Comparing Test-Retest Reliability of Entropy Methods: Complexity Analysis of Resting-State fMRI

In recent years, there has been growing interest in studying the complexity of resting-state functional magnetic resonance imaging (rs-fMRI) brain signals. As one of the most commonly used complexity methods, entropy measures have been used to quantitatively characterize abnormal brain activity in aged individuals and patients with psychopathic and neurological disorders, and most studies have analyzed brain signals from a single channel. The widely used entropy methods include approximate entropy (AE), sample entropy (SE), permutation entropy (PE), and fuzzy entropy (FE). However, the test-retest reliability of different entropy methods remains to be explored. In this study, we investigated the distribution and test-retest reliability of four entropy measures and a new entropy algorithm we proposed, permutation fuzzy entropy (PFE), in three independent data sets at three levels, i.e., based on voxels, brain regions, and functional networks. Our results showed that analyzing fMRI signals with entropy showed strong tissue sensitivity. The highest reliability was achieved with PFE, and PE and FE were superior to AE and SE at all three levels. The percentage of nodes with good to excellent reliability in PFE, PE, FE, SE and AE was 94.31%, 52.65%, 18.56%, 11.36% and 0.76%, respectively. PFE and PE showed fair to good reliability in the visual network, auditory network, default-mode network, etc. In conclusion, characterizing brain entropy may provide an informative tool to assess the complexity of brain functions. Our results suggested that PFE and PE had better reliability and reflected more topological information related to normal and disordered functioning of the human brain.