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A transient finite-element model has been developed to simulate an extracellular action potential recording in a tissue slice by a planar microelectrode array. The thin-film approximation of the active neuron membrane allows the simulation within single finite-element software of the intracellular and extracellular potential fields. In comparison with a compartmental neuron model, it is shown that the thin-film approximation-based model is able to properly represent the neuron bioelectrical behavior in terms of transmembrane current and potential. Moreover, the model is able to simulate extracellular action potential recordings with properties similar to those observed in biological experiments. It is demonstrated that an ideal measurement system model can be used to represent the recording microelectrode, provided that the electronic recording system adapts to the electrode-tissue interface impedance. By comparing it with a point source approximated neuron, it is also shown that the neuron three-dimensional volume should be taken into account to simulate the extracellular action potential recording. Finally, the influence of the electrode size on the signal amplitude is evaluated. This parameter, together with the microelectrode noise, should be taken into account in order to optimize future microelectrode designs in terms of the signal-to-noise ratio.