Validation of an original mathematical model of CO(2) elimination and dead space ventilation

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 PaCO(2) and airway pressures (P(AW)) to the patient mean during use of the DLT and a single-lumen tube (SLT). The model's resulting PaCO(2), PECO(2) 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, CO(2) production, temperature, and alveolar and anatomical dead spaces were matched to each mechanically ventilated subject. Bias and precision in predictions of PaCO(2) and PECO(2) 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 PaCO(2) was 1.2% (DLT) and 1.5% (SLT) and of PECO(2) was 1.7% (DLT) and 1.3% (SLT). Prediction of PaCO(2) and PECO(2) in the second investigation (as 95% confidence interval of bias): PaCO(2) -2.6% to 0.8% and PECO(2) -4.9% to 1.2%. This validation allows future application of our model in appropriate theoretical investigations.

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.