A Functional Mathematical Model to Simulate the Single-Breath Nitrogen Washout

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.