An empirical model of end-tidal CO2 response to minute ventilation

This paper presents an empirical model of end-tidal CO₂ (P_ETCO₂) response to minute ventilation (MV) for use in the closed-loop control of artificial respiration. An affine model structure consisting of a linear dynamic system followed by an affine transform is presented. It is proposed that this derives a low-order, high-fidelity representation of the respiratory process that can describe the positive and inversely proportional relationship between P_ETCO₂ and MV. The efficacy of the model is evaluated using experimental respiratory data from 18 human subjects. The model performed well with a root-mean-squared error (RMSE) of 0.22+/-0.15mmHg and a coefficient of determination (r²) of 0.81+/-0.18 (mean+/-SD) when a 2^nd-order rational transfer function was used as the linear component of the model. The physiologic implication of the model is analyzed by comparison with a traditional compartment model that is widely used in pharmacological modeling.