From Finite Element Simulations to Equivalent Circuit Models of Extracellular Neuronal Recording Systems based on Planar and Mushroom Electrodes

Objective: define a new methodology to build multicompartment lumped-elements equivalent circuit models for the neuron/electrode systems. Methods: the equivalent circuit topology is derived by careful scrutiny of accurate and validated multiphysics finite-elements method (FEM) simulations that couple ion transport in the intra- and extracellular fluids, activation of the neuron membrane ion channels, and signal acquisition by the electronic readout. Results: robust and accurate circuit models are systematically derived with the proposed method, suited to represent the dynamics of the sensed extracellular signals over a wide range of geometrical/physical parameters (neuron and electrode sizes, electrolytic cleft thicknesses, readout input impedance, non-uniform ion channel distributions). FEM simulations point out phenomena that escape an accurate description by equivalent circuits; notably: steric effects in the thin electrolytic cleft and the impact of extracellular ion transport on the reversal potentials of the Hodgkin-Huxley neuron model. Conclusion: the multi-compartment equivalent circuits derived with our method match with good accuracy the FEM simulations. They unveil the existence of an optimum number of compartments for accurate circuit simulation. FEM simulations suggest that while steric effects are in most instances negligible, the extracellular ion transport remarkably affects the reversal potentials and consequently the recorded signal if the electrolytic cleft becomes thinner than approximately 100 nm. Significance: the proposed methodology and circuit models improve upon the existing area and point contact models. The coupling between the extracellular concentrations and reversal potential highlighted by FEM simulations emerges as a challenge for future developments in lumped-element modeling of the neuron/sensor interface.