Computation of neuromagnetic fields using finite-element method and Biot-Savart law

The finite-element method in combination with the Biot-Savart law is described to compute the magnetic field distribution generated by a dipolar source within a homogeneous volume conductor of an arbitrary shape. In order to calculate the three independent components of the magnetic field outside the volume conductor by means of the Biot-Savart law, the distribution of the current throughout the medium is required. A finite-element mesh is constructed using four-node tetrahedral elements. The potential in each node is computed numerically by the finite-element method using the proper continuity conditions across the boundaries. The gradient of the potential denotes the current density within an element. The components of the magnetic induction are calculated by numerical integration, applying the current density within the tetrahedrons. Simulations are carried out to assess the numerical accuracy for a homogeneous spherical volume conductor. Errors of 3% can be obtained with a locally refined spherical mesh containing about 1000 nodes, for dipoles at any depth and any orientation. A homogeneous realistically shaped model with the shape of the inside of the skull is obtained from magnetic resonance images.