1. Functional Brain Signal Processing: EEG & fMRI Lesson 14
M.Tech. (CS), Semester III, Course B50
Functional Brain Signal Processing: EEG & fMRI Lesson 14
Kaushik Majumdar
Indian Statistical Institute Bangalore Center

2. Why Statistics in fMRI?

3. Reading Exercise on Multiple Comparison Correction

4. Step 1: Gaussian Smoothing
Gaussian smoothing with 8 mm FWHM.

5. 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.

6. BOLD Activation Detection amidst Noise
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.

7. 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.

8. FFT of MR Signal During Activation
Buxton, 2009
FFT of MR Signal During Activation

9. Buxton, 2009
Noise vs. Activation

10. BOLD Activation Time Course
Buxton, 2009
BOLD Activation Time Course

11. More on BOLD Activation Detection
Subtraction
t – test
Correlation (next slide)
Fourier transform (slide after the next)

12. Detection by Subtraction
Noll, 2001
Detection by Subtraction

13. Statistical Parametric Map
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:

14. Monti, 2011
GLM in fMRI Time Series

15. Detection by Correlation
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. 6s 2s

16. Detection by Fourier Transform
Poldrack et al., 2011
Buxton, 2009

17. General Linear Model (GLM)
Buxton, 2009
General Linear Model (GLM)

18. GLM – Geometrical Representation

19. GLM – Mathematical Derivation

20. 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.
Since projection of data on the model space, not on the error space, determines magnitude a = LYM.

21. 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.

22. SNR in fMRI Experiment
This is the SNR in an fMRI experiment according to GLM.

23. References
R. B. Buxton, Introduction to Functional Magnetic Resonance Imaging, 2e, Cambridge University Press, Cambridge, UK, 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

24. THANK YOU This lecture is available at http://www. isibang. ac