A Mathematical Model for Evaluating the Functional Connectivity Strongness in Healthy People

Area of Science:

• Neuroscience
• Graph Theory
• Mathematical Modeling

Background:

• Human brain connectivity, involving neurons, synapses, and regions, remains incompletely understood.
• Graph Theory offers tools to investigate brain structure, but mathematical and neuroscientific approaches sometimes mismatch.
• Neural connectivity is categorized into structural, functional, and effective types, each requiring different graph representations.

Purpose of the Study:

• To propose a mathematical model for functional connectivity using directed graphs with weighted edges.
• To rigorously define the model's parameters, including the dual role of distance (discrete and Euclidean) and time (local and global).
• To validate the model's applicability to both healthy volunteers and potentially neurological disease subjects.

Main Methods:

• Developed a mathematical model based on directed graphs with weighted edges, W(i,j,t).
• Split the model into two parts, introducing parameters motivated by neuroscientific literature.
• Incorporated both local (task-specific) and global (lifespan) temporal aspects, and discrete/Euclidean distance metrics.

Main Results:

• The proposed model successfully treats functional connectivity.
• In the resting state, the model simplifies to established probabilistic growth laws for edge formation.
• Simulations using synthetic data aligned with expected outcomes, validating the model's correctness.

Conclusions:

• The developed mathematical model provides a robust framework for analyzing functional brain connectivity.
• The model's flexibility in handling distance and time offers new insights into neural network dynamics.
• Further research with real data and applications to neurological pathologies are encouraged.