Sensitivity of EEG and MEG measurements to tissue conductivity

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.

[1]  B. Cuffin.  Effects of inhomogeneous regions on electric potentials and magnetic fields: Two special cases , 1982 .

[2]  The MEG topography and the source model of abnormal neural activities associated with brain lesions , 1986 .

[3]  Toshimitsu Musha,et al.  Electric Dipole Tracing in the Brain by Means of the Boundary Element Method and Its Accuracy , 1987, IEEE Transactions on Biomedical Engineering.

[4]  D C Barber,et al.  Localisation of cardiac related impedance changes in the thorax. , 1987, Clinical physics and physiological measurement : an official journal of the Hospital Physicists' Association, Deutsche Gesellschaft fur Medizinische Physik and the European Federation of Organisations for Medical Physics.

[5]  Cees J. Stok,et al.  The influence of model parameters on EEG/MEG single dipole source estimation , 1987, IEEE Transactions on Biomedical Engineering.

[6]  Onno W. Weier,et al.  On the numerical accuracy of the boundary element method (EEG application) , 1989, IEEE Transactions on Biomedical Engineering.

[7]  M. Hämäläinen,et al.  Realistic conductivity geometry model of the human head for interpretation of neuromagnetic data , 1989, IEEE Transactions on Biomedical Engineering.

[8]  C. Nicholson,et al.  Distortion of magnetic evoked fields and surface potentials by conductivity differences at boundaries in brain tissue. , 1990, Biophysical journal.

[9]  Russell M. Mersereau,et al.  Automatic detection of brain contours in MRI data sets. , 1993, IEEE transactions on medical imaging.

[10]  R. Ilmoniemi,et al.  Magnetoencephalography-theory, instrumentation, and applications to noninvasive studies of the working human brain , 1993 .

[11]  Jian-Ming Jin,et al.  The Finite Element Method in Electromagnetics , 1993 .

[12]  N G Gençer,et al.  A comparative study of several exciting magnetic fields for induced current EIT. , 1994, Physiological measurement.

[13]  W. Eric L. Grimson,et al.  Statistical intensity correction and segmentation of MRI data , 1994, Other Conferences.

[14]  Mustafa Kuzuoglu,et al.  Electrical impedance tomography using induced currents , 1994, IEEE Trans. Medical Imaging.

[15]  B. Radich,et al.  EEG dipole localization bounds and MAP algorithms for head models with parameter uncertainties , 1995, IEEE Transactions on Biomedical Engineering.

[16]  William Gropp,et al.  Efficient Management of Parallelism in Object-Oriented Numerical Software Libraries , 1997, SciTools.

[17]  Andrew J. Pullan.  A high-order coupled finite element/boundary element torso model , 1996 .

[18]  J. Haueisen,et al.  Influence of tissue resistivities on neuromagnetic fields and electric potentials studied with a finite element model of the head , 1997, IEEE Transactions on Biomedical Engineering.

[19]  R. Gulrajani.  Bioelectricity and biomagnetism , 1998 .

[20]  M. Peters,et al.  Volume conduction effects in EEG and MEG. , 1998, Electroencephalography and clinical neurophysiology.

[21]  M. Stella Atkins,et al.  Fully automatic segmentation of the brain in MRI , 1998, IEEE Transactions on Medical Imaging.

[22]  G. Huiskamp,et al.  The need for correct realistic geometry in the inverse EEG problem , 1999, IEEE Transactions on Biomedical Engineering.

[23]  J P Kaipio,et al.  Effects of local skull inhomogeneities on EEG source estimation. , 1999, Medical engineering & physics.

[24]  Nevzat G. Gencer,et al.  Electrical conductivity imaging via contactless measurements , 1999, IEEE Transactions on Medical Imaging.

[25]  Z. Akalm,et al.  Forward Problem Solution of EMSI’s with BEM Using Realistic Head Models , 2001 .

[26]  J. Gotman,et al.  Modeling of post-surgical brain and skull defects in the EEG inverse problem with the boundary element method , 2002, Clinical Neurophysiology.

[27]  R. T. Hart,et al.  Finite-element model of the human head: scalp potentials due to dipole sources , 1991, Medical and Biological Engineering and Computing.

[28]  I. Lemahieu,et al.  Dipole location errors in electroencephalogram source analysis due to volume conductor model errors , 2000, Medical and Biological Engineering and Computing.

[29]  L. Geddes,et al.  The specific resistance of biological material—A compendium of data for the biomedical engineer and physiologist , 1967, Medical and biological engineering.