Application Of Refined Composite Permutation Fuzzy Entropy In Resting-state FMRI Signal

The brain is essentially a nonlinear and complex system,and the changes in the intrinsic characteristics of its neural signals can reflect the abnormality of brain structure and function.In the characteristics of most neural signals,complexity research has been the focus of researchers.Entropy,as a commonly used complexity analysis method,can effectively describe the disorder and chaos of neural signals.With the development of technology,multiscale entropy has also been widely used in the field of neural signal analysis,showing significant advantages when it is used to analyze non-stationary signals.In recent years,a large number of researchers have applied entropy to analyze the complexity change of resting-state functional magnetic resonance imaging(rs-f MRI)signals,and finally achieved good research results.According to the requirements of time series analysis,the researchers proposed Permutation Fuzzy Entropy(PFEN)to solve the problem that fuzzy entropy is sensitive to noise,and then proposed Multiscale PFEN(MPFEN),which can analyze the complexity of the time series in different scale.However,the MPFEN still has some shortcomings in the analysis and research of rs-f MRI signals.Firstly,in the coarse-grained process of MPFEN,with the increase of scale factor,the coarse-grained sequence gradually shortens,which may produce inaccurate entropy estimates;secondly,if the time sequence is too short,the entropy may be unclear or undefined during calculation.Therefore,it is necessary to solve the problem of MPFEN in order to better reflect the complexity of the brain state.Therefore,this study aims to solve the problems of multiscale permutation fuzzy entropy,and applys the entropy index to analyze the changes of complexity of bipolar disorder(BD)patients.Firstly,the refined composite multiscale permutation fuzzy entropy(RCMPFEN)is proposed to solve the inaccuracy and undefined entropy estimation caused by the multiscale permutation fuzzy entropy;secondly,this study analyzes the test-retest reliability of MPFEN and RCMPFEN;finally,this study uses entropy to analyze the changes of f MRI signal complexity in BD patients.The main contents and results of this research are as follows:(1)According to the shortcomings of multiscale permutation fuzzy entropy,refine composite multiscale permutation fuzzy entropy is proposed.When using MPFEN to analyze neural signals,with the increase of the scale,the entropy value may be inaccurate or undefined,which will affect the results of the experiment.Based on this,the coarse-grained process and entropy calculation of MPFEN are improved,and RCMPFEN is proposed.The coarse-grained process of RCMPFEN is to generate s coarsegrained sequences when the scale factor is s;in order to reduce the probability of the occurrence of undefined entropy values,all coarse-grained sequences on different dimensions are summed up and then calculate permutation fuzzy entropy values.Through these two aspects of improvement,to improve the performance of MPFEN.(2)Analyze the test-retest reliability of refined composite multiscale permutation fuzzy entropy.RCMPFEN theoretically solves the shortcomings of MPFEN,in order to further illustrate that RCMPFEN still has stability in analyzing repeated measurement data.In this study,two sets of f MRI signals test-retest datasets(NYU and IBA)are used to analyze the test-retest reliability of MPFEN and RCMPFEN from three perspectives of whole brain voxels,brain regions and functional networks.The results show that the test-retest reliability of RCMPFEN is better than that of MPFEN in three aspects.When analyzing NYU dataset,it is found that the test-retest reliability of the inter is better than that of the intra.At the time,the test-retest reliability of default mode network,fronto-parietal network and visual network is better than that of other functional networks.(3)Application of refined composite multiscale permutation fuzzy entropy.MPFEN and RCMPFEN were applied to analyze the complexity of f MRI signals in BD patients.The results show that RCMPFEN obtained more different brain regions at various scales.And the significant differences brain regions between the two groups were different at different scales.More different brain regions were found at high scale than at low scale,which reflect the abnormal brain activities of BD patients at different scales,and the abnormal brain regions are mainly concentrated in the frontal lobe,occipital lobe,temporal lobe and parietal lobe.