Where Volume I left off
Volume I taught you the canonical ladder — EEG → ECoG → intracortical — and its iron rule: signal quality rises with invasiveness. Volume II asks the harder, more useful question. Can we get implant-grade signals without the implant? This track is the honest accounting: what the emerging non-invasive and minimally-invasive modalities can and cannot buy, and why.
Keep this picture in mind. Each guide picks one region of the axis and asks how far it can be pushed: the magnetic route (OPM-MEG), the optical/hemodynamic route (fNIRS, HD-DOT, functional ultrasound), the minimally-invasive route (the endovascular Stentrode, ultrasonic motes), and finally the wearable/consumer edge. The organising concept is the invasiveness–signal-quality tradeoff.
Why the skull wins
The head is a volume conductor. Neural currents at the cortex spread through brain, cerebrospinal fluid, skull and scalp before reaching a sensor. At neural frequencies we are in the quasi-static regime — no wave propagation, just instantaneous spread of current — so a patch of active cortex looks, from outside, like a current dipole whose field the tissue attenuates and smears.
V(\mathbf{r}) = \frac{1}{4\pi\sigma}\,\frac{\mathbf{p}\cdot\hat{\mathbf{r}}}{r^{2}} = \frac{p\cos\theta}{4\pi\sigma\,r^{2}}A current dipole's potential falls as 1/r² even in a uniform medium; add the low-conductivity skull, which spatially low-pass filters the field, and you get EEG's centimetre-scale point spread.
The voltage from a tiny current dipole in the brain fades as the square of distance r — double the distance and it drops to a quarter. Add a skull that smears the field sideways, and by the time it reaches scalp electrodes a pinpoint source looks like a broad, centimetre-wide blur. That blur is why EEG can't localize sharply.
- V(\mathbf{r})
- The potential (voltage) measured at position \mathbf{r}.
- \mathbf{p}
- The current dipole — the strength and direction of the neural source.
- r
- Distance from the source; note the 1/r^2 falloff.
- \cos\theta
- The angle factor between dipole and sensor line; a sideways-facing dipole is nearly invisible.
A source 2 cm deep produces four times the surface voltage of one 4 cm deep, all else equal — so EEG is biased toward shallow, radially-oriented cortex.
Two consequences define this track. First, spatial resolution: because the skull blurs the field, scalp sensors cannot resolve sources finer than a few centimetres — deep and superficial generators overlap. Second, bandwidth: the tissue and the distance suppress high-spatial-frequency, high-amplitude spike activity, so non-invasively you see rhythms and evoked potentials, not single units. Every modality in this track fights one or both of these.
What 'implant-grade' means — in numbers
'Implant-grade' is not one number; it is a vector. The axes that matter are bandwidth (spikes demand kHz sampling; LFP/EEG live below ~200 Hz), spatial resolution (sub-millimetre for intracortical vs centimetres for scalp), independent degrees of freedom / channel count, SNR, and the bottom line that combines them: information transfer rate.
B = \log_{2} N + P\log_{2} P + (1-P)\log_{2}\!\left(\frac{1-P}{N-1}\right)Wolpaw bits-per-selection for N equiprobable choices at accuracy P; multiply by selections per minute for ITR. This is the common yardstick when we ask whether a non-invasive system is 'good enough'.
A single formula for "how much information does one choice carry?" Pick among N options with accuracy P: perfect accuracy gives the full \log_2 N bits, but mistakes claw some back. Multiply by choices per minute and you get the information transfer rate, the field's common scorecard for whether a BCI is fast enough.
- B
- Bits per selection — the information carried by one choice.
- N
- The number of possible choices.
- P
- The accuracy — the probability the choice is correct.
- \log_2 N
- The ceiling in bits if every choice were perfect.
Choosing among 4 letters (\log_2 4 = 2 bits) at 90% accuracy nets about 1.4 bits per selection; drop to chance (25%) and B falls to zero.
The gap is real and worth stating honestly. Intracortical systems have driven imagined-handwriting and speech decoders to the tens-to-~hundred-symbols-per-minute range; the best non-invasive spellers (P300, SSVEP) sit far lower, typically a handful of symbols per minute. The whole point of this track is to understand where that gap comes from — and which modalities can shrink it without a craniotomy.