Minimal model quantification of pulmonary gas exchange in intensive care patients

Mathematical modeling of extracorporeal CO2 removal therapy

“…The impairments of pulmonary gas exchange is described by two parameters: f s which describes the importance of the pulmonary shunt (this parameter is also used in the works of D. S. Kabring et al [16] and of S. E. Rees et al [29]) andV L which is the mean effective ventilation (the ventilation that actually participates in gas exchange). In addition, the production of CO 2 (M R CO 2 ) and the consumption of O 2 (M R O 2 ) by metabolism are two important parameters for the appropriate description of the respiratory system.…”

“…Indeed, during ARDS, many alveoli do not work properly and the increase of the pulmonary shunt with ARDS is observed in physiology [2,31]. The value of f s during ARDS (45.7±3.6%) is larger than in previous studies of human ARDS (31±10% [16]) but note that the experiments are carried out on pigs and that ARDS is not "real" since it is only simulated by injecting water into the lungs. The value of f s at baseline (6.3±0.9%) is also larger than expected for a healthy human (2% [13]) but the pigs are intubated and anesthetized and thus not in a truly physiologically healthy state.…”

“…This assumption does not hold for gas exchanges abnormalities and this model need to be completed with additional parameters and additional equations. Our model considers two physiological parameters: f s which describes the importance of the pulmonary shunt (like in the work of D. S. Kabring et al [16] and S. E. Rees et al [29]) andV L which is the mean effective ventilation. In this context, the material balance of CO 2 in the lungs can be written as :…”

“…Some authors have proposed modeling these abnormalities by including a perfusion/ventilation mismatch [16] or by decreasing the diffusion across the alveolar capillary membrane [29]. However, very few authors have developed models of the respiratory system connected to an extracorporeal lung support [6,36,22,20].…”

Robustness Analysis of a Mathematical Gas Exchange Model

“…The model generally consists of three model parameters: shunt fraction (f s ), the fractions of ventilation (f A ) and perfusion distribution (f Q ). Karbing et al reduced the number of free parameters to two by setting f Q = 0.9 meaning that 90% of the non shunted blood (1-f s ) circulates to the first alveolar compartment as described in [2]. The structure of the analysed gas exchange model is shown in Fig.1.…”