ICA and GABA to keep You awake !

Explore this website by Mr. German Gomez-Herrero if You are interested in ICA , brain synchrony and EEGLab. Enjoy his (G) ABA synchrony

I very much enjoyed his crystal clear explanation on ICA principles in the EEGLab list Read here how Mr German Gomez-Herrero explains: Imagine that in an ERP or EEG experiment we have only 2 brain populations (P1,P2) that are active and whose bioelectrical activity are producing most of the variance in the scalp EEG. Let us call s1(t) and s2(t) the electrical activation patterns that are being generated at P1 and P2, respectively. Then, if we call x1(t) and x2(t) the signals acquired in two scalp electrodes we can write (based on the quasistatic approximation of brain volume conduction): EQUATION 1: x1(t) = a11*s1(t)+a12*s2(t) x2(t) = a21*s1(t)+a22*s2(t) where a11,a12,a21,a22 are just some scalar values modeling the electrical transfer from the locations P1,P2 to the electrodes locations (i.e. the volume conduction effects). Then, if we further assume that s1(t) and s2(t) are statistically independent from each other then, we can use ICA to estimate a (randomly scaled version of) the transfer coefficients a11,a12,a21,a22 as well as a (randomly scaled version of the) source activations s1(t) and s2(t) based on only on the observed scalp signals x1(t) and x2(t), that is: [a11/k, a12/k, a21/k, a22/k, k*s1(t), k*s2(t)] = ICA(x1(t),x2(t)) Where k is an unknown scaling factor. Since the brain generators P1,P2 are independent it makes sense to study each of them separately. Thanks to ICA we know all the variables involved in the system of equations above (EQUATION 1) except for the factor k. Then to study the contribution to the EEG of the first ICA component (s1(t)) we can just set to zero s2(t) and see that EQUATION 1 becomes: EQUATION 2: x1(t) = (a11/k)*(k*s1(t)) = a11*s1(t) x2(t) = (a21/k)*(k*s1(t)) = a21*s1(t) So this means that the scalp EEG at any electrode is just a scaled version of the source activation computed by ICA. Therefore, each independent component is identified by its (randomly scaled) activation k*s1(t) and the scaling factors for each electrode a11/k,a21/k. EEGLAB uses k*s1(t) to plot the spectrum and the component ERP (if epoched). Therefore the component spectrum plotted in EEGLAB does not correspond to any scalp location, it is just the spectrum of a randomly scaled version of the signal that is actually being generated inside the brain, in the brain population P1. When EEGLAB plots the scalp topography of component 1 it actually plots the values (a11/k),(a21/k). Note from EQUATION 2 that those values would be the values of the actual scalp potentials only when s1(t)=1/k. In what time instant does that happen? We can't know since the scaling factor k is unknown and therefore we can't know when s1(t) is going to take an unknown value :). However, note that that the ratio between the potentials at different scalp locations is constant at ANY time: x1(t)/x2(t) = [(a11/k)*(k*s1(t))] / [(a21/k)*(k*s1(t))] = a11/a21 These relative values x1(t)/x2(t) conceptually tell us whether component 1 was generated in an brain area closer to electrode x1 or closer to electrode x2. Thus, they are all we need for localizing in the brain the population P1 using any of the inverse methods available in the literature (e.g. LORETA or just your own intuition). Then to your question that at what time the scalp distribution is plotted you can say that the relative values of that scalp distribution x1(t)/x2(t) are the same for ANY time but the actual values x1(t),x2(t) are arbitrary and do not correspond to any certain time instant. So summarizing, you have to understand each ICA component as a signal generated inside the brain. Imagine that s1(t) would be a sinusoid generated somewhere in the temporal cortex, imagine also that electrode x1 is located in the temporal lobe and x2 in the occipital lobe. Then, component 1 has a single spectrum (an impulse at the frequency of the sinusoid). If only component 1 would be active, the signals acquired in the scalp would be just scaled sinusoids and so their spectrums would also be just scaled impulses at the frequency of that sinusoid. Furthermore, the fact that (a11/k)/(a21/k) is quite large tells you that component 1 might be located much closer to electrode x1 than to electrode x2, i.e. it is located in the temporal cortex. Note that we know this without knowing the actual values of a11 and a21 (i.e. we do not know k) but just from the fact that (a11/k)/(a21/k)=a11/a21 is large. My explanations above quite simplistic and discard many important issues but I think they capture the main idea. Probably other EEGLAB users or developers will tell you more. Hope that helps, Germán --------------------------------------------------------------------- Germán Gómez-Herrero M. Sc., Researcher Tampere University of Technology P.O. Box 553, FI-33101, Tampere, Finland Phone: +358 3 3115 4519 Mobile: +358 40 5011256 Fax: +358 3 3115 4989 http://www.cs.tut.fi/~gomezher/index.htm