Assessment of Linear Inverse Problems in Magnetocardiography and Lorentz Force Eddy Current Testing

Lineare inverse Probleme tauchen in vielen Bereichen von Wissenschaft und Technik auf. Effiziente Lösungsstrategien für diese inversen Probleme erfordern Informationen darüber, ob das Problem schlecht-gestellt und in welchem Ausmaß dies der Fall ist. In der vorliegenden Dissertation wird eine umfassende theoretische Analyse existierender Bewertungsmaße durchgeführt. Aus diesen Untersuchungen werden schließlich zwei neue Bewertungsmaße abgeleitet. Beide können bei einer Vielzahl linearer inverser Probleme angewendet werden, einschließlich biomedizinische Anwendungen oder der zerstörungsfreien Materialprüfung. Die theoretischen Betrachtungen zur Behandlung linearer inverser Probleme werden auf zwei Beispiele angewendet. Das erste ist die Magnetkardiographie, wo die Optimierung magnetischer Sensoren in einem westenähnlichen Sensorfeld untersucht wird. Für die Messungen der magnetischen Flussdichte werden üblicherweise monoaxiale Sensoren in einem Feld perfekt parallel angeordnet. Eine zufällige Variation ihrer Ausrichtungen kann die Kondition des entsprechenden linearen inversen Problems verbessern. Eine theoretische Definition des Falls, in dem zufällige Variationen monoaxialer Sensoren den Zustand der Kernmatrix mit einer Wahrscheinlichkeit gleich Eins verbessern wird ebenfalls in der Dissertation vorgestellt. Diese theoretische Beobachtung ist allgemein gültig.Positionen und Orientierungen der Magnetsensoren rund um den Oberkörper wurden mit drei aus der Literatur bekannten Bewertungsmaßen und einem neu in dieser Arbeit vorgeschlagenen Maß optimiert. Die besten Ergebnisse ergeben sich bei einer unregelmäßigen Verteilung der Sensoren auf der Oberfläche des Brustkorbes. Im Vergleich zu früheren Untersuchungsergebnissen kann daraus geschlussfolgert werden, dass mit geringfügig abweichenden Sensoranordnungen ebenso gute Ergebnisse erzielt werden können. Ein zweites Anwendungsbeispiel ist ein Verfahren der zerstörungsfreien Materialprüfung, das auch als Lorentzkraft-Wirbelstromprüfung bekannt geworden ist. In dieser Arbeit wird eine neue Methode für die kontaktlose, zerstörungsfreie Untersuchung leitfähiger Materialien vorgestellt. Dabei wird die Lorentzkraft gemessen, die auf einen Dauermagneten wirkt, der relativ zu einem Testkörper bewegt. Es wird eine neue Approximationsmethode für die Berechnung der magnetischen Felder und der Lorentzkräfte vorgeschlagen.Linear inverse problems arise throughout a variety of branches of science and engineering. Efficient solution strategies for these inverse problems need to know whether a problem is ill-conditioned as well as its degree of ill-conditioning. In this thesis, a comprehensive theoretical analysis of known figures of merit has been done and finally two new figures of merit have been developed. Both can be applied in a large variety of linear inverse problems, including biomedical applications and nondestructive testing of materials. Theoretical considerations of the conditioning of linear inverse problems are applied to two examples. The first one is magnetocardiography, where the optimization of magnetic sensors in a vest-like sensor array has been considered. When measuring magnetic flux density, usually mono-axial magnetic sensors are arranged in an array, perfectly in parallel. It has been shown that a random variation of their orientations can improve the condition of the corresponding linear inverse problem. Thus, in this thesis a theoretical definition of the case when random variations of mono-axial sensors orientations improve the condition of the kernel matrix with a probability equal to one is presented. This theoretical observation is valid in general. Positions and orientations of magnetic sensors around the torso have been optimized minimizing three figures of merit given in the literature and a novel one presented in the thesis. Best results have been found for non-uniform sensors distribution on the whole torso surface. In comparison to previous findings can be concluded that quite different sensor sets can perform equally well.The second application example is nondestructive testing of materials named Lorentz force eddy current testing, where the Lorentz force exerting on a permanent magnet, which is moving relative to the specimen, is determined. A novel approximation method for the calculation of the magnetic fields and Lorentz forces is proposed. Based on the new approximation method, a new inverse procedure for defect reconstruction is proposed. A successful reconstruction using data from finite elements method analysis and measurements is obtained

Sepelvaltimotaudin noninvasiivinen tutkiminen

Conventional invasive coronary angiography is the clinical gold standard for detecting of coronary artery stenoses. Noninvasive multidetector computed tomography (MDCT) in combination with retrospective ECG gating has recently been shown to permit visualization of the coronary artery lumen and detection of coronary artery stenoses. Single photon emission tomography (SPECT) perfusion imaging has been considered the reference method for evaluation of nonviable myocardium, but magnetic resonance imaging (MRI) can accurately depict structure, function, effusion, and myocardial viability, with an overall capacity unmatched by any other single imaging modality. Magnetocardiography (MCG) provides noninvasively information about myocardial excitation propagation and repolarization without the use of electrodes. This evolving technique may be considered the magnetic equivalent to electrocardiography. The aim of the present series of studies was to evaluate changes in the myocardium assessed with SPECT and MRI caused by coronary artery disease, examine the capability of multidetector computed tomography coronary angiography (MDCT-CA) to detect significant stenoses in the coronary arteries, and MCG to assess remote myocardial infarctions. Our study showed that in severe, progressing coronary artery disease laser treatment does not improve global left ventricular function or myocardial perfusion, but it does preserve systolic wall thickening in fixed defects (scar). It also prevents changes from ischemic myocardial regions to scar. The MCG repolarization variables are informative in remote myocardial infarction, and may perform as well as the conventional QRS criteria in detection of healed myocardial infarction. These STT abnormalities are more pronounced in patients with Q-wave infarction than in patients with non-Q-wave infarctions. MDCT-CA had a sensitivity of 82%, a specificity of 94%, a positive predictive value of 79%, and a negative predictive value of 95% for stenoses over 50% in the main coronary arteries as compared with conventional coronary angiography in patients with known coronary artery disease. Left ventricular wall dysfunction, perfusion defects, and infarctions were detected in 50-78% of sectors assigned to calcifications or stenoses, but also in sectors supplied by normally perfused coronary arteries. Our study showed a low sensitivity (sensitivity 63%) in detecting obstructive coronary artery disease assessed by MDCT in patients with severe aortic stenosis. Massive calcifications complicated correct assessment of the lumen of coronary arteries.Sepelvaltimotaudin noninvasiivinen tutkiminen Perinteinen sepelvaltimoiden varjoainekuvaus on ollut kulmakivi sepelvaltimotaudin tutkimisessa. Kuitenkin pieni vakavien komplikaatioiden riski, tutkimuksen epämukavuus ja sairaalahoitopäivät potilaalle ovat johtaneet potilaasta vähemmän rasittavien, noninvasiivisten, tutkimusmenetelmien etsimiseen. Sydämen noninvasiivisen tutkimisen mahdollisuudet ovat kehittyneet viime vuosina huimaa vauhtia. Tutkimuksessa selvitettiin sydämen isotooppitutkimuksen lisäksi uusien tutkimusmenetelmien, monileiketietokonetomografian, magneettikuvauksen ja magnetokardiografian, käyttökelpoisuutta sepelvaltimotaudin eri ilmentymien tutkimisessa. Sepelvaltimoiden tietokonetomografia on uusi lupaava menetelmä sepelvaltimoahtaumien, kalkkikertymien ja pehmeiden plakkien tutkimisessa. Magneettikuvauksella voidaan arvioida sydänlihaksen toimintaa ja mahdollisia infarktialueita. Monikanavainen magnetokardiografia antaa tarkkaa tietoa sydämen sähköisestä toiminnasta. Tutkimukseen osallistui 43 eriasteista sepelvaltimotautia, 23 aorttaläpän ahtaumaa sairastavaa potilasta ja 26 tervettä verrokkihenkilöä. Tutkimuksessa todettiin, että sydänlihaksen laserkanavointi pitkälle edenneessä sepelvaltimotaudissa ei parantanut sydänlihaksen pumppaus- tehokkuutta eikä sydänlihaskudoksen verenvirtausta, joita mitattiin magneetti- ja isotooppikuvauksella. Laserkanavointi näytti 6 kk:n seurannassa kuitenkin hidastavan sydänlihaksen pysyvien vaurioiden syntyä. Yhdistämällä informaatiota sydämen magneettikuvauksesta ja sepelvaltimoiden monileiketietokonetomografiasta, totesimme että sydämen seinämän liikehäiriöitä, verenvirtauspoikkeavuuksia ja infarkteja oli myös alueilla, joiden sepelvaltimoissa ei todettu mitään poikkeavaa. Tietokonetomografian osuvuus perinteiseen varjoainekuvaukseen verrattuna on varsin hyvä, mutta aorttaläpän ahtaumaa sairastavilla potilailla runsaat kalkkikertymät vaikeuttivat sepelvaltimoahtaumien löytymistä. Monikanavaisen magnetokardiografia osuvuus perinteiseen 12-kytkentäiseen EKG:hen ja magneettikuvaukseen sydäninfarktiarpien osoittamisessa todettiin hyväksi sekä Q- että non-Q-aalto infarkteissa. Noninvasiivisten tutkimusmenetelmien käyttö tulee lisääntymään laitteiden kehittyessä nopeasti. Monileiketietokonetomografia sepelvaltimoiden kuvantamisessa voi osalla potilaista korvata perinteisen sepelvaltimoiden varjoainekuvauksen. Myös magneettikuvauksen antamat mahdollisuudet sydänlihaksen toimintahäiriöiden ja infarktien kuvantamisessa sopivat enenevässä määrin kliiniseen käyttöön

Non-Invasive Electrocardiographic Imaging of Ventricular Activities: Data-Driven and Model-Based Approaches

Die vorliegende Arbeit beleuchtet ausgewählte Aspekte der Vorwärtsmodellierung, so zum Beispiel die Simulation von Elektro- und Magnetokardiogrammen im Falle einer elektrisch stillen Ischämie sowie die Anpassung der elektrischen Potentiale unter Variation der Leitfähigkeiten. Besonderer Fokus liegt auf der Entwicklung neuer Regularisierungsalgorithmen sowie der Anwendung und Bewertung aktuell verwendeter Methoden in realistischen in silico bzw. klinischen Studien

Improving Condition and Sensitivity of Linear Inverse Problems in Magnetic Applications

Die Identifikation nicht direkt zugänglicher Prozesse anhand gemessener Daten ist von großer Bedeutung in vielen Bereichen. Im Fokus dieser Arbeit liegen Applikationen in der Magnetostatik, Magnetokardiographie und Magnetinduktionstomographie. Ein Ansatz zur Identifikation besteht in der Lösung eines entsprechenden linear inversen Problems. Unglücklicherweise haben in den Daten enthaltene Fehler und Rauschen einen signifikanten Einfluss auf die inverse Lösung. Ziel dieser Arbeit ist die Reduktion der Einflüsse von Fehlern und Rauschen durch eine Verbesserung der Kondition des Problems, sowie eine Steigerung der Sensitivität der Messanordnungen. Zur Bestimmung der Kondition wird das Verhältnis des größten und mittleren Singulärwerts der Kernmatrix als neues Maß vorgeschlagen. Darüber hinaus werden Ansätze zur Analyse der Sensitivität hinsichtlich der Messung elektromagnetischer Quellen und der Erfassung elektrischer Leitfähigkeitsveränderungen präsentiert.Strategien zur Verbesserung von Kondition und Sensitivität werden in vier Simulationsstudien beschrieben. In der ersten Studie wird ein Tabu-Suche-Ansatz zur Optimierung der Anordnung magnetischer Sensoren vorgestellt. Anordnungen mit optimierte Sensorpositionen resultieren dabei in einer deutlich besseren Kondition als regelmäßige Anordnungen. In einer zweiten Studie werden Parameter adaptiert,welche den Quellenraum für die Bildgebung durch magnetische Nanopartikel definieren. Als eine Schlussfolgerung sollte der Quellenraum etwas größer als das Sensorareal definiert werden. Diese Arbeit zeigt ebenfalls, dass Variationen in den Sensorrichtungen für monoaxiale Sensorarrays zu einer Verbesserung der Kondition führen. Zudem wird die Sensitivität von Spulenanordnungen für die Magnetinduktionstomographie bewertet und verglichen. Durch Nutzung relativ großer Spulen, die das Messgebiet nahezu vollständig abdecken, können Kondition und Sensitivität wesentlich verbessert werden.Die präsentierten Methoden und Strategien ermöglichen eine substantielle Verbesserung der Kondition des linear inversen Problems bei der Analyse magnetischer Messungen. Insbesondere die Anordnung von Sensoren in Bezug auf das Messobjekt ist kritisch für die Kondition, sowie die Qualität inverser Lösungen. Die vorgestellten Methoden sind darüber hinaus für linear inverse Probleme in zahlreichen Bereichen einsetzbar.The identification and reconstruction of hidden, not directly accessible processes from measured data is important in many areas of research and engineering. This thesis focusses on applications in magnetostatics, magnetocardiography, and magneticinduction tomography. One approach to identify these processes is to solve a related linear inverse problem. Unfortunately, noise and errors in the data have a significant impact on inverse solutions.The aim of this work is to reduce the effects of noise and errors by improving the condition of the problem and to increase the sensitivity of measurement setups. To quantify the condition, we propose the ratio of the largest and the mean singular value of the kernel matrix. Moreover, we outline approaches to analyse quantitatively and qualitatively the sensitivity to electromagnetic sources and electrical conductivity changes.In four simulation studies, strategies to improve the condition and sensitivity inmagnetic applications are described. First, we present a tabu search algorithm to optimize arrangements of magnetic sensors. Optimized sensor arrays result in a considerably improved condition compared with regular arrangements. Second, we adapt parameters that define source space grids for magnetic nanoparticle imaging. One conclusion is that the source space should be defined slightly larger than the sensor area. Third, we demonstrate for mono-axial sensor arrays that variations in thesensor directions and small variations in the sensor positions lead to improvements of the condition, too. Finally, we evaluate and compare the sensitivities of six coil setups for magnetic induction tomography. Our investigations indicate a rapid decay of sensitivity by several orders of magnitude within a range of a few centimetres. By using relatively large coils that cover the measurement region almost completely, the condition and sensitivity can be improved clearly.The methods and strategies presented in this thesis facilitate substantial improvements of the condition for linear inverse problems in magnetic applications. In particular, the arrangement of sensors relative to the measurement object is critical to the condition and to the quality of inverse solutions. Moreover, the presented methods are applicable to linear inverse problems in various fields

Value of Topology Approach to Diagnose of CAD Based on Magnetocardiographic Current Distribu-tion Maps in Difficult-to-Diagnose Patients

Abstract Objective: The purpose of this work is to examine the usefulness of the topological approach for analysis of current density maps during ST-T interval in detection of coronary artery disease (CAD) in patients with proved CAD but normal results of routine tests. Materials and Methods: The patient group included 123 patients. Coronary angiography was done due to chest pain. The control group consisted of 124 healthy volunteers. The MCG test was done by 4-channels MCG system installed at unshielded setting. An integral topological index Kideal, consisting of 4 parameters, has been counted. Results and Conclusions: It is shown that K ideal was higher in patient group compared to control one. Sensitivity was 87%, and specificity was 64%. The topological analysis of MCG current density maps is a valuable tool in noninvasive detection of CAD in difficult-to-diagnose patients with uninformative results of routine tests

Non-invasive procedure for fetal electrocardiography

Antenatal fetal surveillance is a field of increasing importance in modern obstetrics. Measurements extracted (such as fetal heart rate) from antenatal fetal monitoring techniques have the potential to reduce the social, personal and financial burdens of fetal death on families, health care systems and the community. Techniques to monitor the fetus through pregnancy have been developed with the aim of providing information to enable the clinician to diagnose fetal wellbeing, characterise development and detect abnormality. An early diagnosis before delivery may increase the effectiveness of the appropriate treatment. Over the years, various research efforts have been carried out in the field of fetal electrocardiography by attaching surface electrodes to the maternal body. Unfortunately the desired fetal heartbeat signals at the electrode output are buried in an additive mixture of undesired interference disturbances. In this thesis, a non-invasive fetal electrocardiogram machine has been designed, constructed and implemented. This machine is composed of three modified electrocardiogram circuits and an external soundcard. Data was acquired from four surface electrodes placed on the maternal body. Eleven pregnant subjects, with a gestation age between the 30th and 40th weeks of pregnancy, were used to investigate the validity of this machine. Fetal R-waves were detected in 72.7 percent of subjects. The development of a non-invasive machine, capable of detecting and recording valuable anatomic and electrophysiological information of a fetus, represents an important tool in clinical and investigative obstetrics

Theory, modelling and applications of electrocardiographic mapping

In this thesis, the genesis and applications of electromagnetic signals from the human heart are investigated through theory, modelling, signal processing and clinical studies. One objective of the thesis was to develop and test signal processing methods that would be applicable to multichannel electro- and magnetocardiographic data. A signal processing method based on a type of neural networks called the self-organizing maps is introduced for spatiotemporal analysis of the body surface potential maps produced by the beating heart. This method is capable of utilizing both the spatial morphology of the potential distributions on the body surface as well as their temporal development. A signal processing method aimed at providing a reliable electric baseline for more traditional isointegral analysis of the body surface potential mapping (BSPM) data is also introduced. Another objective of the thesis was to show the utility of electrocardiographic mapping in clinical use. This was demonstrated by applying electro- and magnetocardiographic mapping to evaluation of the propensity to life-threatening arrhythmias in postinfarction patients. Electrocardiographic mapping was found to perform equally well compared to more traditional SA-ECG, but electrocardiographic mapping may be more robust against individual variability in anatomy. A third objective of the thesis was to build a computer model of the human heart that is capable of simulating the normal ventricular activation. The propagation model is based on a bidomain formulation of the cardiac tissue applied to realistic geometry of the ventricles. An anatomically accurate model of the human conduction system that reproduces measured activation sequence of the human heart was developed in this thesis. The body surface potentials and the magnetic fields computed from the simulated activation corresponded to recordings from normal subjects. In summary, the thesis demonstrates the utility of electrocardiographic mapping in clinical use and introduces new signal processing methods that can be applied to this use. Finally, a computer model of the human heart binds together the physiology and anatomy of the human heart and body, classical electromagnetic theory, and computer science to explain the genesis and characteristics of the electromagnetic signals from the human heart.reviewe

A Biomagnetic Field Mapping System for Detection of Heart Disease in a Clinical Environment

This PhD was inspired by the clinical demand for a system to triage chest pain and the untapped diagnostic potential of magnetocardiography (MCG) to reliably detect silent ischaemic heart disease, which is responsible for the highest mortality rate of any single disease category. The aim was to develop a low cost and portable biomagnetic field mapping system capable of differentiating between healthy and diseased hearts within an unshielded hospital environment. This entailed the development of a system based on an array of magnetometers with sufficient sensitivity (104fT/ Hz at 10Hz) and noise rejection performance (68.4 ± 3.9 dB) to measure the small magnetic field associated with the heart beat, the magneocardiogram, within a much larger background noise. The array of induction coil magnetometers (ICM) we developed had sufficient sensitivity and were robust to high amplitude noise. These sensors were also cheap to manufacture and capable of operating on battery power, allowing a low cost, portable device to be developed. The key element that allowed us to achieve unshielded operation was the development of an algorithmic spatial filter, used as a substitute to operation within a magnetically shielded room. This coherent noise rejection (CNR) algorithm exploits the difference in spatial coherence between the local cardiac signals and the distant background noise sources. The observed coherence width during a clinical trial of the system within a hospital ward was 2.8 ± 0.9 × 10 6 mm 2 . This allowed us to capture MCG signals with a signal to noise ratio of SNR QRS = 0.93 ± 4.43dB. The performance of CNR was found to improve by 9dB per order of magnitude increase in environmental spatial coherence width. The coherence width can be increased by changes to hospital architecture, electromagnetic field regulation and device design optimisation. The thesis also explores a variety of approaches to obtain binary diagnostic information from MCG, from traditional statistical learning on manually engineered features to machine learning. I found that machine learning techniques, in particular convolutional neural networks (CNN), were able to capture more diagnostic information than traditional techniques and achieved world class prediction accuracy of 88% on the clinical trial dataset

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

Development of a Novel Dataset and Tools for Non-Invasive Fetal Electrocardiography Research

This PhD thesis presents the development of a novel open multi-modal dataset for advanced studies on fetal cardiological assessment, along with a set of signal processing tools for its exploitation. The Non-Invasive Fetal Electrocardiography (ECG) Analysis (NInFEA) dataset features multi-channel electrophysiological recordings characterized by high sampling frequency and digital resolution, maternal respiration signal, synchronized fetal trans-abdominal pulsed-wave Doppler (PWD) recordings and clinical annotations provided by expert clinicians at the time of the signal collection. To the best of our knowledge, there are no similar dataset available. The signal processing tools targeted both the PWD and the non-invasive fetal ECG, exploiting the recorded dataset. About the former, the study focuses on the processing aimed at the preparation of the signal for the automatic measurement of relevant morphological features, already adopted in the clinical practice for cardiac assessment. To this aim, a relevant step is the automatic identification of the complete and measurable cardiac cycles in the PWD videos: a rigorous methodology was deployed for the analysis of the different processing steps involved in the automatic delineation of the PWD envelope, then implementing different approaches for the supervised classification of the cardiac cycles, discriminating between complete and measurable vs. malformed or incomplete ones. Finally, preliminary measurement algorithms were also developed in order to extract clinically relevant parameters from the PWD. About the fetal ECG, this thesis concentrated on the systematic analysis of the adaptive filters performance for non-invasive fetal ECG extraction processing, identified as the reference tool throughout the thesis. Then, two studies are reported: one on the wavelet-based denoising of the extracted fetal ECG and another one on the fetal ECG quality assessment from the analysis of the raw abdominal recordings. Overall, the thesis represents an important milestone in the field, by promoting the open-data approach and introducing automated analysis tools that could be easily integrated in future medical devices