Transcript Lesson 14
M.Tech. (CS), Semester III, Course B50 Functional Brain Signal Processing: EEG & fMRI Lesson 14 Kaushik Majumdar Indian Statistical Institute Bangalore Center [email protected] http://psuc5d.files.wordpress.com/2012/02/bennett-salmon-2009.jpeg Why Statistics in fMRI? Reading Exercise on Multiple Comparison Correction http://blogs.discovermagazine.com/neuroske ptic/2009/09/16/fmri-gets-slap-in-the-facewith-a-dead-fish/#.UlWjfz_3EdX Step 1: Gaussian Smoothing Gaussian smoothing with 8 mm FWHM. http://blogs.discovermagazine.com /neuroskeptic/2009/09/16/fmrigets-slap-in-the-face-with-a-deadfish/#.UlWjfz_3EdX Step 2: Z Score Thresholding Euler characteristics 2 after Z score thresholding. So region of activation is 2 and they are shown in the figure. http://blogs.discovermaga zine.com/neuroskeptic/20 09/09/16/fmri-gets-slap-inthe-face-with-a-deadfish/#.UlWjfz_3EdX Buxton, 2009, p. 369 BOLD Activation Detection amidst Noise During activation, change in BOLD signal is 1% due to a 50% change in cerebral blood flow, when scanned by a 1.5 T scanner. Noise in the BOLD signal due to blood and CSF motion caused by pulsating heart often causes around 1% fluctuation. In single shot EPI a large number of images during activation and control are required to average to detect BOLD changes due to activation. Vasomotion A regular oscillation of blood flow and oxygenation called vasomotion has been observed in numerous optical studies at frequencies around 0.1 Hz. It is significant at high magnetic field, but its origin is not well understood yet. Buxton, 2009 FFT of MR Signal During Activation Buxton, 2009 Noise vs. Activation Buxton, 2009 BOLD Activation Time Course More on BOLD Activation Detection Subtraction t – test Correlation (next slide) Fourier transform (slide after the next) Noll, 2001 Detection by Subtraction Statistical Parametric Map yij M (i, k )akj eij k In matrix form: Y Ma e yij is the response of the ith voxel at the jth time instance, M(i,k) unit kth effect on the ith voxel, akj is intensity of kth effect in jth time instance and eij is error in calculating yij assumed to be independently and identically distributed across all the voxels and time instances. Monti, 2011 GLM in fMRI Time Series Buxton, 2009 Detection by Correlation A simple approximation for the model response to block stimulus pattern is a trapezoid with a 6s ramp delayed by 2s from the onset of the stimulus block. At voxel correlation coefficient between model function and the actual time series at the voxel is calculated the thresholded. 2s 6s Detection by Fourier Transform Poldrack et al., 2011 h * f (t ) h( ) f (t )d Buxton, 2009 Buxton, 2009 General Linear Model (GLM) GLM – Geometrical Representation GLM – Mathematical Derivation Y YM YE YM Ma M [M 1 M 2 ] MT Y MT YM MT YE M T Ma 1 a (M M ) M Y T a LY T Buxton, 2009, p. 384 Contrast Any linear combination of model amplitudes can be thought of as a contrast of the form c = w1a1 + w2a2. So c = aTw. c (a w ) (a w ) w (aa )w 2 T T T T T c 2 wT aaT w aaT (LYM )(LYM )T L(YM YMT )LT aaT L YM YMT LT Since projection of data on the model space, not on the error space, determines magnitude a = LYM. Noise Sensitivity of the fMRI If both YM and YE are independent Gaussian noise, then Y Y I. The variance aaT is given by M T aa T M 2 L YM Y T M 1 T L LL (M M ) M M (M M ) T 2 T T 1 T T aaT 2 (MT M) 1 So for any contrast of interest defined by a vector of weight w the variance is w2 2 wT (MT M ) 1 w, which gives noise sensitivity of an fMRI experiment. SNR in fMRI Experiment SNR(w ) c w T a w w (M M ) w T T 1 This is the SNR in an fMRI experiment according to GLM. References R. B. Buxton, Introduction to Functional Magnetic Resonance Imaging, 2e, Cambridge University Press, Cambridge, UK, 2009. Chapter 15. M. M. Monti, Statistical analysis of fMRI time series: a critical review of GLM approach, Frontiers in Human Neuroscience, 5: 28, 2011, available online at http://www.ncbi.nlm.nih.gov/pmc/articles/PMC306 2970/ THANK YOU This lecture is available at http://www.isibang.ac.in/~kaushik