Solving the Inverse Problem in Spirometry with the Methods of Global and Local Estimation

Forced expiration is the most commonly applied lung function tests. The forward problem in spirometry was solved a few decades ago, nevertheless, a relatively small amount of work has been devoted to indirect measurements of lung properties based on spirometry data. Just recently, a reduced model for forced expiration was used to create and evaluate an artificial neural network approximating the inverse mapping (InvNN) between spirometric data and model parameters. The aim of this work was to evaluate the accuracy of an extended approach to this inverse problem, consisting of two stages: global estimation using the InvNN and then local estimation with the Levenberg-Marquardt algorithm (LM). To this end, 8000 synthetic spirometry results were generated. 6800 of them were used to train and validate the InvNN, and the remaining 1200 to test the entire method. The results show that the InvNN is not able to fit the model well enough to the data, and that the LM compensates this deficiency. The total estimation errors for particular model parameters are between 4 and 19 % in relation to their variability ranges. Higher errors mainly stem from the correlations between some of parameter estimators, as well as from noise present in the data. These outcomes encourage further analysis of the method using synthetic data generated by a more complex model and its application to the results of bronchial challenge tests.