Refined Multiscale Entropy Using Fuzzy Metrics: Validation and Application to Nociception Assessment

Area of Science:

• Complexity analysis
• Entropy measures
• Time series analysis

Background:

• Refined multiscale entropy (RMSE) commonly uses sample entropy (SampEn) to assess time series complexity.
• SampEn's dependency on data length and standard deviation limits its application.
• Fuzzy entropy (FuzEn) and its variants offer potential improvements over SampEn.

Purpose of the Study:

• To evaluate FuzEn and its variants (TFuzEn, TRFuzEn, IFuzEn, ITFuzEn) within the RMSE framework.
• To compare the performance of FuzEn-based RMSE with SampEn-based RMSE.
• To assess the consistency and applicability of these entropy measures across varying data lengths and real-world physiological signals.

Main Methods:

• Application of FuzEn, TFuzEn, TRFuzEn, IFuzEn, and ITFuzEn for RMSE computation.
• Testing on synthetic time series of varying lengths to assess consistency.
• Analysis of electroencephalograms (EEGs) from patients undergoing sedation-analgesia, correlating with pain responses to stimuli.

Main Results:

• FuzEn-based RMSE showed similar performance to SampEn-based RMSE with long time series.
• FuzEn-based RMSE demonstrated superior consistency compared to SampEn-based RMSE with short time series, validated in simulations and EEG data.
• Significant differences in FuzEn metrics were observed based on data length and pain responses in patient EEGs.

Conclusions:

• FuzEn is a robust alternative to SampEn for RMSE, particularly advantageous for short time series analysis.
• FuzEn variants require careful consideration, especially for deterministic processes or long-scale nociception prediction.
• The study highlights FuzEn's potential for more reliable complexity assessment in physiological data.