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The authors develop a method for estimating regional head tissue conductivities in vivo, by injecting small (1-10 μA) electric currents into the scalp, and measuring the potentials at the remaining electrodes of a dense-array electroencephalography net. They first derive analytic expressions for the potentials generated by scalp current injection In a four-sphere model of the human head. They then use a multistart downhill simplex algorithm to find regional tissue conductivities which minimize the error between measured and computed scalp potentials. Two error functions are studied, with similar results. The results show that, despite the low skull conductivity and expected shunting by the scalp, all four regional conductivities can be determined to within a few percent error. The method is robust to the noise levels expected in practice. To obtain accurate results the cerebrospinal fluid must be included In the forward solution, but may be treated as a known parameter in the inverse solution.