ABSTRACT
Atrial flutter is a common supraventricular tachycardia that can be treated using radiofrequency catheter ablation, a procedure that is guided by electroanatomical mapping systems. In this paper, we propose an algorithm for incorporating mapping data into computer simulations of atrial electrical activity with the purpose of creating a more accurate map of electrical activation. The algorithm takes as input the extracellular potential values recorded at a number of sites throughout the atria and estimates the activation time for the entire atrial domain. We test the algorithm using synthetic mapping data and an anatomically detailed atrial geometry with an activation pattern typical of atrial flutter. The results show that the algorithm performs well with synthetic mapping data with information from relatively few mapping sites and in the presence of modeling and measurement error.
Subject(s)
Atrial Flutter/physiopathology , Body Surface Potential Mapping/methods , Heart Atria/physiopathology , Heart Conduction System/physiopathology , Models, Cardiovascular , Action Potentials , Computer Simulation , HumansABSTRACT
Mathematical models for the electrical activity in cardiac cells are normally formulated as systems of ordinary differential equations (ODEs). The equations are nonlinear and describe processes occurring on a wide range of time scales. Under normal accuracy requirements, this makes the systems stiff and therefore challenging to solve numerically. As standard implicit solvers are difficult to implement, explicit solvers such as the forward Euler method are commonly used, despite their poor efficiency. Non-standard formulations of the forward Euler method, derived from the analytical solution of linear ODEs, can give significantly improved performance while maintaining simplicity of implementation. In this paper we study the performance of three non-standard methods on two different cell models with comparable complexity but very different stiffness characteristics.
Subject(s)
Action Potentials/physiology , Algorithms , Heart Conduction System/physiology , Ion Channel Gating/physiology , Ion Channels/physiology , Models, Cardiovascular , Myocytes, Cardiac/physiology , Animals , Computer Simulation , Humans , Programming Languages , Reproducibility of Results , Sensitivity and Specificity , Software , Software ValidationABSTRACT
Ischemic ST-segment shift has been modeled using scalar stationary approximations of the bidomain model. Here, we propose an alternative simplification of the bidomain equations: a linear system modeling the resting potential, to be used in determining ischemic TP shift. Results of 2D and 3D simulations show that the linear system model is much more accurate than the scalar model. This improved accuracy is important if the model is to be used for solving the inverse problem of determining the size and location of an ischemic region. Furthermore, the model can provide insight into how the resting potential depends on the variations in the extracellular potassium concentration that characterize ischemic regions.
Subject(s)
Models, Cardiovascular , Myocardial Ischemia/physiopathology , Animals , Dogs , Electrophysiology , Humans , Imaging, Three-Dimensional , Linear Models , Mathematics , Models, Anatomic , Myocardial Ischemia/pathologyABSTRACT
It is well known that the presence of myocardial ischemia can be observed as a shift in the ST segment of an electrocardiogram (ECG) recording. The question we address in this paper is whether or not ST shift can be used to compute approximations of the size and location of the ischemic region. We begin by investigating a cost functional (measuring the difference between synthetic recorded data and simulated values of ST shift) for a parameter identification problem to locate the ischemic region. We then formulate a more flexible representation of the ischemia using a level set framework and solve the associated minimization problem for the size and position of the ischemia. We apply this framework to a set of ECG data generated by the Bidomain model using the cell model of Winslow et al. Based on this data, we show that values of ST shift recorded at the body surface are capable of identifying the position and (roughly) the size of the ischemia.
Subject(s)
Arrhythmias, Cardiac/diagnosis , Arrhythmias, Cardiac/physiopathology , Body Surface Potential Mapping/methods , Diagnosis, Computer-Assisted/methods , Heart Conduction System/physiopathology , Myocardial Ischemia/diagnosis , Myocardial Ischemia/physiopathology , Animals , Arrhythmias, Cardiac/classification , Arrhythmias, Cardiac/etiology , Computer Simulation , Electrocardiography/methods , Humans , Models, Cardiovascular , Myocardial Ischemia/classification , Myocardial Ischemia/complications , Severity of Illness IndexABSTRACT
The mechanisms underlying the ST segment shifts associated with subendocardial ischemia remain unclear. The aim of this paper is to shed further light on the subject through numerical simulations of these shifts. A realistic three-dimensional model of the ventricles, including fiber rotation and anisotropy, is embedded in a nonhomogeneous torso model. A simplification of the bidomain model is used to calculate only the ST segment shift, assuming known values of the transmembrane potential during the plateau and rest phases. A similar simulation is performed in two dimensions. The simulation results suggest that subendocardial ischemia can be located by ST segment shift on the epicardial and torso surfaces. It is shown that ST elevation is associated with the transmural ischemic boundary, while ST depression is associated with the lateral ischemic boundaries.
