A Strategy to Reduce Bias of Entropy Estimates in Resting-State fMRI Signals

Albert C. Yang, Shih-Jen Tsai, Ching-Po Lin, Chung-Kang Peng

Complexity analysis of resting-state blood oxygen level-dependent (BOLD) signals using entropy methods has attracted considerable attention. However, investigation on the bias of entropy estimates in resting-state functional magnetic resonance imaging (fMRI) signals and a general strategy for selecting entropy parameters is lacking. In this paper, we present a minimizing error approach to reduce the bias of sample entropy (SampEn) and multiscale entropy (MSE) in resting-state fMRI data. The strategy explored a range of parameters that minimized the relative error of SampEn of BOLD signals in cerebrospinal fluids where minimal physiologic information was present, and applied these parameters to calculate SampEn of BOLD signals in gray matter regions. We examined the effect of various parameters on the results of SampEn and MSE analyses of a large normal aging adult cohort (354 healthy subjects aged 21-89 years). The results showed that a tradeoff between pattern length m and tolerance factor r was necessary to maintain the accuracy of SampEn estimates. Furthermore, an increased relative error of SampEn was associated with an increased coefficient of variation in voxel-wise statistics. Overall, the parameters m = 1 and r = 0.20-0.45 provided reliable MSE estimates in short resting-state fMRI signals. For a single-scale SampEn analysis, a wide range of parameters was available with data lengths of at least 97 time points. This study provides a minimization error strategy for future studies on the non-linear analysis of resting-state fMRI signals to account for the bias of entropy estimates.