A fast and intuitive method for calculating dynamic network reconfiguration and node flexibility

Abstract

Dynamic interactions between brain regions, either during rest or performance of cognitive tasks, have been studied extensively using a wide variance of methods. Although some of these methods allow elegant mathematical interpretations of the data, they can easily become computationally expensive or difficult to interpret and compare between subjects or groups. Here, we propose an intuitive and computationally efficient method to measure dynamic reconfiguration of brain regions, also termed flexibility. Our flexibility measure is defined in relation to an a-priori set of biologically plausible brain modules (or networks) and does not rely on a stochastic data-driven module estimation, which, in turn, minimizes computational burden. The change of affiliation of brain regions over time with respect to these a-priori template modules is used as an indicator of brain network flexibility. We demonstrate that our proposed method yields highly similar patterns of whole-brain network reconfiguration (i.e., flexibility) during a working memory task as compared to a previous study that uses a data-driven, but computationally more expensive method. This result illustrates that the use of a fixed modular framework allows for valid, yet more efficient estimation of whole-brain flexibility, while the method additionally supports more fine-grained (e.g. node and group of nodes scale) flexibility analyses restricted to biologically plausible brain networks.

Keywords: community detection; dynamic functional connectivity; dynamical network analysis; modular structure; network neuroscience; task-based fMRI; template-based flexibility.

Figure 1

Schematic overview of the template-based flexibility method. (A) Each node has an a-priori affiliation to a template module, not allowing overlap. In this paper, we use the Brainnetome atlas for node definition (Fan et al., 2016) and the FIND Lab network templates as predefined modules [http://findlab.stanford.edu/; Shirer et al., 2012]. Importantly, matrix M, describing the a-priori module affiliation for each node, is predetermined and serves as a reference. (B) Using a sliding-window approach, an adjacency matrix is constructed for each time window by calculating Pearson correlation coefficients between the time series of all possible pairs of nodes. Then, for each node and time window the reference module receiving the highest normalized connection weight will serve as the new modular affiliation for that node in that time window. (C) Last, the number of affiliation changes between affiliation vector in t and its successive vector in t + 1 is defined as the flexibility F_t of the network between two time points. The average of F_t across participants (called $\overline{F_t}$) can be plotted for all consecutive time points (an example presented later in Figure 3).

Figure 2

Task and signals. (A) Example of the N-back working memory task with a 0-back and 2-back condition, during which participants were asked to choose the value that was either shown at the current step or 2 steps ago, respectively. (B) Four blocks of each condition were presented in alternated fashion for 30 s. (C) After preprocessing, mean time courses were extracted from 246 Brainnetome atlas regions (Fan et al., 2016). (D) Windowed time series were extracted using a sliding-window approach, moving a window of 15 time points over the time series one volume at a time.

Figure 3

Comparison of flexibility generated by the generalized Louvain-like locally greedy heuristic algorithm (Blondel et al., ; Jeub et al., 2022) and the template-based method during an N-back working memory task. (A) Flexibility plot from Braun et al. (2015) illustrating the probability that a brain region changes its modular allegiance between two consecutive windows in a sample of 344 healthy subjects. The original plot is used with permission of the publisher. (B) Flexibility plot generated by the template-based method. Here, the flexibility number in each time-window is the fraction of regions that change their affiliation from one time window to the next (i.e., the number of changed regions divided by the total number of nodes). The plots are generated using a subset of 331 subjects from the same cohort as used in Braun et al. (2015). Note that in both plots a time window covers 15 EPI volumes with a TR of 2 s, corresponding to a window length of 30 s. The window was shifted with one volume at a time, allowing for 14 EPI volumes overlap between consecutive windows, which yielded 114 windows in total.

Figure 4

Brainnetome atlas brain regions switching. Number of affiliation switches between consecutive windows for regions of the Brainnetome Atlas, averaged across all subjects and normalized to the most frequently switching node to yield values between 0 and 1. The visualized regions are those with values higher than 0.7.

Figure 5

Findlab brain areas switching. (A) Average number of affiliation switches between consecutive windows for each FIND lab template network, averaged across all subjects. Abbreviations are listed in Table 2. (B) Illustration of the four template networks for which its constituent nodes demonstrated the highest flexibility [http://findlab.stanford.edu/; Shirer et al. (2012)]. See Figure 6 for more statistics.

Figure 6

Additional statistics for Figure 5. Independent t and p values between boxplot modules in Figure 5, shown as [t-value, p-value]. The last column called “Comp. w Rest” calculates the t-test between the specific module and the whole brain. For visualization purpose the table is cut to two parts.

Figure 7

Modular allegiance and integration. Diagonal elements of the matrices are set to be zero. (A) Modular allegiance of the two conditions 2-back and 0-back; to calculate a T matrix for one condition, we used only the windows with 80% of their time-points in that condition. (B) Integration matrix for 0-back and 2-back. (C) Change in the integration values R_2−back − R_0−back (left plot) and sum of rows (from the left plot matrix) as each modules integration value (right plot).

Figure 8

Schematic steps to calculate dynamical flexibility. The time series are extracted from brain scans. Selected sliding windows are used to generate adjacency/connectivity matrices. The groups/clusters/modules are found in each matrix^* using a feasible clustering method. In this step, the method of choice can be a well-known method like the optimization of Newman's modularity Q using greedy Louvain algorithm or it can be our template-based method that considers the a-priori information about brain as pre-assumption. Finally the assigned affiliations in windows are compared and the differences are found. ^*In some methods, different sliding window matrices are put together to make a multi-layer network and then an adjusted version of modularity optimization is employed to find module through all layers.