## Background

Previous work using fMRI has established that large-scale functional connectivity networks in the human brain display graph theoretical properties such as the combination of a short characteristic path length and high clustering coefficient (small-world topology) as well as high betweenness centrality indicating the presence of network hubs (Basset & Bullmore, 2006; van den Heuvel & Sporns, 2013). These properties have been identified initially in slowly fluctuating resting state networks but are increasingly applied to task-based connectivity data. In contrast to resting state data, the analysis of task-based fMRI data commonly presupposes control over the stimulus in order to test hypotheses about the observed effects of an experimental manipulation. The results obtained from such experiments suffer from restricted ecological validity and it is questionable to what degree their conclusions can be generalized.

Our contribution to the *studyforrest* challenge is motivated by the idea that graph
theoretical properties are able to 'replace' control over the stimulus as the
set of a priori assumptions necessary for the analysis of task-based functional
connectivity. Instead of searching for functional networks related to certain
stimulus events and measuring their graph theoretical properties, we aim to
find networks that exhibit certain graph theoretical properties and to compare
their topology to known activity patterns related to cognitive processes
presumably involved in the task.

### Hypotheses

The stimulus used in the creation of the *studyforrest* data is an audio-only
version of the movie 'Forrest Gump'. We therefore expect to find activity
patterns in superior and middle temporal gyri, inferior frontal gyrus, and
medial temporal lobe related to auditory perception, spoken language
processing, and memory.

## Methods

From the available T2* images, we used motion and distortion corrected raw BOLD images that have been linearly aligned to the group template image. Using fslmaths we created a binary gray matter mask using the template (templateSpace_avg152T1_gray.nii.gz) and masked each individual T2* image in template space to restrict the search space for network nodes to the cortical gray matter.

To find networks that periodically increase certain network properties, we used simulated annealing on the power spectrum of temporal graph properties. The basic idea is to randomly generate networks, measure the periodicity of their network property and keep the best network. To generate network nodes, we randomly select 12 gray matter voxels. Using a moving time window, we calculate the connection weights between each pair of nodes as the correlation coefficient of their time series. For each time point in the resulting series of adjacency matrices, we then compute one graph theoretical measure (average shortest path length, average betweenness-centrality, or average clustering coefficient).

In order to find periodically changing networks, we band pass filtered the time series of graph measures and projected it into the frequency domain using a Fast Fourier transform. Next, we counted the number of peaks (defined as zero crossings of the first derivative) and calculated the maximum and the median of the power spectrum. From these we derive a final singular measure, which is higher the more 'peaky' the power spectrum and hence the more periodic the changes in network properties (measure = maximum/[median*peaks]).

To find those networks that cyclically change their network properties, we then compare the new network with the current best network and retained it as the current best if its measure is higher. In order to avoid local maxima, we use the concept of temperature to accept new measures that are lower than the current best measure: If the new measure is lower than the current best measure by max 20%, it replaces the new current best measure with probability p. p is the product of the temperature and the fractional difference between current and current best measure. The temperature decreases with each iteration from an initial value of 1 to a final value of 0.01.

After 5000 iterations for each 15 min T2* block and each participant, we used fslmaths to merge all resulting images into a 4D NIfTI file, binarized and smoothed it with a 3mm Gaussian kernel, and calculated the final average image. Final images were thresholded at 2 standard deviations above the mean, which equates to p < 0.05.

MATLAB Code: FIND_NETWORKS_V3.M

Code was compiled and run on the University of Queensland's Linux cluster. We used the Brain Connectivity Toolbox for calculation of graph properties and the NIfTI toolbox to manipulate image files.

## Results

### Average shortest path length

Average shortest path length in a network is one of two factors (together with clustering coefficient) that determine whether a network shares the small-world property or not.

### Effect of viewing experience

To further investigate our method, we compared the average networks of participants who had previously seen the movie not more than 3 times (blue, n=8) and participants who had seen the movie at least 3 times (red, n=8).

### Average betweenness centrality

### Average clustering coefficient

not finished computing yet!

## Conclusions

Our results show that different networks alter their network properties at separate low frequencies: while the networks related to memory, auditory perception, visual imagery and language peak in their average shortest path length every 65 seconds, the salience network shows a high average betweenness centrality every 45 seconds. Taken together, our results provide evidence for the view that task-related functional brain activity can be analyzed without prior knowledge about the stimulus structure using only periodic graph properties.

## About this work

This article was a submission to the real-life cognition contest by Lars Marstaller (U Queensland), Jeiran Choupan (U Queensland), and Arend Hintze (Michigan State U).

All source code and materials related to this submission are copyright (c) 2014 by Lars Marstaller and are made available under the terms of the MIT license.