source localization
DESCRIPTION
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). - PowerPoint PPT PresentationTRANSCRIPT
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?
+-
+ -
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
+-
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
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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