic zone (EZ) and seizure evolution. We have modeled brain connectivity constructed from stereoelectroencephalography (SEEG) data during seizures using multilayer networks to incorporate the continuity of neural dynamics. After introducing a new measure of brain connectivity for temporal networks, named multilayer eigenvector centrality (mlEVC), we applied a consensus hierarchical clustering to the developed model to identify the epileptogenic zone (EZ) as a cluster of nodes with distinctive brain connectivity in the ictal period. Our algorithm could successfully predict electrodes inside the resected volume as EZ for 88% of participants, who all were seizure-free for at least 12 months after surgery. Our findings illustrated significant and unique desynchronization between EZ and the rest of the brain in early to mid-seizure. We showed that aging and the duration of epilepsy intensify this desynchronization, which can be the outcome of abnormal neuroplasticity. Additionally, we illustrated that seizures evolve with various network topologies, confirming the existence of different epileptogenic networks in each patient. Our findings suggest the importance of early intervention in epilepsy and the possible factor that correlates with disease severity. Moreover, by analyzing the propagation patterns of different seizures, we asserted the necessity of collecting sufficient data for identifying the epileptogenic networks.
In chapter 3, we compared cortico-cortical evoked potentials (CCEPs) as measures of effective brain connectivity in 25 FCD patients with drug-resistant focal epilepsy who underwent intracranial evaluation with stereoelectroencephalography (SEEG). We analyzed the amplitude and latency of CCEPs responses following ictal onset single-pulse electrical stimulation (iSPES). Our findings showed that compared to FCD type II, patients with type I demonstrated significantly larger responses in electrodes near the ictal onset zone (<50mm). These findings persisted when controlling for the location of the epileptogenic zone, as noted in patients with temporal lobe epilepsies, and controlling for seizure type, as indicated in patients with focal to bilateral tonic-clonic seizures (FBTCS). In type II, the root mean square (RMS) of CCEPs responses dropped substantially from the early segment (10-60ms) to the middle and late segments (60-600ms). The middle and late CCEPs latency segments showed the most considerable differences between FCD types I and II. FCD type II displayed a more restrictive area of hyperexcitability in both temporal and spatial domains. In patients with FBTCS and type I FCD, the increased amplitudes of RMS in the middle and late CCEPs periods appear consistent with cortico-thalamo-cortical network involvement of FBTCS. The degree and extent of hyperexcitability differences may contribute to the different postsurgical seizure outcomes noted between these two pathological substrates.
In chapter 4, we first explained the current challenges in incorporating the data of different patients. We first proposed a methodology to identify the abnormal elements of a vector. We applied this technique to the CCEPs data of our patients to construct an effective connectivity atlas (connectome). Furthermore, we used node-variant graph filters to identify the epileptogenic regions of the brain using the estimated connectome. Results revealed that in most patients with seizure freedom after surgery, the brain areas with the highest score are inside the resected region. These findings suggest the applicability of this technique for identifying the epileptogenic zone.

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Asset Metadata

Creator Shahabi, Hossein (author)

Core Title Brain connectivity in epilepsy

School Viterbi School of Engineering

Degree Doctor of Philosophy

Degree Program Electrical Engineering

Degree Conferral Date 2022-08

Publication Date 06/09/2022

Defense Date 05/09/2022

Publisher University of Southern California (original), University of Southern California. Libraries (digital)

Tag biomarkers,brain networks,brain stimulation,CCEPs,connectome,electrophysiology,epilepsy,epileptogenic zone,graph signal processing,machine learning,multilayer networks,OAI-PMH Harvest,SEEG

Format application/pdf (imt)

Language English

Contributor Electronically uploaded by the author (provenance)

Advisor Leahy, Richard (committee chair), Haldar, Justin (committee member), Marmarelis, Vasilis (committee member)

Creator Email hshahabi@usc.edu,shahabi.h27@gmail.com

Permanent Link (DOI) https://doi.org/10.25549/usctheses-oUC111339682

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