0. fMRI design and analysis
Basic designs

1. MRI vs. fMRI Functional MRI (fMRI) studies brain function.
MRI studies brain anatomy.

2.  neural activity   blood oxygen   fMRI signal
MRI vs. fMRI
MRI
fMRI
high resolution
(1 mm)
low resolution
(~3 mm but can be better)
one image …
fMRI
Blood Oxygenation Level Dependent (BOLD) signal
indirect measure of neural activity
many images
(e.g., every 2 sec for 5 mins)
 neural activity   blood oxygen   fMRI signal

3. fMRI Activation Flickering Checkerboard Brain Activity Time 
OFF (60 s) - ON (60 s) -OFF (60 s) - ON (60 s) - OFF (60 s)
Brain
Activity
Time 
Source: Kwong et al., 1992

4. fMRI Experiment Stages: Prep
1) Prepare subject
Consent form
Safety screening
Instructions and practice trials if appropriate
2) Shimming
putting body in magnetic field makes it non-uniform
adjust 3 orthogonal weak magnets to make magnetic field as homogenous as possible
3) Sagittals
Take images along the midline to use to plan slices
Perhaps the most frequently misspelled word in fMRI: Should have one g, two t’s
In this example, these are the functional slices we want: 12 slices x 6 mm

5. fMRI Experiment Stages: Anatomicals
4) Take anatomical (T1) images
high-resolution images (e.g., 0.75 x 0.75 x 3.0 mm)
3D data: 3 spatial dimensions, sampled at one point in time
64 anatomical slices takes ~4 minutes
64 slices x 3 mm

6. Slice Terminology VOXEL (Volumetric Pixel) IN-PLANE SLICE
Slice Thickness
e.g., 6 mm
Number of Slices
e.g., 10
SAGITTAL SLICE
VOXEL
(Volumetric Pixel)
3 mm
6 mm
Matrix Size
e.g., 64 x 64
In-plane resolution
e.g., 192 mm / 64
= 3 mm
IN-PLANE SLICE
Field of View (FOV)
e.g., 19.2 cm

7. Coordinates - Anatomy 3 Common Views of Brain: Coronal (head on)
sagittal
coronal
axial
3 Common Views of Brain:
Coronal (head on)
Axial (bird’s eye), aka Transverse.
Sagittal (profile)

8. fMRI Experiment Stages: Functionals
5) Take functional (T2*) images
images are indirectly related to neural activity
usually low resolution images (3 x 3 x 6 mm)
all slices at one time = a volume (sometimes also called an image)
sample many volumes (time points) (e.g., 1 volume every 2 seconds for 136 volumes = 272 sec = 4:32)
4D data: 3 spatial, 1 temporal …

9. Activation Statistics
Functional images
Time
fMRI
Signal
(% change)
ROI Time Course
Condition
~2s
Region of interest (ROI)
Condition 1
Statistical Map
superimposed on anatomical MRI image
Condition 2
Time
...
~ 5 min

10. 2D  3D

11. Overview fMRI time-series Statistical Parametric Map Smoothing kernel
General Linear Model
Design matrix
Motion
correction
Parameter Estimates
Spatial
normalisation
Standard
template

13. Spatial Realignment: Reasons for Motion Correction
Subjects will always move in the scanner
The sensitivity of the analysis depends on the residual noise in the image series, so movement that is unrelated to the subject’s task will add to this noise and hence realignment will increase the sensitivity
However, subject movement may also correlate with the task…
…in which case realignment may reduce sensitivity (and it may not be possible to discount artefacts that owe to motion)
Realignment (of same-modality images from same subject) involves two stages:
1. Registration - estimate the 6 parameters that describe the rigid body transformation between each image and a reference image
2. Reslicing - re-sample each image according to the determined transformation parameters

14. Motion Correction Algorithms
pitch
roll
yaw
z translation
y translation
x translation
Most algorithms assume a rigid body (i.e., that brain doesn’t deform with movement)
Align each volume of the brain to a target volume using six parameters: three translations and three rotations
Target volume: the functional volume that is closest in time to the anatomical image

15. Head Motion: Good, Bad,…
Slide from Duke course

16. … and catastrophically bad
Slide from Duke course

17. 2. Reslicing
Nearest Neighbour
Linear
Application of registration parameters involves re-sampling the image to create new voxels by interpolation from existing voxels
Interpolation can be nearest neighbour (0-order), tri-linear (1st-order), (windowed) fourier/sinc, or nth-order “b-splines”
Full sinc (no alias)
Windowed sinc

18. Temporal Realignment (Slice-Timing Correction)
Most functional MRI uses Echo-Planar Imaging (EPI)
Each plane (slice) is typically acquired every 3mm
normally axial…
… requiring ~32 slices to cover cortex (40 to cover cerebellum too)
(actually consists of slice-thickness, eg 2mm, and interslice gap, eg 1mm, sometimes expressed in terms of “distance factor”)
(slices can be acquired contiguously, eg [ ], or interleaved, eg [ ])
Each plane (slice) takes about ~60ms to acquire…
…entailing a typical TR for whole volume of 2-3s
Volumes normally acquired continuously (though sometimes gap so that TR>TA)
2-3s between sampling the BOLD response in the first slice and the last slice
(a problem for transient neural activity; less so for sustained neural activity)

19. Between Modality Co-registration
Useful, for example, to display functional results (EPI) onto high resolution structural image (T1)…
…indeed, necessary if spatial normalisation is determined by T1 image
Because different modality images have different properties (e.g., relative intensity of gray/white matter), cannot simply minimise difference between images
Therefore, use Mutual Information as cost function, rather than squared differences…
EPI T2 T1
Transm PD
PET

20. DARTEL: Diffeomorphic Registration (SPM8)
Grey matter average of 452 subjects
Affine
Grey matter average of 471 subjects
DARTEL

21. Coordinates - normalization
Different people’s brains look different
‘Normalizing’ adjusts overall size and orientation
Normalized Images
Raw Images

22. Reasons for Smoothing
Potentially increase signal to noise (matched filter theorem)
Inter-subject averaging (allowing for residual differences after normalisation)
Increase validity of statistics (more likely that errors distributed normally)
Kernel defined in terms of FWHM (full width at half maximum) of filter - usually ~16-20mm (PET) or ~6-8mm (fMRI) of a Gaussian
Ultimate smoothness is function of applied smoothing and intrinsic image smoothness (sometimes expressed as “resels” - RESolvable Elements)
Gaussian smoothing kernel
FWHM

23. Overview fMRI time-series Statistical Parametric Map Smoothing kernel
General Linear Model
Design matrix
Motion
correction
Parameter Estimates
Spatial
normalisation
Standard
template

25. General Linear Model… Parametric statistics one sample t-test
two sample t-test
paired t-test
Anova
AnCova
correlation
linear regression
multiple regression
F-tests
etc…
all cases of the General Linear Model

26. The General Linear Model
T-tests, correlations and Fourier analysis work for simple designs and were common in the early days of imaging
The General Linear Model (GLM) is now available in many software packages and tends to be the analysis of choice
Why is the GLM so great?
the GLM is an overarching tool that can do anything that the simpler tests do
you can examine any combination of contrasts (e.g., intact - scrambled, scrambled - baseline) with one GLM rather than multiple correlations
the GLM allows much greater flexibility for combining data within subjects and between subjects
it also makes it much easier to counterbalance orders and discard bad sections of data
the GLM allows you to model things that may account for variability in the data even though they aren’t interesting in and of themselves (e.g., head motion)
as we will see later in the course, the GLM also allows you to use more complex designs (e.g., factorial designs)

27. Equation for single (and all) voxels:
General Linear Model
Equation for single (and all) voxels:
yj = xj1 b1 + … xjL bL + ej ej ~ N(0,s2)
yj : data for scan, j = 1…J
xjl : explanatory variables / covariates / regressors, l = 1…L
bl : parameters / regression slopes / fixed effects
ej : residual errors, independent & identically distributed (“iid”)
(Gaussian, mean of zero and standard deviation of σ)
Equivalent matrix form:
y = Xb + e
X : “design matrix” / model

28. Matrix Formulation Equation for scan j Simultaneous equations for
scans 1.. J
…that can be solved
for parameters b1.. L
Regressors
Scans

29. A Simple Experiment TIME Blank Screen Intact Objects Scrambled Objects
Lateral Occipital Complex
responds when subject views objects
Blank
Screen
Intact
Objects
Scrambled
Objects
TIME
One volume (12 slices) every 2 seconds for 272 seconds (4 minutes, 32 seconds)
Condition changes every 16 seconds (8 volumes)

30. What’s real? A. C. B. D.

31. What’s real?
I created each of those time courses based by taking the predictor function and adding a variable amount of random noise
signal = +
noise

32. Linear Drift
Huettel, Song & McCarthy, 2004, Functional Magnetic Resonance Imaging

33. Physiological Noise Respiration every 4-10 sec (0.3 Hz)
moving chest distorts susceptibility
Cardiac Cycle
every ~1 sec (0.9 Hz)
pulsing motion, blood changes
Solutions
gating
avoiding paradigms at those frequencies

34. Low and High Frequency Noise
Source: Smith chapter in Functional MRI: An Introduction to Methods

35. We create a GLM with 2 predictors
× 1 = + +
× 2 =
fMRI Signal
Design Matrix x
Betas +
Residuals
“what we CAN explain”
“how much of it we CAN explain”
“what we CANNOT explain” =
“our data” x +
Statistical significance is basically a ratio of explained to unexplained variance

36. Implementation of GLM in SPM
Intact
Predictor
Scrambled
Predictor
Many thanks to Øystein Bech Gadmar for creating this figure in SPM
 Time
SPM represents time as going down
SPM represents predictors within the design matrix as grayscale plots (where black = low, white = high) over time
SPM includes a constant to take care of the average activation level throughout each run

37. Contrasts in the GLM
We can examine whether a single predictor is significant (compared to the baseline)
We can also examine whether a single predictor is significantly greater than another predictor