Cascade of nonlinear entropy and statistics to discriminate fetal heart rates

Fetal heart rate discrimination is an evolving field in biomedical engineering with many efforts dedicated to avoid preterm deliveries by way of improving fetus monitoring methods and devices. Entropy analysis is a nonlinear signal analysis technique that has been progressively developed to improve the discriminability of a several physiological signals, with Kernel based entropy parameters (KBEPs) found advantageous over standard techniques. This study is the first to apply KBEPs to analyze fetal heart rates. Specifically, it explores the usability of the cutting-edge nonlinear KBEPs in discriminating between healthy fetuses and fetuses under distress. The database used in this study comprises 50 healthy and 50 distressed fetal heart rate signals with severe intrauterine growth restriction. The Cascade analysis investigates six kernel based entropy measures on fetal heart rates discrimination, and compares them to four standard entropies. The study presents a statistical evaluation of the discrimination power of each parameter (paired t-test statistics and distribution spread). Simulation results showed that the distribution ranges in 80% of the entropy parameters in the distressed heart group are higher than those in the healthy control group. Moreover, the results show that it is advantageous to choose Circular entropy then Cauchy entropy (p <; 0.001) over the standard techniques, in order to discriminate fetal heart rates.

I. Introduction

Nonlinear and statistical analysis of Fetal Heart Rate (FHR) is crucial for evaluating the fetal condition. Despite the widespread use of electronic FHR monitoring, its effect on decreasing the risk of fetal mortality has not been fully established [1]–[3]. To reduce inter- and intra- observer variability of visual analysis, computerized analysis was developed, but it did not result in significant clinical improvement [2]. Accordingly, there have been many efforts to develop new monitoring methods to provide an automatic differentiation between healthy and distressed fetal conditions [4]. In 2006, the identification of risky conditions during pregnancy was thought to be open to univariate analysis, multivariate or to both to determine the potential of FHR in screening for distressed fetuses [5]. Later, Ferrario et al. considered multiparametric approaches which improved the identification of risky conditions specifically in Fetal Heart Variability (FHV) [6]. Entropy quantification was used for such discrimination and for prediction purposes. Entropy analysis measures the correction and persistence of a signal in a nonlinear mathematical approach to quantify the irregularity or disorder and complexity of a system [7]–[13]. Ferrario et al have used both approximate entropy and sample entropy, Ferrario et al have also used ANOVA test [6]. In 2013, Liu et al. have used different entropy measures including the Approximate entropy (ApEn), Sample entropy (SamEn), fuzzy entropy and multi-scale Fuzzy entropy to discriminate between healthy fetuses and fetuses with heart failure [14]. Later, these methods have also been used by Lim et la. to discriminate between healthy, severe intrauterine growth restricted fetuses and non severe intrauterine growth restricted fetuses [4]. In 2015, Mekyska et al. used cutting edge kernel based entropy parameters (KBEPs) in speech signal processing [15], and Zaylaa et al. applied few of these parameters to Electroencephalogram (EEG) [10]. However, according to our literature research kernel-based entropy parameters were not applied on FHR discrimination.