390 likes | 709 Views
Event Related Potentials (ERP). Analysis of the Electrical Brain Activity. EEG Sapling. Head and Source Model Definition. Temporal Averaging and/or Filtering. Spetial Filtering / Laplasian. Spatio-temporal Signal Decomposition. Source Localization of each Component .
E N D
Event Related Potentials (ERP) Analysis of the Electrical Brain Activity
EEG Sapling Head and Source Model Definition Temporal Averaging and/or Filtering Spetial Filtering / Laplasian Spatio-temporal Signal Decomposition Source Localization of each Component Spatio-Temporal Flow Activity Pattern Recognition Neuro-Psychological Pattern Correction and Translation The General Scheme of Spatio-Temporal EEG Analysis
The Forward (direct) Problem Physics - propagation of currents through voltage conductance Lead Field (projection) Matrix - K
Distribute Sources on fMRI Scalp Skull Brain CSF
The Inverse Problems Forward problem: Find K that translates dipoles J to Scalp potentials Φ. Inverse problem: Find function F that transforms Scalp potentials Φ to dipoles J. Model F Ne measurements Nv unknowns Ill posed for Ne < Nv
Under Determined Models Instantaneous Distributed Discrete Linear ! Forward problem: Find K that translates dipoles J to Scalp potentials Φ. Inverse problem: Find T that translates Scalp potentials Φ to dipoles J. Ideally: But:
Linear Solutions The electrode data is of much lower dimension then the sources. Forward problem: Find K that translates dipoles J to Scalp potentials Φ. Infinite number of source patterns J that produce a given set of measurements. Inverse problem: Find T that translates Scalp potentials Φ to dipoles J. If J is of full rank Jcannot be exactly reconstructed - not enough data on the scalp. Ideally: If the sources are highly dependant in time and space, reconstruction of the observable portion of J is possible. NΦ≈102 NJ≈105-106
LORETA (LOW RESOLUTION BRAIN ELECTROMAGNETIC TOMOGRAPHY):Roberto Pascual-Marqui • Relatively effective EEG source localization methods were developed • Their results are relatively established • Precision is in process of improvement
Linear Solution The solution: J = TΦ, T = W-1KT[K W-1KT]-1, W=ATA It is easy to see that Φ = KJ = KTΦ = Φ. In cases of noisy data or inaccurate model, a regularization term is introduced: T = W-1KT[K W-1KT+αI]-1 Smaller α Bigger α ||AJ|| ||Φ-KJ|| Misfit Interdependency
Instantaneous Linear Solutions Minimum Norm (min spatial independence): Weighted Minimum Norm: LORETA (min neighbor difference): sLORETA: Standardization: • Same independent solution for each time point: J(t) = TΦ(t), T = W-1KT[K W-1KT+αI]-1, W=ATA A: Spatial Filter NJ x NJ T: NJ x NФ
LORETA(LOW RESOLUTION BRAIN ELECTROMAGNETIC TOMOGRAPHY): Roberto Pascual-Marqui • Relatively effective EEG source localization methods were developed • Their results are relatively established • Precision is in process of improvement
Functional brain areas It is accepted that the brain is divisible to functional units