Magnetoencephalography (MEG) is a noninvasive technique for investigating neuronal activity in the living human brain. The time resolution of the method is better than 1 ms and the spatial discrimination is, under favorable circumstances, 2-3 mm for sources in the cerebral cortex. In MEG studies, the weak 10 fT-1 pT magnetic fields produced by electric currents flowing in neurons are measured with multichannel SQUID (superconducting quantum interference device) gradiometers. The sites in the cerebral cortex that are activated by a stimulus can be found from the detected magnetic-field distribution, provided that appropriate assumptions about the source render the solution of the inverse problem unique. Many interesting properties of the working human brain can be studied, including spontaneous activity and signal processing following external stimuli. For clinical purposes, determination of the locations of epileptic foci is of interest. The authors begin with a general introduction and a short discussion of the neural basis of MEG. The mathematical theory of the method is then explained in detail, followed by a thorough description of MEG instrumentation, data analysis, and practical construction of multi-SQUID devices. Finally, several MEG experiments performed in the authors' laboratory are described, covering studies of evoked responses and of spontaneous activity in both healthy and diseased brains. Many MEG studies by other groups are discussed briefly as well.

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Magnetoencephalography—theory, instrumentation, and applications to noninvasive studies of the working human brain

This paper reviews the literature on the Nl wave of the human auditory evoked potential. It concludes that at least six different cerebral processes can contribute to (he negative wave recorded from the scalp with a peak latency between 50 and 150 ms: a component generated in the auditory-cortex on the supratemporal plane, a component generated in the association cortex on the lateral aspect of the temporal and parietal cortex, a component generated in the motor and premotor cortices, the mismatch negativity, a temporal component of the processing negativity, and a frontal component of the processing negativity, The first three, which can be considered ‘true’ N1 components, are controlled by the physical and temporal aspects of the stimulus and by the general state of the subject. The other three components are not necessarily elicited by a stimulus but depend on the conditions in which the stimulus occurs. They often last much longer than the true N1 components that they overlap.

The N1 wave of the human electric and magnetic response to sound: a review and an analysis of the component structure

Low resolution electromagnetic tomography: a new method for localizing electrical activity in the brain.

In this paper basic mathematical and physical concepts of the biomagnetic inverse problem are reviewed with some new approaches. The forward problem is discussed for both homogeneous and inhomogeneous media. Geselowitz' formulae and a surface integral equation are presented to handle a piecewise homogeneous conductor. The special cases of a spherically symmetric conductor and a horizontally layered medium are discussed in detail. The non-uniqueness of the solution of the magnetic inverse problem is discussed and the difficulty caused by the contribution of the electric potential to the magnetic field outside the conductor is studied. As practical methods of solving the inverse problem, a weighted least-squares search with confidence limits and the method of minimum norm estimate are discussed.

https://iopscience.iop.org/article/10.1088/0031-9155/32/1/004/pdf

Basic mathematical and electromagnetic concepts of the biomagnetic inverse problem

The authors have applied estimation theory to the problem of determining primary current distributions from measured neuromagnetic fields. In this procedure, essentially nothing is assumed about the source currents, except that they are spatially restricted to a certain region. Simulation experiments show that the results can describe the structure of the current flow fairly well. By increasing the number of measurements, the estimate can be made more localised. The current distributions may be also used as an interpolation and an extrapolation for the measured field patterns.

Interpreting magnetic fields of the brain: minimum norm estimates

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. >

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

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.

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

Spatial resolution of neuromagnetic records: theoretical calculations in a spherical model.

Magnetic responses evoked by stimulation of the mixed median nerve at the wrist and its cutaneous branches on the glabrous skin of the index and middle fingers were studied. The first responses to mixed nerve stimulation peaked at 19-24 ms, and those to cutaneous nerve stimulation about 4 ms later. The responses, up to a latency of 150 ms, reversed in polarity between the upper and lower parts of the rolandic fissure. Equivalent dipoles for the mixed nerve stimulation were stronger and they lay statistically significantly deeper from the scalp than those activated by the cutaneous nerve stimulation. It is suggested that mixed nerve stimulation activates areas 3a and 3b whereas cutaneous stimulation activates mainly area 3b at the human primary somatosensory cortex. Statistical procedures were developed for comparison of different field patterns and for determining confidence limits of source model parameters. For these purposes the quality and quantity of the noise were studied. The error caused by inaccuracies in the positioning of the magnetometer was found to be minimal in comparison with the signal noise which was estimated from the standard deviation of the averaged response.

Mixed and sensory nerve stimulations activate different cytoarchitectonic areas in the human primary somatosensory cortex SI. Neuromagnetic recordings and statistical considerations.

Jukka Sarvas

Papers

Basic mathematical and electromagnetic concepts of the biomagnetic inverse problem

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

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

Spatial resolution of neuromagnetic records: theoretical calculations in a spherical model.

Mixed and sensory nerve stimulations activate different cytoarchitectonic areas in the human primary somatosensory cortex SI. Neuromagnetic recordings and statistical considerations.