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.     

Development of a concentric water-displacement model lung

Simulation of lung ventilation using a model lung can provide a means of evaluating lung function tests, mathematical models and computer algorithms. We describe a new water-displacement lung model, which can simulate lung volumes up to 3.8 l and tidal volumes up to 1 l. Gas mixing is ensured by using a ring of venturi devices. Model compliance and airways resistance are described.     

Calculation of dose distribution near an innovative concentric balloon catheter for endovascular brachytherapy

Purpose: Using a radioactive solution-filled catheter for intravascular irradiation has the potential problem of chemical and radiological toxicity in the case of a balloon rupture. In order to reduce this risk, an innovative concentric balloon catheter was developed.Methods and Materials: The concentric balloon was made by inner and outer balloons filled with saline and radioactive solution, respectively. The optimal inner radius was determined by comparing the dose rate reduction vs. the volume reduction for various inner and outer radii for 188Re, 32P, and 90Y solutions.Results: For a balloon with an outer radius of 1.5 mm, there was no advantage of a concentric balloon. For balloons with outer radii of 3.0 and 5 mm, the optimal inner radius was 1.5 and 3 mm, respectively.Conclusions: With the newly designed concentric balloon, the risk of toxicity can be reduced while keeping the dose rate high enough so that the treatment times within tolerable limits are still maintained.     

Construction and evaluation of a coronary catheter for chronic implantation in dogs

Construction of a Silastic catheter and the procedure for chronic implantation in a coronary artery in dogs is described. In addition, studies designed to evaluate whether chronic coronary artery catheterization altered coronary vascular reactivity and myocardial function are presented. The results of these studies indicate that chronic implantation of the catheter in a coronary artery of conscious dogs does not significantly interfere with the normal reactivity of the coronary vascular bed, does not compromise regional or global left ventricular function, and does not induce collateral vessel development. This technique will be useful in studies involving the neural and metabolic regulation of the coronary circulation in animals subjected to exercise and/or exercise training.     

Capillary-elastic instabilities of liquid-lined lung airways

To model the competition between capillary and elastic forces in controlling the shape of a small lung airway and its interior liquid lining, we compute the equilibrium configurations of a liquid-lined, externally pressurized, buckled elastic tube. We impose axial uniformity and assume that the liquid wets the tube wall with zero contact angle. Non-zero surface tension has a profound effect on the tube's quasi-steady inflation-deflation characteristics. At low liquid volumes, hysteresis arises through two distinct mechanisms, depending on the buckling wavenumber. Sufficient compression always leads to abrupt and irreversible collapse and flooding of the tube; flooding is promoted by increasing liquid volumes or surface tension. The model captures mechanisms whereby capillary-elastic instabilities can lead to airway closure.     

E-NTPDases in human airways: Regulation and relevance for chronic lung diseases

Chronic obstructive lung diseases are characterized by the inability to prevent bacterial infection and a gradual loss of lung function caused by recurrent inflammatory responses. In the past decade, numerous studies have demonstrated the importance of nucleotide-mediated bacterial clearance. Their interaction with P2 receptors on airway epithelia provides a rapid ‘on-and-off’ signal stimulating mucus secretion, cilia beating activity and surface hydration. On the other hand, abnormally high ATP levels resulting from damaged epithelia and bacterial lysis may cause lung edema and exacerbate inflammatory responses. Airway ATP concentrations are regulated by ecto nucleoside triphosphate diphosphohydrolases (E-NTPDases) which are expressed on the mucosal surface and catalyze the sequential dephosphorylation of nucleoside triphosphates to nucleoside monophosphates (ATP → ADP → AMP). The common bacterial product, Pseudomonas aeruginosa lipopolysaccharide (LPS), induces an acute reduction in azide-sensitive E-NTPDase activities, followed by a sustained increase in activity as well as NTPDase 1 and NTPDase 3 expression. Accordingly, chronic lung diseases, including cystic fibrosis (CF) and primary ciliary dyskinesia, are characterized by higher rates of nucleotide elimination, azide-sensitive E-NTPDase activities and expression. This review integrates the biphasic regulation of airway E-NTPDases with the function of purine signaling in lung diseases. During acute insults, a transient reduction in E-NTPDase activities may be beneficial to stimulate ATP-mediated bacterial clearance. In chronic lung diseases, elevating E-NTPDase activities may represent an attempt to prevent P2 receptor desensitization and nucleotide-mediated lung damage.     

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.     

An axisymmetric single-path model for gas transport in the conducting airways

In conventional one-dimensional single-path models, radially averaged concentration is calculated as a function of time and longitudinal position in the lungs, and coupled convection and diffusion are accounted for with a dispersion coefficient. The axisymmetric single-path model developed in this paper is a two-dimensional model that incorporates convective-diffusion processes in a more fundamental manner by simultaneously solving the Navier-Stokes and continuity equations with the convection-diffusion equation. A single airway path was represented by a series of straight tube segments interconnected by leaky transition regions that provide for flow loss at the airway bifurcations. As a sample application, the model equations were solved by a finite element method to predict the unsteady state dispersion of an inhaled pulse of inert gas along an airway path having dimensions consistent with Weibel's symmetric airway geometry. Assuming steady, incompressible, and laminar flow, a finite element analysis was used to solve for the axisymmetric pressure, velocity and concentration fields. The dispersion calculated from these numerical solutions exhibited good qualitative agreement with the experimental values, but quantitatively was in error by 20%-30% due to the assumption of axial symmetry and the inability of the model to capture the complex recirculatory flows near bifurcations.     

High resolution 4-D spectroscopy with sparse concentric shell sampling and FFT-CLEAN

Recent efforts to reduce the measurement time for multidimensional NMR experiments have fostered the development of a variety of new procedures for sampling and data processing. We recently described concentric ring sampling for 3-D NMR experiments, which is superior to radial sampling as input for processing by a multidimensional discrete Fourier transform. Here, we report the extension of this approach to 4-D spectroscopy as Randomized Concentric Shell Sampling (RCSS), where sampling points for the indirect dimensions are positioned on concentric shells, and where random rotations in the angular space are used to avoid coherent artifacts. With simulations, we show that RCSS produces a very low level of artifacts, even with a very limited number of sampling points. The RCSS sampling patterns can be adapted to fine rectangular grids to permit use of the Fast Fourier Transform in data processing, without an apparent increase in the artifact level. These artifacts can be further reduced to the noise level using the iterative CLEAN algorithm developed in radioastronomy. We demonstrate these methods on the high resolution 4-D HCCH-TOCSY spectrum of protein G's B1 domain, using only 1.2% of the sampling that would be needed conventionally for this resolution. The use of a multidimensional FFT instead of the slow DFT for initial data processing and for subsequent CLEAN significantly reduces the calculation time, yielding an artifact level that is on par with the level of the true spectral noise.     

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.     

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.     

A two-component theory of aerosol deposition in lung airways

The deposition of aerosol particles in the human lung airways is due to two distinct mechanisms. One is by direct deposition resulting from diffusion, sedimentation and impaction as the aerosol moves in and out of the lung. The other is an indirect mechanism by which particles are transported mechanically from the tidal air to the residential air and eventually captured by the airways due to intrinsic particle motion. This last mechanism is not well understood at present. Using a trumpet airway model constructed from Weibel's data, a two-component theory is developed. In this theory, the particle concentrations in the airways and the alveoli at a given airway depth are considered to be quantitatively different. This difference in concentrations will cause a net mixing between the tidal and residential aerosol as the aerosol is breathed in and out. A distribution parameter is then introduced to account for the distribution of ventilation. The effect of intrinsic particle motion on the aerosol mixing is also included. From this theory, total and regional deposition in the lung at the steady mouth breathing without pause is calculated for several different respiratory cycles. The results agree reasonably well with the experimental data.