Identifying mathematical models of the mechanically ventilated lung using equation discovery

Mechanical ventilation is the live-saving therapy in intensive care medicine by all means. Nevertheless, it can induce severe mechanical stress to the lung, which generally impairs the outcome of the therapy. To reduce the risk of a ventilator induced lung injury (VILI), lung protective ventilation is essential, especially for patients with a previous medical history like the adult respiratory distress syndrome (ARDS). The prerequisite for lung protective ventilation approaches is the knowledge about the physical behavior of the human lung under the condition of mechanical ventilation. This knowledge is commonly described by mathematical models. Diverse models have been introduced to represent particular aspects of mechanical characteristics of the lung. A commonly accepted general model is the equation of motion, which relates the airway pressure to the airflow and the volume applied by the ventilator and describes the influence of the distensibility and resistance of the respiratory system. Equation Discovery systems extract mathematical models from observed time series data. To reduce the vast search space associated with this task, the LAGRAMGE-system introduced the application of declarative bias in Equation Discovery, which furthermore allows the presentation of domain specific knowledge. We introduce a modification of this system and apply it to data obtained during mechanical ventilation of ARDS-patients. We experimentally validate the effectiveness of our approach and show that the equation of motion model can automatically be rediscovered from real-world data.