An analysis of pollutant gas transport and absorption in pulmonary airways

A mathematical model of ozone absorption, or for any soluble gas that has similar transport properties, is developed for a branching network of liquid-lined cylinders. In particular, we investigate specific flow regimes for finite length tubes where boundary layer phenomena and entrance effects exist in high Reynolds and Peclet (Pe) number airways. The smaller airways which have lower Reynolds and Peclet number flows are modelled by incorporating the detailed analysis found in [10] and modifying it for airways which have alveolated surfaces. We also consider a reacting gas and treat specific regimes where the reaction front is located at the air-liquid interface, within the liquid or at the liquid-tissue interface. Asymptotic methods are used in regions of the tracheobronchial tree where Pe much less than 1 and Pe much greater than 1. In addition, the fact that the radial transport parameter gamma much less than 1 for this toxin, and others such as nitrous oxides, is employed to simplify the analysis. The ozone concentrations, airway absorption and tissue dose are examined as a function of airway generation for several values of the governing parameters. The general result is a maximal dosing in airway generations 17 to 18 that is much larger (up to an order of magnitude) than the predictions of previous theories.     

Convective and diffusive gas transport in canine intrapulmonary airways.

The significance of convective and diffusive gas transport in the respiratory system was assessed from the response of combined inert gas and particle boluses inhaled into the conducting airways. Particles, considered as "nondiffusing gas," served as tracers for convection and two inert gases with widely different diffusive characteristics (He and SF6) as tracers for convection and diffusion. Six-milliliter boluses labeled with monodisperse di-2-ethylhexyl sebacate droplets of 0.86-microns aerodynamic diameter, 2% He, and 2% SF6 were inspired by three anesthetized mechanically ventilated beagle dogs to volumetric lung depths up to 170 ml. Mixing between inspired and residual air caused dispersion of the inspired bolus, which was quantified in terms of the bolus half-width. Dispersion of particles increased with increasing lung depth to which the boluses were inhaled. The increase followed a power law with exponents less than 0.5 (mean 0.39), indicating that the effect of convective mixing per unit volume was reduced with depth. Within the pulmonary dead space, the behavior of the inert gases He and SF6 was similar to that of the particles, suggesting that gas transport was almost solely due to convection. Beyond the dead space, dispersion of He and SF6 increased more rapidly than dispersion of particles, indicating that diffusion became significant. The gas and particle bolus technique offers a suitable approach to differential analysis of gas transport in intrapulmonary airways of lungs.     

A new drift-flux model for particle transport and deposition in human airways

Particle deposition and transport in human airways isfrequently modeled numerically by the Lagrangian approach. Current formulations of such models always require some ad hoc assumptions, and they are computationally expensive. A new drift-flux model is developed and incorporated into a commercial finite volume code. Because it is Eulerian in nature, the model is able to simulate particle deposition patterns, distribution and transport both spatially and temporally. Brownian diffusion, gravitational settling, and electrostatic force are three major particle deposition mechanisms in human airways. The model is validated against analytical results for three deposition mechanisms in a straight tube prior to applying the method to a single bifurcation G3-G4. Two laminar flows with Reynolds numbers 500 and 2000 are simulated. Particle concentration contour deposition pattern, and enhancement factor are evaluated. To demonstrate how the diffusion and settling influence the deposition and transport along the bifurcation, particle sizes from 1 nm to 10 microm are studied. Different deposition mechanisms can be combined into the mass conversation equation. Combined deposition efficiency for the three mechanisms simultaneously was evaluated and compared with two commonly used empirical expressions.     

Further considerations in a theoretical description of gas transport in lung airways

A discrete one-dimensional model of convection-diffusion in branching alveolar ducts is described and it is shown that, for a suitable choice of effective axial dispersion, the solution closely approximates that for an axially symmetric representation, at least for Peclet numbers Pe<1. Following earlier work a composite model of a uniform lung is formed by matching such a respiratory pathway (now having the more convenient one-dimensional form) onto a trumpet representation of the conducting airways. Enhanced mixing due to heart action, and isotropic volume changes of trumpet (in addition to the pathway) during breathing are additional factors included. Calculations are made of O₂ concentrations during steady-state breathing and of the concentration of inert gas during single breath wash-out of a gas mixture containing it. Predicted alveolar levels in each case agree extremely well with published data, although no alveolar slope is obtained for the inert gas.     

A rat lung model of instilled liquid transport in the pulmonary airways.

When a liquid is instilled in the pulmonary airways during medical therapy, the method of instillation affects the liquid distribution throughout the lung. To investigate the fluid transport dynamics, exogenous surfactant (Survanta) mixed with a radiopaque tracer is instilled into tracheae of vertical, excised rat lungs (ventilation 40 breaths/min, 4 ml tidal volume). Two methods are compared: For case A, the liquid drains by gravity into the upper airways followed by inspiration; for case B, the liquid initially forms a plug in the trachea, followed by inspiration. Experiments are continuously recorded using a microfocal X-ray source and an image-intensifier, charge-coupled device image train. Video images recorded at 30 images/s are digitized and analyzed. Transport dynamics during the first few breaths are quantified statistically and follow trends for liquid plug propagation theory. A plug of liquid driven by forced air can reach alveolar regions within the first few breaths. Homogeneity of distribution measured at end inspiration for several breaths demonstrates that case B is twice as homogeneous as case A. The formation of a liquid plug in the trachea, before inspiration, is important in creating a more uniform liquid distribution throughout the lungs.     

Volume of the conducting airways calculated from morphometric parameters

A method of calculating the volume of a tree distal to a cut at the origin of a branch, using branching, diameter and length ratios, has been developed. The method was applied to bronchial tree casts from human, dog, sheep, hamster, and rat lungs. It was found that the exponenta in the equation weight=k×diameter ^a is approximately equal to 3.0 in sheep lung casts, as found by Hooper (1977), but it is greater than 3.0 in casts from the other four species.     

Secondary velocity fields in the conducting airways of the human lung

An understanding of flow and dispersion in the human respiratory airways is necessary to assess the toxicological impact of inhaled particulate matter as well as to optimize the design of inhalable pharmaceutical aerosols and their delivery systems. Secondary flows affect dispersion in the lung by mixing solute in the lumen cross section. The goal of this study is to measure and interpret these secondary velocity fields using in vitro lung models. Particle image velocimetry experiments were conducted in a three-generational, anatomically accurate model of the conducting region of the lung. Inspiration and expiration flows were examined under steady and oscillatory flow conditions. Results illustrate secondary flow fields as a function of flow direction, Reynolds number, axial location with respect to the bifurcation junction, generation, branch, phase in the oscillatory cycle, and Womersley number. Critical Dean number for the formation of secondary vortices in the airways, as well as the strength and development length of secondary flow, is characterized. The normalized secondary velocity magnitude was similar on inspiration and expiration and did not vary appreciably with generation or branch. Oscillatory flow fields were not significantly different from corresponding steady flow fields up to a Womersley number of 1 and no instabilities related to shear were detected on flow reversal. These observations were qualitatively interpreted with respect to the simple streaming, augmented dispersion, and steady streaming convective dispersion mechanisms.     

Mucus transport in the airways by two-phase gas-liquid flow mechanism: continuous flow model

Mucus transport speed induced by two-phase gas-liquid interaction was measured in the continuous two-phase annular flow tube models, and factors influencing the transport speed were assessed in conjunction with rheological properties of mucus. The flow model was made with 1.0-cm-ID glass tubes and positioned either vertically or horizontally. During a continuous passage of airflow through the model tube, mucus stimulants were supplied into the tube at a rate of 0.5-2.0 ml/min. The advancing speed of the leading edge of the mucous layer and mean mucous layer thickness were then measured. The transport speed in the vertical tube model ranged from 1.1 to 3.1 cm/min with a mucus feed rate of 0.5 ml/min at airflow rates of 0.33-1.17 l/s and increased with increasing airflow rates but decreased rapidly with increasing viscosity of mucus. The transport speed increased almost proportionally with increasing mucus feed rate. Elasticity of mucus did not affect the transport speed itself. However, more elastic mucus caused lower flow resistance and thereby could be transported with a much reduced work load. The transport speed in the horizontal tube model was 5-60% faster than that in the vertical tube model. The mean mucous layer thickness in the vertical tube model was found to be in the range of 0.5-1.5 mm in the experimental conditions used, and decreased rapidly with increasing airflow rate and decreasing viscosity of mucus. From these data the transport speed could be functionally related to airway diameter, mucous layer thickness, and mucus production rate.     

Bronchial distribution of gas mixing in a model of the upper and central airways

Longitudinal mixing of He, O2, and sulfur hexafluoride boluses with air flowing through a three-generation tracheobronchial airway model was evaluated as the increase in volume variance of gas concentration distributions monitored at upstream and downstream sampling ports. Mixing was partitioned between tracheal and branched regions of the model at steady inspiratory and expiratory airflows from 0.044 to 0.884 l/s, both in the absence and in the presence of a removable larynx cast. During inspiration in the absence of the larynx, mixing increased as airflow increased, reaching a peak value at 0.2 l/s, and decreasing as airflow increased further. This mixing peak was higher in the branched region than in the tracheal region and was inversely related to the diffusion coefficient of the indicator gas-air mixture. During inspiration in the presence of the larynx, a mixing peak was observed in the tracheal region, but mixing peaks in the branched region were eliminated by turbulence propagated downstream from the larynx. During expiration, laryngeal turbulence was propagated far enough downstream (i.e., proximal to the trachea) that mixing peaks could be observed in both tracheal and branched regions whether or not the larynx cast was present.     

Convective dispersion during steady flow in the conducting airways of the human lung

The adverse health effects of inhaled particulate matter from the environment depend on its dispersion, transport, and deposition in the human airways. Similarly, precise targeting of deposition sites by pulmonary drug delivery systems also relies on characterizing the dispersion and transport of therapeutic aerosols in the respiratory tract. A variety of mechanisms may contribute to convective dispersion in the lung; simple axial streaming, augmented dispersion, and steady streaming are investigated in this effort. Flow visualization of a bolus during inhalation and exhalation, and dispersion measurements were conducted during steady flow in a three-generational, anatomically accurate in vitro model of the conducting airways to support this goal. Control variables included Reynolds number, flow direction, generation, and branch. Experiments illustrate transport patterns in the lumen cross section and map their relation to dispersion metrics. These results indicate that simple axial streaming, rather than augmented dispersion, is the dominant steady convective dispersion mechanism in symmetric Weibel generations 7-13 during normal respiration. Experimental evidence supports the branching nature of the airways as a possible contributor to steady streaming in the lung.     

Criteria for mucus transport in the airways by two-phase gas-liquid flow mechanism

The critical conditions for mucous layer transport in the respiratory airways by two-phase gas-liquid flow mechanism were investigated by using 0.5- and 1.0-cm-ID tube models. Several test liquids with rheological properties comparable to human sputum were supplied continuously into the vertically positioned tube models in such a way that the liquid could form a uniform layer while traveling upward through the tube with a continuous upward airflow. The critical airflow rate and critical liquid layer thickness required for the upward transport of the liquids were determined. The critical airflow rate was in the Reynolds number (Re) range of 142-1,132 in the 0.5-cm-ID tube model and 708-2,830 in the 1.0-cm-ID tube model depending on the types of liquids tested. In both models, the critical airflow rate was lower with viscoelastic liquids than with viscous oils. The critical liquid layer thickness ranged from 0.2 to 0.5 mm in the 0.5-cm-ID tube model and 0.8 to 1.4 mm in the 1.0-cm-ID tube model at Re of 2,800. These values decreased rapidly with increasing airflow rate. The critical thickness relative to the tube diameter ranged from 3 to 15% of the respective tube diameter and was lower by approximately 30-50% in the 0.5-cm-ID tube model than in the 1.0-cm-ID tube model over the entire Re range tested. The results indicate that the critical conditions for the mucus transport by two-phase gas-liquid flow mechanism are within the range that can be achieved in patients with bronchial hypersecretions during normal breathing.     

An inverting basket model for AE1 transport

We describe an "inverting basket" model for transport in the erythrocyte anion exchanger, AE1. The inverting basket is formed by the side chains of three putative key residues, two positively (Lys 826 and Arg 730) and one negatively (Glu 681) charged residue. We have tentatively chosen seven transmembrane helices, TM1, TM2, TM4, TM8, TM10, TM12 and TM13 to form a conical channel using the well-established Glu 681 of TM8 and candidates Lys 826 and Arg 730 of TM12-13 and TM10, respectively, to form the inverting basket. We assume that these residues bind to an anion and shift from outward facing (C(o)) to inward facing (C(i)) conformation without significant backbone movements to transport an anion across the membrane. The transition of the complex (residues and ion) from outward facing (C(o)) to inward facing (C(i)) constitutes one "basket" inversion. The barrier to inversion is composed of two major components: that of the anhydrous complex, which we refer to as a steric energy barrier and a dehydration effect due to the removal of charges in the complex from water in the channel. The steric barrier is dependent on the side chain charge and configuration and on the ion charge and size. The dehydration effect, for our model, ameliorates the steric barrier, in the case of the empty complex but less so for the monovalent and divalent ions. We conclude, that it is possible for a seven-helix bundle to have a steric barrier to basket inversion, but that hydration effects in thin hydrophobic barrier models may be more complex than usually envisioned.     

An allosteric pore model for sugar transport in human erythrocytes

Glucose transport in human erythrocytes is characterized by a marked asymmetry in the $\text{V}$ and $\text{K}{}_{\mathrm{<mtext>m</mtext>}}$ values for entry and for exit. In addition, they show a high $\text{K}{}_{\mathrm{<mtext>m</mtext>}}$ and a high $\text{V}$ for equilibrium exchange but low $\text{K}{}_{\mathrm{<mtext>m</mtext>}}$ values for infinite cis and for infinite trans exit and entry. An allosteric pore model has been proposed to account for these characteristics. In this model, substrate-induced conformational changes destabilize the interfaces between protein subunits (the pore gates).Pores doubly occupied from inside destabilize the transport gates and result in high $\text{K}{}_{\mathrm{<mtext>m</mtext>}}$ and high $\text{V}$ transport parameters. This effect is less marked when pores are doubly occupied from outside and therefore transport asymmetry results.     

Aerosol transport and deposition in sequentially bifurcating airways

Deposition patterns and efficiencies of a dilute suspension of inhaled particles in three-dimensional double bifurcating airway models for both in-plane and 90 deg out-of-plane configurations have been numerically simulated assuming steady, laminar, constant-property air flow with symmetry about the first bifurcation. Particle diameters of 3, 5, and 7 microns were used in the simulation, while the inlet Stokes and Reynolds numbers varied from 0.037 to 0.23 and 500 to 2000, respectively. Comparisons between these results and experimental data based on the same geometric configuration showed good agreement. The overall trend of the particle deposition efficiency, i.e., an exponential increase with Stokes number, was somewhat similar for all bifurcations. However, the deposition efficiency of the first bifurcation was always larger than that of the second bifurcation, while in general the particle efficiency of the out-of-plane configuration was larger than that of the in-plane configuration. The local deposition patterns consistently showed that the majority of the deposition occurred in the carinal region. The distribution pattern in the first bifurcation for both configurations were symmetric about the carina, which was a direct result of the uniaxial flow at the inlet. The deposition patterns about the second carina showed increased asymmetry due to highly nonuniform flow generated by the first bifurcation and were extremely sensitive to bifurcation orientation. Based on the deposition variations between bifurcation levels and orientations, the use of single bifurcation models was determined to be inadequate to resolve the complex fluid-particle interactions that occur in multigenerational airways.     

Secretion and ion transport in airways during inflammation

Water and secretions interact in airways to produce the sol and gel layers that allow for entrapment of foreign materials and subsequent clearance by ciliary movement and by cough. Active Cl ion transport produces fluid, and this process is activated by products of mast cells (leukotrienes), eosinophils (major basic protein), and by other inflammatory mediators (prostaglandins, bradykinin). Gland secretions produce the bulk of the volume of secretions. Airway irritation stimulates gland secretion reflexly via vagal muscarinic pathways. Recently, the sensory nerves have been discovered to release substance P and other neuropeptides when the airways are irritated. The stimulatory effects of neuropeptides on gland secretion (and on other inflammatory sites) are modulated by enkephalinase a membrane-bound enzyme that cleaves neuropeptides and thereby inactivates them. Up- or down-regulation of enkephalinase is predicted to change the degree of inflammatory response to neuropeptides. Finally, the cell surface of airway epithelial cells have been discovered to secrete large molecular weight glycoconjugates; these secreted products are increased markedly by a series of proteinases produced by inflammatory cells (neutrophils, mast cells) and by bacteria. Their exact physiologic roles are still unknown but they may contribute to the bulk and viscoelastic properties of airway secretions, and they may serve an important role in bacterial, viral and inflammatory cell adhesion.