One-dimensional simulation of aerosol transport and deposition in the human lung

Influence of alveolar mixing and multiple breaths of aerosol intake on particle deposition in the human lungs

Predictive dosimetry models play an important role in assessing health effect of inhaled particulate matter and in optimizing delivery of inhaled pharmaceutical aerosols. In this study, the commonly used 1D Multiple-Path Particle Dosimetry model (MPPD) was improved by including a mechanistically based model component for alveolar mixing of particles and by extending the model capabilities to account for multiple breaths of aerosol intake. These modifications increased the retained fraction of particles and consequently particle deposition predictions in the deep lung during tidal breathing. Comparison with an existing dataset (J. Aerosol Sci., 99:27-39, 2016) obtained under two breathing conditions referred to as slow and fast breathing showed significant differences in 1 μm particle deposition between predictions based on subject-specific breathing patterns and lung volume (slow: 30 ± 1%, fast: 21 ± 1%, (average ± standard deviation), N = 7) and measurements (slow: 43 ± 9%, fast: 30 ± 5%) when the prior version of MPPD (single breath and no mixing, J. Aerosol Sci., 151:105647, 2021) was used. Adding a mixing model and multiple breaths moved the predictions (slow: 34 ± 2%, fast:25 ± 2%) closer to the range of deposition measurements. For 2.9 μm particles, predictions from both the original (slow: 70 ± 2%, fast: 57 ± 2%) and the revised MPPD model (slow: 71 ± 2%, fast: 59 ± 3%) compared well with experiments (slow: 67 ± 8%, fast: 58 ± 10%). This was expected as suspended fraction of 2.9 μm particles was small and thus the addition of alveolar mixing and multi breath capability only slightly increased the retained fraction for particles of this size and greater. The revised 1D model improves dose predictions in the deep lung and support human risk assessment from exposure to airborne particles.

Aerosol Transport Modeling: The Key Link Between Lung Infections of Individuals and Populations

The recent COVID-19 pandemic has propelled the field of aerosol science to the forefront, particularly the central role of virus-laden respiratory droplets and aerosols. The pandemic has also highlighted the critical need, and value for, an information bridge between epidemiological models (that inform policymakers to develop public health responses) and within-host models (that inform the public and health care providers how individuals develop respiratory infections). Here, we review existing data and models of generation of respiratory droplets and aerosols, their exhalation and inhalation, and the fate of infectious droplet transport and deposition throughout the respiratory tract. We then articulate how aerosol transport modeling can serve as a bridge between and guide calibration of within-host and epidemiological models, forming a comprehensive tool to formulate and test hypotheses about respiratory tract exposure and infection within and between individuals.

Computational lung modelling in respiratory medicine

Computational modelling of the lungs is an active field of study that integrates computational advances with lung biophysics, biomechanics, physiology and medical imaging to promote individualized diagnosis, prognosis and therapy evaluation in lung diseases. The complex and hierarchical architecture of the lung offers a rich, but also challenging, research area demanding a cross-scale understanding of lung mechanics and advanced computational tools to effectively model lung biomechanics in both health and disease. Various approaches have been proposed to study different aspects of respiration, ranging from compartmental to discrete micromechanical and continuum representations of the lungs. This article reviews several developments in computational lung modelling and how they are integrated with preclinical and clinical data. We begin with a description of lung anatomy and how different tissue components across multiple length scales affect lung mechanics at the organ level. We then review common physiological and imaging data acquisition methods used to inform modelling efforts. Building on these reviews, we next present a selection of model-based paradigms that integrate data acquisitions with modelling to understand, simulate and predict lung dynamics in health and disease. Finally, we highlight possible future directions where computational modelling can improve our understanding of the structure–function relationship in the lung.

Pulmonary drug delivery and retention: A computational study to identify plausible parameters based on a coupled airway-mucus flow model

Pulmonary drug delivery systems rely on inhalation of drug-laden aerosols produced from aerosol generators such as inhalers, nebulizers etc. On deposition, the drug molecules diffuse in the mucus layer and are also subjected to mucociliary advection which transports the drugs away from the initial deposition site. The availability of the drug at a particular region of the lung is, thus, determined by a balance between these two phenomena. A mathematical analysis of drug deposition and retention in the lungs is developed through a coupled mathematical model of aerosol transport in air as well as drug molecule transport in the mucus layer. The mathematical model is solved computationally to identify suitable conditions for the transport of drug-laden aerosols to the deep lungs. This study identifies the conditions conducive for delivering drugs to the deep lungs which is crucial for achieving systemic drug delivery. The effect of different parameters on drug retention is also characterized for various regions of the lungs, which is important in determining the availability of the inhaled drugs at a target location. Our analysis confirms that drug delivery efficacy remains highest for aerosols in the size range of 1-5 μm. Moreover, it is observed that amount of drugs deposited in the deep lung increases by a factor of 2 when the breathing time period is doubled, with respect to normal breathing, suggesting breath control as a means to increase the efficacy of drug delivery to the deep lung. A higher efficacy also reduces the drug load required to be inhaled to produce the same health effects and hence, can help in minimizing the side effects of a drug.

Pulmonary drug delivery systems utilize the respiratory mechanism to directly deliver drugs to a target region of the lungs. The drug molecules deposit in the mucus lining, on reaching the target region, and are simultaneously transported away from the target region due to mucociliary transport and molecular diffusion. The availability of drugs at a target lung region and hence, efficacy of the drugs, therefore, determined by the delivery and retention of the drugs at the target region. The present study computationally solves the coupled transport equations to identify the conditions conducive for drug delivery and retention in the deep lungs. Drug delivery efficacy to the deep lung is observed to be highest for 1–5 μm aerosols. Breathing time period is also observed to influence efficacy. The amount of drugs deposited in the deep lung is observed to increase by a factor of 2 when the breathing time period is doubled with respect to normal breathing period. Such insights gained from this analysis will potentially help in devising mechanisms for increasing drug availability in the deep lung which is essential in achieving systemic drug delivery.

Regional Deposition: Deposition Models

Modeling particle deposition in the human lung requires information about the morphology of the lung in terms of simple geometric units, e.g., characterizing bronchial airways by straight cylindrical tubes. Five different regional deposition models are discussed in this section with respect to morphometric lung models and related mathematical modeling techniques: 1) one-dimensional cross-section or "trumpet" model, 2) deterministic symmetric generation or "single-path" model, 3) deterministic asymmetric generation or "multiple-path" model, 4) stochastic asymmetric generation or "multiple-path" model, and 5) single-path computational fluid and particle dynamics (CFPD) model. Current deposition models can predict the following regional deposition quantities relevant for the administration of medical aerosols: 1) regional bronchial and alveolar deposition, 2) generational lung deposition, 3) lobar deposition, 4) generational lobar deposition, and 5) generational surface deposition. Although deposition fractions predicted by the different models depend on the selection of a specific morphometric lung model and a specific set of analytical deposition equations, all models predict the same trends as functions of particle diameter and breathing parameters. In general, the overall agreement between the modeling predictions obtained by the various deposition models and the available experimental evidence indicates that current deposition models correctly predict regional and generational deposition.

Anthropometry-based generation of personalized and population-specific human airway models

Understanding aerosol deposition in the human lung is of great significance in pulmonary toxicology and inhalation pharmacology. Adverse effects of inhaled environmental aerosols and pharmacological efficacy of inhaled therapeutics are dependent on aerosol properties as well as person-specific respiratory tract anatomy and physiology. Anatomical geometry and physiological function of human airways depend on age, gender, weight, fitness, health, and disease status. Tools for the generation of the population- and subject-specific virtual airway anatomical geometry based on anthropometric data and physiological vitals are invaluable in respiratory diagnostics, personalized pulmonary pharmacology, and model-based management of chronic respiratory diseases. Here we present a novel protocol and software framework for the generation of subject-specific airways based on anthropometric measurements of the subject's body, using the anatomical input, and the conventional spirometry, providing the functional (physiological) data. This model can be used for subject-specific simulations of respiration physiology, gas exchange, and aerosol inhalation and deposition.

Innovative preclinical models for pulmonary drug delivery research

Introduction: Pulmonary drug delivery is a complex field of research combining physics which drive aerosol transport and deposition and biology which underpins efficacy and toxicity of inhaled drugs. A myriad of preclinical methods, ranging from in-silico to in-vitro, ex-vivo and in-vivo, can be implemented.Areas covered: The present review covers in-silico mathematical and computational fluid dynamics modelization of aerosol deposition, cascade impactor technology to estimated drug delivery and deposition, advanced in-vitro cell culture methods and associated aerosol exposure, lung-on-chip technology, ex-vivo modeling, in-vivo inhaled drug delivery, lung imaging, and longitudinal pharmacokinetic analysis.Expert opinion: No single preclinical model can be advocated; all methods are fundamentally complementary and should be implemented based on benefits and drawbacks to answer specific scientific questions. The overall best scientific strategy depends, among others, on the product under investigations, inhalation device design, disease of interest, clinical patient population, previous knowledge. Preclinical testing is not to be separated from clinical evaluation, as small proof-of-concept clinical studies or conversely large-scale clinical big data may inform preclinical testing. The extend of expertise required for such translational research is unlikely to be found in one single laboratory calling for the setup of multinational large-scale research consortiums.

Aerosol transport throughout inspiration and expiration in the pulmonary airways

Little is known about transport throughout the respiration cycle in the conducting airways. It is challenging to appropriately describe the time-dependent number of particles entering back into the model during exhalation. Modeling the entire lung is not feasible; therefore, multidomain methods must be used. Here, we present a new framework that is designed to simulate particles throughout the respiration cycle, incorporating realistic airway geometry and respiration. This framework is applied for a healthy rat lung exposed to  ∼ 1μm diameter particles, chosen to facilitate parameterization and validation. The flow field is calculated in the conducting airways (3D domain) by solving the incompressible Navier-Stokes equations with experimentally derived boundary conditions. Particles are tracked throughout inspiration by solving a modified Maxey-Riley equation. Next, we pass the time-dependent particle concentrations exiting the 3D model to the 1D volume conservation and advection-diffusion models (1D domain). Once the 1D models are solved, we prescribe the time-dependent number of particles entering back into the 3D airways to again solve for 3D transport. The coupled simulations highlight that about twice as many particles deposit during inhalation compared to exhalation for the entire lung. In contrast to inhalation, where most particles deposit at the bifurcation zones, particles deposit relatively uniformly on the gravitationally dependent side of the 3D airways during exhalation. Strong agreement to previously collected regional experimental data is shown, as the 1D models account for lobe-dependent morphology. This framework may be applied to investigate dosimetry in other species and pathological lungs.

Streamline crossing: An essential mechanism for aerosol dispersion in the pulmonary acinus

The dispersion of inhaled microparticles in the pulmonary acinus of the lungs is often attributed to the complex interplay between convective mixing, due to irreversible flows, and intrinsic particle motion (i.e. gravity and diffusion). However, the role of each mechanism, the exact nature of such interplay between them and their relative importance still remain unclear. To gain insight into these dispersive mechanisms, we track liquid-suspended microparticles and extract their effective diffusivities inside an anatomically-inspired microfluidic acinar model. Such results are then compared to experiments and numerical simulations in a straight channel. While alveoli of the proximal acinar generations exhibit convective mixing characteristics that lead to irreversible particle trajectories, this local effect is overshadowed by a more dominant dispersion mechanism across the ductal branching network that arises from small but significant streamline crossing due to intrinsic diffusional motion in the presence of high velocity gradients. We anticipate that for true airborne particles, which exhibit much higher intrinsic motion, streamline crossing would be even more significant.

Computationally efficient analysis of particle transport and deposition in a human whole-lung-airway model. Part I: Theory and model validation

Computational predictions of aerosol transport and deposition in the human respiratory tract can assist in evaluating detrimental or therapeutic health effects when inhaling toxic particles or administering drugs. However, the sheer complexity of the human lung, featuring a total of 16 million tubular airways, prohibits detailed computer simulations of the fluid-particle dynamics for the entire respiratory system. Thus, in order to obtain useful and efficient particle deposition results, an alternative modeling approach is necessary where the whole-lung geometry is approximated and physiological boundary conditions are implemented to simulate breathing. In Part I, the present new whole-lung-airway model (WLAM) represents the actual lung geometry via a basic 3-D mouth-to-trachea configuration while all subsequent airways are lumped together, i.e., reduced to an exponentially expanding 1-D conduit. The diameter for each generation of the 1-D extension can be obtained on a subject-specific basis from the calculated total volume which represents each generation of the individual. The alveolar volume was added based on the approximate number of alveoli per generation. A wall-displacement boundary condition was applied at the bottom surface of the first-generation WLAM, so that any breathing pattern due to the negative alveolar pressure can be reproduced. Specifically, different inhalation/exhalation scenarios (rest, exercise, etc.) were implemented by controlling the wall/mesh displacements to simulate realistic breathing cycles in the WLAM. Total and regional particle deposition results agree with experimental lung deposition results. The outcomes provide critical insight to and quantitative results of aerosol deposition in human whole-lung airways with modest computational resources. Hence, the WLAM can be used in analyzing human exposure to toxic particulate matter or it can assist in estimating pharmacological effects of administered drug-aerosols. As a practical WLAM application, the transport and deposition of asthma drugs from a commercial dry-powder inhaler is discussed in Part II.

Prediction of particle deposition in the lungs based on simple modeling of alveolar mixing

A simplified model of particle deposition in the lungs has been developed and implemented, based on the hypothesis that perfect mixing takes place in the alveolar volume of each airway generation. This key idea is combined with purely convective transport along airways, driven by steady alveolar expansion and contraction, and results in an analytically tractable model. Predictions of the model, and in particular pulmonary deposition, are found in very good agreement with detailed benchmark data in the literature for particle diameters d ≥ 0.1 μm. The success of this simple model provides indirect evidence in favor of the role of alveolar mixing in the deposition process.

A Lagrangian Approach for Calculating Microsphere Deposition in a One-Dimensional Lung-Airway Model

Using the open-source software openfoam as the solver, a novel approach to calculate microsphere transport and deposition in a 1D human lung-equivalent trumpet model (TM) is presented. Specifically, for particle deposition in a nonlinear trumpetlike configuration a new radial force has been developed which, along with the regular drag force, generates particle trajectories toward the wall. The new semi-empirical force is a function of any given inlet volumetric flow rate, micron-particle diameter, and lung volume. Particle-deposition fractions (DFs) in the size range from 2 μm to 10 μm are in agreement with experimental datasets for different laminar and turbulent inhalation flow rates as well as total volumes. Typical run times on a single processor workstation to obtain actual total deposition results at comparable accuracy are 200 times less than that for an idealized whole-lung geometry (i.e., a 3D–1D model with airways up to 23rd generation in single-path only).

Distribution of aerosolized particles in healthy and emphysematous rat lungs: comparison between experimental and numerical studies

In silico models of airflow and particle deposition in the lungs are increasingly used to determine the therapeutic or toxic effects of inhaled aerosols. While computational methods have advanced significantly, relatively few studies have directly compared model predictions to experimental data. Furthermore, few prior studies have examined the influence of emphysema on particle deposition. In this work we performed airflow and particle simulations to compare numerical predictions to data from our previous aerosol exposure experiments. Employing an image-based 3D rat airway geometry, we first compared steady flow simulations to coupled 3D-0D unsteady simulations in the healthy rat lung. Then, in 3D-0D simulations, the influence of emphysema was investigated by matching disease location to the experimental study. In both the healthy unsteady and steady simulations, good agreement was found between numerical predictions of aerosol delivery and experimental deposition data. However, deposition patterns in the 3D geometry differed between the unsteady and steady cases. On the contrary, satisfactory agreement was not found between the numerical predictions and experimental data for the emphysematous lungs. This indicates that the deposition rate downstream of the 3D geometry is likely proportional to airflow delivery in the healthy lungs, but not in the emphysematous lungs. Including small airway collapse, variations in downstream airway size and tissue properties, and tracking particles throughout expiration may result in a more favorable agreement in future studies.

Aerosol deposition in the human lung in reduced gravity

The deposition of aerosol in the human lung occurs mainly through a combination of inertial impaction, gravitational sedimentation, and diffusion. For 0.5- to 5-μm-diameter particles and resting breathing conditions, the primary mechanism of deposition in the intrathoracic airways is sedimentation, and therefore the fate of these particles is markedly affected by gravity. Studies of aerosol deposition in altered gravity have mostly been performed in humans during parabolic flights in both microgravity (μG) and hypergravity (~1.6G), where both total deposition during continuous aerosol mouth breathing and regional deposition using aerosol bolus inhalations were performed with 0.5- to 3-μm particles. Although total deposition increased with increasing gravity level, only peripheral deposition as measured by aerosol bolus inhalations was strongly dependent on gravity, with central deposition (lung depth<200 mL) being similar between gravity levels. More recently, the spatial distribution of coarse particles (mass median aerodynamic diameter≈5 μm) deposited in the human lung was assessed using planar gamma scintigraphy. The absence of gravity caused a smaller portion of 5-μm particles to deposit in the lung periphery than in the central region, where deposition occurred mainly in the airways. Indeed, 5-μm-diameter particles deposit either by inertial impaction, a mechanism most efficient in the large and medium-sized airways, or by gravitational sedimentation, which is most efficient in the distal lung. On the contrary, for fine particles (~1 μm), both aerosol bolus inhalations and studies in small animals suggest that particles deposit more peripherally in μG than in 1G, beyond the reach of the mucociliary clearance system.

Variability in uptake efficiency for pulsed versus constant concentration delivery of inhaled nitric oxide

Background

Nitric oxide (NO) is currently administered using devices that maintain constant inspired NO concentrations. Alternatively, devices that deliver a pulse of NO during the early phase of inspiration may have use in optimizing NO dosing efficiency and in extending application of NO to long-term use by ambulatory, spontaneously breathing patients. The extent to which the amount of NO delivered for a given pulse sequence determines alveolar concentrations and uptake, and the extent to which this relationship varies with breathing pattern, physiological, and pathophysiological parameters, warrants investigation.

Methods

A mathematical model was used to analyze inhaled nitric oxide (NO) transport through the conducting airways, and to predict uptake from the alveolar region of the lung. Pulsed delivery was compared with delivery of a constant concentration of NO in the inhaled gas.

Results

Pulsed delivery was predicted to offer significant improvement in uptake efficiency compared with constant concentration delivery. Uptake from the alveolar region depended on pulse timing, tidal volume, respiratory rate, lung and dead space volume, and the diffusing capacity of the lung for NO (D_LNO). It was predicted that variation in uptake efficiency with breathing pattern can be limited using a pulse time of less than 100 ms, with a delay of less than 50 ms between the onset of inhalation and pulse delivery. Nonlinear variation in uptake efficiency with D_LNO was predicted, with uptake efficiency falling off sharply as D_LNO decreased below ~50-60 ml/min/mm Hg. Gas mixing in the conducting airways played an important role in determining uptake, such that consideration of bulk convection alone would lead to errors in assessing efficiency of pulsed delivery systems.

Conclusions

Pulsed NO delivery improves uptake efficiency compared with constant concentration delivery. Optimization of pulse timing is critical in limiting intra- and inter-subject variability in dosing.

Transport of gases between the environment and alveoli--theoretical foundations

The transport of oxygen and carbon dioxide in the gas phase from the ambient environment to and from the alveolar gas/blood interface is accomplished through the tracheobronchial tree, and involves mechanisms of bulk or convective transport and diffusive net transport. The geometry of the airway tree and the fluid dynamics of these two transport processes combine in such a way that promotes a classical fractionation of ventilation into dead space and alveolar ventilation, respectively. This simple picture continues to capture much of the essence of gas phase transport. On the other hand, a more detailed look at the interaction of convection and diffusion leads to significant new issues, many of which remain open questions. These are associated with parallel and serial inhomogeneities especially within the distal acinar units, velocity profiles in distal airways and terminal spaces subject to moving boundary conditions, and the serial transport of respiratory gases within the complex acinar architecture. This article focuses specifically on the theoretical foundations of gas transport, addressing two broad areas. The first deals with the reasons why the classical picture of alveolar and dead space ventilation is so successful; the second examines the underlying assumptions within current approximations to convective and diffusive transport, and how they interact to effect net gas exchange.

Removal of sedimentation decreases relative deposition of coarse particles in the lung periphery

Lung deposition of >0.5-μm particles is strongly influenced by gravitational sedimentation, with deposition being reduced in microgravity (μG) compared with normal gravity (1G). Gravity not only affects total deposition, but may also alter regional deposition. Using gamma scintigraphy, we measured the distribution of regional deposition and retention of radiolabeled particles ((99m)Tc-labeled sulfur colloid, 5-μm diameter) in five healthy volunteers. Particles were inhaled in a controlled fashion (0.5 l/s, 15 breaths/min) during multiple periods of μG aboard the National Aeronautics and Space Administration Microgravity Research Aircraft and in 1G. In both cases, deposition scans were obtained immediately postinhalation and at 1 h 30 min, 4 h, and 22 h postinhalation. Regional deposition was characterized by the central-to-peripheral ratio and by the skew of the distribution of deposited particles on scans acquired directly postinhalation. Relative distribution of deposition between the airways and the alveolar region was derived from data acquired at the various time points. Compared with inhalation in 1G, subjects show an increase in central-to-peripheral ratio (P = 0.043), skew (P = 0.043), and tracheobronchial deposition (P < 0.001) when particles were inhaled in μG. The absence of gravity caused fewer particles to deposit in the lung periphery than in the central region where deposition occurred mainly in the airways in μG. Furthermore, the increased skew observed in μG likely illustrates the presence of localized areas of deposition, i.e., "hot spots", resulting from inertial impaction. In conclusion, gravity has a significant effect on deposition patterns of coarse particles, with most of deposition occurring in the alveolar region in 1G but in the large airways in μG.

Aerosol deposition characteristics in distal acinar airways under cyclic breathing conditions

Although the major mechanisms of aerosol deposition in the lung are known, detailed quantitative data in anatomically realistic models are still lacking, especially in the acinar airways. In this study, an algorithm was developed to build multigenerational three-dimensional models of alveolated airways with arbitrary bifurcation angles and spherical alveolar shape. Using computational fluid dynamics, the deposition of 1- and 3-μm aerosol particles was predicted in models of human alveolar sac and terminal acinar bifurcation under rhythmic wall motion for two breathing conditions (functional residual capacity = 3 liter, tidal volume = 0.5 and 0.9 liter, breathing period = 4 s). Particles entering the model during one inspiration period were tracked for multiple breathing cycles until all particles deposited or escaped from the model. Flow recirculation inside alveoli occurred only during transition between inspiration and expiration and accounted for no more than 1% of the whole cycle. Weak flow irreversibility and convective transport were observed in both models. The average deposition efficiency was similar for both breathing conditions and for both models. Under normal gravity, total deposition was ~33 and 75%, of which ~67 and 96% occurred during the first cycle, for 1- and 3-μm particles, respectively. Under zero gravity, total deposition was ~2-5% for both particle sizes. These results support previous findings that gravitational sedimentation is the dominant deposition mechanism for micrometer-sized aerosols in acinar airways. The results also showed that moving walls and multiple breathing cycles are needed for accurate estimation of aerosol deposition in acinar airways.

Modelling particle deposition in human lungs: modelling concepts and comparison with experimental data

Deposition of inhaled particles in the human lung is determined by biological factors, such as lung morphology and respiratory physiology, as well as by physical factors, such as fluid dynamics of the inhaled air and physical deposition mechanisms acting upon inhaled particles. Different conceptual particle deposition models vary primarily with respect to lung morphometry and mathematical modelling technique, rather than by using different deposition equations. Current whole lung deposition models permit the prediction of particle deposition in single airway generations or defined regions of the human lung for any combination of particle size and breathing pattern. Although comparisons with experimental data in human subjects indicate that all presently available deposition models correctly predict total and regional deposition, they cannot be validated by comparison with experimental data at the single airway or airway generation level.

Alveolar duct expansion greatly enhances aerosol deposition: a three-dimensional computational fluid dynamics study

Obtaining in vivo data of particle transport in the human lung is often difficult, if not impossible. Computational fluid dynamics (CFD) can provide detailed information on aerosol transport in realistic airway geometries. This paper provides a review of the key CFD studies of aerosol transport in the acinar region of the human lung. It also describes the first ever three-dimensional model of a single fully alveolated duct with moving boundaries allowing for the cyclic expansion and contraction that occurs during breathing. Studies of intra-acinar aerosol transport performed in models with stationary walls (SWs) showed that flow patterns were influenced by the geometric characteristics of the alveolar aperture, the presence of the alveolar septa contributed to the penetration of the particles into the lung periphery and there were large inhomogeneities in deposition patterns within the acinar structure. Recent studies have now used acinar models with moving walls. In these cases, particles penetrate the alveolar cavities not only as a result of sedimentation and diffusion but also as a result of convective transport, resulting in a much higher deposition prediction than that in SW models. Thus, models that fail to incorporate alveolar wall motions probably underestimate aerosol deposition in the acinar region of the lung.

Semi-empirical stochastic model of aerosol bolus dispersion in the human lung

Aerosol bolus dispersion, that is, the broadening of an inhaled narrow aerosol bolus upon exhalation, was simulated by Monte Carlo methods using a stochastic, asymmetric morphometric model of the human lung. Physical mechanisms considered to contribute to bolus dispersion were (1) axial diffusion in conductive airways, approximated by effective diffusivities, (2) convective mixing at airway bifurcation sites, (3) differences in inspiratory and expiratory velocity profiles, (4) mixing with residual air in alveoli, and (5) inhomogeneous ventilation of the lung lobes due to asymmetric flow spitting at bifurcations and asymmetric and asynchronous filling of the five lung lobes. Theoretical predictions of the bolus dispersion model were compared to experimental data for 79 healthy volunteers, which provide detailed information on statistical bolus parameters (half-width, standard deviation, skewness, and mode shift) and total bolus deposition as a function of the depth of bolus penetration into the airway system. Predicted bolus dispersion and deposition data show excellent agreement with the published experimental data, suggesting that axial diffusion in conductive airways and convective mixing in alveoli, resulting in irreversible particle transport, are the major determinants of bolus dispersion. The variability and asymmetry of the branching airway network, leading to asymmetric flow splitting at airway bifurcations, greatly enhances the effect of irreversibility and the resulting dispersion of the inhaled bolus.

CFD Simulation and Experimental Validation of Fluid Flow and Particle Transport in a Model of Alveolated Airways

Accurate modeling of air flow and aerosol transport in the alveolated airways is essential for quantitative predictions of pulmonary aerosol deposition. However, experimental validation of such modeling studies has been scarce. The objective of this study is to validate CFD predictions of flow field and particle trajectory with experiments within a scaled-up model of alveolated airways. Steady flow (Re = 0.13) of silicone oil was captured by particle image velocimetry (PIV), and the trajectories of 0.5 mm and 1.2 mm spherical iron beads (representing 0.7 to 14.6 mum aerosol in vivo) were obtained by particle tracking velocimetry (PTV). At twelve selected cross sections, the velocity profiles obtained by CFD matched well with those by PIV (within 1.7% on average). The CFD predicted trajectories also matched well with PTV experiments. These results showed that air flow and aerosol transport in models of human alveolated airways can be simulated by CFD techniques with reasonable accuracy.

Explaining clustered ventilation defects via a minimal number of airway closure locations

Computational models of the human lung have been developed to study lung physiology and have been used to identify the airways responsible for mechanical dysfunction in asthmatics. Tgavalekos et al. used models anatomically consistent with the human lung to link ventilation defects to the heterogeneous closure of small airways. Their approach implicitly assumed a high degree of independence between airway closures as indicated by the low compactness of the airway structures mapped to individual ventilation defects. Venegas et al. however, have found that significant mutual dependence of airways may play a role in patchy ventilation of asthmatics. This led us to explore the question to what extent anatomically consistent models can be built which do not implicitly assume high independence of airways but instead allow for the mutual dependence of airways responsible for ventilation defects. We propose an algorithm for generating subject-specific airway-tree models that minimize the number of airways that must be closed or severely constricted to cause observed ventilation defects. We also propose novel approaches for measuring the compactness of airway structures. Our approach shows that anatomically consistent models which link compact airway structures to ventilation defects can be built. Our model also shows that some ventilation defects may be caused by closures of larger airways than previously reported.

Contribution of upper airway geometry to convective mixing

We investigated the axial dispersive effect of the upper airway structure (comprising mouth cavity, oropharynx, and trachea) on a traversing aerosol bolus. This was done by means of aerosol bolus experiments on a hollow cast of a realistic upper airway model (UAM) and three-dimensional computational fluid dynamics (CFD) simulations in the same UAM geometry. The experiments showed that 50-ml boluses injected into the UAM dispersed to boluses with a half-width ranging from 80 to 90 ml at the UAM exit, across both flow rates (250, 500 ml/s) and both flow directions (inspiration, expiration). These experimental results imply that the net half-width induced by the UAM typically was 69 ml. Comparison of experimental bolus traces with a one-dimensional Gaussian-derived analytical solution resulted in an axial dispersion coefficient of 200–250 cm2/s, depending on whether the bolus peak and its half-width or the bolus tail needed to be fully accounted for. CFD simulations agreed well with experimental results for inspiratory boluses and were compatible with an axial dispersion of 200 cm2/s. However, for expiratory boluses the CFD simulations showed a very tight bolus peak followed by an elongated tail, in sharp contrast to the expiratory bolus experiments. This indicates that CFD methods that are widely used to predict the fate of aerosols in the human upper airway, where flow is transitional, need to be critically assessed, possibly via aerosol bolus simulations. We conclude that, with all its geometric complexity, the upper airway introduces a relatively mild dispersion on a traversing aerosol bolus for normal breathing flow rates in inspiratory and expiratory flow directions.

Gas and aerosol mixing in the acinus

This review is concerned with mixing and transport in the human pulmonary acinus. We first examine the current understanding of the anatomy of the acinus and introduce elements of fluid mechanics used to characterize the transport of momentum, gas and aerosol particles. We then review gas transport in more detail and highlight some areas of current research. Next we turn our attention to aerosol transport and in particular to mixing within the alveoli. We examine the factors influencing the level of mixing, review the concept of chaotic convective mixing, and make some brief comments on how mixing affects particle deposition. We end with a few comments on some issues unique to the neonatal and developing lung.

Mathematical analysis of particle deposition in human lungs: an improved single path transport model

A dynamic single-path mathematical model was developed that is capable of analyzing detailed deposition patterns of inhaled particles in human lungs. Weibel's symmetric lung morphology was adopted as the basic lung structure, and detailed transport processes were evaluated numerically using the fully implicit procedure. Deposition efficiencies by specific mechanisms were individually examined for accuracy and new empirical formulas were incorporated whenever appropriate. Deposition in the alveolar region was divided into deposition fractions in the alveolar duct and alveoli, considering active transport processes between the two regions. The deposition fractions were obtained for each airway generation, serial lung volumetric compartments, and conventional three-compartment anatomic lung regions. In addition, the surface dose and cumulative deposition with time were analyzed. The results showed excellent agreement with available experimental data. The present model provides an improvement from the previously reported models and can be used as a tool in assessing internal dose of inhaled particles under various inhalation conditions.

Two mathematical models for predicting dispersion of particles in the human lung

The dispersion of particles in the human lung is modeled as a series of virtual mixing tanks. Using the experimental results of Scherer et al. (1975, J. Appl. Physiol., 38(4), pp. 719-723) for a five-generation glass lung model, it is shown that each generation of the glass lung behaves like an independent virtual mixing tank. The corresponding resident time distribution is shown to have a variance approximately equal to the square of the average time a particle spends in the generation. By assuming that each generation of the human lung behaves as an independent virtual mixing tank, the realistic lung data provided by Weibel (1963, Morphometry of the Human Lung, Spinger-Verlag, New York) are used to validate this assumption in two ways. First, the half-width of the exhaled particle concentration profile is obtained. Second, a system of differential equations, with the concentration of particles in each mixing tank as its solution, is derived and solved numerically. This gives the exhaled concentration profile. Both techniques yield similar results to each other, and both give excellent agreement with the experimental data. The virtual mixing tank approach allows the complex mixing that occurs in the branching pathways of the lung to be more simply modeled. The model, thereby derived, is simple to change and could lead to enhancements in the understanding of the underlying processes contributing to the ventilation of the lung in health and disease.

Computed tomography studies of lung ventilation and perfusion

With the emergence of multidetector-row computed tomography (CT) it is now possible to image both structure and function via use of a single imaging modality. Breath-hold spiral CT provides detail of the airway and vascular trees along with texture reflective of the state of the lung parenchyma. Use of stable xenon gas wash-in and/or wash-out methods using an axial mode of the CT scanner whereby images are acquired through gating to the respiratory cycle provide detailed images of regional ventilation with isotropic voxel dimensions now on the order of 0.4 mm. Axial scanning during a breath hold and gating to the electrocardiogram during the passage of a sharp bolus injection of iodinated contrast agent provide detailed images of regional pulmonary perfusion. These dynamic CT methods for the study of regional lung function are discussed in the context of other methods that have been used to study heterogeneity of lung function.

The Lung in Space

The lung is exquisitely sensitive to gravity, which induces gradients in ventilation, blood flow, and gas exchange. Studies of lungs in microgravity provide a means of elucidating the effects of gravity. They suggest a mechanism by which gravity serves to match ventilation to perfusion, making for a more efficient lung than anticipated. Despite predictions, lungs do not become edematous, and there is no disruption to, gas exchange in microgravity. Sleep disturbances in microgravity are not a result of respiratory-related events; obstructive sleep apnea is caused principally by the gravitational effects on the upper airways. In microgravity, lungs may be at greater risk to the effects of inhaled aerosols.

Effect of small flow reversals on aerosol mixing in the alveolar region of the human lung

It has been suggested that irreversibility of alveolar flow combined with a stretched and folded pattern of streamlines can lead to a sudden increase in mixing in the lung. To determine whether this phenomenon is operative in the human lung in vivo, we performed a series of bolus studies with a protocol designed to induce complex folding patterns. Boli of 0.5- and 1-microm-diameter particles were inhaled at penetration volumes (V(p)) of 300 and 1,200 ml in eight subjects during short periods of microgravity aboard the National Aeronautics and Space Administration Microgravity Research Aircraft. Inspiration was from residual volume to 1 liter above 1 G functional residual capacity. This was followed by a 10-s breathhold, during which up to seven 100-ml flow reversals (FR) were imposed at V(p) = 300 ml and up to four 500-ml FR at V(p) = 1,200 ml, and by an expiration to residual volume. Bolus dispersion and deposition were calculated from aerosol concentration and flow rate continuously monitored at the mouth. There was no significant increase in dispersion and deposition with increasing FR except for dispersion between 0 and 7 FR at V(p) = 300 ml with 0.5-microm-diameter particles, and this increase was small. This suggested that either the phenomenon of stretch and fold did not occur within the number of FR we performed or that it had already occurred during the one breathing cycle included in the basic maneuver. We speculate that the phenomenon occurred during the basic maneuver, which is consistent with the high degree of dispersion and deposition observed previously in microgravity.

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.

Local particle deposition patterns may play a key role in the development of lung cancer

The apparent discrepancy between the reported preferential occurrence of bronchial carcinomas in central bronchial airways and current dose estimates for inhaled particles suggests that experimentally observed local accumulations of particles within bronchial airway bifurcations may play a crucial role in lung cancer induction. Here, we computed three-dimensional particle deposition patterns in lobar-segmental airway bifurcations and quantified the resulting inhomogeneous deposition patterns in terms of deposition enhancement factors, which are defined as the ratio of local to average deposition densities. Our results revealed that a small fraction of epithelial cells located at carinal ridges can receive massive doses that may be even a few hundred times higher than the average dose for the whole airway. This lends further credence to the hypothesis that the apparent site selectivity of neoplastic lesions may indeed be caused by the enhanced deposition of toxic particulate matter at bronchial airway bifurcations.

Kinematically irreversible acinar flow: a departure from classical dispersive aerosol transport theories

Current theories describe aerosol transport in the lung as a dispersive (diffusion-like) process, characterized by an effective diffusion coefficient in the context of reversible alveolar flow. Our recent experimental data, however, question the validity of these basic assumptions. In this study, we describe the behavior of fluid particles (or bolus) in a realistic, numerical, alveolated duct model with rhythmically expanding walls. We found acinar flow exhibiting multiple saddle points, characteristic of chaotic flow, resulting in substantial flow irreversibility. Computations of axial variance of bolus spreading indicate that the growth of the variance with respect to time is faster than linear, a finding inconsistent with dispersion theory. Lateral behavior of the bolus shows fine-scale, stretch-and-fold striations, exhibiting fractal-like patterns with a fractal dimension of 1.2, which compares well with the fractal dimension of 1.1 observed in our experimental studies performed with rat lungs. We conclude that kinematic irreversibility of acinar flow due to chaotic flow may be the dominant mechanism of aerosol transport deep in the lungs.

Integrated exposure and dose modeling and analysis system. 3. Deposition of inhaled particles in the human respiratory tract

Detailed information on the composition-resolved size distribution of particulate matter deposited along the human respiratory tract can help linking epidemiological, toxicological, and pathological studies and thus potentially improve the understanding of the origin of pulmonary disorders induced by respirable pathogens. For this purpose, a new mechanistic dosimetry model describing the dynamics of respirable particles in the human airways was developed. Model predictions of transport and fate of inhaled aerosols are based on solutions of the aerosol general dynamic equation, which describes changes in particle size and mass distributions resulting from processes such as nucleation, condensation, coagulation, gas phase chemical reaction, and deposition. To compensate for approximating the three-dimensional problem by considering only axial variations along the airways, boundary layer effects are introduced via appropriate dimensionless transport parameters. The architecture of the human lung is described by Weibel's simple regular dichotomous model. An important advantage of the present approach is that it allows testing the significance of intersubject lung morphology and ventilation variability for particle deposition and dose calculations. The model predicts the evolution of size and composition distributions of inhaled particles and the deposition profile along the human lower respiratory tract: in general, model predictions are in qualitative and quantitative agreement with tracheobronchial and alveolar deposition data.

Saline aerosol bolus dispersion. II. The effect of conductive airway alteration

In a companion study (Verbanck S, Schuermans D, Vincken W, and Paiva M, J Appl Physiol 90: 1754-1762, 2001), we investigated whether saline aerosol bolus tests could also be used to detect proximal, as opposed to peripheral, airway alterations. We studied 10 never-smokers before and after histamine challenge, obtaining, for various volumetric lung depths (VLD), saline bolus-derived indexes computed by discarding aerosol concentrations below either 50% of the exhaled bolus maximum (half-width, H) or below cutoffs ranging from 5 to 25% (standard deviation, sigma(5%)-sigma(25%)) and skew (sk(5)-sk(25%)). Multiple-breath N(2) washout-derived indexes of conductive (S(cond)) and acinar (S(acin)) ventilation inhomogeneity were also determined. After histamine, S(cond) significantly increased (P = 0.008) whereas S(acin) remained unaffected, indicating purely conductive airway alteration. Consistent with this observation, sk(5%) (or sk(25%)) was increased to the same extent at all VLD, and sigma(5%) was increased preferentially at low VLD. By contrast, H and sigma(25%) displayed preferential increases at high VLD, a pattern similar to that induced by peripheral alterations. The present work shows that proximal airway alteration can be reliably identified by saline bolus tests only if these include measurements at low and high VLD and if bolus dispersion is quantified as a standard deviation with a low cutoff.

Saline aerosol bolus dispersion. I. The effect of acinar airway alteration

We explored the possibility of using a saline aerosol for bolus dispersion measurements to detect peripheral airway alterations in smokers. Indexes of ventilation inhomogeneity in conductive (S(cond)) and acinar (S(acin)) lung zones, as derived from the multiple-breath N(2) washout (Verbanck S, Schuermans D, Van Muylem A, Noppen M, Paiva M, and Vincken W, J Appl Physiol 83: 1807-1816, 1997), were also measured. The saline bolus test consisted of inhaling 60-ml saline aerosol boluses to different volumetric lung depths (VLD) in the 1.1 liter volume above functional residual capacity. In the never-smoker group (n = 12), saline boluses showed bolus dispersion values consistent with normal values reported in the literature for 0.5- to 1-microm aerosols. In the smoker group (n = 12; 28 +/- 9 pack years, mean +/- SD), significant increases were seen on dispersion and skew of the most peripherally inhaled saline boluses (VLD = 800 ml; P < 0.05) as well as on S(acin) (P = 0.007) with respect to never-smokers. Shallow inhaled boluses (VLD = 200 ml) and S(cond) did not reveal any significant differences between smokers and never-smokers. This study shows the consistent response of two conceptually independent tests, in which both saline aerosol and gas-derived indexes point to a heterogeneous distribution of smoking-induced structural alterations in the lung periphery.

Microgravity and the lung

Although environmental physiologists are readily able to alter many aspects of the environment, it is not possible to remove the effects of gravity on Earth. During the past decade, a series of space flights were conducted in which comprehensive studies of the lung in microgravity (weightlessness) were performed. Stroke volume increases on initial exposure to microgravity and then decreases as circulating blood volume is reduced. Diffusing capacity increases markedly, due to increases in both pulmonary capillary blood volume and membrane diffusing capacity, likely due to more uniform pulmonary perfusion. Both ventilation and perfusion become more uniform throughout the lung, although much residual inhomogeneity remains. Despite the improvement in the distribution of both ventilation and perfusion, the range of the ventilation-to-perfusion ratio seen during a normal breath remains unaltered, possibly because of a spatial mismatch between ventilation and perfusion on a small scale. There are unexpected changes in the mixing of gas in the periphery of the lung, and evidence suggests that the intrinsic inhomogeneity of the lung exists at a scale of an acinus or a few acini. In addition, aerosol deposition in the alveolar region is unexpectedly high compared with existing models.

Effect of microgravity and hypergravity on deposition of 0.5- to 3-micron-diameter aerosol in the human lung

We measured intrapulmonary deposition of 0. 5-, 1-, 2-, and 3-micron-diameter particles in four subjects on the ground (1 G) and during parabolic flights both in microgravity (microG) and at approximately 1.6 G. Subjects breathed aerosols at a constant flow rate (0.4 l/s) and tidal volume (0.75 liter). At 1 G and approximately 1.6 G, deposition increased with increasing particle size. In microG, differences in deposition as a function of particle size were almost abolished. Deposition was a nearly linear function of the G level for 2- and 3-micron-diameter particles, whereas for 0.5- and 1.0-micron-diameter particles, deposition increased less between microG and 1 G than between 1 G and approximately 1.6 G. Comparison with numerical predictions showed good agreement for 1-, 2-, and 3-micron-diameter particles at 1 and approximately 1.6 G, whereas the model consistently underestimated deposition in microG. The higher deposition observed in microG compared with model predictions might be explained by a larger deposition by diffusion because of a higher alveolar concentration of aerosol in microG and to the nonreversibility of the flow, causing additional mixing of the aerosols.

Aerosol dispersion in human lung: comparison between numerical simulations and experiments for bolus tests

Bolus inhalations of 0.87-micron-diameter particles were administered to 10 healthy subjects, and data were compared with numerical simulations based on a one-dimensional model of aerosol transport and deposition in the human lung (J. Appl. Physiol. 77: 2889-2898, 1994). Aerosol boluses were inhaled at a constant flow rate into various volumetric lung depths up to 1,500 ml. Parameters such as bolus half-width, mode shift, skewness, and deposition were used to characterize the bolus and to display convective mixing. The simulations described the experimental results reasonably well. The sensitivity of the simulations to different parameters was tested. Simulated half-width appeared to be insensitive to altered values of the deposition term, whereas it was greatly affected by modified values of the apparent diffusion in the alveolar zone of the lung. Finally, further simulations were compared in experiments with a fixed penetration volume and various flow rates. Comparison showed good agreement, which may be explained by the fact that half-width, mode shift, and skewness were little affected by the flow rate.

High-resolution maps of regional ventilation utilizing inhaled fluorescent microspheres

The regional deposition of an inhaled aerosol of 1.0-micron diameter fluorescent microspheres (FMS) was used to produce high-resolution maps of regional ventilation. Five anesthetized, prone, mechanically ventilated pigs received two 10-min inhalations of pairs of different FMS labels, accompanied by intravenous injection of 15.0-micron radioactive microspheres. The lungs were air dried and cut into 1.9-cm3 pieces, with notation of the spatial coordinates for each piece. After measurement of radioactive energy peaks, the tissue samples were soaked in 2-ethoxyethyl acetate, and fluorescent emission peaks were recorded for the wavelengths specific to each fluorescence label. The correlation of fluorescence activity between simultaneously administered inhaled FMS ranged from 0.98 to 0.99. The mean coefficient of variation for ventilation for all 10 trials (47.9 +/- 8.1%) was similar to that for perfusion (46.2 +/- 6.3%). No physiologically significant gravitational gradient of ventilation or perfusion was present in the prone animals. The strongest predictor of the magnitude of regional ventilation among all animals was regional perfusion (r = 0.77 +/- 0.13).

Aerosol transport and deposition in the rhythmically expanding pulmonary acinus

Little is known about factors controlling the dynamics of aerosol dispersion and deposition in the lung periphery, though this knowledge becomes increasingly important in many fields such as environmental and occupational exposure, diagnostic applications, and therapeutic deliver of drugs via aerosols. For the last several years, we have been studying aerosol behavior in the pulmonary acinus, where the airway structure and the associated fluid mechanics are distinctly different from those in the conducting airways. Our major research efforts have been focused on the basic physics underlying acinar fluid mechanics and particle dynamics, which are likely to be conditioned by the two key geometric factors of acinar airways: structural alveolation and rhythmic expansion and contraction of the alveolar walls. A combination of computational and experimental analyses revealed that due to these unique geometric features acinar flow can be extremely complex despite the low Reynolds number, and can have substantial effects on particle dynamics. In particular, chaotic mixing can occur in the lung periphery. In the course of such a mixing process, the inhaled aerosol particles quickly mix with the residual alveolar gas in a manner that is radically different from the previously considered classical diffusion process. The objective of this paper is to briefly review our current understanding of these processes, to discuss existing deposition models, and to describe our ongoing research efforts toward a basic understanding of aerosol behavior in the pulmonary acinus.