Untitled

Abstract

Misunderstanding of the dynamical behavior of the ventilatory system, especially under assisted ventilation, may explain the problems encountered in ventilatory support monitoring. Proportional assist ventilation (PAV) that theoretically gives a breath by breath assistance presents instability with high levels of assistance. We have constructed a mathematical model of interactions between three objects: the central respiratory pattern generator modelled by a modified Van der Pol oscillator, the mechanical respiratory system which is the passive part of the system and a controlled ventilator that follows its own law. The dynamical study of our model shows the existence of two crucial behaviors, i.e. oscillations and damping, depending on only two parameters, namely the time constant of the mechanical respiratory system and a cumulative interaction index. The same result is observed in simulations of spontaneous breathing as well as of PAV. In this last case, increasing assistance leads first to an increase of the tidal volume (VT), a further increase in assistance inducing a decrease in VT, ending in damping of the whole system to an attractive fixed point. We conclude that instabilities observed in PAV may be explained by the different possible dynamical behaviors of the system rather than changes in mechanical characteristics of the respiratory system.

A model of mechanical interactions between heart and lungs

“…First, as described in §2, the respiratory system model includes a respiratory oscillator. Various oscillators have been presented in the literature (Younes & Riddle 1981;Pham Dinh et al 1983;Thibault et al 2002). Younes & Riddle proposed a complete and complex oscillator, but, owing to the great number of parameters involved, their model does not meet our demands.…”

“…In this paper, we develop a model that combines a respiratory pattern generator module (Thibault et al 2002) with a simple respiratory model module simulating rib cage internal mechanics and a minimal haemodynamic system model (Smith et al 2004), taking into account cardiogenic oscillations. To achieve our goals, we consider, on the one hand, pleural pressure as the functional output of the respiratory model and we insert it into the CVS where the effect of pleural pressure is considered significant.…”

“…This system simulates the activity of the respiratory centres, the respiratory muscles and rib cage internal mechanics. It combines a central respiratory pattern generator and a passive mechanical respiratory system (Thibault et al 2002). There are two physiological interactions between the central respiratory pattern generator and the mechanical respiratory system: (i) the respiratory pattern generator activity is modulated by the lung volume variations, and (ii) the lung volume is periodically modified by the respiratory pattern generator activity through the respiratory muscles.…”

“…For the central respiratory pattern generator, we do not use the modified Van der Pol oscillator developed by Pham Dinh et al (1983) as in Thibault et al (2002); a Liénard system is proposed as the basis for modelling the respiratory rhythm generator.…”