The computational environment for estimation of unknown regional electrical conductivities of the human head, based on reali stic geometry from seg- mented MRI up to2563 resolution, is described. A finite difference alternating d i- rection implicit (ADI) algorithm, parallelized using OpenMP, is used to solve the forward problem describing the electrical field distributi on throughout the head given known electrical sources. A simplex search in the multi-dimensional para- meter space of tissue conductivities is conducted in parall el using a distributed system of heterogeneous computational resources. The theoretical and computa- tional formulation of the problem is presented. Results from test studies are pro- vided, comparing retrieved conductivities to known solutions from simulation. Performance statistics are also given showing both the scaling of the forward problem and the performance dynamics of the distributed search.