The best part of Maccabee’s article is the pictures. I reproduce three of them below, somewhat modified from the originals.
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| Fig. 1. The electric field and its derivative produced by magnetic stimulation using a figure-of-eight coil. Based on an illustration in Maccabee et al. (1993). |
The main topic of the paper was how an electric field induced in tissue during magnetic stimulation could excite a nerve. The first order of business was to map the induced electric field. Figure 1 shows the measured y-component of the electric field, Ey, and its derivative dEy/dy, in a plane below a figure-of-eight coil. The electric field was strongest under the center of the coil, while the derivative had a large positive peak about 2 cm from the center, with a large negative peak roughly 2 cm in the other direction. Maccabee et al. included the derivative of the electric field in their figure because cable theory predicted that if you placed a nerve below the coil parallel to the y axis, the nerve would be excited where −dEy/dy was largest.
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| Fig. 2. An experiment to show how the stimulus location changes with the stimulus polarity. Based on an illustration in Maccabee et al. (1993). |
The most important experiment is shown in Figure 2. The goal was to test the prediction that the nerve was excited where −dEy/dy is maximum. The method was to simulate the nerve using one polarity and then the other, and determine if the location where the nerve is stimulated shifted by about 4 cm, as Figure 1 suggests.
A bullfrog sciatic nerve (green) was dissected out of the animal and placed in a bath containing saline (light blue). An electrode (dark blue dot) recorded the action potential as it reached the end of the nerve. A figure-of-eight coil (red) was placed under the bath. First Maccabee et al. stimulated with one polarity so the stimulation site was to the right of the coil center, relatively close to the recording electrode. The recorded signal (yellow) consisted of a large, brief stimulus artifact followed by an action potential that propagated down the nerve with a speed of 40.5 m/s. Then, they reversed the stimulus polarity. As we saw in Fig. 1, this shifted the location of excitation to another point to the left of the coil center. The recorded signal (purple) again consisted of a stimulus artifact followed by an action potential. The action potential, however, arrived 0.9 ms later because it started from the left side of the coil and therefore had to travel farther to reach the recording electrode. They could determine the distance between the stimulation sites by dividing the speed by the latency shift; (40.5 m/s)/(0.9 ms) = 4.5 cm. This was almost the same as the distance between the two peaks in the plot of dEy/dy in Figure 1. The cable theory prediction was confirmed.
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| Fig. 3. The effect of insulating obstacles on the site of magnetic stimulation. Based on an illustration in Maccabee et al. (1993). |
In another experiment, Maccabee and his coworkers further tested the theory (Fig. 3). The electric field induced during magnetic stimulation was perturbed by an obstruction. They placed two insulating lucite cylinders (yellow) on either side of the nerve, which forced the induced current to pass through the narrow opening between them. This increased the strength of the electric field (green), and caused the negative and positive peaks of the derivative of the electric field (dark blue) to move closer together. Cable theory predicted that if the cylinders were not present the latency shift upon change in polarity would be relatively long, while with the cylinders the latency shift would be relatively short. The experiment found a long latency (1.2 ms) without the cylinders and a short latency (0.3 ms) with them, confirming the prediction. This behavior might be important when stimulating, say, the median nerve as it passes between two bones in the arm.
In addition, Maccabee examined nerves containing bends, which created “hot spots” where excitation preferentially occurred. They also examined polyphasic stimuli, which caused excitation at both the negative and positive peaks of dEy/dy nearly simultaneously. I won’t reproduce all their figures, but I recommend you download a copy of the paper and see them for yourself.
Why do I like this paper so much? For several reasons.
- It’s an elegant example of how theory suggests an experiment, which once confirmed leads to additional predictions, resulting in even more experiments, and so on; a virtuous cycle.
- Their illustrations are informative and clear (although I do like the color in my versions). You should be able to get the main point of a scientific paper by merely looking through the figures, and you can do that with Maccabee et al.’s article.
- In vitro experiments (nerve in a dish) are nice because they strip away all the confounding details of in vivo (nerve in an arm) experiments. You can manipulate the system (say, by adding a couple lucite cylinders) and determine how the nerve responds. Of course, some would say in vivo experiments are better because they include all the complexities of an actual arm. As you might guess, I prefer the simplicity and elegance of in vitro experiments.
- If you want a coil that stimulates a peripheral nerve below its center, as opposed to off to one side, you can use a four-leaf-coil.
- Finally, I like this article because Peter Basser and I were the ones who made the theoretical prediction that magnetic stimulation should occur where −dEy/dy, not Ey, is maximum (Roth and Basser, “Model of the Stimulation of a Nerve Fiber by Electromagnetic Induction,” IEEE Transactions on Biomedical Engineering, Volume 37, Pages 588-597, 1990). I always love to see my own predictions verified.
I’ve lost track of my friend Paul Maccabee, but I can assure you that he did good work studying magnetic stimulation of nerves. His article is well worth reading.
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