Functional brain connectivity from EEG in epilepsy: seizure prediction and epileptogenic focus localization.

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PRONEU-1339; No. of Pages 17 Progress in Neurobiology xxx (2014) xxx–xxx

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Progress in Neurobiology journal homepage: www.elsevier.com/locate/pneurobio

Functional brain connectivity from EEG in epilepsy: Seizure prediction and epileptogenic focus localization Pieter van Mierlo a,*, Margarita Papadopoulou b, Evelien Carrette c, Paul Boon c, Stefaan Vandenberghe a, Kristl Vonck c, Daniele Marinazzo b a

Medical Imaging and Signal Processing Group, Department of Electronics and Information Systems, Ghent University – iMinds Medical IT Department, Ghent, Belgium Department of Data Analysis, Faculty of Psychology and Pedagogical Sciences, Ghent University, Ghent, Belgium c Laboratory for Clinical and Experimental Neurophysiology, Neurobiology and Neuropsychology, Ghent University, Ghent, Belgium b

A R T I C L E I N F O

A B S T R A C T

Article history: Received 13 November 2013 Received in revised form 21 June 2014 Accepted 29 June 2014 Available online xxx

Today, neuroimaging techniques are frequently used to investigate the integration of functionally specialized brain regions in a network. Functional connectivity, which quantifies the statistical dependencies among the dynamics of simultaneously recorded signals, allows to infer the dynamical interactions of segregated brain regions. In this review we discuss how the functional connectivity patterns obtained from intracranial and scalp electroencephalographic (EEG) recordings reveal information about the dynamics of the epileptic brain and can be used to predict upcoming seizures and to localize the seizure onset zone. The added value of extracting information that is not visibly identifiable in the EEG data using functional connectivity analysis is stressed. Despite the fact that many studies have showed promising results, we must conclude that functional connectivity analysis has not made its way into clinical practice yet. ß 2014 Elsevier Ltd. All rights reserved.

Keywords: Functional brain connectivity EEG Epilepsy Seizure prediction Epileptogenic focus localization Epileptic networks

Contents 1. 2.

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Epilepsy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Definition, prevalence and incidence . . . . 2.1. Seizures . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2. Epileptiform activity in the EEG 2.2.1. Brain region terminology . . . . . 2.2.2. Treatment . . . . . . . . . . . . . . . . . . . . . . . . . 2.3. Refractory epilepsy . . . . . . . . . . . . . . . . . . 2.4. Presurgical evaluation. . . . . . . . . . . . . . . . 2.5. 2.5.1. Scalp video-EEG monitoring . . .

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Abbreviations: ADT, adaptive DTF; AED, antiepileptic drug; AIC, Akaike’s Information Criterion; APDC, adaptive PDC; AR, autoregressive; DC, directed coherence; DCM, dynamic causal modeling; DTF, directed transfer function; ECoG, electrocorticography; EEG, electroencephalography; ESI, EEG source imaging; EZ, epileptogenic zone; ffADTF, full-frequency ADTF; ffDTF, full-frequency DTF; FINE, first principle vectors; fMRI, functional MRI; GCI, Granger causality index; HD EEG, high-density EEG; iADTF, integrated ADTF; iAPDC, integrated APDC; ICA, independent component analysis; iDTF, integrated DTF; IED, interictal epileptiform discharge; IEEG, intracranial EEG; IFCN, International Federation of Clinical Neurophysiology; ILAE, International League Against Epilepsy; iPDC, integrated PDC; IPI, initial precipitating insult; IVEM, invasive video/ EEG monitoring; L, lateral; LGS, Lennox-Gastaut syndrome; LM, lateral–medial; M, medial; MEG, magnetoencephalography; MI, mutual information; ML, medial–lateral; MRI, magnetic resonance imaging; MVAR, multivariate autoregressive; PC, partial coherence; PDC, partial directed coherence; PET, positron emission tomography; PLI, phase lag index; PLV, phase locking value; SBC, Schwarz’s Bayesian Criterion; SDTF, short-window DTF; SEEG, stereo EEG; SOZ, seizure onset zone; SPECT, single photon emission computed tomography; SVEM, scalp/video EEG monitoring; swADTF, spectrum weighted ADTF; TE, transfer entropy; TLE, temporal lobe epilepsy. * Corresponding author. Tel.: +32 93324326. E-mail address: [email protected] (P. van Mierlo). http://dx.doi.org/10.1016/j.pneurobio.2014.06.004 0301-0082/ß 2014 Elsevier Ltd. All rights reserved.

Please cite this article in press as: van Mierlo, P., et al., Functional brain connectivity from EEG in epilepsy: Seizure prediction and epileptogenic focus localization. Prog. Neurobiol. (2014), http://dx.doi.org/10.1016/j.pneurobio.2014.06.004

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2.5.2. Structural magnetic resonance imaging . . . . . . . . . . . . . . . . . . . . . . Invasive video-EEG monitoring . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.5.3. Functional brain connectivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Definition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1. Conceptual distinction between different functional connectivity measures. 3.2. Precautions during analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3. Seizure prediction using functional brain connectivity . . . . . . . . . . . . . . . . . . . . . . . Intracranial EEG . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1. 4.2. Scalp EEG . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Epileptogenic focus localization using functional brain connectivity . . . . . . . . . . . . Intracranial EEG . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.1. 5.1.1. Seizure networks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Interictal networks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.1.2. Scalp EEG . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2. Sensor space . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2.1. 5.2.2. Source space . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Discussion and future directions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1. Introduction Epilepsy is a neurological disorder characterized by recurrent seizures. During the seizures there is abnormal excessive firing of neurons in the brain resulting in diverse symptoms such as staring, muscle stiffness (tonic movements), muscle spasms (clonic movements) and impaired consciousness. The unpredictability of when seizures occur dramatically impacts the life of patients with epilepsy. Therefore, seizure prediction can help to warn patients and to improve their quality of life. Seizure prediction aims at predicting an upcoming seizure before the clinical manifestation of the seizure occurs. If antiepileptic drugs do not result in adequate treatment of the patient, a possible treatment is the surgical resection of the epileptogenic focus, i.e. the region in the brain responsible for causing the seizures. This makes the localization of the epileptogenic focus of utmost clinical importance. The aim of epileptogenic focus localization is to provide information on the location and delineation of the epileptogenic focus to the epileptologists in order to support their decision making. Electroencephalography (EEG) is the most important technique for the diagnosis and treatment follow-up in epilepsy patients. EEG records the electric field generated by the neurons in the brain with high temporal resolution (order of ms). It is used to classify the type of seizures and to localize the epileptogenic focus. Because brain areas are highly interconnected, many (distant) brain regions are potentially involved during a seizure. This makes the localization of the epileptogenic focus from ictal EEG recordings a true challenge. Three decades ago, functional neuroimaging was mainly used to establish functional segregation as a principle of organization in the human brain, addressing how specific brain regions are used to execute specific tasks (Friston, 1994). Lately functional neuroimaging is used to study functional integration rather than segregation: the integration of functionally specialized brain regions is investigated. How these intercommunications take place and which brain regions are involved is addressed in the research domain of brain connectivity. Brain connectivity can reveal pathways between brain regions or reveal how information is processed, sent to, received by or shared between different brain regions. In this review paper we discuss how functional brain connectivity obtained from EEG recordings can be used to localize the epileptogenic focus. Because of the growing appreciation that a single focus may not be the best way of understanding the

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pathophysiology underlying seizure activity we emphasize the role of networks or distributed processing in epilepsy. We start by giving a general introduction on epilepsy and the treatment of epilepsy patients. Afterwards we introduce functional connectivity measures, discuss the conceptual difference between them and draw attention to important issues during the functional connectivity analysis. We give an overview how these functional connectivity measures can be used to predict seizures and localize the epileptogenic focus. In the last section we discuss the current state of use of functional brain connectivity in clinical practice and suggest possible future directions. 2. Epilepsy 2.1. Definition, prevalence and incidence Epilepsy is one of the most common neurological disorders affecting roughly 0.5–1% of the population worldwide. Epilepsy is characterized by recurrent, unprovoked seizures (Fisher et al., 2005), defined as the manifestation(s) of epileptic (excessive and/ or hypersynchronous), usually self-limited activity of neurons in the brain (Blume et al., 2001). During a seizure, a sudden burst of uncontrolled electrical activity occurs within a group of neurons in the cerebral cortex (So¨rnmo and Laguna, 2005). Epilepsy is usually diagnosed after a person has experienced at least two unprovoked seizures that were not caused by some known condition like alcohol withdrawal or extremely low blood sugar. Epilepsy can develop at any age, but the incidence of epilepsy is highest during the first years of life and after the age of 65. During the adult years the incidence is the lowest (Jallon, 2006). In many cases the precise etiology of epilepsy in a specific patient is unknown. Nevertheless, many factors can cause epilepsy: genetic factors, head trauma, tumors, stroke, dementia, meningitis, prenatal injury, oxygen deprivation and many more. This is called the initial precipitating insult (IPI) generating a symptomatic form of epilepsy. The process in which epilepsy develops until spontaneous seizures occur is called epileptogenesis. 2.2. Seizures Epilepsy can be divided into two subtypes based on the location in the brain where the seizures start from and how it propagates. On the one hand, seizures in primary generalized epilepsy begin with a widespread electrical discharge that involves the entire brain. On the other hand, partial seizures begin with an electrical


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discharge in a limited area of the brain. This type of epilepsy can be further classified based on the involved brain lobe during the partial seizures into temporal, frontal, occipital and parietal lobe epilepsy. The clinical manifestation of the seizures has many forms depending on which brain areas are affected by the seizure, i.e. the symptomatic zone. They diverge from auras, tonic–clonic movements to impairment or loss of consciousness. A summary of the ictal and postictal symptoms for temporal, frontal, occipital and parietal lobe epilepsy can be found in Panayiotopoulos (2010). Despite the fact that the term generalized epilepsy is commonly used, it should be noted that the concept of generalization is highly questionable. It has been demonstrated that epilepsies that appeared to be generalized, had a focal onset from which propagation takes place very rapidly (Leutmezer et al., 2002; Lu¨ders et al., 2009; Pati and Cole, 2014). 2.2.1. Epileptiform activity in the EEG During a seizure synchronous rhythmical ictal discharges occur. This is usually reflected in the EEG as a periodic waveform with higher amplitude compared to the interictal periods. An example of seizure activity is shown in the left panel of Fig. 1. The International Federation of Clinical Neurophysiology (IFCN) defines a seizure pattern in the EEG as a phenomenon consisting of repetitive EEG discharges with relatively abrupt onset and termination, and a characteristic pattern of evolution lasting at least several seconds. The component waves or complexes vary in form, frequency, and topography. They are generally rhythmic and frequently display increasing amplitude and decreasing frequency during the same episode. When focal in onset, they tend to spread subsequently to other areas. The EEG seizure patterns unaccompanied by clinical epileptic manifestations are called subclinical. During the interictal period there can also be manifestations of epileptiform activity, namely interictal epileptic discharges (IEDs). They can be divided morphologically into sharp waves, spikes, spike-wave complexes, and polyspike-wave complexes. IEDs can occur in isolation or in brief bursts; bursts longer than a few

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seconds are likely to represent seizure activity rather than interictal discharges. An example of a spike-wave complex is shown in the right panel of Fig. 1. 2.2.2. Brain region terminology A specific terminology is used to precisely denominate epileptic brain regions. The epileptogenic zone (EZ) is the area of the cerebral cortex responsible for causing habitual seizures. Surgical removal of this brain area is required and sufficient to render the patient seizure free (Luders et al., 1987). Currently no available technique is able to precisely delineate this zone. Therefore a number of techniques are combined and their results give a certain estimate of the true EZ. The irritative zone is defined as the area of cortical tissue that generates interictal electrographic spikes. The ictal onset zone, also called seizure onset zone (SOZ), is the area of cortex from which clinical seizures are generated based on ictal EEG recordings (Rosenow and Luders, 2001). 2.3. Treatment The aim of epilepsy treatment is to suppress the seizures. Treatment with antiepileptic drugs (AEDs) is successful in 60–70% of epilepsy patients (Brodie and Kwan, 2002), who go into remission and are then seizure free, without unacceptable AED related side-effects. In 40–60% of these successfully treated patients, AEDs can be withdrawn after a reasonable time without recurrence of seizures (AED, 1991). 2.4. Refractory epilepsy Patients that cannot be adequately treated with AEDs are diagnosed with pharmaco-resistant or refractory epilepsy. The seizures are not (completely) suppressed or the patient suffers from adverse drug reactions. According to the ILAE a patient has refractory epilepsy when there has been failure of adequate trials of two tolerated and appropriately chosen and used AED schedules

IED

Seizure Fp1-F3 F3-C3 C3-P3 P3-O1

Fp1-F3 F3-C3 C3-P3 P3-O1

Fp2-F4 F4-C4 C4-P4 P4-O2

Fp2-F4 F4-C4 C4-P4 P4-O2

Fp1-F7 F7-T3 T3-T5 T5-O1

Fp1-F7 F7-T3 T3-T5 T5-O1

Fp2-F8 F8-T4 T4-T6 T6-O2

Fp2-F8 F8-T4 T4-T6 T6-O2

20 s

1s

Fig. 1. Epileptiform activity in the EEG. The left panel shows a EEG epoch during a seizure of a patient with right mesial temporal lobe epilepsy. Rhythmic activity can be noticed especially at the electrodes covering the right hemisphere. The right panel shows an interictal epileptiform discharge in another patient. The spike-wave complex has phase reversal over F7-T3 (sensitivity 10 mV/mm). Figure adapted from Javidan (2012).


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whether as monotherapy or in combination to achieve sustained seizure freedom (Kwan et al., 2010). In newly diagnosed patients, 50% of the patients will become seizure free on their first AED, 10% on their second AED, but no more than 5% on the third or a combination of two AEDs (Kwan and Brodie, 2000; Mohanraj and Brodie, 2005, 2006). Possible treatments for these refractory epilepsy patients are epilepsy surgery (Luders and Youssef, 2001) or electric stimulation such as deep brain stimulation (Vonck et al., 2013) or vagus nerve stimulation (Vonck et al., 2009). To assess whether a patient is eligible for epilepsy surgery a battery of tests are performed during the presurgical evaluation. 2.5. Presurgical evaluation The question whether surgery can be considered as a treatment option is addressed during the presurgical evaluation (Engel et al., 1992; Boon et al., 1999; Rosenow and Luders, 2001). A multidisciplinary team of epileptologists, neurosurgeons, radiologists, psychologists and engineers investigates whether surgery could be beneficial for the patient. During the presurgical evaluation the team tries to localize the epileptogenic focus based on the results of multi-modal (structural and functional) neuroimaging techniques as accurate as possible. Next to this possible overlap with eloquent cortex is investigated. Afterwards a decision is taken whether it is beneficial for the patient to have epilepsy surgery. Here the epileptogenic focus can be surgically removed or disconnected to stop seizure spreading. Here the current status, how many seizures the patient has and how they affect his/her quality-of-life, should be balanced against the risks of surgery. During the presurgical evaluation the patient’s history, neurophysiological testing, scalp video/EEG monitoring (SVEM) (Noachtar and Re´mi, 2009; Cascino, 2002), EEG source imaging (ESI), structural and functional magnetic resonance imaging (MRI and fMRI) (Bronen, 1992; Deblaere and Achten, 2008), EEG/fMRI, magnetoencephalography (MEG) (Stefan et al., 2011), interictal Positron Emission Tomography (PET) and ictal Single Photon Emission Tomography (SPECT) (La Fouge`re et al., 2009; Desai et al., 2013) are combined to localize the EZ as precisely as possible and to define overlap between the EZ and eloquent cortex. All results are integrated and a decision is made in the best interest of the patient’s health. The two cornerstone investigations to identify the EZ prior to epilepsy surgery are SVEM and structural MRI. The absence of structural anomalies, non-localizing SVEM, or conflicting results between these two investigations frequently results into referral of patients to invasive video-EEG monitoring (IVEM). 2.5.1. Scalp video-EEG monitoring For SVEM, the patient is admitted to the hospital for several days. During this period, scalp EEG is continuously recorded and the patient stays in a specially equipped room with video monitoring. The investigation of ictal discharges on the EEG corresponding to a specific semiology on video helps the classification of the epilepsy and the localization of the ictal onset zone. The video is used to identify specific movements and behavior of the patient during the seizures. The seizure semiology has a localizing value, although the first clinical symptoms do not necessarily arise from the SOZ but can be caused by seizure spreading (Rosenow and Luders, 2001). 2.5.2. Structural magnetic resonance imaging The structural MRI protocol (T1, T2, Diffusion Weighted Imaging, etc.) is used to reveal anomalies in the brain such as atrophy, focal cortical dysplasia and lesions that may underly seizure occurrence. The most common observed anomalies in

epilepsy are hippocampal sclerosis, developmental cortical dysplasia, cavernous angiomas and low-grade neoplasms (Wehner and Lu¨ders, 2008). The observation of these anomalies in the brain is not directly indicative for epilepsy. The relation between the lesion and the EZ needs to be explicitly assessed. 2.5.3. Invasive video-EEG monitoring In approximately 15–25% of the refractory epilepsy patients included in the presurgical evaluation protocol, IVEM is required to identify the ictal onset zone (Carrette et al., 2010). The electric field generated by the neurons is measured intracranially. Here, electrodes are placed inside the skull to allow a more direct measurement of the brain’s potential field and to reveal brain activity that cannot be observed with scalp EEG recordings alone. The intracranial electroencephalogram (IEEG) records electrical activity of various brain regions by means of subdural strip or grid electrodes placed on the cortex and/or depth electrodes inserted deep within the brain’s parenchyma. The term electrocorticography (ECoG) is preferred when only grids or strips are placed on the cortex and the brain is not penetrated. Stereoelectroencephalography (SEEG) (Chauvel et al., 1987) is a technique in which multiple depth electrodes are used to simultaneously record the brain activity from superficial and deep brain sources. SEEG results in a dynamic three-dimensional temporo-spatial picture of brain activity ideally suited to the study of the relations between structures involved in seizure production and propagation (McGonigal et al., 2007). IVEM is an invasive procedure that is accompanied by risks (such as hemorrhage, cerebrospinal fluid leaks, infections and mortality) (Van Loo et al., 2011) and should be carefully considered. There needs to be a clear hypothesis that is tested by the IVEM, which either rejects or confirms the hypothesis. In IVEM, only a limited number of electrodes can be implanted, making the choice of implanted regions very important. The implantation scheme defines the spatial sampling. The IVEM can show the spread of ictal activity instead of the initial onset if the actual SOZ is not covered by the electrodes. The spread of the ictal activity is usually visually analyzed by the epileptologist. Here functional brain connectivity analysis may provide additional information to the epileptologist about the spreading of the seizure and can be used to localize the epileptogenic focus.

3. Functional brain connectivity 3.1. Definition There are two analytic approaches to functional brain architecture; namely, functional segregation and functional integration. Functional segregation refers to the anatomical segregation of functionally specialized brain regions, while functional integration refers to the functional interaction between these functionally segregated brain regions (Zeki and Shipp, 1988). The functional integration can be studied by functional and effective connectivity. Functional connectivity is defined as the study of temporal correlations between spatially distinct neurophysiological events (Friston et al., 1993b). It investigates the statistical dependency between two or more time series by investigating whether the null hypothesis of independence can be rejected. Effective connectivity is defined as the influence one neural system exerts over another (Friston et al., 1993) and is based on different hidden neuronal states generating the measurements (Friston et al., 2013). Effective connectivity depends critically on state-space models with biophysiologically informed observation and state equations (Valdes-Sosa et al., 2011). In this review we will restrict ourselves to functional brain connectivity.


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3.2. Conceptual distinction between different functional connectivity measures There are several conceptual distinctions between the different functional connectivity measures: they either reveal directed or undirected, linear or nonlinear connections in the time or frequency domain. The calculation of the measures is either amplitude or phase-based and the measure can be bivariate or multivariate. An overview of the distinctions between the functional connectivity measures is given in Table 1. Mathematical details of the described functional connectivity measures can be found in the appendix. Below we briefly introduce 4 categories of functional connectivity measures: (1) Correlation and coherence, (2) Phase synchronization measures, (3) Information-based measures and (4) Granger causality measures. The most well known functional connectivity measure is the correlation, also called the Pearson correlation coefficient. It calculates the instantaneous linear relation between two signals based on the amplitudes of the signals. A variant of this measure is the cross-correlation that investigates the correlation between two time series that are shifted in time with respect to each other. This allows to assess the directionality of the correlation. The counterpart of the cross-correlation in the frequency domain is the coherency. The absolute value of the coherency is the coherence, which detects the linear relation between two signals at a certain frequency. The phase of the coherency can be used to infer the directionality of the connection. All previous discussed measures are bivariate, they can only show the relationship between 2 signals at a time. This makes differentiation between direct and indirect interrelations impossible. To overcome this issue, the partial coherence was introduced (Jenkins and Watts, 1969). Instead of investigating the relation between the amplitudes of the signals, one could also investigate how the phases of the considered signals are coupled, the so-called phase synchronization measures. Here the most commonly used measures are the phase locking value (Lachaux et al., 1999), also called mean phase coherence (Mormann et al., 2000), and the phase lag index (Stam and Reijneveld, 2007). A third group of functional connectivity measures originate from information theory. The most frequently used informationbased measures are the mutual information and the transfer entropy. They are both based on the probability functions of the considered variables and the joint probability. The mutual information assesses the undirected nonlinear relations between two signals and the transfer entropy the directed nonlinear relations.

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A fourth category of functional connectivity measures is based on the concept of Granger causality. The concept of Granger causality was developed when Clive Granger adapted the definition of causality proposed by Norbert Wiener (Wiener, 1956) into a practical form (Granger, 1969). One time series is said to Granger cause a second one, if inclusion of the past values of the first into the modeling of the second significantly reduces the variance of the modeling error. Most of the Granger causality measures are constructed based on an autoregressive (AR) model, in which the present samples of the signals are predicted using a linear combination of the past samples. From the coefficients of the AR model many measures can be derived: the Granger-causality index (Geweke, 1984), the directed coherence (Saito and Harashima, 1981), the directed transfer function (Kaminski and Blinowska, 1991) and the partial directed coherence (Baccala´ and Sameshima, 2001). 3.3. Precautions during analysis Although connectivity analysis seems straightforward, several precautions should be taken into account. During the preprocessing one should take care that phase-invariant frequency filters are used, otherwise spurious connections can be introduced. Florin et al. (2010) suggested that filtering of neuronal data disturbs the time ordering and information content of the data, leading to spurious and missed causalities. Barnett and Seth (2011) state that filtering can be a useful preprocessing step for removing artifacts when applied carefully and for furnishing or improving stationarity; however filtering is inappropriate for isolating causal influences within specific frequency bands. Resampling to limit the amount of data should also always be approached with care in order not to introduce spurious self connections due to the interpolation procedure. Another issue is the montage chosen as starting point for the connectivity analysis. By using a referential montage, where the potential differences between each electrode and a designated reference electrode are acquired, there will be redundant information in the dataset. Here, partial conditioning to a limited subset of variables while estimating functional connectivity as an alternative to full conditioning can help (Marinazzo et al., 2012). Methods have also been developed to investigate the interaction among groups, or ‘‘ensembles’’, of variables instead of the single variables (Barrett et al., 2010). By using a bipolar montage, where the potential differences between adjacent electrodes are recorded, the redundant information will be smaller but one could cancel out sources that are picked up by both electrodes.

Table 1 The properties of the different described functional connectivity measures.

Undirec Correlation Coherency Cross-correlation Directed coherence Directed transfer function Granger causality index Mutual information Partial coherence Partial directed coherence Phase locking value Phase lag index Transfer entropy

Direc

X X X X X X X X X X X X

Bivar

Multivar

X X X X X X X X X X X X

Ampl

Phase

X X X X X X X X X

Nonlin

X X X X X X

Time

Freq

X X X X X X

X X

X X X X

X

Lin

X X X X X

X X X

Abbreviations: Undirec = undirected, Direc = directed, Bivar = bivariate, Multivar = multivariate, Ampl = amplitude, Lin = linear, Nonlin = nonlinear, Freq = frequency.


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One thing we must keep in mind at all times is the limited spatial sampling of EEG recordings. Especially during invasive monitoring, only a limited number of brain regions can be sampled. If a relation between signal x and y is found, this is either because x and y are directly related or the relation between x and y is mediated by a third missing variable z. Another important issue when analyzing EEG recordings is the problem of volume conduction. It has been shown that volume conduction limits the neurophysiological interpretability of sensor-space connectivity analyses (Haufe et al., 2013). Techniques, such as the phase slope index (Nolte et al., 2008), have been developed that allow to distinguish the zero-lag correlations from the time-delayed brain interactions. 4. Seizure prediction using functional brain connectivity The possibility to predict epileptic seizures is an issue that interests both researchers and clinicians. The ability to predict an upcoming seizure would open the opportunity for the development of closed loop treatment with drugs or stimulation (electrical deep brain or vagus nerve stimulation), which could possibly prevent the outburst of a seizure, improving treatment efficacy and decrease treatment related side effects (Litt and Lehnertz, 2002). In this section we will describe how functional connectivity measures can be used for seizure prediction. It has been noted that insufficient statistical validation and limited assessment of the specificity of the seizure prediction algorithm have so far been serious limitations. These issues are discussed in detail in Mormann et al. (2007) and Schulze-Bonhage et al. (2011). 4.1. Intracranial EEG Back in the 1970s, Viglione and Walsh (1975) posed the idea that the transition between the interictal and ictal period is not abrupt, but is rather mediated by changes in the pre-ictal stage indicative of seizure onset. Further evidence of the gradual transition between the interictal and ictal state was achieved in the 1980s (Rogowski et al., 1981; Siegel et al., 1982; Lange et al., 1983; Gotman and Marciani, 1985). Lange et al. (1983) investigated the relation between different IEEG channels. By constructing spatial maps indicating at which channels interictal spikes simultaneously occurred in 10 s bins, they found that the degree of bilateral independence decreased several minutes prior to the seizures onset, possibly reflecting the mechanism underlying the transition from the interictal to the ictal state. Iasemidis et al. (1990) observed phase locking between focal sites and a progressive phase entrainment of the nonfocal sites by the focal ones several minutes before seizure onset. In the same study the authors reported a higher value of the Lyapunov exponent, a measure of the level of chaos in a time series, for the focal electrodes. This idea of investigating the brain of an epileptic patient by treating it as a complex system, where timely identification of transitions of the system from a lower to higher complexity aid the prediction of an upcoming seizure, was later adopted by other studies. In Lehnertz and Elger (1998) significant changes in nonlinear dynamics, investigated using the derivative of the correlation, were noticed in IEEG channels covering the epileptogenic focus up to several minutes prior to the clinical seizure onset and not in other recording sites. Mormann et al. (2003b) reported that a drop in synchronization, investigated by using the mean phase coherence, anticipated the seizure onset. This evidence could be used as a criterion to identify a ‘‘pro-ictal’’ state. In Mormann et al. (2003a) these findings were confirmed using the mean phase coherence as a measure for phase synchronization together with the maximum linear cross-correlation as a measure for lag

synchronization. Le Van Quyen et al. (2005) investigated the phase locking value for all pairs of EEG channels in the epileptogenic temporal lobe (14–20 channels) using a sliding window over 305 h of IEEG data. They showed that in 70% of the seizures a specific state of brain synchronization is observed several hours before the actual seizure. These changes involved both increases and decreases of the synchronization levels and were often localized near the primary epileptogenic zone. They conclude that phase synchronization offers a way to distinguish between a preictal state and normal interictal activity. Winterhalder et al. (2006) confirmed the finding that both decreases and increases in synchronization may precede seizures depending on the investigated structures. A waveletbased and frequency specific nonlinear similarity index has been applied by Ouyang et al. (2007) on IEEG to predict epileptic seizures. They showed that hidden dynamical changes of brain electrical activity in the beta frequency band are useful to predict seizures. The idea that pathological activity is strongly associated with abnormal synchronization of neurons is widely adopted. Here phase synchronization methods still remain among the most successfully applied (Osorio and Lai, 2011). A multivariate seizure prediction and detection analysis comparing the performance achieved with scalp and intracranial EEG was conducted by Schad et al. (2008). Sensitivities of 73% and 62% for seizure detection and 59% and 50% for seizure prediction were achieved for EEG and IEEG, respectively. The method initially designed for scalp EEG was successfully applied to IEEG and the reached sensitivities allow this method to be applicable in practice during EEG monitoring. Furthermore they found that the best performance was achieved in some patients using scalp EEG and in others using IEEG. Kerr et al. (2011) revealed how to exploit the network structure by using multivariate analysis to improve early seizure detection. The authors investigated multi-site SEEG recordings in epileptic patients by constructing coherence connectivity matrices during different time windows. In order to track the dominant structure over time these matrices were examined using singular value decomposition. Here all recorded channels were considered compared to earlier studies only using a small selection of channels. They found that the first singular vector is indicative for the seizure state. This idea was exploited and optimized in Santaniello et al. (2011), in which the time course of the maximum singular value of the connectivity matrix obtained by spectral coherence underwent a fast detection procedure which minimized the false positives. 4.2. Scalp EEG Mirowski et al. (2009) analyzed bivariate features of EEG synchronization (cross-correlation, nonlinear interdependence, dynamical entrainment or wavelet synchrony) coupled to machine learning technique on the 21-patient Freiburg dataset. The study revealed that the best machine learning technique applied to spatio-temporal patterns of EEG synchronization outperformed previous seizure prediction methods on the Freiburg dataset. This indicates that the inclusion of spatiotemporal dynamics of EEG synchronization can improve seizure prediction. In a more recent study, Williamson et al. (2012) combined multivariate EEG features with patient-specific machine learning and tested the algorithm on 19 of 21 patients in the Freiburg EEG data set who had three or more seizures. The were able to predict 71 out of 83 seizures, with 15 false predictions and 13.8 h in seizure warning during 448.3 h of interictal EEG data. The added value of using multivariate analysis compared to analyzing the channels independently was also shown in Hunyadi et al. (2012).


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5. Epileptogenic focus localization using functional brain connectivity A common approach for focus localization is to consider the recorded sites of the brain as nodes in a graph and to detect the region/node that acts as a synchronizing source that transfers information to and influences other brain regions/nodes. Being able to distinguish which of the nodes starts to behave abnormally, mainly around the seizure onset, can give valuable information to localize the focus. In this context, frequency domain methods are commonly preferred because the information content that is transferred from one node to another is mainly restricted to specific frequency bands. Measures of directed connectivity can be more informative in detecting such behavior in comparison to their undirected counterpart. Below we will give an overview of the epileptogenic focus localization studies based on intracranial and scalp EEG. Afterwards, we will discuss the present status and possible future directions. 5.1. Intracranial EEG 5.1.1. Seizure networks 5.1.1.1. Bivariate studies. The first attempt to localize the epileptogenic focus from IEEG recordings was performed in 1970 by Gersch and Goddard (1970). IEEG recordings in the cat brain during seizures produced by kindling of the piriform cortex were analyzed using the coherence and partial coherence. They concluded that the dynamics of the kindling site could explain a great part of the coherence between various pairs of channels. Mary Brazier was the pioneer in analyzing human ictal IEEG recordings using functional connectivity measures. She used a method based on coherence and phase analysis to infer the causal relations between two channels. The coherence was used to estimate the strength of the connection while the phase was used to assess information about the directionality. Brazier (1972) reported: ‘The path followed by spontaneous seizure activity in spreading to other structures is a feature peculiar to each individual (n = 4) and can be established for that patient by this method, possibly offering a more restricted therapeutic surgery than a lobectomy. Coherency and phase analysis was also applied by Gotman (1983), who found that the area of the focus had a consistent time lead (range 5–30 ms) over the other recording sites in patients and showed the applicability of the method to localize the focus in a cat model of epilepsy with known focus (penicillin focus and kindling). He concluded that the coherence and phase method is capable of identifying the epileptic focus even when only widespread seizure activity is recorded. The mutual information (MI) was applied to the EEG of 2 patients with focal onset and 1 with generalized seizures (Mars et al., 1985). It was shown that high MI values characterized the site of the epileptogenic focus in patients with focal onset while high MI values were found for all electrodes for the patient with generalized epilepsy. Later, Gotman (1987) showed that the interhemispheric coherence was generally low throughout seizures, with highest values being reached early in the seizure at the time of spread, or at the very end. The time delays most often indicated a lead from the side of onset except in 2 patients with bilateral independent onsets, where interhemispheric time leads were always from the same side, independently of the side of onset. Lieb et al. (1987) analyzed the intra- and interhemispheric connectivity during ictal discharges recorded with depth electrodes in 10 patients by using the coherence and phase analysis method. They reported: ‘Although strong intrahemispheric coherences and linear phase spectra reliably emerged in both the epileptogenic and nonepileptogenic hemispheres during seizure onset and contralateral

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spread, these relationships were usually not observed for interhemispheric comparisons. Fabrice Bartolomei and Fabrice Wendling performed many interesting studies investigating the network during temporal lobe epilepsy (TLE) seizures using SEEG. Using the coherence they were able to classify TLE seizures into 4 distinct categories, i.e. medial (M), medial–lateral (ML), lateral–medial (LM), and lateral (L) (Bartolomei et al., 1999). They used the nonlinear correlation coefficient coupled to the direction index1 to investigate the degree and direction of coupling between medial and neocortical areas during TLE seizures in patients with the M, ML, and LM subtypes (Bartolomei et al., 2001). The same connectivity measure was used to study epileptogenic networks that might be responsible for the triggering of seizures (Wendling and Bartolomei, 2001). The nonlinear correlation method was also used to analyze different periods (before, during and after rapid discharges that occur during seizure onset) with or without the occurrence of prior spiking (Bartolomei et al., 2004). They showed that if there was prior spiking, the hippocampus was always the leader during the seizure, while if there was no prior spiking, the entorhinal cortex was most often the leading structure. During the rapid discharges period there was a significant decrease of correlation values. This corresponded with earlier findings based on correlation analysis (Wendling et al., 2003). Furthermore, they found a correlation between the strength of coupling from the entorhinal cortex to the hippocampus and the degree of atrophy in the entorhinal cortex (Bartolomei et al., 2005). A more in depth overview of these studies can be found in Wendling et al. (2010). Ponten et al. (2007) applied the synchronization likelihood on ictal IEEG recordings in 7 patients and showed that the neuronal network moves in the direction of a more ordered configuration (higher clustering coefficient combined with a slightly, but significantly, higher path length) compared to the more randomly organized interictal network. Kramer et al. (2008) found a diffuse breakdown in global coupling at seizure onset. They concluded that they can identify spatially localized brain regions that may facilitate seizures and may be potential targets for focal therapies. Recently Bialonski and Lehnertz (2013) investigated the assortative mixing2 in functional brain networks during epileptic seizures using the correlation and cross-correlation. Their results revealed that while seizures evolve, the assortativity increases. This indicates that there is a segregation of the underlying functional network into groups of brain regions that are only sparsely interconnected. Furthermore they showed that prior to the seizure end the assortativity decreases. 5.1.1.2. Multivariate studies. In 1994, Franaszczuk et al. (1994) used a multivariate Granger causality measure, the directed transfer function (DTF), to localize the epileptogenic focus from human IEEG recordings. Visual analysis of the propagation pattern during the onset of mesial TLE seizures in 3 patients identified the deep mesial structures as source of the seizure activity. Later, Franaszczuk and Bergey (1998) used the integrated DTF (iDTF), the sum of the DTF in a frequency band of interest, in 5 patients to reveal patterns during mesial onset and lateral onset temporal lobe seizures. They showed the potential to determine patterns of flow of activity using DTF analysis, even during periods when visual analysis of the ictal IEEG does not allow for definitive focus localization. The added value of iDTF based SOZ localization in neocortical epilepsy has also been shown (Wilke et al., 2010). In 11

1 This is the nonlinear extension of the linear correlation coefficient. The mathematical details how to calculate the nonlinear correlation and the direction index can be found in the appendix. 2 Assortative mixing is a bias in favor of connections between network nodes with similar characteristics.


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patients, iDTF based localization of the EZ highly correlated with the clinically identified foci. Kim et al. (2010) combined ECoG-based ictal source localization with DTF analysis in 6 patients. The EZ, estimated based on the connectivity pattern between the source waveforms of the estimated dipoles, coincided with surgical resection areas and with traditional electrode-based source estimates. The authors believe that the proposed method is useful, especially when ictal sources are located in a deep sulcus or beyond recording planes. Jung et al. (2011) revealed in 3 pediatric patients with Lennox-Gastaut syndrome (LGS), having generalized seizures characterized by bilateral synchronous epileptiform discharges, that regions with high average outgoing information based on iDTF analysis corresponded with the surgical resection. In a very recent study, Kim et al. (2014) combined DTF analysis with time delay estimation to enhance localization accuracy in patients with LGS. They showed that the localized EZ coincided more strongly with the surgical resection in patients with successful surgical outcome, compared to those with unsuccessful outcome. They suggest that the proposed method has the potential to predict patient outcome before resective surgery. Because of the need to track the evolution of connectivity over time, time-variant versions of the DTF have been developed, namely the short time DTF (SDTF) (Ding et al., 2000), the DTF calculated in a short time sliding window, and the adaptive DTF (ADTF) (Astolfi et al., 2008; Wilke et al., 2008), calculated based on Kalman filtering. SDTF analysis between ICA components of ictal IEEG epochs revealed a seizure stage dependent shift in connectivity between components including the epileptogenic focus (Mullen et al., 2011). SOZ localization was also proven successful based on ictal IEEG recordings using modified versions of the ADTF, namely the full-frequency ADTF (Van Mierlo et al., 2011) and the spectrum weighted ADTF (Van Mierlo et al., 2013). In the former study, we showed that SOZ localization based on ADTF analysis is feasible and that the connectivity pattern is similar during the onset of clinical and subclinical seizures. In the latter study, we performed SOZ localization from 20 s long ictal IEEG epochs in eight patients. We showed that the SOZ localization corresponded both with the visual analysis of the epileptologist as well as with the resected region that rendered the patients seizure free and the obtained connectivity patterns were consistent over multiple seizures in each patient. 5.1.2. Interictal networks Wilke et al. (2008) showed by analysing interictal spikes in one patient that the time-variant integrated ADTF (iADTF) was able to capture connectivity patterns which the conventional iDTF missed. In a follow-up study, Wilke et al. (2009) correctly identified the irritative zone using iADTF analysis of interictal spikes in 8 patients with neocortical epilepsy. In Wilke et al. (2011), a cohort of 25 patients was analyzed using DTF (ictal and resting interictal epochs) and ADTF (interictal spikes). They found that the betweenness centrality3 of the DTF and ADTF derived networks correlated with the location of the resection in patients who were seizure-free following surgical intervention. More importantly they found that these network interactions were also observed during random nonictal periods as well as during interictal spike activity. The sole analysis of seizure free segments revealed an excess of synchronization on the side of the EZ in 82% of the patients (n = 17) using phase locking value analysis (Mormann et al., 3 Betweenness centrality is a graph theoretical measure that depicts the node’s centrality in a network. It is equal to the number of shortest paths from all nodes to all others that pass through that node.

2000). This indicates that the epileptogenic region distinguishes itself by an increased level of synchronization and that the ability to localize the EZ from seizure free segments could be of high diagnostical value. Sabesan et al. (2009) showed that the transfer entropy was also able to identify the epileptogenic focus when applied to the available whole-duration multichannel intracranial EEG, without any subjective prior selection of EEG segments or electrodes for analysis, in 4 patients with TLE. An asymmetry in the connectivity structure, able to reveal the existence of an epileptic focus even in the absence of ongoing seizure activity was revealed using Granger Causality analysis applied to both scalp and intracranial EEG recordings (Wu et al., 2011). Recently, Adhikari et al. (2013) showed that high-frequency (>80 Hz) Granger causality occurs before the onset of any visible ictal activity in the IEEG and that the observed relationships involve the recording electrodes where clinically identifiable seizures develop later on. This suggests that high-frequency oscillatory network activities precede and underlie epileptic seizures. Van Dellen et al. (2009) investigated interictal ECoG recordings of 27 TLE patients using the PLI. They showed that temporal lobe functional connectivity is lower in patients with longer TLE history, and longer TLE duration is correlated with more random network configuration. These findings suggest that the neural networks of TLE patients become more pathological over time, possibly due to temporal lobe changes associated with longstanding lesional epilepsy. Van Diessen et al. (2013) found using PLI analysis that the EZ was associated with a decreased hub-value in the theta frequency band suggesting a pathological functional ‘isolation’ of the EZ in the interictal state. 5.2. Scalp EEG 5.2.1. Sensor space In 1975, Brazier et al. (1975) related the coherence and phase analysis of scalp EEG with respect to the surgical outcome. They illustrated that the neuronal tissue pinpointed by the functional connectivity analysis as EZ was abnormal and they were able to correlate the clinical and behavioral improvement with respect to the normalization of the EEG. Mars et al. (1977) showed, by investigating the coherence and phase spectra between EEG signals during seizures, that in some cases consistent delay times were found, but in many others this was not achieved. Gotman (1981) compared the coherence and phase difference between the homologous EEG channels of the two hemispheres in two groups of patients (generalized corticoreticular and focal epilepsy) during bilateral synchronous spike-and-wave activity. In the group of focal epilepsy patients, there was an interhemispheric time difference (mean of 15 ms from the affected to the healthy hemisphere) that was not found in the generalized epilepsy group. The transfer entropy, that allows to investigate the direction of the nonlinear connections, was able to reliably identify the hemisphere containing the epileptic focus without observing actual seizure activity using multichannel EEG recordings in 15 epilepsy patients (Staniek and Lehnertz, 2008). In 2004, partial directed coherence (PDC) (Baccala´ and Sameshima, 2001) analysis of scalp EEG traces coupled to graph analysis (strongly connected subgraphs) provided correct focal localization (Baccala´ et al., 2004). Furthermore PDC analysis coupled to betweenness centrality has also been successfully used to localize the epileptogenic focus in epilepsy secondary to type II focal cortical dysplasia (Varotto et al., 2012). Swiderski et al. (2009) investigated localization based on scalp EEG using the iDTF. In a retrospective dataset containing 4 TLE patients, they were able to localize the electrode in close vicinity of the resected brain region rendering the patient seizure free. In a prospective dataset containing 8 TLE patients they were able to correctly lateralize


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the seizures. They stated that the developed method can be used for rough localization or for lateralization. 5.2.2. Source space In a few studies (Ding et al., 2007; Lu et al., 2012; Song et al., 2013), EEG source imaging has been combined with functional connectivity analysis to localize the EZ. Ding et al. (2007) were able to image the ictal sources by combining first principle vector (FINE) spatio-temporal EEG source localization with iDTF connectivity analysis. In a follow-up study, Lu et al. (2012) applied the method to 76-channel EEG in 10 patients with partial epilepsy and evaluated the effect of the number of used electrodes. They found that combining FINE with DTF analysis led to the correct SOZ localization and that a higher number of electrodes is beneficial. Song et al. (2013) investigated the epileptiform discharges (spikes) with dense array EEG (256 electrodes) in 5 patients to search for the possible engagement of pathological networks. The coherence among cortical source waveforms revealed characteristic connectivity patterns in each patient during the pre-spike, spike, and postspike intervals. 6. Discussion and future directions On balance, evidence has accumulated that the measures quantifying relations between recording sites to characterize interaction between different brain regions, show a promising performance that exceeds the chance level as evidenced by statistical validation (Mormann et al., 2007). This opens opportunities for closed loop neurostimulation treatments. In such a closed loop vagus nerve or deep brain stimulation setup, a pulse could be given when the pre-ictal stage is detected. This could possibly prevent the seizure from arising. Despite the fact that many studies showed promising results to localize the epileptogenic focus based on ictal intracranial EEG recordings since 1972 (Brazier, 1972), functional connectivity is currently not used in standard clinical practice to localize the EZ. This is because the methods to calculate functional connectivity measures are not always available in the software packages used by the epileptologist to record the intracranial EEG. Although a few open source toolboxes exist, such as the Brainstorm (Tadel et al., 2011) and the eConnectome (He et al., 2011) toolbox, not all epileptologists have the necessary technical background to use these toolboxes to compute functional connectivity patterns from the IEEG recordings. Most of the discussed studies focused on a small and specific patient group. The proposed connectivity measure always performed well in that particular case. However, there are difficulties to compare the performance of the different measures, since they all are applied in different conditions. There is a growing need for standardized testing conditions. Recently, the European project EPILEPSIAE has been set up with the aim to provide a wide database to test seizure prediction algorithms (Klatt et al., 2012). The EPILEPSIAE database provides long-term EEG recordings of 275 patients as well as extensive metadata and standardized annotation of the data sets. Such a database makes it possible to compare different techniques based on the same data and allows epileptologists and researchers to access the data that has been worked on. Such a standard large EEG database could help to compare the performance of different functional connectivity measures to localize the epileptogenic focus. Despite the large number of studies localizing the epileptogenic focus based on network analysis, there is currently no study investigating how the connectivity pattern can be used to plan the extent of the resection. There is clearly potential in incorporating the information gained by connectivity analysis for identification of the EZ, but there is a need for studies that

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define a resection strategy based on the connectivity analysis. Connectivity analysis has the potential to pinpoint a smaller resection, allowing to retain more functionality. However, we need to keep in mind that we will always be limited by the spatial sampling of the used intracranial electrodes. If the SOZ is not covered, connectivity analysis could lead to incomplete image of how the seizure spreads. In several studies (Wilke et al., 2011; Mormann et al., 2000; Sabesan et al., 2009; Wu et al., 2011; Van Diessen et al., 2013), it has been shown that the epileptogenic focus can be localized based on interictal IEEG recordings. This should be confirmed in a larger population to gain insight whether this is true for all types of epilepsies. This could be of utmost importance in patients that did not have a seizure during the invasive monitoring. Recently, EEG source localization has been combined with functional connectivity analysis (Ding et al., 2007; Lu et al., 2012; Song et al., 2013). These methods showed promising results and can easily be applied to EEG recorded during the video/scalp EEG monitoring. In the scalp EEG monitoring there is a trend towards the use of high density (HD) EEG caps (Michel and Murray, 2012), because of the better spatial resolution. It has already been shown that HD EEG source imaging of IEDs using a patient specific head model had a sensitivity of 84% and a specificity of 88% that dropped to 57% and 59% when a lower number of electrodes and a template head model was used (Brodbeck et al., 2011). The use of HD EEG source imaging in combination with functional connectivity will help epileptologists gain more insight in the epileptic network based on non-invasive recordings. Epileptic network analysis is not only important to localize the EZ for possible surgical resection or disconnective surgery, but also opens opportunities for neurostimulation treatments. Functional connectivity analysis can be used to optimize deep brain stimulation protocols. The location where to stimulate as well as the time when to stimulate could be derived from the estimated connectivity patterns. Furthermore, treatment options could be planned in order to interfere with the seizure network, rather than interfering with the seizure source. Here neurostimulation could be considered to alter the seizure networks and eventually induce changes in connections in the brain capable of inhibiting the seizure. Another promising application of functional connectivity analysis is to investigate the mechanism of action of neuromodulation treatments. For example functional brain network changes due to deep brain stimulation, vagus nerve stimulation or transcranial magnetic stimulation can be investigated using the described measures. This could help in discovering the mechanisms of action of the different stimulation techniques and could possibly help fine-tuning the individual treatment of patients. Currently, there is a growing need for pre-clinical as well as clinical studies showing how connectivity analysis can be used in the treatment with the amelioration of the quality-of-life of refractory epilepsy patients as main goal. Despite many years of research there is little evidence that functional connectivity analyses have affected patient treatment. This is partly because functional connectivity measures are largely descriptive (as opposed to mechanistic characterizations). The interpretation of the statistical dependencies between brain regions is not straightforward, let alone adjusting treatment based on these results. Here, the emergence of effective connectivity measures for EEG, such as dynamic causal modeling (DCM) (Kiebel et al., 2009), may play an important role. The effective connectivity measures can allow epileptologists to elucidate findings about the underlying neural mass models during ictal and interictal periods. These can help to gain insight in the underlying mechanisms of ictogenesis and can allow a more straightforward rationale for adjusting treatment. However, there are also several limitations


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that apply to effective connectivity analysis, such as the lack of appropriate sampling of the brain activity using (I)EEG could lead to biased results. For more information about the limitations and benefits of effective connectivity analysis, more specific in the case of DCM, we refer the reader to (Roebroeck et al., 2011; Valdes-Sosa et al., 2011; Friston, 2011; David, 2011; Lopes da Silva, 2013). A first study that applied DCM to IEEG recordings in epilepsy was performed by David et al. (2008). They studied the parameters trajectory during 1 Hz electrical stimulation in 20 patients and were able to reveal which structures expressed a strong modulatory input to the epileptic focus. In a more recent paper, effective connectivity was used by Hocepied et al. (2013) to predict seizures based on a neural mass model. Using a physiologically based model, key parameters to underlying neurological mechanisms can be estimated. This means that by tracking the model’s parameters, shifts over time might reveal crucial links in understanding the physiological processes. The model parameters are initially estimated by iteratively fitting a simulated EEG signal, based on the model of Jansen and Rit (1995), to the recorded EEG signals. The occurrence of a seizure was estimated by evaluating the shift over time of excitation and inhibition model parameters and more specifically the ratio of them called the ExcitatoryInhibitory Index. Their method was tested on IEEG data from 16 patients with various types of epilepsy but performed considerably better for those with temporal lobe epilepsy (TLE). This is not surprising as the simulated Jansen model used in this study has been reported to be capable of simulating seizures similar to the ones recorded from TLE patients. These studies indicates the potential value of effective connectivity measures applied to EEG in epilepsy. Acknowledgements Research is funded by a PhD grant of the Institute for the Promotion of Innovation through Science and Technology in Flanders (IWT-Vlaanderen, 178TW1610T), the Fund for Scientific Research Flanders (FWO, Belgium, 3G42710) and the Research Fund of the Ghent University (BOF08/GOA/018).

follows:

rxy ¼

¼

E½ðx mx Þðy my Þ

sx sy

N ðxðnÞ mx ÞðyðnÞ my Þ 1X N n¼1 sx sy

(1)

(2)

where N is the number of samples, E[x] is the expected value of x, mx and my are the mean values and sx and sy are the standard deviations of signal x and y, respectively. The resulting value lies between 1 and +1. A value of 1 indicates that there is a positive correlation between the signals, while a value of 1 indicates negative correlation. A value equal to 0 means that there is no correlation. A.1.2. Cross-correlation The cross-correlation estimates the correlation between two signals in function of a time lag t:

rxy ðt Þ ¼

¼

E½ðxn mx Þðynþt my Þ

sx sy

N t ðxðnÞ mx Þðyðn þ t Þ my Þ 1 X N t n¼1 sx sy

(3)

(4)

Here the time lag allows to assess the directionality of the correlation.

A.1.3. Nonlinear correlation coefficient and direction index The nonlinear correlation coefficient h2xy is an extension of the correlation that models nonlinear interactions between EEG signals. It is defined as the maximum of following equation with respect to txy: 2 P PN 2 yðk þ t xy Þ N k¼1 yðk þ t xy Þ f ðxðkÞÞ h2xy ðt xy Þ ¼ k¼1 (5) PN 2 k¼1 yðk þ t xy Þ

Appendix A. Mathematical details to calculate functional brain connectivity

where f is a nonlinear fitting curve that approximates the statistical relationship between signal x and y. In practice, this function can be obtained from the piece-wise linear approximation between the samples of the two time series.

In this section we review the mathematical details of the different functional brain connectivity measures. We provide an overview of the most commonly used measures of following 4 categories: (1) Correlation and coherence, (2) Phase synchronization measures, (3) Information-based measures and (4) Granger causality measures.

The direction index (Wendling and Bartolomei, 2001) is calculated out of the nonlinear correlation coefficients h2xy and h2yx and the corresponding time delay txy and tyx: 1 2 D ¼ ðsgnðDh Þ þ sgnðDt ÞÞ (6) 2

A.1. Correlation and coherence The dependency between signals can be estimated in the timedomain by the correlation coefficient, cross-correlation or the nonlinear correlation coefficient coupled to the direction index. In the frequency domain the information flow can be assessed by the spectral density function, coherency (coherence) and partial coherence.

A.1.1. Correlation coefficient The Pearson correlation coefficient (rxy) is a simple connectivity measure to assess the interdependency between two time series (x and y). It examines the linear relation between two signals as

2

with Dh ¼ h2xy h2yx and Dt = tyx txy. D = +1 (respectively 1) denotes that y (respectively x) is dependent on and delayed with respect to x (respectively y). Conversely, D = 0 denotes either (i) a situation where there is a constant discrepancy between the information provided by the asymmetry (Dh2) and by the time delay (Dt) or (ii) a situation where the sign of Dh2 and the sign of Dt continuously fluctuates over the considered time window (Wendling et al., 2010).

A.1.4. Spectral density function The Fourier transform of the cross-correlation leads to the cross spectral density function Sxy(f). Sxy ð f Þ ¼

þ1 X

E½xn ynþt e j2p f t

(7)

t¼1


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In practice, the considered data has a finite size, meaning that only an estimation of the true spectrum can be obtained. Several methods such as the covariance method, the Burg method, the Welch’s method, the Yule Walker Autoregressive method and many more can be applied to obtain an estimate of the power spectral densities (Marple, 1987; Stoica and Moses, 1997). The spectral density function for K signals xi(n), with i = 1, . . ., K, can be derived from all the cross spectral density functions of the pairwise combinations of channels. The spectral density function S(f) is defined as: 2 3 S11 ð f Þ S12 ð f Þ S1K ð f Þ 6 S21 ð f Þ S22 ð f Þ S2K ð f Þ 7 6 7 (8) Sð f Þ ¼ 6 7 .. .. .. 4 5 . } . . SK1 ð f Þ SK2 ð f Þ SKK ð f Þ

A.1.5. Coherency and coherence The cross spectral density function is used to estimate the coherency, that shows the interconnections between two signals in the frequency domain: Sxy ð f Þ C xy ð f Þ ¼ pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Sxx ð f ÞSyy ð f Þ

(9)

The cross spectral density of signal x and y is normalized by the individual autospectral density functions. The coherence is defined as the magnitude of the coherency: COHxy ð f Þ ¼ C xy ð f Þ (10) Because of the normalization, the value of the coherence lies between 0 and 1. If the value is close to 1 at a frequency f, then the two processes are maximally interdependent at that frequency. On the other hand, a value near 0 indicates independence of the two processes at frequency f. The coherency and coherence are bivariate measures: they investigates only two signals simultaneously. The magnitude-squared coherence is also commonly referred to as the coherence.

A.1.5.1. Phase of the coherence The coherency can be written as: C xy ð f Þ ¼ C xy ð f Þe jfð f Þ ¼ COHxy ð f Þe jfð f Þ

where f(f) is the phase of the coherency at a specific frequency. The phase can be studied to assess the directionality of the information transfer. A particular frequency can be chosen and the phase difference can be converted into a time delay (Brazier, 1972). Another option is to choose a range of frequencies and to transform the slope of the phase spectrum over that range into a time delay (Gotman, 1983).

A.1.5.2. Imaginary component of the coherency Instead of looking at the magnitude and phase of the coherency, one can also investigate the real and imaginary part of the coherency: C xy ¼ RC xy þ IC xy

A.1.5.3. Phase slope index In general, a positive imaginary part of the coherency Cxy indicates that y drives x. However, if the period length of the oscillations has the same order of the found delay, earlier and later are ambiguous due to the periodicity of the processes. This can be resolved by aggregating the information contained in nonzero phase lags within a frequency band-of-interest [f1, f2], which is the idea of the phase-slope index (Nolte et al., 2008): 0 1 f2 X @ cxy ¼ I Cxy ð f ÞC xy ð f ÞA (13) f¼ f1

where I(x) depicts the imaginary part of x and * depicts the complex conjugate. The phase slope index is antisymmetric and invariant with respect to rescaling of the data. A.1.6. Partial coherence The partial coherence was developed to differentiate direct and indirect (cascade) interrelations: it calculates the coherence remaining between two time series after the influence of all the other time series is removed from each of the first two (Jenkins and Watts, 1969). It can be constructed out of the spectral density function as follows: M ij ð f Þ PC ij ð f Þ ¼ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Mii ð f ÞM jj ð f Þ

(12)

Nolte et al. (2004) argue that the Cartesian representation of the coherency is far superior than the magnitude and phase representation to study brain interactions from scalp EEG data. This is because the imaginary part of the coherency is not affected by the volume conduction effects.

(14)

where Mij(f) is the minor of the spectral density function S(f) given by Eq. (8). This is the determinant of S(f) with ith row and jth column removed. A.2. Phase synchronization Commonly used methods to obtain the strength of phase synchronization between different areas of the brain are the phase locking value (PLV) (Lachaux et al., 1999) and the phase lag index (PLI) (Stam et al., 2007). If we consider two signals x1 and x2 that are band-pass filtered to a frequency band of interest, we can calculate for both signals xi following analytical signals zi using the Hilbert Transform with i = 1, 2: zi ðtÞ ¼ xi ðtÞ þ jHðxi ðtÞÞ ¼ Ai ðtÞe jfðtÞ

(11)

11

where H is the Hilbert transform operator defined as: Z 1 1 xi ðtÞ dt Hðxi ðtÞÞ ¼ PV p 1 t t

(15)

(16)

with PV denoting the Cauchy principal value. From the analytical signals zi the phase difference or relative phase can be computed as: z ðtÞz ðtÞ DfðtÞ ¼ arg 1 2 (17) jz1 ðtÞjjz2 ðtÞj Based on the phase difference, the PLV and PLI can be calculated.

A.2.1. Phase locking value The PLV is defined based on the relative phase difference as: (18) PLV ¼ E½e jDfðtÞ The PLV has values in the interval [0, 1]. A value close to 1 means perfect phase locking, while a value that tends to 0 results from a random phase distribution over time. Note that the PLV is


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insensitive to the amplitudes of the signals and only depends upon the phase relation between the considered signals.

If the generalized Markov property holds, the past of signal Y will not influence the prediction of the current sample of X: pX ðxn jxn1 ; . . . ; xnk Þ ¼ pX ðxn jxn1 ; . . . ; xnk ; yn1 ; . . . ; ynl Þ

A.2.2. Phase lag index The PLI captures the asymmetry of the distribution of phase differences between two signals (Stam et al., 2007) and is calculated based on the relative phase difference between the two signals.

(23)

The TE (Schreiber, 2000) from signal X to Y investigates the violation of the generalized Markov property: X

T XY ðk; lÞ ¼

pXY ðxn ; . . . ; xnk ; yn1 ; . . . ; ynl Þ

x;y

PLI ¼ E½signðDfðtÞÞ

(19)

The resulting value lies in the interval [0, 1], where a higher value indicates more phase synchrony.

log

pX ðxn jxn1 ; . . . ; xnk ; yn1 ; . . . ; ynl Þ pX ðxn jxn1 ; . . . ; xnk Þ

(24)

It is an asymmetric measure, TXY(k, l) differs from TYX(k, l). If the l previous samples of signal Y do not influence the estimation of the current sample of X, pXY(xnjxn1, . . ., xnk, yn1, . . ., ynl) = pX(xnjxn1, . . ., xnk) and the transfer entropy from Y to X will be zero.

A.3. Information-based measures The information-based measures are model free nonlinear techniques to estimate the information between signals. Nonlinear methods are not designed to outperform linear methods but rather to provide complementary information. Nonlinear neural time series analysis was motivated by the fact that many crucial neural processes have nonlinear characteristics (Sakkalis, 2011). Below we introduce the most commonly used information-based measures: mutual information (MI) and transfer entropy (TE).

A.3.1. Mutual information The MI measures the mutual dependence of two random variables:

MIXY ¼

X

pXY ðx; yÞ log

x;y

pXY ðx; yÞ pX ðxÞ pY ðyÞ

(20)

with pX(x) and pY(y) the probabilities corresponding to signal X and Y respectively and pXY(x, y) the joint probabilities of X and Y. The probabilities pX(x) and pY(y) can be obtained from the individual histograms of the signals and the joint probability pXY(x, y) from the combined histogram of X and Y. A drawback of the MI is that many samples and small histograms bins are required to obtain a correct estimate (Quian Quiroga et al., 2002). If there is no relation between the two variables X and Y, pXY(x, y) = pX(x)pY(y), which is the case for independent processes, then the MI becomes zero. For two identical signals X = Y, the MI will be equal to the Shannon entropy of the signal MIXY = IX = IY which is equal to: IX ¼

X

pX ðxÞ log

x

1 pX ðxÞ

A.4. Granger causality In this section we will describe functional brain connectivity measures that are based on autoregressive models, namely the Granger causality measures (Goure´vitch et al., 2006; Barrett et al., 2010; Bressler and Seth, 2011). The concept of Granger causality was developed when Clive Granger adapted the definition of causality proposed by Norbert Wiener (Wiener, 1956) into a practical form (Granger, 1969) and applied it to the field of econometrics to study the relationships between economic indices. One time series is said to Granger cause a second one if inclusion of the past values of the first into the modeling of the second significantly reduces the variance of the modeling error. According to Granger causality, if the past values of x1 contain information that helps to predict x2 above and beyond the information contained in past values of x2 alone then signal x1 ‘‘Granger-causes’’ (or ‘‘G-causes’’) signal x2. The Granger causality from signal x1 to x2 and the one from signal x2 to x1 can be investigated separately. This allows investigation of directed functional connectivity or statistical dependence between multiple signals. In this section we will introduce how to assess Granger causality by means of autoregressive modeling.

A.4.1. Autoregressive modeling A.4.1.1. Definition Granger causality is based on autoregressive (AR) models, in which the signals are represented as a linear combination of their own past plus additional uncorrelated white noise. The Granger causality between signals x1 and x2 can be assessed by comparing the univariate AR model fitting with the bivariate model fitting. For signal x the univariate AR model is described as follows:

(21) xðnÞ ¼

p X

aðmÞxðn mÞ þ eðnÞ

(25)

m¼1

A.3.2. Transfer entropy The Shannon entropy was extended by taking the probability of obtaining a value at time n if the previous k values are incorporated. This defines the entropy rate of a signal X as: HX ðkÞ ¼

X

pX ðxn ; xn1 ; . . . ; xnk Þ logð pX ðxn jxn1 ; . . . ; xnk ÞÞ

(22)

where p is the model order, a(m) are the model coefficients and e(n) is the residual. For two signals (x1 and x2) we can construct the following bivariate autoregressive model: x1 ðnÞ ¼

x

where pX(xnjxn1, . . ., xnk) is the probability of obtaining value xn of signal X given that the k previous values were equal to xn1, . . ., xnk.

p X

a11 ðmÞx1 ðn mÞ þ

m¼1

x2 ðnÞ ¼

p X m¼1

p X

a12 ðmÞx2 ðn mÞ þ e1 ðnÞ

(26)

m¼1

a21 ðmÞx1 ðn mÞ þ

p X

a22 ðmÞx2 ðn mÞ þ e2 ðnÞ

(27)

m¼1


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with a11, a12, a21 and a22 the model coefficients and e1 and e2 are the residuals of signals x1 and x2, respectively. This can be rewritten in matrix formulation:

x1 ðnÞ x2 ðnÞ

p X a11 ðmÞ ¼ a21 ðmÞ m¼1

a12 ðmÞ a22 ðmÞ

x1 ðn mÞ e ðnÞ þ 1 x2 ðn mÞ e2 ðnÞ

(28)

We can generalize Eq. (28) for K simultaneously recorded signals. This is called a multivariate autoregressive (MVAR) model, where the K signals are modeled as a linear combination of their own past plus additional uncorrelated white noise: XðnÞ ¼

p X

AðmÞXðn mÞ þ EðnÞ

(29)

13

noise, the multivariate dataset and the coefficient matrices, respectively. This equation can be rewritten as: Xð f Þ ¼ A1 ð f Þ Eð f Þ ¼ Hð f Þ Eð f Þ;

(34)

where H(f) is defined as the transfer matrix of the MVAR model. H(f) is a K K matrix, in which the element Hij(f) estimates the information flow from signal xj to xi at frequency f. The power spectral density matrix, S(f), can be calculated out of the coefficients and residuals of the MVAR model as follows: Sð f Þ ¼ Xð f Þ X ð f Þ ¼ Hð f Þ Eð f Þ E ð f Þ H ð f Þ ¼ Hð f Þ Se H ð f Þ ¼ Hð f Þ s e I H ð f Þ ¼ s e Hð f Þ H ð f Þ;

(35)

m¼1

where X(n) = [x1(n) x2(n) xK(n)]T is the signal matrix at time n, E(n) = [e1(n) e2(n) eK(n)]T is the matrix containing the uncorrelated white noise at time n, p is the model order and A(m) is the K K coefficient matrix for delay m. The model order defines the number of past time points that are included to estimate the current sample. Element Aij(m) estimates the influence of the sample xj(n m) on the current sample xi(n). All coefficient matrices together provide knowledge about the directed information flow between all signals. A.4.1.2. Estimation of the model parameters The model order defines the time window used to estimate the current samples based on a linear combination of the past samples. It can be estimated using a criterion like the Akaike Information Criterion (Akaike, 1974) or the Schwarz’s Bayesian Criterion (Schwarz, 1978). Both criteria are based on the covariance of the residuals and an additional term penalizing overfitting. The Akaike Information Criterion for MVAR models can be calculated as follows: 2pK 2 AICð pÞ ¼ lnSe ð pÞ þ N

(31)

with Se(p) the covariance matrix of the residuals, N the number of time points, p the model order and K the number of considered signals. Both above criteria need to be minimized, meaning that the model order corresponding with the minimum of the AIC function or the SBC function is chosen for further analysis. Another option is to use leave-one-out cross validation to estimate the model order (Cawley, 2006). Once the model order is selected, the coefficients can be estimated with the ordinary least squares procedure or with the method of moments (out of the Yule-Walker equations (Pardey et al., 1996)).

A.4.1.3. Transformation to the frequency domain The Fourier transformation of Eq. (29) results in the following representation of a MVAR process in the spectral domain: Eð f Þ ¼ Að f ÞXð f Þ

(32)

where Að f Þ ¼

p X

i 2 p

AðmÞ e

f fs

m

Sˆ ii ð f Þ ¼ s e

K K X X 2 Hik ð f ÞHki ð f Þ ¼ s e jHik ð f Þj k¼1

(36)

k¼1

Out of the parameters of the AR models we can derive several linear dynamic connectivity measures. In the time domain we can investigate the Granger causality between two signals by estimating the Granger-causality index. Saito and Harashima (1981) and Geweke (1982) translated the time domain approach of bivariate Granger causality to the frequency domain. Geweke extended this 2 years later to the multivariate case (Geweke, 1984). This allows investigating the Granger causal relations in the different frequency bands between multiple signals. The Granger causality is studied in the frequency domain by calculating the directed coherence, the directed transfer function or the partial directed coherence.

(30)

and the Schwarz’s Bayesian Criterion as follows: lnðNÞpK 2 SBCð pÞ ¼ lnSe ð pÞ þ N

where * denotes the complex conjugate and Se is the noise covariance matrix. Since we assume the error time series are uncorrelated white noise, the covariance matrix Se will be a diagonal matrix approximated by sI. This allows to estimate the autospectrum of signal xi as:

A.4.2. Granger-causality index The bivariate Granger causality index (GCI) from y to x can be derived out of the univariate AR models and the bivariate model of x and y. It is defined as: V xjx GCIxy ¼ ln (37) V xjxy where Vxjx is the variance of the residual in the univariate case and Vxjxy is the variance of the residual in the bivariate model. If the past values of y do not improve the prediction of x, then Vxjx Vxjxy and GCIxy 0. A better prediction will decrease Vxjxy and result in a value of GCIxy bigger than 0. The Granger causality from x to y can be investigated accordingly.

A.4.3. Directed coherence Since the coherence and the partial coherence are not able to reveal the direction of the information transfer, the directed coherence (DC) was constructed by Saito and Harashima in 1981. The basic consideration of the DC is that the direction can be determined according to the temporal relations of time series, because a time delay must exist in information transmission (Wang and Takigawa, 1992). The DC reveals the direction of information transfer from one channel y to another x (Saito and Harashima, 1981):

(33)

m¼0

with fs the sampling frequency and A(0) = I (I the K K identity matrix). E(f), X(f) and A(f) are the Fourier transform of the white

s yy Hxy ð f Þ dxy ð f Þ ¼ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 s xx jHxx ð f Þj2 þ s 2yy Hxy ð f Þ2

(38)


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14

It is based on the residuals and transfer matrix of a bivariate autoregressive model. The measure is bivariate, which requires that all pairwise combinations of recorded signals need to be investigated separately. This can be circumvented when MVAR modeling is used to investigate the Granger causality between the signals. In 1998 the DC was extended to the multivariate case by Baccala and Sameshima (1998):

another weighting that prioritizes connections at frequencies that are prominent both in the sending signal’s (xi) as in the receiving signal’s (xj) spectrum, namely the spectrum weighted ADTF (swADTF), was proposed by (Van Mierlo et al., 2013): swADTFij ðtÞ ¼

Z

f2 f¼ f1

Hij ð f ; tÞ2 PK Hjl ð f ; tÞ2 l¼1 2 PK 2 PK R f 2 0 0 Hik ð f ; tÞ k¼1 f 0 ¼ f s¼1 Hks ð f ; tÞ 1

s jj Hij ð f Þ ffi dij ð f Þ ¼ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi PK 2 2 k¼1 s kk jHik ð f Þj

The DC is based on the residuals and transfer matrix of a multivariate autoregressive model. If the number of signals K = 2 Eq. (39) is equal to Eq. (38). Following normalization condition holds: K X

d2ik ð f Þ ¼ 1

(45)

(39)

A.4.5. Partial directed coherence In 2001, Baccala and Sameshima constructed the partial directed coherence, a multivariate directional connectivity measure that only shows the direct interrelations between the signals (Baccala´ and Sameshima, 2001):

(40)

A ð fÞ

ij pij ð f Þ ¼ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi P

k¼1

This means that the DC is normalized with respect to the incoming information transfer at each frequency.

A.4.4. Directed transfer function The directed transfer function (DTF) was defined by Kaminski and Blinowska in 1991 to reveal indirect information transfer between multiple signals (Kaminski and Blinowska, 1991) as follows: H ð fÞ

ij ffi g ij ð f Þ ¼ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi P K k¼1

(41)

2

jHik ð f Þj

g 2ik ð f Þ ¼ 1

(46)

Akj ð f Þ2

The construction of the PDC is based on the Fourier transform of the coefficients, Aij(f), and does not require the inverse of it to calculate the transfer matrix, Hij(f). It has following normalization condition: K X

p2kj ð f Þ ¼ 1

(47)

k¼1

which indicates that the total outgoing flow from each channel equals 1 at each frequency. The mean PDC values in the predefined frequency band can be investigated using the integrated PDC (iPDC) (Astolfi et al., 2007):

with corresponding normalization condition: K X

K k¼1

(42)

iPDCij ð f Þ ¼

k¼1

this indicates that the total incoming information transfer into each channel is equal to 1 at each frequency. The construction of the DTF does solely include the transfer function H(f) and not the noise matrix S. Therefore possible correlation of input noises among themselves, manifested in the presence of non-diagonal elements in S, do not influence the DTF. The DTF is a measure that displays the indirect and direct information transfer between multiple signals at each frequency. The integrated DTF (iDTF) (Franaszczuk and Bergey, 1998) is the mean DTF in a pre-defined frequency band-of-interest in which each frequency contributes with equal weight to the connectivity pattern: Z f2 Hij ð f Þ2 1 iDTFij ¼ (43) P f 2 f 1 f ¼ f 1 K jHik ð f Þj2 k¼1 Another weighting that prioritizes connections at prominent frequencies in the receiving signal’s (xj) spectrum is called the fullfrequency DTF (ffDTF) (Korzeniewska et al., 2003): Z f2 Hij ð f Þ2 (44) ffDTFij ¼ R PK f2 Hik ð f 0 Þ2 f¼ f1 k¼1 f 0 ¼ f 1

To be able to model non-stationary signals the adaptive DTF (ADTF) was developed by (Astolfi et al., 2008; Wilke et al., 2008). This measure was extended to the integrated ADTF (iADTF) (Astolfi et al., 2008; Wilke et al., 2008) and the full-frequency ADTF (ffADTF) (Van Mierlo et al., 2011) to estimate time-variant connectivity pattern in a frequency band of interest. Recently,

1 f2 f1

Z

f2

Aij ð f Þ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi P K f¼ f1 Akj ð f Þ2

(48)

k¼1

The time-variant version of the PDC, the adaptive PDC (APDC) and the integrated APDC (iAPDC) were introduced by Astolfi et al. (2008) to allow time-variant connectivity analysis. A.4.6. Nonlinear Granger causality Several methods exist to estimate nonlinear Granger causality. Freiwald et al. (1999) introduced a framework to assess nonlinear Granger causality using local linear nonlinear autoregressive models. In Cha´vez et al. (2003) and Goure´vitch et al. (2006) an information-theoretic test for general Granger causality is introduced. Here, nonlinear Granger causality is assessed by investigating the violation of the Markov property. Another technique is to search for linear relations in the Hilbert space (Vapnik, 1998; Shawe-Taylor and Cristianini, 2004; Marinazzo et al., 2008). The method investigates linear Granger causality in the feature space of suitable kernel functions, assuming an arbitrary degree of nonlinearity. For more information about nonlinear Kernel Granger causality we refer the reader to Marinazzo et al. (2011). References AED, 1991. Randomised study of antiepileptic drug withdrawal in patients in remission. Medical Research Council Antiepileptic Drug Withdrawal Study Group. Lancet 337, 1175–1180. Adhikari, B.M., Epstein, C.M., Dhamala, M., 2013. Localizing epileptic seizure onsets with Granger causality. Phys. Rev. E 88, 030701, http://dx.doi.org/10.1103/ PhysRevE.88.030701. Akaike, H., 1974. A new look at the statistical model identification. IEEE Trans. Autom. Control 19, 716–723, http://dx.doi.org/10.1109/TAC.1974.1100705. Astolfi, L., Cincotti, F., Mattia, D., De Vico Fallani, F., Tocci, A., Colosimo, A., Salinari, S., Marciani, M.G., Hesse, W., Witte, H., Ursino, M., Zavaglia, M., Babiloni, F., 2008. Tracking the time-varying cortical connectivity patterns by adaptive


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Scalp EEG brain functional connectivity networks in pediatric epilepsy.

Automated localization of the seizure focus using interictal intracranial EEG.

Multimodal effective connectivity analysis reveals seizure focus and propagation in musicogenic epilepsy.

Functional connectivity estimated from intracranial EEG predicts surgical outcome in intractable temporal lobe epilepsy.

Bilateral intracranial EEG with corpus callosotomy may uncover seizure focus in nonlocalizing focal epilepsy.

EEG and neuroimaging localization in partial epilepsy.

Functional Connectivity Alterations in Epilepsy from Resting-State Functional MRI.

Scale invariance properties of intracerebral EEG improve seizure prediction in mesial temporal lobe epilepsy.

Identification of the Epileptogenic Zone from Stereo-EEG Signals: A Connectivity-Graph Theory Approach.

Functional connectivity in preterm infants derived from EEG coherence analysis.

Periodicity in functional brain networks: application to scalp EEG from epilepsy patients.

Sequential EEG characteristics may predict seizure recurrence in rolandic epilepsy.

EEG Resting State Functional Connectivity Analysis in Children with Benign Epilepsy with Centrotemporal Spikes.

Resected Brain Tissue, Seizure Onset Zone and Quantitative EEG Measures: Towards Prediction of Post-Surgical Seizure Control.

Functional hemispherectomy: EEG findings, spiking from isolated brain postoperatively, and prediction of outcome.

Lateralization of the epileptogenic focus by computerized EEG study and neuropsychological evaluation.

Abnormal EEG Complexity and Functional Connectivity of Brain in Patients with Acute Thalamic Ischemic Stroke.

Resting-state EEG oscillatory dynamics in fragile X syndrome: abnormal functional connectivity and brain network organization.

Is functional brain connectivity atypical in autism? A systematic review of EEG and MEG studies.

Seizure detection, seizure prediction, and closed-loop warning systems in epilepsy.

Chronic unlimited recording electrocorticography-guided resective epilepsy surgery: technology-enabled enhanced fidelity in seizure focus localization with improved surgical efficacy.

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[Epilepsy and functional brain networks].

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