How rebreathing anaesthetic systems control Paco 2: Studies with a mechanical and a mathematical model

Results from a proposed equation for rebreathing systems, \(Pa_{CO_2 } = \frac{{\dot V_{CO_2 } (P_B - P_{H_2 O} )}}{\begin{gathered} \dot V_E (1 - V_D /V_T ) \\ + \frac{{\dot V_{CO_2 } (P_B - P_{H_2 O} )}}{{\dot V_F }} \\ \times \frac{{\dot V_E - \dot V_F }}{{\dot V_E }} \\ \end{gathered} }\) were compared with results from a mechanical model “lung” ventilated either with a Bain Breathing Circuit, or a circle system (Eger-Ethans type A) without soda lime. When values for carbon dioxide excretion (Vco₂), dead space-tidal volume ratio (Vd/Vt), minute volume ventilation (Ve), and fresh gas flow (Vf) were varied over a wide range, the model and the equation yielded identical values of Pa_{co 2}. When Vco₂ = 2.25 ml/kg, Vd/Vt = 0.5, and Ve = 140 ml/kg, then fresh gas flows (Vf) with both the equation and the model produced values of Pa_{co 2} which were very close to those found by Bain and Spoerel in anaesthetized, artificially ventilated humans. It is concluded that the equation is an accurate mathematical representation of how rebreathing anaesthetic systems control Pa_{co 2}. It is expected that the equation will be useful in the clinical application of rebreathing anaesthetic systems, allowing the selection of minute volumes and fresh gas flows which will yield predictable Pa_{co 2} values. Les auteurs proposent un modèle mathématique représentatif du contrôle de la Pco₂ dans les circuits anesthésiques avec réinspiration. Ľusage ďun modèle mécanique de poumon, ventilé au moyen ďun circuit de Bain ou ďun circuit sans réinspiration (Eger-Ethans) a permis de vérifier la validité de ľéquation. La formule proposée est la suivante: \(Pa_{CO_2 } = \frac{{\dot V_{CO_2 } (P_B - P_{H_2 O} )}}{\begin{gathered} \dot V_E (1 - V_D /V_T ) \\ + \frac{{\dot V_{CO_2 } (P_B - P_{H_2 O} )}}{{\dot V_F }} \\ \times \frac{{\dot V_E - \dot V_F }}{{\dot V_E }} \\ \end{gathered} }\) Pa_{co 2} = Pression partielle de la Pco₂ artérielle Vco₂ = Excrétion-minute de CO₂ Ve = Ventilation-minute Vd/Vt = Rapport espace mort/volume courant Vf = Apport de gaz frais-minute Pb - Ph₂o = Pression barométrique - Pression de vapeur ďeau. Cette équation apparaît ďutilité clinique car elle permet la sélection des volumes de ventilation-minute et des débits de gaz frais nécessaires pour maintenir la Pco₂ à des niveaux prévisibles.