title: Generalized estimation of the ventilatory distribution from the multiple-breath nitrogen washout.
abstract: BACKGROUND
  This 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 (V T ) and the end-expiratory lung volume (EELV) are allowed to vary during the maneuver. In addition, the volume of the series dead space (v d ), unlike the classical model, is considered a common series unit connected to a set of parallel alveolar units.
  
  
  METHODS
  The 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 (V T , EELV and v d ) 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.
  
  
  RESULTS
  The 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.
  
  
  CONCLUSIONS
  In conclusion this generalized method was able to identify v/V distributions from a lung model with a common series dead space even with variable V T . Although limitations remain in presence of experimental noise, appropriate combination of processing steps were also found to reduce estimation errors.
authors.affiliation: Pulmonary Engineering Laboratory, Biomedical Engineering Programme, COPPE, Universidade Federal do Rio de Janeiro, Rio de Janeiro, Brazil.
authors.forename: Gabriel Casulari
authors.identifier: http://orcid.org/0000-0001-5982-8863
authors.initials: GC
authors.lastname: Motta-Ribeiro
authors.affiliation: Pulmonary Engineering Laboratory, Biomedical Engineering Programme, COPPE, Universidade Federal do Rio de Janeiro, Rio de Janeiro, Brazil.
authors.forename: Frederico Caetano
authors.initials: FC
authors.lastname: Jandre
authors.affiliation: Department of Anesthesiology and Intensive Care Medicine, University of Leipzig, Leipzig, Germany.
authors.forename: Hermann
authors.initials: H
authors.lastname: Wrigge
authors.affiliation: Pulmonary Engineering Laboratory, Biomedical Engineering Programme, COPPE, Universidade Federal do Rio de Janeiro, Rio de Janeiro, Brazil. agn@peb.ufrj.br.|Department of Anesthesiology and Intensive Care Medicine, University of Leipzig, Leipzig, Germany. agn@peb.ufrj.br.
authors.forename: Antonio
authors.initials: A
authors.lastname: Giannella-Neto
mesh_terms: D006801:Humans; D016018:Least-Squares Analysis; D008954:Models, Biological; D009584:Nitrogen / Q000378:metabolism*; D012123:Pulmonary Ventilation; D012119:Respiration; D013990:Tidal Volume
chemical_list: D009584:Nitrogen
keywords: Common dead space; Dead space; End-expiratory lung volume; Functional residual capacity; Multiple-breath washout; Nitrogen; Pulmonary function tests; Tikhonov regularization; Ventilation to volume; Ventilatory distributions