A fast and robust finite volume solver of the two-dimensional induced current electrical impedance forward problem was developed. The numerical solver was validated by comparison with an existing analytical solution for a symmetrical geometry case, showing an accuracy of 0.07%. The solver was used to theoretically examine the sensitivity of the induced current impedance technique for the medical procedure of monitoring brain cryosurgery. The simulation was performed using a two-dimensional approximation of otherwise realistic geometry model of the head with different ice-ball sizes, simulating the expansion of the frozen lesion. The sensitivity of the scalp potential to the ice-ball size was found to be 53 x 10(-4) (relative scalp potential mm(-2)).