A Mathematical Model of Gas Exchange Predicting CO2 Response to Respiratory Rate Changes

Jörn Kretschmer, Christoph Schranz, and Knut Möller


Gas exchange, Mathematical modeling, Respiration frequency alteration, Medical decision support


A mathematical model of gas exchange is proposed to fit experimental data of end-tidal CO2 (etCO2) response to changes in respiratory frequency. Measurements were taken in patients while undergoing general anesthesia. The gas exchange model proposed by Chiari et al. has been extended to reduce differences in amplitude by a variable alveolar dead space compartment. This compartment, which represents the component of tidal volume that does not participate in gas exchange, changes size depending on ventilation frequency. Parameter identification has been conducted in two steps. First, metabolic production of CO2 has been determined to have the model reproduce the correct etCO2 at 12 breaths per minute and a dead space of 150ml. Then, parameters describing a hyperbolic dead space function have been identified so that etCO2 results of the model are close to the measured data. The proposed model showed to be able to reproduce the measured etCO2 levels.

Important Links:

Go Back