Boundary element method in spatial characterization of the electrocardiogram

The electrochemical activity of the heart gives rise to an electric field. In electrocardiography, cardiac electrical activity is assessed by analyzing the potential distribution of this field on the body surface. The potential distribution, or the set of measured surface-voltage signals, is called the electrocardiogram (ECG). Spatial properties of the ECG can be captured with body surface potential mapping (BSPM), in which the electrocardiogram is measured using dozens of electrodes. In this Thesis, methods for solving the forward and inverse problems of electrocardiography are developed and applied to characterization of acute myocardial ischemia. The methodology is based on numerical computation of quasi-static electric fields in a volume conductor model. An open-source Matlab toolbox for solving volume conductor problems with the boundary element method (BEM) is presented. The Galerkin BEM and analytical operator-integrals are, for the first time, applied to the epicardial potential problem; the formulation for a piece-wise homogeneous volume conductor is presented in detail, enabling straightforward inclusion of the lungs or other inhomogeneities in the thorax model. The results show that errors due to discretization and forward-computation are smaller with the linear Galerkin (LG) method than with the conventional methods. These benefits do, however, not reflect to the Tikhonov-regularized inverse solution. If the lungs are omitted, as commonly is done, the choice of the computational method is not significant. In a set of 22 patients measured with BSPM during coronary angioplasty (PTCA), the application of a BEM thorax model with dipolar equivalent sources enabled accurate discrimination between occluded coronary arteries: the correct classification was obtained in 21 patients using the BSPM and in 20 patients using a 5-electrode set suggested elsewhere. The ischemic regions could also be localized anatomically correctly with simplified epicardial potential imaging, even though patient-specific thorax models were not used. In another set, comprising 79 acute ischemic patients and 84 controls, dipole-markers performed well in detection and quantification of acute ischemia. These results show that the modeling-approach can provide valuable information also without patient-specific models and complicated protocols

Mathematical Modeling and Simulation of Ventricular Activation Sequences: Implications for Cardiac Resynchronization Therapy

Next to clinical and experimental research, mathematical modeling plays a crucial role in medicine. Biomedical research takes place on many different levels, from molecules to the whole organism. Due to the complexity of biological systems, the interactions between components are often difficult or impossible to understand without the help of mathematical models. Mathematical models of cardiac electrophysiology have made a tremendous progress since the first numerical ECG simulations in the 1960s. This paper briefly reviews the development of this field and discusses some example cases where models have helped us forward, emphasizing applications that are relevant for the study of heart failure and cardiac resynchronization therapy

Advanced Source Reconstruction and Volume Conductor Modeling for Fetal Magnetocardiography

Abstract Fetuses that are identified with cardiac hypotrophy, hypertension and metabolic anomalies have higher risk of suffering from various health problems in their later life. Therefore, the early detection of congenital heart anomalies is critical for monitoring or prompt interventions, which can reduce the risks of congestive heart failure. Compared to adult cardiac monitoring, fetal electrophysiological heart monitoring using fetal ECG is extremely difficult due to the low signal amplitude and interferences from the maternal cardiac signal and to the complex environment inside the mother's womb. This problem is even worse in conditions such as diabetic pregnancies because of further signal reduction due to maternal obesity. At the same time, the prevalence of congenital heart anomalies is higher for fetuses of diabetic mothers. The purpose of this thesis is to develop and test fetal magnetocardiography (fMCG) techniques as an alternative diagnostic tool for the detection and monitoring of the fetal heart. fMCG is a novel technique that records the magnetic fields generated by the fetal heart's electric activity. From the aspect of signal processing, magnetic signals generated by the fetal heart are less affected by the low electrical conductivity of the surrounding fetal and maternal tissues compared to the electric signals recorded over the maternal abdomen, and can provide reliable recordings as early as 12 weeks of gestation. However, the fetal heart signals recorded with an array of magnetic sensors at a small distance from the maternal abdomen are affected by the source-to-sensor distance as well as by the geometry of the volume conductor, which is variable in different subjects or in the same subject when recordings are made at different gestational ages. The scope of this thesis is to develop a novel methodology for modeling the fetal heart and volume conductor and to use advanced source reconstruction techniques that can reduce the effect of these confounding factors in evaluating heart magnetic signals. Furthermore, we aim to use these new methods for developing a normative database of fMCG metrics at different gestational ages and test their reliability to detect abnormal patterns of cardiac electrophysiology in pregnancies complicated by maternal diabetes. In the first part of the thesis, we review three current fetal heart monitoring modalities, including fetal electrocardiography (ECG), ultrasonography, and fetal magnetocardiography (fMCG). The advantages and drawbacks of each technique are comparatively discussed. Finally, we discuss the developmental changes of fetal heart through gestation as well as the electromagnetic characteristics of the fetal cardiac activation

Strategies for optimal design of biomagnetic sensor systems

Magnetic field imaging (MFI) is a technique to record contact free the magnetic field distribution and estimate the underlying source distribution in the heart. Currently, the cardiomagnetic fields are recorded with superconducting quantum interference devices (SQUIDs), which are restricted to the inside of a cryostat filled with liquid helium or nitrogen. New room temperature optical magnetometers allow less restrictive sensor positioning, which raises the question of how to optimally place the sensors for robust field reconstruction. The objective in this study is to develop a generic object-oriented framework for optimizing sensor arrangements (sensor positions and orientations) which supports the necessary constraints of a limited search volume (only outside the body) and the technical minimum distance of sensors (e.g. 1 cm). In order to test the framework, a new quasi-continuous particle swarm optimizer (PSO) component is developed as well as an exemplary goal function component using the condition number (CN) of the leadfield matrix. Generic constraint handling algorithms are designed and implemented, that decompose complex constraints into basic ones. The constraint components interface to an operational exemplary optimization strategy which is validated on the magnetocardiographic sensor arrangement problem. The simulation setup includes a three compartment boundary element model of a torso with a fitted multi-dipole heart model. The results show that the CN, representing the reconstruction robustness of the inverse problem, can be reduced with our optimization by one order of magnitude within a sensor plane (the cryostat bottom) in front of the torso compared to a regular sensor grid. Reduction of another order of magnitude is achieved by optimizing sensor positions on the entire torso surface. Results also indicate that the number of sensors may be reduced to 20-30 without loss of robustness in terms of CN. The original contributions are the generic reusable framework and exemplary components, the quasicontinuous PSO algorithm with constraint support and the composite constraint handling algorithms

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

Simulating human sleep spindle MEG and EEG from ion channel and circuit level dynamics

Although they form a unitary phenomenon, the relationship between extracranial M/EEG and transmembrane ion flows is understood only as a general principle rather than as a well-articulated and quantified causal chain.We present an integrated multiscale model, consisting of a neural simulation of thalamus and cortex during stage N2 sleep and a biophysical model projecting cortical current densities to M/EEG fields. Sleep spindles were generated through the interactions of local and distant network connections and intrinsic currents within thalamocortical circuits. 32,652 cortical neurons were mapped onto the cortical surface reconstructed from subjects' MRI, interconnected based on geodesic distances, and scaled-up to current dipole densities based on laminar recordings in humans. MRIs were used to generate a quasi-static electromagnetic model enabling simulated cortical activity to be projected to the M/EEG sensors.The simulated M/EEG spindles were similar in amplitude and topography to empirical examples in the same subjects. Simulated spindles with more core-dominant activity were more MEG weighted.Previous models lacked either spindle-generating thalamic neural dynamics or whole head biophysical modeling; the framework presented here is the first to simultaneously capture these disparate scales.This multiscale model provides a platform for the principled quantitative integration of existing information relevant to the generation of sleep spindles, and allows the implications of future findings to be explored. It provides a proof of principle for a methodological framework allowing large-scale integrative brain oscillations to be understood in terms of their underlying channels and synapses

Larval zebrafish electrocardiography electrodynmaic modelling and sensor design

This thesis presents the first model of the electrical activity of the larval zebrafish heart as well as the design and fabrication of novel electrode arrays that were created to measure the electrocardiogram. The model consists of realistic 3D geometry of a 3 day’s post fertilisation zebrafish heart and body with a bidomain electrical model that uses the Fitzhugh-Nagumo equations as the ionic model. The model is able to replicate experimentally observed conduction velocities and action potentials by using region specific parameters and simulate electrocardiograms that are comparable to measurements. The electrode arrays are constructed from flexible polyimide films with gold microelectrodes. These devices have the potential to improve the measurement of the electrocardiogram for drug screening applications as an alternative to the use of micropipette electrodes. Gold plating and PEDOT:PSS coating techniques were applied to the devices to successfully reduce electrode impedance with the effectiveness of each technique categorised using impedance spectroscopy. The devices were tested $in$ $vivo$ with larval zebrafish with limited success and so $in$ $vitro$ tests were conducted using an artificial current source