Comparison of Parametric and Nonparametric Thresholding Methods for Small Group Analyses

Talk given as ISMRM 2003

The Human Functional Brain Network Demonstrates Structural and Dynamical Resilience to Targeted Attack

<div><p>In recent years, the field of network science has enabled researchers to represent the highly complex interactions in the brain in an approachable yet quantitative manner. One exciting finding since the advent of brain network research was that the brain network can withstand extensive damage, even to highly connected regions. However, these highly connected nodes may not be the most critical regions of the brain network, and it is unclear how the network dynamics are impacted by removal of these key nodes. This work seeks to further investigate the resilience of the human functional brain network. Network attack experiments were conducted on voxel-wise functional brain networks and region-of-interest (ROI) networks of 5 healthy volunteers. Networks were attacked at key nodes using several criteria for assessing node importance, and the impact on network structure and dynamics was evaluated. The findings presented here echo previous findings that the functional human brain network is highly resilient to targeted attacks, both in terms of network structure and dynamics.</p> </div

Changes in final total activity in networks as nodes are removed.

<p>The total activity attained at the end of the simulation (t = 100 iterations) is shown, averaged across all nodes in the network.</p

Impact of targeted attack on accuracy of solving the density classification task.

<p>Each panel depicts the mean accuracy curve for each type of targeted attack, averaged across subjects. The mean accuracy curves were generated for the original network (A) and after removing 10% of the nodes based on degree centrality (B), leverage centrality (C), betweenness centrality (D), eigenvector centrality (E), and at random (F). In panels B–E, solid lines indicate results when targeting hubs, and dashed lines indicate results when targeting antihubs.</p

Total activity in the network after targeted attack and random failure in an example subject.

<p>Nodes are targeted by degree (A), leverage (B), betweenness (C), and eigenvector centrality (D), as well as at random (E). Curves represent networks after removing 20% (stars), 40% (triangles), 60% (squares), and 80% of the network (circles). The total activity of the original network is shown in yellow for comparison.</p

Topological changes in brain networks due to targeted attack and random failure.

<p>Panels depict changes in the size of the giant component (A), global efficiency (B), and local efficiency (C). The size of the giant component (S), was normalized to its original size (S0) in order to provide a consistent upper bound across subjects. All curves represent averages across 5 subjects, and error bars indicate standard deviations. Four centrality metrics were used to identify hubs: degree centrality (red), leverage centrality (blue), betweenness centrality (green), and eigenvector centrality (pink). Random failure (black) is included for comparison.</p

Changes in total activity after targeted attack or random failure.

<p>High centrality hubs (open symbols) and low centrality antihubs (filled symbols) were targeted for removal to compare the impact on dynamics in an example subject.</p

Generating a functional brain network.

<p>Functional magnetic resonance imaging (fMRI) data are collected from a subject, yielding a time series for each gray matter voxel in the cerebrum. The correlation values between each voxel are calculated to produce a correlation matrix. A threshold is applied to the correlation matrix to create an adjacency matrix, where all values surviving the threshold are set to 1. This adjacency matrix defines the links present in the functional brain network.</p

Summary of networks used to evaluate network topology and dynamics.

<p>S: size of giant component, E_glob: global efficiency, E_loc: local efficiency, SA: spreading activation, ABBM: agent-based brain-inspired model.</p

Spreading activation in an intact brain network and after targeted attack.

<p>(A) The activity of the 9 nodes shown exponentially increases, while the activity in all other nodes has decayed to zero. (B) The total activity, defined to be the sum of activation across all nodes at a given time step, illustrates the exponentially increasing activation. This network is exhibiting Phase II behavior. (C) After removing 20% of the highest degree centrality nodes, there are 14 nodes exhibiting exponentially increasing behavior, where nodes 6 through 14 are the same as pictured in (A). (D) The total activity of the attacked network (dashed red line) is greater than that of the intact network (solid black line).</p