fMRI processing

The main goal of fMRI pre-processing is to minimise the impact of physical and physiological artefacts and to validate model assumptions of parametric statistics used for fMRI analysis (Lindquist, 2008), which will be discussed in the next paragraph (3.3.2). This paragraph serves as a brief overview of some predominant pre-processing steps that are relevant for the univariate analyses of fMRI data that will be presented in this thesis.

Brain volumes are acquired in slices, often with an inter slice time of 70 milliseconds or more. In contrast, statistical analyses assume that data in all voxels was acquired simultaneously. With a repetition time (TR) of 2 seconds for instance, the true temporal difference between slices may be, however, up to two seconds. Moreover, within this time the participant may have moved their head. fMRI analyses assume that each data point in a time series from a given voxel only consists of data from a specific voxel. Hence, two important early pre-processing steps in fMRI data analysis are slice timing correction and head motion correction (Ashby, 2011; Lindquist, 2008). During slice timing correction, time courses are shifted with respect to an indicator. Head motion represents one main source for variation in fMRI time series

(Lindquist, 2008), which varies between contextual factors such as the task and certain clinical populations such as stroke (Seto et al., 2001), or age groups (Yuan et al., 2009). When uncorrected, head motion violates model assumptions because signal from neighbouring voxels “contaminates” the signal from a specific voxel of interest (Lindquist, 2008). At the beginning of motion correction procedures, a refence image is determined to which other volumes are registered and corrected, e.g. based on contrast differences at edges of the image. This reference image may be the first volume of a scan, such that all following volumes and scans within a scan session are aligned to this image (“intrasession alignment”). Different approaches exist to solve this optimisation problem, which vary between fMRI analysis software (Oakes et al., 2005) and can be characterised by the interpolation method (e.g. Fourier or trilinear), the optimisation technique (e.g. iterative gradient descent), and the cost function used to avoid overfitting and control optimisation speed (e.g. weighted lest squares). One predominant technique of motion correction is a rigid body transformation, which involves 3 translation variables and 3 rotation variables (along the x, y, and z axis, respectively). During the process, a cost function is minimised to achieve optimal parameter estimates for displacement along these 6 dimensions between a given image and a reference image. Transformation parameters can further be used as nuisance regressors in subsequent statistical analyses to account for spurious variations in the BOLD signal that have occurred due to head motion. Once motion correction is completed, estimated displacement parameters are used to interpolate a new image which is assumed/treated as “motion free” for the parametric analysis (Lindquist, 2008).

The spatial resolution of BOLD fMRI is limited by the architecture of the brain’s vascular system. Hence, compared to a structural anatomical acquired at the same field strength, the BOLD image will feature less spatial acuity. However, spatial acuity in the evaluation of functional images can be increased by co-registering functional to structural data. Specifically, the co-registration of functional and anatomical data allows to map functional activity onto a high-resolution anatomical image. Moreover, a transformation to a standard space such as Talairach (Talairach and Tournoux, 1988) or MNI (Evans et al., 1992) allows comparing coordinates across participants and studies. Transformation to a standard space hence makes it possible to pool data across participants and perform group analyses, which greatly improves statistical power (Desmond and Glover, 2002). However, in contrast to image alignment within one acquisition mode (e.g. functional BOLD imaging), co-registration across acquisition modes (e.g. functional BOLD imaging and structural T1 weighted imaging) entails a higher degree of interindividual anatomical variations, requiring non-linear transformations (for

instance trilinear or sinc interpolation) as opposed to mere rigid-body transformations (Ashby, 2011; Lindquist, 2008).

When working with group data and mass univariate statistics (Chapter 3.3.2), spatial smoothing is another commonly practiced pre-processing step. Spatial smoothing is a form of data filtering such that the intensity values of voxels become more similar to neighbouring voxels. Practically, smoothing kernel is a function that is convolved with image, yielding voxel intensities that represent a weighted average of neighbouring voxel intensities (Lindquist, 2008). Smoothing reduces between subject variations in anatomical and functional variations, which may interfere with the co-registration process. Spatial smoothing can increase the signal- to-noise ratio because it reduces the effect of random voxel fluctuations due to noise. Moreover, smoothing reduces the effect of outliers on the data and thereby contributes to a normal distribution of residuals (Ashby, 2011). This latter aspect increases the validity of inferential parametric statistical tests (such as a t-test) that are commonly applied in imaging data. The size of smoothing kernels (measured in mm) is dependent on factors such as regions of interest as well as the task at hand (Ashby, 2011). One disadvantage of spatial smoothing, however, is that the spatial resolution is compromised. It may hence reduce the power for other sets of statistical techniques such as multivariate pattern analysis (Hendriks et al., 2017). Taken together, the application of smoothing kernels should be informed by the research question.

3.3.2 fMRI analysis

General Liner Models (GLMs) represent the predominant statistical approach in analysing univariate neuroimaging data (Ashby, 2011). GLMs are statistical models that can be solved with ordinary least square methods. In principle, GLMs as used in most block design fMRI experiments attempt to model a measured time series (Y) of every voxel using a given set of predictors and an assumed shape of the hemodynamic response function (HRF) that is convolved with (and hence scaled by) predictor variables. Predictors may represent events, for instance the onset and offset of a task (“box-car” function”), or confounding variables such as head motion parameters as well as other factors that may impact the BOLD signal. If available, physiological signals such as respiration or end-tidal carbon dioxide (PET CO2) can for instance

be measured and included as predictor variables once it has been pre-processed accordingly (Murphy et al., 2013). All predictors are entered into a matrix (X), for which the number of

predictors determines the number of columns, and the number of time points determines the number of rows:

Eq. (3.1): Y = XB + e,

It is hence another way to represent a multiple linear regression model in the form of

Eq. (3.2): Y = β0 + X1β1 … Xnβn + ε

, β0 isthe estimated constant (baseline), the numerated betas correspond to the estimated beta

regression weights of the entered predictors, and ε represents the residual error. Predictors are entered into the GLM and regression weights (i.e. βn) are estimated using a closed form

ordinary least square approximation. Through rearrangement of the equation, it can be solved with ordinary least square methods (Friston et al., 1994). One main assumption that parametric methods make is that residuals (errors) are normally distributed. However, due to the nature of the BOLD response, which is related to cerebral blood flow and other physiological noise such as heart rate and respiration but also other factors, periodic fluctuations in the BOLD signal that have not been modelled in the GLM result in autocorrelated residuals. One way to tackle temporal autocorrelation is by estimating the temporal dependencies, readjust the time course and re-iterate the model estimation (Bullmore et al., 1996). In approaches that study the representational geometry of functional imaging data (e.g. representational similarly analysis), one can also normalise for spatial dependencies using spatial “pre-whitening” (Ejaz et al., 2015). Lastly, multivariate techniques, so called model-free techniques such as independent component analysis (ICA), represent an alternative to model-based correction procedures. ICA allows dissociating the BOLD signal into additive subcomponents (Beckmann and Smith, 2004) such that signal components related to noise can be identified and discarded in a semi- automatised way.

With regards to statistical analysis of model-based mass univariate statistics fMRI data, appropriate procedures for multiple comparisons need to be considered to allow valid inferences and minimise false positives (see Chapter 3.4.1.3 for more details). Specifically, contrasting of beta weights between conditions (e.g. in form of a t-test) is performed on a voxel- by-voxel basis and hence requires appropriate correction methods. Frequentist statistics assume that no effect is present, i.e. that the null hypothesis is true (Chapter 3.4.1.1). The null

hypothesis can only be rejected if the data is more surprising than it could be expected with a certain probability if there was no effect, which is commonly called a significant effect. This probability is represented as the alpha level, an error rate that is considered tolerable and that is usually defined as 5% (i.e. p < 0.05) in the life sciences. However, this error rate is set per test and as the number of tests increase, the overall error rate increases proportionally (see Chapter 3.4.1.3). To maintain the validity of statistical inferences, multiple comparison correction is required, in particular for fMRI data which comprises many thousand voxels and hence often many thousand (univariate) tests. Four main approaches of multiple testing correction shall be shortly reviewed here (Ashby, 2011): 1) family-wise-error-rate (FWER) correction aims to retain the α-level at 5% across experiments and represents one of the most conservative approaches. 2) False discovery rate (FDR) based approaches aim to limit the number of false positives per experiment. It thus aims to control the α-level per experiment. 3) Another set of techniques are cluster wise inference approaches, which instead of correcting at voxel level, estimate the minimum number of adjacent voxels one would expect to find under the null hypothesis. Cluster extent-based correction techniques use information about the spatial smoothness of the data and require users to set two thresholds: a cluster defined threshold (CDT) that retains only voxels whose p-value is below it (e.g. CDT p < 0.001), and a cluster-level extent threshold (e.g. p < 0.05), which represents the error rate of falsely retained clusters (assuming that an appropriate CDT was applied, and all other model assumptions are met). Parametric cluster wise inference methods are widely used to correct for multiple testing and reliable in controlling for the type-I error rate when appropriate thresholds are chosen (Eklund et al., 2016). 4) Another set of techniques are non-parametric permutation tests. In contrast to parametric approaches that assume the distribution of the statistic of interest under the null hypothesis, non-parametric permutation based procedures can find the statistic under the null hypothesis by permuting the labels and reiterating analyses (Smith and Nichols, 2009; Winkler et al., 2014). Both techniques have been shown to reliably control FWER around the nominal 5% level, although permutation tests show slightly better performance (Eklund et al., 2016), and cluster inference based methods can control reliably for FDR nominal 5% level (Kessler et al., 2017). One advantage of cluster wise inference over permutation based methods is their higher sensitivity in detecting effects (Woo et al., 2014). This sensitivity may come at the cost of inflated false positives if too liberal CDTs are chosen (Eklund et al., 2016). However, if used with appropriate primary thresholds (CDT p < 0.001), they represent a reliable and economic way to control for multiple testing and hence a justifiable trade-off

between statistical rigorousness and sensitivity. For this reason, they have been the primary method that was applied to inferential whole brain analyses reported in this thesis.

3.3.3 Real-time fMRI setup and processing

Most real-time fMRI setups consist of three main elements that require computing infrastructure: an acquisition element, a real-time analysis and processing element, and a feedback presentation element (Figure 3.1). In many current setups, these three elements are processed by at least two dedicated computing units. The real time acquisition assures timely export of data and performs real-time image reconstruction. Reconstructed images are transmitted (often via a Transmission Control Protocol/Internet Protocol [TCP/IP] network connection) to the analysis element, a computer system that is equipped with fMRI analysis software capable of performing real-time analyses. The experiments presented in this thesis were exclusively analysed with the commercial software package Turbo-BrainVoyager (Brain innovation, Maastricht, The Netherlands). However, it should be noted that freely available alternatives have been more recently developed as well (Koush et al., 2017; Sato et al., 2013). Similar to conventional (offline) fMRI analyses, real-time fMRI analyses include pre- processing steps. In particular realignment to reference volumes to correct for head motion is critical to ensure that training can be performed on selected voxels. Also, spatial smoothing is usually performed to increase the signal to noise ratio. When feedback is provided based on model estimates obtained from an incremental GLM, head motion regressors can be included to account for spurious correlations caused by the head motion. Also linear drift term can be included to account for scanner drifts, e.g. due to thermic changes and instabilities (Lindquist, 2008). These result in relatively slow confounding changes of voxels intensities which can be modelled within the incremental GLM. Given that real-time analyses are usually constrained to regions of interest (but also limited with regards to the temporal signal to noise ratio), real- time fMRI experiments usually do not control for multiple comparison correction during online analyses.

Figure 3.1 Schematic real-time neurofeedback setup. Modified from (Arns et al., 2017).

3.4 Statistical approaches to hypothesis testing

Statistics play a central role in the interpretation and presentation of data (Chapter 1.1). In this thesis statistical approaches more recently introduced to neuroscience will be applied, including frequentist equivalence tests and Bayesian statistics. Hence the rationale of classical frequentist hypothesis testing, potential pitfalls, and basics of Bayesian hypothesis testing will be shortly reviewed. The goal of this section is to provide the reader with an intuition of these techniques and refer to relevant literature for a more detailed discussion.