Generalized estimation of the ventilatory distribution from the multiple-breath nitrogen washout

Abstract

BackgroundThis work presents a generalized technique to estimate pulmonary ventilation-to-volume (v/V) distributions using the multiple-breath nitrogen washout, in which both tidal volume (VT) and the end-expiratory lung volume (EELV) are allowed to vary during the maneuver. In addition, the volume of the series dead space (vd), unlike the classical model, is considered a common series unit connected to a set of parallel alveolar units.MethodsThe numerical solution for simulated data, either error-free or with the N2 measurement contaminated with the addition of Gaussian random noise of 3 or 5 % standard deviation was tested under several conditions in a computational model constituted by 50 alveolar units with unimodal and bimodal distributions of v/V. Non-negative least squares regression with Tikhonov regularization was employed for parameter retrieval. The solution was obtained with either unconstrained or constrained (VT, EELV and vd) conditions. The Tikhonov gain was fixed or estimated and a weighting matrix (WM) was considered. The quality of estimation was evaluated by the sum of the squared errors (SSE) (between reference and recovered distributions) and by the deviations of the first three moments calculated for both distributions. Additionally, a shape classification method was tested to identify the solution as unimodal or bimodal, by counting the number of shape agreements after 1000 repetitions.ResultsThe accuracy of the results showed a high dependence on the noise amplitude. The best algorithm for SSE and moments included the constrained and the WM solvers, whereas shape agreement improved without WM, resulting in 97.2 % for unimodal and 90.0 % for bimodal distributions in the highest noise condition.ConclusionsIn conclusion this generalized method was able to identify v/V distributions from a lung model with a common series dead space even with variable VT. Although limitations remain in presence of experimental noise, appropriate combination of processing steps were also found to reduce estimation errors.Electronic supplementary materialThe online version of this article (doi:10.1186/s12938-016-0213-y) contains supplementary material, which is available to authorized users.

Generalized estimation of the ventilatory distribution from the multiple-breath washout: a bench evaluation study

“…This also allows the model to be driven by a non-ideal step in inspiratory concentration of the tracer gas. Variable V T is admitted by defining S(J) with respect to a reference V T , and variable EELV is achieved by tracking the differences between inspired and expired volumes, returning the distribution corresponding to EELV at the onset of maneuver [ 5 ].…”

“…The parameters of the multiple compartment model were estimated with nonnegative least squares and Tikhonov regularization with a fixed gain (4 × 10 −3 for 1C and 3.3 × 10 −2 for 4C) and a weighting matrix proportional to the compartmental washout ratio [ 2 ]. The generalized model was also estimated with a constrained least squares solver, imposing the sum of compartmental volume equal to the EELV-v d and unitary total ventilation [ 5 ]. Overall resistance and elastance were calculated from pressure and flow signals to ensure similar mechanical behaviors of the compartments.…”

“…The generalized approach adds a constrained least squares solver with imposed EELV, V T and v d . The results previously obtained by us [ 5 ], with numerically simulated experimental noise, directed the choice of the weighting matrix.…”

“…For instance, it disregards the effects of the series dead space (v d ), whose volume may be estimated via the Fowler’s method [ 4 ] throughout the washout; not only the EELV but also the tidal volume (V T ) must remain constant during the MBN 2 W; the inspired fraction of tracer gas should decrease instantaneously to zero. Recently, we [ 5 ] proposed a generalized multicompartmental model for MBN 2 W that includes a series dead space and copes with a non-ideal step change in gas concentration, variable V T during the maneuver, and changes in EELV, as long as no compartment is completely emptied. Computational simulations showed that this model, together with an algorithm to estimate its parameters from measurements taken at the airway opening during MBN 2 W, usually retrieved more correct estimations of the v/V distribution than previous proposals [ 5 ].…”

“…Recently, we [ 5 ] proposed a generalized multicompartmental model for MBN 2 W that includes a series dead space and copes with a non-ideal step change in gas concentration, variable V T during the maneuver, and changes in EELV, as long as no compartment is completely emptied. Computational simulations showed that this model, together with an algorithm to estimate its parameters from measurements taken at the airway opening during MBN 2 W, usually retrieved more correct estimations of the v/V distribution than previous proposals [ 5 ]. Furthermore, the alternative to impose a priori constraints determined along the MBN 2 W limits the set of the v/V parameters estimates.…”