Nonlinear interactions between respiration and heart rate: classical physiology or entrained nonlinear oscillators

Heart-rate fluctuations at low frequencies (between 0.01 and 0.08 Hz) are often accompanied by changes in respiratory tidal volume and rate at the same low frequency. These respiratory fluctuations are a type of amplitude and frequency modulation of the instantaneous lung volume. Consequently, the respiratory signal itself has little spectral content at the modulation frequency, whereas a nonlinear transformation of the signal, such as the envelope formed by its inspiratory and expiratory peaks, has a clear spectral peak at the modulation frequency. The authors propose three possible mechanisms for this nonlinear relationship between respiration and heart rate. One is based on a classical feedback and control model of regulatory physiology; one considers the effect of forcing a Van der Pol oscillator with a low-frequency sine wave; and one considers the interactions between two simple nonlinear oscillators whose intrinsic frequencies are near the primary respiratory frequency