Research On Cross Modularization Of Brain Networks Based On Multi-objective Optimization

Modular brain networks are important tools to understand brain structures,functions and its development.A lot of community detection methods have been employed on either structural network or functional network with single optimization criteria.Yet it is not clear how these modules related to each other cross modalities.Or more specially,what kind of transitions happen when the structural modules shift to the functional ones.In view of this phenomenon,multi-objective optimization algorithm comes in handy.Multi-objective optimization algorithm refers to the selection of multiple sub-objectives.When different sub-objectives are optimized at the same time,a series of solutions will be generated.After one iteration after another,an optimal set of solutions,namely Pareto-front,can be obtained in this paper.Here we present a novel framework that we name as Community Chain(CC)to support the cross modalities investigation of community structures.Firstly,this paper uses brain imaging technology and a community detection algorithm to obtain the consensus partition of structural networks and functional networks,structural resolution parameters,and corresponding adjacency matrices from the individual level.The consensus partition of individuals is used to construct a group network with common characteristics of individuals.Similarly,this paper constructs a representative group structural network and group functional network.Next,the multi-objective optimization algorithm NSGA-II is used to design and implement the Community Chain,a technical framework proposed in this paper.NSGA-II selects two target functions,one from the brain structure network and the other from the brain function network.The maximum value of modularity from brain structural network to brain functional network and its corresponding community division were calculated.In order to obtain better local optimal solutions and global optimal solutions,experiments were conducted for many times,and the relevant parameters(including the parameters in the genetic operation and community division)were constantly adjusted and optimized to form a relatively continuous Pareto Front,so that the obtained optimal solutions have better convergence and robustness.Finally,starting from the individual level and the group level respectively,this paper studies the main components of a series of solutions on the Pareto front and the changes of brain regions,so as to analyze the change characteristics of the cross modules of brain structure network and brain function network.In this process,it is found that(1)from the average rate of change of brain regions of all individuals,the changes of left and right hemispheres are basically the same,among which several major modules,such as visual module(VIS)and somatomotor module(SOM),are stable in this process and will always exist.However,the regions near the frontoparietal control module(FPC)and the default mode network module(DMN)in the lower half of the brain,such as the complex PFm region,have more drastic changes.(2)this phenomenon is basically consistent at the group level,and is more significant.(3)this paper reveals the weak correlation between the change rate of nodes on the Pareto front and the individual's age,cognitive ability and behavioral ability.