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Physica is an integrated software package designed as part of a course for distance learning students from non-traditional educational backgrounds. It gives students access to an extensive hyperlinked physics glossary, computer algebra and graph-plotting tools. The package aims to give students a framework for solving physics problems and to help them acquire some higher level skills of quantitative problem-solving. This paper outlines rationales underlying various protocols for solving physics problems, and discusses the extent to which frameworks may be useful in helping students develop appropriate strategies for representing problems in formal terms, selecting targets, planning solutions and checking answers. Pedagogical issues underlying the design and implementation of the software are discussed.

A general method for obtaining continuous solutions to the biomagnetic inverse problem was first presented during the 1989 Biomagnetism conference. From the outset, the method was developed for three-dimensional source spaces [1, 2] but, partly to reduce computational demands and partly for ease of presentation, the first major publication of the method [3] used two-dimensional reconstructions. Soon afterwards the algorithms were ported to a transputer, making possible the analysis of large sets of MEG data. The output (estimates of the primary current density in a three-dimensional source space) was displayed by taking slices (tomes) through the source space leading to a series of MFT (Magnetic Field Tomographie) images. Later forms of representation included time integrals and activation curves, describing the evolution of activity within specified Regions of Interest (ROI). Animations run on the transputer array and recorded on video, were by far the most effective presentation tool, showing in colour-coded form the changes in the activity against a background of coregistered MRI slices[4]. Early reconstructions used averaged data but the emphasis has recently shifted to analysis of single trial or continuous data [5, 6]. Each three-dimensional study was underpinned by thorough tests with Computer generated data which, however, have been only superficially reported because of space limitations. We have previously described our philosophy and method [3], the transputer based implementation [7] and the logic in the various algorithmic steps [8]. However, the lack of published material on the background tests must be the cause of misrepresentations of MFT in some recent publications dealing with distributed source analysis, e.g. [9]. The present paper makes good this omission and uses computer-generated data to illustrate the power and limitations of MFT as a 3D imaging method, using realistic sensor configurations and signals that are neurophysiologically realistic in terms of location and temporal characteristics.

A method of analysing biomagnetic signals is presented which focuses attention on activity in a specific region of interest. The method is based on the construction of virtual sensors, corresponding to linear combinations of lead fields that are optimally localized within the region of interest. This method is fast and stable. It is tested against physiologically plausible computer generated signals and also against more elaborate analysis of real data. The results show that the method can be very effective as a fast scanning tool identifying activity from pre-defined regions of interest.

Until recently, equivalent current dipole sources have been used almost universally to describe the biomagnetic signals generated by ionic currents in conducting body tissues but, as the performance of multichannel systems improves, clinical applications will emerge which require PET-like pictures demonstrating increased activity (or the absence of activity) in relation to normal background levels. A vital step in this direction is the development of a reliable, efficient and mathematically well-founded method of studying continuous source densities. A number of attempts to treat biomagnetic data in a model-independent way have been reported [1,2,3,4]Starting from maximum entropy arguments [5] we have developed a very general method of inversion. In a certain limit, our method reduces to that of reference [1] but, in general, it is more powerful in its ability to take account of prior information about the source space and the noise spectrum of the magnetometers. It is implemented within a comprehensive computing environment that can deal with a wide range of experimental geometries and accommodate discrete or continuous sources, including both ionic flows and magnetic dipoles. In this paper we provide an outline of the method and computing environment and we discuss two simple examples. A more detailed description of the method will be given elsewhere, but its application to 3D inversions and the analysis of real MEG data is given in the next paper [6].