Dipole in Conductive Sphere

Dipole Position

Dipole Orientation

Dipole Magnitude

Sphere Opacity

Electrodes

Click on sphere to place electrodes (max 2)

Dipole in Conductive Sphere: EEG Forward Problem

Overview

This simulation demonstrates the EEG forward problem — how electrical activity from a single current dipole source inside the brain generates measurable voltage patterns on the scalp surface. This is fundamental to understanding electroencephalography (EEG) and source localization in clinical neurophysiology.

The Physics

The human head can be approximated as a conductive sphere containing the brain. When neurons fire synchronously, they create an electrical dipole — a pair of positive and negative charges separated by a small distance. This dipole generates an electric field that conducts through brain tissue, cerebrospinal fluid, skull, and scalp to create voltage differences measurable by EEG electrodes.

Mathematical Solution

This simulation implements the Berg-Scherg analytical solution using spherical harmonics and Legendre polynomial expansions. The solution accounts for:

• Direct dipole potential: The primary field from the source
• Boundary corrections: Effects of the insulating sphere boundary (representing the skull-air interface)
• Volume conduction: How the field spreads through the conductive medium

The result is a smooth, monotonic potential distribution showing characteristic positive and negative poles on opposite sides of the sphere.

Clinical Relevance to EEG

Understanding the forward problem is essential for:

• Source localization: Working backward from scalp recordings to identify the location and orientation of neural generators (the inverse problem)
• EEG interpretation: Understanding why certain electrode montages show specific patterns
• Dipole fitting: Estimating the location of epileptic foci or other focal brain activity
• Brain mapping: Relating cognitive processes to their neural sources
• Clinical diagnosis: Localizing abnormal brain activity in epilepsy, tumors, or strokes

Key Observations

Experiment with the simulation to observe:

• Dipole depth: Deeper sources (closer to center) produce broader, lower-amplitude surface patterns
• Dipole orientation: Radial dipoles (pointing toward/away from surface) create different patterns than tangential dipoles
• Electrode placement: Voltage differences depend critically on electrode positions relative to the dipole
• Field distribution: The field is always smooth and continuous — no sharp transitions

Simplifications

This model uses a homogeneous spherical conductor. Real heads have:

• Multiple tissue layers with different conductivities (brain, CSF, skull, scalp)
• Non-spherical geometry
• Thousands of simultaneous dipole sources

However, the single-sphere model captures the essential physics and provides excellent intuition for EEG interpretation and source analysis.

Applications

This forward model is used in:

• EEG source imaging software (BESA, Curry, Brainstorm, FieldTrip)
• Pre-surgical planning for epilepsy surgery
• Brain-computer interfaces (BCI)
• Cognitive neuroscience research
• Real-time neurofeedback systems

About This Simulation

The visualization shows the electrical potential field as a color map (red = positive, blue = negative, white = zero). The yellow sphere marks the dipole location, the magenta arrow shows its orientation, and colored axis lines help visualize its 3D position. Click the sphere to place electrodes and measure voltage differences just as in real EEG recordings.