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.

/pdf/magnetoencephalography-theory-instrumentation-and-1oezfk882m.pdf

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

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

t. This paper surveys some of the work our group has done in electrical impedance tomography.

Electrical Impedance Tomography

There has been tremendous advances in our ability to produce images of human brain function. Applications of functional brain imaging extend from improving our understanding of the basic mechanisms of cognitive processes to better characterization of pathologies that impair normal function. Magnetoencephalography (MEG) and electroencephalography (EEG) (MEG/EEG) localize neural electrical activity using noninvasive measurements of external electromagnetic signals. Among the available functional imaging techniques, MEG and EEG uniquely have temporal resolutions below 100 ms. This temporal precision allows us to explore the timing of basic neural processes at the level of cell assemblies. MEG/EEG source localization draws on a wide range of signal processing techniques including digital filtering, three-dimensional image analysis, array signal processing, image modeling and reconstruction, and, blind source separation and phase synchrony estimation. We describe the underlying models currently used in MEG/EEG source estimation and describe the various signal processing steps required to compute these sources. In particular we describe methods for computing the forward fields for known source distributions and parametric and imaging-based approaches to the inverse problem.

Electromagnetic brain mapping

The discontinuous nature of propagation in normal canine cardiac muscle. Evidence for recurrent discontinuities of intracellular resistance that affect the membrane currents.

The change in mutual impedance ?Z resulting from a change ?g in the conductivity of a particular region of a volume conductor is shown to be given by ?Z = - ?g?Lt?·L? dv. L? and L? are the lead fields associated with the two ports used to measure ?Z. The integration is over the region where the conductivity has changed. The superscript t indicates that the lead field is to be evaluated following the change in conductivity. An example involving a spherical conductor is provided.

An Application of Electrocardiographic Lead Theory to Impedance Plethysmography

A digital computer model is presented for the simulation of the body surface electrocardiogram (ECG) during ventricular activation and recovery. The ventricles of the heart are represented in detail by a three-dimensional array of approximately 4000 points which is subdivided into 23 regions. Excitation sequence and cellular action potential data taken from the literature are used to determine the spatial distribution of intracellular potentials at each instant of time during a simulated cardiac cycle. The moment of the single dipole representing each region is determined by summing the spatial gradient of the intracellular potential distribution throughout the region. The resulting set of 23 dipoles is then used to calculate the potentials on the surface of a bounded homogeneous volume conductor with the shape of an adult torso. Simulated isopotential surface maps during both activation and recovery are in good agreement with data for humans reported in the literature.

Simulation studies of the electrocardiogram. I. The normal heart.

On bioelectric potentials in an inhomogeneous volume conductor.

The magnetocardiogram results from the detection of magnetic fields generated outside the body by electric current sources in the heart. Let the source current dipole moment per unit volume be Ji, the conductivity g , the electric potential V , and the electric field intensity E . Then it may be shown that the magnetic field H is given by either H = (1/4\pi) \int J^{i} \times \nabla(1/r) dv + \sum_{i} \int (g' - g")(E \times dS_{i}/r) , or H = (1/4\pi) \int J^{i} \times \nabla(1/r) dv + \sum_{i} \int (g' - g")V\nabla(1/r) \times dS_{i} , where the surface integral is over all surfaces S i separating regions of different conductivity, i.e., g ' and g ", and r is the distance from the point of measurement to the element of volume or surface. The magnetic dipole moment m is given by m = \frac{1}{2} \int r_{1} \times J^{i}dv - \frac{1}{2} \sum_{i} \int (g'-g")Vr_{1} \times dS_{i} , where r 1 is a radius vector from an arbitrary origin.

David B. Geselowitz

Papers

The discontinuous nature of propagation in normal canine cardiac muscle. Evidence for recurrent discontinuities of intracellular resistance that affect the membrane currents.

An Application of Electrocardiographic Lead Theory to Impedance Plethysmography

Simulation studies of the electrocardiogram. I. The normal heart.

On bioelectric potentials in an inhomogeneous volume conductor.

On the magnetic field generated outside an inhomogeneous volume conductor by internal current sources