A mathematical model of the human ventilatory response to isocapnic hypoxia

Abstract

A mathematical model of the ventilatory response to a period of sustained isocapnic hypoxia in humans has been developed. After a step into hypoxia, there is an initial rapid increase in ventilation (on-transient) followed by a slow decline. At the relief of hypoxia, there is a rapid decrease in ventilation (off-transient); the magnitude of this off-transient is smaller than that of the on-transient. Previously, the asymmetry between the on- and off-transients has been dealt with by modeling the steps into and out of hypoxia separately. The current objective was to model the whole of the response by allowing the peripheral sensitivity to hypoxia to decline during the sustained exposure to hypoxia. The model was fitted to breath-by-breath data from 20-min periods of hypoxia (end-tidal oxygen 50 Torr) at two different levels of end-tidal carbon dioxide tension from five subjects. The model was able to describe the features of the ventilatory changes well, including the slow decline and the asymmetry.

An integrated model of the human ventilatory control system: the response to hypercapnia

“…In fact, these authors reproduced the hypoxic depression of respiratory centres through an additive term to ventilation, which is independent both of central and peripheral chemoreceptors. Although this choice might have some support from experiments on animals it seems inadequate to describe CVD in humans (Khamnei & Robbins, 1990; Painter et al ., 1993; Robbins, 1995). This aspect is especially evident when analysing the off transient responses to hypoxia and will be discussed in the second companion paper (Ursino et al ., 2001).…”

“…The second is that CVD causes a reduction of the ventilatory response to peripheral chemoreceptor stimulation (Khamnei & Robbins, 1990) (i.e. CVD would act by lessening the second term in the right hand member of Eqn (2)) (Painter et al ., 1993; Robbins, 1995). We tried to simulate both hypotheses with our model (unpublished simulations), but we reached the conclusion that only the second one may provide realistic results in humans.…”

“…The first are based on a few simple differential equations which directly link ventilation to CO 2 and O 2 pressure. Minimal models have been extensively used to achieve individual estimation of the main parameters (gains, time constants and pure delays) of the controller (Bellville et al ., 1979; Dahan et al ., 1990, 1994; Khamnei & Robbins, 1990), to examine the possible site of action of the hypoxic ventilatory decline (Khamnei & Robbins, 1990; Painter et al ., 1993; Liang et al ., 1997), and to analyse the stability margin of the ventilatory control system (Carley & Shannon, 1988). The main advantage of these models is that they can be easily solved on a computer with little computation time, hence are particularly suitable to fit real clinical curves through parameter estimation procedures.…”

An integrated model of the human ventilatory control system: the response to hypoxia

“…2, suggesting that, during normocapnia, HVD may cause a decline of ventilation as great as 2/3 of the initial peak. Similar patterns are reported by Painter et al. (1993).…”

“…The latter responds by increasing the ventilatory drive, in an effort to restore normal oxygen delivery to tissues. Various additional secondary mechanisms, however, interfere with this primary response, making analysis of the respiratory behaviour during hypoxia quite complex and contributing to the large inter‐individual variability reported in the literature (Khamnei & Robbins, 1990; Painter et al. , 1993; Dahan et al.…”