Non-local impact of distal airway constrictions on patterns of inhaled particle deposition

Abstract

Airway constriction and blockage in obstructive lung diseases cause ventilation heterogeneity and create barriers to effective drug deposition. Established computational particle-deposition models have not accounted for these impacts of disease. We present a new particle-deposition model that calculates ventilation based on the resistance of each airway, such that ventilation responds to airway constriction. The model incorporates distal airway constrictions representative of cystic fibrosis, allowing us to investigate the resulting impact on patterns of deposition. Unlike previous models, our model predicts how constrictions affect deposition in airways throughout the lungs, not just in the constricted airways. Deposition is reduced in airways directly distal and proximal to constrictions. When constrictions are clustered together, central-airways deposition can increase significantly in regions away from constrictions, but distal-airways deposition in those regions remains largely unchanged. We use our model to calculate lung clearance index (LCI), a clinical measure of ventilation heterogeneity, after applying constrictions of varying severities in one lobe. We find an increase in LCI coinciding with significantly reduced deposition in the affected lobe. Our results show how the model provides a framework for development of computational tools that capture the impacts of airway disease, which could significantly affect predictions of regional dosing.

Keywords: airway disease; cystic fibrosis; inhaled therapies; network modelling; particle deposition.

Figure 1.

(a) Conducting airways in one lung network geometry, with the five lobes (right upper (RU), right middle (RM), right lower (RL), left upper (LU), left lower (LL)) highlighted. The three-dimensional network (left) is represented schematically as a planar graph (right). Path lengths from trachea (centre) to periphery are proportional to number of generations. (b) Acini, illustrated as spheres connected to the terminal conducting airways, for the same geometry.

Figure 2.

Data from simulations in the unconstricted lung geometries. In (a)–(d), particle diameter is ${\displaystyle 4}$ μm. (a) Deposited fraction within each conducting airway in one geometry, shown as a planar graph. Deposition at bifurcations is assigned to the parent airway. (b) Simulated scintigraphy plot for the same example. (c) Deposited fraction in each lobe, showing mean $\pm$ 1 standard deviation (s.d.) across the four geometries. Deposited fraction separated into conducting-airways and acinar deposition. (d) Deposited fraction in each generation, showing mean $\pm$ 1 s.d. across the four geometries, with conducting-airways and acinar deposition indicated. Generational deposition from MPPD is also shown. (e) Total and conducting-airways deposition, versus particle diameter, with comparison to MPPD.

Figure 3.

Simulations in which all generation 12–15 airways in the left upper (LU) lobe are constricted with varying severities (fraction by which airway radii are reduced). In each simulation, the constriction severity is the same for all LU lobe airways. (a) Change in deposition in the affected lobe (LU) and the other lobes, separated into central conducting-airways deposition, distal conducting-airways deposition and acinar deposition. (b) Lung clearance index (LCI), from MBW simulations in the same constricted geometries. (c) Change in individual airway deposition in the simulation with constriction severity 0.825.

Figure 4.

Comparison of two patterns of distal airway constrictions. In (a), constrictions (severity 0.9) are applied in 12 clusters. Each cluster is generated by randomly selecting a generation-12 airway, then constricting all generation-12 airways within a radius of ${\displaystyle R_{\mathrm{C}}=2.4\mathrm{c}\mathrm{m}}$ of it and all of their descendants down to generation 15. We enforce that no clusters overlap. In total, 322 generation-12 airways, and all of their descendants down to generation 15, were constricted. In (b), 322 generation-12 airways were chosen at random, and they and their descendants down to generation 15 were constricted (severity 0.9). (i) Constricted airways highlighted in the three-dimensional networks, and (ii) in the planar graph representations. (iii) Change in airway deposition versus deposition in the unconstricted geometry. (iv) Change in individual airway deposition as box plots for generations 1–9.

Figure 5.

Data from simulations with six clusters of distal airway constriction (severity 0.9) in the upper lobes. In each simulation, six generation-12 airways were selected at random in the upper lobes, and all airways within a radius of ${\displaystyle R_{\mathrm{C}}}$ of any of these were constricted, along with all of their descendants down to generation 15. Four realizations were simulated for each of ${\displaystyle R_{\mathrm{C}}=2.4\mathrm{c}\mathrm{m}}$, ${\displaystyle R_{\mathrm{C}}=3.2\mathrm{c}\mathrm{m}}$ and ${\displaystyle R_{\mathrm{C}}=4\mathrm{c}\mathrm{m}}$. (a) An example with ${\displaystyle R_{\mathrm{C}}=2.4\mathrm{c}\mathrm{m}}$, and (b) an example with ${\displaystyle R_{\mathrm{C}}=4\mathrm{c}\mathrm{m}}$, showing constricted airways (left) and simulated scintigraphy (right). (c) Percentage change in deposition versus the unconstricted case, showing change in the upper lobes (left), and in the other lobes (right). These data are also separated into central conducting, distal conducting and acinar deposition. Mean $\pm$ standard deviation across the four realizations is plotted for each case. (d) Change in individual airway deposition for an example with ${\displaystyle R_{\mathrm{C}}=3.2\mathrm{c}\mathrm{m}}$.