Source localization

Sensor space

Signal at sensors

Surface potentials

Positive & negative potentials

Always with respect to the reference

Current source density (CSD)

CSD = -1 * scalp conductivity * Laplacian of scalp potential

Current source density (CSD)

'scalp current density‘Divergence of the current density

in the scalp. The rate of change of current

flowing into and through the scalp.

Current source density (CSD)

CSDs are three dimensional vectors (direction and amplitude)

They are a function of spatial voltage differences across electrodes

Dipoles

Neural activity (inside the brain) is modeled by electric dipole(created by the movement of electrically charged ions).

Source localization

Which neurons (dipoles) are creating the signal at the scalp?

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+ -

Locate the dipoles creating the potential at the scalp…

Inverse solution

CSD measurement at time x

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Dipole location and strength at time x

How do we know which one is correct?

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+ -

We can’t. There is no correct answer.

We can only see which one is better

Can we find the best answer?

Source localization is an ILL-DEFINED PROBLEM

Only among the alternatives that you have considered.

Forward solution

EEG measurement at time x

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Dipole location and strength at time x

Build a forward modelIndividual anatomy (gyri and sulci)

Conduction/Resistance boundaries (electricity travels differently across different mediums: skull, CSF)

Electrode locations and reference

Examples of expected potentials

Simulate many dipole sources

If then

If then

If then

If then

And on and on and on and …

Find the simulation with the best fit

Forward Model Experimental DATA

Model with multiple dipoles, not just two…

HUNTING for best possible solution

Forward

Inverse Solution

DATA

Iterative ProcessUntil solution stops getting better (error stabilises) iteration

erro

r

Mathematical definition

This problem is ill posed because there are many more dipoles than electrodes (P >> N).

Remember that each dipole is an x,y,z vector…

Mathematical definition

Different models use different numbers of dipoles (from one to many) and put different constraints on the solution.

Different solutions - BESA

Assumes sparse predetermined (fixed) dipoles

Different solutions - LORETA

Estimates the direction and amplitude of many (thousands) dipoles throughout the brain using a smoothness constraint.

Different solutions - Beamforming

Estimates the behavior of multiple dipoles using a set of “spatial filters”.

y(t) = WTm(t)

Where WT is a spatial filter applied to the electrode measures m(t) to compute the dipole activity y(t).

Many hundreds of simultaneous dipoles can be estimated.

Different approach

Computing ICA componentsIndependent spatio-temporal components

This approach keeps the data in sensory space, but re-structures (transforms) it into parts with “maximal statistical

independence”

Open Matlab!

Before and after CSD analysis

Note that the top row contains potentials µV and the bottom row contains CSD units µV/m²

CSD measures are more focal than potential measures.

Using the EEGLAB plugin for computing CSD