Magnetoencephalography

Outside the head, the magnetic field of a working brain is typically 50–500 fT. Against an Earth field of 25–65 µT that is a billionth to a hundred-millionth of the background, and traffic, lifts and power lines disturb a laboratory far more than the brain does. Magnetoencephalography was a problem of sensors and shielding long before it was a neuroscience result; solved, it showed the currents that EEG records, through a skull that barely distorts them.

From a coil to a SQUID

David Cohen’s first recording, published in 1968, used an induction coil — two million turns of copper wire on a ferrite core — in a shielded chamber. A coil senses the rate of change of flux, and the alpha rhythm, about 10 Hz and by Cohen’s estimate 0.1 pT peak to peak near the scalp, emerged only by averaging against the EEG.

The sensor that made the method practical came from a car company. In 1964 Jaklevic, Lambe, Silver and Mercereau, at Ford’s Scientific Laboratory in Dearborn, reported quantum interference in a superconducting ring broken by two Josephson junctions: the dc SQUID, whose output repeats with every flux quantum through the ring. By 1970 James Zimmerman’s rf-biased point-contact devices were stable and resolved about 100 fT per root hertz.

With one in the shielded room Cohen had built at MIT — moly-permalloy and aluminium, 100 dB of attenuation above 10 Hz — he, Edgar Edelsack and Zimmerman recorded the heart without averaging in 1970. In 1972 Cohen did the same for the brain: a healthy subject’s alpha rhythm, and a patient’s slow waves with a direct-current component no coil could register.

Subtraction and feedback

Even shielded, a bare magnetometer hears nearby sources — the heart’s field at the chest exceeds the brain’s by two to three orders of magnitude — so the pickup coil is wired in series with an identical coil wound the opposite way, a few centimetres further out: a spatial filter that cancels uniform fields and passes steep ones. With a source 3 cm below the pickup and a 5 cm baseline, a field falling as the square of distance reaches the second coil at $(3/8)^2$, a seventh of its strength, so most of the signal survives. A magnetised object 10 m away, its field falling as the cube of distance, differs between the coils by about 1.5%, and only that survives.

The SQUID’s response is periodic in flux, so a feedback loop holds the ring at one working point and reports the flux that took — the null balance of the voltage clamp, applied to flux. Read that way, dc SQUIDs reached a few femtotesla per root hertz by the late 1980s, and the noise that then limited them was thermal: Johnson currents in the aluminium foil of the dewar’s insulation, too close to the coils for any gradiometer to cancel.

What the skull does not do

MEG and EEG record the same currents, mostly in pyramidal cells whose apical dendrites run perpendicular to the cortex, so a patch’s net current points along its local normal. The poorly conducting skull smears the potentials, but the magnetic field comes mainly from currents inside it, and with conductivity varying essentially only along the head’s radius, the field outside a spherically symmetric conductor does not depend on the conductivities at all. Measured in pigs with and without the skull, evoked fields were virtually undistorted (Okada and colleagues, 1999), deeper sources less so.

The symmetry costs an orientation: a radial current in a spherical conductor produces no field outside. MEG is most sensitive to the walls of sulci, where current runs tangential to the skull, and much less to the crowns of gyri, which EEG picks up more readily.

It also sees only crowds. One postsynaptic current is a dipole of about 20 fA·m; a typical evoked source of 10 nA·m takes about a million synapses active at once. Like EEG, MEG reports what a population does in step, and its first signal was a rhythm, the alpha oscillation.

TMS, run backwards

Transcranial magnetic stimulation is the same coupling driven from the other end: in MEG, current in the cortex sends flux through a coil; in TMS, a changing current in the coil induces an electric field that drives current in the cortex. Reciprocity, the reason a mutual inductance is the same whichever winding is driven, ties the two exactly at low frequencies. For a current dipole $\mathbf{Q}$ at position $\mathbf{r}$,

$$\Phi = -\,\mathbf{Q} \cdot \mathbf{e}(\mathbf{r})$$

where $\Phi$ is the flux through the coil, volume currents included, and $\mathbf{e}(\mathbf{r})$ the electric field the coil would induce at $\mathbf{r}$ per unit rate of change of its own current, boundary charges included. A coil’s map of sensitivity is its map of stimulation, as Eaton set out for both uses in 1992.

So each property of MEG has a twin. Its blindness to radial currents is a coil’s near-inability to induce a radial electric field in a spherical head: none for a steadily ramping current, Eaton showed, and little for an oscillating one. Its indifference to the skull is the stimulating field’s, which in a spherically symmetric head does not depend on the conductivity profile — why, Heller and van Hulsteyn noted in 1992, skull conductivity barely matters to stimulation. They also proved that external sources cannot put a three-dimensional maximum of electric field strength inside the brain, so by reciprocity neither a coil nor any weighting of MEG sensors can peak at a deep point.

Human cortical responses, located and timed

What neuroscience got was a timetable of human cortex with places attached. Riitta Hari and colleagues placed the 100 ms auditory response in supratemporal auditory cortex in 1980. In 1985 Charles Wood, Cohen and colleagues found the magnetic and electric maps of the response 20–30 ms after median-nerve stimulation about 90 degrees apart, as a tangential source in somatosensory cortex predicts and neither a thalamic nor a radial cortical source alone could; the orientation MEG cannot see became a way of telling sources apart.

The clinic followed. In 1982 Barth and colleagues argued that the field over an epileptic focus could establish the location, depth and orientation of a spike’s currents, and MEG has since helped locate foci before surgery, though it was slow to become routine.

What it cost

Most of the price is the cold. SQUIDs sit in liquid helium at about 4 K behind a vacuum that keeps an adult’s brain about 3 cm from the sensors and a child’s further, and the signal falls as the square of that distance. The helmet is one size, a 5 mm movement of the head can spoil a recording, and the helium must be delivered or reliquefied on site. In 1993, with EEG routine in thousands of laboratories, there were fewer than 50 MEG installations.

The inverse costs the rest. Helmholtz showed in 1853 that currents inside a conductor cannot be recovered uniquely from the fields outside, so every MEG map is a model — one dipole, a few, or a distributed minimum-norm estimate — and the problem is often ill-conditioned, small errors in the data becoming large errors in the answer. Even the advantage over EEG was disputed, by the method’s pioneer: in 1990 Cohen and colleagues passed current through depth electrodes in three epilepsy patients and found localisation errors averaging 8 mm for MEG and 10 mm for EEG. Critics replied that the test sources were nearly radial, the orientation MEG barely sees, and a 1992 consensus statement called the two methods complementary.

Wearable MEG attacks the cold. Optically pumped magnetometers sense the field through the precession of spin-polarised alkali atoms near zero field, without cryogenics, and sit on the scalp: in 2017 a single one recorded somatosensory responses about four times larger than a SQUID system did. In 2018 Elena Boto and colleagues mounted 13 in a 3D-printed cast and located beta-band changes in motor cortex while the subject bounced a table-tennis ball on a bat. Each sensor works only within ±1.5 nT, which in their shielded room’s remnant 25 nT a head turn of under 4° would exceed, so coils on two planes, under feedback from reference sensors, cut the remnant 50-fold. The head could move; the room was still needed.