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GENERAL ARTICLES

Validation of an Original Mathematical Model of CO₂ Elimination and Dead Space Ventilation

From the University Department of Anesthesia, University Hospital, Nottingham, UK

Address correspondence and reprint requests to Dr. Jonathan G. Hardman, Clinical Senior Lecturer, University Department of Anesthesia, University Hospital, Nottingham, NG7 2UH, UK. Address email to j.hardman{at}nottingham.ac.uk

We present an original, mathematical model of ventilation and gas-exchange. Our aim was to validate it using data from previous clinical investigations, allowing our use of it in future investigations. The first previous investigation used a low-dead space, double-lumen, tracheal tube (DLT). We matched the model’s PaCO₂ and airway pressures (P_AW) to the patient mean during use of the DLT and a single-lumen tube (SLT). The model’s resulting PaCO₂, PÉCO₂ and P_AW were compared with the patients’ as tidal volume (VT) changed with constant minute volume. The second investigation examined dead space during anesthesia. The model’s VT, respiratory rate, CO₂ production, temperature, and alveolar and anatomical dead spaces were matched to each mechanically ventilated subject. Bias and precision in predictions of PaCO₂ and PÉCO₂ were calculated. The model’s bias in prediction of dead space reduction by the DLT was 6.9%. Bias in prediction of P_AW was 0.1% (peak) and -5.13% (mean), of PaCO₂ was 1.2% (DLT) and 1.5% (SLT) and of PÉCO₂ was 1.7% (DLT) and 1.3% (SLT). Prediction of PaCO₂ and PÉCO₂ in the second investigation (as 95% confidence interval of bias): PaCO₂ -2.6% to 0.8% and PÉCO₂ -4.9% to 1.2%. This validation allows future application of our model in appropriate theoretical investigations.

IMPLICATIONS: We present an original, mathematical model of ventilation and gas exchange. We validate it against previously published clinical data to allow its use in future theoretical investigations where data may be unavailable from patients.

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