Refined Composite Multiscale Dispersion Entropy and its Application to Biomedical Signals (1606.01379v3)

Abstract: Multiscale entropy (MSE) is a widely-used tool to analyze biomedical signals. It was proposed to overcome the deficiencies of conventional entropy methods when quantifying the complexity of time series. However, MSE is undefined for very short signals and slow for real-time applications because of the use of sample entropy (SampEn). To overcome these shortcomings, we introduce multiscale dispersion entropy (DisEn - MDE) as a very fast and powerful method to quantify the complexity of signals. MDE is based on our recently developed DisEn, which has a computation cost of O(N), compared with O(N2) for SampEn. We also propose the refined composite MDE (RCMDE) to improve the stability of MDE. We evaluate MDE, RCMDE, and refined composite MSE (RCMSE) on synthetic signals and find that these methods have similar behaviors but the MDE and RCMDE are significantly faster than MSE and RCMSE, respectively. The results also illustrate that RCMDE is more stable than MDE for short and noisy signals, which are common in biomedical applications. To evaluate the proposed methods on real signals, we employ three biomedical datasets, including focal and non-focal electroencephalograms (EEGs), blood pressure recordings in Fantasia database, and resting-state EEGs activity in Alzheimer's disease (AD). The results again demonstrate a similar behavior of RCMSE, MDE and RCMDE, although the RCMDE and MDE are significantly faster and lead to larger differences between physiological conditions known to alter the complexity of the physiological recordings. To sum up, MDE and RCMDE are expected to be useful for the analysis of physiological signals thanks to their ability to distinguish different types of dynamics.

• The paper introduces Refined Composite Multiscale Dispersion Entropy (RCMDE), a novel complexity measure designed for robust and efficient analysis of biomedical signals, improving upon existing methods.
• RCMDE enhances computational efficiency (O(N) vs O(N^2)) and stability, especially for short or noisy signals, by averaging results from multiple coarse-grained time series at each scale.
• Evaluations show RCMDE effectively differentiates various physiological states in EEG and blood pressure data while demonstrating robustness against noise in synthetic signals.

Refined Composite Multiscale Dispersion Entropy and its Application to Biomedical Signals

The manuscript introduces a novel complexity measure, Multiscale Dispersion Entropy (MDE), and its refined version, Refined Composite Multiscale Dispersion Entropy (RCMDE), enhancing upon traditional Multiscale Entropy (MSE) for analyzing biomedical signals. The key motivation is to address the computational inefficiencies and instability of MSE, particularly with short signals, while offering a robust real-time tool that maintains discriminative power across different physiological and synthetic datasets.

Methodological Innovations

Dispersion entropy (DisEn) is foundational to MDE, offering a computational advantage over sample entropy (SampEn) by reducing the computation cost from $O(N^2)$ to $O(N)$. This efficiency is crucial for real-time applications and processing long signals. MDE extends DisEn across multiple temporal scales, maintaining the normal cumulative distribution function (NCDF) to overcome limitations in traditional methods where entropy values become undefined in short signals.

RCMDE further stabilizes MDE by generating multiple coarse-grained time series at each scale factor and averaging the results. This compositing method resolves issues associated with the original RCMSE, where entropy measurements can fluctuate significantly with noise and signal length, presenting undefined values in shorter datasets.

Evaluation and Results

The robustness and efficiency of MDE and RCMDE are evaluated on synthetic time series (including white Gaussian noise and $1/f$ noise) and biomedical datasets such as EEG recordings and blood pressure measurements. The computational efficiency of MDE and RCMDE demonstrates significant advantages over MSE and RCMSE, with the computation time noticeably reduced as signals increase in length.

RCMDE consistently exhibits more stable results across various noise conditions and outperforms MDE in synthetic signal tests by maintaining coherence in the presence of noise. In biomedical applications, both MDE and RCMDE are employed to differentiate pathological states from normal physiological signals, successfully distinguishing between focal and non-focal brain signals, age-related changes in blood pressure data, and EEG alterations associated with Alzheimer's disease.

Implications and Future Directions

The introduction of MDE and RCMDE has direct implications for biomedical signal analysis, offering a blend of computational efficiency and robust complexity analysis. Their ability to provide stable, reliable entropy measurements across multiple scales without undefined values makes them well-suited for real-time monitoring and diagnostics.

In future research, there is potential to extend these methods to multivariate contexts. The proposed Multivariate MDE (mvMDE) and its refined versions would consider channel interdependencies in multivariate time series data, broadening applicability to complex physiological datasets, where signals are interlinked across different channels or modalities.

In summary, MDE and RCMDE offer significant improvements over existing entropy-based metrics, with substantial benefits for both theoretical explorations and practical applications in the analysis of biomedical time series. They pave the way for future research in entropy-based complexity estimations, both enhancing existing frameworks and expanding understanding in new domains.