  An analytic equation for electrochemical impedance of a single-cell measured
with a microelectrode is presented. A previously reported equation had a
practical problem that it is valid only when the microelectrode resides at the
center of the cell under test. In this work, we propose a new analytic equation
incorporating dependence on cell position, and confirmed its effectiveness by
numerical simulation. Comparisons show that our proposed equation gives an
excellent agreement with simulated impedance values. Discrepancies between
results from our equation and numerical simulation is suppressed within 13%,
which is a dramatic reduction from the previously-reported equation as large as
58%. The proposed analytic equation is expected to enable more accurate
analysis in actual cell experiments.
