Methodology · Scalp Fusion Locator (USC²)

The unified coordinate layer aligns the six naming languages of brain-region localization (MNI / CPC / EEG 10-20 / WHO acupoint / scalp-acu line / needle vector) onto one MNI-keyed record. Our coordinate math is BUILT ON and ALIGNED TO the established industry standard — CPC proportional coordinates (Xiao 2018 / Liu 2023), the 10-20 system, MNI152, IDW registration. This is by design and a credibility signal: we externally validated that our (u,v) agrees with the published MNI2CPC group CPC to ~10.3 mm.

To be plain: we did NOT invent a novel proprietary coordinate primitive. Our (u,v) is a SIMPLER (IDW) approximation of CPC, about 10 mm coarser than the group CPC — we describe it as "aligned to the CPC standard," never "more accurate" or "a coordinate system we invented." What this layer does sits at the APPLICATION level: (1) UNIFICATION of six naming systems onto one MNI-keyed record; (2) the fusion-error + confidence-halo AUDIT layer with outer/inner separation; (3) integration with the 120-target / 19-condition literature-derived evidence catalog.

In one line: the coordinate basis aligns to the industry standard (by design); this layer unifies and audits — it is not a claim of novel coordinate math.

We do not overlay images. We build a landmark-anchored normalized-proportion surface coordinate system (USC²) so the three localization languages land on one coordinate — measurable, reproducible, and update-able as the literature changes.

USC² five layers: A standard head model + fiducials (Nz/Iz/LPA/RPA/Cz); B proportional surface (u,v) — u = antero-posterior arc proportion (nasion→inion), v = coronal arc proportion (left→right ear), dimensionless and head-size-invariant; C registration of all three systems to (u,v); D nearest-neighbour fusion by inverse-distance weighting over the standard-head anchors (Euclidean chord, not scalp-mesh geodesic); E individualization tiers L1–L4 (only L1, the standard head model, is implemented at this stage).

EEG 10–20 splits the arcs between Nz, Iz, LPA, RPA into 10%/20% proportions; scalp-acupuncture uses bone-proportional cun (e.g. anterior→posterior hairline midline = 12 cun), body-relative with no absolute unit; MNI152 supplies the cortical source. Their shared language is landmark-anchored normalized proportion — the mathematical explanation of how cun "auto-fits" head size.

EEG ↔ MNI: Jurcak-style proportional registration (proportional interpolation on the standard 10–20/10–10 MNI coordinates), with the Towle 1993 / Okamoto 2004 scalp-electrode atlas kept as a cross-check; discrepancies are logged.

Cortex → scalp: Probabilistic projection, following MNI2CPC — a probabilistic cortex-to-scalp mapping (Liu F, Zhang Z, Chen Y, et al. Brain Stimulation 2023;16:1733–1742, doi:10.1016/j.brs.2023.11.011), which uses a ~2.5 cm conservative cortical mask. To be precise: our current implementation is an L1 radial-depth approximation aligned with that mask concept — not a reimplementation of the MNI2CPC algorithm.

Neighbours + uncertainty: Nearest acupoint / EEG / scalp-line uses inverse-distance weighting over Euclidean chord distance to the standard-head anchors (Shepard IDW, power 2; no scalp mesh at this stage, hence not geodesic); the only arc-length / angular computation feeds the deprecated CPC cross-check. Every registered point carries a confidence — probabilistic fusion, not hard point-stacking. Each coordinate object is stamped with its source + version.

Every target is shown with its source publication and an evidence tier label (Direct / Indirect / No direct study). Tiers describe how the literature supports an association — not whether a target is suitable for treatment.

Evidence tiers are research-use literature labels only — not an efficacy, safety, regulatory or treatment claim.

• C1 · Evidence tiers. Each target is labelled with its source publication and evidence tier; tiers describe how the literature supports an association — not an efficacy ranking or a suitability judgment.
• C2 · Pain system. Pain spans multiple nodes (M1/SMA/mPFC …) and mood–sleep comorbidity hubs; presented as anatomy + evidence, with no protocol prescribed.
• C4 · Statistical vs clinical significance. Peak-T / cluster size index statistical localization strength, not clinical benefit.
• C5 · Single vs multi-point. A condition often has several candidate targets; single vs combination is a clinical judgment — the tool only surfaces candidates + evidence.
• C6 · EEG's role. EEG 10–20 provides a measurable, standardized scalp-coordinate scaffold as the cortex↔scalp intermediary reference — no functional-readout claim.
• C7 · Proportional coordinates. (u,v) uses Euclidean-chord IDW proportion (an approximation of CPC’s geodesic arc-length proportion, agreeing to first order at the standard head) — intrinsically consistent with all three systems and head-size-invariant; proportional relations are drawn measurably on the figure, not only described in words.

Unified wording: literature-derived association, not causal; a candidate target for hypothesis generation and prospective validation — not a treatment recommendation.

We localize cortex↔scalp on two independent tracks that cross-check each other, not a single formula:

• Track A · USC² proportional surface: A normalized proportional coordinate (u,v) anchored on the same five fiducials the CPC industry standard uses (Nz/Iz/LPA/RPA/Cz) — closed-form, mesh-free, computable in real time on an iPad.
• Track B · MNI2CPC probabilistic projection: the published probabilistic cortex→scalp mapping (Liu 2023), used as the external reference for (u,v) and the source of our error budget.

Because both tracks share CPC’s same fiducials, USC’s u≈pNZ and v≈pAL agree to first order at the standard head by shared-endpoint construction; we do NOT claim they are identical — we measure and log the gap (our Euclidean-chord IDW vs their geodesic arc-length).

Error budget (cited external literature, NOT a product claim):

• Population-level MNI2CPC localization error of about 4.0 ± 0.7 mm (scalp) and 3.3 ± 0.6 mm (cortex), as reported in Liu 2023 (Brain Stimulation 2023;16:1733–1742).
• In a prospective, calibrated setting the best markerless expectation reported in the literature is about 2.3 mm.
• The dominant error source is inter-individual inion (Iz) variability, so the system automatically lowers confidence for occipital/parietal targets (a wider confidence halo).

These millimetre figures are a cited external-literature expectation range, used to convey the order of magnitude of method uncertainty — not a product precision guarantee for any individual, nor an efficacy or safety claim.

Our own internal cross-validation (LOO: interior accuracy + boundary stress test)partial

We run TWO leave-one-anchor-out validations with deliberately different purposes (each drops one EEG 10-20 anchor and recomputes from the rest via the same forward map), separating INTERIOR interpolation accuracy from a BOUNDARY extrapolation stress test. Both are our own measured numbers:

• Interior interpolation accuracy (the meaningful number): 5.5 ± 6.3 mm (n=2560 = 128 interior cortical targets × 20 folds; median 3.4, p95 18.8, max 46.6 mm). This is the interpolation stability at interior target points under one-anchor ablation — the interpolation regime a real cortical target actually sits in.
• Boundary extrapolation stress test (conservative upper bound): 57.3 ± 12.8 mm (n=20; median 56.8, p95 75.7, max 75.8 mm). Here the held-out anchor itself sits on the head-shell boundary, where an inverse-distance interpolant cannot extrapolate and collapses toward the remaining-anchor centroid — deliberately reported as an upper bound, far larger than the interior error.
• Reported alongside (NOT a parity claim): the published MNI2CPC population-level 4.0 ± 0.7 mm (Liu 2023).

Honesty framing: these numbers are NOT on the same footing as MNI2CPC and this is in NO way a parity or beat-MNI2CPC claim. Both LOO designs are geometric self-consistency / stability checks, not a 114-subject population validation; a cortical target has no external ground-truth (u,v), so the interior number measures interpolation SENSITIVITY to losing one control point (an honest interior proxy), labelled as such so it is not misread as absolute accuracy. Reported alongside (never claimed equal to) MNI2CPC.

External validation · vs MNI2CPC (Liu 2023 Fig 2b)partial

Our standard-head (u,v) agrees with the published group CPC in Liu et al. 2023 (Brain Stimulation 16:1733–1742) Fig 2b to ~10.3 ± 5.9 mm across 23 cited cortical targets. This is agreement-with-the-published-group-CPC at the standard head — a DIFFERENT quantity from Liu’s own leave-one-subject-out (n=114) per-subject scalp error of 4.03 ± 0.69 mm; shown side by side, explicitly NOT a parity or beat claim. See the validation page.

Enter an MNI152 coordinate (or pick a public landmark) to get the USC² proportional (u,v), named region, human-readable local address, clinical side and nearest 10-20 electrode in real time. Computed entirely in your browser using the same standard-head (L1) forward IDW map.

Proportional (u,v)

0.336, 0.348

Named region

FRONTAL-LEFT

Local address

FRONTAL-LEFT, 68% back, 87% lateral

Clinical side

Left (L)

Nearest 10-20

F3 · 1.9 cm

CPC estimate ≈ (u,v)

0.336, 0.348 (validated: agrees with published group CPC to ~10.3±5.9mm, Liu 2023 Fig 2b; n=23)

Arc-length CPC (pNZ, pAL) · secondary

0.198, 0.256 (arc-length reimpl, validates worse vs Liu, deprecated-as-primary; standard-head, ±~6.5mm)

Cortex→scalp depth

Pro / Research only

All outputs are standard-head-model (L1) approximate localization + uncertainty, a literature-derived association, not causal; not an efficacy, safety, regulatory, endorsement or treatment claim. The CPC antero-posterior axis (pNZ) is computed from NZ/IZ sourced via the MNE standard_1020 montage (affine-aligned to the repo MNI frame) — a standard-head estimate carrying ~6.5 mm uncertainty, not a per-subject measurement, never guessed. Individualized precision still awaits a cited external source.

The unified coordinate layer (in clinician language):

• Five fiducials. The exact nasion, inion, two pre-auricular points and vertex (Nz/Iz/LPA/RPA/Cz) used in everyday CPC/EEG practice — no extra measurement needed to align.
• A 5×3 named region grid. The proportional square is binned into prefrontal/frontal/central/parietal/occipital × left/midline/right — 15 human-readable cells, so any coordinate reads as “frontal-left, 30% back, 35% left.”
• One nested warp family. The default is always the conservative standard head; higher-fidelity tiers are opt-in. Per-tier implementation status:L1 standard head (default, zero regression)shippedL2 five-point affine + global TPSshippedL3 head-shape covariate / ellipsoid (individualization, awaits per-subject head-shape data)pending citationL4 full MRI / SimNIBS (reserved)methodology
• A confidence halo. On the /scd render, localization uncertainty is shown as the size of the halo around a target — tighter is more precise, wider is less certain.

All localization is a literature-derived association, not causal; any evidence tier is a literature label, not an efficacy/safety claim. Internal millimetre-level audit numbers are not surfaced as a product precision claim.

• Jurcak V, Tsuzuki D, Dan I. 10/20, 10/10, and 10/5 systems revisited — standardized MNI scalp coordinates. NeuroImage 2007.
• Okamoto M, et al. Three-dimensional probabilistic cranio-cerebral correlation via the 10-20 system. NeuroImage 2004.
• Towle VL, et al. The spatial location of EEG electrodes. Electroenceph Clin Neurophysiol 1993.
• Koessler L, et al. Automated cortical projection of EEG sensors. NeuroImage 2009.
• Liu F, Zhang Z, Chen Y, et al. MNI2CPC: a probabilistic cortex-to-scalp mapping for non-invasive brain stimulation targeting. Brain Stimulation 2023;16:1733–1742. doi:10.1016/j.brs.2023.11.011.
• WHO Standard Acupuncture Nomenclature (1990/1991); GB/T 21709.2–2021 (scalp acupuncture).
• GRADE / Evidence-to-Decision framework.
• Wu Y, Kong Q, et al. Chin Med 2025;20:58 (PMID 40329319) — the SCD/cognitive target source.

Only verified sources are listed.