Error propagation and uncertainty analysis in a virtual patient model for lung mechanics

Predictive models can offer significant aid in optimizing patient care. However, physiological models are imperfect due to errors or biases in modeling, identification, and/or the data used to personalize them. Data collection, model identification, and model prediction can all include inevitable errors and uncertainties which propagate and impact model prediction. Error propagation and uncertainty analysis are helpful for understanding model development, and yield insights into model design and potential improvement.

A well-validated predictive lung mechanics model is analyzed step-by-step through model identification and prediction to analyze four different types of uncertainties from input data, parameter estimation, model structure, and prediction. Propagated errors are analyzed as well. Data from 18 volume-controlled ventilation patients undergoing a staircase recruitment maneuver is used to assess overall prediction error for peak-inspiratory pressure (PIP) at different levels of positive end expiratory pressure (PEEP).

Uncertainties for three segments of a pressure-volume (P-V) loop during inspiration and associated PIP prediction errors indicate error cancellation occurs as overall error is lower than the sum of each specific error. It arises partially from differently signed errors cancelling during propagation and partially due to model structure. Model structure plays an important role in overall model performance robustness and cannot be isolated and analyzed alone.

To develop an effective physiological model, moderate simplification while retaining physiologically relevant features is necessary to ensure model identifiability and robustness. Errors and uncertainties arise from the combination of model structure and error propagation in identified model predictions. In the nonlinear mechanics model analyzed, these errors tend to be cancelled leading to lower overall prediction errors. Overall, physiological models used to guide care are increasing and should examine specific sources of error propagation and their impact on overall outcome prediction error to better understand the causes. The approach presented provides a generalizable overall template for such analyses.