CFD simulations of enhanced condensational growth (ECG) applied to respiratory drug delivery with comparisons to in vitro data

Abstract

Enhanced condensational growth (ECG) is a newly proposed concept for respiratory drug delivery in which a submicrometer aerosol is inhaled in combination with saturated or supersaturated water vapor. The initially small aerosol size provides for very low extrathoracic deposition, whereas condensation onto droplets in vivo results in size increase and improved lung retention. The objective of this study was to develop and evaluate a CFD model of ECG in a simple tubular geometry with direct comparisons to in vitro results. The length (29 cm) and diameter (2 cm) of the tubular geometry were representative of respiratory airways of an adult from the mouth to the first tracheobronchial bifurcation. At the model inlet, separate streams of humidified air (25, 30, and 39 °C) and submicrometer aerosol droplets with mass median aerodynamic diameters (MMADs) of 150, 560, and 900 nm were combined. The effects of condensation and droplet growth on water vapor concentrations and temperatures in the continuous phase (i.e., two-way coupling) were also considered. For an inlet saturated air temperature of 39 °C, the two-way coupled numerical (and in vitro) final aerosol MMADs for initial sizes of 150, 560, and 900 nm were 1.75 μm (vs. 1.23 μm), 2.58 μm (vs. 2.66 μm), and 2.65 μm (vs. 2.63 μm), respectively. By including the effects of two-way coupling in the model, agreements with the in vitro results were significantly improved compared with a one-way coupled assumption. Results indicated that both mass and thermal two-way coupling effects were important in the ECG process. Considering the initial aerosol sizes of 560 and 900 nm, the final sizes were most influenced by inlet saturated air temperature and aerosol number concentration and were not largely influenced by initial size. Considering the growth of submicrometer aerosols to above 2 μm at realistic number concentrations, ECG may be an effective respiratory drug delivery approach for minimizing mouth–throat deposition and maximizing aerosol retention in a safe and simple manner. However, future studies are needed to explore effects of in vivo boundary conditions, more realistic respiratory geometries, and transient breathing.

Introduction

It is well known that inhaled pharmaceutical aerosols are often deposited in the lung at very low deposition efficiencies (Borgstrom, Olsson, & Thorsson (2006), Byron (2004), Cheng, Fu, Yazzie, & Zhou (2001), Leach, Davidson, & Bouhuys (1998), Zhang, Gilbertson, & Finlay (2007)). Perhaps more significant than the quantity of drug deposited is the large inter- and intra-subject variability that is often observed with these medicinal aerosols and the associated dose delivered to the lung. In order to make many next-generation inhaled medications a viable drug delivery alternative, increased lung delivery and decreased inter- and intra-subject variability are of critical importance (Byron (2004), Smaldone (2006)).

To improve the delivery of inhaled drugs, a number of well known and novel generation techniques are becoming commercially available that can create relatively monodisperse nanoparticle and submicrometer aerosols without significant spray inertia effects (Gupta, Hindle, Byron, Cox, & McRae (2003), Mazumder et al. (2006), Newth & Clark (1989), Rabinowitz et al. (2004), Sham, Zhang, Finlay, Roa, & Lobenberg (2004)). Submicrometer aerosols (100–1000 nm) delivered in a low inertia airstream can significantly reduce unwanted deposition in the mouth–throat region (Longest, Hindle, Das Choudhuri, & Xi, 2008). In a recent study, Borgstrom et al. (2006) showed that reduced deposition in the mouth–throat region can significantly decrease inter-subject lung deposition variability. However, a major problem with this delivery approach is that a high percentage of nanoparticle and submicrometer aerosols are not retained in the lung and are exhaled (Heyder, Gebhart, Rudolf, Schiller, & Stahlhofen (1986), Hofmann, Morawska, & Bergmann (2001), Jaques & Kim (2000), Morawska, Barron, & Hitchins (1999), Morawska, Hofmann, Hitchins-Loveday, Swanson, & Mengersen (2005), Stahlhofen, Rudolf, & James (1989)). For example, Jaques and Kim (2000) report that the total lung retention of 100 nm aerosols can be as low as 25% without a breath hold.

Enhanced condensational growth (ECG) applied to respiratory drug delivery is a recently proposed concept that seeks to combine the advantages of both submicrometer and micrometer aerosols. In this approach, a submicrometer aerosol is delivered to the respiratory airways in conjunction with an airstream that is saturated or supersaturated with water vapor and above body temperature. The initially submicrometer particles or droplets, in the approximate size range of 100–900 nm, have very low deposition values in the mouth–throat (MT) and upper tracheobronchial regions (Cheng (2003), Cohen, Sussman, & Lippmann (1990), Xi & Longest (2008a), Xi & Longest (2008b)). As a result, aerosol loss in the MT can be largely eliminated. The inhaled water vapor is used to create supersaturated conditions within the respiratory airways. Submicrometer droplets in this supersaturated environment will increase in size at a controlled rate due to condensation. Size increases to within the range of 2–3 μm can be used to ensure deposition and full lung retention of the aerosol. Furthermore, engineering the rate of size increase can be used to target deposition within specific regions of the lung. Factors influencing the amount and rate of size increase with the ECG approach include the degree of supersaturation, temperature, particle or droplet hygroscopicity, initial size, and aerosol number concentration. However, the effects of these variables on aerosol size growth have been investigated only on a very limited basis.

The relative humidity (RH) of the tracheobronchial airways beyond the first several bronchi is generally expected to be 99.5% (Ferron, 1977). Furthermore, many inhaled environmental and pharmaceutical aerosols are soluble. As a result, hygroscopic effects are known to influence the deposition of these inhaled respiratory aerosols (Ferron (1977), Ferron, Kreyling, & Haider (1988), Finlay & Stapleton (1995), Li & Hopke (1993), Martonen, Bell, Phalen, Wilson, & Ho (1982), Zhang, Kleinstreuer, & Kim (2006b)). Hygroscopic particle growth has been investigated experimentally for NaCl particles (Cinkotai, 1971), pharmaceutical aerosols (Peng, Chow, & Chan, 2000), and combustion droplets (Li & Hopke, 1993). A number of mathematical models have also been formulated for hygroscopic growth of respiratory aerosols at RH values below 100% (Broday & Georgopoulous (2001), Ferron (1977), Ferron, Kreyling, & Haider (1988), Ferron, Oberdorster, & Hennenberg (1989), Finlay & Stapleton (1995), Robinson & Yu (1998), Varghese & Gangamma (2009)). These studies typically indicate a maximum size increase of approximately 400% for NaCl particles. Hygroscopic growth of most other salts and pharmaceutical aerosols results in size increases less than 100% at RH values of 99.5% and below (Ferron, Kreyling, & Haider (1988), Ferron, Oberdorster, & Hennenberg (1989)). Recently, Zhang, Kleinstreuer, and Kim (2006a) developed a CFD model of hygroscopic growth in the upper respiratory tract. It was found that saline concentrations of 10% and higher were required for hygroscopic growth to have a significant impact on deposition. Finlay and Stapleton (1995) applied a numerical model to show that mass coupling between aerosol droplets and the continuous phase was significant for droplet concentrations above 25,000 particles (part)/cm³. However, all of these previous studies considered RH conditions only up to 100%.

Very little work has been done to evaluate the effects of RH conditions above 100% (i.e., supersaturated conditions) on the condensational growth of respiratory aerosols. However, supersaturated conditions can be achieved in the respiratory tract through the inhalation of warm (T>T_body) saturated air. Ferron, Haider, and Kreyling (1984) have shown that RH above 100% is possible in the upper respiratory tract under some inhalation conditions. Significant growth of NaCl particles was observed for very localized supersaturation in the nasal cavity (Ferron et al., 1984). Longest and Xi (2008) considered the inhalation of warm humidified air during smoking. Computational fluid dynamics simulations indicated that inhalation of warm saturated air approximately 3 °C above body temperature could result in supersaturation conditions (RH>100%) through approximately the 6th respiratory bifurcation. Moreover, submicrometer aerosols exposed to RH conditions in the range of 101% experienced a large and rapid increase in size.

The concept of ECG applied to improve respiratory drug delivery was originally introduced by Longest, McLeskey, and Hindle (2010). In this previous study, the effects of saturated air inlet temperature and initial aerosol particle size on submicrometer aerosol growth were considered based on in vitro experiments and a numerical model in a simple tubular system. The numerical model considered only condensation (and evaporation) of individual droplets with constant far-field temperature and relative humidity conditions based on droplet heat and mass transport equations. The loss of water vapor in the air phase due to condensation on the droplet surface was neglected, i.e., one-way heat and mass coupling was assumed. Results of this simple numerical model in comparison with in vitro experiments indicated that (i) two-way coupling between the continuous and discrete phases may significantly affect aerosol growth in some cases and (ii) predictions of final size may be improved by considering spatially variable three-dimensional (3-D) temperature and humidity fields in conjunction with droplet trajectories. Furthermore, the single-droplet condensation model cannot account for aerosol deposition. As a result, a validated computational fluid dynamics (CFD) model of ECG is needed that can accurately simulate local temperature and humidity fields, droplet trajectories, condensation and evaporation, and two-way coupling between the continuous and discrete phases. This model can then be applied to optimize the ECG approach for minimum MT deposition and maximum lung retention for engineering targeted deposition within the respiratory airways.

The objective of this study is to develop and evaluate a CFD model for simulating ECG in a simple tubular geometry with direct comparisons to in vitro results. Model results are also used to evaluate the potential of ECG for improving respiratory drug delivery. The length and diameter of the tubular geometry are consistent with the respiratory airways of an adult from the mouth to the first tracheobronchial bifurcation. At the model inlet, separate streams of humidified air and submicrometer droplets are combined. Initial aerosol mass median aerodynamic diameters (MMADs) ranging from 150 to 900 nm are considered in conjunction with saturated air temperatures from 25 to 39 °C. The CFD model is used to simulate mixing of these air streams based on a well tested k–ω turbulence model, as well as heat and mass transfer relations. Individual particle trajectories are simulated using a previously developed Lagrangian tracking algorithm supplemented with a new routine to calculate condensation and evaporation for hygroscopic aerosols. The effect of condensation and droplet growth on water vapor in the continuous phase (i.e., two-way coupling) is also considered. Numerical predictions are compared with previously reported in vitro results of final droplet size at outlet aerosol concentrations ranging from 6.0×10⁴ to 2.8×10⁵ part/cm³. Comparisons of one-way and two-way coupled model results are used to determine conditions for which the more complicated process of air-phase water loss due to aerosol growth needs to be evaluated. Once developed and tested in comparison with in vitro data, the CFD model of ECG can be applied to more realistic geometries and boundary conditions for optimizing respiratory drug delivery in the lungs.