Practical Identifiability in a Viscoelastic Respiratory Model for Mechanical Ventilation

Mechanical ventilation is a life support system for patients with acute respiratory distress syndrome (ARDS). As part of strategies to protect the lung during ventilation, plateau pressure can be determined via an end-inspiratory pause; however, there is no agreed-upon pause duration in medical protocols. Mechanical ventilation can be modelled using the Viscoelastic model (VEM) for respiration. The identification of static compliance is of clinical interest, as it can be used to estimate plateau pressure. Practical identifiability analysis quantifies the confidence with which model parameters can be estimated from finite, noisy data. This paper evaluates the robustness of plateau pressure estimates in clinical data by analysing practical identifiability of the VEM identified in data with varying durations of end expiratory pauses. Profile likelihood and Hamiltonian Monte Carlo (HMC) simulations were used to determine estimation robustness. The methods were applied to mechanical ventilation data from a previous ARDS study. Profile likelihood and HMC showed strong agreement in both parameter estimates and identifiability results with similar confidence distributions. Both methods demonstrated a loss of parameter robustness that would preclude clinical utility when the end expiratory pause was reduced. By quantifying the confidence in parameter estimation and finding trade-offs in parameters that may be previously unknown when parameters are estimated, the methods give insight into the certainty of the estimate and parameter behaviours, even when the model fits the data well.