By Alan Macy, BIOPAC Systems, Inc.
All stimulators incorporate a fundamental characteristic known as “compliance.” Compliance comes in two flavors, namely voltage compliance and current compliance. Voltage stimulators emulate a voltage source, up to a certain current compliance. Current stimulators emulate a current source, up to a certain voltage compliance. The stimulator compliance limit is important information. Here are examples:
A voltage stimulator is being used to establish a field stimulation in a tissue bath. The voltage pulse is 100 volts, with a width of 1 ms. The bath establishes a 1000 ohm impedance between stimulation electrodes. Therefore, 100 volts/1000 ohms is 100 ma. In this situation, the voltage stimulator must be able to provide a current compliance up to 100 ma for at least 1 ms. If the stimulator’s current compliance is limited to 50 ma, then the output voltage will be limited to 50 ma * 1000 ohms or 50 volts, even if the stimulator is being instructed to output 100 volts.
Voltage stimulators commonly operate with the help of high voltage DC-DC converters and storage capacitors to provide the needed compliance current. If the storage capacitors can’t store enough charge or are not sufficiently supplied, then voltage stimulators may exhibit a quality known as voltage droop. Voltage droop is the quality when the stimulator output voltage can’t be maintained over a specific time interval, due to lack of sufficient current compliance. If the above stimulator can only be current compliant to 100 ma for 0.5 ms, then the output voltage pulse will be 100 volts for 0.5 ms and then will decay in direct proportion to the current compliance limit.
A current stimulator is being used for neuromuscular stimulation between two small electrodes. The current pulse is 10 ma, with a width of 1 ms and there is a 10,000 ohm impedance between stimulation electrodes. Therefore, 10 ma * 10,000 ohms is 100 volts. In this situation, the current stimulator must be able to provide a voltage compliance up to 100 volts for at least 1 ms. If the stimulator’s voltage compliance is limited to 50 volts, then the output voltage will be limited to 50 volts / 10,000 ohms or 5 ma, even if the stimulator is being instructed to output 10 ma.
Current stimulators commonly operate with the help of high voltage DC-DC converters and storage capacitors to provide the needed compliance voltage. If the storage capacitors can’t store enough charge or are not sufficiently supplied, then current stimulators may exhibit a quality known as current droop. Current droop is the quality when the stimulator output current can’t be maintained over a specific time interval, due to lack of sufficient voltage compliance. If the above stimulator can only be voltage compliant to 100 volts for 0.5 ms, then the current pulse will be 10 ma for 0.5 ms and then will decay in direct proportion to the voltage compliance limit.
In the case of transcranial Direct Current Stimulation (tDCS), a constant current of up to 2 ma (Is) may be applied through the cranium. Assuming a combined series electrode / skin junction resistance of 20 Kohms, a cranium resistance of 100 ohms and other loop series resistances considered negligible, then the total stimulation loop impedance (Zs) is 20.1 Kohms. Accordingly, in this situation, the voltage compliance (Vs) of the tDCS current stimulator must be at least:
Is * Zs = Vs
0.002 amp * 20,100 ohms = 40.2 volts
Given the variable nature of the combined series resistances in the stimulation loop, it’s generally helpful to double the expected compliance voltage requirement of the stimulator. Accordingly, in this case, a stimulator compliance voltage of 80 volts or higher is recommended. Because the series resistance in the loop is largely a function of the electrode / skin interface junctions, the choice of electrode type and contact area has a great effect on the voltage compliance requirements of the current stimulator. Other factors contributing to the voltage compliance requirement are the equilibrium potentials and over-potentials associated with the specified electrode / electrolyte / skin junctions. Furthermore, if high resistance electrode leads are used, the potential across the leads may become material.
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