The authors have declared that no competing interests exist.
Took part in interpretation of results: RC CG JML. Overall reading of the paper: EK JML CG. Conceived and designed the experiments: RC JML CG. Performed the experiments: RC EK. Analyzed the data: RC CG. Wrote the paper: RC JML CG.
Localizing the generators of epileptic activity in the brain using Electro-EncephaloGraphy (EEG) or Magneto-EncephaloGraphy (MEG) signals is of particular interest during the pre-surgical investigation of epilepsy. Epileptic discharges can be detectable from background brain activity, provided they are associated with spatially extended generators. Using realistic simulations of epileptic activity, this study evaluates the ability of distributed source localization methods to accurately estimate the location of the generators and their sensitivity to the spatial extent of such generators when using MEG data. Source localization methods based on two types of realistic models have been investigated: (i) brain activity may be modeled using cortical parcels and (ii) brain activity is assumed to be locally smooth within each parcel. A Data Driven Parcellization (DDP) method was used to segment the cortical surface into non-overlapping parcels and diffusion-based spatial priors were used to model local spatial smoothness within parcels. These models were implemented within the Maximum Entropy on the Mean (MEM) and the Hierarchical Bayesian (HB) source localization frameworks. We proposed new methods in this context and compared them with other standard ones using Monte Carlo simulations of realistic MEG data involving sources of several spatial extents and depths. Detection accuracy of each method was quantified using Receiver Operating Characteristic (ROC) analysis and localization error metrics. Our results showed that methods implemented within the MEM framework were sensitive to all spatial extents of the sources ranging from 3 cm2 to 30 cm2, whatever were the number and size of the parcels defining the model. To reach a similar level of accuracy within the HB framework, a model using parcels larger than the size of the sources should be considered.
Epilepsy is a neurological disorder characterized by the recurrence of clinical seizures. The state during which the seizure takes place is called the ictal state. In between the seizures, abnormal neuronal discharges, the so-called inter-ictal spikes may take place and usually occur more frequently than the seizures. They are generated by the brain without any clinical manifestations and originate partially from brain regions similar to the ones involved during the seizures, i.e., from the epileptogenic focus. Thus analysis of inter-ictal spikes is widely used as a marker of epilepsy
Epileptic activity originates from abnormal excitability and synchronization of neurons. The large pyramidal neurons of the cortical layer V, which are oriented perpendicularly to the cortical surface of the brain, are the main generators of brain electro-magnetic activity. Magneto-Encephalography (MEG) measures the magnetic fields generated by the neuronal currents, using a helmet of few hundred sensors uniformly distributed around the head
The amplitude of MEG signals for physiological brain activity is expected to range from femto-Teslas to pico-Teslas. As mentioned by Huiskamp et al.
The MEG inverse problem of source localization consists in inferring the location of the generators of brain activity from signals detected outside the head
MEG source localization is an ill-posed problem, as it admits no unique solution unless additional information is used to regularize the problem. Such regularizations consist in adding some
In order to obtain a unique solution, additional constraints in the form of a regularization scheme are required. Minimum Norm Estimate (MNE), which chooses the minimum energy solution
Based on the rationale of obtaining realistic constraint models describing the generators of epileptic activity, 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
In order to implement these above-mentioned spatial models, we proposed two new source localization methods within the MEM framework (MEM-s and CMEM-s) and one within the HB framework (COH-s). MEM-s refers to the MEM approach proposed in Grova et al.
After introducing the MEG inverse problem using a distributed source model, the definition of the two general spatial models considered in this study is provided: (i) the DDP and (ii) the local spatial smoothness. Then, the MEM framework and the implementation of MEM-s and CMEM-s methods are described, followed by the description of the HB framework and the corresponding methods (COH-s, COH and IID). The evaluation procedure of the source localization methods using realistic simulations is then introduced. Finally the results and a detailed discussion are presented.
A distributed source model consists of a large number of dipolar sources distributed along the cortical surface. We considered the orientation of each dipole to be fixed perpendicular to the cortical surface. Using this anatomical constraint, the relationship between source amplitudes and MEG measurements is expressed by the following linear model
However, the inverse problem is still an ill-posed problem as the forward matrix
We first assume that brain activity can be organized into functional cortical parcels. Characterizing brain activity, assuming functional homogeneity within brain parcels has proved to be an efficient approach to analyze neuroimaging data, either in EEG/MEG
In the present study, we proposed a Data Driven Parcellization (DDP) method performing full parceling of the tessellated cortical surface into non-overlapping parcels (see
Examples of clustering of the cortical surface at different spatial scales s obtained using the DDP technique (each color represents one parcel).
The key aspect of DDP lies in the pre-localization of the sources of brain activity using the Multivariate Source Pre-localization (MSP) method
Defining brain activity in terms of K parcels of functionally homogenous activity (K<<p) aims at better conditioning the under-determined inverse problem, while the inverse method will infer the local source intensity inside each parcel.
Spatial smoothness model assumes that nearby dipoles are more likely to have similar intensities. In this context, LORETA - originally proposed by Pascual-Marqui et al.
In order to introduce local spatial smoothness over a geodesic surface, we used the diffusion-based spatial prior proposed by Harrison et al.
Let us define
Note that the non-null entries of
In the MEM framework, we consider the amplitude of the sources
Among all the distributions
Each cortical parcel k is characterized by an activation state
The purpose of the present study was to evaluate different initialization of
When incorporating the parcels P(s) through A spatio-temporal Activation Probability Map (stAPM) was generated (see In the reference model ( The covariance matrix for each parcel is a time varying matrix Σ
Accordingly, under these assumptions, we propose the two following methods:
For MEM-s and CMEM-s, we defined the reference distribution with mean
Solving the MEG inverse problem within the HB framework offers the advantage of accommodating multiple priors and proposes inference techniques to select the most likely combination of priors using model selection approaches
HB model allows integrating uncertainties at different levels, modeling the covariance in each level as linear combination of covariance components. The different levels are the sensor noise level and the source noise level.
At the sensor level (1st level), the relationship between the MEG measurements (M) and the source amplitudes (
At the source level (2nd level), the prior distribution of the source amplitudes (
The source spatial covariance
In addition to two standard source reconstruction methods (IID and COH) implemented in SPM8 software package
Note that COH-s is an extension of COH method using the concept of multiple parcels introduced in the Multiple Sparse Prior method proposed by Friston et al. (2008)
We evaluated the performance of the five above-mentioned source localization methods in their ability to localize spatial extended sources. To perform this validation, we proposed a fully controlled environment to generate realistic simulations of MEG data mimicking the generators of epileptic spikes with different spatial extents, similarly to the evaluation proposed for EEG source localization in Grova et al. (2006)
Realistic simulations were generated using MEG data obtained from a patient with focal epilepsy showing normal tracing with no epileptic activity. This patient participated as a research subject of the project entitled: “Application of magnetoencephalography in the assessment of the epileptic focus” (Dr. E. Kobayashi being the principal investigator for this project). Written informed consent for this study was obtained from the subject as approved by the Research Ethics Committee of the Montreal Neurological Institute and Hospital (MNI/H). At its full board meeting of June 14, 2011, the Research Ethics Board (REB) of the MNI/H has endorsed the review of this project and found this research to be acceptable for continuation at the McGill University Healthcare Centers. The REB of the MNI/H acts in conformity with standards set forth in the (US) Code of Federal Regulations governing human subjects’ research and functioning in a manner consistent with internationally accepted principles of good clinical practice.
The subject we selected to generate our realistic simulations had normal cortical surface segmented from his anatomical Magnetic Resonance Imaging data. This acquisition was done at the MEG center of Université de Montréal on a 275 channels CTF whole-head MEG system. The detection coils used in the system were first order radial gradiometers. The CTF system is equipped with reference sensors using a 3rd order gradient correction to subtract background interferences. During the acquisition, the head position of the subject was tracked using localization coils placed on three fiducial points (nasion, left and right peri-auricular points).
A high resolution T1 weighted MRI was acquired on the same subject at the MRI center of the Montreal Neurological Institute. Co-registration between MEG sensors position and the anatomical T1-weighted MRI of the subject was obtained in three steps: (i) manual identification of the three fiducial points on the MRI, (ii) digitalization of the position of the fiducials on the head of the subject using a 3D Polhemus localizer and (iii) the rigid geometrical transformation between the MRI’s space and the subject’s space was obtained by fitting these points using Procrustes method
A realistic head model was obtained by segmenting the surface of the brain from the subject’s anatomical T1-weighted MRI
100 simulation configurations involving one extended source were generated. The position of each source was selected by choosing a seed point randomly on the cortical surface mesh. The spatial extent of each source was obtained by region growing around the seed following the cortical surface using different spatial neighborhood orders ranging from a source spatial extent
The time course of the simulated sources was the time course of an epileptic spike modeled with three Gamma functions, although only signal around the main peak of the spike was analyzed (about 21 samples around the peak with a sampling rate of 600 Hz). Let us refer to
In order to investigate the influence of the spatial clustering scale
We also performed the following investigations: 1) to compare the performance of the methods that uses DDP model (MEM-s, CMEM-s and COH-s) when initializing parcels P(s) either with the data of interest or with some background MEG activity and 2) to compare the ability of the methods to localize single spike versus averaged spike data (average of 20 spikes). For these two tests we considered 50 source configurations of spatial extent
All the simulations were performed with Matlab (R2010a) using the simulation environment Pipeline System for Octave and Matlab (PSOM)
In this section we describe the validation metrics used to evaluate the detection accuracy of the source localization methods presented in
However, to interpret the area under the ROC curve as a detection accuracy index, one should provide the same number of active and inactive sources to the ROC analysis
In addition, AUC was measured as a function of eccentricity to check for the influence of the depth of the source on detection accuracy. The eccentricity of a simulated source was defined as the distance between the seed point of the spatially extended source to the center of the head, whereby the deepest source have a lower eccentricity value (10 mm) and the most superficial ones have a higher eccentricity value (90 mm). Sources with eccentricity ranging between 40 mm and 60 mm corresponded mainly to mesio-temporal sources and the ones with eccentricity less than 40 mm corresponded to the sub-cortical sources.
The purpose of this first section is to evaluate qualitatively the performance of three simulations together with the corresponding validation metrics AUC, MSE and Dmin. To visualize the results, we showed the absolute value of the reconstructed activity at the peak of the simulated spike, thresholded upon the level of background activity
Visual analysis of source localization results together with Area Under the ROC curve (AUC) values for a simulated source of spatial extent
We also illustrated the impact of the clustering scale
Visual analysis of source localization results together with Area Under the ROC curve (AUC) values for a simulated source of spatial extent
Visual analysis of source localization results together with Area Under the ROC curve (AUC) values for a simulated source of spatial extent
Methods - AUC median | |||||
Spatial Extents | IID | COH | MEM-s (s = 5) | CMEM-s (s = 5) | COH-s (s = 5) |
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0.77 |
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0.78 |
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0.75 |
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0.74 |
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0.77 | |
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0.74 |
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0.72 |
(in bold font: median AUC>0.80).
The above results are presented with more details in
Distribution of AUC results using boxplot representations over 100 simulations of randomly placed sources for all source localization methods. x-axis from left to right: source spatial extent
Methods | Metrics | se = 2 Med(Disp) | se = 3 Med(Disp) | se = 4 Med(Disp) | se = 5 Med(Disp) | se = 6 Med(Disp) | |
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1.1 (0.14) 4.9(45.0) | 0.93(0.08) 0(21.8) | 0.90(0.05) 0(17.9) | 0.91(0.04) 0(9.1) | 0.92(0.02) 0(5.4) | |
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1.1(0.16) 0(44.8) | 0.91(0.12) 0(19.5) | 0.86(0.11) 0(14.0) | 0.82(0.07) 0(6.9) | 0.83(0.05) 0(5.1) | |
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0.94(0.08) 9.2(28.7) | 0.91(0.08) 0(20.3) | 0.90(0.07) 0(13.3) | 0.91(0.05) 0(5.4) | 0.93(0.03) 0(3.6) |
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0.94(0.07) 11.7(29.1) | 0.92(0.07) 2.6(16.1) | 0.91(0.06) 0(13.6) | 0.92(0.05) 0(5.5) | 0.93(0.03) 0(4.8) | |
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0.96(0.06) 12.3(28.7) | 0.92(0.07) 4.2(18.1) | 0.92(0.06) 0(14.0) | 0.93(0.04) 0(6.7) | 0.93(0.03) 0(3.5) | |
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0.96(0.05) 17.9(31.7) | 0.93(0.06) 4.7(22.1) | 0.92(0.05) 0(14.3) | 0.93(0.04) 0(7.7) | 0.93(0.03) 0(4.5) | |
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0.94(0.08) 10.7(34.2) | 0.90(0.08) 0(18.7) | 0.89(0.07) 0(8.9) | 0.90(0.06) 0(5.7) | 0.90(0.04) 0(3.9) |
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0.95(0.07) 12.9(31.7) | 0.91(0.09) 0(19.5) | 0.89(0.07) 0(9.9) | 0.90(0.06) 0(6.7) | 0.90(0.04) 0(3.2) | |
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0.96(0.06) 12.0(26.7) | 0.90(0.08) 3.5(20.7) | 0.89(0.07) 0(11.0) | 0.91(0.06) 0(6.8) | 0.91(0.04) 0(4.1) | |
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0.96(0.06) 14.3(35.6) | 0.91(0.07) 0(21.1) | 0.90(0.07) 0(12.0) | 0.91(0.06) 0(5.4) | 0.90(0.04) 0(3.1) | |
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6.67(44.4) 59.5(50.9) | 4.04(13.0) 28.7(35.7) | 3.26(15.5) 25.4(34.5) | 3.05(17.1) 25.6(29.3) | 2.86(10.1) 29.5(31.5) |
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2.87(19.1) 41.6(56.7) | 1.26(6.4) 4.6(41.9) | 1.06(119) 0(29.0) | 1.13(2.50) 0(17.8) | 1.27(2.02) 0(13.9) | |
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2.28(5.2) 27.2(55.7) | 0.81(0.93) 0(28.4) | 0.77(0.53) 0(19.0) | 0.79(2.07) 0(21.1) | 0.83(0.36) 0(14.6) | |
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2.09(3.4) 22.7(55.4) | 0.84(13361) 0(27.1) | 0.70(1.5) 0(18.7) | 0.77(0.44) 0(12.0) | 0.78(0.31) 0(7.3) |
MSE = Mean Squared Error, Dmin = Minimum geodesic distance between the local extrema of the reconstructed source and the simulated source, L1 Dispersion = the average of the absolute deviations from the median.
The minimum geodesic Dmin distance indicated that in most cases the maximum of reconstructed activity was located within the simulated sources (Dmin = 0), except for some large false detections observed with COH-s at smaller cluster scales
Whereas
This section aims at assessing the impact of the clustering scale
Distribution of AUC results using boxplot representations over 100 simulations of randomly placed sources for all source localization methods (x-axis from left to right: MEM-s with
We assessed the effect of the depth of sources on detection accuracy by plotting for each method, AUC as a function of eccentricity of the source for source spatial extents
Plot showing AUC values as a function of the eccentricity (in mm) of the 100 simulated sources (with spatial extent
This analysis also confirmed that most of the low AUC values considered as outliers in boxplot distributions, presented in
Plot showing the (a) effect of background activity versus data of interest for the parcellization: MEM-s (purple), CMEM-s (red) and COH-s (blue) (x-axis: AUC value for Baseline, y-axis: AUC value for data), and (b) effect of single spike localization versus average spike localization: IID (green), COH (black), MEM-s (purple), CMEM-s (red) and COH-s (blue) (x-axis: AUC value for single spike localization, y-axis: AUC value for averaged spike localization).
We can see that there was no impact on the detection accuracy of MEM-s, CMEM-s and COH-s when using the data of interest or MEG background activity to initialize the DDP model (
We have presented an evaluation of source localization methods for their ability to localize spatially extended sources of epileptic activity by incorporating realistic spatial models. We proposed three new source localization techniques that can detect the location of the sources with a good sensitivity to their spatial extent when using MEG data: MEM-s, CMEM-s and COH-s.
To be detectable from background activity on MEG, epileptic discharges need to be associated with spatially extended generators
Standard localization metrics (Dmin and MSE) demonstrated overall good accuracy for most of the evaluated methods (except COH-s when
Whereas it is generally accepted that the minimum norm model (IID) is suitable for localizing the maximum of the activity
All approaches, except COH, presented a loss of performance when increasing the spatial extent of the source. Although, a slight decrease in the localization accuracy of MEM-s and CMEM-s was noticed for more extended sources (
Detection of deep sources is a difficult issue since deep generators will generate very low amplitude MEG data on the scalp, almost undetectable except under specific conditions. This usually requires lots of averaging to increase the SNR
The two realistic spatial models considered in this study, i.e. data driven parcellization P(s) and local spatial smoothness
The first model assumed brain activity to be organized into several spatial clusters P(s) using DDP of the brain activity along the tessellated cortical surface. Few studies demonstrated how introducing parceling of the brain (obtained from some anatomical atlases) was quite useful to better condition the inverse problem
However, MEM-s was unable to accurately recover the spatial smoothness of the source along its extent. This led us to incorporate the second model
Two statistical regularization schemes, the MEM and the HB frameworks, were compared in this study.
COH-s method, in which we incorporated the parcellization model P(s) and the local spatial smoothness prior, was proposed to be the equivalent of CMEM-s method. It incorporates the same constraints as the CMEM-s method, but it uses the ReML algorithm within the HB framework to estimate the solution. Our findings show a good concordance between the MEM and HB frameworks when comparing the CMEM-s and COH-s for their detection accuracy, suggesting that both frameworks offer sufficient flexibility to build efficient source localization methods, especially in the context of MEG epileptic data.
In addition, we have tested the influence of the clustering scale
MEM-s and CMEM-s provided very accurate results for any evaluated spatial clustering scale s. This is an important result, suggesting that MEM regularization is able to adapt the number of active parcels, whatever is the spatial scale of the clustering. In order to localize a spatially extended source as accurately as possible, MEM is able to “switch on” several parcels when using a lower clustering scale (small parcels) or only few of them when using a larger clustering scale (large parcels). Once the parcels have been identified as active, our results demonstrated that MEM inference is still able to create some local contrasts of dipole intensities within the active parcels, leading to the ability of localizing sources of different spatial extents. The regularization process was a bit different when using COH-s with ReML, as the hyper-parameters of the source covariance components (i.e., the parcels for COH-s) are first estimated through an Automatic Relevance Determination (ARD) scheme. Then, once the covariance model and its “weights” are estimated, sources are estimated using a regularized pseudo-inverse method. The diffusion-weighted prior will then push forward a spatially smooth solution over the selected parcels. When using smaller parcels with COH-s (
Note that, in this work, we compared the performances of the five methods using the same forward model for both source simulation and source localization. This is a standard approach when assessing the performances of source localization methods
In distributed source modeling, the cortical surface constraint is defined from large cortical assemblies of pyramidal cells organized orthogonally to the grey-white matter interface. Most distributed methods adopt this constraint with either restricting the orientation to be perpendicular
When dealing with real data, it is important to study the impact of the quality of segmentation and resolution of the cortical surface on the source reconstruction, and especially in pathological conditions. On the other hand, Henson et al. (2009)
Our simulation paradigm was a spatial validation, studying detection accuracy only at the main peak of the simulated spike. In our future work, we plan to assess the spatio-temporal features of the sources by simulating different propagation patterns of epileptic discharges using models such as the extended source model developed by Cosandier-Rimélé et al.
We have proposed three new methods (MEM-s, CMEM-s and COH-s) and evaluated their performance when localizing spatially extended generators of epileptic discharges using MEG data. We demonstrated that modeling brain activity using Data Driven Parcellization of the cortical surface and applying local smoothness within each parcel is particularly relevant to localize sources together with their spatial extent. Both MEM and HB frameworks are sufficiently flexible to allow the implementation of such spatial models. The present study is in agreement with the good performance of MEM we previously demonstrated on EEG data, although we added the evaluation of several other parameters such as a larger range of spatial extents and depths of the sources, as well as the scale of the spatial clustering.
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