Spatial preprocessing of fMRI data Methods & models for fMRI data analysis 30 September 2009 Klaas...
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Spatial preprocessing of fMRI data
Methods & models for fMRI data analysis30 September 2009
Klaas Enno Stephan
Laboratory for Social and Neural Systrems ResearchInstitute for Empirical Research in EconomicsUniversity of Zurich
Functional Imaging Laboratory (FIL)Wellcome Trust Centre for NeuroimagingUniversity College London
With many thanks for helpful slides to:
John Ashburner
Meike Grol
Ged Ridgway
Overview of SPM
RealignmentRealignment SmoothingSmoothing
NormalisationNormalisation
General linear modelGeneral linear model
Statistical parametric map (SPM)Statistical parametric map (SPM)Image time-seriesImage time-series
Parameter estimatesParameter estimates
Design matrixDesign matrix
TemplateTemplate
KernelKernel
Gaussian Gaussian field theoryfield theory
p <0.05p <0.05
StatisticalStatisticalinferenceinference
Functional MRI (fMRI)
• Uses echo planar imaging (EPI) for fast acquisition of T2*-weighted images.
• Spatial resolution:– 3 mm (standard 1.5 T scanner)– < 200 μm (high-field systems)
• Sampling speed:– 1 slice: 50-100 ms
• Requires spatial pre-processing and statistical analysis.
EPI(T2*)
T1
dropout
subjects
sessions
runs
single run
volume
slices
Terminology of fMRI
TR = repetition timetime required to scan one volume
voxel
Terminology of fMRI
Slice thicknesse.g., 3 mm
Scan Volume:Field of View
(FOV),e.g. 192 mm
Axial slices
3 mm
3 mm
3 mm
Voxel Size(volumetric pixel)
Matrix Sizee.g., 64 x 64
In-plane resolution192 mm / 64
= 3 mm
Standard space
The Talairach Atlas The MNI/ICBM AVG152 Template
World coords(2, 4, -4) mm
(4, 4, -2)
(2, 2, -4)
Voxel index(45, 66, 35)
(44, 66, 36)
(45, 65, 35)
x 2 92
y 2 -128
z 2 -74
W V
W V
W V
x
y
z
World space & voxel space
74
128
92
z
y
x
200
020
002
z
y
x
V
V
V
W
W
W
1
z
y
x
1000
74200
128020
92002
1
z
y
x
V
V
V
W
W
WBy moving to 4D, one can includetranslations within a single matrix multiplication
These 4-by-4 “homogeneous matrices” are the currency of voxel-world mappings, affine coreg. and realignment. In SPM5 & SPM8, they are stored in the .hdr files. In SPM2, they are stored in .mat files.
To find inverse mappings, or results of concatenating multiple transformations, we simply follow the rules of matrix algebra
Changing coordinate systems
74-2zz
128-2y
922x
VW
VW
VW
y
x
Why does fMRI require spatial preprocessing?
• Head motion artefacts during scanning
• Problems of EPI acquisition: distortion and signal dropouts
• Brains are quite different across subjects
→ Realignment
→ “Unwarping”
→ Normalisation (“Warping”)→ Smoothing
Realignment or “motion correction”
• Even small head movements can be a major problem:– increase in residual variance– data may get completely lost if sudden movements occur
during a single volume– movements may be correlated with the task performed
• Therefore:– always constrain the volunteer’s head– instruct him/her explicitly to remain as calm as possible– do not scan for too long – everyone will move after while !
minimising movements is one of the most important factors for ensuring good data quality!
Realignment = rigid-body registration
• Assumes that all movements are those of a rigid body, i.e. the shape of the brain does not change
• Two steps:Registration: optimising six parameters that ptimising six parameters that
describe a rigid body transformation between describe a rigid body transformation between the source and a reference imagethe source and a reference image
Transformation: re-sampling according to the re-sampling according to the determined transformationdetermined transformation
Linear (affine) transformations
• Rigid-body transformations are a subset
• Parallel lines remain parallel
• Operations can be represented by: x1 = m11x0 + m12y0 + m13z0 + m14
y1 = m21x0 + m22y0 + m23z0 + m24
z1 = m31x0 + m32y0 + m33z0 + m34
• Or as matrices:
1
z
y
x
1000
mmmm
mmmm
mmmm
1
z
y
x
0
0
0
34333231
24232221
14131211
1
1
1
2D affine transforms
• Translations by tx and ty
x1 = 1 x0 + 0 y0 + tx
y1 = 0 x0 + 1 y0 + ty
• Rotation around the origin by radiansx1 = cos() x0 + sin() y0 + 0
y1 = -sin() x0 + cos() y0 + 0
• Zooms by sx and sy:x1 = sx x0 + 0 y0 + 0
y1 = 0 x0 + sy y0 + 0
Shearx1 = 1 x0 + h y0 + 0y1 = 0 x0 + 1 y0 + 0
Representing rotations
0
0
1
1
y
x
)θcos(θ)sin(
θ)sin()θcos(
y
x
0
0
0
1
1
1
z
y
x
100
0)θcos()θsin(
0)θsin()θcos(
z
y
x
3D rigid-body transformations
• A 3D rigid body transform is defined by:– 3 translations - in X, Y & Z directions– 3 rotations - about X, Y & Z axes
• Non-commutative: the order of the operations matters
1000
0100
00cossin
00sincos
1000
0cos0sin
0010
0sin0cos
1000
0cossin0
0sincos0
0001
1000
Zt100
Y010
X001
rans
trans
trans
ΩΩ
ΩΩ
ΘΘ
ΘΘ
ΦΦ
ΦΦ
Translations Pitchabout x axis
Rollabout y axis
Yawabout z axis
Realignment
• Goal: minimise squared differences between source and reference image
• Other methods available (e.g. mutual information)
A special case ...
• If a subject remained perfectly still during a fMRI study, would realignment still be a good idea to perform?
• When is this issue of practical relevance?
• Nearest neighbour– Take the value of the
closest voxel
• linear (2D: bilinear; 3D: trilinear)– Just a weighted average
of the neighbouring voxels
– f5 = f1 x2 + f2 x1
– f6 = f3 x2 + f4 x1
– f7 = f5 y2 + f6 y1
Simple interpolation
B-spline interpolation
B-splines are piecewise polynomials
A continuous function is represented by a linear combination of basis functions
2D B-spline basis functions of degrees 0, 1, 2 and 3
Nearest neighbour and trilinear interpolation are the same as B-spline interpolation with degrees 0 and 1.
Why does fMRI require spatial preprocessing?
• Head motion artefacts during scanning
• Problems of EPI acquisition: distortion and signal dropouts
• Brains are quite different across subjects
→ Realignment
→ “Unwarping”
→ Normalisation (“Warping”)→ Smoothing
Residual errors after realignment
• Resampling can introduce interpolation errors
• Slices are not acquired simultaneously– 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 included as confound regressors in subsequent statistical analyses.
Movement by distortion interactions
• Subject disrupts B0 field, rendering it inhomogeneous
→ distortions in phase-encode direction
• Subject moves during EPI time series
→ distortions vary with subject orientation→ shape of imaged brain
varies
Andersson et al. 2001, NeuroImage
Movement by distortion interaction
Movement by distortion interactions
after head rotationoriginal deformations
deformations after realignment mismatch in deformationsAndersson et al. 2001, NeuroImage
Different strategies for correcting movement artefacts
• liberal control:realignment only
• moderate control:realignment + “unwarping”
• strict control:realignment + inclusion of realignment parameters in statistical model
Why does fMRI require spatial preprocessing?
• Head motion artefacts during scanning
• Problems of EPI acquisition: distortion and signal dropouts
• Brains are quite different across subjects
→ Realignment
→ “Unwarping”
→ Normalisation (“Warping”)→ Smoothing
Individual brains differ in size, shape and folding
Spatial normalisation: why necessary?
• Inter-subject averaging– Increase sensitivity with more subjects
• Fixed-effects analysis
– Extrapolate findings to the population as a whole• Random / mixed-effects analysis
• Make results from different studies comparable by bringing them into a standard coordinate system– e.g. MNI space
Spatial normalisation: objective
• Warp the images such that functionally corresponding regions from different subjects are as close together as possible
• Problems:– Not always exact match between structure and function– Different brains are organised differently– Computational problems (local minima, not enough
information in the images, computationally expensive)
• Compromise by correcting gross differences followed by smoothing of normalised images
Spatial normalisation: affine step
• The first part is a 12 parameter affine transform– 3 translations– 3 rotations– 3 zooms– 3 shears
• Fits overall shape and size
Spatial normalisation: non-linear step
Deformations consist of a linear combination of smooth basis functions.
These basis functions result from a 3D discrete cosine transform (DCT).
Spatial normalisation: Bayesian regularisation
Deformations consist of a linear combination of smooth basis functions
set of frequencies from a 3D discrete cosine transform.
Find maximum a posteriori (MAP) estimates: simultaneously minimise – squared difference between template and source image – squared difference between parameters and their priors
)(log)(log)|(log)|(log yppypyp MAP:
MAP:
Deformation parametersDeformation parameters
“Difference” between template and source image
“Difference” between template and source image
Squared distance between parameters and their expected values
(regularisation)
Squared distance between parameters and their expected values
(regularisation)
Templateimage
Affine registration.(2 = 472.1)
Non-linearregistration
withoutregularisation.(2 = 287.3)
Non-linearregistration
usingregularisation.(2 = 302.7)
Without regularisation, the non-linear spatial normalisation can introduce unnecessary warps.
Spatial normalisation: overfitting
Segmentation
GM and WM segmentations overlaid on original images
Structural image, GM and WM segments, and brain-mask (sum of GM and WM)
Unified segmentation with tissue class priors
•Goal: for each voxel, compute probability that it belongs to a particular tissue type, given its intensity
•Likelihood model: Intensities are modelled by a mixture of Gaussian distributions representing different tissue classes (e.g. GM, WM, CSF).
•Priors are obtained from tissue probability maps (segmented images of 151 subjects).
•Goal: for each voxel, compute probability that it belongs to a particular tissue type, given its intensity
•Likelihood model: Intensities are modelled by a mixture of Gaussian distributions representing different tissue classes (e.g. GM, WM, CSF).
•Priors are obtained from tissue probability maps (segmented images of 151 subjects). Ashburner & Friston 2005, NeuroImage
p (tissue | intensity)
p (intensity | tissue) ∙ p (tissue)
Segmentation & normalisation
• Circular relationship between segmentation & normalisation:– Knowing which tissue type a voxel belongs to helps normalisation.– Knowing where a voxel is (in standard space) helps segmentation.
• Build a joint generative model:– model how voxel intensities result from mixture of tissue type distributions– model how tissue types of one brain have to be spatially deformed to
match those of another brain
• Using a priori knowledge about the parameters: adopt Bayesian approach and maximise the posterior probability
Ashburner & Friston 2005, NeuroImage
Normalisation options in practice
• Conventional normalisation:– either warp functional scans to EPI template directly– or coregister structural scan to functional scans and then
warp structural scan to T1 template; then apply these parameters to functional scans (“Normalise: Write”)
• Unified segmentation:– coregister structural scan to functional scans– unified segmentation provides normalisation parameters– apply these parameters to functional scans (“Normalise:
Write”)
Smoothing• Why smooth?
– increase signal to noise– inter-subject averaging– increase validity of Gaussian Random Field theory
• In SPM, smoothing is a convolution with a Gaussian kernel.
• Kernel defined in terms of FWHM (full width at half maximum).
Gaussian convolution is separable Gaussian smoothing kernel
Smoothing
Before convolution Convolved with a circleConvolved with a Gaussian
Smoothing is done by convolving with a 3D Gaussian which is defined by its full width at half maximum (FWHM).
Each voxel after smoothing effectively becomes the result of applying a weighted region of interest.
Summary: spatial preprocessing steps
• Head motion artefacts during scanning
• Problems of EPI acquisition: distortion and signal dropouts
• Brains are quite different across subjects
→ Realignment
→ “Unwarping”
→ Normalisation (“Warping”)→ Smoothing
Thank you!