Abstract: Mathematical modeling of cardiac electrophysiology is an insightful method to investigate the underlying mechanisms responsible for arrhythmias such as atrial fibrillation. In past years, five models of human atrial electrophysiology with different formulations of ionic currents, and consequently diverging properties, have been published. The aim of this work is to give an overview of strengths and weaknesses of these models depending on the purpose and the general requirements of simulations. Therefore, these models were systematically benchmarked with respect to general mathematical properties and their ability to reproduce certain electrophysiological phenomena, such as action potential alternans. To assess the models ability to replicate modified properties of human myocytes and tissue in cardiac disease, electrical remodeling in chronic atrial fibrillation was chosen as test case. The healthy and remodeled model variants were compared with experimental results in single-cell, 1D and 2D tissue simulations to investigate action potential and restitution properties, as well as the initiation of reentrant circuits.
Abstract: Aims Amiodarone and cisapride are both known to prolong the QT interval, yet the two drugs have different effects on arrhythmia. Cisapride can cause torsades de pointes while amiodarone is found to be anti-arrhythmic. A computational model was used to investigate the action of these two drugs.
Methods and results In a biophysically detailed model, the ion current conductivities affected by both drugs were reduced in order to simulate the pharmacological effects in healthy and ischaemic cells. Furthermore, restitution curves of the action potential duration (APD), effective refractory period, conduction velocity, wavelength, and the vulnerable window were determined in a one-dimensional (1D) tissue strand. Moreover, cardiac excitation propagation was computed in a 3D model of healthy ventricles. The corresponding body surface potentials were calculated and standard 12-lead electrocardiograms were derived. Both cisapride and amiodarone caused a prolongation of the QT interval and the refractory period. However, cisapride did not significantly alter the conduction-related properties, such as e.g. the wavelength or vulnerable window, whereas amiodarone had a larger impact on them. It slightly flattened the APD restitution slope and furthermore reduced the conduction velocity and wavelength.
Conclusion Both drugs show similar prolongation of the QT interval, although they present different electrophysiological properties in the single-cell as well as in tissue simulations of cardiac excitation propagation. These computer simulations help to better understand the underlying mechanisms responsible for the initiation or termination of arrhythmias caused by amiodarone and cisapride.
M. Wilhelms, O. Dössel, and G. Seemann. In silico investigation of electrically silent acute cardiac ischemia in the human ventricles. In IEEE Transactions on Biomedical Engineering, vol. 58(10) , pp. 2961-2964, 2011[request PDF][doi]
Abstract: Acute cardiac ischemia, which is caused by the occlusion of a coronary artery, often leads to lethal ventricular arrhythmias or heart failure. The early diagnosis of this pathology is based on changes of the electrocardiogram (ECG), i.e. mainly shifts of the ST segment. However, the underlying mechanisms responsible for these shifts are not completely understood. Furthermore, clinical observations indicate that some acute ischemia cases can hardly be detected using standard 12-lead ECG only. Therefore, multi-scale computer simulations of cardiac ischemia using realistic models of human ventricles were carried out in this work. For this purpose, the transmembrane voltage distributions in the heart and the corresponding body surface potentials were computed with varying transmural extent of the ischemic region at different ischemia stages. Some of the simulated ischemia cases were electrically silent, i.e. they could hardly be identified in the 12-lead ECG.
Abstract: This review article gives a comprehensive survey of the progress made in computa- tional modeling of the human atria during the last 10 years. Modeling the anatomy has emerged from simple ”peanut”-like structures to very detailed models including atrial wall and fiber di- rection. Electrophysiological models started with just two cellular models in 1998. Today, five models exist considering e.g. details of intracellular compartments and atrial heterogeneity. On the pathological side, modeling atrial remodeling and fibrotic tissue are other important aspects. The bridge to data that are measured in the catheter laboratory and on the body surface (ECG) is under construction. Every measurement can be used either for model personalization or for validation. Potential clinical applications are briefly outlined and future research perspectives are suggested.
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.
Abstract: Generally, models of cardiac electrophysiology describe physiologic conditions in detail. However, other conditions, such as drug interactions or mutations of ion channels are of interest for research. Therefore, the simulated ion currents have to be fitted to measured voltage or patch clamp data. In this work, three different methods for the model parametrization were compared: one based on Powell’s algorithm implemented in a modular C++ framework and two optimization techniques realized in Matlab. The latter two approaches differed in solving the ordinary differential equations describing the channel gating. They can either be approximated numerically or solved analytically, since the transmembrane voltage is a piecewise constant function during the applied clamp protocol. All three methods were compared regarding computing time and quality of the fit using least squares. The modular C++ framework was slower than the numerical Matlab method, which took longer than the analytical one. The quality of the fit was similar for almost all analyzed methods. Therefore, the analytical method grants a fast and reliable solution for the calibration of ion current models for applications with constant membrane voltage, as e.g. in case of voltage or patch clamp data.
Abstract: Diagnosis of acute cardiac ischemia depends on characteristic shifts of the ST segment. The transmural extent of the ischemic region and the temporal stage of ischemia have an impact on these changes. In this work, computer simulations of realistic ventricles with different transmural extent of the ischemic region were carried out. Furthermore, three stages within the first half hour after the occlusion of the distal left anterior descending coronary artery were regarded. The transmembrane voltage distributions and the corresponding body surface ECGs were calculated. It was observed how the electrophysiological properties worsen in the course of ischemia, so that almost no excitation was initiated in the central ischemic zone 30 minutes after the occlusion. In addition to these temporal effects, also the transmural extent of the ischemic region had an impact on the direction and intensity of the ST segment shift.
Abstract: During acute cardiac ischemia, electrophysiological properties of the affected tissue are altered in the subendocardium firstly. If the occlusion worsens, the effects spread transmurally. Diagnosis of cardiac ischemia, which should be improved by computer simulations, is based on shifts of the ST segment. In this work, we simulated heterogeneous ischemic regions with varying transmural extent. The excitation propagation and ECGs were calculated for the different setups. We showed that ST segment polarity can be dependent on the transmural extent of the ischemic region. In case of subendocardial ischemia, short action potentials were initiated in the ischemic zone causing a slight transmural gradient of the transmembrane voltage. Therefore, the ST segment was depressed in leads near the ischemic region in the chosen case. During transmural ischemia, this gradient showed in the opposite direction from epicardium to endocardium leading to ST segment elevation.
Abstract: The monodomain model is a mathematical description of the electrical excitation propagation in the heart. The numerical solution of this reaction-diffusion equation is a computationally demanding task. Aspects that have to be considered are the accuracy and stability of the solution on the one hand and the computing time on the other hand. Two first order methods – an explicit and a semi-implicit scheme – solving the monodomain equation were compared in this work. For the benchmark of the solvers, three cell models with different computational complexity were used. Thus, the contribution of the solvers to the total computing time could be analyzed. Generally, if the same time step was used, the semi-implicit was slower than the explicit one, since an additional linear system of equations had to be solved. However, the semi-implicit solver was more accurate and showed better stability behavior than the explicit one, especially at high spatial resolutions. Therefore, larger time steps could be used, achieving the same accuracy and a shorter total computing time as the explicit solver. However, this effect was present only, if the additional calculations of the semi-implicit solver contributed less to the total computing time, i.e. the cell model had to be computationally complex.
A. Loewe, W. H. W. Schulze, Y. Jiang, M. Wilhelms, and O. Dössel. Determination of optimal electrode positions of a wearable ECG monitoring system for detection of myocardial ischemia: a simulation study. In Computing in Cardiology (Best Poster Award), vol. 38, pp. 741 - 744, 2011[request PDF][url]
Abstract: The early detection of myocardial ischemia is an essential lever for its successful treatment. We investigated an ECG monitoring system with 3 electrodes. Optimal electrode positions are determined using a cellular automaton. The spatially heterogeneous effects of myocardial ischemia were modeled by altering 4 electrophysiological parameters: action potential amplitude and duration, conduction velocity as well as resting membrane voltage. Both, transmural heterogeneity and the influence of the border zone were considered in the simulations on three patient models. The detection of myocardial ischemia is based on ST segment deviation from the physiological case. The signals used to find the best electrode positions comprise ischemic regions with different transmural extents in all 17 AHA segments. We show which ischemic ECGs can be detected given a realistic signal-to-noise ratio, false positive rate and maximum response time of the system.
Abstract: Atrial fibrillation (AF) is a common pathology. AF modifies the electrophysiological properties of cells (remodeling) promoting the occurrence and maintenance of AF.
Electrical remodeling includes changes in ICa,L, Ito, IK1 and IK,ACh. These effects were integrated in a human atrial computer model. Gap junction remodeling was considered in the conductivity of the monodomain equation calculating excitation. Specific features were calculated to determine the risk of AF initiation and perpetuation.
ERP was reduced from 330ms to 103ms. CV was lowered from 755mm/s to 608mm/s. The WL reduction was even higher (from 249mm to 63mm) leading to a higher probability of occurrence and maintenance of AF. A maximum of 7 spirals waves were initiated leading to a peak in the power spectrum at 10.32Hz.
The computer model underlines the relevance of remodeling in AF chronification. The results add to the knowledge of AF maintenance. Our model might prove to be a tool for the development of novel therapeutic strategies.
Preis für bestes Poster im Rahmen der Tagung Computers in Cardiology in Hangzhou:A. Loewe, W. H. W. Schulze, Yuan Jiang, M. Wilhelms, O. Dössel
Determination of optimal electrode positions of a wearable ECG monitoring system for detection of myocardial ischemia: a simulation study; Computing in Cardiology, vol. 38, pp. 741 - 744, 2011
[request PDF] [doi] [url] 