Modelling the dynamic ventilatory response to hypoxia in normal subjects

We have developed a mathematical model to describe the dynamic ventilatory response to hypoxia. The ventilatory response to both transient (two to three breaths nitrogen) and 3 min step change hypoxic stimuli were measured in ten normal subjects during moderate exercise (oxygen consumption 0.96 +/- 0.08 1 min-1). The simplest model relating ventilation to ear oxygen saturation which adequately described the responses in all subjects consisted of two linear differential equations in parallel; both using the fall in oxygen saturation as input, and with the outputs summed to give the rise in ventilation. One equation had a fast time constant (< 3 sec), and the other a slow time constant. Non-linear terms included were (i) a "saturating" effect, similar to that described by the Michaelis-Menten equation, reducing the gain of the equation with the slow time constant as oxygen saturation falls, and (ii) "inhibition" or "potentiation" of the gain of the equation with a slow time constant as the output of the fast time constant equation increased. Repeated measurements in four subjects showed intra- and inter-subject variability for all parameters, with significant between-subject variability for the gain of the fast time constant equation. The final model structure is similar to that describing the peripheral chemoreceptor-mediated hypoxic ventilatory response in anaesthetized cats.