Mixed‐integer quadratic programming approach for noninvasive estimation of respiratory effort profile during pressure support ventilation

Information about respiratory mechanics such as resistance, elastance, and muscular pressure is important to mitigate ventilator-induced lung injury. Particularly during pressure support ventilation, the available options to quantify breathing effort and calculate respiratory system mechanics are often invasive or complex. We herein propose a robust and flexible estimation of respiratory effort better than current methods. We developed a method for non-invasively estimating breathing effort using only flow and pressure signals. Mixed-integer quadratic programming (MIQP) was employed, and the binary variables were the switching moments of the respiratory effort waveform. Mathematical constraints, based on ventilation physiology, were set for some variables to restrict feasible solutions. Simulated and patient data were used to verify our method, and the results were compared to an established estimation methodology. Our algorithm successfully estimated the respiratory effort, resistance, and elastance of the respiratory system, resulting in more robust performance and faster solver times than a previously proposed algorithm that used quadratic programming (QP) techniques. In a numerical simulation benchmark, the worst-case errors for resistance and elastance were 25% and 23% for QP versus <0.1% and <0.1% for MIQP, whose solver times were 4.7 s and 0.5 s, respectively. This approach can estimate several breathing effort profiles and identify the respiratory system's mechanical properties in invasively ventilated critically ill patients.