Current multipole expansion to estimate lateral extent of neuronal activity: a theoretical analysis

High-resolution magnetoencephalography (MEG) allows for a detailed description of focal neuronal current sources going far beyond the dipole approximation which merely indicates the center and magnitude of neuronal activity. Higher order multipole coefficients can be related to other bulk properties, like spatial extent or curvature. The possibility and limitations of measuring spatial extent by interpreting reconstructed multipole coefficients was tested under realistic noise conditions and for model misspecifications; for this analysis the primary cortical response ("N20") to electric median nerve stimulation was modeled by a one dimensional source distribution. The forward calculation was done analytically up to octapolar order for a spherical volume conductor. The multipole expansion is shown to estimate the lateral source extent with negligible bias; this estimate is to first-order stable against additional source features, like gyral curvature or spatial extent in a second direction (gyral depth, neuronal length). For a dipole moment of 20 nAm a lateral extent of 2 cm can be detected for a realistic noise level with large but experimentally still reasonable effort. Approximating a realistic head model by a sphere results in errors larger than the extent to be estimated; accordingly, studies on human cortical evoked responses will require multipole fitting in realistic head models.