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.

Density is defined as mass per unit volume. The classical technique to measure the density of fluids consists of a determination of mass and volume. Blood density is proportional to hematocrit or, more exactly, to the total protein concentration of blood; only to a minor extent is blood density influenced by other plasma solutes. Since the introduction of the mechanical oscillator technique for the continuous recording of fluid density a sizeable amount of experience has accumulated. This review summarizes recent work performed with this technique. It appears that the scientific interest in a variable like blood density depends on the availability of a suitable and simple method. Until the oscillator technique was available the measurement of density was too complicated or too inaccurate for routine laboratory use. A further new technique permits us to determine fluid densities by measuring sound velocity transmission. The density dilution method can be used for the determination of distribution volumes, of flow through organs, and of the cardiac output. The influence of temperature and of certain artifacts like acceleration forces in the density measuring device have to be considered any may be used for additional diagnostic purposes like determination of erythrocyte sedimentation velocity. The new technique opens a reasonable simple way to study fluid shift between interstitial space and capillaries. The arterio-venous density gradient in an organ depends on the lymph production. The injection of a hypertonic solution leads to an osmotic fluid shift from the extravascular space towards the blood. This fluid shift can be recognized by a reduction of the blood density. A simple model for the description of this reaction is presented.

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