Perpetual atrial arrhythmias causing a prolonged returning cycle as an expression of cardiac resonant oscillation

A theoretical method of calculating ventricular myocardial voltage and time constant from the findings of 40 portions in electrocardiographic (ECG) tracings of 25 cases, in which atrial premature beats with full returning cycle can be observed, is presented. An resonant electric circuit of an alternating current series element containing resistance (R) of 500 ohms, inductance (L), and capacitance (C) was assumed as a model in this study. The steady-state voltage (Vm) was calculated in terms of the real part of the complex expression L(d2q/dt2) + 500(dq/dt) + (1/C)q = Vmej omega t, where L = 250/ zeta omega n, 1/C = omega n2 L, and Vm = A(zero) omega n2 Lx 100. The effective voltage derived ranged from 0.77 to 0.88 (mean, 0.82) V. The mean value approximated the mean voltage stimulation threshould of the human right ventricle. The time constant RC ranged from 73 to 135 ms. This is the first paper to establish that this method is clinically applicable. The dynamical system regulating the heart rhythm was described as a finite-dimensional matrix representation, which possesses diagonal elements, i.e. eigenvalues, of I/4 square root of 2 pi and 1/2.