A new computational framework for simulating airway resistance, fraction of exhaled nitric oxide, and diffusing capacity for nitric oxide

Abstract

In this paper, we present a new computational framework for the simulation of airway resistance, the fraction of exhaled nitric oxide, and the diffusion capacity for nitric oxide in healthy and unhealthy lungs. Our approach is firstly based on a realistic representation of the geometry of healthy lungs as a function of body mass, which compares well with data from the literature, particularly in terms of lung volume and alveolar surface area. The original way in which this geometry is created, including an individual definition of the airways in the first seven generations of the lungs, makes it possible to consider the heterogeneous nature of the lungs in terms of perfusion and ventilation. In addition, a geometry can be easily modified to simulate various abnormalities, local or global (constriction, inflammation, perfusion defect). The natural variability of the lungs at constant body mass is also considered. The computational framework includes the possibility to simulate, on a given (possibly modified) geometry, a test to measure the flow resistance of the lungs (including its component due to the not fully developed flow in the first generations of lungs), a test to measure the concentration of nitric oxide in the exhaled air, and a test to measure the diffusion capacity for nitric oxide. This is implemented in the framework by solving different transport equations (momentum and convection/diffusion) describing these tests. Through numerous simulations, we demonstrate the ability of our model to reproduce results from the literature, both for healthy lungs and lungs of patients with asthma or chronic obstructive pulmonary disease. Such a computational framework, through the possibilities of numerous and rapid tests that it allows, sheds new light on experimental data by providing information on the phenomena that take place in the distal generations of the lungs, which are difficult to access with imaging.

Fig 1

On the left, a schematic representation of the tracheobronchial tree as a dichotomous tubular tree structure (own figure). On the right, a drawing of the alveoli budding from the airway walls of an acinus (Image by Patrick J. Lynch, medical illustrator / Wikimedia Commons. License: Creative Commons Attribution 2.5 License 2006. Bronchial anatomy detail of alveoli and pulmonary circulation).

Fig 2. Schematic representation of the geometry of the lungs created by the computational framework.

Fig 3. Total lung volume and total alveolar surface area as functions of the body mass, calculated with our model.

The dashed lines are the allometric scaling laws reported in [35].

Fig 4. Histogram of the number of generations between the top of the trachea and the end of the alveolar region, averaged on 30 lung geometries created for a body mass of 75 kg.

Fig 5. Alveolar pressure ΔP (in cm of H₂O) as a function of the inspiratory flow rate (in l/min), for lung geometries produced with body masses of 55 kg, 65 kg, and 75 kg.

The data given by Pedley et al. [23] are also presented in this figure, to show that a similar order of magnitude is recovered.

Fig 6. Specific airway resistance, as a function of COPD severity, defined here as the percentage of the small airways (diameter less than 2 mm) affected by constriction, for a body mass of 75 kg.

The shaded area gives the 95% confidence interval, reflecting the fact that, for a given body mass, there is a natural variation in lung geometry, and that the same percentage of constriction does not always correspond to the same choice of airways.

Fig 7. FeNO as a function of the expiratory flow rate, calculated on a single lung geometry obtained for a body mass of 80 kg.

The blue dots are the experimental data given by Silkoff et al. [47].

Fig 8. NO concentration profile along the different pathways toward the end of the lungs, at stationary state during a FeNO test with an expiratory flow rate of 3 l/min, on a geometry created for a body mass of 75 kg.

Fig 9. Calculated FeNO values for a population of 80 healthy adults and a population of 160 asthmatics at a fixed expiratory flow rate of 12 l/min.

FeNO values are rounded to the nearest ppb and the length of the bars is proportional to the number of people with the corresponding FeNO. The horizontal red dashed lines show the mean values for each population. These results can be compared with those reported by Dupont et al. [48], which provide a similar analysis of the variability of FeNO in healthy and asthmatic adults.

Fig 10. FeNO as a function of the percentage of the bronchial airways affected by constriction.

Body mass of 75 kg, expiratory flow rate of 12 l/min. The horizontal dashed line gives the limit between moderate and light asthma.

Fig 11. Calculated relative variation of DLNO as a function of the severity of COPD.