  An analytical formula for electrical impedance between an adherent living
cell and sensor substrate measured using a microelectrode is presented for the
first time. Previously-reported formula has been applicable only for the case
where many cells are on a large electrode. In contrast, our formula is valid
even when a microelectrode smaller than the cell size is underneath the cell,
which is often the case for the state-of-the-art single-cell analysis.
Numerical simulations for verifying the accuracy of our formula reveals that
the discrepancies between the theoretical impedances calculated by our formula
and numerical simulation results are negligibly small. Our formula will be
useful for describing cell-substrate impedance properties in equivalent circuit
model analysis or sensor design optimizations.
