Degree‐based statistic and center persistency for brain connectivity analysis

Abstract

Brain connectivity analyses have been widely performed to investigate the organization and functioning of the brain, or to observe changes in neurological or psychiatric conditions. However, connectivity analysis inevitably introduces the problem of mass-univariate hypothesis testing. Although, several cluster-wise correction methods have been suggested to address this problem and shown to provide high sensitivity, these approaches fundamentally have two drawbacks: the lack of spatial specificity (localization power) and the arbitrariness of an initial cluster-forming threshold. In this study, we propose a novel method, degree-based statistic (DBS), performing cluster-wise inference. DBS is designed to overcome the above-mentioned two shortcomings. From a network perspective, a few brain regions are of critical importance and considered to play pivotal roles in network integration. Regarding this notion, DBS defines a cluster as a set of edges of which one ending node is shared. This definition enables the efficient detection of clusters and their center nodes. Furthermore, a new measure of a cluster, center persistency (CP) was introduced. The efficiency of DBS with a known "ground truth" simulation was demonstrated. Then they applied DBS to two experimental datasets and showed that DBS successfully detects the persistent clusters. In conclusion, by adopting a graph theoretical concept of degrees and borrowing the concept of persistence from algebraic topology, DBS could sensitively identify clusters with centric nodes that would play pivotal roles in an effect of interest. DBS is potentially widely applicable to variable cognitive or clinical situations and allows us to obtain statistically reliable and easily interpretable results. Hum Brain Mapp 38:165-181, 2017. © 2016 Wiley Periodicals, Inc.

A concise and persistent feature to study brain resting‐state network dynamics: Findings from the Alzheimer's Disease Neuroimaging Initiative

“…According to Proposition , the IPF plot over all possible filtration values is a monotonically decreasing convergence function, so the IPF is also a persistent topology feature like the zeroth Betti number. Similar to the BNP plot methods (Choi et al, ; Chung et al, ; Lee et al, ; Lee et al, ; Yoo et al, ), we define the slope of IPF plot (SIP) as a novel univariate network measure. When the filtration value λ evolves, the number of connected components is getting smaller and the connected component aggregation cost is getting less until all nodes are connected when the IPF is equal to zero.…”

“…Moreover, they are usually used to visualize how the feature varies over different thresholds but the pattern of change is rarely quantified. In contrast, persistent homology-based framework (Choi et al, 2014;Chung et al, 2015;Giusti et al, 2016;Lee et al, 2012;Lee et al, 2017;Yoo et al, 2017) can be used to quantify such dynamic patterns in a more general and coherent way. Bottleneck distance maps of subject-wise networks (a) and group-wise networks (b).…”

“…To address the issue of network threshold selection, a set of brain network analysis methods called graph filtration based on persistent homology (Chen & Edelsbrunner, ; Edelsbrunner & Harer, ; Wu et al, ) has been proposed to measure persistent brain network topology features generated over all possible thresholds (Choi et al, ; Chung, Hanson, Ye, Davidson, & Pollak, ; Lee et al, ; Lee, Kang, Chung, Kim, & Lee, ; Yoo et al, ). It quantifies various persistent topological features at different scales in a coherent manner and avoids the thresholding selection.…”

Integrated multimodal network approach to PET and MRI based on multidimensional persistent homology

“…., 100%. Each data of two groups consisted of 20 subjects and 100 nodes [Yoo et al, 2017]. We sampled the data for the first subject from a normal distribution of zero mean and 0.3 standard deviation (s.d.).…”

“…These results provide a multidimensional homological understanding of disease-related PET and MRI networks that disclose the network association with ASD and ADHD. Hum Brain Mapp 38:1387-1402, 2017…”