Application of boundary perturbations on medical monitoring and imaging techniques
The paper aims at providing an analytic overview on the application of boundary perturbations for forward and inverse problems related to Electroencephalography (EEG) and Magnetoencephalography (MEG) predominantly for the spherical geometry, allowing a systematic presentation of the mathematical complexity associated. Extensive use is made of special functions and especially spherical harmonics. The surface of reference has been the homogeneous sphere, leading to solutions with corrections incorporating the deviation from the spherical geometry, included up to the first correction. A major impediment are the constrains, which are brought in by the Neumann condition, leading to the fact that components of either the moment of the dipole or its location or both, remain concealed. Two specific examples are provided for the obtained solutions of both EEG and MEG. For the entire collection see [Zbl 1471.34005].
scientific article; zbMATH DE number 7392141