Lead Fields, Reciprocity & Sensitivity

Build an EEG lead matrix, verify Helmholtz reciprocity numerically, and inspect depth sensitivity and singular-value decay.

Chapter 7
lead field
reciprocity
SVD

Forward voltage

2.86300 µV

Reciprocal voltage

2.86300 µV

Relative discrepancy

1.48e-16

Dimensions

12 × 40

Lead sensitivity along source arc

Lead 5

Singular spectrum of lead matrix

log₁₀ singular value / largest

Lead-field matrix

Rows: electrodes · Columns: source angle −54° to +54° · Red positive / blue negative

Model scope

Infinite homogeneous 0.33 S/m conductor, radial sources along a 2D cortical arc; south-pole bipolar reference. One source coefficient represents 10 nA·m; L is µV per source unit. Reciprocity compares the reciprocal electric field per unit injected current with the physical dipole, not unconverted current density.

Preparing the simulation…

Conceptual bridges & related modules

Volume Conduction & Spherical Head Models
prerequisite · Chapter 7
Compare layered radial conduction with differential infinite-medium lead sensitivity.
Minimum-Norm Source Localization
prerequisite · Chapter 7
Invert the same scaled source basis and inspect its unresolved combinations.