Fig 1.
Overview of BRAPH software architecture.
BRAPH consists of three layers, from left to right: Graph, Data Structures and Graphical User Interfaces (GUIs). These layers are connected by unidirectional software interfaces (arrows). Graph contains the functions to perform graph analyses. In Data Structures, Brain Atlas allows defining the nodes of the network, Cohort allows defining the subjects to be studied and dividing them into groups, and Graph Analysis permits building the connectivity matrices and calculating network measures; each of these is implemented in an object, whose functionalities can be called by command line. For each of these objects, a GUI is provided (i.e. GUI Brain Atlas, GUI Cohort and GUI Graph Analysis). Thanks to this architecture BRAPH can be very easily maintained, expanded and customized.
Fig 2.
Graphs can be classified based on their edge weights (weighted or binary) and directionality (directed or undirected). It is possible to transform a directed graph into an undirected one by symmetrization (i.e. by removing the information about the edge directions), and a weighted graph into a binary one by thresholding (i.e. by assigning a value of 1 to the edges above a given threshold and 0 to those below threshold).
Fig 3.
Workflow for a graph theory analysis in BRAPH and relative graphical user interfaces (GUIs). A) The brain regions are defined in the GUI Brain Atlas. B) The data of the subjects are imported in the GUI Cohort and the user can define groups and edit their age, gender and other relevant data. C) The connectivity matrix is calculated in the GUI Graph Analysis after selecting the parameters defining the type of correlation, how to deal with negative correlation coefficients, and which type of graph to analyze: D) binary undirected graphs at a fixed density (GUI Graph Analysis BUD); E) binary undirected graphs at a fixed threshold (GUI Graph Analysis BUT); F) weighted undirected graphs (GUI Graph Analysis WU).
Table 1.
Characteristics of the structural MRI sample.
Table 2.
Characteristics of the fMRI sample.
Fig 4.
Structural brain networks in controls, MCI patients, and AD patients.
From left to right: weighted correlation matrices of 82 regions, binary correlation matrices after fixing density at 15%, and corresponding brain graphs from A) controls (CTR), B) patients with amnestic mild cognitive impairment (MCI), and C) Alzheimer’s disease (AD) patients.
Fig 5.
Differences between groups in global structural topology.
Left: differences between controls (CTR) and Alzheimer’s disease (AD) patients; middle: differences between controls (CTR) and patients with mild cognitive impairment (MCI); right: differences between patients with mild cognitive impairment (MCI) and Alzheimer’s disease (AD) patients for A) characteristic path length, B) local efficiency, C) transitivity and D) modularity. The plots show the lower and upper bounds (blue circles) of the 95% Confidence Intervals (CI) (gray shade) as a function of density. The orange circles show the differences between groups and, when falling outside the CI, indicate that the difference was statistically significant at p<0.05. The blue dots in the middle with values around zero indicate the mean values of the difference in global network measures between the randomized groups after permutation tests.
Fig 6.
Differences between groups in nodal structural measures.
Nodes showing significant differences between groups in the nodal degree and nodal local efficiency after FDR corrections. Orange indicates increases in nodal measures, while blue indicates decreases.
Fig 7.
Functional brain networks and modules in controls and PD-MCI patients.
Weighted connectivity matrices and modules in A) controls (CTR) and Parkinson’s disease patients B) with normal cognition (PD-CN) and C) with mild cognitive impairment (PD-MCI). Five modules were identified in each group.
Fig 8.
Differences between groups in the nodal functional degree.
Significant decreases in the nodal degree of regions from Module III or fronto-parietal network in Parkinson’s disease patients with mild cognitive impairment (PD-MCI) compared to controls (CTR) after FDR corrections.