Analysis of forced expired volume signals using multi-exponential functions

Patients with pulmonary disease are often unable to complete forced expiration manoeuvres. The aim of the study is to evaluate whether forced vital capacity (FVC), the volume exhaled at the end of completed forced expiration, can be estimated by extrapolating volume-time curves obtained from uncompleted manoeuvres. The suitability of mono-, bi-, and tri-exponential functions to characterise complete volume-time curves from 50 subjects is investigated. Mono-exponential modelling is insufficient, whereas bi-exponential fitting yields an adequate description for 47 data sets. Tri-exponential models lead to overfitting in all but three cases (normalised sum of least squares: 50.2 +/- 34.5 for mono-, 2.76 +/- 4.11 for bi-, 2.74 +/- 4.19 for tri-exponential modelling; condition number of the correlation matrix: 1.0025 +/- 0.0004 for mono-, 1.08 +/- 0.08 for bi-, 34.7 +/- 100.1 for tri-exponential fitting (mean +/- SD)). Thus, FVC is estimated by the extrapolation of 27 uncompleted spirograms using bi- or tri-exponential models, depending on their accordance with measured data and on the identifiability of their parameters. This algorithm yields unbiased estimates (difference from measured inspiratory vital capacity: 0.01 +/- 0.21 L). This method can be used for investigation of the lung function of subjects who cannot complete the forced expiration manoeuvre.