Use of the reciprocal problems in electro-magnetic source imaging of the human brain

In this work, solution of the electro-magnetic source imaging forward problem is formulated using the reciprocity theorem. Lead field solutions for electrode potentials and sensor magnetic fields are computed for a realistic head model using the finite element method. Potentials and magnetic fields obtained using the lead fields are compared to analytical solutions and direct numerical solutions. It is found that the accuracy of lead field based solution is comparable to the accuracy of direct numerical solutions. Compared to the analytical solutions, the error for numerical methods is below 1% inside the volume. The error increases up to 3% near the boundary. Once the matrices defining the lead field are formed, it is possible to obtain very fast forward problem solutions. For a linear realistic head mesh with 450000 nodes, directly obtaining a forward problem solution for a single dipole takes about 110 seconds on an 8 processor parallel computer. Using the same computing platform, it takes 11 hours to form the lead field matrix for 256 sensors. Once the matrix is formed, individual solutions can be obtained in under 1 second using a single processor.