n-Order and maximum fuzzy similarity entropy for discrimination of signals of different complexity: Application to fetal heart rate signals

Abstract

This paper presents two new concepts for discrimination of signals of different complexity. The first focused initially on solving the problem of setting entropy descriptors by varying the pattern size instead of the tolerance. This led to the search for the optimal pattern size that maximized the similarity entropy. The second paradigm was based on the n-order similarity entropy that encompasses the 1-order similarity entropy. To improve the statistical stability, n-order fuzzy similarity entropy was proposed. Fractional Brownian motion was simulated to validate the different methods proposed, and fetal heart rate signals were used to discriminate normal from abnormal fetuses. In all cases, it was found that it was possible to discriminate time series of different complexity such as fractional Brownian motion and fetal heart rate signals. The best levels of performance in terms of sensitivity (90%) and specificity (90%) were obtained with the n-order fuzzy similarity entropy. However, it was shown that the optimal pattern size and the maximum similarity measurement were related to intrinsic features of the time series.

Complexity analysis of fetal heart rate preceding intrauterine demise

“…Whether the pathophysiology involves a decline in complexity over time or a failure to achieve a gestation-age-appropriate level of complexity could not be determined from the limited number of subjects. Our findings do support previous studies, 3,7–11 indicating that fetal maturation and well-being correlate with increased fetal heart rate complexity.…”

“…7 The complexity over the two hours prior to delivery was significantly lower for acidemic fetuses than for non-acidemic fetuses. Other studies 6, 8–11 also support the use of entropy-based complexity measures in assessing fetal health status during gestation and labor.…”

“…One promising approach expands the analysis of FHR time series by using measures derived from dynamical systems theory, also called nonlinear dynamics or complexity science. 6–11 …”

“…6–11 Biologic complexity arises from the interaction of myriad physiologic processes and regulatory feedback loops that operate over a wide range of temporal and spatial scales, enabling the organism to adapt to the stresses of everyday life. 13–16 Complexity and variability are two distinct concepts.…”

Advanced Discrimination between Healthy and Intrauterine Growth Restricted Fetuses by Unbiased Recurrence Plots

“…Some of these tools were quantitative, such as the entropy (En) analysis and types including, but not limited to, the approximated entropy, sample entropy, fuzzy entropy and recently n-order entropy [4,5,7,8,11]. Other methods were qualitative such as the Recurrence Plots (RPs) and their corresponding Recurrence Quantification Analysis (RQA) [2,3,10].…”