Functional Brain Signal Processing: EEG & fMRI

Lesson 14

Kaushik Majumdar

Indian Statistical Institute Bangalore Center

kmajumdar@isibang.ac.in

M.Tech. (CS), Semester III, Course B50

Why Statistics in fMRI?

http://psuc5d.files.wordpress.com/2012/02/bennett-salmon-2009.jpeg

Reading Exercise on Multiple Comparison Correction

http://blogs.discovermagazine.com/neuroskeptic/2009/09/16/fmri-gets-slap-in-the-face-with-a-dead-fish/#.UlWjfz_3EdX

Step 1: Gaussian Smoothing

Gaussian smoothing with 8 mm FWHM.

http://blogs.discovermagazine.com/neuroskeptic/2009/09/16/fmri-gets-slap-in-the-face-with-a-dead-fish/#.UlWjfz_3EdX

Step 2: Z Score Thresholding

Euler characteristics 2 after Z score thresholding.So region of activation is2 and they are shown in the figure.

http://blogs.discovermagazine.com/neuroskeptic/2009/09/16/fmri-gets-slap-in-the-face-with-a-dead-fish/#.UlWjfz_3EdX

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.

Buxton, 2009, p. 369

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.

FFT of MR Signal During Activation

Buxton, 2009

Noise vs. Activation

Buxton, 2009

BOLD Activation Time Course

Buxton, 2009

More on BOLD Activation Detection

Subtraction t – test Correlation (next slide) Fourier transform (slide after the next)

Detection by Subtraction

Noll, 2001

Statistical Parametric Map

( , )ij kj ijk

y M i k a 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.

In matrix form:

Y Ma e

GLM in fMRI Time Series

Monti, 2011

Detection by Correlation

Buxton, 2009

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

Buxton, 2009

Poldrack et al., 2011

* ( ) ( ) ( )h f t h f t d

General Linear Model (GLM)

Buxton, 2009

GLM – Geometrical Representation

GLM – Mathematical Derivation

1

[ ]

( )

T T T T

T T

M E

M

1 2

M E

Y Y Y

Y Ma

M M M

M Y M Y M Y M Ma

a M M M Y

a LY

Contrast

Any linear combination of model amplitudes can be thought of as a contrast of the form c = w1a1 + w2a2. So c = aTw.2

2

( ) ( ) ( )

( )( ) ( )

T T T T T

T T

T T T TM M M M

T T TM M

c

c

a w a w w aa w

w aa w

aa LY LY L Y Y L

aa L Y Y L

Buxton, 2009, p. 384

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 . The variance is given by

So for any contrast of interest defined by a vector of weight w the variance is

, which gives noise sensitivity of an fMRI experiment.

2TM M Y Y I

2 1 1

2 1

( ) ( )

( )

TT T T T T T TM M

T T

aa L Y Y L LL M M M M M M

aa M M

2 2 1( )T Tw w M M w

Taa

SNR in fMRI Experiment

1( )

( )

T

T T

cSNR

w

a ww

w M M w

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/PMC3062970/

THANK YOU

This lecture is available at http://www.isibang.ac.in/~kaushik