Depth and Surface EEG: Generation and Propagation ME (Signal Processing), IISc: Neural Signal Processing, Spring 2014 Depth and Surface EEG: Generation and Propagation Kaushik Majumdar Indian Statistical Institute Bangalore Center kmajumdar@isibang.ac.in ME (Signal Processing), IISc: Neural Signal Processing

ME (Signal Processing), IISc: Neural Signal Processing Baillet et al., IEEE Sig. Proc. Mag., Nov 2001, p. 16 Head, Brain and Signal ME (Signal Processing), IISc: Neural Signal Processing ME (Signal Processing), IISc: Neural Signal Processing

ME (Signal Processing), IISc: Neural Signal Processing Mountcastle, Brain, 120:701-722, 1997 Six Layer Brain Excitatory post synaptic potential (EPSP) ME (Signal Processing), IISc: Neural Signal Processing

Chemical-Electrical-Sequence ME (Signal Processing), IISc: Neural Signal Processing ME (Signal Processing), IISc: Neural Signal Processing

Electroencephalogram (EEG) and Electrocorticogram (ECoG) LFP Surface electrode Depth electrode ME (Signal Processing), IISc: Neural Signal Processing

ME (Signal Processing), IISc: Neural Signal Processing LFP, ECoG and EEG Comparison of SNR in EEG and ECoG for four patients P1 – P4. The ratio of SNR varies from 21 to 173. Ball et al., NeuroImage, 46: 708 – 716, 2009. Buzsaki et al., Nat. Rev. Neurosci., 13: 407 – 420, 2012 ME (Signal Processing), IISc: Neural Signal Processing

ME (Signal Processing), IISc: Neural Signal Processing Signal Acquisition Depth EEG Scalp EEG Curtsey: Freiburg Seizure Prediction Project, Germany International 10-20 system. http://en.wikipedia.org/wiki/File:21_electrodes_of_International_10-20_system_for_EEG.svg ME (Signal Processing), IISc: Neural Signal Processing

Information Propagation from Cortex to Scalp Local field potential (LFP) is the most information-rich among all the functional brain signals. LFP is also strongly correlated with blood oxygen level dependent (BOLD) functional magnetic resonance imaging (fMRI) signal. ME (Signal Processing), IISc: Neural Signal Processing

ME (Signal Processing), IISc: Neural Signal Processing http://www.hindawi.com/journals/cin/2009/656092/fig1/ EEG Forward Problem ME (Signal Processing), IISc: Neural Signal Processing

3-Layer Realistic Head Model Hallez et al., 2007 3-Layer Realistic Head Model Brain Skull Head ME (Signal Processing), IISc: Neural Signal Processing

Different Model Paradigms Source Models Head Models Dipole Source Model Distributed Source Model Boundary Elements Method (previous slide) Finite Elements Method Finite Difference Method Hallez et al., 2007 Majumdar, IEEE TBME, 56(4): 1228 – 1235, 2009 ME (Signal Processing), IISc: Neural Signal Processing

ME (Signal Processing), IISc: Neural Signal Processing Dipole Orientations In a dipole source model number of dipoles must have to be fixed beforehand. ME (Signal Processing), IISc: Neural Signal Processing

Mathematical Formulation Hallez et al., 2007 Mathematical Formulation EEG Lead filed matrix or gain matrix Dipoles ME (Signal Processing), IISc: Neural Signal Processing

ME (Signal Processing), IISc: Neural Signal Processing Hallez et al., 2007 Tissue Impedance ME (Signal Processing), IISc: Neural Signal Processing

Poisson’s Equation for the Head Kybic et al., Phys. Med. Biol., 51: 1333 – 1346, 2006 Poisson’s Equation for the Head ME (Signal Processing), IISc: Neural Signal Processing

Potential at any Single Scalp Electrode Due to All Dipoles r is the position vector of the scalp electrode rdip - i is the position vector of the ith dipole di is the dipole moment of the ith dipole ME (Signal Processing), IISc: Neural Signal Processing

EEG Gain Matrix Calculation For detail of potential calculations see Geselowitz, Biophysical J., 7, 1967, 1-11. ME (Signal Processing), IISc: Neural Signal Processing

Gain Matrix : Elaboration The whole purpose of the forward problem or head modeling is to determine the gain matrix, which will have to be inverted in some sense during solving the inverse problem. ME (Signal Processing), IISc: Neural Signal Processing

Boundary Elements Method for Distributed Source Model If on the complement of a smooth surface then can be completely determined by its values and the values of its derivatives on that surface. This is utilized to solve the forward problem, with distributed source, by BEM. For detail see Kybic, et al., IEEE Trans. Med. Imag., 24(1): 12 – 28, 2005. ME (Signal Processing), IISc: Neural Signal Processing

Inverse Problem : Peculiarities Inverse problem is ill-posed, because the number of sensors is less than the number of possible sources. Solution is unstable, i.e., susceptible to small changes in the input values. Scalp EEG is full of artifacts and noise, so identified sources are likely to be spurious. ME (Signal Processing), IISc: Neural Signal Processing

Geometric Interpretation ||V-BJ||2Wn ||J||2Wp Convex combination of the two terms with λ very small. minU(J) ME (Signal Processing), IISc: Neural Signal Processing

ME (Signal Processing), IISc: Neural Signal Processing Derivation U(J) = ||V – BJ||2Wn + λ||J||2Wp = <Wn(V – BJ), Wn(V – BJ)> + λ<WpJ, WpJ> ΔJU(J) = 0 implies (using <AB,C> = <B,ATC>) J = CpBT[BCpBT + Cn]-1V where Cp = (WTpWp)-1 and Cn = λ(WTnWn)-1. ME (Signal Processing), IISc: Neural Signal Processing

ME (Signal Processing), IISc: Neural Signal Processing Derivation U(J) = ||V – BJ||2Wn + λ||J||2Wp = <Wn(V – BJ), Wn(V – BJ)> + λ<WpJ, WpJ> ΔJU(J) = 0 implies (using <AB,C> = <B,ATC>) J = CpBT[BCpBT + Cn]-1V where Cp = (WTpWp)-1 and Cn = λ(WTnWn)-1. ME (Signal Processing), IISc: Neural Signal Processing

ME (Signal Processing), IISc: Neural Signal Processing Different Types When Cp = Ip (the p x p identity matrix) it reduces to classical minimum norm inverse solution. If we derive the current density estimate by the minimum norm inverse and then standardize it using its variance, which is hypothesized to be due to the source variance, then that is called sLORETA. ME (Signal Processing), IISc: Neural Signal Processing

Low Resolution Brain Electromagnetic Tomography (LORETA) ME (Signal Processing), IISc: Neural Signal Processing Low Resolution Brain Electromagnetic Tomography (LORETA) Pascual-Marqui et al., Int. J. Psychophysiol., vol. 18, p. 49 – 65, 1994.

Standardized Low Resolution Brain Electromagnetic Tomography (sLORETA) U(J) = ||V – BJ||2 + λ||J||2 Ĵ = TV, where T = BT[BBT + λH]+, where H = I – LLT/LTL is the centering matrix. Pascual-Marqui at http://www.uzh.ch/keyinst/NewLORETA/sLORETA/sLORETA-Math02.htm ME (Signal Processing), IISc: Neural Signal Processing

ME (Signal Processing), IISc: Neural Signal Processing sLORETA (cont) Ĵ is estimate of J, A+ denotes the Moore-Penrose inverse of the matrix A, I is n x n identity matrix where n is the number of scalp electrodes, L is a n dimensional vector of 1’s. Hypothesis : Variance in Ĵ is due to the variance of the actual source vector J. Ĵ = BT[BBT + λH]+BJ. ME (Signal Processing), IISc: Neural Signal Processing

ME (Signal Processing), IISc: Neural Signal Processing Form of H ME (Signal Processing), IISc: Neural Signal Processing

If # Source = # Electrodes = n B and BT both will be n x n identity matrix. with λ = 0 ME (Signal Processing), IISc: Neural Signal Processing

ME (Signal Processing), IISc: Neural Signal Processing http://www.uzh.ch/keyinst/loreta.htm sLORETA Result ME (Signal Processing), IISc: Neural Signal Processing

EEG Source Modeling at DLPFC http://mindblog.dericbownds.net/2009/12/inhibited-behavior-and-our-right.html EEG Source Modeling at DLPFC During behavioral inhibition the right DLPFC is more active than the left. ME (Signal Processing), IISc: Neural Signal Processing

ME (Signal Processing), IISc: Neural Signal Processing References S. Baillet, J. C. Mosher and R. M. Leahy, Electromagnetic brain mapping, IEEE Sig. Proc. Mag., 18(6): 14 – 30, 2001. H. Hallez et al., Review on solving the forward problem in EEG source analysis, J. Neuroeng. Rehab., 4: 46, 2007. Available online at http://www.jneuroengrehab.com/content/4/1/46 ME (Signal Processing), IISc: Neural Signal Processing