A whole lung in silico model to estimate age dependent particle dosimetry

Abstract

Anatomical and physiological changes alter airflow characteristics and aerosol distribution in the developing lung. Correlation between age and aerosol dosimetry is needed, specifically because youth are more susceptible to medication side effects. In this study, we estimate aerosol dosages (particle diameters of 1, 3, and 5 [Formula: see text]m) in a 3 month-old infant, a 6 year-old child, and a 36 year-old adult by performing whole lung subject-specific particle simulations throughout respiration. For 3 [Formula: see text]m diameter particles we estimate total deposition as 88, 73, and [Formula: see text] and the conducting versus respiratory deposition ratios as 4.0, 0.5, and 0.4 for the infant, child, and adult, respectively. Due to their lower tidal volumes and functional residual capacities the deposited mass is smaller while the tissue concentrations are larger in the infant and child subjects, compared to the adult. Furthermore, we find that dose cannot be predicted by simply scaling by tidal volumes. These results highlight the need for additional clinical and computational studies that investigate the efficiency of treatment, while optimizing dosage levels in order to alleviate side effects, in youth.

Figure 1

Simulation pipeline for the multi-dimensional airflow and transport simulations. Airway geometries were previously created from CT images and airway morphometry was measured from the geometric models (Step 1). In Oakes et al. airflow was simulated throughout the respiration cycle by a pressure differential that overcame the respiratory resistance and compliance to drive air in and out of the lungs (Step 2). Particles are then tracked throughout the respiration cycle by first calculating their individual trajectories in the 3D models for inspiration (Step 3). Next, the aerosol bolus is convected through the distal regions of the lung by solving reduced-order models with a deposition loss term (Step 4). Finally, the particle trajectories are solved throughout expiration in the 3D airways (Step 5) and the regional deposition patterns are assessed (Step 6).

Figure 2

Cross-sectional areas of representative branches in the lower left lobe of the adult (panel A), child (panel B), and infant (panel C) models. Note, for the outlined 3D regions, the areas are measured directly from the image-based models (error bars represent the standard deviation of the airways within each generation). The 1D regions are idealized and scaled to match FRC (Table 2). The conducting and respiratory zones are highlighted in panel (A), where the blue and gray lines represent the total cross-sectional area at the end and beginning of inspiration, respectively.

Figure 3

Whole lung deposition percentages for the three models are shown for each of the particle sizes simulated. Note, the conducting (C) and respiratory (R) zones are shown in dark and light shades, respectively. The ratio of deposited particles between the conducting and respiratory zones, CR ratio, are displayed above each bar. Figure 2 points to the conducting and respiratory zones. Note, the conducting zone includes both the 3D model and part of the 1D model.

Figure 4

Whole lung deposition percentages (for 3 $\mathrm{\mu }$m diameter particles) for the infant (A), child (B), and adult (C) airways. The 3D geometry as well as the five lobes are highlighted, with expiration represented with the lighter shades. The percentage of particles exhaled out of the lungs are also shown for each of the age groups.

Figure 5

Deposited particle locations for infant (panels A,D), child (panels B,E), and adult (panels C,F) for the 3 $\mathrm{\mu }$m diameter particles. Panels (A–C) highlight deposited hotspots for inspiration, where the values represent the regional deposition percentage (based on the number of particles depositing during inhalation only). Hotspots for expiration are shown in panels (D–F); the particles are color coded based on the lobe that they originated from. Presented values (panels D–F) are the percent of deposited particles, calculated from the number of particles released back into the 3D model (not total deposition percentages).

Figure 6

Deposited particle element concentrations ($NP=\frac{N_e{\sum }_T}{N_T{\sum }_e}$) for the infant model (panel A–C), for the child model (panel D–F), and for the adult model (panel G–I) for $d_p=$ 1 $\mathrm{\mu }$m, 3 $\mathrm{\mu }$m, and 5 $\mathrm{\mu }$m (inspiration and expiration are plotted together). NP is unit-less.

Figure 7

Total deposited dose for 1 $\mathrm{\mu }$m, 3 $\mathrm{\mu }$m, and 5 $\mathrm{\mu }$m diameter particles, with respect to Reynolds number ($Re=\frac{4\rho Q_{\mathit{mean}}}{\pi \mathrm{\mu }{D}_{\mathit{trachea}}}$) times Stokes number ($Stk=\frac{{\rho }_p{d}_p^{2}w}{18\mathrm{\mu }{d}_c}$, where $d_p$ is the particle diameter, ${\rho }_p$ is the particle density, w the mean flow velocity, and $d_c$ the diameter of the airway), in both modeling (M) and experimental (E) studies. Infants are shown as blue, child as red, and adult subjects as black. Details on $Re\times Stk$ for each study are provided within the supplementary material.