MODELING 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. © 1994 Academic Press. All rights reserved.