Time course of etCO2 response to alterations in respiration rate predicted by a mathematical model of human gas exchange

A mathematical model of gas exchange is proposed to predict time course of end-tidal CO
₂
(etCO
₂
) response to alterations in ventilation frequency. The model has been fit to experimental data of patients undergoing general anesthesia. The gas exchange model proposed by Chiari et al. has been extended by a variable dead space compartment (V
_D
) to reduce differences in response amplitude. The dead space compartment represents the component of tidal volume that does not participate in gas exchange and changes size depending on ventilation frequency. Additionally, time course of CO
₂
response in the model has been fit to the measured data. Parameter identification has been conducted in three steps. First, metabolic production of CO
₂
has been determined to have the model reproduce the correct etCO
₂
at 12 breaths per minute and a dead space of 150 ml. Then, parameters describing a hyperbolic dead space function have been identified so that etCO
₂
results of the model are close to the measured data. Finally, reaction time of the model was fit employing individual V
_D
steps, so that the model shows the same time course to reach a new CO
₂
equilibrium as measured in the patients. Results show that employing a hyperbolic V
_D
function leads to a good match of the measured etCO
₂
equilibrium levels. The model itself is not able to reproduce the same reaction time as measured in the patient, but when applying a multiplication factor to speed gas equilibrium, it is possible to match model time course with measured data.