Harmonic-balance circuit analysis for electro-neural interfaces

Avoidance of the adverse electrochemical reactions at the electrode-electrolyte interface defines the voltage safety window and limits the charge injection capacity (CIC) of an electrode material. For an electrode that is not ideally capacitive, the CIC depends on the waveform of the stimulus. We study the modeling of the charge injection dynamics to optimize the waveforms for efficient neural stimulation within the electrochemical safety limits.

The charge injection dynamics at the electrode-electrolyte interface is typically characterized by the electrochemical impedance spectrum, and is often approximated by discrete-element circuit models. We compare the modeling of the complete circuit, including a non-linear driver such as a photodiode, based on the harmonic-balance (HB) analysis with the analysis based on various - (discrete-element) approximations. To validate the modeling results, we performed experiments with iridium-oxide electrodes driven by a current source with diodes in parallel, which mimics a photovoltaic circuit.

Application of HB analysis based on a full impedance spectrum eliminates the complication of finding the discrete-element circuit model in traditional approaches. HB-based results agree with the experimental data better than the discrete-element circuit. HB technique can be applied not only to demonstrate the circuit response to periodic stimulation, but also to describe the initial transient behavior when a burst waveform is applied.

HB-based circuit analysis accurately describes the dynamics of electrode-electrolyte interfaces and driving circuits for all pulsing schemes. This allows optimizing the stimulus waveform to maximize the CIC, based on the impedance spectrum alone.