Monitoring the electrical activity inside the human brain using electrical and magnetic field measurements requires a mathematical head model. Using this model the potential distribution in the head and magnetic fields outside the head are computed for a given source distribution. This is called the forward problem of the electro-magnetic source imaging. Accurate representation of the source distribution requires a realistic geometry and an accurate conductivity model. Deviation from the actual head is one of the reasons for the localization errors. In this study, the mathematical basis for the sensitivity of voltage and magnetic field measurements to perturbations from the actual conductivity model is investigated. Two mathematical expressions are derived relating the changes in the potentials and magnetic fields to conductivity perturbations. These equations show that measurements change due to secondary sources at the perturbation points. A finite element method (FEM) based formulation is developed for computing the sensitivity of measurements to tissue conductivities efficiently. The sensitivity matrices are calculated for both a concentric spheres model of the head and a realistic head model. The rows of the sensitivity matrix show that the sensitivity of a voltage measurement is greater to conductivity perturbations on the brain tissue in the vicinity of the dipole, the skull and the scalp beneath the electrodes. The sensitivity values for perturbations in the skull and brain conductivity are comparable and they are, in general, greater than the sensitivity for the scalp conductivity. The effects of the perturbations on the skull are more pronounced for shallow dipoles, whereas, for deep dipoles, the measurements are more sensitive to the conductivity of the brain tissue near the dipole. The magnetic measurements are found to be more sensitive to perturbations near the dipole location. The sensitivity to perturbations in the brain tissue is much greater when the primary source is tangential and it decreases as the dipole depth increases. The resultant linear system of equations can be used to update the initially assumed conductivity distribution for the head. They may be further exploited to image the conductivity distribution of the head from EEG and/or MEG measurements. This may be a fast and promising new imaging modality.

Accurate electroencephalographic (EEG) source localization requires an electrical head model incorporating accurate geometries and conductivity values for the major head tissues. While consistent conductivity values have been reported for scalp, brain, and cerebrospinal fluid, measured brain-to-skull conductivity ratio (BSCR) estimates have varied between 8 and 80, likely reflecting both inter-subject and measurement method differences. In simulations, mis-estimation of skull conductivity can produce source localization errors as large as 3 cm. Here, we describe an iterative gradient-based approach to Simultaneous tissue Conductivity And source Location Estimation (SCALE). The scalp projection maps used by SCALE are obtained from near-dipolar effective EEG sources found by adequate independent component analysis (ICA) decomposition of sufficient high-density EEG data. We applied SCALE to simulated scalp projections of 15 cm2-scale cortical patch sources in an MR image-based electrical head model with simulated BSCR of 30. Initialized either with a BSCR of 80 or 20, SCALE estimated BSCR as 32.6. In Adaptive Mixture ICA (AMICA) decompositions of (45-min, 128-channel) EEG data from two young adults we identified sets of 13 independent components having near-dipolar scalp maps compatible with a single cortical source patch. Again initialized with either BSCR 80 or 25, SCALE gave BSCR estimates of 34 and 54 for the two subjects respectively. The ability to accurately estimate skull conductivity non-invasively from any well-recorded EEG data in combination with a stable and non-invasively acquired MR imaging-derived electrical head model could remove a critical barrier to using EEG as a sub-cm2-scale accurate 3-D functional cortical imaging modality.

Boundary element method (BEM) is one of the numerical methods which is commonly used to solve the forward problem (FP) of electro-magnetic source imaging with realistic head geometries. Application of BEM generates large systems of linear equations with dense matrices. Generation and solution of these matrix equations are time and memory consuming. This study presents a relatively cheap and effective solution for parallel implementation of the BEM to reduce the processing times to clinically acceptable values. This is achieved using a parallel cluster of personal computers on a local area network. We used eight workstations and implemented a parallel version of the accelerated BEM approach that distributes the computation and the BEM matrix efficiently to the processors. The performance of the solver is evaluated in terms of the CPU operations and memory usage for different number of processors. Once the transfer matrix is computed, for a 12,294 node mesh, a single FP solution takes 676 ms on a single processor and 72 ms on eight processors. It was observed that workstation clusters are cost effective tools for solving the complex BEM models in a clinically acceptable time.

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Abstract-In this work, a methodology is developed to solve the forward problem of electromagnetic source imaging using realistic head models. For this purpose, first segmentation of the 3 dimensional MR head images is performed. Then triangular, quadratic meshes are formed for the interfaces of the tissues. Thus, realistic meshes, representing scalp, skull, CSF, brain and eye tissues, are formed. At least 2000 nodes for the scalp and 5000 for the cortex are needed to obtain reasonable geometrical approximation. Solution of the forward problem using our previous Boundary Element Method (BEM) formulation with quadratic elements remains to be made.Keywords -BEM, realistic head model, segmentation, mesh generation. I. INTRODUCTIONElectrical activities of the human brain due to body functions can be measured with electrodes placed on the scalp (EEG) and with magnetic sensors (MEG) placed near the scalp surface. The representation of electrical activity of the brain using electrical and magnetic measurements is called electromagnetic source imaging (EMSI). The source of an electrical activity is usually modeled by electrical dipoles and the purpose of EMSI is to obtain information about the spatiotemporal behavior of these dipoles. An essential part of obtaining EMSIs is the solution of the electric and magnetic fields (the forward problem) for a given dipoleassuming a head model. The solution of the inverse problem (i.e., given the measured data, finding the location and direction of dipoles) is based on the comparison of the measured and calculated fields. To increase accuracy in EMSIs, the human head must be modeled accurately. The purpose of this study is twofold: 1) to obtain an accurate head model, 2) to solve the forward problem of EMSI for this model.In the earliest studies, head models with simple geometries having analytical solutions for a dipole inside the conductor model were used. The simplest head model is the homogeneous sphere. Other homogenous head models that may represent the head shape are prolate spheroid (eggshape). In order to represent layers like skull, scalp and cerebrospinal fluid (CSF), concentric and eccentric spheres models were used. Such models also have analytical solutions for a dipole inside conductor model [1]. . Thereafter a coarsening algorithm is used to represent the tissues with less number of triangles [7]. Finally, the resulting mesh is corrected topologically [8]. Up to this step linear elements are used. After obtaining the coarse mesh, the elements are converted to quadratic elements using the original segmentation data.In this study, the segmentation and mesh generation algorithms are explained. Meshes created for cortex, white matter, scalp and skull meshes are presented. The BEM formulation [9] which employs triangular, quadratic, isoparametric elements will be used to solve the forward problem of EMSI. II. SEGMENTATIONSegmentation is a process of classifying elements having the same properties in one group. In this work, segmentation of scalp, skull, CSF, eyes, gray m...