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To study the interaction of forces that produce chest wall motion, we propose a model based on the lever system of Hillman and Finucane (J Appl Physiol 63(3):951-961, 1987) and introduce some dynamic properties of the respiratory system. The passive elements (rib cage and abdomen) are considered as elastic compartments linked to the open air via a resistive tube, an image of airways. The respiratory muscles (active) force is applied to both compartments. Parameters of the model are identified in using experimental data of airflow signal measured by pneumotachography and rib cage and abdomen signals measured by respiratory inductive plethysmography on eleven healthy volunteers in five conditions: at rest and with four level of added loads. A breath by breath analysis showed, whatever the individual and the condition are, that there are several breaths on which the airflow simulated by our model is well fitted to the airflow measured by pneumotachography as estimated by a determination coefficient R(2) > or = 0.70. This very simple model may well represent the behaviour of the chest wall and thus may be useful to interpret the relative motion of rib cage and abdomen during quiet breathing.

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.

Several models of oscillators defined by a system of non-linear differential equations have been built which simulate quite well some entrainment characteristics of the respiratory system: the range of entrainment, positioning of the stimulus at entrainment and the variation of inspiratory duration with entrainment periods. The construction of the model has been guided by consideration of the isochron configuration and the phase response curve of the system, which may yield a good qualitative fit between simulation and experimental results.