Development of a Group Dynamic Functional Connectivity Pipeline for Magnetoencephalography Data and its Application to the Human Face Processing Network

Since its inception, functional neuroimaging has focused on identifying sources of neural activity. Recently, interest has turned to the analysis of connectivity between neural sources in dynamic brain networks. This new interest calls for the development of appropriate investigative techniques. A problem occurs in connectivity studies when the differing networks of individually analyzed subjects must be reconciled. One solution, the estimation of group models, has become common in fMRI, but is largely untried with electromagnetic data. Additionally, the assumption of stationarity has crept into the field, precluding the analysis of dynamic systems. Group extensions are applied to the sparse irMxNE localizer of MNE-Python. Spectral estimation requires individual source trials, and a multivariate multiple regression procedure is established to accomplish this based on the irMxNE output. A program based on the Fieldtrip software is created to estimate conditional Granger causality spectra in the time-frequency domain based on these trials. End-to-end simulations support the correctness of the pipeline with single and multiple subjects. Group-irMxNE makes no attempt to generalize a solution between subjects with clearly distinct patterns of source connectivity, but shows signs of doing so when subjects patterns of activity are similar. The pipeline is applied to MEG data from the facial emotion protocol in an attempt to validate the Adolphs model. Both irMxNE and Group-irMxNE place numerous sources during post-stimulus periods of high evoked power but neglect those of low power. This identifies a conflict between power-based localizations and information-centric processing models. It is also noted that neural processing is more diffuse than the neatly specified Adolphs model indicates. Individual and group results generally support early processing in the occipital, parietal, and temporal regions, but later stage frontal localizations are missing. The morphing of individual subjects\u27 brain topology to a common source-space is currently inoperable in MNE. MEG data is therefore co-registered directly onto an average brain, resulting in loss of accuracy. For this as well as reasons related to uneven power and computational limitations, the early stages of the Adolphs model are only generally validated. Encouraging results indicate that actual non-stationary group connectivity estimates are produced however

Review on solving the forward problem in EEG source analysis

Background. The aim of electroencephalogram (EEG) source localization is to find the brain areas responsible for EEG waves of interest. It consists of solving forward and inverse problems. The forward problem is solved by starting from a given electrical source and calculating the potentials at the electrodes. These evaluations are necessary to solve the inverse problem which is defined as finding brain sources which are responsible for the measured potentials at the EEG electrodes. Methods. While other reviews give an extensive summary of the both forward and inverse problem, this review article focuses on different aspects of solving the forward problem and it is intended for newcomers in this research field. Results. It starts with focusing on the generators of the EEG: the post-synaptic potentials in the apical dendrites of pyramidal neurons. These cells generate an extracellular current which can be modeled by Poisson's differential equation, and Neumann and Dirichlet boundary conditions. The compartments in which these currents flow can be anisotropic (e.g. skull and white matter). In a three-shell spherical head model an analytical expression exists to solve the forward problem. During the last two decades researchers have tried to solve Poisson's equation in a realistically shaped head model obtained from 3D medical images, which requires numerical methods. The following methods are compared with each other: the boundary element method (BEM), the finite element method (FEM) and the finite difference method (FDM). In the last two methods anisotropic conducting compartments can conveniently be introduced. Then the focus will be set on the use of reciprocity in EEG source localization. It is introduced to speed up the forward calculations which are here performed for each electrode position rather than for each dipole position. Solving Poisson's equation utilizing FEM and FDM corresponds to solving a large sparse linear system. Iterative methods are required to solve these sparse linear systems. The following iterative methods are discussed: successive over-relaxation, conjugate gradients method and algebraic multigrid method. Conclusion. Solving the forward problem has been well documented in the past decades. In the past simplified spherical head models are used, whereas nowadays a combination of imaging modalities are used to accurately describe the geometry of the head model. Efforts have been done on realistically describing the shape of the head model, as well as the heterogenity of the tissue types and realistically determining the conductivity. However, the determination and validation of the in vivo conductivity values is still an important topic in this field. In addition, more studies have to be done on the influence of all the parameters of the head model and of the numerical techniques on the solution of the forward problem.peer-reviewe

Within-Subject Joint Independent Component Analysis of Simultaneous fMRI/ERP in an Auditory Oddball Paradigm

The integration of event-related potential (ERP) and functional magnetic resonance imaging (fMRI) can contribute to characterizing neural networks with high temporal and spatial resolution. This research aimed to determine the sensitivity and limitations of applying joint independent component analysis (jICA) within-subjects, for ERP and fMRI data collected simultaneously in a parametric auditory frequency oddball paradigm. In a group of 20 subjects, an increase in ERP peak amplitude ranging 1–8 μV in the time window of the P300 (350–700 ms), and a correlated increase in fMRI signal in a network of regions including the right superior temporal and supramarginal gyri, was observed with the increase in deviant frequency difference. JICA of the same ERP and fMRI group data revealed activity in a similar network, albeit with stronger amplitude and larger extent. In addition, activity in the left pre- and post-central gyri, likely associated with right hand somato-motor response, was observed only with the jICA approach. Within-subject, the jICA approach revealed significantly stronger and more extensive activity in the brain regions associated with the auditory P300 than the P300 linear regression analysis. The results suggest that with the incorporation of spatial and temporal information from both imaging modalities, jICA may be a more sensitive method for extracting common sources of activity between ERP and fMRI

The Surface Laplacian Technique in EEG: Theory and Methods

This paper reviews the method of surface Laplacian differentiation to study EEG. We focus on topics that are helpful for a clear understanding of the underlying concepts and its efficient implementation, which is especially important for EEG researchers unfamiliar with the technique. The popular methods of finite difference and splines are reviewed in detail. The former has the advantage of simplicity and low computational cost, but its estimates are prone to a variety of errors due to discretization. The latter eliminates all issues related to discretization and incorporates a regularization mechanism to reduce spatial noise, but at the cost of increasing mathematical and computational complexity. These and several others issues deserving further development are highlighted, some of which we address to the extent possible. Here we develop a set of discrete approximations for Laplacian estimates at peripheral electrodes and a possible solution to the problem of multiple-frame regularization. We also provide the mathematical details of finite difference approximations that are missing in the literature, and discuss the problem of computational performance, which is particularly important in the context of EEG splines where data sets can be very large. Along this line, the matrix representation of the surface Laplacian operator is carefully discussed and some figures are given illustrating the advantages of this approach. In the final remarks, we briefly sketch a possible way to incorporate finite-size electrodes into Laplacian estimates that could guide further developments.Comment: 43 pages, 8 figure

Proceedings of the EAA Spatial Audio Signal Processing symposium: SASP 2019

International audienc

Multimodal Integration: fMRI, MRI, EEG, MEG

This chapter provides a comprehensive survey of the motivations, assumptions and pitfalls associated with combining signals such as fMRI with EEG or MEG. Our initial focus in the chapter concerns mathematical approaches for solving the localization problem in EEG and MEG. Next we document the most recent and promising ways in which these signals can be combined with fMRI. Specically, we look at correlative analysis, decomposition techniques, equivalent dipole tting, distributed sources modeling, beamforming, and Bayesian methods. Due to difculties in assessing ground truth of a combined signal in any realistic experiment difculty further confounded by lack of accurate biophysical models of BOLD signal we are cautious to be optimistic about multimodal integration. Nonetheless, as we highlight and explore the technical and methodological difculties of fusing heterogeneous signals, it seems likely that correct fusion of multimodal data will allow previously inaccessible spatiotemporal structures to be visualized and formalized and thus eventually become a useful tool in brain imaging research

Incorporation of anisotropic conductivities in EEG source analysis

The electroencephalogram (EEG) is a measurement of brain activity over a period of time by placing electrodes at the scalp (surface EEG) or in the brain (depth EEG) and is used extensively in the clinical practice. In the past 20 years, EEG source analysis has been increasingly used as a tool in the diagnosis of neurological disorders (like epilepsy) and in the research of brain functionality. EEG source analysis estimates the origin of brain activity given the electrode potentials measured at the scalp. This involves solving an inverse problem where a forward solution, which depends on the source parameters, is fitted to the given set of electrode potentials. The forward solution are the electrode potentials caused by a source in a given head model. The head model is dependent on the geometry and the conductivity. Often an isotropic conductivity (i.e. the conductivity is equal in all directions) is used, although the skull and white matter have an anisotropic conductivity (i.e. the conductivity can differ depending on the direction the current flows). In this dissertation a way to incorporate the anisotropic conductivities is presented and the effect of not incorporating these anisotropic conductivities is investigated. Spherical head models are simple head models where an analytical solution to the forward problem exists. A small simulation study in a 5 shell spherical head model was performed to investigate the estimation error due to neglecting the anisotropic properties of skull and white matter. The results show that the errors in the dipole location can be larger than 15 mm, which is unacceptable for an accurate dipole estimation in the clinical practice. Therefore, anisotropic conductivities have to be included in the head model. However, these spherical head models are not representative for the human head. Realistic head models are usually made from magnetic resonance scans through segmentation and are a better approximation to the geometry of the human head. To solve the forward problem in these head models numerical methods are needed. In this dissertation we proposed a finite difference technique that can incorporate anisotropic conductivities. Moreover, by using the reciprocity theorem the forward calculation time during an dipole source estimation procedure can be significantly reduced. By comparing the analytical solution for the dipole estimation problem with the one using the numerical method, the anisotropic finite difference with reciprocity method (AFDRM) is validated. Therefore, a cubic grid is made on the 5 shell spherical head model. The electrode potentials are obtained in the spherical head model with anisotropic conductivities by solving the forward problem using the analytical solution. Using these electrode potentials the inverse problem was solved in the spherical head model using the AFDRM. In this way we can determine the location error due to using the numerical technique. We found that the incorporation of anisotropic conductivities results in a larger location error when the head models are fully isotropical conducting. Furthermore, the location error due to the numerical technique is smaller if the cubic grid is made finer. To minimize the errors due to the numerical technique, the cubic grid should be smaller than or equal to 1 mm. Once the numerical technique is validated, a realistic head model can now be constructed. As a cubic grid should be used of at most 1 mm, the use of segmented T1 magnetic resonance images is best suited the construction. The anisotropic conductivities of skull and white matter are added as follows: The anisotropic conductivity of the skull is derived by calculating the normal and tangential direction to the skull at each voxel. The conductivity in the tangential direction was set 10 times larger than the normal direction. The conductivity of the white matter was derived using diffusion weighted magnetic resonance imaging (DW-MRI), a technique that measures the diffusion of water in several directions. As diffusion is larger along the nerve fibers, it is assumed that the conductivity along the nerve fibers is larger than the perpendicular directions to the nerve bundle. From the diffusion along each direction, the conductivity can be derived using two approaches. A simplified approach takes the direction with the largest diffusion and sets the conductivity along that direction 9 times larger than the orthogonal direction. However, by calculating the fractional anisotropy, a well-known measure indicating the degree of anisotropy, we can appreciate that a fractional anisotropy of 0.8715 is an overestimation. In reality, the fractional anisotorpy is mostly smaller and variable throughout the white matter. A realistic approach was therefore presented, which states that the conductivity tensor is a scaling of the diffusion tensor. The volume constraint is used to determine the scaling factor. A comparison between the realistic approach and the simplified approach was made. The results showed that the location error was on average 4.0 mm with a maximum of 10 mm. The orientation error was found that the orientation could range up to 60 degrees. The large orientation error was located at regions where the anisotropic ratio was low using the realistic approach but was 9 using the simplified approach. Furthermore, as the DW-MRI can also be used to measure the anisotropic diffusion in a gray matter voxel, we can derive a conductivity tensor. After investigating the errors due to neglecting these anisotropic conductivities of the gray matter, we found that the location error was very small (average dipole location error: 2.8 mm). The orientation error was ranged up to 40 degrees, although the mean was 5.0 degrees. The large errors were mostly found at the regions that had a high anisotropic ratio in the anisotropic conducting gray matter. Mostly these effects were due to missegmentation or to partial volume effects near the boundary interfaces of the gray and white matter compartment. After the incorporation of the anisotropic conductivities in the realistic head model, simulation studies can be performed to investigate the dipole estimation errors when these anisotropic conductivities of the skull and brain tissues are not taken into account. This can be done by comparing the solution to the dipole estimation problem in a head model with anisotropic conductivities with the one in a head model, where all compartments are isotropic conducting. This way we determine the error when a simplified head model is used instead of a more realistic one. When the anisotropic conductivity of both the skull and white matter or the skull only was neglected, it was found that the location error between the original and the estimated dipole was on average, 10 mm (maximum: 25 mm). When the anisotropic conductivity of the brain tissue was neglected, the location error was much smaller (an average location error of 1.1 mm). It was found that the anisotropy of the skull acts as an extra shielding of the electrical activity as opposed to an isotropic skull. Moreover, we saw that if the dipole is close to a highly anisotropic region, the potential field is changed reasonable in the near vicinity of the location of the dipole. In reality EEG contains noise contributions. These noise contribution will interact with the systematical error by neglecting anisotropic conductivities. The question we wanted to solve was “Is it worthwhile to incorporate anisotropic conductivities, even if the EEG contains noise?” and “How much noise should the EEG contain so that incorporating anisotropic conductivities improves the accuracy of EEG source analysis?”. When considering the anisotropic conductivities of the skull and brain tissues and the skull only, the location error due to the noise and neglecting the anisotropic conductivities is larger then the location error due to noise only. When only neglecting the anisotropic conductivities of the brain tissues only, the location error due to noise is similar to the location error due to noise and neglecting the anisotropic conductivities. When more advanced MR techniques can be used a better model to construct the anisotropic conductivities of the soft brain tissues can be used, which could result in larger errors even in the presence of noise. However, this is subject to further investigation. This suggests that the anisotropic conductivities of the skull should be incorporated. The technique presented in the dissertation can be used to epileptic patients in the presurgical evaluation. In this procedure patients are evaluated by means of medical investigations to determine the cause of the epileptic seizures. Afterwards, a surgical procedure can be performed to render the patient seizure free. A data set from a patiënt was obtained from a database of the Reference Center of Refractory Epilepsy of the Department of Neurology and the Department of Radiology of the Ghent University Hospital (Ghent, Belgium). The patient was monitored with a video/EEG monitoring with scalp and with implanted depth electrodes. An MR image was taken from the patient with the implanted depth electrodes, therefore, we could pinpoint the hippocampus as the onset zone of the epileptic seizures. The patient underwent a resective surgery removing the hippocampus, which rendered the patient seizure free. As DW-MRI images were not available, the head model constructed in chapter 4 and 5 was used. A neuroradiologist aligned the hippocampus in the MR image from which the head model was constructed. A spike was picked from a dataset and was used to estimate the source in a head model where all compartments were isotropic conducting, on one hand, and where the skull and brain tissues were anisotropic conducting, on the other. It was found that using the anisotropic head model, the source was estimated closer to the segmented hippocampus than the isotropic head model. This example shows the possibilities of this technique and allows us to apply it in the clinical practice. Moreover, a thorough validation of the technique has yet to be performed. There is a lot of discussion in the clinical community whether the spikes and epileptical seizures originate from the same origin in the brain. This question can be solved by applying our technique in patient studies