A new finite element formulation for the forward problem of electro-magnetic source imaging

Özdemir, Mustafa; Gençer, N.G.

doi:10.1109/iembs.1997.758767

Cited by 3 publications

(2 citation statements)

References 14 publications

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“…The elements can have various shapes (tetrahedral or hexahedral), allowing the use of an irregular grid. In this study, a FEM formulation with linear and quadratic hexahedral isoparametric elements is used ( Özdemir andGençer 1997, Gençer et al 2003). This formulation defines the source as a constant volume current density inside the elements.…”

Section: Numerical Solution Of Potentials and Magnetic Fieldsmentioning

confidence: 99%

Sensitivity of EEG and MEG measurements to tissue conductivity

Gençer

Acar

2004

Phys. Med. Biol.

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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.

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Section: Numerical Solution Of Potentials and Magnetic Fieldsmentioning

confidence: 99%

Sensitivity of EEG and MEG measurements to tissue conductivity

Gençer

Acar

2004

Phys. Med. Biol.

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“…The model is based on the concentric three-spheres model with an additional inhomogeneity intersecting the outer-skull layer to model a single eye. Since an analytical solution is not possible for such a head geometry, the numerical solutions are compared with the results obtained by FEM ( Özdemir and Genc ¸er 1997, Acar and Genc ¸er 1999, Genc ¸er et al 2003.…”

Section: Validation Of the Intersecting Meshesmentioning

confidence: 99%

An advanced boundary element method (BEM) implementation for the forward problem of electromagnetic source imaging

Akalin-Acar

Gençer

2004

Phys. Med. Biol.

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The forward problem of electromagnetic source imaging has two components: a numerical model to solve the related integral equations and a model of the head geometry. This study is on the boundary element method (BEM) implementation for numerical solutions and realistic head modelling. The use of second-order (quadratic) isoparametric elements and the recursive integration technique increase the accuracy in the solutions. Two new formulations are developed for the calculation of the transfer matrices to obtain the potential and magnetic field patterns using realistic head models. The formulations incorporate the use of the isolated problem approach for increased accuracy in solutions. If a personal computer is used for computations, each transfer matrix is calculated in 2.2 h. After this pre-computation period, solutions for arbitrary source configurations can be obtained in milliseconds for a realistic head model. A hybrid algorithm that uses snakes, morphological operations, region growing and thresholding is used for segmentation. The scalp, skull, grey matter, white matter and eyes are segmented from the multimodal magnetic resonance images and meshes for the corresponding surfaces are created. A mesh generation algorithm is developed for modelling the intersecting tissue compartments, such as eyes. To obtain more accurate results quadratic elements are used in the realistic meshes. The resultant BEM implementation provides more accurate forward problem solutions and more efficient calculations. Thus it can be the firm basis of the future inverse problem solutions.

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Forward problem solution of ESI using FEM and BEM with quadratic isoparametric elements

Acar

Gençer²

Proceedings of the First Joint BMES/EMBS Conference. 1999 IEEE Engineering in Medicine and Biology 21st Annual Conference and T

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A new finite element formulation for the forward problem of electro-magnetic source imaging

Cited by 3 publications

References 14 publications

Sensitivity of EEG and MEG measurements to tissue conductivity

Sensitivity of EEG and MEG measurements to tissue conductivity

An advanced boundary element method (BEM) implementation for the forward problem of electromagnetic source imaging

Forward problem solution of ESI using FEM and BEM with quadratic isoparametric elements

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