A simple gas exchange model predicting arterial oxygen content for various FiO<inf>2</inf> levels

Abstract

The application of mechanical ventilation is a life-saving routine therapy that allows the patient to overcome the physiological impact of surgeries, trauma or critical illness by ensuring vital oxygenation and carbon dioxide removal. Above a certain level of minute ventilation (usually set to ensure acceptable carbon dioxide removal and oxygenation) oxygenation is only marginally affected by a further increase in minute ventilation. Thus, oxygenation is predominantly influenced by inspiratory oxygen fraction (FiO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> ) Usually, finding the appropriate setting is a trial-and-error procedure, as the clinician is unaware of the exact value that needs to be set in order to reach the desired arterial oxygen partial pressures (PaO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> ) in the patient. Mathematical models of physiological processes in the human body may be used to predict patient reactions towards alterations in the therapy regime. These predictions can be exploited by Medical Decision Support Systems to find optimal therapy settings. A simple mathematical model is presented, that allows calculation of a patient's shunt fraction, i.e. the percentage of blood that is not participating in lung gas exchange. On this basis, it predicts PaO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> at various FiO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> -levels and thus allows reaching desired PaO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> in just one step. Due to its simple design it does not require complicated - and possibly error-prone - parameter identification procedures, thus allowing its application at the bedside. Retrospective analysis of oxygenation data from a patient data management system showed that the presented model predicted PaO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> with less than 10% deviation in 23 out of 29 measurements, proving the practical applicability of the presented model approach.