## 4 Modelling Neural Interfaces
Neuronal excitation is elicited under current-clamp by two mechanisms: (i) falling voltage ramps and pulses depolarize the attached membrane triggering an action potential (Figure 17b); (ii) rising voltage ramps and pulses, instead, depolarize the free membrane, hence an action potential is triggered (Figure 17c). Finally, to underline the importance of equivalent circuit models in investigating the nature of the sensor/electrolyte interface, it is worth to remark that electrochemical impedance spectroscopy (EIS) is a powerful tool that can help to rationalize the different phenomena occurring at the interface between neurons and sensors [153; 154; 155; 156]. Remarkably, opportune equivalent impedance models can be combined with in vivo electrochemical impedance spectroscopy to monitor the state of the implant during time [157; 158; 159; 160; 161; 162]. For instance, [PERSON] et al. performed EIS measurements of implanted electrodes upon implants duration from 7 up to 21 days [52]. Figure 18a reports an example of  
Figure 17: (**a**) Intracellular voltage V\({}_{\rm M}\) elicited by injection of current measured with a micropipette (upper row) and extracellular voltage V\({}_{\rm J}\) measured with a EOSFET (lower row): (i) capacitive response; (ii) ohmic response; (iii) anti-capacitive response; (iv) Early anti-capacitive response; (v) Early capacitive response with secondary positive response; (**b**) Capacitive stimulation under current-clamp by falling ramps; (**c**) Capacitive stimulation under current-clamp by rising ramps. (**a**) Reproduced from [146]. Copyright 1999, with permission of Springer; (**b,c**) Reprinted from [148]. Copyright 2007, with permission from Elsevier. impedance variation due to an extensive histological reaction that lead to a significant increase of the measured impedance and consequently, to the implant failure. Another example of using EIS as a tool to characterize the implant during in vivo applications was reported by [PERSON] et al. [157]. They characterized deep-brain stimulation electrodes using the model in Figure 18b, where they separated the tissue components by the electrode components and they monitor variations in the model parameters after implantations and after a neural stimulation. As previously reported by [PERSON] et al. following the implantation, the electrode impedance increases. Remarkably, the stimulation produces a rapid decrease in electrode impedance with extensive changes in the tissue component promoting the use of voltage pulses to improve the performance of implanted electrodes [57; 58]. Similarly, [PERSON] et al. performed EIS measurement to investigated the formation of undesired conductive paths and consequent loss of functionality in the implant [162]. By analysing the impedance of the implant, the authors showed that such unwanted paths are due to the damaging of the electrode insulator, as reported in the model of Figure 18c. In fact, a comprehensive model of the metal/organic semiconductor/electrolyte describing the percolation of solution through the organic material has been recently proposed [156]. Hence proving how the combination of EIS measurements and proper models can pave the way to intimately understand and optimize neural interfaces for long term in vivo implants. Figure 18: **(a)** Nyquist plots for an electrode characterized by an extensive reaction. Data are presented immediately following implant and on each of the first 7 days post-implant; **(b)** (i) Equivalent circuit model discriminating the electrode component and the tissue component; (ii) example of resistance increase after 15 days implantation (iii) example of resistance decrease after stimulation; **(c)** Dielectric coating on a neural electrode emphasizing how the insulation damage creates undesired current pathways. **(a)** From [52], copyright 2007. © IOP Publishing. Reproduced with permission. All rights reserved.