An Unusual Form of Phase Walk in a System of Coupled Oscillators

Abstract

The authors describe an unusual form of phase walk (i.e., a progressive change in phase angle between coupled oscillators) using the 10-Hz rhythmic discharges of the inferior cardiac and vertebral postganglionic sympathetic nerves (CN and VN, respectively) in hypercapnic, baroreceptor-denervated, and vagotomized cats anesthetized with urethane. Unlike phase walk ascribable to weakened coupling (desynchronization of oscillators), the phase walk of VN 10- Hz activity relative to CN10-Hz activity 1) recurred on the time scale of the respiratory cycle, 2) was bidirectional with CN-VN phase angle increasing during expiration and decreasing during inspiration, and 3) occurred over a range equivalent to one-half the period of the 10-Hz rhythm rather than a full cycle. Moreover, this form of phase walk occurred during strong coupling of the 10-Hz oscillators, as reflected by CN-VN coherence values approaching 1.0. The authors propose that the bidirectional phase walk reflects a state of strong coupling of the 10-Hz oscillators controlling the CN and VN, the angle of which is reset from cycle to cycle by the continuously changing level of activity in their respiratory inputs. In addition, the data demonstrate that frequency and amplitude modulation of sympathetic nerve discharge can be independently regulated by respiratory inputs.