The impedance of electrodes with adherent biological cells correlates with cell viability and proliferation. To model this correlation, we exploited the idea that the introduction of a highly conductive layer into the equatorial equipotential slice of a system with an oriented, freely suspended, single ellipsoidal cell may split the system into mirror-symmetrical halves without changing the field distribution. Each half possesses half of the system's impedance and contains a hemiellipsoidal cell attached to the conductive layer, which can be considered a bottom electrode. For a hemiellipsoidal adherent cell model (ACM) with standard electrical properties for the external and cellular media, the assumption of a bottom membrane and a subcellular cleft in the 100 nm range, as found in adherent cells, changed the potential distribution over a one-% range up to frequencies of 1 MHz. For simplicity, potential distributions for slices of spheroidal objects can be numerically calculated in 2D. The 2D distributions can be converted into three dimensions using simplified equations for the influential radii of spheroids. After the ACM approach was expanded to adherent cell patch models (APMs), the feasibility of our model modifications was tested using two criteria: the constancy of the equipotential plane touching the poles of ACMs or APMs and a comparison of the impedance, which could be numerically calculated from the overall current between the bottom electrode and a plane-parallel counter-electrode, with the impedance of the suspension obtained from Maxwell-Wagner's mixing equation applied to hemiellipsoidal cells.
Keywords: 2D/3D conversion; Cell impedance; Comsol Multiphysics®; Influential radius; Interdigitated electrode structures (IDES); Maxwell-Wagner's mixing equation.
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