A DUAL COORDINATE SYSTEM FINITE-DIFFERENCE METHOD FOR FORWARD AND INVERSE SOLUTIONS OF THE VOLUME CONDUCTOR PROBLEM IN NEUROLOGY

Finite difference methods for the volume conductor problem have used a single coordinate system for the mesh and made approximations of Lapl ace's equation. This method is simple but has two major problems. Firs tly, to deal with boundary conditions properly, the normal potential g radient at the boundary must be known. However it is complicated to co mpute at a curved surface point. Secondly, for an inverse solution the equation on a curved boundary is difficult to reverse since more than one inner mesh node appears in the approximation equation for each su rface point. The new method developed in this paper is a dual coordina te system. One system serves as a frame mesh, the other is a sub-coord inate system in which surface points become mesh points (regular nodes ). The equation at each surface point is then directly reversible sinc e only one inner point appears in the equation. The forward solution i s applied to both centric and eccentric bone models and uses the conve ntional successive over-relaxation (SOR) method. Noise is added to thi s solution for input to the inverse procedure which is a direct step-i n non-iterative method. Low pass filtering was effective in reducing t he effects of noise. In the examples given, only one coordinate subsys tem is used but, for complex shape boundaries, multiple subsystems wou ld be necessary. (C) 1997 Elsevier Science for IPEM.