Transcranial magnetic stimulation

The skull is a poor conductor and an excellent obstacle. Current applied at the scalp spreads through it and mostly misses the target. A changing magnetic field, however, does not care about the skull at all — bone is essentially transparent to it, and the induced electric field appears directly in the tissue underneath.

What it is

A capacitor bank, some hundreds of microfarads charged to a couple of kilovolts, discharged through a coil held against the scalp by a thyristor or IGBT. Peak currents run to several kiloamps over a hundred microseconds or so. By Faraday’s law the collapsing field induces an electric field in the cortex, and where that field’s gradient along an axon is steep enough, the axon fires.

The coil ties those numbers together, because it is an inductor. A common 70 mm figure-of-eight coil measures about 16 µH. Ignoring the cable and the losses, a current that peaks 100 µs after the switch closes — a quarter of the ringing period — needs about 250 µF, and the pair then has a characteristic impedance $\sqrt{L/C}$ of about a quarter of an ohm, where $L$ is the coil’s inductance and $C$ the capacitance. So 5 kA at the peak needs some 1.3 kV on the capacitor, and at that instant about 200 J sits in the magnetic field, which near the coil reaches the order of a tesla, like the static field of an MRI scanner.

Why it matters

TMS made it possible to intervene in a specific piece of human cortex without surgery, which is a genuinely rare capability. Its clinical use in depression follows from that, as does a large fraction of what is known about human motor cortex, since a coil over the motor strip produces a twitch you can measure at the hand.

The interesting engineering constraint is that the pulse shape has, historically, not been a design choice. It is whatever the LC ringdown of the capacitor and coil produces — typically a damped cosine, because that is what the circuit does, not because anyone chose it for neural efficiency. The energy stored per pulse is

$$E = \tfrac{1}{2} C V^2$$

where $V$ is the charging voltage, and whatever the circuit does not return to the capacitor by the end of the pulse becomes heat, in the coil and the rest of the circuit. Coil heating, not biology, is what limits how long a session can run.

That gap between the waveform the circuit produces and the waveform a neuron would prefer is where power electronics has something to offer, and it is the subject of my own work on flexible pulse shaping.

From phosphenes to motor cortex

Induction had been tried on the head long before it worked. In 1896 d’Arsonval reported that an alternating magnetic field could stimulate living tissue; among the effects were the flickering lights now called magnetophosphenes, usually traced to the retina, not the brain. Silvanus Thompson tried it on his own head in London in 1910, and in 1959 Kolin, Brill and Broberg made a frog nerve–muscle preparation contract with an alternating field. In Barker and Freeston’s account these attempts largely failed because nobody could yet make fields that were both large and rapidly changing.

The method TMS displaced was electrical, pioneered by Merton and Morton in 1980: high-voltage shocks between electrodes on the scalp of a conscious subject. Much of the current runs along the scalp and only a small part enters the brain, and the shocks are uncomfortable; once a painless alternative existed, the method’s use declined rapidly.

The alternative came from Sheffield. A programme begun in 1976 at the Royal Hallamshire Hospital and the University of Sheffield set out to stimulate nerves with magnetic pulses short enough for the evoked response to be recorded, and in 1982 Polson, Barker and Freeston reported supramaximal stimulation of peripheral nerve trunks. In February 1985 Anthony Barker, Reza Jalinous and Ian Freeston stimulated the human motor cortex; their letter to The Lancet appeared on 11 May. Because the induced current does not pass through the skin, where most pain endings lie, the method was essentially painless. By 1991 Barker counted some 500 magnetic stimulators in use worldwide.

What the field actually excites

The rule in the first section is the classical one, and it holds for a long, straight axon. In 1990 Roth and Basser fed the field from a capacitor discharge into a Hodgkin–Huxley cable model of a nerve fibre and found the fibre driven by the gradient of the field component parallel to it. Maccabee and colleagues tested that in 1993 on nerves in a trough of Ringer’s solution. A straight nerve under a figure-of-eight coil fired where the field fell away along its length, not under the centre of the coil, where the field was strongest. Bending the nerve, with the current running towards the bend, lowered the threshold there, more so the sharper the bend, and in a straight nerve the threshold was lowest with the current running towards a cut end.

A bend or an ending is where the field component along an axon changes abruptly even when the field itself is smooth, so the rule survives in cortex, where axons bend and terminate everywhere; what changes is where it bites. In a 2020 model that set morphologically realistic neurons inside a head, Aberra and colleagues found the lowest thresholds at the terminals of intracortical axons in the crowns and lips of gyri, layer 5 pyramidal cells the most excitable, and activation set mainly by the field’s magnitude rather than its component normal to the cortical surface.

Physiology agrees that near threshold the pulse works mostly through synapses. Over the hand area, a just-suprathreshold pulse evokes a muscle response about 1.5 ms later than electrical stimulation does. Recordings of the descending volleys show why: depending on coil orientation, it recruits the indirect, synaptically driven I-waves first, and the direct D-wave only at much higher intensity.

Coils, and the depth–focality trade-off

TMS was introduced with circular coils about 10 cm across. A circular coil induces concentric loops of current that are zero on its axis and strongest under the winding, which leaves considerable uncertainty about where stimulation occurs. In 1988 Ueno, Tashiro and Harada proposed a pair of coils driving their fields through the head in opposite directions, so that the induced currents flow together under the junction. In their finite-element calculations the current density there was two to three times that elsewhere, and frog nerve–muscle preparations bore it out. The figure-of-eight is generally credited to them, although the same geometry had been proposed earlier as a pickup coil for magnetoencephalography, the same coupling run backwards.

No geometry can focus at depth. Heller and van Hulsteyn proved in 1992 that no arrangement of external sources can produce a three-dimensional maximum of field strength inside the brain; the maximum always lies on a boundary where conductivity changes. The same analysis explains the opening of this entry: in a spherically symmetric head, the field from a coil does not depend on the conductivity profile at all, skull included.

In 2013 Deng, Lisanby and Peterchev simulated 50 coil designs in a spherical head and found every one on the same trade-off. Half-value depths — how far below the cortical surface the field stays above half its surface maximum — ran from 0.9 to 3.5 cm, and the deeper a coil’s field reached, the wider it spread. Figure-of-eight designs were the focal ones, with a tangential spread (half-value volume over half-value depth) as small as 5 cm² against 34 cm² for the best circular-type coil, but they reached no deeper. The deep-stimulation H-coils (Roth, Zangen and Hallett, 2002) came out 22–72% deeper than a 70 mm figure-of-eight, with a spread five to nine times as large.

Real heads are not spheres. Finite-element models of an individual head, with conductivities mapped by diffusion MRI, show the field concentrated on the crowns and lips of gyri and strongest where the induced current crosses them (Opitz and colleagues, 2011). In 2015 the developers of one such modelling pipeline, SimNIBS, judged these models still far from being standard tools for planning TMS in practice.

Two waveforms, then a parameter

Within the capacitor discharge there were two choices, and they differ in where the energy goes. A monophasic stimulator hands the coil current to a diode and resistor once the capacitor has emptied, a quarter-cycle in; only the first phase of the induced field stimulates, and the whole pulse energy ends as heat. A biphasic stimulator lets the current ring through a full cycle and back into the capacitor, recovering part of the energy for the next pulse — up to about 60% of it, in Barker and Freeston’s 2007 account. The monophasic penalty, as Goetz and colleagues put it in 2013, belongs to the circuit, which damps the pulse with a resistor on purpose, not to the waveform. It is why repetitive TMS usually runs on biphasic pulses, although its after-effects have been stronger and longer-lasting with monophasic ones. Either way, less than one percent of the pulse energy reaches the tissue.

The rise time, at least, was chosen. Barker’s group found in 1991 that the stored energy needed to stimulate varied by about two to one across the waveforms they tested, shorter rises being more efficient, and from the same measurements estimated membrane time constants of about 150 µs in nerve and cortex. The shape stayed the circuit’s because the switch could not stop: a thyristor, once fired, conducts until the coil current falls to zero.

Peterchev, Jalinous and Lisanby replaced it with an IGBT, which can be turned off mid-pulse. Their cTMS of 2008 produced near-rectangular field pulses with widths from 5 µs to over 100 µs and 67–72% less coil heating than matched cosine pulses. A second version (2011), with two capacitors and two IGBT modules, set the number, polarity, width and amplitude of the phases, ran 3,000-pulse trains at up to 50 Hz, and dissipated up to 82% less energy than conventional monophasic stimulation and up to 57% less than biphasic. A third (2014) gave the coil four voltage levels, one of them close to zero, and could deliver theta bursts of predominantly unidirectional pulses. The pulse was becoming something specified rather than inherited.

Human motor cortex, mapped non-invasively

Penfield and Boldrey’s homunculus of 1937 was assembled from electrical stimulation of the cortex in 126 awake patients, operated on under local anaesthesia between 1928 and 1936. TMS made the measurement possible in healthy volunteers, and repeatable.

In 1992 Wassermann and colleagues stepped a coil across scalp positions 1 cm apart in ten subjects, recording motor evoked potentials from four muscles between thumb and shoulder. Distal muscles had larger representations and lower thresholds, and the maps ran in somatotopic order, proximal to distal, along a posteromedial-to-anterolateral line on the scalp. With nothing to open, mapping can be repeated daily: Pascual-Leone and colleagues (1995) mapped people learning a five-finger piano exercise over five days and watched the areas targeting the long finger flexors and extensors enlarge and their thresholds fall, for the practising hand only.

Two pulses reach circuits that one cannot. Kujirai and colleagues (1993) preceded a test pulse with a subthreshold conditioning pulse: at intervals of 1–6 ms the response shrank and at 10 and 15 ms it grew, and two control experiments pointed to cortex rather than spinal cord as the site of the suppression — intracortical inhibition, measured in a conscious person. Clinically, TMS was first used to time the motor pathway: subtract the conduction time from spinal roots to muscle from the latency of the response to a cortical pulse, about 20 ms in a hand muscle, and what remains is the central motor conduction time. Away from motor cortex the pulse became a reversible lesion. Amassian and colleagues (1989) gave an occipital pulse 80–100 ms after a brief display of three letters, and subjects saw a blur or nothing.

From the motor strip to the clinic

Daily left prefrontal rTMS for depression appeared in the mid-1990s, in a six-patient pilot from George and colleagues (1995) and a sham-controlled crossover study from Pascual-Leone and colleagues (1996). In 2007 O’Reardon and colleagues reported a multisite trial that randomised 301 medication-free patients to active or sham stimulation over the left dorsolateral prefrontal cortex: ten pulses a second at 120% of motor threshold, 3,000 pulses a session, five sessions a week for four to six weeks. Active stimulation beat sham on the primary measure at four weeks, after a post hoc correction for unequal baseline severity, and on two Hamilton scales; remission at six weeks was about twice as common.

On 7 October 2008 the FDA classified Neuronetics’ NeuroStar, by the de novo route, for major depression in patients who had not benefited from one antidepressant trial. The order created a device type, the repetitive transcranial magnetic stimulation system, and later machines were cleared through 510(k) notifications, each as substantially equivalent to one already on the market.

Theta burst came out of motor cortex physiology. Huang, Rothwell and colleagues (2005) gave bursts of three pulses at 50 Hz, five bursts a second, and after only 20–190 s of stimulation saw effects on motor cortex more consistent and longer-lasting than conventional rTMS usually managed. The THREE-D trial (Blumberger and colleagues, 2018) randomised 414 patients to a 37.5-minute 10 Hz session or a 3-minute intermittent theta-burst session; depression scores fell by the same amount, and theta burst was non-inferior. In August 2018 the FDA cleared MagVenture’s theta-burst system, 600 pulses in 3 minutes 9 seconds, on the strength of a large randomised multicentre trial — THREE-D, by the account of a later clearance.

Stanford’s SAINT protocol, later renamed SNT, then compressed the course rather than the session: ten sessions of 1,800 pulses a day for five days, 90,000 pulses in all at 90% of motor threshold, aimed at the patch of left dorsolateral prefrontal cortex whose resting fMRI signal is most anticorrelated with the subgenual anterior cingulate. In its sham-controlled trial, at a planned interim analysis of 29 participants, depression scores four weeks after treatment had fallen by 52.5% with active stimulation and 11.1% with sham (Cole and colleagues, 2022). The FDA cleared Magnus Medical’s system on 1 September 2022. A course in 2008 delivered 3,000 pulses a day; this one delivers 18,000, through a MagVenture stimulator with a coil cooler.

What it costs

Depth is the hard limit. Deep targets are reached only by stimulating everything above them more strongly, and coils designed for depth, the H-coil among them, have not solved that.

The dose is a proxy. Intensity is set as a percentage of the motor threshold, the lowest intensity that evokes a 50 µV response from a hand muscle in at least half of ten trials, and then applied to prefrontal cortex, which may sit at a different distance from the coil. Magnus corrects for that difference in depth; Nexstim’s cleared system goes as far as a proprietary field model, used to orient the coil.

How repeated pulses change excitability is still, as Barker and Shields wrote in 2017, not fully understood — the same gap between effect and mechanism as in deep brain stimulation.

The response depends on the brain’s state at the moment of the pulse. In 2018 Zrenner and colleagues used a real-time EEG system to fire identical bursts on the negative or the positive peak of the sensorimotor mu rhythm; one produced a lasting LTP-like rise in excitability and the other no change. That is an argument for closed-loop stimulation, and for stimulators that can be told when to fire and, eventually, what.

And the hardware still runs hot. The 2009 safety guidelines called coil overheating a severe limitation on rTMS, and accelerated protocols have since multiplied the daily pulse count by six.

A dated log of clearances, papers and machines in the field is kept at /tms/.