Aerosol deposition in the human upper airways

Application Challenge AC7-01 © copyright ERCOFTAC 2019

Description

Introduction

The objective of the current application Challenge is to present a benchmark case that can be used for the validation of computational tools intended for regional deposition studies in the upper airways. In the present application Challenge, in vitro deposition measurements in a complex realistic geometry are provided at various inhalation ﬂow rates. CFD results are then compared against the measured data. Since deposition in the upper airways is determined by the airﬂow features, a second application Challenge will follow where airﬂow measurements using Particle Image Velocimetry (PIV) are reported in the same geometry. These will again be compared against the LES and RANS predictions. In this manner, a complete benchmark case for the validation of computational packages intended for deposition predictions in the upper airways will be established and made available to the wider community. Furthermore, best practice guidelines for numerical predictions of regional deposition in the airways, which can assist in the design and optimization of inhalation therapies, will be provided.

In the current application Challenge, the in vitro deposition measurements have been conducted in a human-based model of the upper airways, shown in figure 3, using positron emission tomography (PET). The experiments were performed at steady-state inhalation with ﬂow rates of 15, 30 and 60 L/min. The ﬂow conditions at these ﬂowrates are in the transitional to turbulent regime. The CFD simulations were carried out in the same geometry and under the same ventilation conditions. Two sets of simulations were performed: Large Eddy Simulations using the dynamic version of the Smagorinsky-Lilly subgrid scale model and RANS simulations using the k-ω-SST model. In both methods, the Lagrangian approach has been adopted to track spherical particles in the airway geometry and determine regional deposition patterns. The methods and results described in the present Application Challenge are mainly adopted from Lizal et al. (2012) (experimental part) and Koullapis et al. (2018) (numerical part).

Relevance to Industrial Sector

Aerosolized delivery of drugs to the lungs is used to treat a number of respiratory diseases. Regional deposition effects play a critical role in applications where targeted drug delivery is needed in order to maximize efﬁcacy and minimize side-effects. Quantifying regional deposition is therefore important in assessing and optimizing treatment. Validated computational ﬂuid-particle dynamics (CFPD) methods offer a powerful tool to predict airﬂow and localized deposition in the respiratory airways, in order to further our understanding of the ﬂow and aerosol dynamics, and test and optimize inhaler therapies. However, accurate and efﬁcient numerical simulations of the respiratory airways pose a challenge due to the complexities associated with the airway geometry, the ﬂow dynamics and the aerosol physics. Numerical studies conducted to date have adopted a variety of computational techniques, a range of airway geometries varying in complexity, and differing assumptions on the ﬂow and aerosol physics. In addition to the wide variability in the modelling approaches, validation of CFPD methods in the respiratory airways is limited.

Design or Assessment Parameters

Deposition fractions (DF) in the various segments of the geometry were measured (in the experiments) and predicted in the numerical simulations. The procedure to calculate DF in the PET experiments is described in the Test Data section. DF in the simulations, where particles are tracked individually, are simply deﬁned as the ratio of the number of deposited particles in a segment to the total number of particles injected in the model.

Flow Domain Geometry

The description that follows was adopted from Lizal et al. (2012). The model basically comes from two distinct realistic geometries that were carefully connected in the trachea. These are described separately in the following sections. The geometry segments are provided in stl format www.kbwiki.ercoftac.org/data/AC7-01/STL_geometry.zip The numbering of the stl segments is the one shown in ﬁgure 4. However, the 10 larger outlet segments along with their attached outlet patches are separated from the airway branches (segments 13 – 22) and are designated as segments 23 – 32 (segment 13 is attached to outlet segment 23, segment 14 is attached to outlet segment 24 and so on).

Digital reference model of bronchial tree

The digital reference model of Schmidt et al. (2004) served as a basis for the new model. The original geometry was produced by high resolution computerized tomography (HRCT) of an excised lung of an adult male free of pathological alterations. Their model development uses special image processing algorithms for the segmentation and delineation of the bronchi. The model does not include upper airways, it begins with trachea and spans down to the 17th generation of branching. Our model currently extends only to the seventh bifurcation, but geometry through the 17th Horsﬁeld order is available and could be used for a more complete airway model. The measured branching angles are shown in Figure 1 (Lizal et al. (2012)). Schmidt's geometry was supplemented with the oral cavity described in the following paragraph.

Figure 1: Branching angles of tracheobronchial airways.

The oral cavity

The upper part of the Lovelace Respiratory Research Institutes (LRRI) “A model” (Zhou & Cheng, 2005) was used to construct the current model. The anterior oral cavity was molded from in vivo dental impression of a living Caucasian male at approximately 50 percent of the full opening (Lizal et al. (2015) The wax model provided by LRRI was scanned by an Atos (GOM) device, converted to STL format, and concatenated with our original model at the trachea (Figure 3). The dimensions of current models are summarized in Tables 1 and 2. In Table 2, the dimensions of the current model are compared to previously published model geometries.

Table 1: Dimensions of the realistic model (notation corresponds to ﬁgure 2).

Figure 2: A scheme of the model with nomenclature used for the description of dimensions.

Table 2: Comparison of published model geometries.

Figure 3: Flow domain in the current model of the upper airways.

Manufacturing of the physical model for deposition studies

For measurements of regional deposition by gravimetry or ﬂuorometry, it is necessary to divide the model into separable segments that are connected so as to ensure an airtight model. The model spans branches whose diameter is above 3mm and contains airways down to the seventh bifurcation. There was no need for optical transparency so the model could be directly produced by rapid prototyping. A 3mm thick envelope was formed around the airways and ﬂanges were added to each segment. The terminal bronchi segments end up in 10 funnels that lead to the 10 outlets of the system (segments 13 – 22 in fig. 4). Segments involving branches from the fourth to the seventh bifurcation (dark segments in Figure 4) are connected by bayonet joints. The outlets are connected using screw connections and sealed with silicone. The model was fabricated by stereolithography (Viper, 3D Systems) using WaterShed XC 11122. The built layer capability is ${20\mu m}$ vertical resolution is ${25\mu m}$ and position repeatability is ${7.6\mu m}$ .

Figure 4: Visualization of the physical model with the nomenclature of segments that is used in

the evaluation of aerosol deposition.

Limitations of the model

The users of the model should be aware of its limitations. Some of the following points arose from discussion with experts from the medical community. The ﬁrst question concerns the realism of combining two realistic geometries. It should be noted that acquiring the complete realistic geometry is complicated as there are antagonistic requirements for imaging the oral cavity and the tracheobronchial airways. And even when one subject was imaged during two different sessions, the airway dimensions would change and thus the created geometry would not truly represent the real airways at a certain instant. Combining of two well-deﬁned geometries in our case forms a realistic, although, non-speciﬁc individual geometry. It should also be emphasized that the current model serves primarily for comparison of experiments and numerical simulations, and therefore the combined geometry is acceptable. Another remark concerns the circular connection of the two geometries. As both the geometries had realistic cross-sections in the connecting region in trachea, it was necessary to provide the transition from one to another. In our case we selected the circular shape as the optimal transition, since the lower geometry began with a circular-like shape. Another frequent question concerns the moving boundaries. The model is rigid and therefore the boundaries do not move. In reality, the trachea and the main bronchi are supported by cartilages and do not contract or stretch signiﬁcantly. However, the more distal airways are not perfectly rigid and there could be signiﬁcant motion as we move in the terminal bronchioles.

A more signiﬁcant remark concerns the electrical conductivity of the physical model. The problem inheres in the possible deposition of particles due to the electrostatic force. The conductive material of the model walls would allow the charge to be grounded. In our case the particles were brought into electric charge equilibrium using the ${\,^{85}Kr}$ based NEKR-10 charge equilibrator (Eckert and Ziegler Cesio), hence the particles had zero net charge. However, electrostatic deposition cannot be completely ruled out due to the possible mirror charge conceivably exerted on the particles close to the wall. A discussion of the effects of electrostatic charge on deposition in the upper airways can be found at Koullapis et al. (2016).

Flow Physics and Fluid Dynamics Data

Due to the geometrical complexity and high Reynolds numbers, especially at ﬂowrates that are relevant to drug delivery via Dry Powder Inhalers (DPIs), airﬂow in the upper airways usually transitions to turbulence. For the geometry used herein, the Reynolds numbers in the trachea are approximately 1150, 2300 and 5600 at inhalation ﬂowrates of 15, 30 and 60 L/min, respectively. Under these conditions, airﬂow is incompressible and is assumed isothermal although in reality there is heat exchange between the airway walls and the incoming ambient air. Moreover, in reality the vapor concentration of air changes due to the high humidity inside the airways. This effect is also omitted in both experimental and numerical parts of this study. Therefore, the density and kinematic viscosity of air are kept constant with values ${\rho =1.2kg/m^{3}}$ and ${\nu =1.7\times 10^{-5}m^{2}/s}$ , respectively.

Contributed by: P. Koullapis^a, F. Lizal^b, J. Jedelsky^b, L. Nicolaou^c, K. Bauer^d, O. Sgrott^e, M. Jicha^b, M. Sommerfeld^e, S. C. Kassinos^a —
^aDepartment of Mechanical and Manufacturing Engineering, University of Cyprus, Nicosia, Cyprus
^bFaculty of Mechanical Engineering, Brno University of Technology, Brno, Czech Republic
^cDivision of Pulmonary and Critical Care, School of Medicine, Johns Hopkins University, Baltimore, USA
^dInstitute of Mechanics and Fluid Dynamics, TU Bergakademie Freiberg, Freiberg, Germany
^eInstitute Process Engineering, Otto von Guericke University, Halle (Saale), Germany