Markov models for fMRI correlation structure: Is brain functional connectivity small world, or decomposable into...

Area of Science:

• Neuroscience
• Computational Neuroscience
• Brain Imaging Analysis

Background:

• Functional Magnetic Resonance Imaging (fMRI) correlations reveal neural interactions via hemodynamic responses, highlighting distributed brain networks.
• Graph theory suggests neural connections form a highly integrated system with small-world properties (local clustering, short pathways).
• Reconciling these views requires understanding the assumptions underlying functional connectivity observed in fMRI.

Purpose of the Study:

• To examine conditional independence properties (Markov structure) of fMRI signals.
• To identify realistic assumptions on connectivity structure explaining observed functional connectivity.
• To decompose the Markov structure into segregated functional networks using decomposable graphs (overlapping cliques).

Main Methods:

• Analysis of fMRI signal conditional independence properties to infer Markov structure.
• Development of a novel method for efficiently extracting cliques from large, strongly-connected graphs.
• Comparison of different graph structure learning methods by testing model goodness-of-fit on new data.

Main Results:

• Summarizing brain structure as strongly-connected networks provides a good description only for very large and overlapping networks.
• Markov models are effective tools for identifying brain connectivity structure from fMRI signals.
• The effectiveness of Markov models depends on their ability to reflect the small-world properties of neural systems.

Conclusions:

• Conditional independence analysis (Markov models) offers a powerful framework for understanding brain connectivity from fMRI.
• The study introduces an efficient clique extraction method for large-scale brain graphs.
• Accurate representation of brain connectivity using Markov models necessitates incorporating small-world network properties.