This paper describes FieldTrip, an open source software package that we developed for the analysis of MEG, EEG, and other electrophysiological data. The software is implemented as a MATLAB toolbox and includes a complete set of consistent and user-friendly high-level functions that allow experimental neuroscientists to analyze experimental data. It includes algorithms for simple and advanced analysis, such as time-frequency analysis using multitapers, source reconstruction using dipoles, distributed sources and beamformers, connectivity analysis, and nonparametric statistical permutation tests at the channel and source level. The implementation as toolbox allows the user to perform elaborate and structured analyses of large data sets using the MATLAB command line and batch scripting. Furthermore, users and developers can easily extend the functionality and implement new algorithms. The modular design facilitates the reuse in other software packages.

/pdf/fieldtrip-open-source-software-for-advanced-analysis-of-meg-1cxn1l5h6y.pdf

FieldTrip: open source software for advanced analysis of MEG, EEG, and invasive electrophysiological data

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

We describe a comprehensive linear approach to the problem of imaging brain activity with high temporal as well as spatial resolution based on combining EEG and MEG data with anatomical constraints derived from MRI images. The "inverse problem" of estimating the distribution of dipole strengths over the cortical surface is highly underdetermined, even given closely spaced EEG and MEG recordings. We have obtained much better solutions to this problem by explicitly incorporating both local cortical orientation as well as spatial covariance of sources and sensors into our formulation. An explicit polygonal model of the cortical manifold is first constructed as follows: (1) slice data in three orthogonal planes of section (needle-shaped voxels) are combined with a linear deblurring technique to make a single high-resolution 3-D image (cubic voxels), (2) the image is recursively flood-filled to determine the topology of the gray-white matter border, and (3) the resulting continuous surface is refined by relaxing it against the original 3-D gray-scale image using a deformable template method, which is also used to computationally flatten the cortex for easier viewing. The explicit solution to an error minimization formulation of an optimal inverse linear operator (for a particular cortical manifold, sensor placement, noise and prior source covariance) gives rise to a compact expression that is practically computable for hundreds of sensors and thousands of sources. The inverse solution can then be weighted for a particular (averaged) event using the sensor covariance for that event. Model studies suggest that we may be able to localize multiple cortical sources with spatial resolution as good as PET with this technique, while retaining a much finer grained picture of activity over time.

Improved localizadon of cortical activity by combining eeg and meg with mri cortical surface reconstruction: A linear approach

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

Demonstration of useful differences between magnetoencephalogram and electroencephalogram

Comparison of the magnetoencephalogram and electroencephalogram

Expressions are presented for the magnetic fields produced by current dipoles in four basic volume conductor shapes. These shapes are the semi-infinite volume, the sphere, the prolate spheroid (egg-shape), and the oblate spheroid (discus-shape). The latter three shapes approximate the shape of the human head and can serve as a basis for understanding the measurements of the brain's magnetic fields. The semi-infinite volume is included in order to investigate the effect of the simplest boundary between a conductor and nonconductor. The expressions for the fields are presented in a form which separates the total field into two parts. One part is due to the dipole alone (the dipole field); the other is due to the current generated in the volume conductor by the dipole (the volume current field). Representative plots of the total field and the volume current field are presented for each shape. The results show that for these shapes the component of the total field normal to the surface of the volume conductor is produced completely or in large part by the dipole alone. Therefore, measurement and use of this component will greatly reduce the complexity of determining the sources of electrical activity inside a body from measurements outside the body by removing the necessity of dealing with the volume current field.

Magnetic Fields of a Dipole in Special Volume Conductor Shapes

Moving dipole inverse solutions provide a very useful method of estimating the location of an electrical source in the brain from EEG's or MEG's measured at the surface of the head. In this method, a dipolar source model is moved about in a model of the head while its amplitude and orientation are also adjusted to obtain the least-squares error fit between the measured EEG's or MEG's and those produced by the dipolar source.

A Comparison of Moving Dipole Inverse Solutions Using EEG's and MEG's

Several aspects of the forward and inverse problems of electrocardiography are investigated through the use of digital computer models. Two forms of a fixed location, variable moment, 20-dipole cardiac model of QRS are developed from actual cardiac excitation data. One form uses time-varying orientation dipoles; the other uses fixed orientation dipoles. An electric multipole expansion (EME) cardiac model employing the dipole, quadrupole, and octupole terms is also developed and used as an equivalent forward and inverse cardiac model. Two realistically shaped torso models are used. The homogeneous torso has uniform conductivity; the inhomogeneous torso contains realistically shaped lung regions with reduced conductivity. It is found that when the EME model is used as an equivalent forward cardiac model, it can accurately represent the actual 20-dipole cardiac model in the homogeneous torso. Limb leads are accurately represented by the dipole terms alone while the precordial leads require the quadrupole and octupole terms. It is also found that while the lung regions have little effect on the ECG's produced by the models, these regions can have a significant effect on the inverse solutions for certain dipoles in the 20-dipole cardiac model. These lung regions appear to have a much smaller effect on the dipole terms in the EME model. Solutions of the inverse problem for the terms in the EME model indicate that when a limited number of measurements are used, the best results can be obtained by uniform distribution of the measurements over the torso.

B. Neil Cuffin

Papers

Demonstration of useful differences between magnetoencephalogram and electroencephalogram

Comparison of the magnetoencephalogram and electroencephalogram

Magnetic Fields of a Dipole in Special Volume Conductor Shapes

A Comparison of Moving Dipole Inverse Solutions Using EEG's and MEG's

Studies of the Electrocardiogram Using Realistic Cardiac and Torso Models