Nonlinear projective filtering I: Application to real time series

We discuss applications of nonlinear filtering of time series by locally linear phase space projections. Noise can be reduced whenever the error due to the manifold approximation is smaller than the noise in the system. Examples include the real time extraction of the fetal electrocardiogram from abdominal recordings.Comment: 4 pages, PS figures, needs nolta.st

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

A Machine Learning Approach to Monitor the Emergence of Late Intrauterine Growth Restriction

Late intrauterine growth restriction (IUGR) is a fetal pathological condition characterized by chronic hypoxia secondary to placental insufficiency, resulting in an abnormal rate of fetal growth. This pathology has been associated with increased fetal and neonatal morbidity and mortality. In standard clinical practice, late IUGR diagnosis can only be suspected in the third trimester and ultimately confirmed at birth. This study presents a radial basis function support vector machine (RBF-SVM) classification based on quantitative features extracted from fetal heart rate (FHR) signals acquired using routine cardiotocography (CTG) in a population of 160 healthy and 102 late IUGR fetuses. First, the individual performance of each time, frequency, and nonlinear feature was tested. To improve the unsatisfactory results of univariate analysis we firstly adopted a Recursive Feature Elimination approach to select the best subset of FHR-based parameters contributing to the discrimination of healthy vs. late IUGR fetuses. A fine tuning of the RBF-SVM model parameters resulted in a satisfactory classification performance in the training set (accuracy 0.93, sensitivity 0.93, specificity 0.84). Comparable results were obtained when applying the model on a totally independent testing set. This investigation supports the use of a multivariate approach for the in utero identification of late IUGR condition based on quantitative FHR features encompassing different domains. The proposed model allows describing the relationships among features beyond the traditional linear approaches, thus improving the classification performance. This framework has the potential to be proposed as a screening tool for the identification of late IUGR fetuses

Non-invasive fetal electrocardiogram : analysis and interpretation

High-risk pregnancies are becoming more and more prevalent because of the progressively higher age at which women get pregnant. Nowadays about twenty percent of all pregnancies are complicated to some degree, for instance because of preterm delivery, fetal oxygen deficiency, fetal growth restriction, or hypertension. Early detection of these complications is critical to permit timely medical intervention, but is hampered by strong limitations of existing monitoring technology. This technology is either only applicable in hospital settings, is obtrusive, or is incapable of providing, in a robust way, reliable information for diagnosis of the well-being of the fetus. The most prominent method for monitoring of the fetal health condition is monitoring of heart rate variability in response to activity of the uterus (cardiotocography; CTG). Generally, in obstetrical practice, the heart rate is determined in either of two ways: unobtrusively with a (Doppler) ultrasound probe on the maternal abdomen, or obtrusively with an invasive electrode fixed onto the fetal scalp. The first method is relatively inaccurate but is non-invasive and applicable in all stages of pregnancy. The latter method is far more accurate but can only be applied following rupture of the membranes and sufficient dilatation, restricting its applicability to only the very last phase of pregnancy. Besides these accuracy and applicability issues, the use of CTG in obstetrical practice also has another limitation: despite its high sensitivity, the specificity of CTG is relatively low. This means that in most cases of fetal distress the CTG reveals specific patterns of heart rate variability, but that these specific patterns can also be encountered for healthy fetuses, complicating accurate diagnosis of the fetal condition. Hence, a prerequisite for preventing unnecessary interventions that are based on CTG alone, is the inclusion of additional information in diagnostics. Monitoring of the fetal electrocardiogram (ECG), as a supplement of CTG, has been demonstrated to have added value for monitoring of the fetal health condition. Unfortunately the application of the fetal ECG in obstetrical diagnostics is limited because at present the fetal ECG can only be measured reliably by means of an invasive scalp electrode. To overcome this limited applicability, many attempts have been made to record the fetal ECG non-invasively from the maternal abdomen, but these attempts have not yet led to approaches that permit widespread clinical application. One key difficulty is that the signal to noise ratio (SNR) of the transabdominal ECG recordings is relatively low. Perhaps even more importantly, the abdominal ECG recordings yield ECG signals for which the morphology depends strongly on the orientation of the fetus within the maternal uterus. Accordingly, for any fetal orientation, the ECG morphology is different. This renders correct clinical interpretation of the recorded ECG signals complicated, if not impossible. This thesis aims to address these difficulties and to provide new contributions on the clinical interpretation of the fetal ECG. At first the SNR of the recorded signals is enhanced through a series of signal processing steps that exploit specific and a priori known properties of the fetal ECG. More particularly, the dominant interference (i.e. the maternal ECG) is suppressed by exploiting the absence of temporal correlation between the maternal and fetal ECG. In this suppression, the maternal ECG complex is dynamically segmented into individual ECG waves and each of these waves is estimated through averaging corresponding waves from preceding ECG complexes. The maternal ECG template generated by combining the estimated waves is subsequently subtracted from the original signal to yield a non-invasive recording in which the maternal ECG has been suppressed. This suppression method is demonstrated to be more accurate than existing methods. Other interferences and noise are (partly) suppressed by exploiting the quasiperiodicity of the fetal ECG through averaging consecutive ECG complexes or by exploiting the spatial correlation of the ECG. The averaging of several consecutive ECG complexes, synchronized on their QRS complex, enhances the SNR of the ECG but also can suppress morphological variations in the ECG that are clinically relevant. The number of ECG complexes included in the average hence constitutes a trade-off between SNR enhancement on the one hand and loss of morphological variability on the other hand. To relax this trade-off, in this thesis a method is presented that can adaptively estimate the number of ECG complexes included in the average. In cases of morphological variations, this number is decreased ensuring that the variations are not suppressed. In cases of no morphological variability, this number is increased to ensure adequate SNR enhancement. The further suppression of noise by exploiting the spatial correlation of the ECG is based on the fact that all ECG signals recorded at several locations on the maternal abdomen originate from the same electrical source, namely the fetal heart. The electrical activity of the fetal heart at any point in time can be modeled as a single electrical field vector with stationary origin. This vector varies in both amplitude and orientation in three-dimensional space during the cardiac cycle and the time-path described by this vector is referred to as the fetal vectorcardiogram (VCG). In this model, the abdominal ECG constitutes the projection of the VCG onto the vector that describes the position of the abdominal electrode with respect to a reference electrode. This means that when the VCG is known, any desired ECG signal can be calculated. Equivalently, this also means that when enough ECG signals (i.e. at least three independent signals) are known, the VCG can be calculated. By using more than three ECG signals for the calculation of the VCG, redundancy in the ECG signals can be exploited for added noise suppression. Unfortunately, when calculating the fetal VCG from the ECG signals recorded from the maternal abdomen, the distance between the fetal heart and the electrodes is not the same for each electrode. Because the amplitude of the ECG signals decreases with propagation to the abdominal surface, these different distances yield a specific, unknown attenuation for each ECG signal. Existing methods for estimating the VCG operate with a fixed linear combination of the ECG signals and, hence, cannot account for variations in signal attenuation. To overcome this problem and be able to account for fetal movement, in this thesis a method is presented that estimates both the VCG and, to some extent, also the signal attenuation. This is done by determining for which VCG and signal attenuation the joint probability over both these variables is maximal given the observed ECG signals. The underlying joint probability distribution is determined by assuming the ECG signals to originate from scaled VCG projections and additive noise. With this method, a VCG, tailored to each specific patient, is determined. With respect to the fixed linear combinations, the presented method performs significantly better in the accurate estimation of the VCG. Besides describing the electrical activity of the fetal heart in three dimensions, the fetal VCG also provides a framework to account for the fetal orientation in the uterus. This framework enables the detection of the fetal orientation over time and allows for rotating the fetal VCG towards a prescribed orientation. From the normalized fetal VCG obtained in this manner, standardized ECG signals can be calculated, facilitating correct clinical interpretation of the non-invasive fetal ECG signals. The potential of the presented approach (i.e. the combination of all methods described above) is illustrated for three different clinical cases. In the first case, the fetal ECG is analyzed to demonstrate that the electrical behavior of the fetal heart differs significantly from the adult heart. In fact, this difference is so substantial that diagnostics based on the fetal ECG should be based on different guidelines than those for adult ECG diagnostics. In the second case, the fetal ECG is used to visualize the origin of fetal supraventricular extrasystoles and the results suggest that the fetal ECG might in future serve as diagnostic tool for relating fetal arrhythmia to congenital heart diseases. In the last case, the non-invasive fetal ECG is compared to the invasively recorded fetal ECG to gauge the SNR of the transabdominal recordings and to demonstrate the suitability of the non-invasive fetal ECG in clinical applications that, as yet, are only possible for the invasive fetal ECG