We calculated the magnetic field from the current moments based on the Sarvas formula in the forward problem. Similarly, we will estimate the current moments from the measured magnetic field based on the lead field matrix (LFM) in the inverse problem. The solutions of the inverse problem can be broadly classified as overdetermined or underdetermined system depending on the number of the current moments.
The representative overdetermined solution is the single-current dipole estimation, which has been used as the standard method for estimating epileptic foci and somatosensory evoked magnetic fields in clinical practice [1].
Underdetermined system is variously called as spatial filters, beamformers, distributed models, reconstructions, virtual sensors, etc. The system also has various solutions depending on various methods, but the adaptive beamformer has been preferred for fundamental research in recent years [2]. Authors sometimes use different names depending on the solutions, so it is safe to check the reference when reading articles.
Let us begin the discussion of the inverse problem in the next section.
(References)
- E Kaukoranta, M Hämäläinen, J Sarvas, R Hari: Mixed and sensory nerve stimulations activate different cytoarchitectonic areas in the human primary somatosensory cortex SI. Neuromagnetic recordings and statistical considerations. Exp Brain Res. 1986;63(1):60-6.
- K Sekihara, SS Nagarajan, D Poeppel, A Marantz, Y Miyashita: Reconstructing spatio-temporal activities of neural sources using an MEG vector beamformer technique. IEEE Trans Biomed Eng. 2001 Jul;48(7):760-71.