Multiple electrode mapping of the ventricles during complex tachyarrhythmias has revealed focal subendocardial activation whose mechanism remains unexplained We hypothesized that reentry involving the Purkinje-muscle junctions (PMJs) may be a mechanism for such focal excitations We have constructed an anatomically appropriate computerized 3-dimensional model of the mammalian ventricles that includes the Purkinje conduction system and 214 PMJs distributed throughout the endocardium Isochronal maps during normal excitation, as well as during right or left bundle branch block, resembled experimental measurements and compared well with isochronal maps of propagation in the human heart Activity observed at both sides of a PMJ in the model showed that propagation from Purkinje fibers to muscle was slower than in the opposite direction Under these realistic and normal conditions, the evolution of reentrant activity involving muscle and the Purkinje network was simulated The reentry pattern was independent of the initiation site It evolved with drifting epicardial breakthroughs and transformed on the endocardium from focal activity to figure-of-8 reentry In addition, the ECG amplitude undulated during the evolution, and decrease in the cycle period, apparent wavelength, and propagation velocity were observed Finally, the reentry was terminated if the Purkinje system was disconnected from the muscle before it reached a relative steady state The simulation results suggest the following: (1) Epicardial breakthroughs and endocardial focal activity may originate at the PMJs (2) The ECG amplitude may decrease as the reentry stabilizes and the excitation wavelength decreases (3) The Purkinje system may have a double role in the evolution of reentry: first, it is essential to the reentry at the initial stage; second, it may lead to the establishment of intramyocardial reentry, at which time the Purkinje system becomes irrelevant

Purkinje-Muscle Reentry as a Mechanism of Polymorphic Ventricular Arrhythmias in a 3-Dimensional Model of the Ventricles

The biophysical basis for understanding the electrocardiogram is set forth. Bioelectric sources arise from electrical activity in the heart at the cellular level. The relation of these sources, which can be formally represented as impressed currents, to potentials involves solution of the volume conductor problem. This solution is based on Green's theorem. Sources are related to the transmembrane action potential through a bidomain model of heart muscle. Microscopic and macroscopic aspects of the bidomain model are developed. Various transformations of the source are considered, including multipoles, multiple dipoles, and replacement of the volume distribution with distributions on the heart surface. Time integrals of the waveform are related to excitation time and action potential duration. The theoretical results form the basis of a computer model of the electrocardiogram that relates skin potentials to the spatial and temporal distribution of action potentials in the heart. >

On the theory of the electrocardiogram

Recent studies have analyzed the high-fidelity surface electrocardiographic signal, and efforts have been made to increase the diagnostic sensitivity of the electrocardiogram by observing its high-frequency components. It was found that the high-frequency (150-250-Hz) electrocardiogram appears to detect evidence of transient ischemia with greater sensitivity than visual inspection of the surface electrocardiogram. A finite-element three-dimensional model of the ventricles with a self-similar (fractal) conduction system has been introduced as a bridge to the understanding of electrocardiographic phenomena related to high-frequency potentials. The model was activated, and the dipole potential generated by adjacent activated and resting cells was calculated to obtain a high-resolution QRS complex. Normal and ischemic activation processes was stimulated by regional reduction in conduction velocity. It was found that although the resulted low-frequency QRS complex was not significantly altered from normal conditions, the high-frequency components exhibited morphological changes similar to the ones observed during animal experiments and human studies. Based on the results obtained from the model, it can be concluded that these morphological changes can be attributed to a slowing of conduction velocity in the region of ischemia and that the model is adequate for meeting the challenges imposed by the requirements of high-frequency methods applied in clinical cardiology.

Simulation of high-resolution QRS complex using a ventricular model with a fractal conduction system. Effects of ischemia on high-frequency QRS potentials.

We have developed a new approach for imaging cardiac transmembrane potentials (TMPs) within the three-dimensional (3-D) myocardium by means of an anisotropic heart model. The cardiac TMP distribution is estimated from body surface electrocardiograms by minimizing objective functions of the "measured" body surface potential maps (BSPMs) and the heart-model-generated BSPMs. Computer simulation studies have been conducted to evaluate the present 3-D TMP imaging approach using pacing protocols. Simulations of single-site pacing at 24 sites throughout the ventricles, as well as dual-site pacing at 12 pairs of sites in the vicinity of atrio-ventricular ring were performed. The present simulation results show that the correlation coefficient (CC) and relative error (RE) between the "true" and inversely estimated TMP distributions were 0.9915/spl plusmn/0.0041 and 0.1266/spl plusmn/0.0326, for single-site pacing, and 0.9889/spl plusmn/0.0034 and 0.1473/spl plusmn/0.0237 for dual-site pacing, respectively, when 10 /spl mu/V Gaussian white noise (GWN) was added to the BSPMs. The effects of heart and torso geometry uncertainty were also evaluated by shifting the heart position by 10 mm and altering the torso size by 10%. The CC between the "true" and inversely estimated TMP distributions was above 0.97 when these geometry uncertainties were considered. The present simulation results demonstrate the feasibility of noninvasive estimation of TMP distribution throughout the ventricles from body surface electrocardiographic measurements, and suggest that the present method may become a useful alternative in noninvasive imaging of distributed cardiac electrophysiological processes within the 3-D myocardium.

Noninvasive imaging of cardiac transmembrane potentials within three-dimensional myocardium by means of a realistic geometry anisotropic heart model

The His-Purkinje conduction system initiates the normal excitation of the ventricles and is a major component of the specialized conduction system of the heart. Abnormalities and propagation blocks in the Purkinje system result in abnormal excitation of the heart. Experimental findings suggest that the Purkinje network plays an important role in ventricular tachycardia and fibrillation, which is the major cause of sudden cardiac death. Nowadays an important area in the study of cardiac arrhythmias is anatomically accurate modelling. The majority of current anatomical models have not included a description of the Purkinje network. As a consequence, these models cannot be used to study the important role of the Purkinje system in arrhythmia initiation and maintenance. In this article we provide an overview of previous work on modelling of the Purkinje system and report on the development of a His-Purkinje system for our human ventricular model. We use the model to simulate the normal activation pattern as well as abnormal activation patterns resulting from bundle branch block and bundle branch reentry.

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Modelling of the ventricular conduction system.

A three-dimensional computer model has been constructed to simulate the ventricular depolarization and repolarization processes in a human heart. The electrocardiogram (ECG), the vectorcardiogram(VCG), and the body surface potential map (BSPM) during the QRS-T period are obtained automatically under certain heart conditions such as bundle branch block and myocardial infarctions. The ventricles, together with bundle branches and the Purkinje fibers, are composed of approximately 50 000 cell units which are arranged in a cubic close-packed structure. A different action potential waveform was assigned to each unit. The heart model is mounted in a homogeneous human torso model. Electric dipoles, which are proportional to the spatial gradient of the action potential, are generated in all the cell units. These dipoles give rise to a potential distribution on the torso surface, which is calculated by means of the boundary element method. The resulting ECG's, VCG's, and BSPM's are within the expected range of clinical observations.

Three-Dimensional Simulation of the Ventricular Depolarization and Repolarization Processes and Body Surface Potentials: Nornal Heart and Bundle Branch Block

The relationship between the location of an accessory pathway and body surface ECG waveforms was investigated by computer simulation of the WPW syndrome using a human heart model. The 3-dimensional heart model is composed of 50,000 units so as to represent the details of ventricular excitation. Ten typical accessory pathways near the A-V groove were examined, which correspond to Gallagher's classification of the WPW syndrome based on their surgical experience. Twelve-lead ECG waveforms were calculated for these 10 cases and were compared with the clinical observations of Gallagher et al. The polarities of the delta waves at 40 msec after the onset of the QRS were listed. The agreement of our model with the clinical data obtained by Gallagher et al is 87%. Details of changes in the ECG waveforms were also examined by changing ther terminal location of the accessory pathway along the radial and longitudinal directions in the ventricles, and it was found that the ECG waveforms of the limb leads are more sensitive to this difference in the preexcited location than those of the chest leads. The simulated epicardial isochronic patterns also agree with the measurements.

Computer simulation of the Wolff-Parkinson-White syndrome utilizing a human heart model.

A computer algorithm for 3-dimensional computer simulation of electric phenomena in the human heart has been completed, in which the heart model consists of 50,000 functional cells arranged in the cubic close-packed structure and various waveforms of the action potential have been allotted to these functional cells. The present model allows one to estimate time courses of ECG, VCG, and body surface potential distribution from the P-wave up to the T-wave. It also can simulate electric phenomena in the heart with anomalies in the conduction system and the myocardium.

3-dimensional computer simulation of depolarization and repolarization processes in the myocardium.

PURPOSE:To theoretically and directly analyze an intracardiac excitation and to apply the analysis to a diagnosis, by constructing a minute three-dimensional myocardial model for exactly reproducing an electric phenomenon occurring in a heart and by simulating a myocardial excitation-propagation and its recovery process. CONSTITUTION:Various cardiac conditions are simulated by altering a basic cardiac model by a means of geometrically changing a cardiac model construction 1, a means of changing a waveform of a myocardial action potential 2 and a means of changing the ratio of a propagation velocity of a special myocardium 3 to that of a heart myocardium and by altering a cardiac barning model memory means 4 by a means of changing a barning condition 5. The basic cardiac model includes many myocardial cells, all of which are calculated by an excitation wavefront processing means 6. A body surface potential processing means 7 divides the cardiac model into an appropriate number of blocks and calculates a body surface potential from the mean dipole value of each block. In the above manner, a diagnosis of an abnormal part, an analysis of the relation between each cardiac part and a coronary symptom and a reproduction of various cardiac conditions are easily attained.

Masanori Aoki

Papers

Three-Dimensional Simulation of the Ventricular Depolarization and Repolarization Processes and Body Surface Potentials: Nornal Heart and Bundle Branch Block

Computer simulation of the Wolff-Parkinson-White syndrome utilizing a human heart model.

3-dimensional computer simulation of depolarization and repolarization processes in the myocardium.

Simulator for cardiac electric phenomenon