Fluid Dynamics in Airway Bifurcations: I. Primary Flows

Effect of inhaled gas density on the pendelluft-induced lung injury

Helium, sulfur hexafluoride-oxygen, and air were modeled to examine the role of the gas density on the pendelluft-induced lung injury (PILI) under high frequency oscillatory ventilation (HFOV). Large eddy simulation coupled with physiological resistance-compliance boundary conditions was applied to capture pendelluft-induced gas entrapment and mechanical stresses in an image-based human lung model. The flow characteristics were strongly dependent on the inspired gas density. The flow partitioning, globally between the left and right lung and locally between adjacent units branches, was significantly affected by the density of inhaled gas and was more balanced when inspiring lighter gas. The incomplete loops of flow-volume and volume-pressure curves were significantly influenced by the variations of the flow redistribution, resistance, and turbulence associated with the pendelluft mechanism. Inhaling light gas reduced the entrapped gas volume and mechanical stress surrounding carina ridges signifying the important role of inhaled gas properties on PILI. In general, lung ventilation by HFOV with a gas mixture of large amounts of Helium is thought to mitigate ventilator complications.

A biomechanical model of pendelluft induced lung injury

Lung ventilation using high frequency oscillatory techniques have been documented to attain adequate gas exchange through various gas transport mechanisms. Among them, the pendelluft flow is considered one of the most crucial mechanisms. In this work, we computationally investigate the induction of abnormal mechanical stresses and a regionally trapped volume of gas due to pendelluft flow. Large eddy simulation was used to model the turbulence in an upper tracheobronchial lung geometry that was derived from CT scans. The pendelluft flow was captured by modeling physiological boundary conditions at the truncated level of the lung model that is sensitive to the coupled resistance and compliance of individual patients. The flow-volume and volume-pressure loops are characterized by irregular shapes and suggest abnormal regional lung ventilation. Incomplete loops were observed indicating gas trapping in these regions signifying a potential for local injury due to incomplete ventilation from a residual volume build-up at the end of the expiration phase. In addition, the gas exchange between units was observed to create a velocity gradient causing a region of high wall shear stress surrounding the carina ridges. The recurrence of the pendelluft flow could cause a rupture to the lung epithelium layer. The trapped gas and wall shear stress were observed to amplify with increasing compliance asymmetry and ventilator operating frequency. In general, despite the significant contribution of the pendelluft flow to the gas exchange augmentation there exists significant risks of localized lung injury, phenomena we describe as pendelluft induced lung injury or PILI.

The role of coupled resistance-compliance in upper tracheobronchial airways under high frequency oscillatory ventilation

A large eddy simulation (LES) based computational fluid dynamics (CFD) study was conducted to investigate lung lobar ventilation and gas exchange under high frequency oscillatory ventilation conditions. Time-dependent pressure coupled with the airways resistance and compliance (R&C) were imposed as boundary conditions (BCs) in the upper tracheobronchial tree of patient-specific lung geometry. The flow distribution in the left and right lungs demonstrated significant variations compared to the case in which traditional BCs based on mass flow rate fractions was used and is in agreement with the in vivo data available in the literature. The gas transport due to the pendelluft mechanism was captured in the different lung lobes and units. The computed pendelluft elapsed time was consistent with available physiological data. In contrast to in vivo studies, our simulations were able to predict the volume associated with the pendelluft elapsed time at different frequencies. Significant differences in coaxial counter flow and flow structures were observed between different BCs. The consistency of the results with the physiological in vivo data indicates that computations with coupled R&C BCs provide a suitable alternative tool for understanding the gas transport, diagnosing lung pathway disease severity, and optimizing ventilation management techniques.

Flow transport and gas mixing during invasive high frequency oscillatory ventilation

A large Eddy simulation (LES) based computational fluid dynamics study was performed to investigate gas transport and mixing in patient specific human lung models during high frequency oscillatory ventilation. Different pressure-controlled waveforms (sinusoidal, exponential and square) and ventilator frequencies (15, 10 and 6Hz) were used (tidal volume=50mL). The waveforms were created by solving the equation of motion subjected to constant lung wall compliance and flow resistance. Simulations were conducted with and without endotracheal tube to understand the effect of invasive management device. Variation of pressure-controlled waveform and frequency exhibits significant differences on counter flow pattern, which could lead to a significant impact on the gas mixing efficiency. Pendelluft-like flow was present for the sinusoidal waveform at all frequencies but occurred only at early inspiration for the square waveform at highest frequency. The square waveform was most efficient for gas mixing, resulting in the least wall shear stress on the lung epithelium layer thereby reducing the risk of barotrauma to both airways and the alveoli for patients undergoing therapy.

Optimisations and evolution of the mammalian respiratory system : A suggestion of possible gene sharing in evolution

The respiratory system of mammalians is made of two successive branched structures with different physiological functions. The upper structure, or bronchial tree, is a fluid transportation system made of approximately 15 generations of bifurcations leading to the order of about 2(15) = 30, 000 terminal bronchioles with a diameter of approximately 0.5mm in the human lung. The branching pattern continues up to generation 23 but the structure and function of each of the subsequent structures, called acini, is different. Each acinus consists in a branched system of ducts surrounded by alveoli and plays the role of a diffusion cell where oxygen and carbon dioxide are exchanged with blood across the alveolar membrane. We show here that the bronchial tree simultaneously presents several different optimal properties. It is first energy efficient, second, it is space filling and third it is also "rapid". This physically based multi-optimality suggests that, in the course of evolution, an organ selected against one criterion could have been used later for a totally different purpose. For example, once selected for its energetic efficiency for the transport of a viscous fluid like blood, the same genetic material could have been used for its optimized rapidity. This would have allowed the emergence of atmospheric respiration made of inspiration-expiration cycles. For this phenomenon to exist, rapidity is essential as fresh air has to reach the gas exchange organs, the pulmonary acini, before the beginning of expiration. We finally show that the pulmonary acinus is optimized in the sense that the acinus morphology is directly related to the notion of a "best possible" extraction of entropic energy by a diffusion exchanger that has to feed oxygen efficiently from air to blood across a membrane of finite permeability.

Challenges in Validating CFD-Derived Inhaled Aerosol Deposition Predictions

Computational fluid dynamic (CFD) techniques have provided unprecedented opportunity for investigating inhaled particle deposition in realistic human airway geometries. Several recent articles describing local aerosol deposition predictions based upon "validated" CFD models have highlighted the challenges in validating local aerosol deposition predictions. These challenges include: (1) defining what is meant by validation; (2) defining appropriate experimental data for validation; and (3) determining when the agreement is not fortuitous. The term validation has numerous meanings, depending on the field and context in which it is used. For example, in computer programming it means the code executes as intended, to the experimentalist it means predicted results agree with matched experimental measurements, and to the risk assessor it implies that predictions using new parameters can be trusted. Based on the current literature it is not clear that a consensus exists for what constitutes a validated CFD model. It is also not clear what types of experimental data are needed or how closely the CFD input values and experimental conditions should be matched (similar or identical airway geometries, entrance airflow, or aerosol profiles) to validate CFD derived predictions. Due to the complexity of CFD computer codes and the multiplicity of deposition mechanisms, it is possible that total aerosol deposition may be accurately predicted and the resulting local particle deposition patterns are incorrect, or vice versa. Specific examples and suggestions for several challenges to experimentalists and modelers are presented.

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.

Effects of Oral Airway Geometry Characteristics on the Diffusional Deposition of Inhaled Nanoparticles

The deposition of ultrafine aerosols in the respiratory tract presents a significant health risk due to the increased cellular-level response that these particles may invoke. However, the effects of geometric simplifications on local and regional nanoparticle depositions remain unknown for the oral airway and throughout the respiratory tract. The objective of this study is to assess the effects of geometric simplifications on diffusional transport and deposition characteristics of inhaled ultrafine aerosols in models of the extrathoracic oral airway. A realistic model of the oral airway with the nasopharynx (NP) included has been constructed based on computed tomography scans of a healthy adult in conjunction with measurements reported in the literature. Three other geometries with descending degrees of physical realism were then constructed with successive geometric simplifications of the realistic model. A validated low Reynolds number k-ω turbulence model was employed to simulate laminar, transitional, and fully turbulent flow regimes for the transport of 1–200 nm particles. Results of this study indicate that the geometric simplifications considered did not significantly affect the total deposition efficiency or maximum local deposition enhancement of nanoparticles. However, particle transport dynamics and the underlying flow characteristics such as separation, turbulence intensity, and secondary motions did show an observable sensitivity to the geometric complexity. The orientation of the upper trachea was shown to be a major factor determining local deposition downstream of the glottis and should be retained in future models of the respiratory tract. In contrast, retaining the NP produced negligible variations in airway dynamics and could be excluded for predominantly oral breathing conditions. Results of this study corroborate the use of existing diffusion correlations based on a circular oral airway model. In comparison to previous studies, an improved correlation for the deposition of nanoparticles was developed based on a wider range of particle sizes and flow rates, which captures the dependence of the Sherwood number on both Reynolds and Schmidt numbers.

Mutual enhancements of CFD modeling and experimental data: a case study of 1-mum particle deposition in a branching airway model

In order to better understand aerosol dynamics and deposition in the complex flow field of the respiratory tract, both in vitro experiments and numerical modeling techniques have widely been employed. Computational fluid dynamics (CFD) modeling offers the flexibility of easily modifying system parameters such as flow rates, particle sizes, system geometry, and heterogeneous outlet conditions. However, a number of numerical errors and artifacts can lead to nonphysical CFD results. Experimental methods offer the advantage of physical realism; however, parameter variation is often difficult. The objective of this study is to illustrate the use of CFD to enhance the understanding of experimental results. In parallel, the selected experimental results have been used to partially validate the CFD predictions. A specific case study has been considered focusing on 1-mum particle depositions in a physiologically realistic bifurcation (PRB) model of respiratory generations 3-5. Previous experiments in this system report a deposition rate of approximately 0.01%. An in-depth CFD analysis has been employed to evaluate two cases of the empirical model. The first case consists of only the PRB double bifurcation geometry. The second case includes a portion of the experimental particle delivery system, which may influence the entering velocity and particle profiles. To assess the influence of upstream transition and turbulence, each of the two cases considered has been evaluated using laminar and low Reynolds number k-omega approximations. Results indicate that both upstream flow effects and turbulent or transitional flow play a significant role in determining the deposition of 1-mum particles in the model considered. Simulating upstream flow effects and laminar flow was required to match the empirically reported deposition fraction and provided a two orders of magnitude improvement over initial CFD estimates. This study highlights the need to consider the effects of experimental particle generation systems on velocity and particle profiles entering respiratory models. Future work is necessary to investigate the mechanisms responsible for the experimentally observed local deposition patterns.

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.

Transport and Deposition of Micro-Aerosols in Realistic and Simplified Models of the Oral Airway

A number of in vivo, in vitro and numerical studies have considered flow field characteristics and micro-particle deposition in the oral airway extending from the mouth through the larynx. These studies have highlighted the effects of flow rates, turbulence and particle characteristics on deposition values in realistic and simplified geometries. However, the effect of geometry simplifications on regional and local deposition patterns remains largely un-quantified for the oral airway and throughout the respiratory tract. The objective of this study is to assess the effects of geometry simplifications on regionally averaged and local micro-aerosol deposition characteristics in models of the extrathoracic oral airway. To achieve this objective, a realistic model of the oral airway has been constructed based on CT scans of a healthy adult in conjunction with measurements reported in the literature. Three other geometries with descending degrees of physical realism were constructed based on successive geometric simplifications of the realistic model. A validated low Reynolds number (LRN) k-omega turbulence model was employed to simulate laminar, transitional and fully turbulent flow regimes for 1-31 microm particles. Geometric simplifications were found to have a significant effect on aerosol dynamics, hot spot formations and cellular-level deposition values in the extrathoracic airway models considered. For all models, regional deposition efficiency results were found to be approximately within one standard deviation of available experimental data when plotted as a function of Stokes number. The realistic geometry provided the best predictions of regional deposition in comparison to experimental data as a function of particle diameter. Considering localized deposition, maximum deposition enhancement factors, which represent the ratio of local to total deposition, were one to two orders of magnitude higher for the realistic model. Geometric factors that significantly contributed to enhanced particle localization in the realistic model include a triangular-shaped glottis and a dorsal-sloped trachea. Therefore, highly realistic models of the oral airway geometry may be necessary to evaluate localized deposition patterns and hot spot formations, which are critical for accurately predicting cellular-level dose.

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.

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.

The effect of inlet velocity profile on the bifurcation COPD airway flow

The effect of inlet velocity profile on the flow features in obstructed airways is investigated in this study. In reality, the inlet velocity distributions on such models, which are extracted from medial branches of natural human lung, should be neither uniform, nor symmetric parabolic, but skewed-parabolic due to having been skewed by the upper carina ridges. Four different three-dimensional three-generation models based on the 23 generations model of Weibel have been considered, respectively. The fully three-dimensional incompressible laminar Navier-Stokes equations and continuity equation have been solved using CFD solver on unstructured tetrahedral meshes. To reduce the complexity of the simulations, only one Reynolds number of 900 was used in this calculation. Four types of inlet boundary conditions, namely uniform, parabolic, positive-skewed parabolic (skewed to the positive x-direction), and negative-skewed parabolic, were imposed on the obstructed airway models, which were considered to be obstructed at either the second generation or the third generation airways, respectively. The results show that the inlet velocity profile has significant influence on the flow patterns, mass distributions, and pressure drops in either the symmetric model, or the three obstructed models. The three generation airways may not be enough to study the bifurcation flow in chronic obstructive pulmonary disease (COPD) airways, and a four-generation or more airway model is necessary to get better predictive results.

Phase-contrast velocimetry with hyperpolarized3He for in vitro and in vivo characterization of airflow

This paper describes a technique that combines radial MRI and phase contrast (PC) to map the velocities of hyperpolarized gases ((3)He) in respiratory airways. The method was evaluated on well known geometries (straight and U-shaped pipes) before it was applied in vivo. Dynamic 2D maps of the three velocity components were obtained from a 10-mm slice with an in-plane spatial resolution of 1.6 mm within 1 s. Integration of the in vitro through-plane velocity over the slice matched the input flow within a relative precision of 6.4%. As expected for the given Reynolds number, a parabolic velocity profile was obtained in the straight pipe. In the U-shaped pipe the three velocity components were measured and compared to a fluid-dynamics simulation so the precision was evaluated as fine as 0.025 m s(-1). The technique also demonstrated its ability to visualize vortices and localize characteristic points, such as the maximum velocity and vortex-center positions. Finally, in vivo feasibility was demonstrated in the human trachea during inhalation.

Simulation of the regional manifestation of asthma

Asthma presents serious medical problems of global proportions. Clinical data suggest that the disease occurs preferentially at regions designated by large (0 </= I </= 5), central (6 </= I </= 11), and small (12 </= I </= 16) airways, where I defines branching generations within lungs. Our straightforward hypothesis, therefore, was that the efficacies of pharmacologic drugs proposed for the treatment and prophylaxis of asthma would be enhanced via their targeted delivery to appropriate sites. Hence, we have developed a mathematical model describing the behavior and fate of inhaled aerosols. Original algorithms have been derived to detail the physical manifestation of asthma as distinct components of smooth muscle constriction and inflammation. We have conducted a systematic analysis of the relative effects of morphology, ventilation, and particle size on aerosol deposition. Different intensities of asthma were simulated by reducing airway diameters by prescribed amounts. To show the real clinical applications of modeling, we have also simulated the performance of a popular nebulizer. Regarding therapeutic implications, it is clear that disease-induced changes in airway morphologies have pronounced effects on the administration of inhaled drugs. Likewise, ventilation affects both the total aerosol mass deposited and its relative spatial distribution among airways. By formulating these effects, the computer code allows drugs (e.g., bronchodilators for constriction, steroids for inflammation) to be selectively deposited. We suggest, therefore, that the code can be used in a complementary manner with clinical studies and can be integrated into aerosol therapy regimens.

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.

Interplay between geometry and flow distribution in an airway tree

Uniform flow distribution in a symmetric volume can be realized through a symmetric branched tree. It is shown here, however, by 3D numerical simulation of the Navier-Stokes equations, that the flow partitioning can be highly sensitive to deviations from exact symmetry if inertial effects are present. The flow asymmetry is quantified and found to depend on the Reynolds number. Moreover, for a given Reynolds number, we show that the flow distribution depends on the aspect ratio of the branching elements as well as their angular arrangement. Our results indicate that physiological variability should be severely restricted in order to ensure adequate fluid distribution through a tree.

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.

Measurement of regional lung function in rats using hyperpolarized 3helium dynamic MRI

Dynamic regional lung function was investigated in rats using a radial acquisition cine (RA-CINE) pulse sequence together with hyperpolarized (HP) (3)He gas delivered by a constant flow ventilator. Based on regional differences in the behavior of inspired air, the lung was conceptually divided into two regions (the major airways and the peripheral airspace) for purposes of functional analysis. To measure regional function in the major airways, a large RF flip angle (24 degrees) was applied to reduce (3)He magnetization in the peripheral airspace, and signal intensity (SI) was normalized with the projected airway diameter to estimate local airflow. Higher normalized signal intensity was observed in the left branch airway as compared to the right branch airway. To determine regional function in the peripheral airspace, a small RF flip angle (6 degrees) was used. Incremental increases of peripheral SI in successive lung images were consistent with the increase in lung volume. A new "skipping" scanning strategy using dummy frames allows a trade-off between the number of frames acquired for dynamic information, the RF flip angle, and the penetration depth of (3)He magnetization into the lung. This work provides a novel approach to simultaneously assess dynamic regional function and morphology.