Electrical Source Imaging (ESI)

EEG and MEG are among the non-invasive methods for the study of the neuronal activity at the sub-millisecond timescale. However, the signal measured is a propagation of the neuronal activity on the scalp, and due to the ambiguity of the underlying electromagnetic problem (Helmholtz 1853), infinite different source configurations could potentially generate the same topography on the scalp (de Munck et al. 1988). Therefore, maximal activity at a certain electrode does not mean that the generator is localized in the area underlying it (Michel et al. 2004). In order to solve this problem and properly model the propagation, some a priori constraints need to be taken into account.

Several different constraints have been proposed using different mathematical, biophysical, statistical, anatomical or functional properties and producing different type of solution suitable for distinct type of data.

Electric Source Imaging involves two main processes: (a) the forward model and (b) the inverse problem.

The forward model is a description of the propagation of the electric current across the brain to the scalp (the lead-field matrix): the most important parameter is the head-model, i.e. the head volume conductor model, that takes into account the position of the solution points within the brain (sources- solution space), the position of the scalp electrodes, the head geometry, and the head tissues’ conductivity. A lot of different head-models have been proposed: (a) spherical head models in which the head is approximated by concentric spheres where each sphere corresponds to a

Figure 2: Schematic representation of scalp and source space solution at the peak of an epileptic spike recorded with hd-EEG.

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certain tissue type (Rush and Driscoll 1968) and (b) realistic head models based on the individual MRI.

For the scope of this thesis, the Locally Spherical Model with Anatomical Constrains (LSMAC) has been extensively used. These head models consist of a simplified realistic head model with consideration of scalp, skull and brain thicknesses. LSMAC uses an adaptive local spherical model sequentially at each electrode position, to generate sets of 3-layer spherical models using the conductivities and local radiuses of the scalp, skull and brain under each electrode site. This allows the real geometry between solution points and electrodes to be taken into account (Brunet et al.

2011). It has been previously shown that, as compared to realistic head models based on individual MRI, LSMAC localization of the epileptic zone has the same accuracy (Birot et al. 2014) and it has the advantage of being less computationally demanding.

The inverse problem is used to estimate the source activity, given the EEG recording on the electrodes, based on the solution of the forward problem. The inverse problem is ill-posed, i.e.

infinite source configuration can produce the same topographical map on the scalp electrodes, therefore some a priori hypotheses are needed (source model)(Michel et al. 2004).

Two main types of inverse solution methods are proposed based on different numbers of unknown sources (a) dipole source model (where the number is much smaller than the number of electrodes) and (b) distributed source models (where the number is much higher).

In the dipole source models a search is made for the best dipole position(s) and orientation(s): the assumption is that a single, or only a few, brain area(s) are responsible for the topography seen on the scalp. This could sound optimal for the localization of epileptic activity, but it is known that epileptic activity very quickly within a widespread neuronal network, which can lead to localization of propagated instead of the initial activity.

In the distributed source models, a 3D grid of dipoles (normally around 5000) are computed in a fixed position, with variable strength and either variable or fixed orientation, in the grey matter. No a priori hypotheses are made on the position and on the number of the dipoles, but some assumptions, based on physiological or mathematical information’s, are needed. Two well-known models are the Low Resolution Electromagnetic Tomography (LORETA) (Pascual-Marqui et al. 1994) and the Local Auto-Regressive Averages (LAURA) (Grave De Peralta Menendez et al. 2004).

LORETA assumes smoothness property of the neuronal activity: the a priori hypothesis behind is that neighboring sources must have similar activation and orientation, as the population of neurons must fire synchronously to produce activation (Pascual-Marqui et al. 1994).

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LAURA incorporates biophysical laws as additional constraints: it assumes that the source activity will decrease with the inverse of the cubic distance for vector fields, and with the inverse of the squared distance for potential fields (Grave De Peralta Menendez et al. 2004).

LSMAC and LAURA have been extensively used in this thesis, for comprehensive reviews on ESI as well as the advantages and drawbacks of the different algorithms, we refer the reader to (Grech et al. 2008; Michel et al. 2004, 2009). For clinical application of ESI in the context of presurgical evaluation in focal epilepsy we refer to (Brodbeck et al. 2011; Kaiboriboon et al. 2012; Mégevand et al. 2014).

Other techniques, that include regularization schemes not based on spatial constrained (as described above for LORETA) but based on the following statistical frameworks have been also proposed: (1) the Maximum Entropy on the Mean (MEM) and (2) the Hierarchical Bayesian (HB) framework (Chowdhury et al. 2013; Grova et al. 2006).

In this context two types of spatial models have been investigated. The first one is the idea that brain activity may be modeled as organized among cortical parcels, that can be active or not, when contributing to specific activity (Trujillo-Barreto et al. 2004). The second model is an extension of the spatial smoothness constraint originally proposed in LORETA but locally constrained within cortical parcels. Clustering of the brain activity into non- overlapping cortical parcels is achieved using a data driven parcellization (Chowdhury et al. 2013).

For epileptic activity, the localization accuracy of different source localization methods have been previously evaluated: the minimum norm, the minimum norm weighted by multivariate source prelocalization (MSP), cortical LORETA with or without additional minimum norm regularization, and two derivations of the Maximum Entropy of the Mean (MEM) approach have been tested.

Results showed that LORETA-based and MEM methods were able to accurately recover sources of different spatial extents. However, also several wrong sources are sometimes generated by those methods, it is therefore important to take into account the results from different localization methods when analyzing real interictal spikes (Grova et al. 2006).

4.1 The importance of the number and location of electrodes

When collecting brain signal with EEG, caps with different numbers of electrodes are available. The most commonly used range between 19 and 256 electrodes.

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When the aim of the recording is to perform source reconstruction, two main characteristics need to be taken into account: (a) the whole scalp needs to be equally covered, (b) the number of electrodes (Michel et al. 2004; Michel and Murray 2012).

It is known from the literature that increasing the electrode density in the regions where the maximal activation is expected decreases the localization power of the ESI technique: if the topographic features are not adequately sampled, none of the inverse solutions can retrieve the sources that would have generated these features (Bénar and Gotman 2001; Michel et al. 2004).

It has been previously shown, initially via simulation of single dipoles and later by localization of interictal discharges, that the number of electrodes influences source localization (Lantz et al.

2003a). There is a non-linear relation between the precision of ESI and the number of EEG electrodes: the precision increases from 25 to around 100 electrodes and then it reaches a plateau.

From low density EEG recording, mainly in clinical set-ups (Seeck et al. 2017), it has been also shown that temporal electrodes allow better identification of temporal lobe spikes.

However, the additional value of inferior electrodes for localization of the source activity is still unclear. On the one hand, due to their spatial proximity to the skull base, inferior EEG channels may help in localizing epileptic activity in basal structures such as the temporal lobes. On the other hand, located rather far from the convexity, they might be of less value for ESI in extratemporal structures.

In addition, inferior electrodes placed on the neck and facial muscles are prone to artifacts which, in turn, may reduce their value for ESI.

4.2 The extraction of brain region time-series

The estimation of the source space activity using ESI always leads to a description of the brain as a collection of around 5000 three-dimensional dipoles placed in different brain areas. When the final aim of the reconstruction is to describe the compute connectivity analysis, since the full spatial size of the data is unreasonable, the interest is to parcel the brain in different regions and extract a unique time-series representing the activity in that area.

To solve this step, in the literature, a lot of different approaches have been proposed: (a) computing the norm of all the dipoles, (b) fixing their orientation and (c) selecting one dipole time-course as representative of the signal.

When computing the absolute dipole amplitude (i.e. the norm of the signal) or the power modulation using Hilbert transformation (Baker et al. 2014; Brookes et al. 2011) while discarding the directionality, the phase information of the original signal is lost (Vidaurre et al. 2016) and

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therefore connectivity analysis cannot be applied. Others computed the average cortical activity in each ROI by means of the instantaneous average of the signed magnitude of all the dipoles within the ROI (Astolfi et al. 2007).

When imposing one direction, two steps are needed, first one should either fix the orientation (a) orthogonal to the segmented grey matter, based on the assumption that the orientation of the dipoles should resemble the orientation of the apical dendrites of the pyramidal neurons (Phillips et al. 2002), or (b) maximize the projected power (Barnes et al. 2004) or, (c) as the projection to the refined average direction across time and epochs (Coito et al. 2016). Second, an averaging to all dipole time-series within the ROI (Hassan et al. 2017) or principal component analysis (PCA) needs to be applied to obtain the representative time-series (Gruber et al. 2008; Supp et al. 2007). A common observation in these cases is a drastic amplitude reduction: some sources in the ROI may be almost perfectly parallel to each other, but inverted in orientation, leading to cancelation when averaging them.

When selecting one dipole time-course only, the closest to the geometric center of each ROI, i.e., the centroid (Adebimpe et al. 2016; Coito et al. 2015; Sperdin et al. 2018), is considered. However, the selection of only one dipole out of hundreds does not necessarily properly represent the activity in a given ROI.

4.3 Magnetic Source Imaging

Another technique that can measure neuronal activity not invasively is magnetoencephalography (MEG), which measures the brain magnetic fields. Both EEG and MEG collect signal arising from neuronal activation. There are, however, some differences between the two techniques: EEG is sensitive to both tangential and radial components of the dipolar sources, while MEG is not sensitive to only to tangential components components (Ahlfors et al. 2010). This is why, EEG can pick up the activity of deep and radial current sources in opposition to MEG [90]. However, the EEG is strongly influenced by volume conduction and by the different electrical conductivities of various head tissues that attenuate the sources electrical signal. This has a less strong influence on MEG, given that the head tissues have a constant magnetic permeability(Lopes da Silva 2013). All the ESI described methodology can also be applied in MEG, and in this case, it is called Magnetic Source Imaging (MSI).

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Among others, Minimum Norm Estimate (MNE) is one of the most commonly used inverse solutions methods in MEG. It looks for a distribution of sources with the minimum (L2-norm) current that can give the best account of the measured data. As in the case of EEG, the inverse problem is ill-posed:

MNE uses a regularization procedure that sets the balance between fitting the measured data (minimizing the residual) and minimizing the contributions of noise (Hincapié et al. 2016).

As for EEG, the localization of the generators of epileptic activity in the brain MEG signals is of particular interest during the pre-surgical investigation of epilepsy.

Using realistic simulations of epileptic activity, the Maximum Entropy on the Mean (MEM) framework has been shown to be sensitive to all spatial extents of the sources ranging (Chowdhury et al. 2013). In real data, MEM allows non-invasive localization of the seizure onset zone from both MEG and EEG (Heers et al. 2016). It has been shown that source imaging performed with MEG can provide important additional information to source imaging performed with EEG during both spikes and seizures during presurgical evaluation (Pellegrino et al. 2016).