Estimation of Lung Properties From the Forced Expiration Data

Abstract

Forced expiration is the most commonly applied lung function tests. Despite the problem of spirometry modeling was solved a few decades ago, a relatively small amount of work has been devoted to indirect measurements of lung properties from spirometry data. Just recently, a new method, based on the reduced model for forced expiration and two-stage estimation (global with the feed-forward neural network approximating the inverse mapping (InvNN) and then local with the Levenberg-Marquardt algorithm, starting with the rough estimates yielded by the InvNN) was proposed. The aim of this work was to evaluate the accuracy of the above approach to the indirect measurement of lung properties. To this end, 16,000 synthetic spirometry results were generated, and then used to optimize, train, and validate the InvNN, and to test the entire method. The total estimation errors of model parameters were from 3.7% to 16.6% in relation to their variability ranges. Those original estimates were then recalculated to clinically interpretable airway resistances and compliances, assessed with the relative errors of 7%-35% and 5%-12%, respectively. These outcomes encourage the future use of the method to analyze the results of bronchial challenge or dilation tests.

Quantitative assessment of the airway response to bronchial tests based on a spirometric curve shift

“…The accuracy of InvM parameter estimates strongly depends on the quality of global identification done using the InvNN [29], and thus the effect of InvNN influences also the ultimate results of the proposed method. This is because   are kept unchanged during the estimation of MAR parameters, so their better evaluation in relation to the true values would improves the reduction of systematic errors in this differential measurement (see Apendix).…”

“…The parameters of the nonlinear InvM are estimated in two stages [29]. First, the global identification is performed using the inverse neural network (InvNN), and then the resulting rough estimates are used as the starting vector   are obtained by solving the local optimization problem (minimizing the distance between the post-test spirometric curve and the model output).…”

“…The estimates achieved by analyzing the post-and pre-test spirometry data are used to calculate the values of mentioned earlier Âm, l̂g, α0 and α'0 for each airway generation, specific for the analyzed state of a subject. Then, according to the idea presented in [29], these assessed airway parameters are recalculated into the clinically interpretable resistances and compliances of airway generations as follows:…”

Quantitative Assessment of the Airway Response to Bronchial Tests Based on a Spirometric Curve Shift

“…Though the model could be fitted to data considerably well in these studies, omitting the estimation of other influential parameters has decreased the reliability of this method and prevented its practical application. Just recently, a new approach to the identification of the forced expiration model was proposed, together with the idea how to translate estimated parameter values into the distributions of airway resistances and compliances along the bronchial tree [29]. The identified (inverse) model preserved the entire computational complexity, however, the number of estimated parameters was limited to 6 by applying a sophisticated procedure of model reduction.…”

“…Moreover, recently it was also suggested, how to assess the effects of bronchodilation or provocation tests by fitting this model to pre-and post-test spirometry data [30]. Despite the evaluated errors of both parameter estimates (3.7% to 16.6% in relation to their variability ranges) and the calculated airway resistances and compliances (7-35% and 5-12%, respectively) were rewardingly small [29], that preliminary study was done using merely synthetic data, generated with the model having the same computational structure and values of not estimated parameters as the inverse one.…”