Cardiotocography analysis by empirical dynamic modeling and Gaussian processes

Abstract

Introduction: During labor, fetal heart rate (FHR) and uterine activity (UA) can be continuously monitored using Cardiotocography (CTG). This is the most widely adopted approach for electronic fetal monitoring in hospitals. Both FHR and UA recordings are evaluated by obstetricians for assessing fetal well-being. Due to the complex and noisy nature of these recordings, the evaluation by obstetricians suffers from high interobserver and intraobserver variability. Machine learning is a field that has seen unprecedented advances in the past two decades and many efforts have been made in computerized analysis of CTG using machine learning methods. However, in the literature, the focus is often only on FHR signals unlike in evaluations performed by obstetricians where the UA signals are also taken into account. Methods: Machine learning is a field that has seen unprecedented advances in the past two decades and many efforts have been made in computerized analysis of CTG using machine learning methods. However, in the literature, the focus is often only on FHR signals unlike in evaluations performed by obstetricians where the UA signals are also taken into account. In this paper, we propose to model intrapartum CTG recordings from a dynamical system perspective using empirical dynamic modeling with Gaussian processes, which is a Bayesian nonparametric approach for estimation of functions. Results and Discussion: In the context of our paper, Gaussian processes are capable for simultaneous estimation of the dimensionality of attractor manifolds and reconstructing of attractor manifolds from time series data. This capacity of Gaussian processes allows for revealing causal relationships between the studied time series. Experimental results on real CTG recordings show that FHR and UA signals are causally related. More importantly, this causal relationship and estimated attractor manifolds can be exploited for several important applications in computerized analysis of CTG recordings including estimating missing FHR samples, recovering burst errors in FHR tracings and characterizing the interactions between FHR and UA signals.

Keywords: attractor manifold; cardiotocography; empirical dynamic modelling; fetal heart rate; uterine activity.

FIGURE 1

A segment of CTG recording from an open access intrapartum CTG database [described in (Chudáček et al., 2014)] in US (top two plots) and in EU (bottom two plots) paper formats, respectively.

FIGURE 2

The underlying latent Lorenz attractor (left) generated in the toy example and its projection on the X-axis (right).

FIGURE 3

The reconstructed Lorenz attractor from X(t) using GP-based approach (top) and ARD weights of learned latent dimensions (bottom). The number of dimensions with non-zero ARD weights is three, which is the true dimension of the Lorenz attractor. The GP-based approach is capable of learning the dimension of the latent attractor from data in an automated manner.

FIGURE 4

Raw FHR and UA segments (top), and their corresponding reconstructed attractor manifolds with the GP-based method (bottom).

FIGURE 5

The correlation matrix of features and umbilical artery pH, computed with 552 CTG recordings in an open access CTG database described in Chudáček et al. (2014). The correlation coefficient between $H(M_{\text{FHR}}^{\text{GP}},M_{\text{UA}}^{\text{GP}})$ , denoted as HD, and pH is comparable with popular features such as STV, LTV and LF. Meanwhile $H(M_{\text{FHR}}^{\text{GP}},M_{\text{UA}}^{\text{GP}})$ is not highly correlated with other FHR features.

FIGURE 6

The two CTG segments, i.e., FHR (top) and UA (bottom) recordings, used for estimating of random missing samples in FHR.

FIGURE 7

Experimental results of estimating random missing samples in FHR: The experiment results for the first CTG segment (left), and the experiment results for the second CTG segment (right). The MSE (upper plot, in logarithmic scale) and SNR (bottom plot) of each method under different percentages of missing samples are presented, averaged over 100 experiments.