# Are variations in Functional Connectivity strength driven by variations in spatial topography?

I have argued in the past that fMRI studies are limited by ‘oversimplified assumptions made during pre-processing’  That, by modelling all human brains from the same broad topological structure (enforcing a constant number of functionally specialised regions, organised in a consistent pattern across all brains) we are not capturing true inter-subject variability in cortical organisation. This limits our sensitivity to detect the subtle changes in brain structure that underpin complex patterns of behaviour, cognition and neurological disease.

Evidence is mounting in support of this claim. Increasing numbers of brain parcellation studies are proposing that, in fact, patterns of functional organisation vary across different brains (Glasser et al. 2016, Wang et al. 2015, Gordon et al. 2017, Swaroop Guntupalli et al. 2017). And, in a new pre-print on Biorxiv.org, Bijsterbosch et al. (***DISCLAIMER***  I am a coauthor on this paper) go further to suggest that such discrepancies in spatial organisation may in fact be driving the variations in connectivity strength that have been observed across a broad range of functional network studies.

Specifically, the paper shows that canonical correlation analysis (CCA), applied to spatial maps (reflecting patterns of functional organisation, Fig. 1) is able to predict variability across demographic variables (such as IQ, gender, and personal wellbeing) at least as well as CCA applied to functional connectivity networks. And further, simulations of network variability are used to show, that what in the past was assumed to be changes in functional connectivity strength,  may instead be being driven by these spatial changes.

CCA is a technique that allows questions to be asked about the relationships between two distinct sets of multivariate variables. This makes it a powerful technique for analysis of HCP data, where we have a hugely diverse set of behavioural and demographic variables, complemented by very high dimensional imaging features. Accordingly, it was first used on the HCP data by  Smith et al. 2015, who looked at patterns between HCP demographics and functional connectivity strengths, through first concatenating individual functional networks into long vectors, grouping these across subjects into a matrix, and reducing the dimensionality of the data using PCA.

In this paper, Bijsterbosch et al. repeat the analysis  of Smith et al. 2015, but equally use spatial maps of brain function (Fig 1) to make the comparison, and investigate a range of different techniques for reducing the very high dimensional functional Magnetic Resonance Imaging (fMRI) data into a lower-dimensional configuration of spatial maps and associated time courses. These methods include Independent Component Analysis (ICA), hard brain parcellations (Yeo et al. 2011) and PROFUMO (Harrison et al., 2015). Here, both PROFUMO and ICA seek to identify modes of coherent activity from rfMRI, in other words find regions of the brain with correlated patterns of activity. However, PROFUMO uses a sophisticated variational Bayesian framework to characterise modes both at the group and single subject level, leading to a more thorough characterisation of inter-subject variability.  All data in the study came from the Human Connectome Project, with the majority of the results utilising the S900 release.

The comparisons performed show that the maps of spatial variation perform at least as well as functional connectivity for predicting inter-subject variability of the demographic data (Fig 2). Therefore, Bijsterbosch et al. went further, to investigate what was truly driving the correlations. Using the basic model of PROFUMO:

Where, $D_{s}$ represents the original fMRI data, $P_{s}$ represents subject-specific spatial maps, $A_s$ represents mode time courses and $h_s$, time series amplitudes, they simulated data sets whilst keeping all but one of $P_{s}, A_s$ and $h_s$ constant across all subjects. Simulated datasets were then used to regenerate functional connectivity networks for the range of decomposition methods (ICA, hard parcellation, PROFUMO). The outcome was that the strongest predictions of relationships learnt by CCA was found when spatial maps alone were altered. Note, spatial-only CCA results were marginally weaker than for results obtained from the original data

These results have significant implications for the interpretation of functional network studies, most significantly in patient/control studies where these natural variations in functional organisation (correlated with behaviour and cognition) are not being controlled for.

Examples of the types of spatial variations, that are most significantly impacting the HCP demographic predictions can be seen in Fig 4 (Fig 2 in Bijsterbosch et al., and associated movies ). This suggests variations in the spatial configuration of the default mode, are most impactful to these findings.

It is possible that methods of brain parcellation, more specifically targeted at identifying subject-specific functional topologies (Glasser et al. 2016, Wang et al. 2015, Gordon et al. 2017, Swaroop Guntupalli et al. 2017)), together with efforts to improve the characterisation, and directionality of functional connections, will improve understanding of how fluctuations in functional connectivity strength impact cognition and neurological disease.

Nevertheless, this will require more sensitive techniques for attributing spatial correspondences between subject data sets, either through revised methods for inter-subject registration that relax constraints for spatially-constrained alignment, and/or the discovery of new methods capable of comparing topologically inconsistent functional networks.

Accordingly, (finishing with a shameless plug) those interested on tackling this challenging problem using the power of Deep Learning, or using these tools to link state-of-the-art neuro-developmental data sets with genetics and cognitive outcomes can find PhD opportunities at Kings College London with myself and Professor Julia Schnabel. See the EPSRC CDT,  and MRC DTP programmes for more details. Note, the DTP project catalogue, is available here.