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We introduce the Bioelectric Problem Solving Environment (BioPSE), and demonstrate its utility in solving forward and inverse bioelectric field problems. BioPSE is an extensible software toolkit of modeling, simulation, and visualization tools that have been tightly integrated into a unified, interactive software environment. BioPSE has been developed through the NIH NCRR Center for Bioelectric Field Modeling, Simulation, and Visualization; the software is open source, and is freely available for non-commercial use. To introduce BioPSE we provide a brief overview of the design of the system and then demonstrate the utility of BioPSE by using it to solve a cortical mapping problem.