Recovering interaction of endogenous rhythms from observations is challenging, especially if a mathematical model explaining the behaviour of the system is unknown. The decisive information for successful reconstruction of the dynamics is the sensitivity of an oscillator to external influences, which is quantified by its phase response curve. Here we present a technique that allows the extraction of the phase response curve from a non-invasive observation of a system consisting of two interacting oscillators-in this case heartbeat and respiration-in its natural environment and under free-running conditions. We use this method to obtain the phase-coupling functions describing cardiorespiratory interactions and the phase response curve of 17 healthy humans. We show for the first time the phase at which the cardiac beat is susceptible to respiratory drive and extract the respiratory-related component of heart rate variability. This non-invasive method for the determination of phase response curves of coupled oscillators may find application in many scientific disciplines.

The change of blood volume, of blood and plasma density (rho b, rho p) following a short ultrafiltration pulse (duration: 20 min; mean rate -35 ml/min) within the first hour of hemodialysis was analyzed in 13 hemodynamically stable patients (30 single measurements). Protein concentration of refilling volume (7 g/liter) was calculated from its density (1009.25 +/- 3.7 kg/m3, at 20 degrees C) and from the linear relationship between plasma density and protein concentration (cp) of uremic plasma samples (rho p = 1007.46 + 0.2422 x cp). The filtration coefficient (Lp,calc) determined from a relation derived from Starling's hypothesis was 5.6 +/- 1.4 ml/(min.mm Hg.50 kg lean body mass); N = 13, mean +/- SD, minimum 3.2, maximum 8.0. A model describing the dynamics of blood and plasma volume was developed. It was fit to on-line measurements of relative blood volume changes by variation of the filtration coefficient and of initial blood volume (Lp,fit, Vb,fit). The linear regression between Vb,fit and blood volume determined from anthropometry (Vb,calc) was highly significant (r = 0.79, N = 30, P < 0.001). Compared to Vb,calc, Vb,fit was typically increased by 21 +/- 11%, reflecting a fluid overload at the beginning of the treatment. Lp,fit was not different from Lp,calc. Lp,fit significantly increased with blood volume excess. Due to the small but definite protein content of refilling volume, the model accounts for increased blood volume recovery and occasional overshoot of blood and plasma volumes following ultrafiltration.

1. The effect of a variation in inspiration and expiration times on heart rate variability was studied in 12 healthy subjects (mean age 30+/-6 years; five females). 2. Two 2 min trials of controlled breathing, with either short inspiration followed by long expiration or long inspiration followed by short expiration, were compared. Average expiration/inspiration time ratios were 1.0 and 3.4, respectively. The respiration rate in both trials was approximately 10 cycles/min. 3. In trials with short inspiration followed by long expiration, respiratory sinus arrhythmia (RSA; as measured by mean absolute differences and by the high frequency band) was significantly larger than in trials with long inspiration followed by short expiration. This effect could not be accounted for by differences in respiration rate or respiratory amplitude. The higher RSA during fast/slow respiration is primarily due to a more pronounced phasic heart rate increase during inspiration, indicating that inspiratory vagal blockade is sensitive to the steepness of inspiration. 4. Respiration rate and tidal volume are respiratory variables known to modulate RSA. The results of the present study indicate that RSA can also be modulated by a third respiratory variable, the expiratory/inspiratory time ratio.