Mathematical tools for identifying the fetal response to physical exercise during pregnancy

In the applied mathematics literature there exist a significant number of tools that can reveal the interaction between mother and fetus during rest and also during and after exercise. These tools are based on techniques from a number of areas such as signal processing, time series analysis, neural networks, heart rate variability as well as dynamical systems and chaos. We will briefly review here some of these methods, concentrating on a method of extracting the fetal heart rate from the mixed maternal-fetal heart rate signal, that is based on phase space reconstructio

Efficient fetal-maternal ECG signal separation from two channel maternal abdominal ECG via diffusion-based channel selection

There is a need for affordable, widely deployable maternal-fetal ECG monitors to improve maternal and fetal health during pregnancy and delivery. Based on the diffusion-based channel selection, here we present the mathematical formalism and clinical validation of an algorithm capable of accurate separation of maternal and fetal ECG from a two channel signal acquired over maternal abdomen

Least Dependent Component Analysis Based on Mutual Information

We propose to use precise estimators of mutual information (MI) to find least dependent components in a linearly mixed signal. On the one hand this seems to lead to better blind source separation than with any other presently available algorithm. On the other hand it has the advantage, compared to other implementations of `independent' component analysis (ICA) some of which are based on crude approximations for MI, that the numerical values of the MI can be used for: (i) estimating residual dependencies between the output components; (ii) estimating the reliability of the output, by comparing the pairwise MIs with those of re-mixed components; (iii) clustering the output according to the residual interdependencies. For the MI estimator we use a recently proposed k-nearest neighbor based algorithm. For time sequences we combine this with delay embedding, in order to take into account non-trivial time correlations. After several tests with artificial data, we apply the resulting MILCA (Mutual Information based Least dependent Component Analysis) algorithm to a real-world dataset, the ECG of a pregnant woman. The software implementation of the MILCA algorithm is freely available at http://www.fz-juelich.de/nic/cs/softwareComment: 18 pages, 20 figures, Phys. Rev. E (in press

Improving Maternal and Fetal Cardiac Monitoring Using Artificial Intelligence

Early diagnosis of possible risks in the physiological status of fetus and mother during pregnancy and delivery is critical and can reduce mortality and morbidity. For example, early detection of life-threatening congenital heart disease may increase survival rate and reduce morbidity while allowing parents to make informed decisions. To study cardiac function, a variety of signals are required to be collected. In practice, several heart monitoring methods, such as electrocardiogram (ECG) and photoplethysmography (PPG), are commonly performed. Although there are several methods for monitoring fetal and maternal health, research is currently underway to enhance the mobility, accuracy, automation, and noise resistance of these methods to be used extensively, even at home. Artificial Intelligence (AI) can help to design a precise and convenient monitoring system. To achieve the goals, the following objectives are defined in this research: The first step for a signal acquisition system is to obtain high-quality signals. As the first objective, a signal processing scheme is explored to improve the signal-to-noise ratio (SNR) of signals and extract the desired signal from a noisy one with negative SNR (i.e., power of noise is greater than signal). It is worth mentioning that ECG and PPG signals are sensitive to noise from a variety of sources, increasing the risk of misunderstanding and interfering with the diagnostic process. The noises typically arise from power line interference, white noise, electrode contact noise, muscle contraction, baseline wandering, instrument noise, motion artifacts, electrosurgical noise. Even a slight variation in the obtained ECG waveform can impair the understanding of the patient's heart condition and affect the treatment procedure. Recent solutions, such as adaptive and blind source separation (BSS) algorithms, still have drawbacks, such as the need for noise or desired signal model, tuning and calibration, and inefficiency when dealing with excessively noisy signals. Therefore, the final goal of this step is to develop a robust algorithm that can estimate noise, even when SNR is negative, using the BSS method and remove it based on an adaptive filter. The second objective is defined for monitoring maternal and fetal ECG. Previous methods that were non-invasive used maternal abdominal ECG (MECG) for extracting fetal ECG (FECG). These methods need to be calibrated to generalize well. In other words, for each new subject, a calibration with a trustable device is required, which makes it difficult and time-consuming. The calibration is also susceptible to errors. We explore deep learning (DL) models for domain mapping, such as Cycle-Consistent Adversarial Networks, to map MECG to fetal ECG (FECG) and vice versa. The advantages of the proposed DL method over state-of-the-art approaches, such as adaptive filters or blind source separation, are that the proposed method is generalized well on unseen subjects. Moreover, it does not need calibration and is not sensitive to the heart rate variability of mother and fetal; it can also handle low signal-to-noise ratio (SNR) conditions. Thirdly, AI-based system that can measure continuous systolic blood pressure (SBP) and diastolic blood pressure (DBP) with minimum electrode requirements is explored. The most common method of measuring blood pressure is using cuff-based equipment, which cannot monitor blood pressure continuously, requires calibration, and is difficult to use. Other solutions use a synchronized ECG and PPG combination, which is still inconvenient and challenging to synchronize. The proposed method overcomes those issues and only uses PPG signal, comparing to other solutions. Using only PPG for blood pressure is more convenient since it is only one electrode on the finger where its acquisition is more resilient against error due to movement. The fourth objective is to detect anomalies on FECG data. The requirement of thousands of manually annotated samples is a concern for state-of-the-art detection systems, especially for fetal ECG (FECG), where there are few publicly available FECG datasets annotated for each FECG beat. Therefore, we will utilize active learning and transfer-learning concept to train a FECG anomaly detection system with the least training samples and high accuracy. In this part, a model is trained for detecting ECG anomalies in adults. Later this model is trained to detect anomalies on FECG. We only select more influential samples from the training set for training, which leads to training with the least effort. Because of physician shortages and rural geography, pregnant women's ability to get prenatal care might be improved through remote monitoring, especially when access to prenatal care is limited. Increased compliance with prenatal treatment and linked care amongst various providers are two possible benefits of remote monitoring. If recorded signals are transmitted correctly, maternal and fetal remote monitoring can be effective. Therefore, the last objective is to design a compression algorithm that can compress signals (like ECG) with a higher ratio than state-of-the-art and perform decompression fast without distortion. The proposed compression is fast thanks to the time domain B-Spline approach, and compressed data can be used for visualization and monitoring without decompression owing to the B-spline properties. Moreover, the stochastic optimization is designed to retain the signal quality and does not distort signal for diagnosis purposes while having a high compression ratio. In summary, components for creating an end-to-end system for day-to-day maternal and fetal cardiac monitoring can be envisioned as a mix of all tasks listed above. PPG and ECG recorded from the mother can be denoised using deconvolution strategy. Then, compression can be employed for transmitting signal. The trained CycleGAN model can be used for extracting FECG from MECG. Then, trained model using active transfer learning can detect anomaly on both MECG and FECG. Simultaneously, maternal BP is retrieved from the PPG signal. This information can be used for monitoring the cardiac status of mother and fetus, and also can be used for filling reports such as partogram

Extraction and Detection of Fetal Electrocardiograms from Abdominal Recordings

The non-invasive fetal ECG (NIFECG), derived from abdominal surface electrodes, offers novel diagnostic possibilities for prenatal medicine. Despite its straightforward applicability, NIFECG signals are usually corrupted by many interfering sources. Most significantly, by the maternal ECG (MECG), whose amplitude usually exceeds that of the fetal ECG (FECG) by multiple times. The presence of additional noise sources (e.g. muscular/uterine noise, electrode motion, etc.) further affects the signal-to-noise ratio (SNR) of the FECG. These interfering sources, which typically show a strong non-stationary behavior, render the FECG extraction and fetal QRS (FQRS) detection demanding signal processing tasks. In this thesis, several of the challenges regarding NIFECG signal analysis were addressed. In order to improve NIFECG extraction, the dynamic model of a Kalman filter approach was extended, thus, providing a more adequate representation of the mixture of FECG, MECG, and noise. In addition, aiming at the FECG signal quality assessment, novel metrics were proposed and evaluated. Further, these quality metrics were applied in improving FQRS detection and fetal heart rate estimation based on an innovative evolutionary algorithm and Kalman filtering signal fusion, respectively. The elaborated methods were characterized in depth using both simulated and clinical data, produced throughout this thesis. To stress-test extraction algorithms under ideal circumstances, a comprehensive benchmark protocol was created and contributed to an extensively improved NIFECG simulation toolbox. The developed toolbox and a large simulated dataset were released under an open-source license, allowing researchers to compare results in a reproducible manner. Furthermore, to validate the developed approaches under more realistic and challenging situations, a clinical trial was performed in collaboration with the University Hospital of Leipzig. Aside from serving as a test set for the developed algorithms, the clinical trial enabled an exploratory research. This enables a better understanding about the pathophysiological variables and measurement setup configurations that lead to changes in the abdominal signal's SNR. With such broad scope, this dissertation addresses many of the current aspects of NIFECG analysis and provides future suggestions to establish NIFECG in clinical settings.:Abstract Acknowledgment Contents List of Figures List of Tables List of Abbreviations List of Symbols (1)Introduction 1.1)Background and Motivation 1.2)Aim of this Work 1.3)Dissertation Outline 1.4)Collaborators and Conflicts of Interest (2)Clinical Background 2.1)Physiology 2.1.1)Changes in the maternal circulatory system 2.1.2)Intrauterine structures and feto-maternal connection 2.1.3)Fetal growth and presentation 2.1.4)Fetal circulatory system 2.1.5)Fetal autonomic nervous system 2.1.6)Fetal heart activity and underlying factors 2.2)Pathology 2.2.1)Premature rupture of membrane 2.2.2)Intrauterine growth restriction 2.2.3)Fetal anemia 2.3)Interpretation of Fetal Heart Activity 2.3.1)Summary of clinical studies on FHR/FHRV 2.3.2)Summary of studies on heart conduction 2.4)Chapter Summary (3)Technical State of the Art 3.1)Prenatal Diagnostic and Measuring Technique 3.1.1)Fetal heart monitoring 3.1.2)Related metrics 3.2)Non-Invasive Fetal ECG Acquisition 3.2.1)Overview 3.2.2)Commercial equipment 3.2.3)Electrode configurations 3.2.4)Available NIFECG databases 3.2.5)Validity and usability of the non-invasive fetal ECG 3.3)Non-Invasive Fetal ECG Extraction Methods 3.3.1)Overview on the non-invasive fetal ECG extraction methods 3.3.2)Kalman filtering basics 3.3.3)Nonlinear Kalman filtering 3.3.4)Extended Kalman filter for FECG estimation 3.4)Fetal QRS Detection 3.4.1)Merging multichannel fetal QRS detections 3.4.2)Detection performance 3.5)Fetal Heart Rate Estimation 3.5.1)Preprocessing the fetal heart rate 3.5.2)Fetal heart rate statistics 3.6)Fetal ECG Morphological Analysis 3.7)Problem Description 3.8)Chapter Summary (4)Novel Approaches for Fetal ECG Analysis 4.1)Preliminary Considerations 4.2)Fetal ECG Extraction by means of Kalman Filtering 4.2.1)Optimized Gaussian approximation 4.2.2)Time-varying covariance matrices 4.2.3)Extended Kalman filter with unknown inputs 4.2.4)Filter calibration 4.3)Accurate Fetal QRS and Heart Rate Detection 4.3.1)Multichannel evolutionary QRS correction 4.3.2)Multichannel fetal heart rate estimation using Kalman filters 4.4)Chapter Summary (5)Data Material 5.1)Simulated Data 5.1.1)The FECG Synthetic Generator (FECGSYN) 5.1.2)The FECG Synthetic Database (FECGSYNDB) 5.2)Clinical Data 5.2.1)Clinical NIFECG recording 5.2.2)Scope and limitations of this study 5.2.3)Data annotation: signal quality and fetal amplitude 5.2.4)Data annotation: fetal QRS annotation 5.3)Chapter Summary (6)Results for Data Analysis 6.1)Simulated Data 6.1.1)Fetal QRS detection 6.1.2)Morphological analysis 6.2)Own Clinical Data 6.2.1)FQRS correction using the evolutionary algorithm 6.2.2)FHR correction by means of Kalman filtering (7)Discussion and Prospective 7.1)Data Availability 7.1.1)New measurement protocol 7.2)Signal Quality 7.3)Extraction Methods 7.4)FQRS and FHR Correction Algorithms (8)Conclusion References (A)Appendix A - Signal Quality Annotation (B)Appendix B - Fetal QRS Annotation (C)Appendix C - Data Recording GU

Spatiotemporal Sparse Bayesian Learning with Applications to Compressed Sensing of Multichannel Physiological Signals

Energy consumption is an important issue in continuous wireless telemonitoring of physiological signals. Compressed sensing (CS) is a promising framework to address it, due to its energy-efficient data compression procedure. However, most CS algorithms have difficulty in data recovery due to non-sparsity characteristic of many physiological signals. Block sparse Bayesian learning (BSBL) is an effective approach to recover such signals with satisfactory recovery quality. However, it is time-consuming in recovering multichannel signals, since its computational load almost linearly increases with the number of channels. This work proposes a spatiotemporal sparse Bayesian learning algorithm to recover multichannel signals simultaneously. It not only exploits temporal correlation within each channel signal, but also exploits inter-channel correlation among different channel signals. Furthermore, its computational load is not significantly affected by the number of channels. The proposed algorithm was applied to brain computer interface (BCI) and EEG-based driver's drowsiness estimation. Results showed that the algorithm had both better recovery performance and much higher speed than BSBL. Particularly, the proposed algorithm ensured that the BCI classification and the drowsiness estimation had little degradation even when data were compressed by 80%, making it very suitable for continuous wireless telemonitoring of multichannel signals.Comment: Codes are available at: https://sites.google.com/site/researchbyzhang/stsb

Constrained independent component analysis for non-obtrusive pulse rate measurements using a webcam

Assessment of cardiac function of a patient is very important for understanding a patient\u27s physiological state. Remote measurements of the cardiac pulse can provide comfortable physiological assessment by minimizing the amount of wires and cables and allowing for near continuous measurements. It has been found that state-of-the-art algorithms based on independent component analysis (ICA) suffer from a sorting problem which hinders their performance. This effect is demonstrated in this work. The automated pulse detection techniques are applied to RGB color video recordings of the facial region of a person being monitored for cardiac function in a remote sensing environment. Automated face tracking is employed to locate the region of interest and address motion artefacts. This work proposed and evaluates a novel algorithm based on constrained source separation, aka, constrained independent source separation (cICA) to accurately estimate the pulse rate of a patient by solving the sorting problem observed in the ICA based approach. The constrained optimization problem incorporates prior information and additional requirements in the form of constraints. A reference signal with a single tone frequency corresponding to a possible heart rate is fed to the cICA algorithm. This forces the output signal to match the reference signal embodying prior knowledge about an underlying IC. It is also shown that with this algorithm a near photoplethysmography (PPG) signal corresponding to the variations in blood volume in the body can be extracted. An IRB approved study encompassing 45 subjects resulted in Bland-Altman analysis with an FDA-approved finger blood volume pulse (BVP) sensor demonstrating that the proposed algorithm provides significantly improved accuracy