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A mass balance model for the Mapleson D anaesthesia breathing system

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Abstract

A mathematical model is described which calculates the alveolar concentration of\(CO_2 (F_{ACO_2 } )\) 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,\(F_{ACO_2 } \) is independent of Vf, at low fresh gas flow rates and high respiratory rates,\(F_{ACO_2 } \) is independent of respiratory rate. The model and the data show that the VT influences\(F_{ACO_2 } \) 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\(F_{ACO_2 } \) sucn tnat, for any combination of patient and breathing-system variables, there is a V1 that minimizes the Vf required to maintain\(F_{ACO_2 } \). In addition, expiratory resistance can increase the fresh gas flow rate required to maintain a given\(F_{ACO_2 } \) The respiratory patterns observed with spontaneous and controlled ventilation are responsible for the difference in Vf required with each mode of ventilation.

Résumé

On décrit un modèle mathématique qui calcule la concentration alvéolaire du\(CO_2 (F_{ACO_2 } )\) d’un patient qui ventile avec un système d’anesthésie du type Mapleson D. Le modèle utilise une série d’équlibrage statique pour le CO2 dans l’espace alvéolaire, l’espace mort, le volume des tubulures et le réservoir. Les variables considérées dans le modèle sont le volume courant (VT), la fréquence respiratoire, le débit des gaz frais (Vf), le volume de l’espace mort, le rapport I/E, et le volume du circuit espiratoire (V1), la constante de temps de l’expiration, et la production du CO2. Les prédictions du modèle sont comparées avec des mesures faties sur un simulateur de ventilation mécanique en ventilation spontanée et en ventilation contrôlee. Le modèle mathématique autant que les mesures expérimentales prédisent qu’à hauts débits de gaz frais et à basses fréquences respiratoires, la\(F_{ACO_2 } \) est indépendante du Vf; à bas débits de gaz frais et à hautes fréquences respiratoires, la\(F_{ACO_2 } \) est indépendante de la fréquence respiratoire. Le modèle et les mesures montrent que le volume courant influence la\(F_{ACO_2 } \), indépendamment de la ventilation minute seule, pendant la réinspiration partielle ou sans réinspiration des gaz expirés. Dès lors, décrire l’utilisation du système en termes de ventilation minute est ambigu. On montre aussi que V1 influence\(F_{ACO_2 } \) de tette manière que pour quelle que soit la combinaison entre patient et variables du circuit respiratore, il y a un V1 qui diminue le Vf requis pour maintenir la\(F_{ACO_2 } \). En plus, la résistance expiratoire peut augmenter le débit de gaz frais requis pour maintenir une\(F_{ACO_2 } \) donnée. Les caractéristiques respiratoires observées en ventilation spontanée et contrôlée sont responsables des différents Vf requis dans chaque mode ventilatoire.

Abbreviations

E/I:

Expiratory to inspiratory time ratio

f:

Frequency, respiratory rate

fmin :

Minimum respiratory rate achievable on an isopleth

\(F_{ACO_2 } \) :

Fractional concentration of CO2 in alveolar gas

Fb :

Concentration of reservoir gas

FD :

Concentration of gas occupying the dead space at end inspiration

F0 :

Concentration of fresh gas, equal to 0

\(P_{ACO_2 } \) :

Partial pressure of CO2 in alveolar gas, directly proportional to Fa

t:

time

Tee :

Time taken for the alveolar gas that will remain in the limb to pass the Y piece (zones I and II)

Tel :

Time taken during expiration for all the alveolar gas in V11 to pass the Y piece (zone III)

Teb :

Time from start expiration for all of VEB to flow past the Y piece

T1 :

Time of inspiration

Tpe :

Time period of expiration

TIB :

Time from start inspiration for all of VIB to flow past the Y piece

T :

Time constant of lung expiration

Vb :

Reservoir (bellows/bag) stroke volume

Vb :

Total reservoir volume less Vb

\(V_{CO_2 } \) :

Volume of CO2 produced by metabolic processes per breath

VD :

Physiologic dead space volume

VEB :

Volume of alveolar gas directly expired to the reservoir

VEx(t):

Volume of expired gas as a function of time

V1b :

Volume of gas inspired from reservoir to the alveoli

V11 :

Volume of gas inspired from limb to the alveoli

V1 :

Limb volume (volume between fresh gas inflow and reservoir)

Vr :

Volume of rebreathed alveolar gas

VT :

Tidal volume

VA :

Alveolar ventilation

\(\dot V_{CO_2 } \) :

Metabolic CO2 production rate

VEx(t):

Expiratory flow rate as a function of time

Vf :

Fresh gas flow rate

Vf,min :

Minimum fresh gas flow rate achievable on an isopleth

V1s :

Flow rate of gas delivered from the breathing-system

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Author information

Correspondence to Jeffrey B. Cooper.

Additional information

This work was supported by a grant from Ohmeda, Madison, WI.

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Lovich, M.A., Simon, B.A., Venegas, J.G. et al. A mass balance model for the Mapleson D anaesthesia breathing system. Can J Anaesth 40, 554–567 (1993). https://doi.org/10.1007/BF03009741

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Key words

  • equipment: anaesthesia circuits, non-rebreathing, Mapleson D