Additional Notes on fMRI

TR and TR in MRI

When deciding a suitable MRI sequence, you have to decide the choice between short or long repetition time (TR) and echo time (TE). Different combinations of these two values produce different types of MR images. See below. To recap, the T2* image has transverse magnetization which decays much faster than would be predicted by natural atomic and molecular mechanisms. In practice, T2* can be considered as an effective/observed T2 image, whereas the T2 image is considered the natural or true T2 (i.e. T2* is always less than or equal to T2). The T2* images result principally from inhomogeneities in the main magnetic field.

Statistical power in MRI

Statistical power is defined as the probability of rejecting the null hypothesis when it is false. In most cases, it is dependent on three main factors: (1) the desired effect size; (2) alpha value or Type I error; (3) the sample size tested. Of these 3 values, the sample size is the one that is within the control of the experimenter (Desmond & Glover, 2002). Unlike in usual behavioural tasks, fMRI data of each voxel is typically normalized as percent signal % change between the Task and Rest conditions. Variability in the fMRI data consists of the within-scan and between-scan variability. Increasing scan time and the number of subjects will potentially reduce these two kinds of variation. 

The concept of statistical power in fMRI data is complex because it involves different expected activation patterns, analysis pipelines, and also scanning parameters. Loosely, some rule of thumb to obtain a decent signal, alpha = 0.05 and 80% power. For example:

a)  Total N = 12 - 20 subjects per condition.

b)  Scan time per subject = 10 - 15 min.

c)  Scan volume (time points) = 400 - 500.

Non-parametric Approach to MRI

Like the usual inferential statistics, we want to make a conclusion in our neuroimaging data that apply to the population. As the name implies, non-parametric tests do not depend on the nature of the distribution of the fMRI data (e.g. normality assumption of the residual component). Through resampling, we construct an empirical distribution from the data itself that can accurately estimate the probability of a particular observance. This is the fundamental idea of non-parametric statistics. Some of these approaches have been clearly discussed in Nichols & Holmes, 2001. The use of non-parametric statistics if the data is not normal has been discussed briefly in this blog previously. A more thorough review article that includes the history and logic behind non-parametric tests is by Winkler A, et al. (2014) in the NeuroImage journal.

Basic Concepts
To see why this makes sense, the task-based block design paradigm will be used, i.e. a subject performs a task in one block and rest in the other. If a specific location of the brain is used during tasks, we should expect a task-related activation during the task, but not during the rest period. Here, we reshuffle or scramble the data across TRs. If a particular voxel is involved in the task, we should not expect any strong correlation between the predicted BOLD response and the actual activation because the 'reshuffled data' is just random noise. Reshuffling does not change the mean and variance of the dataset, that is, we don't tamper with the data.

In analyzing task-based fMRI data, for example, you form a design matrix according to your behavioural task and conduct a GLM (using FEAT, let say) to obtain parametric estimates or PEs of the corresponding regressors. To correct for the familywise error, the multiple comparison problem across voxels, we then use GRF theory by defining cluster-forming threshold (Z = 2.30 in FEAT). According to Echlund et al, GRF performance in controlling Type-I Error is poor. In fact, it is recommended to use non-parametric tests such as permutation testing to control for Type-I Error.

Using randomise on my dataset
For my iMac machine purchased in 2011 with Intel i5 Quad-core, 3.1 GHz, it takes me 8-9 minutes to analyze a decent task-based, 100 x 100 x 63 x 250, preprocessed 4D NIFTI file using 1000x permutation. With FEAT-glm using the same GLM design matrix, it takes me 2-3 minutes.

Registration with ANTs

When I first embarked in the fMRI project, I didn't learn about other software package. Recently, I managed to compare the performance of T1 -> MNI normalization done with 3 different popular software package: ANTs, FSL, and AFNI. The performance was measured using "similarity metric" that I took from Nipype, a python-based neuroimaging package. My data came from MRI scans of stroke patients, as part of my project at the Jewish General Hospital. As a reference image, I took the MNI-152 with 1mm resolution. The left panel below shows what happened when I used MNI-152 2mm template instead. In both FSL_1 and FSL_2, I used the 2 mm template to obtain the non-linear transformation matrix. However, in FSL_1, I explicitly specified the 1mm template when I applied the non-linear warping (with applywarp) process.

There are two main types of cost function: intra-modal (least squares and normalised correlation) and inter-modal (correlation ratio and mutual information-based options).


The left panel shows the registration accuracy of the subject's T1 image to the standard MNI 1mm template of 3 different software packages. The right panel also shows what happened when the MNI 2mm template was used instead.

As a side note, the MNI template has been widely used in various neuroimaging software packages. It was historically produced in a report for the International Consortium for Brain Mapping (ICBM) back in 2001. The atlas was based on linear mapping of 152 healthy adults ranging from 18-44 years old, mostly white people. It has gone through 2 major revisions lately to increase the accuracy: the first one was in 2006 that made use of a non-linear mapping, they call this the MNI-152 6th generation. FSL uses this template. Another revision was the most recent one in 2009.

Recent development in functional MRI

More recent contributions in functional MRI have been based on graph theory (Bullmore & Sporns, 2009), which underlines the importance of seeing the brain as complex networks. This analysis of MRI data has been widely used in both healthy and dysfunctional brain networks. 

It is important for understanding normal brain development and functions, the networks involved in affect regulation, motor control and execution, and learning and memory (e.g. motor learning study, see Sami and Miall, 2013). In addition, the graph theory has been beneficial to understand the implication resulting from e.g. Alzheimer's disease, schizophrenia, and stroke. For example, Buckner et al. found a correlation between the site of the targeted regions and the location of major hubs in Alzheimer’s disease (2009). He et al. (2007) demonstrated how the frontoparietal network is implicated in the spatial neglect of stroke patients.

In order to establish a brain network using modern graph theory, there are a number of steps to be taken: 

- define the network nodes (usually from resting-state fMRI), 

- estimate association/correlation between nodes, 

- compile pairwise associations between nodes and generate an association matrix, 

- and, calculate the network characteristics. 

Yet, despite this emerging literature, many researchers using graph theoretical approaches for fMRI data have not closely examined whether their data violate the assumptions of graph-theory. One important assumption that has to be met is the assumption of stationarity. Time series or time-varying data is said to fulfill the stationarity principle if the statistical properties of a time series are time-invariant, meaning, the mean and variance do not change across time. Generally speaking, stationarity implies that the statistic parameter of interest does not change over time. Such assumption is also essential for analyzing fMRI time series in the frequency domain, as the Fourier transform is suitable for stationarity. For more than a decade, most scientists have always assumed that fMRI signals are stationary, however, one may refer to some recent works that warrant doing fMRI analyses with caution (e.g. Muhei-aldin et al., 2014; Ou et al, 2014).