A mass balance model for the Mapleson D anaesthesia breathing system

Abstract

A mathematical model is described which calculates the alveolar concentration of {Mathematical expression} in a patient breathing through a Mapleson D anaesthesia system. The model is derived using a series of mass balances for CO2 in the alveolar space, dead space, breathing system limb volume and reservoir. The variables included in the model are tidal volume (VT), respiratory rate, fresh gas flow rate (Vf), dead space volume, I:E ratio, and expiratory limb volume (V1), time constant of lung expiration, and carbon dioxide production rate. The model predictions are compared with measurements made using a mechanical lung simulator in both spontaneous and controlled ventilation. Both the model and the experimental data predict that at high fresh gas flow rates and low respiratory rates, {Mathematical expression} is independent of Vf, at low fresh gas flow rates and high respiratory rates, {Mathematical expression} is independent of respiratory rate. The model and the data show that the VT influences {Mathematical expression} independent of minute ventilation alone, during both partial rebreathing and non-rebreathing operation. Therefore, describing the operation in terms of minute ventilation is ambiguous. It is also shown that V1 influences {Mathematical expression} sucn tnat, for any combination of patient and breathing-system variables, there is a V1 that minimizes the Vf required to maintain {Mathematical expression}. In addition, expiratory resistance can increase the fresh gas flow rate required to maintain a given {Mathematical expression} The respiratory patterns observed with spontaneous and controlled ventilation are responsible for the difference in Vf required with each mode of ventilation. © 1993 Canadian Anesthesiologists.