EEG Forward Problem & Scalp Potential Mapper

Investigate the biophysical origin of scalp potentials: position and orient an Equivalent Current Dipole (ECD) in a 3-shell concentric spherical head model (Brain, high-resistivity Skull, Scalp), observe volume conduction smearing, and calculate real-time 10-20 scalp topomaps.

Dipole Configuration:

3-Shell Head Model (Brain · Skull · Scalp) · Drag Dipole Position / Angle

Brain (σ = 0.33 S/m)

Skull (σ ≈ 0.0042 S/m)

Scalp (σ = 0.33 S/m)

10-20 Scalp Isopotential Topomap · Voltage Distribution (μV)

Positive Voltage (+)

Neutral (0 μV)

Negative Voltage (−)

Dipole Moment (q)

20 nA·m

Source Depth

0.78 (Superficial)

Dipole Angle (θ)

90° (Radial)

Peak Scalp Voltage

+14.2 μV

Min Scalp Voltage

-3.4 μV

Dipole Orientation Angle (θ): 90°

Dipole Strength (Moment q): 20 nA·m

Skull Resistivity Ratio: 1 : 80 (Standard)

Source Eccentricity / Depth: 0.78

Physical Principles of the EEG Forward Problem:

1. Equivalent Current Dipoles (ECD): Scalp potentials arise not from action potentials, but from synchronized postsynaptic potentials (PSPs) across thousands of aligned pyramidal neurons in cortical layer V. The net current dipole moment q (typically 10–50 nA·m for an active cortical patch) flows from intracellular sinks to sources.

2. The 3-Shell Concentric Head Model: Electrical current generated in the brain must conduct through three distinct media before reaching recording electrodes: the Brain (σ ≈ 0.33 S/m), the Skull (σ ≈ 0.0042 S/m), and the Scalp (σ ≈ 0.33 S/m).

3. Volume Conduction & Skull Smearing: The skull has an electrical resistivity approximately 80 times higher than brain tissue or scalp. Because current seeks the path of least resistance, the skull acts as a spatial low-pass filter, spreading and smearing focal cortical currents laterally across centimeters of scalp surface before they exit into the conductive scalp layer. Try adjusting the skull resistivity slider to see how lower skull resistance sharpens scalp focal peaks!

4. Radial vs. Tangential Dipole Topographies: A radial dipole (located on a gyral crown, pointing outward toward the skull) produces a largely monopolar peak directly above the source. A tangential dipole (located in a sulcal bank, pointing parallel to the skull) produces a classic dipolar split with equal and opposite positive and negative voltage poles separated across the head.

5. The Ill-Posed Inverse Problem: Solving the forward problem (calculating scalp voltage from known dipole sources) has a unique, deterministic mathematical solution. However, solving the inverse problem (inferring brain sources from scalp voltages) is mathematically ill-posed: infinitely many distinct current configurations inside the head can produce the exact same voltage map on the scalp!