1. Foundations of Scalp Electrogenesis and the International 10-20 Standard
Electroencephalography (EEG) is a non-invasive biophysical imaging methodology that detects the brain's macroscopic electrical activity across the human scalp. The electrical potentials measured at the surface of the head do not stem from individual action potentials—whose brief 1-millisecond duration and spatial incoherence cause severe destructive interference—but rather from the synchronous summation of excitatory and inhibitory postsynaptic potentials (EPSPs and IPSPs) generated within the apical dendrites of tens of thousands of vertically oriented neocortical pyramidal neurons [1]. Because these pyramidal cells are aligned perpendicular to the cortical surface, their synchronous activation produces coherent spatial dipole layers that conduct passively across the cerebrospinal fluid, skull bone, and galea aponeurotica.
To enable reproducible recording geometries, clinical diagnostics, and cross-subject neuroimaging comparisons independent of individual head circumferences or craniometric shapes, Dr. Herbert H. Jasper chaired a committee for the International Federation of Societies for Electroencephalography and Clinical Neurophysiology (IFCN) in 1958, formally introducing the International 10-20 System. This reference framework establishes standardized electrode locations by proportionally subdividing anatomical cranial arcs using intervals of 10% and 20% of the total skull dimension measured between established landmarks [2].
2. Mathematical Formulations: Jasper's Cranial Proportions and Spherical Geometry
The standard 10-20 layout is grounded in four cardinal anatomical craniometric landmarks:
- Nasion ($N_z$): The depressed midline anatomical junction between the frontal and nasal bones at the bridge of the nose.
- Inion ($I_z$): The external occipital protuberance located at the inferoposterior midline of the skull.
- Left Preauricular Point ($LPA$): The anterior depression immediately superior to the tragus of the left ear.
- Right Preauricular Point ($RPA$): The corresponding anterior tragal indentation on the right ear.
The anterior-posterior cranial midline arc distance, denoted $S_{AP}$, is measured along the midsagittal curve from the Nasion to the Inion. Electrodes along this midline are distributed at proportional arc intervals:
$$\Delta S_{AP} = S(N_z \rightarrow I_z)$$
$$S(N_z \rightarrow F_{pz}) = 0.10 \times S_{AP}$$
$$S(F_{pz} \rightarrow F_z) = 0.20 \times S_{AP}$$
$$S(F_z \rightarrow C_z) = 0.20 \times S_{AP}$$
$$S(C_z \rightarrow P_z) = 0.20 \times S_{AP}$$
$$S(P_z \rightarrow O_z) = 0.20 \times S_{AP}$$
$$S(O_z \rightarrow I_z) = 0.10 \times S_{AP}$$
The vertex electrode, $C_z$, marks the geometric midpoint situated at 50% of the distance from both $N_z \rightarrow I_z$ and $LPA \rightarrow RPA$. Similarly, the coronal transverse arc $S_{LR}$ is partitioned from $LPA$ to $RPA$ through $C_z$ with 10% boundaries allocated from the preauricular notches to the temporal leads ($T_7, T_8$, historically designated $T_3, T_4$), followed by consecutive 20% intervals bridging $T_7 \rightarrow C_3 \rightarrow C_z \rightarrow C_4 \rightarrow T_8$ [3].
To project 3D spherical scalp coordinates $(\theta, \phi)$ onto a two-dimensional visual workspace, this simulator utilizes conformal stereographic azimuthal projection equations, preserving local angles and relative angular distances:
$$x = \frac{2 R \sin\theta \sin\phi}{1 + \cos\theta}, \quad y = \frac{2 R \sin\theta \cos\phi}{1 + \cos\theta}$$
where $R$ represents the normalized cranial radius, $\theta$ is the polar angle measured from the vertical vertex axis $C_z$, and $\phi$ represents the azimuthal angle counterclockwise from the anterior coronal axis.
3. Nomenclature Architecture: Standard 10-20 vs. Extended 10-10 System
The anatomical naming convention of EEG electrodes encodes regional cortical taxonomy combined with lateralization numbers:
- Alphabetical Prefixes: Define cortical topography:
Fp (Frontopolar / Prefrontal), F (Frontal), C (Central / Rolando sulcus), P (Parietal), T (Temporal), and O (Occipital).
- Numerical Suffixes: Even integers (2, 4, 6, 8, 10) explicitly indicate the right hemisphere. Odd integers (1, 3, 5, 7, 9) designate the left hemisphere. The lowercase suffix
z (Zero) designates midsagittal midline leads. Larger numerical values represent progressively greater lateral distances from the longitudinal cerebral fissure.
While the standard 10-20 layout specifies 19 primary recording electrodes (plus references), modern high-density neuro-engineering and source localization arrays necessitate higher spatial sampling. The Extended 10-10 System (standardized by Nuwer et al., 1998, and the American Clinical Neurophysiology Society) subdivides the standard 20% intervals in half, inserting intermediate 10% coronal planes [4]:
AF: Anterior-Frontal (situated between $F_p$ and $F$)FC: Fronto-Central (situated between $F$ and $C$)CP: Centro-Parietal (situated between $C$ and $P$)PO: Parieto-Occipital (situated between $P$ and $O$)
This high-density expansion accommodates up to 81 scalp electrodes, significantly mitigating spatial aliasing during Current Source Density (CSD) estimation and high-resolution dipolar inverse modeling.
4. Forward Modeling, Montages and Volume Conduction Physics
Scalp potentials are governed by quasi-static Maxwell equations where the extracellular volume conductor is modeled as a multi-layered conductive medium. For an equivalent current dipole $\mathbf{p}$ situated at position $\mathbf{r}_0$ within a conductive volume $\Omega$ with conductivity tensor $\sigma$, the electric potential $\Phi(\mathbf{r})$ on the scalp boundary satisfies Poisson's equation:
$$\nabla \cdot (\sigma \nabla \Phi) = \nabla \cdot \mathbf{J}_p = I \left( \delta(\mathbf{r} - \mathbf{r}_+) - \delta(\mathbf{r} - \mathbf{r}_-) \right)$$
Clinical EEG recording instruments do not evaluate absolute monopolar voltages; every channel reflects a potential difference between two recording points. This simulator models three primary recording montages:
- Longitudinal Bipolar ("Double Banana") Montage (Default): Computes anterior-to-posterior sequential derivations along temporal and parasagittal columns ($F_{p1} - F_7, F_7 - T_7, T_7 - P_7, P_7 - O_1$). Epileptiform spike foci are precisely localized by identifying phase reversals, where the potential deflection flips polarity across adjacent channels sharing the active focal electrode [5].
- Transverse Bipolar Montage: Evaluates coronal lateral-to-medial chains across frontal, central, and parietal arches, optimizing detection of parasagittal asymmetries and vertex wave gradients.
- Monopolar / Referential Montage: Measures the instantaneous differential between each active scalp lead $i$ and a common reference electrode (e.g., $C_z$, average earlobes $A_1/A_2$, or Common Average Reference $\Phi_{\text{CAR}}$):
$$\Phi_i^{\text{CAR}} = \Phi_i - \frac{1}{N}\sum_{j=1}^N \Phi_j$$
5. Cranial Auditory Sonification and Real-Time Spectral Synthesis
The integrated sonification engine maps cranial spatial coordinates into dynamic audio synthesis parameters using the HTML5 Web Audio API. As users hover across or sweep through electrode arrays, frequency $f$ is continuously synthesized via a logarithmic transfer function:
$$f(x, y) = f_{\text{base}} \cdot 2^{(y \cdot 0.65 + x \cdot 0.18)}$$
where $f_{\text{base}} = 220\text{ Hz}$ ($A_3$). Anterior coordinates ($+y$, Frontal/Prefrontal) yield elevated, alert pitches, whereas posterior coordinates ($-y$, Occipital) resonate at warm, fundamental baselines mimicking alpha desynchronization. Spatial stereo panning utilizes a dedicated StereoPannerNode aligned strictly with the normalized lateral coordinate $x \in [-1.0, 1.0]$, directing left-hemispheric channels to the left audio monitor and right-hemispheric channels to the right. A fourth-order low-pass Butterworth-modeled biquad filter ($f_c = 1,400\text{ Hz}$) smooths harmonics, preventing spectral masking during voice-first educational demonstrations.
⚖️ Legal Notices, Nominative Fair Use & Professional Disclaimers
• Editorial Independence & Non-Affiliation: This software laboratory and critical analysis is an independent educational, mathematical, and biophysical simulation engineered by BioniChaos. It is not affiliated with, maintained by, sponsored by, or endorsed by the International Federation of Clinical Neurophysiology (IFCN), the American Clinical Neurophysiology Society (ACNS), or commercial diagnostic EEG instrumentation manufacturers.
• Trademark Attribution: "International 10-20 System", "10-10 System", and associated scientific designations are cited strictly for nominative identification, educational modeling, academic review, and fair technical commentary under international intellectual property provisions.
• Not Medical or Clinical Diagnostic Advice: All computational routines, forward field projections, voltage distributions, and coordinate maps generated within this application are idealized mathematical simulations. This visualizer does not provide medical, neurological, clinical diagnostic, or surgical guidance and must never be utilized for patient evaluation, clinical EEG interpretation, or therapeutic decision-making. Individuals seeking neurological assessment must consult a board-certified neurologist or licensed healthcare clinician.
• Theoretical Model Limitations: Simulated scalp voltage topographies utilize simplified spherical volume conductor approximations and do not substitute for individual MRI-guided boundary element (BEM) or finite element method (FEM) patient reconstructions.