An Experimental Study on Passive Charge Balancing

This paper presents a simplified analysis of the electrode potential upon mismatched, biphasic stimulation using passive discharge techniques, e.g. by shortening of the electrodes. It turns out that especially for microelectrodes the required shorting intervals become as large as to limit a feasible stimulation interval. If no blocking capacitors can be used due to limited space and the degree of miniaturization, the passive discharge even imposes severe risks to the surrounding tissue and the electrode.


Introduction
Biomedical implants for functional electrical stimulation (FES), such as the cochlea implant, cardiac pacemaker, and retinal implant have received an increasing interest [1] [2].The principle is to excite a neural reaction upon the transfer of charge into the tissue.Thereby, constant current based stimulators use pulsatile current stimulation via an electrode, which is attached to the human body.Principally, whenever current is conducted over an electrode into a conducting solution, chemical processes take place at the interface.By applying a large potential over a longer period of time, charge is massively exchanged over the electrode and strong faradaic currents flow which cause electrolysis, pH change, electrode dissolution as well as tissue destruction [3] [4].In order to avoid these irreversible electrochemical reactions, the stimulating current pulse is typically balanced and biphasic, which ensures that no net charge appears at the electrode after each stimulation cycle and the electrochemical processes are balanced to prevent net dc-currents.But especially when integrated circuitry is used for the stimulator, due to imperfections of the fabrication process more than 1%-5% of mismatch of the current pulses has to be taken into account.Therefore, measures to achieve charge balancing are typically implemented.The most common solution is to insert a large, non-integrated dc blocking capacitor in series with the stimulation electrode, which guarantees that no dc-currents can flow to the electrode over time [3][5].Nonetheless, regular discharge of the blocking capacitor is necessary in order to avoid saturation due to dc-current integration and consequently reduced output voltage compliance of the stimulator.In modern FES applications, where many channels have to be provided concurrently [2], dc blocking capacitors can not be realized in the required number due to space limitations.Therefore, the only passive, charge balancing measure is to short the electrodes after the mismatched, biphasic stimulation in order to cancel accumulated charge.In this work we analyze the dependency of current mismatch, electrode impedance and the resulting steady-state electrode dc-voltage.Within this paper, we model the electrode-electrolyte interface, calculate the net dc-voltage due to imbalance and validate the measurement results by experiments with platinum black electrodes in 0.9% saline solution.

Electrode-Tissue Interface Model
A simplified electrode model [5] can be described with three electrical components (Fig. 1), where C H represents the double layer interface capacitor, R S the solution spreading resistance, which is determined by the resistivity of the fluid, while R F represents the faradaic resistance, which is governed by diffusion of reactive species to the electrode for charge-transfer reactions.Generally, in the case of safe operation only R S and C H are of interest.Current through the faradaic resistance R F is, however, the source of corrosion and toxicity when there is no long-term charge balance [6].
It is important to note that the values of R S and C H will vary depending on the material and geometry of the electrodes being used.In this work, two sizes of platinum black electrodes were used with 1000 µm and 150 µm diameter, respectively.Lumped model parameters (R S and C H ) have been measured using impedance spectroscopy with 25mV excitation in a 0.9% saline solution.Average values for these electrodes were found at R S =1.2kΩ, C H =47nF, and R S =4.7kΩ, C H =18nF, respectively.

Electrode Potential Calculation
In the following, the derivation of an analytical expression for the steady-state mismatch voltage on an electrode employing passive charge balancing is found.Stimulation pulses in chronic applications are generally symmetric, biphasic and charge balanced (Fig. 2) [5].The duty cycle of this pulse is If there is charge imbalance between the first ("push") and the second ("pull") current phase, then the average dc-current of this stimulation pulse is % 2 where I STIM is the stimulation current amplitude, %MM is the percentage charge mismatch between the push and pull duration, and DC is the duty cycle from Eq. 1.A stimulation current of ±1mA, a mismatch of 5% and a duty cycle of 20%, for example, corresponds to an averaged dc-current of 10 µA through an electrode.

Fig. 2 Timing of a stimulation cycle
The discharge period t DIS in Fig. 2, determines the maximum time for shorting the electrodes or discharging the blocking capacitor to get to the 0 V reference voltage.
Counter Electrode Working Electrode

Fig. 3 Biphasic current stimulator with blocking capacitor
For the simplicity of the analysis, R F in Fig. 1 is assumed as a very large resistor and is therefore neglected.A stimulation circuit with (optional) blocking capacitor C B and discharge switch is shown in Fig. 3. Normally, the size of a blocking capacitor must be large, such that the voltage drop across C B does not significantly decrease the voltage compliance of the stimulator, which is required to drive the electrode impedance.Since also the counter electrode is assumed much larger as the stimulation electrode (C HC >>C HW ), the time constant of this series connection simplifies to: From the dc-current in Eq. 2, the mismatch charge per each stimulation cycle, Q MM ; can be calculated as: During the discharge period, t DIS , the switch is closed, thus, the blocking capacitor is discharged through R S and R DIS .The charge during this period is: where V 0 is the quasi-static electrode potential during the discharge phase.To simplify the calculation, it is assumed that t DIS is much smaller than τ.Then, the voltage at the capacitor and thus at the electrode remains constant during the discharge period.Hence, Eq. 4 and Eq. 5 are set equal: The electrode voltage can then be calculated to: 0 ( ) This equation can also be used in the case of stimulator without blocking capacitor (since C B >>C HW ).

Experiments and Discussion
The given analysis is verified by circuit level simulations using the circuit in Fig. 3, and additionally with experiments using platinum black electrodes in a 0.9% saline solution.The following parameters were used for the experiments: I STIM =±500µA, a current mismatch of %MM=2%, C B =22µF, while R DIS was small and could be neglected.
For the pulse timing, in this experiment a high repetition rate of 5kHz was chosen, with t PUSH =t PULL =50µs and t FRAME =200µs.Please note that by extending all timings proportionally, the absolute results of the steady state voltage did not change, since the mismatch current depends only on the duty cycle of the frame (Eq.2), while the resulting electrode voltage depends on the ratio of the frame and discharge time (Eq.7).Firstly, the 1000 µm diameter electrode was used.Fig. 4 presents the quasi-static electrode potential after each stimulation and discharge phase.The potential was measured for various discharge times t DIS and is compared to the result in Eq. 7 and a simulation with the simple circuit in Fig. 3.
Obviously, the analytical model and the experimental simulation and measurement results match well.Differences are caused by the rather small time constant of the electrode impedance and by variations of the same over time.A comparison of the calculation, simulation and the experiment on a smaller electrode with 150 µm diameter is given in Fig. 5. Again, the stimulation parameters were chosen as above.
For illustration of the steady state behaviour, also the transient electrode potential is shown in Fig. 6, where the mismatch caused voltage after each stimulation cycle is seen.From the above results, it is obviously seen that even with the help of blocking capacitors, an electrode potential after stimulation can increase to hundreds of mV, if the discharge time becomes very much smaller than the stimulation time.This becomes critical, if for example in multielectrode applications there is no room for external blocking capacitors, and the only charge balancing measure is electrode shortening.In this case, the analytical results are still true, since the series connection of blocking and interface capacitor is dominated by the smaller electrode capacitance.Furthermore, by decreasing the size of the electrode and thereby increasing the electrode impedance, by using short discharge cycles the quasi-static electrode potential can severely increase (Eq.7).Consequently, in order to provide a safe stimulation, different ways of charge balancing must be used, for example, active charge balancing [2][5] [7].

Conclusion
This paper presents an electrode potential calculation method for functional electrical stimulation with passive charge balancing using blocking capacitors or electrode shorting.It is shown that a safe value for the discharging time strongly depends on electrode impedance.Thus, when small electrodes are used, a stimulation current mismatch can cause a quasi-static electrode potential exceeding the water window.Thus, either very large safety margins are required or active charge balancing techniques must be used.