Download Single Subject Analysis I

Yingying Wang
7/15/2014 Tuesday
http://neurobrain.net/2014STBCH/index.html

For MRI, which element within the body is
most important?
a)
b)
c)

Oxygen
Carbon
Hydrogen
An MRI system uses an Radio Frequency (RF)
pulse to change the:
a)
b)
c)
Spin of atoms’ nuclei
Shape of the nuclei
Amount of metal in person’s cells
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
An MRI system creates an image when:
All the hydrogen atoms in your body line up, creating
an outline.
b) Hydrogen atoms facing opposite directions cancel each
other out, creating a reverse outline.
c) The hydrogen atoms go back to their normal position,
releasing energy.
a)

What component of an MRI system allows it to
choose exactly where in the body to acquire an
image?
a)
b)
c)
Gradient magnets
Bore
Contrast injector
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
What does an MRI system use to convert
mathematical data into image?
a)
b)
c)

RF pulse converter
Fourier transform
Electron precession
Higher BOLD signal intensities arise from
increases in the concentration of oxygenated
________ since the blood magnetic
susceptibility now more closely matches the
tissue magnetic susceptibility.
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Preprocessing
Image time-series
Realignment
Kernel
Smoothing
Design matrix
General linear model
Statistical
inference
Normalization
Template
Statistical parametric map (SPM)
Random
field theory
p <0.05
Parameter estimates
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
z
y
3D Blood
Oxygen-Level
Dependent
(BOLD)
contrast images
x
Task
 Run/Session:
Time Series of
Images
Task
No Task
…
scan 1
time
scan N
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 The Localized Time-series
is the Fundamental
Information Unit of fMRI
Signal: Fluctuation through
Blood oxygen level
dependent (BOLD) contrast
Noise: All other fluctuations
 Run/Session:
Time Series of
Images
…
scan 1
time
scan N
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
1.
Preprocessing
Realignment
 Slice-Timing Correction
 Co-registration
 Unified Segmentation &
Normalization
 Smoothing

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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)
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 Acquisition onset
differs between
slices
 STC: temporal
alignment of all
voxels in a volume
 Via sinc
interpolation
Sladky et al, NeuroImage 2011
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Input
Output
fMRI time-series
Anatomical MRI
TPMs
Segmentation
Transformation
(seg_sn.mat)
Kernel
REALIGN
COREG
SEGMENT
 m11

 m21

 m31


 0
Motion corrected
Mean
functional
NORM
WRITE
SMOOTH
m12 m13 m14 

m22 m23 m24 
m32 m33 m34 
0
0
1 
(Headers
changed)
MNI Space
GLM
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fMRI time-series
 Aligns all volumes of all
runs spatially
 Rigid-body
transformation: three
translations, three
rotations
REALIGN
 Objective function: mean
squared error of
corresponding voxel
intensities
Motion corrected
Mean
functional
 Voxel correspondence via
Interpolation
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
Assume that brain of the same subject doesn’t
change shape or size in the scanner.


Head can move, but remains the same shape and
size.
Some exceptions:
 Image distortions.
 Brain slops about slightly because of gravity.
 Brain growth or atrophy over time.

If the subject’s head moves, we need to correct
the images.

Do this by image registration.
Two components:
•
Registration - i.e. Optimise the parameters
that describe a spatial transformation
between the source and reference images
•
Transformation - i.e. Re-sample according
to the determined transformation
parameters

Translations by tx and ty



Rotation around the origin by  radians



x1 = x0 + tx
y1 = y0 + ty
x1 = cos() x0 + sin() y0
y1 = -sin() x0 + cos() y0
Zooms by sx and sy


x1 = sx x0
y1 = sy y0
*Shear
*x1 = x0 + h y0
*y1 = y0

A 3D rigid body transform is defined by:



1


0

0

0
0
1
0
0
3 translations - in X, Y & Z directions
3 rotations - about X, Y & Z axes
The order of the operations matters
0 Xtrans   1
0
0
0   cosΘ 0 sin Θ 0   cosΩ sin Ω 0 0 
0 Ytrans   0 cosΦ sin Φ 0   0
1
0
0    sin Ω cosΩ 0 0 



1 Zt rans   0  sin Φ cosΦ 0    sin Θ 0 cosΘ 0   0
0
1 0 
 
 
 

0
1   0
0
0
1  0
0
0
1  0
0
0 1
Translations
Pitch
about x axis
Roll
about y axis
Yaw
about z axis
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
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
Intra-modal
Mean squared difference (minimise)
 Normalised cross correlation (maximise)


Inter-modal (or intra-modal)
Mutual information (maximise)
 Normalised mutual information
(maximise)
 Entropy correlation coefficient (maximise)



Minimising mean-squared difference works for
intra-modal registration (realignment)
Simple relationship between intensities in one
image, versus those in the other

Assumes normally distributed differences

Nearest neighbour


Take the value of the
closest voxel
Tri-linear




Just a weighted
average of the
neighbouring voxels
f5 = f1 x2 + f2 x1
f6 = f3 x2 + f4 x1
f7 = f5 y2 + f6 y1
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% signal change
Z-Value: 3.9
Time (TRs)
% signal change
Crosshair location:
Postcentral gyrus
Z-Value: 3.8
Time (TRs)
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
Re-sampling can introduce interpolation errors



Gaps between slices can cause aliasing artefacts
Slices are not acquired simultaneously


especially tri-linear interpolation
rapid movements not accounted for by rigid body model
Image artefacts may not move according to a rigid body
model
image distortion
 image dropout
 Nyquist ghost


Functions of the estimated motion parameters can be
modelled as confounds in subsequent analyses
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Anatomical MRI
 Aligns structural image to
mean functional image
 Affine transformation:
translations, rotations,
scaling, shearing
 Objective function:
mutual information, since
contrast different
COREG
 m11

 m21

 m31


 0
Motion corrected
Mean
functional
m12 m13 m14 

m22 m23 m24 
m32 m33 m34 
0
0
1 
(Headers
changed)
Typically only
transformation matrix
(“header”) changed (no
reslicing)
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• Inter-modal registration.
• Match images from same
subject but different
modalities:
–anatomical localisation of
single subject activations
–achieve more precise
spatial normalisation of
functional image using
anatomical image.
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

Used for between-modality registration
Derived from joint histograms

MI=


ab P(a,b) log2 [P(a,b)/( P(a) P(b) )]
Related to entropy: MI = -H(a,b) + H(a) + H(b)
 Where H(a) = -a P(a) log2P(a) and H(a,b) = -a P(a,b)
log2P(a,b)
Mean
functional
Anatomical MRI
 Joint and marginal
Histogram
 Quantify how well one
image predicts the other =
how much shared info
 Joint probability distribution
estimated from joint
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Statistics or
whatever
fMRI time-series
Anatomical MRI
Template
Smoothed
Estimate
Spatial Norm
Motion Correct
Smooth
Coregister
 m11

 m21

 m31


 0
Spatially
normalised
m12 m13 m14 

m22 m23 m24 
m32 m33 m34 
0
0
1 
Deformation
Statistics or
whatever
fMRI time-series
Template
Smoothed
Estimate
Spatial Norm
Motion Correct
Smooth
Spatially
normalised
Deformation
 Inter-subject averaging
 Increase sensitivity with more subjects
 Fixed-effects analysis
 Extrapolate findings to the population as a whole
 Mixed-effects analysis
 Make results from different studies comparable by
aligning them to standard space
 e.g. The T&T convention, using the MNI template
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

Different people’s brains look different
‘Normalizing’ adjusts overall size and orientation
Raw Images
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Normalized Images
The Talairach Atlas
The MNI/ICBM AVG152 Template
The MNI template follows the convention of T&T, but doesn’t match the particular brain
Recommended reading: http://imaging.mrc-cbu.cam.ac.uk/imaging/MniTalairach
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Anatomical MRI
TPMs
Segmentation
Transformation
(seg_sn.mat)
SEGMENT
 m11

 m21

 m31


 0
Motion corrected
Mean
functional
NORM
WRITE
m12 m13 m14 

m22 m23 m24 
m32 m33 m34 
0
0
1 
(Headers
changed)
MNI Space
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


Goal: Probabilistically label voxels into their appropriate
space
How: Bayesian inference
 Use tissue probability maps (TPMs) are used as priors.
Output:
a spatial transformation (i.e. seg_sn.mat) that
can be used for spatially normalising images.
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 MRI imperfections make normalisation harder
 Noise, artefacts, partial volume effect
 Intensity inhomogeneity or “bias” field
 Differences between sequences
 Normalising segmented tissue maps should be more robust
and precise than using the original images ...
 … Tissue segmentation benefits from spatially-aligned prior
tissue probability maps (from other segmentations)
 This circularity motivates simultaneous segmentation and
normalisation in a unified model
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 SPM8 implements a generative model
 Principled Bayesian probabilistic formulation
 Gaussian mixture model segmentation with
deformable tissue probability maps (TPMs, priors)
 The inverse of the transformation that aligns the
TPMs can be used to normalise the original image
 Bias correction is included within the model
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 Classification is based on a Mixture of Gaussians
model (MOG), which represents the intensity
probability density by a number of Gaussian
distributions.
Frequency
Image Intensity
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
Multiple Gaussians per tissue class allow non-Gaussian
intensity distributions to be modelled.
 E.g. accounting for partial volume effects
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
A multiplicative bias field is modelled
as a linear combination of basis functions.
Corrupted
image
Bias Field
Corrected image
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
Tissue probability maps (TPMs) are used as the prior,
instead of the proportion of voxels in each class
ICBM Tissue Probabilistic Atlases. These tissue probability maps
were kindly provided by the International Consortium for Brain Mapping
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 Tissue probability maps
images are warped to
match the subject
 The inverse transform
warps to the TPMs
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Spatially
normalised
BrainWeb
phantoms
(T1, T2, PD)
Tissue
probability
maps of
GM and
WM
Cocosco, Kollokian, Kwan & Evans. “BrainWeb: Online Interface to a 3D MRI Simulated Brain
Database”. NeuroImage 5(4):S425 (1997)
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
The “best” parameters according to the objective
function may not be realistic

In addition to similarity, regularisation terms or
constraints are often needed to ensure a
reasonable solution is found

Also helps avoid poor local optima

Can be considered as priors in a Bayesian framework,
e.g. converting ML to MAP:
 log(posterior) = log(likelihood) + log(prior) + c
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
Seek to match functionally homologous regions, but...
 Challenging high-dimensional optimisation, many local optima
 Different cortices can have different folding patterns
 No exact match between structure and function
 [Interesting recent paper Amiez et al. (2013), PMID:23365257 ]

Compromise
 Correct relatively large-scale variability (sizes of structures)
 Smooth over finer-scale residual differences
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 Why blurring the data?
 Improves spatial overlap by blurring over




anatomical differences
Suppresses thermal noise (averaging)
Increases sensitivity to effects of similar scale
to kernel (matched filter theorem)
Makes data more normally distributed
(central limit theorem)
Reduces the effective number of multiple
comparisons
Kernel
SMOOTH
 How is it implemented?
 Convolution with a 3D Gaussian
kernel, of specified full-width at
half-maximum (FWHM) in mm
MNI Space
GLM
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•
•
Goal: Improve SNR, Matched-Filter
Theorem
How: Smooth with a 3D Gaussian Kernel
o
Each voxel after smoothing effectively becomes
the result of applying a weighted region of
interest (ROI).
Before convolution
Convolved with a Gaussian
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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)
FWHM
Gaussian smoothing kernel
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Signal Change Z-Value
0mm smooth
9
8
7
6
5
4
3
2
1
0
-1
-2
8mm smooth
4mm smooth
20mm smooth
Changes in Z-Values Across Four Random Voxels as a
Function of Kernel Size
(x=18, y=31, z=25)
(x=20, y=20, z=25)
(x=28, y=7, z=13)
(x=18, y=42, z=23)
Average Across Voxels
0
4
8
Kernel Size (mm)
12
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Input
Output
fMRI time-series
Anatomical MRI
TPMs
Segmentation
Transformation
(seg_sn.mat)
Kernel
REALIGN
COREG
SEGMENT
 m11

 m21

 m31


 0
Motion corrected
Mean
functional
NORM
WRITE
SMOOTH
m12 m13 m14 

m22 m23 m24 
m32 m33 m34 
0
0
1 
(Headers
changed)
MNI Space
GLM
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

Spikes are impulsive positive or negative going
discontinuities in the time course, followed by
a return to normal.
Multiple sources:





Electrical sparks (from gradient problems, metal in
bore)
Rapid motion (coughing)
External interference
They cannot be effectively removed by
frequency domain filtering.
ART (from Susan Gabrieli at MIT
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 ART is a GUI tool for remedying a number of
problems in datasets. Among its tools is one for
detecting and removing spikes from fMRI data.
 Examines the global mean signal and motion
parameters to detect “anomalous” time points
that need to be dealt with.
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
Internet resources:
http://www.translationalneuromodeling.org/spmcourse-2014-presentation-slides/
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