Effect of Fixed-Density Thresholding on Structural Brain Networks: A Demonstration in Cerebral Small Vessel Disease

Abstract

A popular solution to control for edge density variability in structural brain network analysis is to threshold the networks to a fixed density across all subjects. However, it remains unclear how this type of thresholding affects the basic network architecture in terms of edge weights, hub location, and hub connectivity and, especially, how it affects the sensitivity to detect disease-related abnormalities. We investigated these two questions in a cohort of patients with cerebral small vessel disease and age-matched controls. Brain networks were reconstructed from diffusion magnetic resonance imaging data using deterministic fiber tractography. Networks were thresholded to a fixed density by removing edges with the lowest number of streamlines. We compared edge length (mm), fractional anisotropy (FA), proportion of hub connections, and hub location between the unthresholded and the thresholded networks of each subject. Moreover, we compared weighted graph measures of global and local connectivity obtained from the (un)thresholded networks between patients and controls. We performed these analyses over a range of densities (2-20%). Results indicate that fixed-density thresholding disproportionally removes edges composed of long streamlines, but is independent of FA. The edges removed were not preferentially connected to hub or nonhub nodes. Over half of the original hubs were reproducible when networks were thresholded to a density ‡10%. Furthermore, the between-group differences in graph measures observed in the unthresholded network remained present after thresholding, irrespective of the chosen density. We therefore conclude that moderate fixed-density thresholds can successfully be applied to control for the effects of density in structural brain network analysis.

Impact of thresholding on the consistency and sensitivity of diffusion MRI‐based brain networks in patients with cerebral small vessel disease

“…This concern can be relevant in studies trying to identify disease effects at the level of subnetwork and/or individual connections, rather than pathological changes in large-scale brain network topology (Petersen et al, 2020) (Heinen et al, 2018). After fixed-density thresholding, a wide-range of densities (.40-.10) preserved the sensitivity to detect these disease-related effects, suggesting that changes in global metrics can be consistently detected over multiple threshold levels (de Brito Robalo et al, 2020;Drakesmith et al, 2015). Absolute thresholding had a stronger impact interindividual variation and sensitivity to time and group effects (see Supporting Information), due to the fact that this thresholding approach creates disconnected nodes during, thereby changing the size of the network and disrupting global network metrics (van Wijk et al, 2010).…”

Systematic validation of structural brain networks in cerebral small vessel disease

“… 47 In addition, others have already reported the effect of density thresholding and concluded that networks weighted by fractional anisotropy might be less prone to network density effects. 48 Still, global efficiency measures might be influenced by the density of the structural network and should thus not be understood as the “efficiency” of the brain network, but rather be interpreted as a global diffusion marker of the brain network. However, to not add another level of complexity, we decided a priori against trying out different arbitrary density thresholds.…”

The eNOS isoform exhibits increased expression and activation in the main olfactory bulb of nNOS knock-out mice

“…For this purpose, a small tail sample was taken from each mouse before weaning and the cells were lysed for DNA extraction. PCR was then performed using primers specific to an exon of nNOS [IMR 0406 (sense) TCAGATCTGATCCGAGGAGG and IMR 0407 (antisense) TTCCAGAGCGCTGTCATAGC] and primers specific to the neomycin gene [IMR 0013 (sense) CTTGGG TGGAGAGGCTATTC and IMR 0014 (antisense) AGGTGAGATGACAGGAGATC] ( De Brito Robalo et al, 2020 ). The products obtained were visualized on a 3% (w/v) agarose gel after electrophoresis.…”

“…Concerning eNOS, its expression was restricted to endothelial cell-like elements that lined the blood vessels throughout the area of the different sections of the MOB analyzed. This labeling was semi-automatically measured considering both the tissue region occupied by the blood vessels (eNOS blood vessels density) and the intensity of their labeling (eNOS “labeling density”; see Section “Results,” Figure 4 and Supplementary Data 1 ); ( Matos et al, 2016 ; Ferreiro et al, 2018 ; De Brito Robalo et al, 2020 ).…”