Graph Theory and Connectivity Flashcards
What is functional connectivity?
- statistical dependencies among spatially remote neurophysiologic events
- GLM
(rest) functional connectivity - method
seed-voxel correlation
- seed = target region/variable
- extract time series from a seed region
- voxel-wise test for correlations (i.e. multiple GLMs with X for each other voxel)
(rest) functional connectivity - pros and cons
pros
- no a priori hypothesis needed (i.e. data-driven)
- useful when we have no model of what caused the data
cons
- no mechanistic insight into the neural system of interest
- inappropriate for situations where we have a priori knowledge and experimental control about the system of interest
(task) functional connectivity - method
Psycho-physiological interaction (PPI)
- factorial design
- 1 task factor (e.g. attention / no attention)
- 1 stimulus factor (movement / no movement)
y = (TA - TB) beta 1 + (S1 - S2) beta2 + (TA - TB)(S1 - S2) beta3 + e
- main effect of task + main effect of stimulus + interaction
- replace main effect in GLM by time series of an area that shows main effect of stimulus type
- 2 possible interpretations of PPI term
(task) functional connectivity - pros & cons
pros
- given a single source region, we can test for its context-dependent connectivity across the entire brain
- complies with KISS principle
cons
- very simplistic model: only allows to model contributions from a single region
- not easily used with event-related data
- limited causal interpretability in neural terms, more powerful models needed
What is effective connectivity?
- influence that the elements of a neuronal system exert over another
models of effective connectivity:
- Granger causality
- Dynamic causal modelling (DCM)
- structural equation modelling (SEM)
- multivariate autoregressive models (MAR)
What is Granger causality?
- model of effective connectivity
- given two time series y1 and y2, y1 is considered to be caused by y2 if its dynamics can be predicted better using past values from y1 and y2 as opposed to using past values of y1 alone
- causal interpretability? not really
- in neural terms? No (time scale)
- more powerful models needed
What is a graph composed of?
nodes and edges
What is the degree of a node?
- the number of its edges
- the higher the degree, the more impact
What is the difference between weighted and binary networks?
- for weighted networks, matrix elements are continous values ranging from strong (high valued) to weak (low valued)
- for binary networks, matrix elements are either 0 (no connection) or 1 (connection)
What are the 3 rules for defining nodes?
Brain nodes should have:
- intrinsic consistency (belong to the same function, homogenous)
- extrinsic differentiation (different from other nodes)
- spatially constrained (no smoothing)
How big should the network be?
- if global properties (efficiency, distribution of nodes) are of interest, it does not make a difference whether using 80 or over 1000 areas
- 200 - 300 areas is a good choice.
What kinds of thresholds can you use to get rid of weak links?
- absolute threshold: set every link below threshold to zero
- proportional: certain percentage of highest correlations are considered as links (normalizing by wiring cost)
- result is called adjacency matrix
Problems edge definition
- thresholding can modify network structure
- thresholding can result in different stages of network fragmentation for each subject and thus in different numbers of nodes forming the network
- low threshold may result in uniformity of networks (no possibility to detect inter-individual differences)
- association of network topology with independent variables may uniquely dependent on the precise threshold value
solution:
- construct each individual network / perform analysis over a range of thresholds
What kinds of network measures are there?
- functional segregation
- functional integration
- centrality
- resilience
functional segregation
- ability for specialized processing of densely interconnected groups of brain regions
- quantifies presence of such groups/clusters/modules within network
- suggests organization of brain regions indicative of segregated neural processing
- simple measures are based on number of triangles in network (more triangles, more segregation)
functional segregation - clustering coefficient
- measure of local connectedness
- proportion of how many nearest neighbors of node i are connected to each other as well
functional segregation - modular/community structure
- subdividing network into groups of nodes with a maximally possible number of within-group links, and a minimally possible number of between-group links
functional integration
- ability to rapidly combine specialized information from distributed brain regions
- characterizes the ease with which brain regions communicate
- commonly based on concept of path (sequence of links between nodes)
- represent potential routes of information flow between pairs of brain regions
functional integration - global network efficiency
- the shorter the paths from one region to another, the higher efficiency
- hub = node embedded in a lot of shortest paths between networks
What is small-worldness?
- optimal balance of functional integration and segregation
- high clustering & low path length
- brain is also organized as small-world network
- high global and local efficiency of parallel information processing facilitates adaptive reconfiguration of neuronal assemblies in supoort of changing cognitive states
centrality
- important brain regions (hubs) often interact with many other regions and facilitate functional integration
- various measures: degree, betweenness (being part of many of the shortest paths), connection between modules
centrality - hubs
- 6% of all connections connect 90% of the brain
- highest edge betweenness centrality
- highest functional connectivity
- above-average FC distance
- organized in a rich-club
resilience
- anatomical brain connectivity influences the capacity of neuropathological lesions to affect functional brain activity
- extent of functional dysfunction is heavily determined by the affected anatomical region in a stroke
What are bridge hubs, connector hubs and provincial hubs?
- bridge hubs connect more than 2 modules
- connector hubs connect 2 modules
- provincial hubs are important in their own module but not relevant for information flow within the entire system
resilience - degeneracy
- capacity of structurally distinct elements of a system to carry out the same function
- ability of distinct neuronal systems to make overlapping contributions to the same output, offering both functional adaptability and robustness to damage
