Week 4: Pre-processing

Question 1

Goals of preprocessing

Answer 1

1. Minimising the influence of data acquisition and physiological artifacts
2. To check statistical assumptions and transform the data to meet these assumptions
3. To standardize the locations of brain regions across subjects to achieve validity and sensitivity in group analysis

Question 2

Different (potential) preprocessing steps

Answer 2

• Visualization and artifact removal
• Slice time correction
• Motion correction
• Physiological corrections
• Co-registration
• Normalization
• Spatial filtering / smoothing
• Temporal filtering

Question 3

Spike artifacts

Answer 3

• sudden large intensity increases in the signal across the entire brain that likely reflect scanner instabilities
• One way to deal with these artifacts is to “censor” bad timepoints using a nuisance predictor
• RMSSD: value that reflects the difference between every timepoint of the signal and the signal at timepoints (t-1), which is then squared (to inflate), averaged (to get a single value) and then rooted (for point 0, we use the same value as point 1).
• Once we have found the spikes, to remove their influence, we can simply add a nuisance predictor for each spike, in which the predictor contains zeros at timepoints without the spike and 1 at the timepoint with a spike.

Question 4

Rigid body registration

Answer 4

• Example of a more general affine registration
• Used in motion correction and co-registration processes
• We assume that the brain is a rigid body that may move around and try to correct for this movement
• The goal is to find the best alignment between an input image and some target image
• The target image is usually defined to be the first (or middle) image in the fMRI time series
• Align all the rest of the images to this one to make sure the voxels are aligned
• HAS 6 DF: 3 sets of translations (X, Y, Z) and 3 sets of rotations (X, Y, Z)

Question 5

Similarity registration

Answer 5

• has 7 DOF: translation, rotation and a single global scaling

Question 6

Affine registration

(and the affine matrix)

Answer 6

• has 12 DF: 3 sets of translations, 3 sets of rotations, 3 sets of scaling and 3 sets of shearing
• the affine matrix describes how the coordinates from the original (non-corrected) image relate to the corrected image
• X, y, z (in the affine matrix) = the translation values in x, y and z directions, which are multiplied by the current coordinates
• We try to look for a cost function that assesses similarity between the image and the target to find rotations and translations that minimize the amount of changes we have to apply to the un-corrected image

Question 7

Warping vs. Shearing

Answer 7

image warping: an image warping is simply a
mapping from the pixels in one
image to pixels in another

image shearing: stretching the image in 3 directions

Overall, non-linear registration operations allow for local transformations (i.e., some voxels might be transformed “more” than others).

Question 8

Cost functions (in the context of motion correction)

Answer 8

assesses similarity between the image and the target to find the best alignement for the minimum cost (least amount of transformations possible)

Question 9

Co-registration

Answer 9

• Process of overlaying an anatomical scan over the functional scan
• PROS: better visualization of results AND it simplifies the later transformation of the fMRI images to a standard coordinate system
• IMPORTANT: it differs from motion correction, which is the process of estimating and correcting for the head motion of the subject during the acquisition of a series of fMRI image

Motion correction happens BEFORE co-registration

Question 10

Issue with slice time correction (STC)

Answer 10

STC is actually quite controversial. Some believe it improves sensitivity of analyses, but others have shown that STC worsens motion-induced noise (by propagating noise-related signal through slices). It seems generally agreed upon that for relatively fast TRs (<2000 ms.), STC does not improve sensitivity of analyses.

Question 11

Normalization (and the associated pros/cons)

Answer 11

• All brains differ in anatomy (e.g., variation in the shape)
• Normalization allows one to stretch, squeeze (using affine registration, 12 DOF) and warp each brain so that it is the same as some standard brain (from a template)
• we warp the co-registered scan into a template space (using a 12 DOF affine + warping, hence non-linear registration, allowing for local - and not global - voxel adjustement)
• PROS: Consistent, Allows to compare subjects, Can be compared across studies, Allows Averaging
• CONS: Reduces spatial resolution, Introduces potential errors

Question 12

Different atlases (Talairach, MNI)

Answer 12

Talairach space:
* Based on a cadaver of 60-year-old woman
* Based on a single hemisphere
* Origin is set in the Anterior Commissure
* Oriented so that a line joining the AC and the PC is horizontal

MNI space:
* Combo of many MRI scans of right-handed controls
* More representative
* We do not have to use the MNI template necessarily, but we almost always report our results in the MNI coordinate space

Question 13

Different normalization methods

Answer 13

• Landmark based method: align anatomical features (landmarks) in different brains
• Volume-based registration (the one we have described so far): linear (e.g., affine) and non-linear transformations (e.g., warping)
• Computational anatomy: diffeomorphic transformations
• Surface-based methods: work on cortical surfaces (e.g., blow-up the brain)

Question 14

Spatial smoothing (and the associated pros/cons)

Answer 14

• Spatial smoothing is a type of low pass filtering, namely, we want to get rid of the high frequencies in the normalized scan
• therefore, we convolve the normalized structural scan with gaussian filter (the width of the gaussian filter si given by the FWHM value)
• by smoothing, we can increase the signal-to-noise ratio & validate distributional assumptions & remove artifacts
• PROS: May overcome limitations by blurring residual anatomical differences; Can increase SNR > we keep the same signal but decrease the noise; May increase the validity of statistical analysis; may improve spatial normalization
• CONS: Reduce the spatial resolution

Question 15

Concept of FWHM

Answer 15

• The size of the gaussian kernel in spatial smoothing is determined by the full width at half maximum height (FWHM), which measures the width of the kernel at 50% of its peak value
• The FWHM is directly proportional to the standard deviation (sigma) of the gaussian kernel

Question 16

Matched filter theorem

Answer 16

• The matched filter theorem states that the optimal filter for maximizing the signal-to-noise ratio (SNR) in the presence of additive noise is the one that matches the shape and size of the expected activation.
• This means that the filter should have the same spatial and temporal characteristics as the signal of interest, and produce a peak output when the signal is present in the data. The matched filter theorem is often used to justify the choice of Gaussian smoothing kernels in fMRI preprocessing, as they are assumed to approximate the shape of the hemodynamic response function (HRF) and the spatial extent of the activated regions.
• However, the matched filter theorem also has some limitations and assumptions that may not hold in fMRI, such as the linearity, stationarity, and independence of the signal and noise. Therefore, the matched filter theorem should be applied with caution and not be considered as a universal rule for fMRI data analysis.

Issues:
* The likelihood that we get our smoothing kernel matched to the signal extent is very unlikely
* The same amount of smoothing is applied throughout the whole image

Soluitons: adaptive smoothing

Question 17

White vs. colored noise

Answer 17

WN: All frequencies have similar power – all frequencies are equally present ; CN: in coloured noise, some frequencies are stronger than others

Question 18

Drift

Answer 18

a term that refers to the unwanted low-frequency trend or variation in the fMRI signal over time. Drift can be caused by various factors, such as physiological artifacts, head motion, scanner instability, neuronal oscillations, and vasomotion. Drift can affect the accuracy and reliability of fMRI measurements, and should be corrected or removed before further analysis.

Question 19

Discrete cosine basis set

Answer 19

used in fMRI data preprocessing. It’s a type of high-pass filter. For any given high-pass cutoff (in hertz), the DCT will yield a set of cosine regressors that is sufficient to filter out any frequency slower than our cutoff.

Question 20

Running line smoothers

Answer 20

result of convolving a gaussian “kernel” with the signal (taking the element-wise product and summing the values) across time; this “line” is then subtracted from the actual signal to perform high-pass filtering. Importantly, the same type of process should be applied to the predicotr of the signal.

Question 21

Sensible HP-filter cutoffs

Answer 21

• In blocked designs: Longer (but not less) than 1 task cycle (1/time_in_seconds) ;
• In event related designs: larger than ~ 66 seconds

e.g., task is 10s, (1/10, 0.1 Hz), then we cut off at 0.1 Hz

e.g., task is 20s, (1/20, 0.05 Hz), then we cut off at 0.05 Hz

e.g., task is 40s, (1/40, 0.025 Hz), then we cut off at 0.025 Hz

> > the more we increase the task length, the less we remove > risk of leaving the drift in our data, but also we do not risk of removing relevant signal (?)

Question 22

Low-pass filters (and why you shouldn’t use them)

Answer 22

We should try to avoid low-pass filters because we are more likely to remove important, task-related data. This is assuming we are talking about a task-related fMRI data collection. If we are talking about resting state, then it’s different.

Question 23

STC (slice-time correction)

Answer 23

STC is a temporal resampling technique that corrects for the fact that, in (most) BOLD-MRI scan sequences, volumes are acquired slice by slice. This means that different slices have different acquisition times within a TR, which can introduce temporal misalignment and phase shifts in the fMRI signal. Slice time correction aims to align all slices to a reference time-point, usually the middle or the first slice, by shifting the time series of each slice using interpolation. Slice time correction has been deemed relevant in the past because it was thought to improve the temporal accuracy and statistical power of fMRI analyses, especially for event-related designs and functional connectivity.

Question 24

Prewhitening in relation to Gauss Markov assumptions (why do we do it?)

Answer 24

fMRI time series are often affected by various sources of noise, such as physiological fluctuations, scanner drift, motion artifacts, or the design of the experiment. These noise sources can introduce autocorrelation in the residuals, which means that the errors in the fMRI time series are not independent but depend on the previous errors. This violates the assumptions of ordinary least squares (OLS) regression.

Fortunately, some methods have been developed by statisticians that transform the data such that the OLS assumptions hold again. One such technique is called PREWHITENING.

Prewhitening uses an estimate of the error covariance matrix — usually denoted by V— to account for possible unequal variance and/or autocovariance of the residuals.

Question 25

Formula for (covariance of) parameters when prewhitening (i.e., generalized least squares)

Answer 25

• Formula for parameter estimate: (X’ * V^(-1) * X)^(-1) * X’ * V^(-1) * y
• Formula for covariance of the parameters: sigma^2 * (X’ * V^(-1) * X)

Question 26

Empirical methods to estimating V
(conceptually)

Answer 26

• SPM: global covariance estimate using a structured correlation estimate, namely the scaled AR1 with correlation 0.2 plus white noise
• FSL: local covariance estimate, which means that it estimates V for each voxel separately. However, to avoid overfitting and noise, FSL also applies spatial smoothing to the AR parameters, which means that it borrows information from neighbouring voxels to stabilize the estimation. FSL also uses a Tukey taper, which is a technique that down-weights the correlation estimates at high lags, because they are less reliable and more noisy

Question 27

Examples of nuisance variables

Answer 27

1. Drift
2. Spikes
3. Physiological noise
4. Head motion

Question 28

Spikes/gradient artifacts (“outliers”) and how to control for them

Answer 28

• Spikes are sudden large intensity increases in the signal across the entire brain that likely reflect scanner instabilities
• use RMSSD to identify them
• include nuisance predictor for each spike, in which the predictor contains zeros at timepoints without the spike and 1 at the timepoint with a spike.

Question 29

Physiological noise (cardiac / respiration)

Answer 29

• we need a low TR (high temporal resolution) to model it
• give rise to periodic noise, often aliased in the task
• sampling rate must be at least twice as big as the frequency of the curve we seek to model
• if left unmodelled, can cause temporal autocorrelation

Question 30

Aliasing

Answer 30

an artifact that occurs in fMRI when the field of view (FOV) is smaller than the body part being imaged. This causes the signals from the part of the body that lies outside the FOV to be projected onto the opposite side of the image, creating a false overlap.

Question 31

Spin-history artifacts

Answer 31

Spin history artifacts are distortions in the fMRI signal intensity that result from changes in the object position during the scan. They occur because the object’s tissue magnetization is not in a steady state, but depends on the previous RF pulses and slice profiles. The disruption of the steady state will propagate to the next few acquired volumes until a new steady state is reached. These artifacts can be reduced by minimizing head motion and using smaller gaps between slices

think of waves after a stone is thrown in the water

Question 32

Head-movement nuisance regression / “scrubbing”

Answer 32

We either model head movement (by adding the 6 realignment parameters - rotation and translation in 3 directions - to the design-matrix) or we drop scans with high movement estimates

Question 33

Task-correlated movement (important!)

Answer 33

Task-correlated movement is a type of artifact that can affect the results of functional magnetic resonance imaging (fMRI) studies. It occurs when the subject’s head or facial movements are synchronized with the task design, such as moving the eyes, mouth, or fingers during certain conditions. This can create false activations in the brain regions that are sensitive to motion, or mask the true activations in other regions. Task-correlated movement can also interfere with the performance of multi-voxel classifiers, which are methods that use patterns of brain activity to decode the cognitive state of the subject. To avoid or reduce task-correlated movement artifacts, researchers can use various strategies, such as:
* Using head restraints or bite-bars to minimize head motion during the scan.
* Using motion correction algorithms to align the brain volumes to a reference volume and remove the effects of motion.
* Using statistical methods to model and remove the motion-related signals from the fMRI data.
* Using experimental designs that minimize the need for movements or randomize the order of the task conditions.
* Using feedback or instructions to encourage the subject to stay still and avoid unnecessary movements