Sloppiness Of Large-scale Brain Network: Resting-task Transition And Individual Difference

When using a dynamical model to describe a complex system,the system can sometimes exhibit sloppiness:A sloppy system is one that displays a logarithmic hierarchy of sensitivity to certain specific combinations of parameters——system's behavior is constrained by only a few parameters or parameter combinations termed "stiff direction",whilst insensitive to the variations of other combinations of parameters that are referred to as "sloppy direction".As a high-dimensional complex system,to fully describe the dynamical patterns of the brain,it is necessary to introduce a vast number of parameters,including the local ones associated with specific brain regions and those associated with the connections within the brain.However,if the brain dynamics can be captured by a “sloppy model”,just as other biological systems behave,there will be a considerable number of parameters whose variations will not significantly affect the dynamics of the brain.In that case,the brain dynamics will be primarily determined by a few kinds of combinations of parameters.Previous study on local neural circuits firing patterns and the spiking activity in the primary auditory cortex of anesthetized rats have partially confirmed these conjectures,suggesting that the brain networks may show high sloppiness.However,the parameter sensitivity,or say,the sloppiness of the large-scale human brain networks,has not been validated.In this research,we address the problems related to the resting-task transition and individual differences of the large-scale brain network based on a dataset of the resting and task state f MRI signals.We construct the functional networks based on the pairwise maximum entropy model(or Ising model in physics)for different individuals and estimate the parameters of the large-scale brain networks.The sloppiness analysis is conducted for the parameters related to the regions and connections of the brain.It is observed that the large-scale brain networks are highly sloppy in both the resting and task states.And the parameter changes due to the task switching along the stiff direction can reflect the differences in each individual's performance on the task.We also employ the sloppiness analysis to elucidate the dynamical reconfiguration process in restingtask switching.We find that the parameter sensitivity of the working memory network(WMN)increases when switching to the task state while the parameter sensitivity of the default mode network(DMN)decreases when switching to the task state.The clustering analysis of parameters reveals that the functional subnetworks arise during resting-task switching,in other words,there is a segregation of sensitivity in the functional network during task switching.Furthermore,we examine the individual differences of the brains in the framework of sloppiness analysis.We find that the subjects' subnetwork parameter sensitivity distributions are correlated with their task performances,suggesting that higher levels of the sensitivity segregation of the whole network can improve task performance.We also discover that the individual difference along the stiff directions may result in a more integrated or segregated brain underlying individual differences in task performance.Along the positive stiff direction,the brain obtains a more separated brain by decreasing the functional connection between the two modules and increasing the degree of integration within the WMN.We also examine the relationship between structural connectivity strength and the corresponding perturbation sensitivity.Contra-intuitively,our study indicates that the weak intersubnetwork connections show high sensitivity and play a crucial role in the resting-task switching process.Our study identifies the sloppiness for the first time on a large-scale brain network and innovatively use the sloppiness analysis framework to discover that individual differences in parameter sensitivity can be reflected in task performance and individual differences in parameters are found to respond to task performance through the functional separation and integration embodied behind the stiff direction.In addition to these,using parameter sensitivity we find that the structurally weaker connected edges play an important role in function.These results provide a new possible research framework for the study of large-scale brain networks and pave the way for our subsequent exploration in the direction of multitask switching,brain diseases,aging and development,and structure-function relationships.