Brain structural connectivity predicts brain functional complexity: DTI derived centrality accounts for variance in fractal properties of fMRI signal

The complexity of brain activity has recently been investigated using the Hurst (H) exponent, which describes the extent to which functional magnetic resonance imaging (fMRI) blood oxygen-level dependent (BOLD) activity is self-similar vs. complex. For example, research has demonstrated that fMRI activity is more complex before than after consumption of alcohol (Weber et al., 2014) and during task than resting state (He, 2011). The measurement of H in fMRI is a novel method that requires the investigation of additional factors contributing to complexity. Graph theory metrics of centrality can assess how centrally important to the brain network each region is, based on diffusion tensor imaging (DTI) counts of probabilistic white matter (WM) tracts. DTI derived centrality was hypothesized to account for the complexity of functional activity, based on the supposition that more sources of information to integrate should result in more complex activity. FMRI BOLD complexity as measured by H was associated with five brain region centrality measures: degree, eigenvector, PageRank, current flow betweenness, and current flow closeness centrality. Multiple regression analyses demonstrated that degree centrality was the most robust predictor of complexity, whereby greater centrality was associated with increased complexity (lower H). Regions known to be highly connected, including the thalamus and hippocampus, notably were among the highest in centrality and complexity. This research has led to a greater understanding of the meaning of the novel Hurst exponent approach to assessing brain activity complexity, and implications for future research that employ these measures are discussed. Author Summary Functional magnetic resonance imaging brain activity is used to calculate a measure of complexity, the Hurst exponent, which has been related to complex cognitive states in past research. For example, when engaged in cognitively demanding tasks brain activity is more complex than when no task is given, and brain activity is more complex when sober than when under the influence of alcohol. We investigated whether patterns of connections between regions in the brain may be related to baseline differences in the complexity of fMRI brain activity between different brain regions. Diffusion tensor imaging allowed us to estimate the number of connections between regions of the brain, and Graph theory allowed us to describe these patterns of connections in the brain. We found that the graph theory metric of degree centrality (the number of connections to a region) is able to most robustly predict how complex the brain activity is, suggesting that the Hurst exponent complexity measure is sensitive to integration of information from multiple sources. Our findings represent important progress towards understanding the biological bases of signal complexity in the brain, and exemplifies how structural connectivity centrality can predict brain function complexity.


Author Summary
Functional magnetic resonance imaging brain activity is used to calculate a measure of complexity, the Hurst exponent, which has been related to complex cognitive states in past research. For example, when engaged in cognitively demanding tasks brain activity is more complex than when no task is given, and brain activity is more complex when sober than when under the influence of alcohol. We investigated whether patterns of connections between regions in the brain may be related to baseline differences in the complexity of fMRI brain activity between different brain regions. Diffusion tensor imaging allowed us to estimate the number of connections between regions of the brain, and Graph theory allowed us to describe these patterns of connections in the brain. We found that the graph theory metric of degree centrality (the number of connections to a region) is able to most robustly predict how complex the brain activity is, suggesting that the Hurst exponent complexity measure is sensitive to integration of information from multiple sources. Our findings represent important progress towards understanding the biological bases of signal complexity in the brain, and exemplifies how structural connectivity centrality can predict brain function complexity.
Brain structural connectivity predicts brain functional complexity: DTI derived centrality accounts for variance in fractal properties of fMRI signal

Introduction
Neuroimaging analyses have evolved since the advent of techniques such as functional magnetic resonance imaging (fMRI) to better understand what the blood oxygen level dependent (BOLD) signal implies about the underlying processing in the brain. For example, analyses have improved from a simple average of BOLD level during task vs. rest, to modeling expected activation time course based on an empirically derived hemodynamic response function convolved with the time course of stimuli presentations. Furthermore, resting state fMRI studies have revealed interesting baseline patterns of activation (i.e., resting state networks), and ushered in an age of network science in brain research. With the rise in resting state fMRI research, predicting resting state fMRI functional connectivity from diffusion tensor imaging (DTI) structural connectivity has been an important recent endeavor for researchers, and the use of graph theory analyses of structural networks have been integral to these investigations (e.g., [1,2,3,4,5]). Furthermore, there has been recent interest in predicting task-based fMRI activation from DTI structural connectivity [6]. An important next-step is to explore the extent to which one can predict the complexity in fMRI activation from the underlying DTI structure.
Since early demonstrations of using the Hurst exponent from the toolbox of chaos theory and fractals to analyse fMRI BOLD signal complexity (e.g., [7,8,9]), interest has grown in this novel method for characterizing complexity of fMRI activation. The Hurst exponent has been applied to many domains of research including Alzheimer's disease [10], signal complexity change over the adult lifespan [11], distress related to medical treatment [12], task versus rest states [13], and alcohol-induced intoxication versus non-intoxicated states [14]. Other measures of complexity such as functional variability have also demonstrated meaningful real-world associations (e.g., children develop more complex brain activity with age, see [15]). In the present research we apply network science graph theory metrics of centrality (i.e., how centrally important a particular region is to the network) as a novel way to further explore this important application of fractal analysis for characterising fMRI activation complexity.

Fractal Analysis of FMRI BOLD Signal Complexity
Fractal analysis of time course data measures the self-similarity or autocorrelation of the signal over different scales. High autocorrelation signifies a "long-memory" process that is similar over shorter and longer time scales, whereas low autocorrelation signifies a "shortmemory" process that varies between shorter and longer time scales. Complexity can be used as a descriptive analogous concept relating to these measures, whereby high autocorrelation (longmemory process) is less complex than low autocorrelation (short-memory process). The Hurst exponent (H) is one method of measuring signal complexity with fractal analysis, and describes the extent to which time course data such as fMRI BOLD signal activity is self-similar (H closer to 1) vs. complex (H closer to 0.5).
The complexity of brain activity has recently been investigated using H. Previous research has demonstrated that fMRI activity is more complex before consumption of alcohol than after consumption of alcohol [14] and more complex during task than resting state [13].
Aging has been associated with a reorganization of complexity, with left parietal and frontal regions losing complexity with age, while increases in complexity with age were observed in the insula, limbic system, and temporal lobe [11]. Alzheimer's disease has been associated with lower complexity than healthy controls in regions of the brain including medial and lateral temporal cortex, dorsal cingulate cortex, premotor cortex, left precentral gyrus, and left postcentral gyrus [10]. The measurement of H in resting state and task fMRI is a novel method that requires the investigation of additional factors contributing to BOLD signal complexity. One possible factor to be investigated is the connective structure of the brain network, which should play a vital role in determining the intrinsic patterns of coactivation of brain regions.

Graph Theory Analysis of Brain Network Centrality
Graph theory analyses of networks such as the diffusion tensor imaging (DTI) structural connectivity network of the brain allow for assessment of how centrally important to the network a particular region is, via calculation of that region's centrality. The most basic example of centrality is degree centrality, which is the count of connections between all other regions in the network to the region of interest. Other methods of calculating centrality represent more specific features of how centrally important to the network that regions is, such as weighting connections to the region based on how connected each other region is (eigenvector centrality; [16]), a method conceptually similar to eigenvector centrality that adjusts for the biased effect of largely connected regions on regions with low connections (PageRank centrality; [17]), counting the number of shortest paths between two regions in the network that pass through the region of interest (betweenness centrality; [18,19]), and average shortest path distance from the region to each other region in the network (closeness centrality; [20]). Variants based on current flow for betweenness centrality (current flow betweenness centrality; [21]) and closeness centrality (current flow closeness centrality; [21,22]) capture similar features while using an electrical current model for information spreading, which may be more applicable to brain activity.
Closeness and betweenness centrality are particularly sensitive to the topological role of a region in routing information between regions along shortest paths, and less sensitive to the number of connections. Graph theory centrality metrics allow for assessing specific ways that information is integrated and communicated through regions in the brain network (see [23] for a description of these methods).

Relating Complexity to Centrality
Task vs. rest [13] and sober vs. intoxicated [14] states have been used to show that BOLD activity is more complex as measured by H during more organized cognitive states. Sufficient understanding has not yet been reached as to the reasons for increased complexity during these states, and one possibility is that this increased complexity during organized brain processing may be due to integrated co-processing of information from various brain regions concurrently.
If this is the case, then regardless of task, regions that are more highly integrated via white matter (WM) tract connections to the rest of the brain network should have more complex activity than regions that are less connected to other brain regions, as these regions would be integrating information from more sources than other regions. The current research tests the hypothesis that DTI structural connectivity derived centrality measures sensitive to integration from many sources should be able to account for variation in the complexity of functional activity, based on the supposition that more sources of information to integrate should result in more complex activity.  Considering the high amount of collinearity between degree centrality, eigenvector centrality, and PageRank centrality, and also between current flow closeness centrality and log approximate betweenness centrality (see Table 1 , and regions of the medial temporal gyrus including the right posterior hippocampus (commonly viewed as being integral in the encoding of multi-modal information from many disparate brain regions, e.g., [24]; see also [25] for a review; see Fig 2 for example sagittal and axial brain slices of degree centrality and H in various regions including the thalamus and hippocampus).

Fig 2. Example brain maps of degree centrality (left) and Hurst exponent (right), where yellow indicates higher values and blue indicates lower values.
Centrality tended to be negatively associated with H, such that higher centrality (greater central importance to the network) was associated with lower H (more complexity).

Discussion
Fractal analysis of fMRI activity is a recent technique demonstrating that lower H is related to higher complexity of cognitive processing (e.g., [10,13,14]). Our research demonstrated that higher complexity fMRI activity (lower H) can be explained in part by the centrality of the region in the structural DTI connectivity network. Specifically, degree centrality, eigenvector centrality, and PageRank centrality were negatively associated with H, meaning higher centrality on these measures produced more complex functional activity (lower H). Conversely, current flow closeness centrality and approximate current flow betweenness centrality were positively associated with H, suggesting that these metrics are associated with less complex activation because they are particularly sensitive to simple routing of information rather than integration of information from many sources. Overall, in both simple and multiple regression analyses, degree centrality consistently showed the strongest negative relationship with H (positive relationship with complexity), and as such may be the most robust metric of centrality to use in the future when associating DTI structural connectivity to resting state fMRI BOLD activity. Conversely, the interesting positive relationship with H demonstrated by current flow closeness centrality and approximate current flow betweenness centrality was not robust, as it was not significant in the multiple regression model. The positive relationship between these current flow centrality metrics and H is likely related to the sensitivity of these regions to topological location along shortest paths, which facilitate communication between distant regions in the network. In general, increased complexity with increased degree centrality suggests that the complexity of fMRI BOLD activation increases in the presence of integration of information from many sources.

Implications
With this evidence that complexity measured by H is related to centrality in the network, baseline expectations for complexity could be assessed at the level of each brain region using DTI structural connectivity networks before assessing task-based differences in fMRI complexity. Task fMRI data could also be examined with respect to complexity measured with H, as an indicator of information integration during tasks that manipulate integration of multiple modalities of information, such as semantic processing involving integration of action, shape, colour, emotional, and auditory modalities. Amodal semantic hubs hypothesized to be involved in integration of multiple modalities (e.g., the anterior temporal lobe; see [26,27]) may have higher complexity as measured by H than modal regions focused on a single modality (e.g., action, shape, colour, etc.) during semantic tasks, and other potential integrative hubs may also be identified in this way. Additionally, this knowledge of the relation of structural connectivity patterns to fMRI signal complexity could help to investigate reorganization of brain signal complexity with age from the lens of comorbid structural connectivity reorganization (see [11]).

Conclusions
The investigation of the fractal indicator, H, of complexity and its relation to DTI structural network dynamics via graph theory centrality analyses undertaken in this research has demonstrated inherent differences in the complexity of fMRI BOLD signals can be accounted for by structural connectivity centrality of the various regions in the brain. This finding suggests that complexity is dependant not just on task (e.g., [13]) or on biological state (e.g., [14]), but also on the structural pattern of the connections as studied through graph theory analysis of DTI probabilistic streamlines. Supporting the validity of our approach, regions known to be highly connected, including the thalamus and hippocampus, were among the highest in centrality and complexity. The number of connections to other regions in the brain (degree centrality) is positively and consistently related to the complexity of brain activity as measured with fMRI.
This research contributes to a greater understanding of the novel use of the Hurst exponent in assessing complexity of fMRI BOLD signals.

Materials and Methods
High quality DTI and resting state fMRI data for 100 unrelated subjects were obtained from the Human Connection Project (HCP) database ( [28]; please see [28] for ethics statements).
The HCP resting state fMRI data was used, which has been FSL FIX [29]  is much more computationally intensive than deterministic tractography, and as such this resulting data represents an important contribution to the field of brain connectome research. The probabilistic tractography produced asymmetric structural connectivity matrices, which were converted to symmetric matrices by calculating the maximum streamline count between the cell in row i column j, and the cell in row j column i. The connectivity matrix was then used to compute streamline weighted graph theory centrality measures of: 1) degree centrality (total connections to the region); 2) eigenvector centrality (number of connections weighted by degree of the connected region); 3) PageRank centrality (computes a ranking of the nodes based on the structure of the incoming links, originally designed as an algorithm to rank web pages; computed with α equal to the default of 0.85); 4) current flow closeness centrality (current flow method based on mean connectivity distance to other regions); and 5) approximate current flow betweenness centrality (current flow method based on the number shortest paths the region is on). These graph theory metrics were calculated using the NetworkX python library, and the definitions provided are informed by the NetworkX documentation [34]. The reciprocal of the DTI connectivity matrix was calculated and used as the weights for the current flow closeness centrality and approximate current flow betweenness centrality, as these models determine shortest paths assuming that edge weights represent effective resistance in that path.
The means for H and degree centrality metrics were computed across participants so that a mean value was assigned to each of the 268 brain regions. Mean H was then modeled as the criterion variable in a linear regression with centrality metrics as predictors. H was regressed on each of these centrality metrics separately and then multiple regression models were examined to investigate shared variance between the centrality metrics. The data that support the findings of this study are openly available in Zenodo at https://doi.org/10.5281/zenodo.3509709 [35].