Identification of weakly coupled multiphysics problems. Application to the inverse problem of electrocardiography

This work addresses the inverse problem of electrocardiography from a new perspective, by combining electrical and mechanical measurements. Our strategy relies on the defini-tion of a model of the electromechanical contraction which is registered on ECG data but also on measured mechanical displacements of the heart tissue typically extracted from medical images. In this respect, we establish in this work the convergence of a sequential estimator which combines for such coupled problems various state of the art sequential data assimilation methods in a unified consistent and efficient framework. Indeed we ag-gregate a Luenberger observer for the mechanical state and a Reduced Order Unscented Kalman Filter applied on the parameters to be identified and a POD projection of the electrical state. Then using synthetic data we show the benefits of our approach for the estimation of the electrical state of the ventricles along the heart beat compared with more classical strategies which only consider an electrophysiological model with ECG measurements. Our numerical results actually show that the mechanical measurements improve the identifiability of the electrical problem allowing to reconstruct the electrical state of the coupled system more precisely. Therefore, this work is intended to be a first proof of concept, with theoretical justifications and numerical investigations, of the ad-vantage of using available multi-modal observations for the estimation and identification of an electromechanical model of the heart

Bayesian Inference with Combined Dynamic and Sparsity Models: Application in 3D Electrophysiological Imaging

Data-driven inference is widely encountered in various scientific domains to convert the observed measurements into information that cannot be directly observed about a system. Despite the quickly-developing sensor and imaging technologies, in many domains, data collection remains an expensive endeavor due to financial and physical constraints. To overcome the limits in data and to reduce the demand on expensive data collection, it is important to incorporate prior information in order to place the data-driven inference in a domain-relevant context and to improve its accuracy. Two sources of assumptions have been used successfully in many inverse problem applications. One is the temporal dynamics of the system (dynamic structure). The other is the low-dimensional structure of a system (sparsity structure). In existing work, these two structures have often been explored separately, while in most high-dimensional dynamic system they are commonly co-existing and contain complementary information. In this work, our main focus is to build a robustness inference framework to combine dynamic and sparsity constraints. The driving application in this work is a biomedical inverse problem of electrophysiological (EP) imaging, which noninvasively and quantitatively reconstruct transmural action potentials from body-surface voltage data with the goal to improve cardiac disease prevention, diagnosis, and treatment. The general framework can be extended to a variety of applications that deal with the inference of high-dimensional dynamic systems

Sequential non-rigid structure from motion using physical priors

© 20xx IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.We propose a new approach to simultaneously recover camera pose and 3D shape of non-rigid and potentially extensible surfaces from a monocular image sequence. For this purpose, we make use of the Extended Kalman Filter based Simultaneous Localization And Mapping (EKF-SLAM) formulation, a Bayesian optimization framework traditionally used in mobile robotics for estimating camera pose and reconstructing rigid scenarios. In order to extend the problem to a deformable domain we represent the object's surface mechanics by means of Navier's equations, which are solved using a Finite Element Method (FEM). With these main ingredients, we can further model the material's stretching, allowing us to go a step further than most of current techniques, typically constrained to surfaces undergoing isometric deformations. We extensively validate our approach in both real and synthetic experiments, and demonstrate its advantages with respect to competing methods. More specifically, we show that besides simultaneously retrieving camera pose and non-rigid shape, our approach is adequate for both isometric and extensible surfaces, does not require neither batch processing all the frames nor tracking points over the whole sequence and runs at several frames per second.Peer ReviewedPostprint (author's final draft

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

Physics-Based Probabilistic Motion Compensation of Elastically Deformable Objects

A predictive tracking approach and a novel method for visual motion compensation are introduced, which accurately reconstruct and compensate the deformation of the elastic object, even in the case of complete measurement information loss. The core of the methods involves a probabilistic physical model of the object, from which all other mathematical models are systematically derived. Due to flexible adaptation of the models, the balance between their complexity and their accuracy is achieved

Self-correcting Bayesian target tracking

The copyright of this thesis rests with the author and no quotation from it or information derived from it may be published without the prior written consent of the authorAbstract Visual tracking, a building block for many applications, has challenges such as occlusions,illumination changes, background clutter and variable motion dynamics that may degrade the tracking performance and are likely to cause failures. In this thesis, we propose Track-Evaluate-Correct framework (self-correlation) for existing trackers in order to achieve a robust tracking. For a tracker in the framework, we embed an evaluation block to check the status of tracking quality and a correction block to avoid upcoming failures or to recover from failures. We present a generic representation and formulation of the self-correcting tracking for Bayesian trackers using a Dynamic Bayesian Network (DBN). The self-correcting tracking is done similarly to a selfaware system where parameters are tuned in the model or different models are fused or selected in a piece-wise way in order to deal with tracking challenges and failures. In the DBN model representation, the parameter tuning, fusion and model selection are done based on evaluation and correction variables that correspond to the evaluation and correction, respectively. The inferences of variables in the DBN model are used to explain the operation of self-correcting tracking. The specific contributions under the generic self-correcting framework are correlation-based selfcorrecting tracking for an extended object with model points and tracker-level fusion as described below. For improving the probabilistic tracking of extended object with a set of model points, we use Track-Evaluate-Correct framework in order to achieve self-correcting tracking. The framework combines the tracker with an on-line performance measure and a correction technique. We correlate model point trajectories to improve on-line the accuracy of a failed or an uncertain tracker. A model point tracker gets assistance from neighbouring trackers whenever degradation in its performance is detected using the on-line performance measure. The correction of the model point state is based on the correlation information from the states of other trackers. Partial Least Square regression is used to model the correlation of point tracker states from short windowed trajectories adaptively. Experimental results on data obtained from optical motion capture systems show the improvement in tracking performance of the proposed framework compared to the baseline tracker and other state-of-the-art trackers. The proposed framework allows appropriate re-initialisation of local trackers to recover from failures that are caused by clutter and missed detections in the motion capture data. Finally, we propose a tracker-level fusion framework to obtain self-correcting tracking. The fusion framework combines trackers addressing different tracking challenges to improve the overall performance. As a novelty of the proposed framework, we include an online performance measure to identify the track quality level of each tracker to guide the fusion. The trackers in the framework assist each other based on appropriate mixing of the prior states. Moreover, the track quality level is used to update the target appearance model. We demonstrate the framework with two Bayesian trackers on video sequences with various challenges and show its robustness compared to the independent use of the trackers used in the framework, and also compared to other state-of-the-art trackers. The appropriate online performance measure based appearance model update and prior mixing on trackers allows the proposed framework to deal with tracking challenges

Stories from different worlds in the universe of complex systems: A journey through microstructural dynamics and emergent behaviours in the human heart and financial markets

A physical system is said to be complex if it exhibits unpredictable structures, patterns or regularities emerging from microstructural dynamics involving a large number of components. The study of complex systems, known as complexity science, is maturing into an independent and multidisciplinary area of research seeking to understand microscopic interactions and macroscopic emergence across a broad spectrum systems, such as the human brain and the economy, by combining specific modelling techniques, data analytics, statistics and computer simulations. In this dissertation we examine two different complex systems, the human heart and financial markets, and present various research projects addressing specific problems in these areas. Cardiac fibrillation is a diffuse pathology in which the periodic planar electrical conduction across the cardiac tissue is disrupted and replaced by fast and disorganised electrical waves. In spite of a century-long history of research, numerous debates and disputes on the mechanisms of cardiac fibrillation are still unresolved while the outcomes of clinical treatments remain far from satisfactory. In this dissertation we use cellular automata and mean-field models to qualitatively replicate the onset and maintenance of cardiac fibrillation from the interactions among neighboring cells and the underlying topology of the cardiac tissue. We use these models to study the transition from paroxysmal to persistent atrial fibrillation, the mechanisms through which the gap-junction enhancer drug Rotigaptide terminates cardiac fibrillation and how focal and circuital drivers of fibrillation may co-exist as projections of transmural electrical activities. Financial markets are hubs in which heterogeneous participants, such as humans and algorithms, adopt different strategic behaviors to exchange financial assets. In recent decades the widespread adoption of algorithmic trading, the electronification of financial transactions, the increased competition among trading venues and the use of sophisticated financial instruments drove the transformation of financial markets into a global and interconnected complex system. In this thesis we introduce agent-based and state-space models to describe specific microstructural dynamics in the stock and foreign exchange markets. We use these models to replicate the emergence of cross-currency correlations from the interactions between heterogeneous participants in the currency market and to disentangle the relationships between price fluctuations, market liquidity and demand/supply imbalances in the stock market.Open Acces

Trendit poistavan fluktuaatioanalyysin edistyneet menetelmät ja niiden sovellukset laskennallisessa kardiologiassa

Fractals are ubiquitous in nature. A defining characteristic of fractality is self-similarity; the phenomenon looks similar when observed at multiple scales, which implies the existence of a power law scaling relation. Detrended fluctuation analysis (DFA) is a popular tool for studying these fractal scaling relations. Power laws become linear relationships in logarithmic scales, and conventionally these scaling exponents are determined by simple linear regression in approximately linear regions in doubly logarithmic plots. However, in practice the scaling is hardly ever exact, and its behavior may often vary at different scales. This thesis extends the fluctuation analysis by introducing robust tools for determining these scaling exponents. A method based on the Kalman smoother is utilized for extracting a whole spectrum of exponents as a function of the scale. The method is parameter-free and resistant to statistical noise, which distinguishes it from prior efforts for determining such local scale exponents. Additionally, an optimization scheme is presented to obtain data-adaptive segmentation of approximately linear regimes. Based on integer linear programming model, the procedure may readily be customized for various purposes. This versatility is demonstrated by applying the method to a group of data to find a common segmentation that is particularly well-suited for machine learning applications. First, the methods are are employed in exploring the details of the scaling by analyzing simulated data with known scaling properties. These findings provide insight into the interpretation of earlier results. Second, the methods are applied to the study of heart rate variability. The beating of the heart follows fractal-like patterns, and deviations in these complex variations may be indicative of cardiac diseases. In this context DFA is traditionally performed by extracting two scaling exponents, for short- and long-range correlations, respectively. This has been criticized as an oversimplification, which is corroborated by the results of this thesis. The heart rate exhibits richer fractal-like variability, which becomes apparent in the full scaling spectra. The additional information provided by these methods facilitate improved classification of cardiac conditions.Fraktaaleja esiintyy kaikkialla luonnossa. Fraktaalisuuden ominaispiirre on itsesimilaarisuus, eli ilmiö näyttää samankaltaiselta, kun sitä tarkastellaan useassa eri skaalassa. Tämä johtaa siihen, että ilmiön skaalautuvuus noudattaa potenssilakia. Tällaisia fraktaalisia skaalausrelaatioita voidaan tutkia trendit poistavan fluktuaatioanalyysin avulla (Detrended Fluctuation Analysis, DFA). Logaritminen skaala muuntaa potenssilait lineaarisiksi riippuvuuksiksi, ja tavallisesti skaalauseksponentit määritetään logaritmisista kuvaajista lineaarisen regression avulla. Kuitenkaan skaalautuvuus ei lähes koskaan ole täydellistä, ja se voi myös muuttua eri skaaloilla. Tämä työ laajentaa fluktuaatioanalyysia esittelemällä paranneltuja menetelmiä näiden skaalauseksponenttien määrittämiseen. Kokonainen spektri skaalauseksponentteja skaalan funktiona määritetään hyödyntämällä Kalman-suodinta. Tämän menetelmän etuja verrattuna aikaisempiin tapoihin määrittää paikallisia skaalauseksponentteja ovat sen parametrivapaa esitys ja vakaus myös kohinaisissa tapauksissa. Lisäksi esitetään lineaariseen kokonaislukuoptimointiin perustuva menetelmä, jonka avulla skaalautuvuudessa voidaan erottaa alueita, jotka noudattavat likimäärin potenssilakia. Tämän mallin muokkaaminen eri tarpeisiin on myös suoraviivaista. Mallia sovelletaan yhteisen segmentaation etsimiseksi datajoukolle, mikä on tarpeen erityisesti koneoppimisen menetelmiä varten. Esitettyjen menetelmien avulla tutkitaan ensin simuloituja prosesseja, joiden teoreettinen skaalautuminen tunnetaan. Menetelmien mahdollistama yksityiskohtainen analyysi selittää aikaisempia havaintoja DFA:n käyttäytymisessä. Menetelmiä sovelletaan myös sykevälivaihtelun fraktaalianalyysiin. Terveen sydämen sykeväleissä on fraktaalisia piirteitä, joita eri sairaudet muokkaavat ja hävittävät. Sykevälivaihtelun fraktaalisuutta on perinteisesti kuvattu lyhyen- ja pitkän kantaman skaalauseksponenteilla. Tätä kahden eksponentin mallia on kritisoitu riittämättömäksi, ja tämän työn tulokset vahvistavat tätä näkökulmaa. Skaalauseksponenttispektri paljastaa, että sykevälivaihtelun fraktaalisuus on kahden eksponentin mallia monimuotoisempaa. Esitetyillä menetelmillä saatava lisäinformaatio mahdollistaa aikaisempaa tarkemman sydänsairauksien luokittelun

Personalized noninvasive imaging of volumetric cardiac electrophysiology

Three-dimensionally distributed electrical functioning is the trigger of mechanical contraction of the heart. Disturbance of this electrical flow is known to predispose to mechanical catastrophe but, due to its amenability to certain intervention techniques, a detailed understanding of subject-specific cardiac electrophysiological conditions is of great medical interest. In current clinical practice, body surface potential recording is the standard tool for diagnosing cardiac electrical dysfunctions. However, successful treatments normally require invasive catheter mapping for a more detailed observation of these dysfunctions. In this dissertation, we take a system approach to pursue personalized noninvasive imaging of volumetric cardiac electrophysiology. Under the guidance of existing scientific knowledge of the cardiac electrophysiological system, we extract the subject specific cardiac electrical information from noninvasive body surface potential mapping and tomographic imaging data of individual subjects. In this way, a priori knowledge of system physiology leads the physiologically meaningful interpretation of personal data; at the same time, subject-specific information contained in the data identifies parameters in individual systems that differ from prior knowledge. Based on this perspective, we develop a physiological model-constrained statistical framework for the quantitative reconstruction of the electrical dynamics and inherent electrophysiological property of each individual cardiac system. To accomplish this, we first develop a coupled meshfree-BE (boundary element) modeling approach to represent existing physiological knowledge of the cardiac electrophysiological system on personalized heart-torso structures. Through a state space system approach and sequential data assimilation techniques, we then develop statistical model-data coupling algorithms for quantitative reconstruction of volumetric transmembrane potential dynamics and tissue property of 3D myocardium from body surface potential recoding of individual subjects. We also introduce a data integration component to build personalized cardiac electrophysiology by fusing tomographic image and BSP sequence of the same subject. In addition, we develop a computational reduction strategy that improves the efficiency and stability of the framework. Phantom experiments and real-data human studies are performed for validating each of the framework’s major components. These experiments demonstrate the potential of our framework in providing quantitative understanding of volumetric cardiac electrophysiology for individual subjects and in identifying latent threats in individual’s heart. This may aid in personalized diagnose, treatment planning, and fundamentally, prevention of fatal cardiac arrhythmia

Characterizing the Noise Associated with Sensor Placement and Motion Artifacts and Overcoming its Effects for Body-worn Physiological Sensors

Wearable sensors for continuous physiological monitoring have the potential to change the paradigm for healthcare by providing information in scenarios not covered by the existing clinical model. One key challenge for wearable physiological sensors is that their signal-to-noise ratios are low compared to those of their medical grade counterparts in hospitals. Two primary sources of noise are the sensor-skin contact interface and motion artifacts due to the user’s daily activities. These are challenging problems because the initial sensor placement by the user may not be ideal, the skin conditions can change over time, and the nature of motion artifacts is not predictable. The objective of this research is twofold. The first is to design sensors with reconfigurable contact to mitigate the effects of misplaced sensors or changing skin conditions. The second is to leverage signal processing techniques for accurate physiological parameter estimation despite the presence of motion artifacts. In this research, the sensor contact problem was specifically addressed for dry-contact electroencephalography (EEG). The proposed novel extension to a popular existing EEG electrode design enabled reconfigurable contact to adjust to variations in sensor placement and skin conditions over time. Experimental results on human subjects showed that reconfiguration of contact can reduce the noise in collected EEG signals without the need for manual intervention. To address the motion artifact problem, a particle filter based approach was employed to track the heart rate in cardiac signals affected by the movements of the user. The algorithm was tested on cardiac signals from human subjects running on a treadmill and showed good performance in accurately tracking heart rate. Moreover, the proposed algorithm enables fusion of multiple modalities and is also computationally more efficient compared to other contemporary approaches