The depth-focality bind
Every non-invasive method fights the same physics. Fields spread as they enter the head, so to reach a deep target you must drive the overlying cortex even harder — you trade focality for depth. This is why non-invasive deep stimulation is the holy grail: escaping the depth-focality bind without opening the skull. Read the modalities below as different attempts to cheat that tradeoff.
TMS: stimulation by induction
Transcranial magnetic stimulation drives a brief, large current through a coil on the scalp. The rapidly changing magnetic field induces an electric field in the cortex strong enough to fire neurons — a genuinely suprathreshold, non-invasive technique. A single pulse over motor cortex twitches a muscle; repetitive TMS (rTMS) over prefrontal cortex is an approved depression therapy.
\mathbf{E} = -\frac{\partial \mathbf{A}}{\partial t}, \qquad \left|\mathbf{E}\right| \propto \frac{dI_{\mathrm{coil}}}{dt}The induced electric field is the (negative) time-derivative of the magnetic vector potential, so what matters is not the field magnitude but how fast the coil current changes. TMS reaches only a few centimeters, and focality is set by coil geometry (a figure-eight coil concentrates the field at its crossing).
TMS doesn't push current in directly — it swings a magnetic field so fast that the change induces an electric field in the brain. What counts is not how big the coil's field is, but how quickly its current rises and falls, which is why TMS uses sharp, rapid pulses.
- \mathbf{E}
- The electric field induced inside the head — what actually stimulates neurons.
- \mathbf{A}
- The magnetic vector potential; its rate of change is the source of \mathbf{E}.
- \frac{dI_{\mathrm{coil}}}{dt}
- How fast the coil current changes — the true lever on field strength.
Doubling how fast you ramp the coil current roughly doubles the induced field, even with the same peak current — so pulse speed, not just amplitude, sets the dose.
tES: nudging, not firing
Transcranial electrical stimulation is a different regime. Only a small fraction of the scalp current reaches the brain, producing weak intracranial fields (on the order of a few tenths of a volt per meter). That is subthreshold — it does not fire neurons, it biases their membrane potential. tDCS shifts excitability up or down depending on polarity; tACS oscillates and can, under some conditions, nudge ongoing rhythms toward its own frequency (entrainment).
Reaching deep without surgery: ultrasound and interference
Focused ultrasound uses a mechanical, not electrical, actuator: an acoustic wave that can be focused to a millimeter-scale spot deep in the brain, steerable without any implant. Its neuromodulatory mechanism (mechanosensitive ion channels, membrane cavitation) is still debated, and at higher intensity the same focus can transiently open the blood-brain barrier for targeted drug delivery — a second, entirely different application.
Temporal interference is a clever electrical trick for deep targeting. Apply two high-frequency currents at slightly different frequencies f_1 and f_2. Neurons cannot follow kilohertz carriers, so each field alone does nothing — but where the two fields overlap, their amplitude envelope beats at the low difference frequency \Delta f = f_2 - f_1, which neurons can follow. By steering where the fields intersect, one can in principle place a low-frequency drive deep in tissue without exciting the cortex above it.
\cos(2\pi f_1 t) + \cos(2\pi f_2 t) = 2\cos\!\big(\pi \Delta f\, t\big)\,\cos\!\big(2\pi \bar{f}\, t\big)The temporal-interference identity: two nearby high frequencies sum to a fast carrier at the mean frequency f-bar, modulated by a slow envelope at half the difference. The neurons demodulate the envelope. In practice, focality and the strength of the deep drive remain active research questions, and human evidence is early.
Add two tones at nearly the same high frequency and you hear a fast note that slowly swells and fades — a "beat." That swelling envelope oscillates at half the difference of the two frequencies. Deep neurons can't follow the fast carrier but can respond to the slow envelope — the idea behind temporal-interference stimulation (still an open question in humans).
- f_1,\,f_2
- The two nearby driving frequencies.
- \bar{f}
- Their mean — the fast carrier you actually get.
- \Delta f
- Their difference; the slow envelope beats at \Delta f/2.
Drive at 2000 Hz and 2010 Hz and the carrier sits near 2005 Hz while the envelope pulses at 5 Hz — a rhythm neurons care about, delivered where the two beams overlap.
The specificity dream: optogenetics and chemogenetics
Electrical stimulation cannot choose which cell type it recruits; biological actuators can. Optogenetics expresses light-sensitive opsins in genetically defined neurons, so a pulse of light can excite or silence exactly one population with millisecond precision — the tool that let neuroscience establish causal circuit roles. Chemogenetics (DREADDs) instead expresses a designer receptor activated only by a designer drug, giving slower, hours-long, hardware-free control.