Limitations in the electrochemical analysis of voltage transients

Objective. Chronopotentiometric voltage transients (VTs) are used to assess the performance of bionic electrodes. The data obtained from VTs are used to define the safe operating conditions of clinical devices. Various approaches to analysing VTs have been reported, and a number of limitations in the accuracy of the measurements in relation to electrode size have been noted previously. Approach. The impact of electronic hardware and electrode configuration on VTs is discussed. Main results. The slew rate, rise time, sample time, minimum pulse length and waveform averaging characteristics of the electronic hardware, and electrode configuration will impact on VT measurement accuracy. Subsequently, activation and polarisation voltage measurements, and the definition of safe stimulation levels can be affected by the electronic hardware and electrode configuration. Significance. This article has identified some limitations in the previous literature related to the measurement and reporting of VTs and subsequent analysis of access and polarisation voltages. Furthermore, the commonly used Shannon plot used to define safe stimulation protocols does not correct for uncompensated resistance, account for electrode roughness or changes in electrode configuration. The creation of a safe stimulation plot which has been corrected for uncompensated resistance would generate more widely applicable stimulation guidelines for clinical devices used in different anatomical locations such as endovascular neural interfaces.


Discussion
While the performance of voltage transients (VTs) and subsequent measurement of the access voltage (E a ), polarisation voltage (E p ) and total voltage (E t = E a + E p ) is common, there are a number of issues which have not been discussed in the literature.As a result, there may be various errors or limitations in some published reports.The following discussion aims to address these limitations and offer key recommendations (table 1) to ensure future use of this technique is more accurate.
E a is a function of uncompensated resistance (iR u ), which occurs within the initial few µs of a current pulse, and has an increasing magnitude with higher current intensities.There have been numerous publications discussing the difficulty in measuring E a from a VT [1][2][3][4].If E a is overestimated, then E p will be underestimated, and potentially an unsafe current intensity will be applied.Conversely, if E a is underestimated, and E p is overestimated, then the electrode may not be utilising its full charge injection capacity (CIC).The main difficulty in measuring E a is due to the shape of a VT, with no clear distinction between voltage changes arising from iR u , capacitance or Faradaic processes, normally just slight variations in gradient.Estimates of E a have been made from the start and end of a VT, and various fittings of gradient from the VT [1,4,5].Application of a reciprocal derivative can also aid in visualizing potential changes associated with different electrochemical processes [6].However, these previous methods for measuring E a have not utilised validation techniques, such as electrochemical impedance spectroscopy (EIS), to determine their accuracy.Where possible, validation should be performed with a secondary technique.If an accurate E a value is required, it may be better measuring R u via another technique such as EIS for subsequent calculation of E a .
Regardless of the accuracy of the measurement, E a is used to calculate a resistance value using Ohm's law by dividing the measured voltage by the applied current.It is also common for Ohm's law to be applied to E p and E t , however these two parameters are not associated with uniform conductors, and application of Ohm's law is not valid, these values should be reported as voltages [6].E p is used to determine the safe CIC of an electrode, with the maximum safe CIC normally defined as the water limit [4,6].E p can be affected by stimulation waveform, solution composition, electrode material and size; while the water limit can be affected by solution composition and electrode material.Subsequently, the CIC must be assessed for every application [6,7].Furthermore, there are other reactions which can occur within the water limit, including electrode oxidation, platinum dissolution and surface rearrangements which may also be unsafe or damage the electrode [8,9].Subsequently, measurement of E p from a simple test may not provide accurate safe stimulation parameters appropriate to long term clinical application, different stimulation protocols, or changes to tissue composition.VTs should be assessed in a series of solutions to determine the impact of solution composition on E p , including saline, relevant artificial body fluids and with addition of relevant proteins etc.
When an electrode is implanted, the uncompensated resistance, and subsequently E a , will be relatively stable over short time periods [2].Some initial changes may occur from surface activation or protein adsorption [10,11], although partial blocking of the electrode by protein fouling has minimal impact on iR u [11].Further changes may occur over longer time periods due to changes in tissue resistivity, bone formation, electrode degradation or electrode movement.Systematic errors in the measurement can also occur such as variations in electrical contact resistance (e.g.dirty connectors and alligator clips).Redox reactions, and subsequently E p and E t , can also vary between sequential VTs.Therefore, small variations in E a may arise from a range of factors and attributing these variations to a specific cause may not be achievable in the complex in vivo environment.In contrast, sudden or large changes may be associated with a specific cause, such as electrode/tissue damage, movement or bone formation, which may not require an accurate measurement of E a to be diagnostically useful.
An aspect of implanted electrodes which is often ignored is the impact of electrode configuration on electrochemical response.In vitro tests are often performed in a three electrode configuration with a large counter electrode and well defined, stable reference electrode.In contrast, when the electrodes are used in vivo, electrochemistry may be performed in a two electrode configuration with similar sized working and counter electrodes, and a poorly defined, unstable reference potential.Changes in electrode configuration can affect assignment of safe potential windows, electrode capacitance and resistance and limit charge transfer kinetics [12].Measurements of E a E p and E t performed in different electrode configurations may not be accurate, and comparison of these terms may not be valid.Appropriate control experiments must be performed to correct for or eliminate impacts arising from different electrode configurations.
It is worth highlighting that safe stimulation intensities of bionics electrodes are typically guided by the charge density and charge per phase of a stimulation waveform, termed the Shannon plot, which is largely based on platinum electrodes placed on the cortical surface of a feline model [13].There are a number of limitations in the wider application of this plot, as neural damage can arise from multiple mechanisms [14].Furthermore, electrode damage can occur at stimulation levels below the 'Shannon limit' , with electrode corrosion dependant on stimulation waveform [9,15,16], which can lead to device failure and neural damage.More detailed analysis is still required to understand which mechanisms result in unsafe neural stimulation and how they vary across different applications.The authors of the original safety study noted that tissue damage occurring above the Shannon limit was most likely due to overexcitation of the tissue, and not by a Faradaic process occurring at the electrode surface [17].In subsequent articles, the authors used an electrochemically activated iridium electrode to measure E a and E p , with no visible tissue damage correlating with E p [18].While this follow-up article used a different electrode material, tissue damage occurred at current intensities below the electrodes safe CIC, which may indicate little need to measure CIC.However, the Shannon plot is based on data with a very small electrode-neuron distance, so that a large charge density through the neurons was achieved with low stimulation intensities.Larger electrode-neuron distances, as occurs with an endovascular neural interface and cochlear implants, will reduce the charge density across the neurons, requiring a larger stimulation current.In the case of cochlear implants, chronic stimulation at intensities well above the Shannon limit resulted in increased platinum corrosion, charge storage capacity and CIC, but no adverse electrophysiological or histopathological effects on the auditory neurons of a feline model [19].This may imply small levels of dissolved platinum species are not of significant concern for neural damage (but will degrade the electrode).A more recent article has discussed further limitations of the Shannon plot, particularly its failure when applied to microelectrodes [20].The plots are also based on geometric electrode area, and may not be accurate for rough or porous electrodes, such as platinum black.Different electrode materials and some stimulation parameters such as frequency or duty cycle are also not taken into account.Furthermore, the Shannon plot (and newer plots), do not accommodate resistance or changes in electrode configuration.Correcting the Shannon plot for iR u would be a simple step to extend its application to other conditions and teasing apart the impact other parameters have on tissue damage.Unfortunately, previous publications do not provide sufficient information to produce new safety plots that correct for iR u .However, it can be assumed that subtracting some amount of current to account for iR u would result in a lower 'corrected' safe stimulation charge density and charge per phase.A corrected safe stimulation plot would be more widely applicable than current versions.Therefore the safety levels defined by the Shannon and newer plots can be applied to electrodes used in similar tissue and configurations, but their validity must be assessed for other conditions, such as stimulation within a blood vessel or when bone formation occurs.
Another issue which has not received attention relates to the electronic hardware used to measure VTs.There are different equipment manufacturers producing a range of instruments which can impact VT measurements.The Gamry 1010E potentiostat has 5 bandwidth settings; the slew rate at the highest bandwidth of 1100 kHz is 10 V µs −1 , while the lowest bandwidth of 0.4 kHz has a slew rate 6 mV µs −1 .When this potentiostat was used to assess an endovascular neural interface, the maximum change in voltage detected with a 400 µA current pulse after 250 µs was 730 mV, giving an average change in potential of 2.92 mV µs −1 , significantly lower than the instruments limit [21].However, there is a faster potential change at the beginning of the pulse of 387 mV in 50 µs or 7.74 mV µs −1 .Subsequently, use of the lowest bandwidth would affect the accuracy of the VT measurement and produce incorrect E a and E p values.This error can be enhanced by reducing the electrode area and CIC, increasing the current amplitude, and reducing the slew rate of the electronics.
Conversely, if the bandwidth of the potentiostat is too high, it can lead to an overshoot on the measured potential and even oscillations.If gain switching is used, there can also be overshooting of signal spikes in a measurement, particularly at the start and end of a waveform.Overshooting can also be caused by stray capacitance between cables and instrumentation [22].These overshoots can affect the measurement of E a .Overshooting or potential spikes should not occur during a VT and should be removed from an equipment setup before commencing experimentation.
A number of other potentiostat manufacturers were contacted for details on their instrument slew rates, but limited information was provided.Some current instrument specifications include information on slew rate or minimum sample times: Edaq EA163 has a slew rate of 3 V µs −1 and minimum sample time of 5 µs.Autolab fitted with a fast sampling ADC10M module has a minimum sample time of 0.1 µs, with a maximum sample length of 1000 000.CHInstruments 660E has further limitations with a minimum sample time of 10 µs and minimum pulse length of 5 ms.To achieve clinically relevant charge densities with the 660E, much lower current amplitudes must be applied, resulting in reduced iR u and E a .
VTs can also be measured via an oscilloscope in combination with an electrical stimulator.Oscilloscopes have a wide range of capabilities, including sample rates below 1 ns and slew rates over 1 kV µs −1 , with some adjustable parameters such as sample length (e.g. 10 kS) and an ability to perform multiwaveform averaging.The appropriate settings must be implemented for each application and reported.
VTs can also be performed with a clinical device which may have further hardware or data transfer limitations.For example, a cochlear implant used for an impedance test was only capable of reporting the final time point of the VT [5].As a result, the VT had to be constructed from multiple pulses of varying length.
As a result of the above differences in equipment, the assessment of VTs may be impacted.For example, measurements with a potentiostat are often analysed on individual current pulses, over relatively short stimulation waveforms (<10 VTs) so that the processes occurring at the electrode-solution interface across multiple VTs may be highly dynamic (e.g.changing electrode structure or oxidation state).In contrast, measurements with an oscilloscope or clinical device can apply very long stimulation waveforms (millions of VTs) which users may average over multiple pulses, as processes occurring at the electrode-solution interface approach a quasiequilibrium condition (relatively stable across multiple VTs).Commercial potentiostats will generally be used with well-defined reference potentials in a three electrode configuration, but may have slow slew rates or sample rates.Conversely, oscilloscopes may be used with a poorly defined reference potential in a two electrode configuration, but with high slew rates and sample rates.Subsequently, measurement of E a on a potentiostat may not be accurate, while measurement of E p and E t on an oscilloscope may not be accurate.The technical specifications of an individual piece of equipment must be assessed before use, and impacts on VT measurements should be clearly communicated.

Conclusions
A range of limitations were identified in the previous literature on the measurement and reporting of VTs and subsequent analysis of E a and E p .In particular, the hardware slew rate, sample rate, minimum pulse length, waveform averaging and electrode configuration are often not reported and may be affecting the accuracy of measurements.Furthermore, the commonly used Shannon plot used to guide safe stimulation protocols does not correct for iR u , account for electrode roughness or changes in electrode configuration.

Table 1 .
Key recommendations for performing and reporting on voltage transients.Report instrument sample rate and bandwidth (slew rate).These values should be adjusted to accurately measure voltage at ≲1 µs sample rate.•Reporthow many VTs were performed and which ones were used for analysis.•Report any waveform averaging performed.