title: Magnetic source imaging based on the minimum-norm least-squares inverse.
abstract: The flow of ionic currents within the neurons of cerebral cortex produces a magnetic field that can be detected outside the human scalp. The dominant contribution is attributed to pyramidal cells, which are preferentially oriented perpendicular to the cortical surface. In general, it is not possible to deduce a unique representation of the spatial configuration of these cortical sources from a measurement of their field pattern alone. However, accurate a priori knowledge of the geometry of the underlying cerebral cortex makes it possible to infer the spatial configuration of these transcortical current sources, moment by moment, without imposing a simplified model such as a small set of current dipoles. To achieve such a realistic magnetic source image, we have introduced what we call the "Minimum-Norm Least-Squares Inverse" (MNLS inverse) for the magnetic problem. The MNLS inverse provides the least residual error in accounting for the measured field pattern, with a source current distribution having minimum power. An extension of this procedure provides an inverse solution for average field power, as opposed to field per se. This makes it possible to define spatial configurations of spontaneous cortical activity not phase-locked to a sensory stimulus. Rhythmic activity such as the occipital alpha rhythm is one example. Thus, it is possible to determine spatial patterns of enhanced or suppressed cortical rhythms that accompany cognitive processes and some pathological conditions. This paper provides the necessary background for understanding these recent developments, as well as examples of how they might be used.
authors.affiliation: Department of Physics, New York University, NY 10003.
authors.forename: J Z
authors.initials: JZ
authors.lastname: Wang
authors.forename: S J
authors.initials: SJ
authors.lastname: Williamson
authors.forename: L
authors.initials: L
authors.lastname: Kaufman
mesh_terms: D001921:Brain / Q000502:physiology*; D001931:Brain Mapping / Q000379:methods; D006801:Humans; D008280:Magnetics; D015225:Magnetoencephalography; D008959:Models, Neurological