%A Gao,Jianbo %A Hu,Jing %A Liu,Feiyan %A Cao,Yinhe %D 2015 %J Frontiers in Computational Neuroscience %C %F %G English %K scaling law,multiscale entropy analysis,Fractal signal,heart rate variability (HRV),adaptive filtering %Q %R 10.3389/fncom.2015.00064 %W %L %M %P %7 %8 2015-June-02 %9 Original Research %+ Prof Jianbo Gao,Institute of Complexity Science and Big Data Technology, Guangxi University,Nanning, China,jbgao.pmb@gmail.com %+ Prof Jianbo Gao,PMB Intelligence LLC,Sunnyvale, CA, USA,jbgao.pmb@gmail.com %# %! Bi-scaling law for MSE of biosignal %* %< %T Multiscale entropy analysis of biological signals: a fundamental bi-scaling law %U https://www.frontiersin.org/articles/10.3389/fncom.2015.00064 %V 9 %0 JOURNAL ARTICLE %@ 1662-5188 %X Since introduced in early 2000, multiscale entropy (MSE) has found many applications in biosignal analysis, and been extended to multivariate MSE. So far, however, no analytic results for MSE or multivariate MSE have been reported. This has severely limited our basic understanding of MSE. For example, it has not been studied whether MSE estimated using default parameter values and short data set is meaningful or not. Nor is it known whether MSE has any relation with other complexity measures, such as the Hurst parameter, which characterizes the correlation structure of the data. To overcome this limitation, and more importantly, to guide more fruitful applications of MSE in various areas of life sciences, we derive a fundamental bi-scaling law for fractal time series, one for the scale in phase space, the other for the block size used for smoothing. We illustrate the usefulness of the approach by examining two types of physiological data. One is heart rate variability (HRV) data, for the purpose of distinguishing healthy subjects from patients with congestive heart failure, a life-threatening condition. The other is electroencephalogram (EEG) data, for the purpose of distinguishing epileptic seizure EEG from normal healthy EEG.