fMRI design and analysis
Basic designs
MRI vs. fMRI
MRI studies brain anatomy.
Functional MRI (fMRI)
studies brain function.
MRI vs. fMRI
high resolution
(1 mm)
MRI
fMRI
low resolution
(~3 mm but can be better)
one image
…
fMRI
Blood Oxygenation Level Dependent (BOLD) signal
indirect measure of neural activity
 neural activity
many images
(e.g., every 2 sec for 5 mins)
  blood oxygen   fMRI signal
fMRI Activation
Flickering Checkerboard
OFF (60 s) - ON (60 s) -OFF (60 s) - ON (60 s) - OFF (60 s)
Brain
Activity
Source: Kwong et al., 1992
Time 
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
Perhaps
most frequently
misspelled
Take images along
thethe
midline
to use to plan
slices 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
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
Slice Terminology
VOXEL
(Volumetric Pixel)
Slice Thickness
e.g., 6 mm
In-plane resolution
e.g., 192 mm / 64
= 3 mm
3 mm
6 mm
IN-PLANE SLICE
SAGITTAL SLICE
Number of Slices
e.g., 10
Matrix Size
e.g., 64 x 64
Field of View (FOV)
e.g., 19.2 cm
3 mm
Coordinates - Anatomy
3 Common Views of Brain:
coronal
sagittal
Coronal (head on)
Axial (bird’s eye), aka Transverse.
Sagittal (profile)
axial
7
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
…
Activation Statistics
Functional images
~2s
ROI Time
Course
fMRI
Signal
(% change)
Time
Condition
Statistical Map
superimposed on
anatomical MRI image
Time
Region of interest (ROI)
~ 5 min
2D  3D
Overview
fMRI time-series
Motion
correction
kernel
Design matrix
Smoothing
General Linear Model
Spatial
normalisation
Statistical Parametric Map
Parameter Estimates
Standard
template
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
Motion Correction Algorithms
roll
yaw
y translation
z translation
pitch
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
Head Motion: Good, Bad,…
Slide from Duke course
… and catastrophically bad
Slide from Duke course
2. Reslicing
Nearest Neighbour
Application of registration parameters
involves re-sampling the image to create
new voxels by interpolation from existing
voxels
Interpolation can be nearest neighbour (0order), tri-linear (1st-order), (windowed)
fourier/sinc, or nth-order “b-splines”
d1
v1
Windowed sinc
d2
v2
d3
d4
v4
v3
Linear
Full sinc (no alias)
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 [1 2 3 4 5 6], or interleaved, eg [1 3 5 2 4 6])
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)
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…
T2
T1
Transm
EPI
PD
PET
DARTEL: Diffeomorphic Registration (SPM8)
Grey matter
average of 452
subjects
Affine
Grey matter
average of 471
subjects
DARTEL
Coordinates - normalization


Different people’s brains look different
‘Normalizing’ adjusts overall size and orientation
Raw Images
Normalized Images
21
Reasons for Smoothing
Potentially increase signal to noise (matched filter theorem)
Inter-subject averaging
normalisation)
(allowing for residual differences after
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)
FWHM
Gaussian smoothing kernel
Overview
fMRI time-series
Motion
correction
kernel
Design matrix
Smoothing
General Linear Model
Spatial
normalisation
Statistical Parametric Map
Parameter Estimates
Standard
template
General Linear Model…
Parametric statistics
 one
sample t-test
 two
sample t-test
 paired
t-test
 Anova
all cases of the
 AnCova
 correlation
 linear
regression
 multiple
 F-tests
 etc…
regression
General Linear Model
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)
General Linear Model
Equation for single (and all) voxels:
yj = xj1 b1 + … xjL bL + ej
yj
xjl
bl
ej
: data for scan, j = 1…J
: explanatory variables / covariates / regressors, l = 1…L
: parameters / regression slopes / fixed effects
: residual errors, independent & identically distributed (“iid”)
(Gaussian, mean of zero and standard deviation of σ)
Equivalent matrix form:
y = Xb + e
X
ej ~ N(0,s2)
: “design matrix” / model
Matrix Formulation
Equation for scan j
Simultaneous
equations for
scans 1.. J
Scans
Regressors
…that can be solved
for parameters b1.. L
A Simple Experiment
Lateral Occipital Complex
• responds when subject
views objects
Intact
Objects
Blank
Screen
TIME
One volume (12 slices) every 2 seconds for 272
seconds (4 minutes, 32 seconds)
Condition changes every 16 seconds (8 volumes)
Scrambled
Objects
What’s real?
A.
C.
B.
D.
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
Linear Drift
Huettel, Song & McCarthy, 2004, Functional Magnetic Resonance Imaging
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
Low and High Frequency Noise
Source: Smith chapter in Functional MRI: An Introduction to Methods
We create a GLM with 2 predictors
× b1
=
+
+
× b2
fMRI Signal
“our data”
=
Design Matrix
=
“what we
CAN explain”x
x
Betas
“how much of
it we CAN
explain”
+
Residuals
+
“what we
CANNOT
explain”
Statistical significance is basically a ratio of explained to
unexplained variance
Implementation of GLM in SPM
 Time
Many thanks to Øystein Bech Gadmar for
creating this figure in SPM
Intact
Predictor
Scrambled
Predictor
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
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