Estimation errors of single dipole model applied to twin dipole activity: Computer simulation study

Various methods have been proposed to solve magnetoencephalographic inverse problems although the problem itself is ill-posed and in principle infinite number of solutions are possible. Among them, the simplest method is the single dipole in a spherical head model, which has been practically used in a lot of papers to get the dipoles activated by the sensory and cognitive tasks. However, if the number of active locations in the brain is more than one, for example two closely located dipoles, this simplest single dipole solution brings an error in location and moment. This error seems to be larger when the distance of the two dipoles is smaller, when the dipole current orientations are parallel or antiparallel, and when the dipole current strengths are equal. Lütkenhöner discussed the separability of two dipoles [1]. In his paper, by simulating localization of a single dipole from the magnetic fields produced by two dipoles with various relationships including the distances and moments, he showed the separability of two dipoles in terms of necessity of introducing multiple dipole solution. In his simulation, he employed all channels of the 296-channel planar type whole-head virtual measurement system to localize a single dipole from the magnetic fields produced by two dipoles. However, if we localize a single dipole using several local channels of a whole-head measurement system that detected the magnetic fields produced by two dipoles, we are able to localize two separated dipoles under some conditions, namely when the two dipoles have some relationships of distance and moment. This is often observed when localizing the auditory N100m dipoles in the left and right hemispheres. Moreover, this localization with several locally selected channels is employed in most of experiments using a partial-head measurement system. Those who are using the partial-head measurement system to record the magnetic fields are implicitly selecting the local channels when they place the channel array over some part of the head for the measurement. When localizing multiple dipole activity by a single dipole method, this local-channel selection method has an advantage over the all-channel selection method. We can get more precise localization of the first dipole by selecting local channels that receive stronger magnetic signals from the first dipole and weaker signals from the second dipole as shown in Fig. 1.