A fast method to compute the potential in the multisphere model (EEG application)

A series expansion is derived for the potential distribution, caused by a dipole source in a multilayered sphere with piecewise constant conductivity. When the radial coordinate of the source approaches the radial coordinate of the field point the spherical harmonics expansion converges only very slowly. It is shown how the convergence can be improved by first calculating an asymptotic approximation of the potential and using the so-called addition-subtraction method. Since the asymptotic solution is an approximation of the true solution, it gives some insight on the dependence of the potential on the conductivities. The formulas are given in Cartesian coordinates, so that difficulties with coordinate transformations are avoided. Attention is paid to the (fast) computation of the partial derivatives of the potential, which is useful for inverse algorithms.<<ETX>>

[1]  E. Frank.  Electric Potential Produced by Two Point Current Sources in a Homogeneous Conducting Sphere , 1952 .

[2]  P. Nicholson,et al.  Specific impedance of cerebral white matter. , 1965, Experimental neurology.

[3]  D. Geselowitz.  On bioelectric potentials in an inhomogeneous volume conductor. , 1967, Biophysical journal.

[4]  D. A. Driscoll,et al.  Current Distribution in the Brain From Surface Electrodes , 1968, Anesthesia and analgesia.

[5]  Anthony Sances,et al.  The Contributions of Intracerebral Currents to the EEG and Evoked Potentials , 1978, IEEE Transactions on Biomedical Engineering.

[6]  Manuel A. Huerta,et al.  The surface potentials produced by electric sources in stratified spherical and prolate spheroidal volume conductors , 1983 .

[7]  J. D. Munck.  The potential distribution in a layered anisotropic spheroidal volume conductor , 1988 .

[8]  D. Wilton,et al.  Accelerating the convergence of series representing the free space periodic Green's function , 1990 .

[9]  B. W. van Dijk,et al.  Symmetry considerations in the quasi-static approximation of volume conductor theory , 1991 .

[10]  J C de Munck,et al.  The use of the asymptotic expansion to speed up the computation of a series of spherical harmonics. , 1991, Clinical physics and physiological measurement : an official journal of the Hospital Physicists' Association, Deutsche Gesellschaft fur Medizinische Physik and the European Federation of Organisations for Medical Physics.