1. Preprocessing In SPM Yingying Wang 7/15/2014 Tuesday

2. QUIZ For MRI, which element within the body is most important?
Oxygen
Carbon
Hydrogen
An MRI system uses an Radio Frequency (RF) pulse to change the:
Spin of atoms’ nuclei
Shape of the nuclei
Amount of metal in person’s cells
Answers:
c) Hydrogen atoms have one proton and a large magnetic moment. This means they react strongly to magnetic fields and are ideal for examination in an MRI machine.
a) An MRI's RF pulse changes the spin, or precession, of atoms' nuclei. The hydrogen atoms line up with the direction of the MRI's magnetic field.

3. QUIZ An MRI system creates an image when:
All the hydrogen atoms in your body line up, creating an outline.
Hydrogen atoms facing opposite directions cancel each other out, creating a reverse outline.
The hydrogen atoms go back to their normal position, releasing energy.
What component of an MRI system allows it to choose exactly where in the body to acquire an image?
Gradient magnets
Bore
Contrast injector
c) Imagine each hydrogen atom as a tiny magnet. In the MRI machine, they all line up. When the RF pulse disappears, they go back to their normal positions, releasing energy, which the system uses to make an image.
a) Gradient magnets are small magnets that change the field within an MRI system. When turned on and off very rapidly, they essentially change the focus of the overall field.

4. QUIZ
What does an MRI system use to convert mathematical data into image?
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.
b) Fourier transform uses mathematical functions to change the data retrieved by the MRI system into a picture that a doctor can examine to make a diagnosis.
- hemoglobin

5. Overview of SPM for fMRI
Preprocessing
Statistical parametric map (SPM)
Design matrix
Image time-series
Kernel
Realignment
Smoothing
General linear model
Statistical
inference
Random
field theory
Normalization
Let’s look at the overview of fMRI data analysis in SPM
p <0.05
Template
Parameter estimates

6. fMRI = Acquiring Moviesy x z
3D Blood Oxygen-Level Dependent (BOLD) contrast images
FMRI time series
Task
Run/Session: Time Series of Images …
scan 1
time
scan N
Task
No Task

7. fMRI = Acquiring Movies
The Localized Time-series is the Fundamental Information Unit of fMRI
Signal: Fluctuation through Blood oxygen level dependent (BOLD) contrast
Noise: All other fluctuations
slice 21…after warping…slice 34 before
Run/Session: Time Series of Images …
scan 1
time
scan N

8. fMRI Movie: An example

9. The SPM Graphical User Interface (GUI)
Preprocessing
Realignment
Slice-Timing Correction
Co-registration
Unified Segmentation & Normalization
Smoothing 1.

10. Temporal preprocessing (slice timing correction)
Temporal preprocessing is a necessary step in preparing your data for analysis.
Filtering, spike removal, and slice time correction can each make a significant contribution to the
power of your analysis (or more precisely, not doing them can significantly degrade your analysis).

12. 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 [ ], or interleaved, eg [ ])
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)

13. Slice-timing correction (STC)
Acquisition onset differs between slices
STC: temporal alignment of all voxels in a volume
Via sinc interpolation
Sladky et al, NeuroImage 2011

17. Spatial Preprocessing
Input
Output
fMRI time-series
Anatomical MRI
TPMs
Segmentation
Transformation
(seg_sn.mat)
Kernel
REALIGN
COREG
SEGMENT
NORM WRITE
SMOOTH
MNI Space
Motion corrected
Mean functional
(Headers changed)
GLM

18. Spatial preprocessing  Realignment  Co-registration  Segmentation &  Normalization  Smoothing

19. Realignment Aligns all volumes of all runs spatially
fMRI time-series
Aligns all volumes of all runs spatially
Rigid-body transformation: three translations, three rotations
Objective function: mean squared error of corresponding voxel intensities
Voxel correspondence via Interpolation
REALIGN
Mean functional
Motion corrected

20. Rigid-Body Transformations
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.

21. 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

22. 2D Affine Transforms Translations by tx and ty
x1 = x0 + tx
y1 = y0 + ty
Rotation around the origin by  radians
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

23. 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
The order of the operations matters
Translations
Pitch
about x axis
Roll
about y axis
Yaw
about z axis

24. Motion Correction Algorithms
pitch
roll
yaw
z translation
y translation
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

25. Objective Functions Intra-modal Inter-modal (or 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)

26. Mean-squared Difference
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

27. Simple Interpolation Nearest neighbour Tri-linear
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

28. B-spline Interpolation

29. Realignment Output: Parameters

30. Motion corrected No Motion correction Z-Value: 3.9
% signal change
Z-Value: 3.9
Crosshair location: Postcentral gyrus
Time (TRs)
Motion corrected
% signal change
Time (TRs)
Z-Value: 3.8

31. Residual Errors from aligned fMRI
Re-sampling can introduce interpolation errors
especially tri-linear interpolation
Gaps between slices can cause aliasing artefacts
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 modelled as confounds in subsequent analyses

32. Spatial preprocessing  Realignment  Co-registration  Segmentation &  Normalization  Smoothing

33. Co-Registration Aligns structural image to mean functional image
Anatomical MRI
Aligns structural image to mean functional image
Affine transformation: translations, rotations, scaling, shearing
Objective function: mutual information, since contrast different
Typically only transformation matrix (“header”) changed (no reslicing)
COREG
Motion corrected
Mean functional
(Headers changed)

34. Inter-modal registration.
Coregistration
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.

35. 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

36. Coregistration maximises Mutual Information
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)

37. Co-Registration: Output
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 histogram

38. Co-Registration: Output

39. Spatial preprocessing  Realignment  Co-registration  Segmentation &  Normalization  Smoothing

40. Pre-processing Overview
Statistics or whatever
fMRI time-series
Template
Anatomical MRI
Smoothed
Estimate Spatial Norm
Motion Correct
Smooth
Coregister
Spatially normalised
Deformation

41. Alternative Pipeline Statistics or whatever fMRI time-series Template
Smoothed
Estimate Spatial Norm
Motion Correct
Smooth
Spatially normalised
Deformation

42. Spatial Normalisation - Reasons
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

43. Inter-subject Variability

44. Coordinates - normalization
Different people’s brains look different
‘Normalizing’ adjusts overall size and orientation
Normalized Images
Raw Images

45. Standard spaces The Talairach Atlas The MNI/ICBM AVG152 Template
Also DICOM scanner-based voxel-world mapping
The MNI template follows the convention of T&T, but doesn’t match the particular brain Recommended reading:

46. Segmentation Anatomical MRI TPMs Segmentation Transformation
(seg_sn.mat)
SEGMENT
NORM WRITE
MNI Space
Motion corrected
Motion corrected
Mean functional
(Headers changed)

47. Segmentation
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.
Mixture of Gaussian model (tissue probabilities)
Bayes is used to model the inhomogeneities in the data (with bases functions), used then to correct it

48. Normalisation via segmentation
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

49. Summary of the unified model
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

50. Mixture of Gaussians (MOG)
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

51. Tissue intensity distributions (T1-w MRI)

52. Non-Gaussian Intensity Distributions
Multiple Gaussians per tissue class allow non-Gaussian intensity distributions to be modelled.
E.g. accounting for partial volume effects

53. Modelling inhomogeneity
A multiplicative bias field is modelled as a linear combination of basis functions.
Corrected image
Corrupted image
Bias Field

54. Tissue Probability Maps
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

55. Deforming the Tissue Probability Maps
Tissue probability maps images are warped to match the subject
The inverse transform warps to the TPMs

56. Segmentation results
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)

57. Spatial normalisation – regularisation
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

58. Spatial normalisation – Limitations
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: ]
Compromise
Correct relatively large-scale variability (sizes of structures)
Smooth over finer-scale residual differences

59. Smoothing 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
MNI Space
How is it implemented?
Convolution with a 3D Gaussian kernel, of specified full-width at half-maximum (FWHM) in mm
GLM

60. Smoothing Goal: Improve SNR, Matched-Filter Theorem
How: Smooth with a 3D Gaussian Kernel
Each voxel after smoothing effectively becomes the result of applying a weighted region of interest (ROI).
Before convolution
Convolved with a Gaussian
Suppresses noise

61. 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)
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)
Gaussian smoothing kernel
FWHM

62. 0mm smooth
4mm smooth
8mm smooth
20mm smooth

63. Spatial Preprocessing
Input
Output
fMRI time-series
Anatomical MRI
TPMs
Segmentation
Transformation
(seg_sn.mat)
Kernel
REALIGN
COREG
SEGMENT
NORM WRITE
SMOOTH
MNI Space
Motion corrected
Mean functional
(Headers changed)
GLM

64. Spike removal
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
Preprocessing strategy:
Detect “abnormal” time points (excessive motion, large change in signal)
Remove the affected time points (volumes) and interpolate
Generate single point regressors to model out the variance

65. Artifact Detection Toolbox (ART)
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.

69. Thank you
Internet resources: