Application of modified simplex method to biomagnetic inverse problem

Difficulty in determination of source brain activities for observed biomagnetic signals (magnetoencephalograms, MEGs) is known as the biomagnetic inverse problem. Moving Dipole Method [1] has been developed for solution of this problem. Two difficulties have been pointed out for this approach. The first problem is that the number of sources must be known before the analysis. However, it is difficult to fix the number of sources for the brain activities which change from time to time. The second problem arises for the case of a relatively large source. The estimated location of the source tended to deviate from that of the real source [2]. We have developed a new algorithm, called Moving Mesh Method (MMM) [3][4] in order to overcome these problems. One of the difficulties in MMM was that it required a large number of iterative calculations. It was also difficult to find good initial conditions for iterative calculations. The first problem was solved by introducing the modified Simplex Method (SM) [5] where the dipoles were assumed at vertexes of tetrahedrons which can be transformed so that it gives the best goodness of fit (GOF) (see Flowchart). We solved the second problem by introducing Singularity Search Method (SSM) [6] to locate dipoles responsible for the radial components of magnetic fields observed on imaginary spheres as singularity points of an indicator function given by a product of the sphere radius and the radial magnetic component. At the same time, the number n of dipoles was assumed by comparing the moment of estimated dipoles (see phantom experiments). The feasibility of the new algorithm was tested in phantom experiments where magnetic signals were generated by current electrodes and the estimates of magnetic sources determined by MMM for the magnetic signals were compared with the real ones, and also in MEG experiments where somatosensory evoked fields (SEFs), the auditory evoked fields (AEFs) and the epileptic fields were analyzed. 2 Methods