Jukka Sarvas

Realistic conductivity geometry model of the human head for interpretation of neuromagnetic data

The computational and practical aspects of a realistically shaped multilayer model for the conductivity geometry of the human head are discussed. A method to handle the numerical difficulties caused by the presence of poorly conducting skull is presented. Using the method, both the potential on the surface of the head and the magnetic field outside the head can be computed accurately. The procedure is tested with the multilayer sphere model, for which analytical expressions are available. The method is then applied to a realistically shaped head model, and it is shown numerically that for the computation of B produced by cerebral current sources, it is sufficient to consider a brain-shaped homogeneous conductor only, since the secondary currents on the outer interfaces give only a negligible contribution to the magnetic field outside the head. Comparisons with the sphere model are included to pinpoint areas where the homogeneous conductor model provides essential improvements in the calculation of the magnetic field outside the head.<<ETX>>

Surface Integral Equation Method for General Composite Metallic and Dielectric Structures with Junctions

The surface integral equation method is applied for the electromagnetic analysis of general metallic and dielectric structures of arbitrary shape. The method is based on the EFIE-CFIE-PMCHWT integral equation formulation with Galerkins type discretization. The numerical implementation is divided into three independent steps: First,the electric and magnetic field integral equations are presented and discretized individually in each non-metallic subdomain with the RWG basis and testing functions. Next the linearly dependent and zero unknowns are removed from the discretized system by enforcing the electromagnetic boundary conditions on interfaces and at junctions. Finally,the extra equations are removed by applying the wanted integral equation formulation,and the reduced system is solved. The division into these three steps has two advantages. Firstly,it greatly simplifies the treatment of composite objects with multiple metallic and dielectric regions and junctions since the boundary conditions are separated from the discretization and integral equation formulation. In particular,no special junction basis functions or special testing procedures at junctions are needed. Secondly,the separation of the integral equation formulation from the two previous steps makes it easy to modify the procedure for other formulations. The method is validated by numerical examples.

Feasibility of the homogeneous head model in the interpretation of neuromagnetic fields

During the past few years it has been demonstrated that active areas in the human brain can be located by measuring the magnetic fields arising from the electric currents in the neurons. An established model for the conductivity geometry of the head in these studies is the layerwise homogeneous sphere. If, however, the measurement grid is too large or the local radius of curvature of the head is changing rapidly in the measurement area, this simple model may become inadequate. In this paper we investigate the feasibility of replacing the conducting sphere by a homogeneous body having the shape of the brain. We show by a semi-quantitative argument that the homogeneous body model is justified. A numerical procedure for the calculation of the magnetic field is presented with examples of the accuracy that can be obtained. An example of significant differences between the predictions of the homogeneous and sphere models is discussed.

Removal of large muscle artifacts from transcranial magnetic stimulation-evoked EEG by independent component analysis

We present two techniques utilizing independent component analysis (ICA) to remove large muscle artifacts from transcranial magnetic stimulation (TMS)-evoked EEG signals. The first one is a novel semi-automatic technique, called enhanced deflation method (EDM). EDM is a modification of the deflation mode of the FastICA algorithm; with an enhanced independent component search, EDM is an effective tool for removing the large, spiky muscle artifacts. The second technique, called manual method (MaM) makes use of the symmetric mode of FastICA and the artifactual components are visually selected by the user. In order to evaluate the success of the artifact removal methods, four different quality parameters, based on curve comparison and frequency analysis, were studied. The dorsal premotor cortex (dPMC) and Broca’s area (BA) were stimulated with TMS. Both methods removed the very large muscle artifacts recorded after stimulation of these brain areas. However, EDM was more stable, less subjective, and thus also faster to use than MaM. Until now, examining lateral areas of the cortex with TMS—EEG has been restricted because of strong muscle artifacts. The methods described here can remove those muscle artifacts, allowing one to study lateral areas of the human brain, e.g., BA, with TMS—EEG.

SINGULARITY SUBTRACTION INTEGRAL FORMULAE FOR SURFACE INTEGRAL EQUATIONS WITH RWG, ROOFTOP AND HYBRID BASIS FUNCTIONS

Numerical solution of electromagnetic scattering problems by the surface integral methods leads to numerical integration of singular integrals in the Method of Moments. The heavy numerical cost of a straightforward numerical treatment of these integrals can be avoided by a more efficient and accurate approach based on the singularity subtraction method. In the literature the information of the closed form integral formulae required by the singularity subtraction method is quite fragmented. In this paper we give a uniform presentation of the singularity subtraction method for planar surface elements with RWG, ˆ n×RWG, rooftop, and ˆ n×rooftop basis functions, the latter three cases being novel applications. We also discuss the hybrid use of these functions. The singularity subtraction formulas are derived recursively and can be used to subtract more than one term in the Taylor series of the Greens function.

TRANSLATION PROCEDURES FOR BROADBAND MLFMA

The multilevel fast multipole algorithm (MLFMA) is used in computing acoustic and electromagnetic fields with integral equation methods. The traditional MLFMA, however, suffers from a lowfrequency breakdown that effectively limits the minimum division cube side length to approximately one wavelength. To overcome this low-frequency breakdown and get a broadband MLFMA, we propose an efficient and relatively straightforward implementation of the field translations based on the spectral representation of the Green’s function. As an alternative we also consider the so called uniform MLFMA, which has a lower computational cost but limited accuracy. We consider the essential implementation details and finally provide numerical examples to demonstrate the error controllability of the translations.

Performing Interpolation and Anterpolation Entirely by Fast Fourier Transform in the 3-D Multilevel Fast Multipole Algorithm

The fast multipole methods are used for solving a scalar acoustic or vector electromagnetic wave equation by integral equation methods with a large number of unknowns. In this paper a new method is presented for performing interpolation and anterpolation in both spherical coordinates

Bioelectromagnetic forward problem: isolated source approach revis(it)ed

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Uncovering neural independent components from highly artifactual TMS-evoked EEG data

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The Spatial and Temporal Distortion of Magnetic Fields Applied Inside a Magnetically Shielded Room

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