Background: Multiscale entropy (MSE) estimates the predictability of a signal over multiple temporal scales. It has been recently applied to study brain signal variability, notably during aging. The grounds of its application and interpretation remain unclear and subject to debate.
Method: We used both simulated and experimental data to provide an intuitive explanation of MSE and to explore how it relates to the frequency content of the signal, depending on the amount of (non)linearity and stochasticity in the underlying dynamics.
Results: The scaling and peak-structure of MSE curves relate to the scaling and peaks of the power spectrum in the presence of linear autocorrelations. MSE also captures nonlinear autocorrelations and their interactions with stochastic dynamical components. The previously reported crossing of young and old adults' MSE curves for EEG data appears to be mainly due to linear stochastic processes, and relates to young adults' EEG dynamics exhibiting a slower time constant.
Comparison with existing methods: We make the relationship between MSE curve and power spectrum as well as with a linear autocorrelation measure, namely multiscale root-mean-square-successive-difference, more explicit. MSE allows gaining insight into the time-structure of brain activity fluctuations. Its combined use with other metrics could prevent any misleading interpretations with regard to underlying stochastic processes.
Conclusions: Although not straightforward, when applied to brain signals, the features of MSE curves can be linked to their power content and provide information about both linear and nonlinear autocorrelations that are present therein.
Keywords: Brain network dynamics; Brain signal variability; Electroencephalogram (EEG); Multiscale entropy (MSE); Multiscale root-mean-square-successive-difference (MRMSSD); Power spectrum (PS).
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