Fluid Dynamics in Airway Bifurcations: III. Localized Flow Conditions

Count- and mass-based dosimetry of MDI spray droplets with polydisperse and monodisperse size distributions

Most previous numerical studies of inhalation drug delivery used monodisperse aerosols or quantified deposition as the ratio of deposited particle number over the total number of released particles (i.e., count-based). These practices are reasonable when the aerosols have a sufficiently narrow size range. However, spray droplets from metered-dose inhalers (MDIs) are often polydisperse with a wide size range, so using monodisperse aerosols and/or count-based deposition quantification may lead to significant errors. The objective of this study was to develop a mass-based dosimetry method and evaluate its performance in lung delivery in a mouth-lung (G9) geometry with an albuterol-CFC inhaler. The conventional practices (monodisperse and polydisperse-count-based) were also simulated for comparison purposes. The MDI actuation in the open space was studied using both high-speed imaging and LES-Lagrangian simulations. Experimentally measured spray velocities and size distribution were implemented in the computational model as boundary conditions. Good agreement was achieved between recorded and simulated spray plume evolution spatially and temporally. The polydisperse-mass-based predictions of MDI doses compared favorably with the measurements in all three regions considered (device, mouth-throat, and lung). Significant errors in MDI regional deposition were predicted using the monodisperse and count-based methods. The new polydisperse-mass-based method also predicted local deposition hot spots that were one order of magnitude higher in intensity than the two conventional methods. The results of this study highlighted that a presentative polydisperse size distribution and appropriate deposition quantification method should be applied to reliably predict the MDI drug delivery in the human respiratory tract.

Gas Uptake in a Three-Generation Model Geometry with a Flat Inlet Velocity During Steady Inspiration: Comparison of Axisymmetric and Three-Dimensional Models

Mass transfer coefficients were predicted and compared for uptake of reactive gas system using an axisymmetric single-path model (ASPM) with experimentally predicted values in a two-generation geometry and with a three-dimensional computational fluid dynamics model (CFDM) in a three-generation model geometry at steady inspiratory flow with a flat inlet velocity profile. The flow and concentration fields in the ASPM were solved using Galerkin's finite element method and in the CFDM using a commercial finite element software FIDAP. ASPM predicted average gas phase mass transfer coefficients within 25% of the experimental values. Numerical results in terms of overall mass transfer coefficients from the two models within each bifurcation unit were compared for two different inlet flow rates, wall mass transfer coefficients, and bifurcation angles. The overall mass transfer coefficients variation with bifurcation unit from the ASPM and CFDM compared qualitatively and quantitatively closely at lower wall mass transfer coefficients for both 40 degree and 70 degree bifurcation angles. But at higher wall mass transfer coefficients, quantitatively they were off in the range of 2-10% for 40 degree bifurcation angle and in the range of 4-15% for 70 degree bifurcation angle. Both CFDM and ASPM predict the same trends of increase in mass transfer coefficients with inlet flow, wall mass transfer coefficients, and during inspiration compared to expiration. Higher mass transfer coefficients were obtained with a flat velocity profile compared to a parabolic velocity profile using ASPM. These results validate the simplified ASPM and the complex CFDM.

Comparison of Axisymmetric and Three-Dimensional Models for Gas Uptake in a Single Bifurcation During Steady Expiration

Reactive gas uptake is predicted and compared in a single bifurcation at steady expiratory flow in terms of Sherwood number using an axisymmetric single-path model (ASPM) and a three-dimensional computational fluid dynamics model (CFDM). ASPM is validated in a two-generation geometry by comparing the average gas-phase mass transfer coefficients with the experimental values. ASPM predicted mass transfer coefficients within 20% of the experimental values. The flow and concentration variables in the ASPM were solved using Galerkin finite element method and in the CFDM using commercial finite element software FIDAP. The simulations were performed for reactive gas flowing at Reynolds numbers ranging from 60 to 350 in both symmetric bifurcation for three bifurcation angles, 30deg, 70deg, and 90deg, and in an asymmetric bifurcation. The numerical models compared with each other qualitatively but quantitatively they were within 0.4–8% due to nonfully developed flow in the parent branch predicted by the CFDM. The radially averaged concentration variation along the axial location matched qualitatively between the CFDM and ASPM but quantitatively they were within 32% due to differences in the flow field. ASPM predictions compared well with the CFDM predictions for an asymmetric bifurcation. These results validate the simplified ASPM and the complex CFDM. ASPM predicts higher Sherwood number with a flat velocity inlet profile compared to a parabolic inlet velocity profile. Sherwood number increases with the inlet average velocity, wall mass transfer coefficient, and bifurcation angle since the boundary layer grows slower in the parent and daughter branches.

3D in silico modeling of the human respiratory system for inhaled drug delivery and imaging analysis

The efficacies of inhaled pharmacologic drugs could be improved if drugs could be targeted to appropriate sites within the human respiratory system. The spatial deposition patterns of particles can now be detected with a high degree of resolution using advanced techniques of imaging (e.g., SPECT). However, the effectiveness of such laboratory regimens has been limited by the inability to clearly identify airway composition within images. Therefore, we have developed a theoretical protocol to map airways within human lungs that is designed to be used in a complementary manner with laboratory investigations. The in silico model has two components: a mathematical model based on concepts of topology; and, a computer algorithm which tracks the millions of constituent lung airways. The in silico model produces 3D lung structures that are anatomically correct and can be customized to each patient. We have applied the protocol to a SPECT study where the interiors of lungs were partitioned into a series of ten nested shells. Airway composition in the respective shells provides a heretofore unavailable quantification of scintigraphy images. The protocol can be employed in a practical manner in the medical arena to aid in the interpretation of SPECT images, and to provide a platform for the design of human subject tests.

Three-Dimensional Simulations of Reactive Gas Uptake in Single Airway Bifurcations

The pattern of lung injury induced by the inhalation of ozone (O(3)) depends on the dose delivered to different tissues in the airways. This study examined the distribution of O(3) uptake in a single, symmetrically branched airway bifurcation. Reaction in the epithelial lining fluid was assumed to be so rapid that O(3) concentration was negligible along the entire surface of the bifurcation wall. Three-dimensional numerical solutions of the continuity, Navier-Stokes and convection-diffusion equations were obtained for steady inspiratory and expiratory flows at Reynolds numbers ranging from 100 to 500. The total rate of O(3) uptake was found to increase with increasing flow rate during both inspiration and expiration. Hot spots of O(3) flux appeared at the carina of the bifurcation for virtually all inspiratory and expiratory Reynolds numbers considered in the simulations. At the lowest expiratory Reynolds number, however, the location of the maximum flux was shifted to the outer wall of the daughter branch. For expiratory flow, additional hot spots of flux were found on the parent branch wall just downstream of the branching region. In all cases, O(3) uptake in the single bifurcation was larger than that in a straight tube of equal inlet radius and wall surface area. This study provides insight into the effect of flow conditions on O(3) uptake and dose distribution in individual bifurcations.

Three-Dimensional Computational Fluid Dynamics Simulations of Particle Deposition in the Tracheobronchial Tree

Simulation of the dynamics and disposition of inhaled particles within human lungs is an invaluable tool in both the development of inhaled pharmacologic drugs and the risk assessment of environmental particulate matter (PM). The goal of the present focused study was to assess the utility of three-dimensional computational fluid dynamics (CFD) models in studying the local deposition patterns of PM in respiratory airways. CFD models were validated using data from published experimental studies in human lung casts. The ability of CFD to appropriately simulate trends in deposition patterns due to changing ventilatory conditions was specifically addressed. CFD simulations of airflow and particle motion were performed in a model of the trachea and main bronchi using Fluent Inc.'s FIDAP CFD software. Particle diameters of 8 microm were considered for input flow rates of 15 and 60 L/min. CFD was able to reproduce the observed spatial heterogeneities of deposition within the modeled bifurcations, and correctly predicted the "hot-spots" of particle deposition on carinal ridges. The CFD methods also predicted observed differences in deposition for high-versus-low flow rates. CFD models may provide an efficient means of studying the complex effects of airway geometry, particle characteristics, and ventilatory parameters on particle deposition and therefore aid in the design of human subject experiments.

Effects of mesh style and grid convergence on particle deposition in bifurcating airway models with comparisons to experimental data

A number of research studies have employed a wide variety of mesh styles and levels of grid convergence to assess velocity fields and particle deposition patterns in models of branching biological systems. Generating structured meshes based on hexahedral elements requires significant time and effort; however, these meshes are often associated with high quality solutions. Unstructured meshes that employ tetrahedral elements can be constructed much faster but may increase levels of numerical diffusion, especially in tubular flow systems with a primary flow direction. The objective of this study is to better establish the effects of mesh generation techniques and grid convergence on velocity fields and particle deposition patterns in bifurcating respiratory models. In order to achieve this objective, four widely used mesh styles including structured hexahedral, unstructured tetrahedral, flow adaptive tetrahedral, and hybrid grids have been considered for two respiratory airway configurations. Initial particle conditions tested are based on the inlet velocity profile or the local inlet mass flow rate. Accuracy of the simulations has been assessed by comparisons to experimental in vitro data available in the literature for the steady-state velocity field in a single bifurcation model as well as the local particle deposition fraction in a double bifurcation model. Quantitative grid convergence was assessed based on a grid convergence index (GCI), which accounts for the degree of grid refinement. The hexahedral mesh was observed to have GCI values that were an order of magnitude below the unstructured tetrahedral mesh values for all resolutions considered. Moreover, the hexahedral mesh style provided GCI values of approximately 1% and reduced run times by a factor of 3. Based on comparisons to empirical data, it was shown that inlet particle seedings should be consistent with the local inlet mass flow rate. Furthermore, the mesh style was found to have an observable effect on cumulative particle depositions with the hexahedral solution most closely matching empirical results. Future studies are needed to assess other mesh generation options including various forms of the hybrid configuration and unstructured hexahedral meshes.

Validating CFD predictions of respiratory aerosol deposition: effects of upstream transition and turbulence

A number of computational fluid dynamics (CFD) studies have explored local deposition patterns of inhaled aerosols in the respiratory tract. These studies have highlighted the effects of multiple physiologic, geometric, and particle characteristics on deposition. However, very few studies have reported local or sub-branch quantitative comparisons to in vitro particle deposition data. The objective of this study is to numerically investigate the effects of transition and turbulence on highly localized particle deposition in a respiratory double bifurcation model in order to quantitatively validate CFD results. To perform the validations, local comparisons have been made to a specific in vitro case study of 10 microm particles depositing in a model of respiratory generations G3-G5. To achieve this objective, two geometric cases have been considered. The first case includes only the double bifurcation model. The second case includes a portion of the experimental particle delivery geometry, where transitional flow is expected. To evaluate the effectiveness of two-equation turbulence models in this system, the flow field solutions have been computed using laminar, standard k-omega, and low Reynolds number (LRN) k-omega approximations. Results indicate that even though the Reynolds number remained below the critical limit required for full turbulence, transition and turbulence have a significant impact on the flow field and local particle deposition patterns. For the experimental case considered, turbulence impacted the local deposition of 10 microm particles primarily by influencing the initial velocity and particle profiles. As such, both the laminar and LRN k-omega flow models provided good local quantitative matches to the in vitro deposition data, provided that the correct initial particle profile was specified. Implications of this study include the need for local quantitative validations of particle deposition results, the importance of correct inlet conditions, and the need to consider upstream effects in experimental and computational studies of the respiratory tract. Applications of these results to realistic respiratory geometries will require consideration on upstream flow conditions in the lung, transient flow, and intermittent turbulent structures.

LES modelling of flow in a simple airway model

Detailed information about the flow field pattern is highly important in accurately predicting particle deposition sites in the human airway. Flow in the upper airway during heavy breathing can have a Reynolds number as high as 9300, and therefore presents turbulent features. Although turbulence is believed to have an important effect on the airflow and other transport processes in the bronchial tree, to date both theoretical and numerical studies have predominantly assumed the flow to be laminar. In this paper, transitional/turbulent flow during inspiration is studied using a large eddy simulation (LES) in a single asymmetric bifurcation model of human upper airway. The influence of the non-laminar flow on the patterns and the particle paths is investigated in both 2D and 3D models. Throughout the investigation, comparisons with the laminar and conventional k- models for the same configuration and flow conditions are made. The LES model is also carefully validated against published experimental data in a stenotic tube model. The results demonstrate that the LES model is capable of capturing instantaneous eddy formation and flow separation in (almost) laminar, transitional and turbulent flow regimes, and hence may be used as a powerful and practical tool to provide much of the detailed flow information required for tracing the particle trajectories and particle deposition in human airways.

In silico modeling of asthma

The incidence of asthma is increasing throughout the world, especially among children, to the extent that it has become a medical issue of serious global concern. Appropriately, numerous pharmacologic drugs and clinical protocols for the treatment and prophylaxis of the disease have been reported. From a scientific perspective, a review of the literature suggests that the targeted delivery of an aerosol would, in a real sense, enhance the efficacy of an inhaled medicine. Therefore, in accordance with published data we have developed a mathematical description of disease-induced effects of disease on airway morphology. A morphological algorithm defining the heterogeneity of asthma has been integrated with a computer code that formulates the behavior and fate of inhaled drugs. In this work, predicted drug particle deposition patterns have been compared with SPECT images from experiments with healthy human subjects (controls) and asthmatic patients. The asthma drug delivery model simulations agree with observations from human testing. The results indicate that in silico modeling provides a technical foundation for addressing effects of disease on the administration of aerosolized drugs, and suggest that modeling should be used in a complementary manner with future inhalation therapy protocols.

Absorbed fraction of alpha-particles emitted in bifurcation regions of the human tracheo-bronchial tree

A model for bifurcation regions of the human tracheo-bronchial tree was developed. Equations for the surfaces are given to enable calculations of doses from alpha-particles emitted in these regions. It has been found that a bifurcation region is well approximated by a quasi-ellipsoid. The absorbed fractions of alpha-particles emitted in bifurcation regions were calculated by the Monte Carlo method. The average absorbed fraction under the bifurcation geometry is close to that found under the cylindrical geometry in the bronchial region. In the bronchiolar region, the absorbed fractions under the bifurcation geometry are up to 20% larger than those under the cylindrical geometry.

Risk assessment dosimetry model for inhaled particulate matter: II. Laboratory surrogates (rat)

Inhalation toxicology investigations are often performed with laboratory animals to address the potential health effects of inhaled air pollutants on human beings. In Part II of this risk assessment study we have considered the deposition of inhaled particulate matter in the laboratory rat as the surrogate of choice. Calculations were performed in an analogous manner to those conducted in Part I for human subjects. To simulate a wide range of human respiratory intensities associated with different levels of physical activities that must be recognized in the determination of air pollution standards, the CO(2) concentrations within animal inhalation exposure chambers may be controlled. Accordingly, we have regulated rat breathing parameters to correspond to a range of human activities, from rest to work. The results of this interspecies modeling study have been presented in a variety of graphical formats to ease comparisons with findings from experiments and to facilitate integration of the results into risk assessment analyses. The findings of our work clearly demonstrate that interspecies simulations can be employed to design animal tests a priori so that the results can be effectively and efficiently extrapolated to human conditions in a meaningful manner.

Risk assessment dosimetry model for inhaled particulate matter: I. Human subjects

Pollutant particulate matter (PM) is a serious global problem, presenting a threat to the health and well being of human subjects. Inhalation exposures tests with surrogate animals can be performed to estimate the threat. However, it is difficult to extrapolate the findings of animal tests to human conditions. In this two-part series, interspecies dosimetry models especially designed for implementation with risk assessment protocols are presented. In Part I, the mathematical integrity of the source model per se was tested with data from human subjects, and theoretical predictions agreed well with experimental measurements. In Part II, for surrogate (rat) simulations, appropriate algorithms for morphologies and ventilatory parameters were used as subroutines in the validated model. We conducted a comprehensive series of computer simulations describing the behavior of a representative air pollutant, secondary cigarette smoke. For risk assessment interests, a range of states from rest to exercise was considered. PM hygroscopicity had a pronounced effect on deposition in a complex but systematic manner, in humans and rats: deposition was increased for particles larger than about 1 microm, but was decreased for particles smaller than about 0.1 microm. The results clearly indicate that dosimetry models can be effectively used to a priori determine the laboratory conditions necessary for animals tests to accurately mimic human conditions. Moreover, the use of interspecies models is very cost effective. We propose, therefore, that mathematical models be used in a complementary manner with inhalation exposure experiments and be actively integrated into PM risk assessment protocols.