Different kind of measurments of the “complexe brain”
name, what, how many regions, what is the outcome
univariate measures - magnitude, power - single region – process
bivariate measures- functional connectivity - two region – interaction
multivariate measures - network analysis - multi regions – patterns
How can we quantitatively asses patterns
(branch of mathematics) Graph theory and (sub-brach) Complex Network Theory
composition of graphs
- nodes and edges.
- degree of node is equal to the number of edges
relation of graphs and matrices
- graphs or networks can be represented by matrices
- graph/network is represented bei columns and rows of the matrix
- connection between two nodes i and j is represented by matrix element (i,j)
- binary networks: matrix elements are either 0 (no connection exists) or 1 ( connection exists)
- weighted networks: matrix elements are continuous values and can range from strong to weak
complex network theory in neuroimaging
= modeling endeavor that provides a set of representational rules to describe the brain subcomponets(regions) and their relationship (white matter tracts/ functional connection)
- brain networks can be constructed in two ways: (1) structural connectivity (Diffusion Tractography (2) functional connectivity (fMRI, EEG, MEG)
Preprocessing during network modeling and its problems
- lack of golden standard
- very sensitive and will reflect any change of network modeling in the topology
- comparability should be given with same modeling strategy
- not too severe for simple preprocessing (but regression of covariates and frequency range of bandbass filter)
- from Paper Neurosci. 2015: Evaluating the reliability….
… a “ broad” frequency range results in more robust networks
…order of preprocessing steps may impact results
…. motion correction pipelines may impact results
approaches to defining nodes
cytoarchtecture probabilistic chemoarchitecture anatomcal random functional data-driven voxel-based myeloarchitecture multimodal (Glasser, Nature, 2016)
building the graph: absolute vs. proportional weight threshold
applying an absolute or proportional threshold solves the problem of weak links (association matrix –> adjacency matrix)
absolute: everything < thr = 0
proportional: % of highest correlations are considered as links
binary s. weigthed, directed vs. undirected networks and combinations
undirected networks: symmetrical outcome; datasets from: diffusion MRI, structural MRI, functional
directed networks: unsymmetrical, datasets from: tract tracing, inference of causality from functional data
undirected binary
undirected weighted
directed binary
undirected weighted
problems with edge definition
- thresholding can modify the network structure (low connectivity –> gain of links, high connectivity –> loss of links)
- thresholding can easily result in different stages of “ network fragmentation” for each subject and thus in different numbers of nodes forming the network
- low edge thresholds may result in “uniformity” of the networks –> no possibility to detect differences between subjects
- results may uniquely dependent on the precise threshold value
–> one solution: construct each individual network over a range of thresholds
Classification of network measurements
(can be characterized on a local basis and a global basis)
functional segregation
functional integration
centrality
resilience
What is the clustering coefficient
- measure of local connectedness ( how many nearest neighbors of node i are connected to each other as well)
- all connected nodes with one node are neighbors
C(A)= 4/10=0.4 [meaning that 40% of connections between neighbors exist]
on what are simple measures of segregation based ?
number of triangles in the network (high number of triangles imply segregation)
- -> describe presence of densely interconnected groups
- -> more sophisticated measures can also find the exact size and composition of these individual groups
what is functional segregation in the brain
- the ability for specialized processing of densly interconnected goups of brain regions
- quantifies the presence of such groups (clusters or modules) within the network
- suggests an organization of brain regions indicative of segregated neural processing
relations between segregation and (A) getting older (B) memory performance
A) the older you get the stronger your executie functions become, this is directly related to increased modularity
B) the ability to reconfigure your network lead to greater memory performance
Modular structure
subdivining the network into groups of nodes, with a amximally possible number of withingroup links, and minimally possible number of between-group links
What is integration of measured brain networks
- ability to rapidly combine specialized infomation from distributed regions
- commonly based on the concept of a path (sequences of links between distinct nodes)
- represent potential routse of information flow between pairs of brain regions
(IQ Study: n= 20: The shorter the path lengths the higher the IQ; replicated study: n=1096 with different thresholds -> not the same findings)
what does small-worldness mean in this context of network measuring?
= optimal balane of functional integration and segregation
- compared to social network: high clustering ( different groups of people in the network are organized in cliquish manner) and a relatively short distance to travel from one person to another person (short pathlength) –> small worldnes = high clustering and low pathlenght –> not in schizophrenia (random; low clustering an pathlength)
- brain is also organized as “ small-world”
- -> high global and local effiency of parallel infomation processing faciliates rapid adaptive reconfiguration of neuronal assamblies in support of changing cognitive states
measurements of centrality
degree
betweenness
connection between modules
hypothesis of the “rich-club”
“rich people only hang out with rich people”–> overlaping of the hubs
the rich club may serve to link different functionsl modules in the brain, through partial overlap with several resting-state network
What are hubs?
important brain regions
- 6 % of all connections connect 90% of the brain
- highest edge betweenness centrality
- highest functional connecivity (FC)
- above avarage FC distance
- organize in a “rich-club”
meaning of centrality?
important brain regions (hubs) often interact with many other regions and facilitate functional integration
What is the concept of degeneracy?
• capacity of structurally distinct elements of a system to carry out the same
function
• describes the ability of distinct neuronal systems to make overlapping
contributions to the same output, offering both functional adaptability and
robustness to damage
resilience of the brain
• Anatomical brain connectivity influences the capacity of neuropathological
lesions to affect functional brain activity
e.g.: The extent of functional dysfunction is heavily determined by the
affected anatomical region in a stroke
