Electrophysiological Modeling for Cardiology: Methods and Potential Applications

Abstract

Simulations of the electrophysiological behavior of the heart improve the comprehension of the mechanisms of the cardiovascular system. Furthermore, the mathematical modeling will support diagnosis and therapy of patients suffering from heart diseases. In this paper, the chain of modeling of the electrical function in the heart is described. The components are explained briefly, namely modeling of cardiac geometry, reconstructing the cardiac electrophysiology and excitation propagation. Additionally, the mathematical methods allowing to implement and solve these models are outlined. The three recently more investigated cases atrial fibrillation, ischemia and long-QT syndrome are described and show how cardiac modeling can support cardiologists in answering their open questions.Zusammenfassung Simulationen des elektrophysiologischen Verhaltens des Herzens fördern das Verständnis über die Mechanismen innerhalb des Herz-Kreislauf-Systems. Darüber hinaus werden diese mathematischen Modelle die Diagnose und Therapie von Patienten, die unter Herzerkrankungen leiden, unterstützen. In dieser Arbeit wird die Vorgehensweise für die Modellierung der elektrischen Funktion des Herzens beschrieben. Hierfür werden die Teilschritte der Modellierung kurz erklärt, nämlich die Modellierung der Geometrie, die Rekonstruktion der kardialen Elektrophysiologie und der elektrischen Erregungsausbreitung sowie die mathematischen Methoden, die eine Implementierung und Lösung dieser Modelle erlauben. Die vor kurzem mehr und mehr untersuchten Fälle Vorhofflimmern, Ischämie und das lange QT Syndrom werden beispielhaft beschrieben und zeigen, wie die Modellierung des Herzens dazu benutzt werden kann, um Kardiologen bei der Beantwortung von offenen Fragen zu unterstüzen.

TV Regularized Low-Rank Framework for Localizing Premature Ventricular Contraction Origin

“…For most electrophysiological imaging purposes, the following materials are required: data of the multi-lead [14] body-surface potentials and a heart torso geometry model, which can be created from computerized tomographic (CT) scanning or magnetic resonance imaging (MRI). From these, a linear or non-linear forward system that relates the cardiac electrophysiology to the bodysurface potential can be derived by means of the boundary element method (BEM) [15], [16] or the finite-element method (FEM) [17]. Finally, to solve the ill-posed inverse problem with any existing successful methods, a formulation must be established to select the best solution with the available prior knowledge.…”

Simplified 2D Bidomain Model of Whole Heart Electrical Activity and ECG Generation

“…Biophysical models of cardiac electrical activity and resulting torso surface potentials are becoming increasingly detailed and computationally onerous: occasionally requiring even the use of supercomputers [1][2][3][4]. This is especially true for bidomain element models of cardiac electrical activity, which couple transmembrane cellular potentials to extracellular fields, requiring relatively high degrees of freedom to solve for all the dependent variables.…”