Implantable microcoils for intracortical magnetic stimulation

When I worked at the National Institutes of Health in the 1990s, I studied transcranial magnetic stimulation. Russ Hobbie and I discuss magnetic stimulation in Chapter 8 of Intermediate Physics for Medicine and Biology. Pass a pulse of current through a coil held near the head; the changing magnetic field of the coil induces an electric field in the brain that stimulates neurons. Typical magnetic stimulation coils are constructed from several turns of wire, each turn carrying kiloamps of current in pulses that last for a tenth of a millisecond. Most are a few centimeters in size. Researchers have tried to make smaller coils, but these typically require even larger currents, resulting in magnetic forces that tear the coil apart as well as prohibitive Joule heating.

Imagine my surprise when Russ told me about a recently published paper describing magnetic stimulation using microcoils, written by Seung Woo Lee and his colleagues (“Implantable microcoils for intracortical magnetic stimulation,” Science Advances, 2:e1600889, 2016). Frankly, I am not sure what to make of this paper. On the one hand, the authors describe a careful study in which they perform all the control experiments I would have insisted on had I reviewed the paper for the journal (I did not). On the other hand, it just doesn’t make sense. 

Lee et al. built a coil by bending a 50 micron insulated copper wire into a single tight turn having a diameter of about 100 microns (see figure). Their current pulse lasted a few tenths of a millisecond, and had a peak current of….drum roll, please….about fifty milliamps. Yes, that would be nearly a million times smaller than the kiloamp currents used in traditional transcranial magnetic stimulation. Can this be? If true, it is a breakthrough, opening up the use of magnetic stimulation with implanted coils at the single neuron level.

 Figure from Lee et al. Science Advances, 2:e1600889, 2016.

Why am I skeptical? You can calculate the induced electric field E from the product of μ_o/4π times the rate of change of the current times an integral over the coil,

where R is the distance from a point on the coil to the point where you calculate E. The constant μ_o/4π is 10^-7 V s/A m. The rate of change of the current is about 0.05 A/0.0001 s = 500 A/s. The product of these two factors is roughly 5 × 10^-5 V/m. The difficult part of the calculation is the integral. However, it is dimensionless and if the coil size and distance to the field point are similar it should be on the order of unity. Maybe a strange geometry could provide a factor of two, or π, or even ten, but you don’t expect a dimensionless integral like this one to be orders of magnitude larger than one (Lee et al. derived an expression for this integral containing a logarithm, and we all know how slowly that function changes). So, the electric field induced by such a microcoil should on the order of 10^-4 V/m. Hause has estimated an electric field threshold for a neuron of about 10 V/m. How do you account for the missing factor of 100,000?

Lee et al. focus on the gradient of the electric field, rather than on the electric field itself. The gradient of the electric field plays an important role when performing traditional magnetic stimulation of a long straight axon, as you might find in the median nerve of the arm. However, when the spatial extent over which the electric field varies is smaller than the length constant, the relationship between the transmembrane potential and the electric field gradient becomes complicated. Also, in the brain neurons bend, branch, and bulge, so that the electric field may be the more appropriate quantity to use when estimating threshold. Yet, the electric field induced by a microcoil is really small.

So what is going on? I don’t know. As I said, the authors do several control experiments, and their data is convincing. My hunch is that they stimulated by capacitive coupling, but they examined that possibility and claim it is not the mechanism. I don’t have an answer, but their results are too strange to believe and too important to ignore. One thing I know for sure: the experiments need to be consistent with the fundamental physical laws outlined in Intermediate Physics for Medicine and Biology.