Local Laplacian Estimate on Spherical Head Surface

Scalp Laplacian is the 2D Laplace operation on the scalp surface potential. In the last thirtyyears, three approaches were developed for the Laplacianestimate. Among them, the moderate and global methodswere both based on various potential interpolation functions for various head model, whereas the earliest and simplest local method, the difference approximation, was stillbased on a planar surface model. In this work, the local difference approximation approach was extended to aspherical surface model. The 2nd and 4th order approximation were derived and a proportional coeffcient difference was revealed between the planar and the sphericalsurface models. This work provided the theoretical basisof the local difference approach for Laplacian on a sphericalhead surface.