Quantifying the effect of uncertainty in input parameters in a simplified bidomain model of partial thickness ischaemia

Reduced blood flow in the coronary arteries can lead to damaged heart tissue (myocardial ischaemia). Although one method for detecting myocardial ischaemia involves changes in the ST segment of the electrocardiogram, the relationship between these changes and subendocardial ischaemia is not fully understood. In this study, we modelled ST-segment epicardial potentials in a slab model of cardiac ventricular tissue, with a central ischaemic region, using the bidomain model, which considers conduction longitudinal, transverse and normal to the cardiac fibres. We systematically quantified the effect of uncertainty on the input parameters, fibre rotation angle, ischaemic depth, blood conductivity and six bidomain conductivities, on outputs that characterise the epicardial potential distribution. We found that three typical types of epicardial potential distributions (one minimum over the central ischaemic region, a tripole of minima, and two minima flanking a central maximum) could all occur for a wide range of ischaemic depths. In addition, the positions of the minima were affected by both the fibre rotation angle and the ischaemic depth, but not by changes in the conductivity values. We also showed that the magnitude of ST depression is affected only by changes in the longitudinal and normal conductivities, but not by the transverse conductivities

ST segment depression: the possible role of global repolarization dynamics

BACKGROUND: At least some clinical data suggests that, regardless of which major coronary artery is narrowed, the early ST segment body surface pattern is characterized by a minimum near precordial lead V5 and a broad area of left precordial negative potentials. Some clinical data also suggests that late ST segment potentials can localize an ischemic heart region. OBJECTIVE: A computer model of a heart/torso system was implemented to study the relationship between transmembrane potentials throughout the heart and clinically observed body surface potential patterns during the early and late ST segments in ischemic patients. METHODS: Transmembrane potentials were selected to produce body surface potentials that matched the clinical data. RESULTS: The early ST segment pattern was matched by assigning: (i) an epicardial transmembrane potential gradient that is consistent with the normal activation/repolarization sequence, according to which the left lateral epicardium activates relatively late; (ii) an endocardial transmembrane potential distribution with the lowest transmembrane potentials in the ischemic region; and (iii) overall lower transmembrane potentials to the endocardium compared to the epicardium. Late ST segment potentials, which localized the area of the ischemic region, were generated by reducing the epicardial transmembrane potential gradient and increasing the endocardial transmembrane potential gradient. CONCLUSION: The non-localizing nature of early ST segment depression could be due to global epicardial and endocardial transmembrane potential gradients related to the activation/repolarization sequence, whereas the possibly localizing nature of late ST segment depression could be due to the relative removal of the epicardial gradient, and an increase of the transmembrane potential gradient across the endocardium

Uncertainty visualization in forward and inverse cardiac models

pre-printQuantification and visualization of uncertainty in cardiac forward and inverse problems with complex geometries is subject to various challenges. Specific to visualization is the observation that occlusion and clutter obscure important regions of interest, making visual assessment difficult. In order to overcome these limitations in uncertainty visualization, we have developed and implemented a collection of novel approaches. To highlight the utility of these techniques, we evaluated the uncertainty associated with two examples of modeling myocardial activity. In one case we studied cardiac potentials during the repolarization phase as a function of variability in tissue conductivities of the ischemic heart (forward case). In a second case, we evaluated uncertainty in reconstructed activation times on the epicardium resulting from variation in the control parameter of Tikhonov regularization (inverse case). To overcome difficulties associated with uncertainty visualization, we implemented linked-view windows and interactive animation to the two respective cases. Through dimensionality reduction and superimposed mean and standard deviation measures over time, we were able to display key features in large ensembles of data and highlight regions of interest where larger uncertainties exist

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

Exploiting GPUs to investigate an inversion method that retrieves cardiac conductivities from potential measurements

Accurate cardiac bidomain conductivity values are essential for realistic simulation of various cardiac electrophysiological phenomena. A method was previously developed that can determine the conductivities from measurements of potential on a multi-electrode array placed on the surface of the heart. These conductivities, as well as a value for fibre rotation, are determined using a mathematical model and a two-pass process that is based on Tikhonov regularisation. Using simulated potentials, to which noise is added, the inversion method was recently shown to retrieve the intracellular conductivities accurately with up to 15% noise and the extracellular conductivities extremely accurately even with 20% noise. Recent work investigated the sensitivity of the method to the choice of the regularisation parameters. Such a study only became possible due to modifications that were made to the C++ code so that it could run on graphical processing units (GPUs) on the CUDA platform. As the method required the solution of a large number of matrix equations, the highly parallel nature of GPUs was exploited to accelerate execution of the code. Reorganisation of the code and more efficient memory management techniques allowed the data to completely fit in the GPU memory. Comparison between the execution time on the GPU versus the original CPU code shows a speedup of up to 60 times. In the future, the speedup could be further increased with greater use of shared memory, which has a much lower latency (access time) than global memory. References Clayton, R. H., Bernus, O., Cherry, E. M., Dierckx, H., Fenton, F. H., Mirabella, L., Panfilov, A. V., Sachse, F. B., Seemann, G., and Zhang, H. Models of cardiac tissue electrophysiology: Progress, challenges and open questions. Progress in Biophysics and Molecular Biology, 104(1–3):22–48, 2011. doi:10.1016/j.pbiomolbio.2010.05.008 Arthur, R. M. and Geselowitz, D. B. 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Intracoronary electrocardiogram as a direct measure of myocardial ischemia

The electrocardiogram is a valuable diagnostic method providing insight into pathologies of the heart, especially rhythm disorders or insufficient myocardial blood supply (myocardial ischemia). The commonly used surface ECG is, however, limited in detecting short-lasting myocardial ischemia, in particular in the territory of the left circumflex coronary artery supplying the postero-lateral wall of the left ventricle. Conversely, an ECG recorded in close vicinity to the myocardium, i.e., within a coronary artery (intracoronary ECG, icECG) has been thought to overcome these limitations. Since its first implementation during cardiac catheterization in 1985, icECG has shown ample evidence for its diagnostic value given the higher sensitivity for myocardial ischemia detection when compared to the surface ECG. In addition, icECG has been demonstrated to be a direct measure of myocardial ischemia in real-time, thus, providing valuable information during percutaneous coronary diagnostics and interventions. However, a lack of analysing systems to obtain and quantify icECG in real-time discourages routine use. The goals of this MD-PhD thesis are two-fold: First, to determine the diagnostic accuracy of icECG ST-segment shift during pharmacologic inotropic stress in comparison to established indices for coronary lesion severity assessment using quantitative angiographic percent diameter stenosis as reference (Project I). Second, to determine the optimal icECG parameter for myocardial ischemia detection and quantification (Project II and III). In essence, this thesis demonstrates that the icECG is an easy available diagnostic method providing highly accurate information on the amount of myocardial ischemia in real-time. Quantitative assessment of acute, transmural myocardial ischemia by icECG is most accurately performed by measuring ST-segment shift at the J-point, while the quantitative assessment during physical exercise, respectively its pharmacologic simulation, is most accurately performed by measuring ST-segment shift 60ms after the J-point