Nonlinear dynamics of the frequency locking of baroreceptor and sympathetic rhythms

We used phase plane analysis to identify modes of frequency locking of the 10-Hz rhythm in sympathetic nerve discharge (SND) to the cardiac cycle in urethan-anesthetized, baroreceptor-innervated cats. Frequency locking occurred in rational ratios predicted by a generic mathematical construct called the Farey tree. Both simple harmonic ratios (e.g., 1:3) and complex ratios (e.g., 2:5) comprised of relatively prime integers (no common divisor) were identified under natural conditions. Frequency locking in such ratios is attributed to forcing of the 10-Hz oscillator by pulse-synchronous baroreceptor afferent nerve activity (BNA). Ventricular pacing changed the frequency of the 10-Hz rhythm as well as heart rate so as to maintain or change the ratio of frequency locking in a predictable way. Intriguingly, frequency locking of the 10-Hz rhythm to medullary raphe sympathoinhibitory stimuli in simple harmonic ratios was accompanied by increased power in the 10-Hz band of SND, whereas locking in complex ratios led to decreased 10-Hz power. These findings raise the possibility that pulse-synchronous BNA also exerts divergent actions on the 10-Hz rhythm depending on the ratio of frequency locking. Augmented 10-Hz power can be attributed to the resonant properties of oscillators that are periodically forced at the same phase in their cycle.