A Full Wave Solution of Deep Sources in the Lossy Human Head to Accurate EEG and MEG

In this paper, by using the electromagnetic modeling of the neuron activity and human head, its electric and magnetic fields (brain waves) have been derived in the full-wave approach (i.e. without any approximation). Traditionally ˗and of course currently˗ the brain waves are only derived by using the quasi-static approximation (QSA) of Maxwell's equations in electromagnetic theory and therefore, source localization in brain imaging will have some errors. So far, the error rate of the QSA on the output results of electric and magnetic fields has not been investigated. This issue becomes more noticeable due to increased sensitivity of recent modern electroencephalography (EEG) and magnetoencephalography (MEG) devices. In this work, first, issues that QSA encountered in this problem are introduced and the necessity of full wave solution is revealed and then, for the first time, the full-wave solution of the problem in closed form format is presented. This solution is done in two scenarios: 1- the source (active neurons) in the center of a sphere and 2- the source in the out of center but deeply inside the sphere. First scenario is simpler but the second scenario is much more complicated and has been solved by using partial-wave series expression (PWSE). One of the important achievements of this modelling is improving the interpretation of EEG and MEG measurement resulting in more accurate source localization.