fMRI design and analysis

Basic 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: 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 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

• 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 rotations

Target volume: the functional volume that is closest in time to the anatomical image

x translation

z tr

ansl

atio

n

y tr

ansl

atio

n

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. Reslicing2. 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 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…

EPI

T2 T1 Transm

PD PET

DARTEL: Diffeomorphic Registration (SPM8)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)

• 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…General Linear Model…

Parametric statistics

one sample t-testtwo sample t-testpaired t-testAnovaAnCovacorrelationlinear regressionmultiple regressionF-testsetc…

all cases of the

General 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

TIME

One 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