IMPROVING PHASE-RECTIFIED SIGNAL AVERAGING FOR FETAL HEART RATE ANALYSIS.

Low umbilical artery pH is a marker for neonatal acidosis and is associated with an increased risk for neonatal complications. The phase-rectified signal averaging (PRSA) features have demonstrated superior discriminatory or diagnostic ability and good interpretability in many biomedical applications including fetal heart rate analysis. However, the performance of PRSA method is sensitive to values of the selected parameters which are usually either chosen based on a grid search or empirically in the literature. In this paper, we examine PRSA method through the lens of dynamical systems theory and reveal the intrinsic connection between state space reconstruction and PRSA. From this perspective, we then introduce a new feature that can better characterize dynamical systems comparing with PRSA. Our experimental results on an open-access intrapartum Cardiotocography database demonstrate that the proposed feature outperforms state-of-the-art PRSA features in pH-based fetal heart rate analysis.

Cardiotocography analysis by empirical dynamic modeling and Gaussian processes.

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.

Electrocorticography reveals thalamic control of cortical dynamics following traumatic brain injury.

The return of consciousness after traumatic brain injury (TBI) is associated with restoring complex cortical dynamics; however, it is unclear what interactions govern these complex dynamics. Here, we set out to uncover the mechanism underlying the return of consciousness by measuring local field potentials (LFP) using invasive electrophysiological recordings in patients recovering from TBI. We found that injury to the thalamus, and its efferent projections, on MRI were associated with repetitive and low complexity LFP signals from a highly structured phase space, resembling a low-dimensional ring attractor. But why do thalamic injuries in TBI patients result in a cortical attractor? We built a simplified thalamocortical model, which connotes that thalamic input facilitates the formation of cortical ensembles required for the return of cognitive function and the content of consciousness. These observations collectively support the view that thalamic input to the cortex enables rich cortical dynamics associated with consciousness.

Exploiting Causality for Improved Prediction of Patient Volumes by Gaussian Processes.

Estimating and surveillance volumes of patients are of great importance for public health and resource allocation. In many situations, the change of these volumes is correlated with many factors, e.g., seasonal environmental variables, medicine sales, and patient medical claims. It is often of interest to predict patient volumes and to that end, discovering causalities can improve the prediction accuracy. Correlations do not imply causations and they can be spurious, which in turn may entail deterioration of prediction performance if the prediction is based on them. By contrast, in this paper, we propose an approach for prediction based on causalities discovered by Gaussian processes. Our interest is in estimating volumes of patients that suffer from allergy and where the model and the results are highly interpretable. In selecting features, instead of only using correlation, we take causal information into account. Specifically, we adopt the Gaussian processes-based convergent cross mapping framework for causal discovery which is proven to be more reliable than the Granger causality when time series are coupled. Moreover, we introduce a novel method for selecting the history or look-back length of features from the perspective of a dynamical system in a principled manner. The quasi-periodicities that commonly exist in observations of volumes of patients and environment variables can readily be accommodated. Further, the proposed method performs well even in cases when the data are scarce. Also, the approach can be modified without much difficulty to forecast other types of patient volumes. We validate the method with synthetic and real-world datasets.

Estimation of Consecutively Missed Samples in Fetal Heart Rate Recordings.

During labor, fetal heart rate (FHR) is monitored externally using Doppler ultrasound. This is done continuously, but for various reasons (e.g., fetal or maternal movements) the system does not record any samples for varying periods of time. In many settings, it would be quite beneficial to estimate the missing samples. In this paper, we propose a (deep) Gaussian process-based approach for estimation of consecutively missing samples in FHR recordings. The method relies on similarities in the state space and on exploiting the concept of attractor manifolds. The proposed approach was tested on a short segment of real FHR recordings. The experimental results indicate that the proposed approach is able to provide more reliable results in comparison to several interpolation methods that are commonly applied for processing of FHR signals.

DISCOVERING CAUSALITIES FROM CARDIOTOCOGRAPHY SIGNALS USING IMPROVED CONVERGENT CROSS MAPPING WITH GAUSSIAN PROCESSES.

Convergent cross mapping (CCM) is designed for causal discovery in coupled time series, where Granger causality may not be applicable because of a separability assumption. However, CCM is not robust to observation noise which limits its applicability on signals that are known to be noisy. Moreover, the parameters for state space reconstruction need to be selected using grid search methods. In this paper, we propose a novel improved version of CCM using Gaussian processes for discovery of causality from noisy time series. Specifically, we adopt the concept of CCM and carry out the key steps using Gaussian processes within a non-parametric Bayesian probabilistic framework in a principled manner. The proposed approach is first validated on simulated data, and then used for understanding the interaction between fetal heart rate and uterine activity in the last two hours before delivery and of interest in obstetrics. Our results indicate that uterine activity affects the fetal heart rate, which agrees with recent clinical studies.

Detecting Causality using Deep Gaussian Processes.

Convergent cross mapping (CCM) is a state space reconstruction (SSR)-based method designed for causal discovery in coupled time series, where Granger causality may not be applicable due to a separability assumption. However, CCM requires a large number of observations and is not robust to observation noise which limits its applicability. Moreover, in CCM and its variants, the SSR step is mostly implemented with delay embedding where the parameters for reconstruction usually need to be selected using grid search-based methods. In this paper, we propose a Bayesian version of CCM using deep Gaussian processes (DGPs), which are naturally connected with deep neural networks. In particular, we adopt the framework of SSR-based causal discovery and carry out the key steps using DGPs within a non-parametric Bayesian probabilistic framework in a principled manner. The proposed approach is first validated on simulated data and then tested on data used in obstetrics for monitoring the well-being of fetuses, i.e., fetal heart rate (FHR) and uterine activity (UA) signals in the last two hours before delivery. Our results indicate that UA affects the FHR, which agrees with recent clinical studies.

EXTRACTING INTERPRETABLE FEATURES FOR FETAL HEART RATE RECORDINGS WITH GAUSSIAN PROCESSES.

During labor, fetal heart rate (FHR) and uterine activity (UA) are continuously monitored with Cardiotocography (CTG). The FHR and UA signals are visually inspected by obstetricians to assess the fetal well-being. However, due to the subjectivity of the visual inspection, the evaluations of CTG recordings performed by obstetricians have high inter- and intra-variability. The computerized analysis of FHR relies on features either hand-crafted by experts or automatically learned by machine learning methods. However, the popular interpretable FHR features, in general, have low correlation with the pH value of the umbilical cord blood at birth, which is the current gold standard for labeling FHRs in the computerized analysis of FHRs. The features found by machine learning methods, by contrast, usually have limited interpretability. In this paper, in a follow up of our previous work on FHR analysis using Gaussian processes (GPs), we explore the possibility of using the hyperparameters of GPs as interpretable features. Our results indicate that some GP features achieve high correlation with the pH values, while at the same time they are not highly correlated with other popular features.

INFERENCE ABOUT CAUSALITY FROM CARDIOTOCOGRAPHY SIGNALS USING GAUSSIAN PROCESSES.

In this paper, we propose a novel and simple method for discovery of Granger causality from noisy time series using Gaussian processes. More specifically, we adopt the concept of Granger causality, but instead of using autoregressive models for establishing it, we work with Gaussian processes. We show that information about the Granger causality is encoded in the hyper-parameters of the used Gaussian processes. The proposed approach is first validated on simulated data, and then used for understanding the interaction between fetal heart rate and uterine activity in the last two hours before delivery and of interest in obstetrics. Our results indicate that uterine activity affects fetal heart rate, which agrees with recent clinical studies.