Simulation study of QRS-T waves based on an eccentric spherical model of the heart

The relationship between the difference in the action potential duration in the myocardium and the T wave investigated by a mathematical model of the electrical activity of the heart. In this study we constructed an eccentric spherical model which duplicates the ventricles except for the interventricular septum. Our model is assumed to be composed of the working myocardium and the excitation conduction system which is uniformly distributed on the endocardial surface. The ventricular gradient was defined as a linear decrease (beta msec/cm) of the duration of the action potential from the endocardium to the epicardium according to the concept proposed by Wilson. Theoretical analysis based on this model strongly suggest that the ventricular gradient of 10-40 msec/cm accounts for the normal QRS-T angle since vectorcardiographic analysis have revealed that the QRS-T angle closely correlates with the angle (theta) between the directions of the propagation waves of depolarization and repolarization. The QRST waves in the standard limb and chest leads were calculated from the sum of the time-varying dipoles derived from the action potential, assuming that the heart was in a homogenous conducting medium. Simulated QRS-T waves were compatible with the clinically observed electrocardiograms not only under normal conditions but also with changes in the spacial position of the heart and the wall thickness. Positive T waves were obtained in the left precordial leads when the ventricular gradient was more than 20 msec/cm and when the amplitude of T wave increased with the transmural gradient. Our model also indicates that differences in the velocities of the excitation wave in the conduction system and the working myocardium may affect the polarity of the T wave.