In Vitro Evaluation of a 4-leaf Coil Design for Magnetic Stimulation of Peripheral Nerve

In the comments to last week’s blog entry, Frankie asks if there is a way to “safely, reversibly block nerve conduction (first in the lab, then in the clinic) with an exogenously applied E&M signal?” This is a fascinating question, and I may have an answer.

When working at the National Institutes of Health in the early 1990’s, Peter Basser and I analyzed magnetic stimulation of a peripheral nerve. The mechanism of excitation is similar to the one Frank Rattay developed for stimulating a nerve axon with an extracellular electrode. You can find Rattay’s method described in Problems 38-41 of Chapter 7 in the 4th edition of Intermediate Physics for Medicine and Biology. The bottom line is that excitation occurs where the spatial derivative of the electric field is largest. I have already recounted how Peter and I derived and tested our model, so I won’t repeat it today.

If you accept the hypothesis that excitation occurs where the electric field derivative is large, then the traditional coil design for magnetic stimulation–a figure-of-eight coil–has a problem: the axon is not excited directly under the center of the coil (where the electric field is largest), but a few centimeters from the center (where the electric field gradient is largest). What a nuisance. Doctors want a simple design like a crosshair: excitation should occur under the center. X marks the spot.

As I pondered this problem, I realized that we could build a coil just like the doctor ordered. It wouldn’t have a figure-of-eight design. Rather, it would be two figure-of-eights side by side. I called this the four leaf coil. With this design, excitation occurs directly under the center.

John Cadwell of Cadwell Labs built a prototype of this coil; an x ray of it is shown above. We wanted to test the coil in a well-controlled animal experiment, so we sent it to Paul Maccabee at the State University of New York Health Science Center in Brooklyn. Paul did the experiments, and we published the results in the journal Electroencephalography and clinical Neurophysiology (Volume 93, Pages 68-74, 1994). The paper begins

“Magnetic stimulation is used extensively for non-invasive activation of human brain, but is not used as widely for exciting limb peripheral nerves because of both the uncertainty about the site of stimulation and the difficulty in obtaining maximal responses. Recently, however, mathematical models have provided insight into one mechanism of peripheral nerve stimulation: peak depolarization occurs where the negative derivative of the component of the induced electric field parallel to nerve fibers is largest (Durand et al. 1989; Roth and Basser 1990). Both in vitro (Maccabee et al. 1993) and in vivo (Nilsson et al. 1992) experiments support this hypothesis for uniform, straight nerves. Based on these results, a 4-leaf magnetic coil (MC) design has been suggested that would provide a well defined site of stimulation directly under the center of the coil (Roth et al. 1990). In this note, we perform in vitro studies which test the performance of this new coil design during magnetic stimulation of a mammalian peripheral nerve.”

Maccabee’s experiments showed that the coil worked as advertised. In the Discussion of the paper we concluded that “the 4-leaf coil design provides a well defined stimulus site directly below the center of the coil”.

This is a nice story, but it’s all about exciting an action potential. What does it have to do with Frankie’s goal of blocking an action potential? Well, if you flip the polarity of the coil current, instead of depolarizing the nerve under the coil center, you hyperpolarize it. A strong enough hyperpolarization should block propagation. We wrote

“In a final type of experiment, performed on 3 nerves, the action potential was elicited electrically, and a hyperpolarizing magnetic stimulus was applied between the stimulus and recording sites at various times. The goal was to determine if a precisely timed stimulus could affect action potential propagation. Using induced hyperpolarizing current at the coil center, with a strength that was approximately 3 times greater than that needed to excite by depolarization at that location, we never observed a block of the action potential. Moreover, no significant effect on the latency of the action potential propagating to the recording site was observed….Our magnetic stimulator was able to deliver stimuli with strengths up to only 2 or 3 times the threshold strength, and therefore the magnetic stimuli were probably too weak to block propagation. It is possible that such phenomena might be observed using a more powerful stimulator.”

Frankie, I have good news and bad news. The good news is that you should be able to reversibly block nerve conduction with magnetic stimulation using a four-leaf coil. The bad news is that it didn’t work with Paul’s stimulator; perhaps a stronger stimulator would do the trick. Give it a try.