## To the Editor:—

Tsui *et al.* in their paper “Electrical Impedance to Distinguish Intraneural from Extraneural Needle Placement in Porcine Nerves during Direct Exposure and Ultrasound Guidance” make a very interesting observation: An increase in electrical impedance on needle entry into a nerve.1However, although interesting, the finding is ascribed to an electrical parameter that it likely does not represent. As such, this is an example of being misled by some of our equipment that is routinely used without questioning what is actually being shown. For reasons not clear to me, a few years ago some nerve stimulators began displaying something called “impedance.” At the time, this struck me as odd, since these devices produce square waveform outputs. Now, with the publication of Tsui *et al.* , this issue needs to be addressed, because it is leading to confusion.

It is well established both theoretically and experimentally that nerves display a *reduced* impedance when compared to surrounding tissues.2–4Yet, Tsui *et al.* carefully document an abrupt increase in “impedance” on needle penetration of a nerve, as determined by a Stimuplex HNS 12 (D. Braun Medical, Bethlehem, PA). So, how do we resolve this apparent contradiction? Although this format does not allow for a comprehensive discussion of the essential issues, there are some details that provide clarification of the disparate data.

All commercially available nerve stimulators for regional anesthesia are constant current devices: They put out a square waveform pulse of user-defined current amplitude. Although such an output results in a square waveform voltage pulse when the current is directed across a resistance, tissue represents a parallel resistance capacitance circuit. When a square waveform current pulse is directed across tissue, the resulting voltage pulse demonstrates a charging component, as shown in figure 1. Note that the voltage pulse requires 2–2.5 ms to achieve its plateau value in response to a square waveform current pulse. Consequently, the 100–200 μs pulse durations of commercial nerve stimulators are not adequate to allow the developed voltage to reach the plateau value. To calculate the impedance of such a circuit, the plateau value must be achieved, reflecting the resistive component of the resistance capacitance circuit. Knowing the resistance, the capacitive component may be approximated from the slope of the charging curve. It may only be approximated, because the actual charging curve is defined by the multiple electrical path components, shown in equation 1, and their individual charging time constants (τ), where τ is defined as the product of R and C.

What the nerve stimulators appear to be doing when displaying “impedance” is taking the maximum developed voltage at the end of the current pulse, dividing it by the known applied current to yield the “impedance” according to Ohm’s Law.

where E is voltage, I is current, Z is impedance, j is the square root of –1, and ϕ is the phase angle. However, the voltage maximum for the applied current has not been reached during the period of the nerve stimulator pulse, so the displayed value clearly does not represent the electrical impedance of the system. What Tsui *et al.* observed was when the needle tip was intraneural, the developed voltage was higher at pulse termination than when the needle was extraneural. This was not a measure of system impedance, but was actually a function of the reduced time constant associated with the changes in capacitance and resistance of the nerve, modeled in figure 2.4

The reduced effective system time constant with intraneural needle tip placement resulted in a more rapid rate of rise of the voltage curve, even though its final value may be unchanged or even reduced. With intraneural placement, the capacitance increased, the resistance decreased, and the resulting impedance was actually reduced, according to equation 3.

where X^{C}is the capacitive reactance and is defined by:

where f is the frequency of the applied waveform. Dependent on the magnitude of the capacitive and resistive changes, the overall impedance decreased dramatically.

This finding of Tsui *et al.* , although it does not demonstrate increased impedance on intraneural needle tip placement, is interesting, because it shows that the complex system time constant changes on close approach to neural tissue when using externally applied electrical fields, an observation I have also made.5Also, individual time constants, equation 1, may be derived from the observed charging/decay voltage curve through additional mathematical methods (logarithmic peeling), and the time constants contributed by the nerve, the insulated needle, or the remaining tissue electrical path determined separately.6

St. James Healthcare, Butte, Montana. pcory@littleappletech.com

## References

*In vivo*impedance measurements on nerves and surrounding skeletal muscles in rats and human body. Med Biol Eng Comput 2002; 40:323–6