fMRI design and analysisBasic designs
MRI studies brain anatomy. Functional MRI (fMRI) studies brain function.
MRI vs. fMRI
MRI vs. fMRI
neural activity blood oxygen fMRI signal
MRI fMRI
one image
many images (e.g., every 2 sec for 5 mins)
high resolution(1 mm)
low resolution(~3 mm but can be better)
fMRI Blood Oxygenation Level Dependent (BOLD) signal
indirect measure of neural activity
…
fMRI Activation
Time
BrainActivity
Source: Kwong et al., 1992
Flickering CheckerboardOFF (60 s) - ON (60 s) -OFF (60 s) - ON (60 s) - OFF (60 s)
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) SagittalsTake 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
fMRI Experiment Stages: Anatomicals4) 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 Thicknesse.g., 6 mm
Number of Slicese.g., 10
SAGITTAL SLICE IN-PLANE SLICE
Field of View (FOV)e.g., 19.2 cm
VOXEL(Volumetric Pixel)
3 mm
3 mm6 mm
Slice Terminology
Matrix Sizee.g., 64 x 64
In-plane resolutione.g., 192 mm / 64
= 3 mm
8
Coordinates - Anatomy
3 Common Views of Brain:Coronal (head on)Axial (bird’s eye), aka Transverse. Sagittal (profile)
sagittalcoronal
axial
fMRI Experiment Stages: Functionals5) 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
…
Statistical Mapsuperimposed on
anatomical MRI image
~2s
Functional images
Time
Condition 1
Condition 2 ...
~ 5 min
Time
fMRISignal
(% change)
ROI Time Course
Condition
Activation Statistics
Region of interest (ROI)
2D 3D
Overview
Motioncorrection
Smoothing
kernel
Spatialnormalisation
Standardtemplate
fMRI time-series Statistical Parametric Map
General Linear Model
Design matrix
Parameter Estimates
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
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 rotationsTarget volume: the functional volume that is closest in time to the anatomical image
x translation
z tra
nsla
tion
y tra
nsla
tion
pitch roll yaw
Head Motion: Good, Bad,…
Slide from Duke course
… and catastrophically bad
Slide from Duke course
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”
2. Reslicing
d1 d2
d3
d4
v1
v4
v2
v3
Nearest Neighbour
Linear
Full sinc (no alias)
Windowed sinc
Temporal Realignment (Slice-Timing Correction)
Most functional MRI uses Echo-Planar Imaging (EPI)Each plane (slice) is typically acquired every 3mmnormally 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…
EPI
T2 T1 Transm
PD PET
DARTEL: Diffeomorphic Registration (SPM8)
Grey matter average of 452 subjects Affine Grey matter
average of 471 subjectsDARTEL
22
Coordinates - normalization
Different people’s brains look different ‘Normalizing’ adjusts overall size and orientation
Raw Images Normalized Images
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)
Gaussian smoothing kernel
• 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
Overview
Motioncorrection
Smoothing
kernel
Spatialnormalisation
Standardtemplate
fMRI time-series Statistical Parametric Map
General Linear Model
Design matrix
Parameter Estimates
General Linear Model…
Parametric statistics
one sample t-testtwo sample t-testpaired t-testAnovaAnCovacorrelationlinear regressionmultiple regressionF-testsetc…
all cases of theGeneral Linear Model
The General Linear ModelT-tests, correlations and Fourier analysis work for simple designs and were common in the early days of imagingThe 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 doyou can examine any combination of contrasts (e.g., intact - scrambled, scrambled - baseline) with one GLM rather than multiple correlationsthe GLM allows much greater flexibility for combining data within subjects and between subjectsit also makes it much easier to counterbalance orders and discard bad sections of datathe 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 1 + … xjL L + j j ~ N(0,2)
yj : data for scan, j = 1…J xjl : explanatory variables / covariates / regressors, l = 1…L
l : parameters / regression slopes / fixed effects j : residual errors, independent & identically distributed (“iid”)
(Gaussian, mean of zero and standard deviation of σ)
Equivalent matrix form:
y = X +
X : “design matrix” / model
Matrix Formulation
Equation for scan j
Simultaneous equations forscans 1.. J
…that can be solvedfor parameters 1.. L
Regressors
Sca
ns
A Simple Experiment
IntactObjects
ScrambledObjects
BlankScreen
TIMEOne volume (12 slices) every 2 seconds for 272 seconds (4 minutes, 32 seconds)
Condition changes every 16 seconds (8 volumes)
Lateral Occipital Complex• responds when subject views 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
fMRI Signal
× 1
× 2
=
ResidualsDesign Matrix
++
“what we CAN explain”
“what we CANNOT explain”
= +Betasx
“how much of it we CAN explain”
“our data” = +x
Statistical significance is basically a ratio of explained to unexplained variance
Implementation of GLM in SPM
SPM represents time as going downSPM represents predictors within the design matrix as grayscale plots (where black = low, white = high) over timeSPM includes a constant to take care of the average activation level throughout each run
T
ime
Many thanks to Øystein Bech Gadmar for creating this figure in SPM
IntactPredictor
ScrambledPredictor
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