Figure 3
From: Glioblastoma multiforme restructures the topological connectivity of cerebrovascular networks
Modular network structure. (a) Schematic graphs of the community unfolding process on an entire vascular network in a healthy brain hemisphere (top) and full U87 glioblastoma (bottom). Each level of partitioning represents a local maximum in modularity Q, attained with increasing community sizes. The rightmost graph shows the clustering scheme with global maximum modularity over a central slice of the original SPIM-image. Communities are depicted by circles with diameter and brightness (blue) proportional to cluster size ej, while the weight of a connection (the number of intercommunity vessel segments) is encoded in the edge thickness and brightness (red). Cluster positions are given by their centroid \({\overrightarrow{r}}_{j}\). The specimens encompass comparable (shrunken) tissue volumes of \({V}_{h}=12.11\,{{\rm{mm}}}^{3}\) and \({V}_{g}=12.87\,{{\rm{mm}}}^{3}\) in healthy control and tumor tissue, respectively (excluding ventricular space in the healthy brain, blinded for analysis). To the right of the partitioning chains, projections of 100 μm thick sections of the skeletonized vessel data show community affiliation (at global maximum Q) through the color of each branch segment. Relative distributions of community size properties from all specimens follow, namely (b) internal number of edges e, (c) mean physical extent R, and (d) community perimeter P. Panel (e) presents the relationship between a community’s number of internal edges e and its perimeter P. Linear fits to the log-log-representation are plotted in lighter colors over the datapoints, presenting slopes \(\xi \). The following plots illustrate the relationships between (f) community edges e and mean physical extent R, as well as (g) perimeter P and R.
