Source localization in reverberation environment based on ...
Source localization
description
Transcript of Source localization
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Source localization
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Sensor space
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Signal at sensors
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Surface potentials
Positive & negative potentials
Always with respect to the reference
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Current source density (CSD)
CSD = -1 * scalp conductivity * Laplacian of scalp potential
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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.
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Current source density (CSD)
CSDs are three dimensional vectors (direction and amplitude)
They are a function of spatial voltage differences across electrodes
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Dipoles
Neural activity (inside the brain) is modeled by electric dipole(created by the movement of electrically charged ions).
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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…
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Inverse solution
CSD measurement at time x
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Dipole location and strength at time x
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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.
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Forward solution
EEG measurement at time x
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Dipole location and strength at time x
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Build a forward modelIndividual anatomy (gyri and sulci)
Conduction/Resistance boundaries (electricity travels differently across different mediums: skull, CSF)
Electrode locations and reference
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Examples of expected potentials
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Simulate many dipole sources
If then
If then
If then
If then
And on and on and on and …
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Find the simulation with the best fit
Forward Model Experimental DATA
Model with multiple dipoles, not just two…
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HUNTING for best possible solution
Forward
Inverse Solution
DATA
Iterative ProcessUntil solution stops getting better (error stabilises) iteration
erro
r
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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…
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Mathematical definition
Different models use different numbers of dipoles (from one to many) and put different constraints on the solution.
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Different solutions - BESA
Assumes sparse predetermined (fixed) dipoles
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Different solutions - LORETA
Estimates the direction and amplitude of many (thousands) dipoles throughout the brain using a smoothness constraint.
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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.
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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”
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Open Matlab!
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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