A quasi-one-dimensional theory for anisotropic propagation of excitation in cardiac muscle

It has been shown that propagation of excitation in cardiac muscle is anisotropic. Compared to propagation at right angles to the long axes of the fibers, propagation along the long axis is faster, the extracellular action potential (AP) is larger in amplitude, and the intracellular AP has a lower maximum rate of depolarization, a larger time constant of the foot, and a lower peak amplitude. These observations are contrary to the predictions of classical one-dimensional (1-D) cable theory and, thus far, no satisfactory theory for them has been reported. As an alternative description of propagation in cardiac muscle, this study provides a quasi-1-D theory that includes a simplified description of the effects of action currents in extracellular space as well as resistive coupling between surface and deeper fibers in cardiac muscle. In terms of classical 1-D theory, this quasi-1-D theory reveals that the anisotropies in the wave form of the AP arise from modifications in the effective membrane ionic current and capacitance. The theory also shows that it is propagation in the longitudinal, not in the transverse direction that deviates from classical 1-D cable theory

Modelling Dynamically Re-sizeable Electrodes (DRE) for Targeted Transcutaneous Measurements in Impedance Plethysmography

Impedance plethysmography of extremities typically uses band electrodes around limbs to monitor changes in blood volume. This often causes monitored blood variations to only generate minuscule impedance values relative to the measured baseline, attributed to the tissue surrounding the artery or vein of interest. Smaller, ECG type electrodes can provide a larger signal, however their output is very easily affected by the placement of the electrodes relative to the targeted vasculature. This paper presents a novel method to adjust the active surface of electrodes, introducing Dynamically Re-sizeable Electrodes (DRE), to only target the exact area of interest, forming localised electrodes, without having to manually re-position them. Elongated rectangular electrodes were partitioned into smaller electrode segments, interconnected through custom circuitry. For the development and assessment of the DRE system, work was carried out both experimentally in-vitro on gelatine phantoms using custom switching circuits and through finite element modelling (FEM) simulations in COMSOL. A scanning sequence made use of DRE in single segment variable tetra-pole (SSVT) mode proved capable to identify the transcutaneous location of the blood vessel of interest and the specific electrode segments located in its vicinity. Impedance measurements were then taken using these segments connected to form localised electrodes only placed over the targeted vessel. The resulting localised electrodes exhibited up to 28% increased sensitivity to blood variations relative to larger electrodes

Comparison of Propagation Models and Forward Calculation Methods on Cellular, Tissue and Organ Scale Atrial Electrophysiology

The bidomain model and the finite element method are an established standard to mathematically describe cardiac electrophysiology, but are both suboptimal choices for fast and large-scale simulations due to high computational costs. We investigate to what extent simplified approaches for propagation models (monodomain, reaction-Eikonal and Eikonal) and forward calculation (boundary element and infinite volume conductor) deliver markedly accelerated, yet physiologically accurate simulation results in atrial electrophysiology. Methods: We compared action potential durations, local activation times (LATs), and electrocardiograms (ECGs) for sinus rhythm simulations on healthy and fibrotically infiltrated atrial models. Results: All simplified model solutions yielded LATs and P waves in accurate accordance with the bidomain results. Only for the Eikonal model with pre-computed action potential templates shifted in time to derive transmembrane voltages, repolarization behavior notably deviated from the bidomain results. ECGs calculated with the boundary element method were characterized by correlation coefficients >0.9 compared to the finite element method. The infinite volume conductor method led to lower correlation coefficients caused predominantly by systematic overestimations of P wave amplitudes in the precordial leads. Conclusion: Our results demonstrate that the Eikonal model yields accurate LATs and combined with the boundary element method precise ECGs compared to markedly more expensive full bidomain simulations. However, for an accurate representation of atrial repolarization dynamics, diffusion terms must be accounted for in simplified models. Significance: Simulations of atrial LATs and ECGs can be notably accelerated to clinically feasible time frames at high accuracy by resorting to the Eikonal and boundary element methods

Paresthesia thresholds in spinal cord stimulation: a comparison of theoretical results with clinical data

The potential distributions produced in the spinal cord and surrounding tissues by dorsal epidural stimulation at the midcervical, midthoracic, and low thoracic levels were calculated with the use of a volume conductor model. Stimulus thresholds of myelinated dorsal column fibers and dorsal root fibers were calculated at each level in models in which the thickness of the dorsal cerebrospinal fluid (CSF) layer was varied. Calculated stimulus thresholds were compared with paresthesia thresholds obtained from measurements at the corresponding spinal levels in patients. The influences of the CSF layer thickness, the contact separation in bipolar stimulation and the laterality of the electrodes on the calculated thresholds were in general agreement with the clinical dat

Doctor of Philosophy

dissertationComputational simulation has become an indispensable tool in the study of both basic mechanisms and pathophysiology of all forms of cardiac electrical activity. Because the heart is comprised of approximately 4 billion electrically active cells, it is not possible to geometrically model or computationally simulate each individual cell. As a result computational models of the heart are, of necessity, abstractions that approximate electrical behavior at the cell, tissue, and whole body level. The goal of this PhD dissertation was to evaluate several aspects of these abstractions by exploring a set of modeling approaches in the field of cardiac electrophysiology and to develop means to evaluate both the amplitude of these errors from a purely technical perspective as well as the impacts of those errors in terms of physiological parameters. The first project used subject specific models and experiments with acute myocardial ischemia to show that one common simplification used to model myocardial ischemia-the simplest form of the border zone between healthy and ischemic tissue-was not supported by the experimental results. We propose a alternative approximation of the border zone that better simulates the experimental results. The second study examined the impact of simplifications in geometric models on simulations of cardiac electrophysiology. Such models consist of a connected mesh of polygonal elements and must often capture complex external and internal boundaries. A conforming mesh contains elements that follow closely the shapes of boundaries; nonconforming meshes fit the boundaries only approximately and are easier to construct but their impact on simulation accuracy has, to our knowledge, remained unknown. We evaluated the impact of this simplification on a set of three different forms of bioelectric field simulations. The third project evaluated the impact of an additional geometric modeling error; positional uncertainty of the heart in simulations of the ECG. We applied a relatively novel and highly efficient statistical approach, the generalized Polynomial Chaos-Stochastic Collocation method (gPC-SC), to a boundary element formulation of the electrocardiographic forward problem to carry out the necessary comprehensive sensitivity analysis. We found variations large enough to mask or to mimic signs of ischemia in the ECG

Modelling the interaction between induced pluripotent stem cells derived cardiomyocytes patches and the recipient hearts

Cardiovascular diseases are the main cause of death worldwide. The single biggest killer is represented by ischemic heart disease. Myocardial infarction causes the formation of non-conductive and non-contractile, scar-like tissue in the heart, which can hamper the heart's physiological function and cause pathologies ranging from arrhythmias to heart failure. The heart can not recover the tissue lost due to myocardial infarction due to the myocardium's limited ability to regenerate. The only available treatment is heart transpalant, which is limited by the number of donors and can elicit an adverse response from the recipients immune system. Recently, regenerative medicine has been proposed as an alternative approach to help post-myocardial infarction hearts recover their functionality. Among the various techniques, the application of cardiac patches of engineered heart tissue in combination with electroactive materials constitutes a promising technology. However, many challenges need to be faced in the development of this treatment. One of the main concerns is represented by the immature phenotype of the stem cells-derived cardiomyocytes used to fabricate the engineered heart tissue. Their electrophysiological differences with respect to the host myocardium may contribute to an increased arrhythmia risk. A large number of animal experiments are needed to optimize the patches' characteristics and to better understand the implications of the electrical interaction between patches and host myocardium. In this Thesis we leveraged cardiac computational modelling to simulate \emph{in silico} electrical propagation in scarred heart tissue in the presence of a patch of engineered heart tissue and conductive polymer engrafted at the epicardium. This work is composed by two studies. In the first study we designed a tissue model with simplified geometry and used machine learning and global sensitivity analysis techniques to identify engineered heart tissue patch design variables that are important for restoring physiological electrophysiology in the host myocardium. Additionally, we showed how engineered heart tissue properties could be tuned to restore physiological activation while reducing arrhythmic risk. In the second study we moved to more realistic geometries and we devised a way to manipulate ventricle meshes obtained from magnetic resonance images to apply \emph{in silico} engineered heart tissue epicardial patches. We then investigated how patches with different conduction velocity and action potential duration influence the host ventricle electrophysiology. Specifically, we showed that appropriately located patches can reduce the predisposition to anatomical isthmus mediated re-entry and that patches with a physiological action potential duration and higher conduction velocity were most effective in reducing this risk. We also demonstrated that patches with conduction velocity and action potential duration typical of immature stem cells-derived cardiomyocytes were associated with the onset of sustained functional re-entry in an ischemic cardiomyopathy model with a large transmural scar. Finally, we demonstrated that patches electrically coupled to host myocardium reduce the likelihood of propagation of focal ectopic impulses. This Thesis demonstrates how computational modelling can be successfully applied to the field of regenerative medicine and constitutes the first step towards the creation of patient-specific models for developing and testing patches for cardiac regeneration.Open Acces

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

Electrophysiology

The outstanding evolution of recording techniques paved the way for better understanding of electrophysiological phenomena within the human organs, including the cardiovascular, ophthalmologic and neural systems. In the field of cardiac electrophysiology, the development of more and more sophisticated recording and mapping techniques made it possible to elucidate the mechanism of various cardiac arrhythmias. This has even led to the evolution of techniques to ablate and cure most complex cardiac arrhythmias. Nevertheless, there is still a long way ahead and this book can be considered a valuable addition to the current knowledge in subjects related to bioelectricity from plants to the human heart

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