A Statistical Strategy For Small-World Characteristics Based On Graph Theory And Its Application In Neuroimaging

In the research of small-world characteristics of brain networks,most study focuses on the differences between two groups such as functional brain related on age,sex,and neurological diseases.Due to the absence of research methods,the small-world networks characteristics statistically difference between two groups was not provided by now.In order to solve this problem,the brain functional image was preprocessed using the technique of PET(positron emission tomography,single factor variable)and fMRI(functional magnetic resonance imaging,multiple factor variable).The following method is employed to study the small-world characteristics statistically difference between two groups.Methods: 1.The single factor variable brain functional imaging technique of Resting-state PET was selected.They are 113 younger subjects aged 26~40years(mean age =36.5 years,73 male)and 110 older subjects aged 51~65 years(mean age =56.3 years,73 male).In order to get the brain networks,the PET brain image were processed,and obtain statistic characters of the small-world parameters(Cp,Lp,Eglobal)by surrogate data method in non linear mathematical.2.The multiple factor variable brain functional imaging technique of Resting-state fMRI was selected.They are 110 healthy subjects(mean age =21.7 years,47 male)and 90 Attention Deficit Hyperactivity Disorder(ADHD)patient subjects(mean age=10.6 years,53 male)}.In order to get the brain networks,the fMRI brain image were processed,and obtain statistic characters of the small-world parameters(Cp,Lp,Eglobal)by surrogate data method in non linear mathematical.Conclusions: The results of PET agree with the results of fMRI,which shows that the methods are feasible.The small-world parameters(Cp,Lp,Eglobal)are subject to normal distribution by surrogate data.Both the standard deviation and different values are very small.This means that the spatio-temporal correlation is not stronger than the data itself and find the standard deviation of small-world parameters(Cp,Lp,Eglobal)decreases when the data increase.This proves the necessity of using big data.Statistically difference of the small-world parameters between difference groups in certain threshold could be estimated by Hypothesis Testing and provide a methodological guidance for future research in neuroimaging.