On the practical identifiability of a two-parameter model of pulmonary gas exchange

Successful application of mechanical ventilation as a life-saving therapy implies appropriate ventilator settings. Decision making is based on clinicians' knowledge, but can be enhanced by mathematical models that determine the individual patient state by calculating parameters that are not directly measurable. Evaluation of models may support the clinician to reach a defined treatment goal. Bedside applicability of mathematical models for decision support requires a robust identification of the model parameters with a minimum of measuring effort. The influence of appropriate data selection on the identification of a two-parameter model of pulmonary gas exchange was analyzed.

The model considers a shunt as well as ventilation-perfusion-mismatch to simulate a variety of pathologic pulmonary gas exchange states, i.e. different severities of pulmonary impairment. Synthetic patient data were generated by model simulation. To incorporate more realistic effects of measurement errors, the simulated data were corrupted with additive noise. In addition, real patient data retrieved from a patient data management system were used retrospectively to confirm the obtained findings. The model was identified to a wide range of different FiO 2 settings. Just one single measurement was used for parameter identification. Subsequently prediction performance was obtained by comparing the identified model predicted oxygen level in arterial blood either to exact data taken from simulations or patients measurements.

Structural identifiability of the model using one single measurement for the identification process could be demonstrated. Minimum prediction error of blood oxygenation depends on blood gas level at the time of system identification i.e. the measurement situation. For severe pulmonary impairment, higher FiO 2 settings were required to achieve a better prediction capability compared to less impaired pulmonary states. Plausibility analysis with real patient data could confirm this finding.

Dependent on patients' pulmonary state, the influence of ventilator settings (here FiO 2) on model identification of the gas exchange model could be demonstrated. To maximize prediction accuracy i.e. to find the best individualized model with as few data as possible, best ranges of FiO 2-settings for parameter identification were obtained. A less effort identification process, which depends on the pulmonary state, can be deduced from the results of this identifiability analysis.