Mathematical models of particle deposition in the human respiratory tract

Several mathematical formalisms have been proposed to calculate particle transport onto airway surfaces: the temporally and spatially discrete Findeisen formalism; the temporally discrete and spatially continuous Altshuler formalism; and the temporally and spatially continuous Taulbee-Yu formalism; they are termed primary deposition models. Models adopting these formalisms are termed secondary deposition models. This review concentrates on the discussion of the general concepts of primary models and their numerical verification and on characteristics of secondary models. Current deposition models predict particle deposition in close agreement with current experimental data.     

Asymmetric human lung morphology induce particle deposition variation

The effect of lung morphology on the heterogeneity of regional ventilation and particle deposition in the bronchial airways is studied using Horsfield's regular-asymmetric lung model. Flow distribution among the airways is calculated by solving the whole tree network, assuming laminar flow hydrodynamic resistances without accounting for gravitationally enhanced preferential airflow distribution. The variation of morphological properties, such as the lung volume and surface area distal to any airway generation, and physiological properties, such as ventilation and particle deposition, is calculated, and fractal dimensions that characterize these properties and processes are computed. The close agreement between the model fractal dimension characterizing ventilation and those found from clinical data assess the validity of the model. It is shown that the fractal dimensions that characterize the morphological properties and the physiological processes are similar, suggesting that all are related and stem from a common underlying attribute—the lung morphology. The variation of particle deposition in the lung, as well as the variation of ventilation and morphological attributes, increases moderately with the lung tree asymmetry. The deposition density, regarded as a key exposure metric or therapeutic index, does not follow a spatial scale-free distribution.     

Physical factors determining particle deposition in the human respiratory tract

Total deposition in the human respiratory tract of uncharged, spherical aerosol particles depends on particle diameter, particle density, period of a breathing cycle and respiratory volumetric flow rate. Total deposition of particles larger than 0.5 μm in diameter increases at mouth-breathing with increasing values of these physical factors with the exception that total deposition of particles in the size range between 0.5 and 1 μm is independent of flow rate. These physical factors can be linked by a deposition parameter so that their complex effects on deposition can be described by an unique relationship.     

Practical control studies of batch reactors using realistic mathematical models

Most of the optimal control studies of batch chemical reactors have assumed simple, ideal systems where heat removal can be changed instantaneously between zero and some maximum rate. These systems are of low order, usually second, so elegant variational mathematics can be employed to compute optimal time-temperature trajectories.This paper reports results of studies of more realistic systems in which the dynamics of the cooling and heating systems are not neglected, giving systems of much higher order (7th–10th). Reversible and consecutive exothermic reactions are considered. A variety of practical heat removal systems are studied. Reactor performance is found to be reasonably insensitive to some of the practical departures from ideality, but quite sensitive to others.     

The influence of lung volume during imaging on CFD within realistic airway models

In this article, we address a fundamental question regarding computational fluid dynamics (CFD) modeling within lung airways: does the inhaled volume during imaging have a significant effect on CFD computations of aerosol deposition? High resolution computed tomography (HRCT) images taken at mean lung volume (MLV) and at total lung capacity (TLC) obtained as part of a previous study of ventilation and aerosol deposition using positron emission tomography (PET) in challenged asthmatics were utilized to construct two airway models for each subject, and the differences in CFD calculated deposition metrics were subsequently quantified. These models included all the airway generations that could be rendered from the HRCT images. CFD calculations for three inhalation flow rates and four monodisperse aerosol sizes used images at MLV and at TLC from 24 volunteer subjects. Both large scale and detailed measures of particle deposition distribution were used in the analysis. The influence of lung volume during imaging is to increase airway dimensions in realistic models and thus reduce flow velocity and deposition due to impaction in the upper airways as calculated by CFD. However, large-scale deposition measures are confounded when the TLC models include deeper generations in the lung that increase the total airway deposition. These trends are modulated by the flow and particle characteristics of the aerosol, making consistent quantifiable differences between MLV and TLC difficult to predict unless both models consider the same anatomical airways.

© 2017 American Association for Aerosol Research     

Comparison of analytical and CFD models with regard to micron particle deposition in a human 16-generation tracheobronchial airway model

A representative human tracheobronchial tree has been geometrically represented with adjustable triple-bifurcation units (TBUs) in order to effectively simulate local and global micron particle depositions. It is the first comprehensive attempt to compute micron-particle transport in a (Weibel Type A) 16-generation model with realistic inlet conditions. The CFD modeling predictions are compared to experimental observations as well as analytical modeling results. Based on the findings with the validated computer simulation model, the following conclusions can be drawn:(i) Surprisingly, simulated inspiratory deposition fractions for the entire tracheobronchial region (say, G0–G15) with repeated TBUs in parallel and in series agree rather well with those calculated using analytical/semi-empirical expressions. However, the predicted particle-deposition fractions based on such analytical formulas differ greatly from the present simulation results for most local bifurcations, due to the effects of local geometry and resulting local flow features and particle distributions. Clearly, the effects of realistic geometries, flow structures and particle distributions in different individual bifurcations accidentally cancel each other so that the simulated deposition efficiencies during inspiration in a relatively large airway region may agree quite well with those obtained from analytical expressions. Furthermore, with the lack of local resolution, analytical models do not provide any physical insight to the air–particle dynamics in the tracheobronchial region.(ii) The maximum deposition enhancement factors (DEF) may be in the order of 10² to 10³ for micron particles in the tracheobronchial airways, implying potential health effects when the inhaled particles are toxic.(iii) The presence of sedimentation for micron particles in lower bronchial airways may change the local impaction-based deposition patterns seen for larger airways and hence reduces the maximum DEF values.(iv) Rotation of an airway bifurcation cause a significant impact on distal bifurcations rather than on the proximal ones. Such geometric effects are minor when compared to the effects of airflow and particle transport/deposition history, i.e., upstream effects.     

Particle deposition in the pulmonary region of the human lung: Multiple breath aerosol transport and deposition

Comprehensive knowledge of aerosol deposition in the lung during multiple breathing cycles is essential to understanding the long term adverse effects of environmental particulate pollution as well as various therapeutic strategies for aerosolized drug delivery. In this work, a simple semi-empirical model for whole lung aerosol bolus dispersion and deposition developed in an accompanying study [Park, S.S. and Wexler, A.S., 2007. Particle deposition in the pulmonary region of the human lung: A semi-empirical model of single breath transport and deposition. Journal of Aerosol Science 38(2), 228–245] was used to estimate regional particulate dosimetry during multiple breaths. To further validate the transport and deposition model of Park and Wexler [2007. Particle deposition in the pulmonary region of the human lung: A semi-empirical model of single breath transport and deposition. Journal of Aerosol Science 38(2), 228–245], the washin and washout experiments of Davies and coworkers were simulated; predictions compared well to observations. Typical models of pulmonary particle deposition simulated transport to these distal airways by a flow-through approximation where particle-laden air is assumed to flow into the airways and out the alveoli, but resting tidal volumes do not transport particles to the distal pulmonary airways in a single breath. By simulating tidal transport and deposition over a series of breath, we find that the concentration of retained particles as a function of lung depth increases with each tidal cycle and these particles penetrate deeper with succeeding breaths. The retained particle concentration increases more slowly with each breath, so that after the 8th breath, the concentration distribution within the lung attains a steady state. Comparison with observed data and previous model predictions is made in terms of total and generational deposition fractions at steady state. After accounting for the retained fractions, the total predicted deposition fraction was similar to the experimental data while other previous model predictions underestimated it. Predicted deposition fraction per generation showed similar patterns to other model simulations yet higher deposition fractions in the more proximal pulmonary regions. This is a result of the enhanced alveolar deposition in the first half of the acinar generations due to alveoli expansion and contraction.     

Effect of the laryngeal jet on particle deposition in the human trachea and upper bronchial airways

Preferential sites of particle deposition within the human respiratory system are known to correlate with primary cancer sites, and are therefore important in the etiology of neoplastic respiratory diseases. In this study, we characterized the intrabronchial and intratracheal patterns of deposition in a hollow cast of a human larynx-tracheobronchial tree, and examined the effects of airflow and turbulence on particle deposition by performing airflow measurements in the hollow cast and an “ideal” airway bifurcation model.

Experimental results revealed a deposition “hot spot” for particles greater than 2 μm in mass median aerodynamic diameter in the trachea at 2 cm below the larynx. The enhancement of deposition in the trachea was studied by making comparative airflow and detailed morphometry measurements in a hollow lung cast and in an “ideal” model. The larynx had a significant effect on the local flow field in the trachea of the hollow cast and this effect extended to and beyond the tracheal bifurcation. This accounted for some of the difference in flow field at the bifurcation between the cast and an “ideal” model. Additional differences were related to the different shapes of the transitional regions near the bifurcation.     

Investigation of particle deposition on a micropatterned surface as an energy-efficient air cleaning technique in ventilation ducting systems

Abstract

Building ventilation ducting systems play a core role in controlling indoor air quality by recirculating the indoor air and mixing with ambient air. The ventilation system can serve as an air cleaning system itself either through the filtration system or integrating other means, while at the same time, attention to energy consumption is needed. The high-efficiency fibrous filters in a conventional filtration system not only cause high-pressure drops that consume fan energy but also add to the high operation cost. This article proposes an air cleaning technique, aimed at submicron particles, by means of installing patterned surfaces on the walls of ventilation ducts, which can be easily cleaned by water and reused. The effect of patterned surfaces on particle deposition was studied numerically. In the numerical simulation, the Reynolds stress turbulent model was correlated at the near-wall regions by turbulent velocity fluctuation at the normal direction. Particle trajectory was solved by using Lagrangian particle tracking. The numerical model was then validated with a particle deposition experiment. A wind tunnel experiment was carried out to quantify the particle deposition on the semicircular micropatterns for a wide range of heights. Based on our numerical results, the semicircular pattern height of 500?µm with a pitch-to-height ratio (p/e) of 10 has 8.58 times enhancement of the energy efficiency compared with a high-efficiency particulate air filter. Our results indicated that adding surface micropatterns to ventilation ducting for submicron particle deposition is a possible energy-efficient air cleaning technique for practical usage.

Copyright © 2020 American Association for Aerosol Research     

Critical particle concentration in electrophoretic deposition

The role of particle concentration in electrophoretic deposition (EPD) was investigated with two different suspension systems. The first system consisted of positively charged TiO₂ nanoparticles dispersed in isopropanol with 1 vol% water. The second system consisted of negatively charged polystyrene (PS) microbeads dispersed in isopropanol. Constant voltage EPD was performed using suspensions with variable particle concentration (0.013–0.43 vol% TiO₂ and 0.06–11.4 vol% PS). Threshold concentration values were identified for both systems after EPD at 100 V (250 V cm^?1) for 1 min. Below these values the deposited mass deviated from the trend dictated by Hamaker's equation. Higher applied voltages and longer deposition times were tested and the results suggested that the threshold concentration did not depend on those parameters. A phenomenological model of particle deposition was proposed, which accounts for the local electrochemical conditions close to the substrate in relation to particle size.     

Theoretical analysis of particle deposition in human lungs considering stochastic variations of airway morphology

Particle deposition in human lungs was investigated theoretically considering a stochastic variation of airway morphology using a Monte Carlo method. In computing the total and regional deposition each airway generation was divided into infinitesimal volume segments and each volume segment was allowed to pass through randomly selected airway branches of which morphology (e.g., airway dimensions and branching angle) was varied randomly. Deposition values obtained by the Monte Carlo method were compared with those obtained by the traditional deterministic method. It was found that the Monte Carlo method predicted deposition values generally comparable to those predicted by deterministic method for sub-micron size particles. However, for micron size particles the Monte Carlo method provided greater deposition values in the proximal airway regions where deposition occurs mainly by inertial impaction. The difference could be attributed to the non-linear relationship between deposition efficiency and airway dimensions in the inertial deposition regime. The results suggest that a Monte Carlo method may be a useful tool for evaluating deposition of inhaled particles in the lungs with a wide variation of airway dimensions.     

Prediction of spouted bed reactor performance using kinetic models

The form of the equation governing the kinetic model of a reactor depends on the mixing regime of the reacting phases and the conversion kinetics. The formation of detached flow in a spouted-bed reactor results in backmixing of the solid material. Therefore, the processes in a spouted-bed reactor can be described by a diffusion (quasihomogeneous) model equation. The paper compares the values of the production capacity of a spouted-bed reactor calculated using the diffusion model with experimental values of the efficiency of green ultramarine oxidation (kinetic region), of oxidative calcination of some metal sulphides (mixed region), and of the ion exchange extraction of copper from solutions (diffusion region). The kinetics of the corresponding conversions are also described.     

Prediction of ternary liquid-liquid equilibria using the NRTL and the UNIQUAC models

The Experimental binodal curve, tie line data, plait point data and the tie lines and plit point, calculated by liquid models for foil wing six ternary liquid liquid equilibria systems: monochlorobenzene-water-acetone, cyclohexane-water-acetone, cyclohexane-water-acetone. chlorform-water-acetone. methylisobutylketone-water-acetone, and n-hexane-water-acetone were reported at 10°C Experimental tie line data were correlated to test consistency with Othmer-Tobias equation [15] And those data were also correlated with the NRTL the UNIQUAC, and the modified UNIQLAC models respectively and the parameters in each model were estimated to predict the value of tie lines by least squares methods.