Objective To study ischemic effects on reentrant activities and cardiac arrhythmias using a computational approach. Method The Noble 98 mathematical model of ventricular cell was used in the study. The operator splitting and adaptive time step methods were utilized to integrate the partial differential equations in cardiac conduction models. The ischemic cells were simulated by decreasing the intracellular ATP concentration, reducing the Na+ conductance, and increasing the extracellular K+ concentration in a two-dimensional tissue. Spiral waves were initiated by the cross field technique. Result The results showed that spiral waves in local severe ischemia displayed three different morphologies,whereas in moderate ischemia only two kinds of wave forms exhibited. When the degree of ischemia reached a critical value, the reentrant wave could break. But for larger areas of ischemia spiral wave formed a typical functional reentry around the obstacle. Conclusion The study demonstrates that size and level of ischemia have effects on VTs and VFs. Large ischemic area is beneficial for maintenance of spiral wave and can provide a high probability in the genesis of VTs. Spiral waves can easily break up and degenerate into VFs under critical area or level of ischemia.

Computer simulation is one of the powerful protocols to study electrophysiology theoretically. In this paper,the algorithm of Rush and Larsen was used to solve the ordinary differential equations (ODE's) in the Luo-Rudy models of mammalian ventricular cell. The operator splitting and adaptive time step methods were used to solve the partial differential equations (PDE's) in cardiac tissue conduction models. Using these methods we accomplished the simulation programs of single ventricular cell model and two-dimensional (2-D) tissue model. The methods of initiating spiral waves were studied with this software. The data obtained from 2-D simulation can be used for further study on isopotential contour lines, spiral wave tip trajectories, and pseudo-ECG.
Algorithms ; Computer Simulation ; Electrocardiography ; Electrophysiology ; Heart Ventricles ; cytology ; Humans ; Models, Cardiovascular ; Myocytes, Cardiac ; physiology ; Software ; Ventricular Function

In order to explore the reason why hypokalemia could increase the vulnerable window (VW) for unidirectional conduction block in Long QT Syndromes (LQTS), we observed the effect of hypokalemia on the spatial gradients of Na channel conductance (G(Na)) and gating factors by using the LR91 1-dimensional heterogeneous virtual cardiac ventricular tissue model quatitively. The computer simulation experiments were divided into two groups, namely control and LQTS groups. The action potential was elicited after the basic stimulus S1 (-70 microA/microF, 1.5 ms) was given 10 times with basic cycle length (BCL) 500, 1000 and 2000 ms. To test the VW in unit of time (VWtime), the S1-S2 programmed stimuli were used with shortening S1S2 interval at the decrement of 1 ms. At the same time, the spatial gradients of Na channel conductance (G(Na)) and gating factors, m, h, j, were investigated. The APD and ionic channel currents were also detected under the conditions of normal and lower concentration of K+ outside of cell. We found that hypokalemia, LQTS and slow pacing rate enhanced the spatial gradient of G(Na) by increasing the spatial gradient of inactive gating factors h x j. The results also showed that hypokalemia deduced the peak values of I(K) and I(K1), which prolonged the action potential duration and enlarged the repolarization dispersion in this 1-D tissue cable model. Possibly these are the important factors to cause the spatial gradient of h x j and G(Na). enlargement. These changes increase the incidence of unidirectional conduction block of VW, and are vital reasons to increase the possibility of ventricular arrhythmia generation.
Computer Simulation ; Extracellular Space ; metabolism ; Humans ; Hypokalemia ; metabolism ; Long QT Syndrome ; etiology ; metabolism ; physiopathology ; Models, Biological ; Myocardium ; metabolism ; Sodium Channels ; metabolism

Ventricular fibrillation (VF) is the main cause of sudden death in cardiovascular diseases. The effects of electrophysiological heterogeneity and dynamic factors bring a lot of difficulties in understanding and revealing the mechanisms of VF. Cardiac short-term memory is one of the factors that make invalidation of restitution curve slope as the criteria for transition from ventricular tachycardia to VF. Therefore, investigation of inherent properties of short-term memory and its role in VF has great significance. In this paper we took advantage of the perturbed down-sweep protocol to measure dynamic and local S1S2 restitution curves on three widely used mathematical models to reveal their memory property. And by making abrupt change of the stimulation cycle length, we examined the attenuation process of the memory. The results showed, the rate-dependent action potendial duration (APD) is related with S1 pacing. The APD difference under different S2 cycle length is more pronounced with short S1 cycle length. Except the Luo-Rudy 1991 model, the Luo-Rudy 1994 and Noble 1991 models can at least reflect some of the short-term memory. And the memory attenuated in exponential way. Therefore, in quantitative electrophysiological study, these two models can be used in the future for investigating the characteristics of the short-term memory and its contribution to VF.
Action Potentials ; Computer Simulation ; Electrocardiography ; Heart Conduction System ; physiopathology ; Humans ; Models, Cardiovascular ; Models, Theoretical ; Myocardial Contraction ; physiology ; Ventricular Fibrillation ; physiopathology ; Ventricular Function

Cardiac reentry is one of the important factors to induce arrhythmias. It could lead to ventricular tachycardia (VT) or even fibrillation (VF), resulting in sudden cardiac death. With the wide use of computer in the quantitative study of electrophysiology, the three-dimensional virtual heart for simulations needs to be developed imminently in computer. In this paper, numerical algorithm of the model was studied. The three-dimensional model was constructed by integrating Luo-Rudy 1991 ventricular cell model and diffusion equation. The operator splitting method was employed to solve the model. The alternate direction iterative (ADI) format and seven-point centered difference method were used for the partial differential equation. And the discrete format with second-order accuracy was taken for the boundary conditions. The results showed that the ADI format and seven-point centered difference method both could successfully figure out the membrane potential and electrical activities with good numerical stability. However, computing consumption could be greatly reduced with the ADI format, implying that the ADI method with large time step was more powerful in numerical simulations.
Action Potentials ; Algorithms ; Heart ; physiology ; Heart Ventricles ; Humans ; Imaging, Three-Dimensional ; Models, Cardiovascular ; Myocardium

Malignant arrhythmias and ventricular fibrillation are generally accepted as one of the major causes of death in cardiovascular diseases. Based on the H-H equations, the mathematical model of the cardiac cell action potential consists of the ion channels, pumps, exchangers and transporters that are closely connected with intra- and extra-cellular ion concentrations, the channel's conditions, nerve transductors and drugs. It can build the link between cell electrophysiology and clinical pathophysiology. By altering the cellular environments the computer simulating study on this kind of model can help us look into the electrophysiological changes of the cardiac tissue and even the whole heart and investigate the mechanisms of the cardiac arrhythmias as well. The components of the model and its computer simulating study are introduced in the paper.
Action Potentials ; Arrhythmias, Cardiac ; physiopathology ; Computer Simulation ; Heart ; physiopathology ; Humans ; Models, Cardiovascular ; Ventricular Fibrillation ; physiopathology

Torsades de Pointes is a kind of severe ventricular arrhythmia. Myocardial ischaemia is one of the major causes leading to TdP. In this paper the mechanisms of the TdP were quantitatively studied under the condition of ischaemia based on the Noble98 dynamic model of the ventricular action potential. The study was conducted on one-dimensional homogeneous myocardium with the method of computer simulation. The models were firstly developed to simulate the lower excitability, extracellular accumulation of the K+ concentration or the decreased gap junctions in ischaemic myocardium. By separately reducing the Na+ conductance, increasing the extracellular K+ concentration or decreasing the conductance of the gap junctions enabled us to study the effect of each change in isolation. Then different degrees of ischaemic models were established to study their physiological features. The study showed that the conduction velocity became slower with the ischaemia aggravation, the action potential duration became shorter and the width of the vulnerable window obviously became larger than the normal conditions. The results illustrated that ischaemia was easily leading to unidirectional conduction block and resulted in re-entry and arrhythmias.
Computer Simulation ; Models, Cardiovascular ; Myocardial Ischemia ; physiopathology

On the basis of mammalian ventricular action potential model Noble98, and with the use of Runge-Kutta for solution, the Wenckebach periodicity phenomenon, the transmural heterogeneity of the ventricular myocardium and its rate dependence are studied. The results indicate that these inherent properties may, lead to temporal-space disorganized in the normal heart,and may become the underlying factors for arrhythmias. At the same time, in this study are established the basic methods for quantitative cellular electrophysiology which is essential for future studies on the mechanism of arrhythmia.
Action Potentials ; physiology ; Arrhythmias, Cardiac ; physiopathology ; Computer Simulation ; Electrophysiology ; Heart Conduction System ; physiology ; Heart Ventricles ; Humans ; Ion Channels ; metabolism ; Models, Cardiovascular ; Myocytes, Cardiac ; physiology