RESEARCH ARTICLE
A Functional Mathematical Model to Simulate the Single-Breath Nitrogen Washout
Paolo Barbini1, *, Chiara Brighenti2, Gianni Gnudi3
Article Information
Identifiers and Pagination:
Year: 2013Volume: 7
First Page: 81
Last Page: 92
Publisher ID: TOBEJ-7-81
DOI: 10.2174/1874120720130701003
Article History:
Received Date: 22/11/2012Revision Received Date: 9/2/2013
Acceptance Date: 11/2/2012
Electronic publication date: 30 /8/2013
Collection year: 2013
open-access license: This is an open access article licensed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/licenses/by-nc/3.0/) which permits unrestricted, non-commercial use, distribution and reproduction in any medium, provided the work is properly cited.
Abstract
A nonlinear dynamic model is proposed to reproduce and interpret the influence of pulmonary inhomogeneities on the single-breath nitrogen washout (SBNW) curve. The model is characterized by two parallel zones. In each zone, the upper airways are described by a Rohrer resistor. Intermediate airways are represented as a collapsible segment, the volume of which depends on transmural pressure. Smaller airways are described by a resistance which increases when transpulmonary pressure decreases. The respiratory region is modeled as a Voigt element. Three different conditions were simulated: a reference case, characterized by airway-parameter values for normal conditions, and two pathological states corresponding to different levels of disease. In the reference case, a straight line was a good approximation of SBNW phase III and the last point of departure of the nitrogen trace from this line unambiguously identified the onset of phase IV. The slope of phase III rose with disease severity (from a 1.1% increase in nitrogen concentration per 1000 ml of expired volume in the reference case to 3.6% and 7.7% in the pathological cases) and the distinction between phases III and IV became less evident. The results obtained indicate that the slope of phase III depends primarily on nitrogen-concentration differences between lung zones, as determined by different mechanical properties of the respiratory airways. In spite of the simplified representation of the lungs, the similarity of the simulation results to actual data suggests that the proposed model describes important physiological mechanisms underlying changes observed during SBNW in normal and pathological patients.
