Processing Stages of Functional Magnetic Resonance Imaging (fMRI)
08/02/20 Medical Reference this
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Critically discuss the stages of processing that fMRI data are subjected to, with an
emphasis on efforts made to improve the quality of signal at the varying levels of
analysis
Functional magnetic resonance imaging (fMRI) is a non-invasive method of recording haemodynamic responses in the brain. Neurons consume oxygen and this converts haemoglobin to deoxyhaemoglobin. The part of the signal used in fMRI is sensitive to deoxyhaemoglobin in the blood, and the distortion, caused by it paramagnetic properties, can be measured. This technique is known as BOLD, which stands for blood-oxygen-level-dependent contrast (Ward, 2006).
The aim for fMRI data analysis is to find the correlations between brain activity and the task an individual performs. The BOLD signal is relatively weak, so sources of noise need to be controlled. The data exhibits a complicated temporal and spatial noise structure. fMRI data analysis is a massive data problem; each brain volume consists of around 100,000 voxel measurements; each experiment consists of hundreds of brain volumes; and each experiment may be repeated for multiple subjects to facilitate population inference (Webb-Vargas et al., 2017). The total amount of data that needs to be analysed is large. Hence, a sequence of steps are performed on the images obtained before statistical analysis can take place.
Pre-processing
fMRI data goes through a series of preprocessing steps, which are aimed at removing artifacts and validating certain analysis assumptions. The goals of preprocessing are to minimise data acquisition and effects of artifacts; check statistical assumptions and transform the data so the assumptions are met; and to standardise locations of brain regions across all subjects to achieve validity and sensitivity in group analysis. The preprocessing steps are performed both on the fMRI data and the structural scans that are collected prior to the experiment (Churchill et al., 2011). There are a number of preprocessing steps. The structural images, which are often T1 weighted, are coregistered to the functional data, and warped onto the Montreal Neurological Institute (MNI) brain atlas space (Dohmatob, Varoquaux & Thirion, 2018). The functional data undergoes a little bit of de-noising, slice time correction, and motion correction. Then the normalisation parameters that were derived from the structural images are also applied to the functional images so that they are also aligned to the MNI space. Finally, often times the functional images are smoothed, and then the data is ready to be analysed (Brook, 2014).
Visualisation and artifact removal is the first part of the preprocessing steps and here we use exploratory data techniques to investigate the raw image data and detect possible problems and artifacts. For example, fMRI data can often contain transient spike artifacts, which can slow drift over time. An exploratory technique such as principal component analysis (PCA) can be used to look for spike-related artifacts (Luo & Nichols, 2003). Often, multiple slices of the brain during each repetition time are sampled to construct a brain volume. However, each slice is typically sampled at slightly different time points because we acquire them sequentially. Thus, slice time correction shifts each voxel’s time series so that they all appear to have been sampled simultaneously (Parker, Liu, & Razlighi, 2017).
Furthermore, very small head movements during an experiment can be a major source of error. When researchers analyse the time series associated with a voxel, it is assumed that it depicts the same region of the brain at every time point. However, head motion may make this assumption incorrect. The goal is to find the best possible alignment between an input image and the target image (mean image), and to align them, one of them needs to be transformed (Skup, 2010). This can be corrected using a rigid body transformation; and this involves 6 variable parameters: 3 sets of translations (in the X, Y, and Z direction, and 3 sets of rotations. The goal is to find the set of parameters which minimise some cost function that assesses similarity between the image and the target (Evans & McCoy, 2007). After motion correction is conducted, a structural MRI is collected in the beginning of the session and is registered to the fMRI images in a process known as “coregistration”. So, by coregistering the structural and the functional images together, this allows us to visualise single-subject task activations overlaid on the individual’s anatomical information (Glover, 2011). It also simplifies later transformation of the fMRI images to a standard coordinate system. There are certain key differences between co-registration and motion correction as functional and structural images do not have the same signal intensity in the same areas because they have different contrasts; so they cannot be directly subtracted from each other. Here, an affine transformation with 12 degrees of freedom is used to perform coregistration and motion correction (Crinion, et al., 2007).
Preprocessing is performed both on the fMRI data and the structural scans collected prior to the experiment. All brains are different. The brain size of two subjects can differ in size by up to 30%. There can also be substantial variation in the shapes of the brain. Normalisation allows one to stretch, squeeze, and warp each brain so that it is the same as some standard brain. This is important when we do group analysis because we want to be able to compare different brains with one another and if we are looking at a single voxel, we want to look at the voxel across the entire population of the subjects there are (Glover, 2011).
The pros of normalisation are: spatial locations can be reported and interpreted in a consistent manner; results can be generalised to larger population; results can be compared across studies; and results can be averaged across subjects. The cons are: it reduces spatial resolution, and introduces potential errors. There are a number of normalisation methods, including: volume-based registration where a linear (e.g. affine) and nonlinear transformations are used (Price, Crinion, & Friston, 2006).
The next thing after normalisation is spatial filtering. In fMRI it is common to spatially smooth the acquired data prior to statistical analysis. This can increase the signal-to-noise ratio, but can also validate distributional assumptions to remove artifacts. Typically, the amount of smoothing is chosen prior to the experiment and is independent of the data. Furthermore, the same amount of smoothing is applied throughout the whole image. The pros of spatial filtering are: it may overcome limitations in the normalisation by blurring any residual anatomical differences; could increase the signal-to-noise ratio; may increase the validity of the statistical analysis; required for Gaussian random fields, which is often used in multiple comparisons. The cons are the the image resolution is reduced (Price, Crinion, & Friston, 2006).
One important consideration one makes when fitting models to fMRI data is the haemodynamic delay. BOLD responses are delayed and dispersed relative to neural activity. It peaks at 4-6s post-stimulus and it often does not return to the baseline until 20-30s after the stimulation has ended (Buxton et al., 1998). The aim is to turn assumed neural responses into a predictor in a GLM model; the solution is to assume a linear time invariant (LTI) system. Here the neuronal activity acts as the input or impulse and the haemodynamic response acts as the impulse response function. This gives a single solution for brief neural events or sustained epochs (Sierra, Versluis, Hoogduin, & Duifhuis, 2008).
Regression applied to fMRI:
The typical analysis is called the Mass Univariate Approach, and this is where a separate model is constructed for each voxel; the data at one voxel is the outcome (Y) and the predictors (X) are a series of regressors that are developed based from the tasks or conditions. The mass univariate approach assumes that the voxels are independent and each are its own separate test. A very common fMRI design is the block design, where similar events are grouped or there is sustained stimulation across a period of time. This can be contrasted with an event-related design, where brief events of different types are intermixed (Stephan, Mattout, David, & Friston, 2006).
In mixed effects model, we choose whether to model each effect as “fixed” or “random” in a mixed-effects model. Fixed effects are always the same, from experiment to experiment; levels are not draws from a random variable. An example is sex (M/F), so in that case a fixed effect model is appropriate. Typical random effects are levels randomly sampled, at random, from a population e.g. subjects or words. Variance across the levels of each random effect is included as a source of error in the model, and this allows us to generalise to unobserved levels. If an effect is treated as fixed, error terms in model do not include variability across levels, and thus cannot generalise to unobserved levels e.g. if subjects if fixed, then you cannot generalise to new subjects. Most of the time, a simple kind of “random effects” model is used, where the contrast images from the subjects put in a second-level design matrix (a constant, all values are 1’s), allowing for a one-sample t-test. The advantages of this approach are: easy to do and easy to add participants; optimal if within-person precisions are equal; and fairly robust to violations in terms of false positives, but we can lose sensitivity in some cases. A fixed-effects analysis is usually not conducted as it assumes the only source of error is within-scanner noise, and does not account for between-subjects error Price, Crinion, & Friston, 2006).
General Linear Model
The general linear model (GLM) approach treats the data as a linear combination of model functions (predictors) plus noise (error). The model functions are assumed to have known shapes ( a straight line or a curve), but their amplitudes (slopes) are unknown and need to be estimated. The GLM framework encompasses many of the commonly used techniques in fMRI data analysis (Zhang, Liang, Anderson, Gatewood, Rottenberg, & Strother, 2008).
The structural model for the GLM is:
y = Xβ+ε
Y is the fMRI data, X is the design matrix, β is the model parameters, and ε is the residuals/error. Looking at the model parameters in detail when there is only one predictor (regressor), B1 is the activation parameter estimate (estimated response amplitude). With the same type of design matrix but with an event-related design i.e. two predictors, there are now three model parameters (β_{0}, β_{1}, β_{2}). β_{1} and β_{2} will estimate the amplitude of activation separately (Ashby & Waldschmidt, 2008).
The GLM is typically a two-level hierarchical analysis:
- Within-subject (individual)
- Across-subject (group)
This can be done in stages (1st, 2nd level). The first level deals with individual subjects, and the second level deals with groups of subjects.
First of all, there is a design specification stage, where we build our model. The goal is to build a design matrix. The second stage is the estimation stage, where we combine the model with the actual image data. We estimate slope activation for every subject. Then finally, we can do contrasts across different conditions within each person, and we can estimate contrast images for every person. These are then taken to the second level for group analysis. Then we are prepared to make anatomical localisation and inference about which areas are activated (Beckmann, Jenkinson & Smith, 2003).
The second level model can be written as:
β = X_{g }β_{g} + η
Here X_{g }is the second level design matrix and β_{g }the vector of second-level parameters. The second level relates the subject specific parameters contained in β to the population parameters β_{g. }It assumes that the first level parameters are randomly sampled from a population of possible regression parameters. This assumption allows us to generalise the results to a whole population (Price, Crinion, & Friston, 2006).
Statistical techniques such as Maximum Likelihood Estimation (MLE) and Restricted Maximum Likelihood Estimation (REML) define the loss function that should be minimised in order to find the parameters of interest. MLE maximises the likelihood of the data but produces biased estimates of the variance components. REML maximises the likelihood of the residuals and produces unbiased estimates of the variance components. Algorithms define the manner in which the chosen loss function is minimised (Speed, 2014).
When using temporal basis steps at the first level, it can be difficult to summarise the response with a single number, making group inference difficult. Here we can perform group analysis using: the “main” basis function, all basis functions, or re-parametrised fitted responses to recreate the HRF and estimate the magnitude, and use this information at the second level (Lindquist, Meng Loh, Atlas & Wager, 2009).
Horn, Dolan, Elliott, Deakin, and Woodruff (2003) used fMRI to examine impulsivity in subjects whilst they performed a Go/NoGo task. The first scan was used as the reference to realign the rest of the other scans. Realigned scans were normalised by transforming them using MNI templates. Analysis was conducted using the GLM, and normalised images were smoothed using an 8mm FWHM isotropic Gaussian kernel. A random effects model was used. For the first level analysis, mean images for each participant were made representing the subtraction of block A BOLD response from block B BOLD response (NoGo/Go). For the second level analysis, the mean images were combined in one-sample t-tests to determine the significant group effects.
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