Sustained slow sinus rhythm entrained by retrograde atrial impulses

Abstract

Sustained slow sinus rhythm due to a returning cycle after a premature atrial P wave is described. It seems possible to consider a model of the forced vibration in a spring-mass system or resonant electric circuit of an alternating current series element containing resistance R, inductance L, and capacitance C as a quantitative approach to describing the slow sinus rhythm. The differential equation expressing cardiac resonant oscillation has for the case $\text{R = 500Ω}$ the form $\text{178(}\text{d}{}^2\text{X}\text{d}\text{t}{}^2\text{) + 500(}\text{d}\text{X}\text{d}\text{t}\text{) + 5600X = 4490 cos 3.57}\text{t}$, where X is 100 q, where q is the capacitor charge. By solving the equation of this special case, we obtained an effective voltage and current of 0.84 V and 1.68 mA, respectively. Determination of cardiac electrical activity by this method was considered to be useful, and may have practical applications in solving problems of nearly linear resonance in vital phenomena. This is the first paper on applying a linear second order differential equation to describing a frequency response modelling of slow sinus rhythm due to entrainment by the retrograde atrial impulses.