Three years ago, I wrote a post in this blog discussing an article by Seung Woo Lee and his coworkers (“ Implantable Microcoils for Intracortical Magnetic Stimulation,” Science Advances, 2:e1600889, 2016). They claimed to have performed magnetic stimulation of nerves by passing a 40 mA, 3 kHz current through a single-turn microcoil with a size less than a millimeter. I claimed that the electric field induced in the surrounding tissue by such a coil would be much smaller than Lee et al. predicted. In their Figure 2 they calculated that a 1 mA current induced an electric field on the order of 2 V/m. I calculated an electric field about a million times smaller, and concluded “their results are too strange to believe and too important to ignore.”
I didn’t ignore them. Recently a graduate student here at Oakland University, Mohammed Alzahrani, and I tested the hypothesis that excitation using microcoils is caused by capacitive coupling rather than magnetic stimulation. The picture below shows our model. The current at the left end of the microcoil passes through the capacitance of the insulation and enters the surrounding tissue. It then flows through the tissue, possibly exciting neurons along its path, until reentering the wire through the capacitance near the right end.
Does this model look familiar? It’s similar to the cable model for a nerve axon (for more about the cable model, see Section 6.11 of Intermediate Physics for Medicine and Biology). The wire in our model is analogous to the intracellular space of the axon in the traditional cable model, and the insulation surrounding the wire is analogous to the cell membrane. Our model’s even simpler than the traditional cable model because the conductance of the insulation is so low that it can be taken as zero; the only way for current to leave the wire is through the capacitance. This model is not new; it was derived in the 19 th century to describe current through the transatlantic telegraph cable.
Our goal was to calculate the electric field assuming capacitive coupling, to see whether it’s larger or smaller than what you’d expect from magnetic stimulation. We concluded
In summary, we predict an electric field in the tissue due to capacitive coupling of about 4 mV/m for a current of 1 mA and 3 kHz. The electric field produced by magnetic stimulation would be thousands of times less, on the order of 0.002 mV/m. Therefore, capacitive coupling should be the dominant mechanism for stimulation with a microcoil.
What’s the moral to this story? As I wrote at the end of my previous post, experiments “need to be consistent with the fundamental physical laws outlined in Intermediate Physics for Medicine and Biology.”