Deposition of inhaled particulate matter in the upper respiratory tract, larynx, and bronchial airways: a mathematical description

Particle Deposition in Children's Lungs: Theory and Experiment

A mathematical model of inhaled aerosol particle deposition for children is presented and validated with data from two published experimental studies. The model accurately predicts deposition fraction (DF) in children as a function of particle size for particles in the size range 1-3 microns for both sedentary and exercise breathing conditions. When the experimental data are grouped according to age, the model is able to predict age-dependent trends in DF at the studied particle sizes under sedentary breathing conditions. The model predicts that when ventilatory conditions are held constant, age-dependent changes in morphology result in decreasing DF with age; however, under realistic conditions these changes may be masked by age-dependent changes in ventilation. Despite the fact that mean DF differs significantly from adult values only in children younger than 9, the model predicted that dose-per-surface area may still be greater in children due to smaller lung sizes.

Development of the PEARLS model (Particulate Exposure from Ambient to Regional Lung by Subgroup) and use of Monte Carlo simulation to predict internal exposure to 2.5 in Toronto

Air pollution is a current and growing concern for Canadians, and there is evidence that ambient levels that meet current exposure standards may be associated with mortality and morbidity in Toronto, Canada. Evaluating exposure is an important step in understanding the relationship between particulate matter (PM) exposure and health outcomes. This report describes the PEARLS model (Particulate Exposure from Ambient to Regional Lung by Subgroup), which predicts exposure distributions for 11 age-gender population subgroups in Toronto to PM2.5 (PM with a median aerodynamic diameter of 2.5 microm or less) using Monte Carlo simulation techniques. The model uses physiological and activity pattern characteristics of each subgroup to determine region-specific lung exposure to PM2.5, which is defined as the mass of PM2.5 deposited per unit time to each of five lung regions (two extrathoracic, bronchial, bronchiolar, and alveolar). The modeling results predict that children, toddlers, and infants have the broadest distributions of exposure, and the greatest chance of experiencing extreme exposures in the alveolar region of the lung. Importance analysis indicates that the most influential model variables are air exchange rate into indoor environments, time spent outdoors, and time spent at high activity levels. Additionally, a "critical point" was defined and introduced to the PEARLS to investigate the effects of possible threshold-pathogenic phenomena on subgroup exposure patterns. The analysis indicates that the subgroups initially predicted to be most highly exposed were likely to have the highest proportion of their population exposed above the critical point. Substantial exposures above the critical point were predicted in all subgroups for ambient concentrations of PM2.5 commonly observed in Toronto after continuous exposure of 24 hours or more.

Inertial deposition effects: a study of aerosol mechanics in the trachea using laser Doppler velocimetry and fluorescent dye

This study characterizes the axial velocity and axial turbulence intensity patterns noted in the tracheal portion of a cadaver-based throat model at two different steady flow rates (18.1 and 41.1 LPM.) This characterization was performed using Phase Doppler Interferometry (Laser Doppler Velocimetry). Deposition, as assessed qualitatively using fluorescent dye, is related to the position of the laryngeal jet within the trachea. The position of the jet is dependent on the downstream conditions of the model. It is proposed therefore that lung/airway conditions may have important effects on aerosol deposition within the throat. There is no correspondence noted between regions of high axial turbulence intensity and deposition.

Environmental tobacco smoke deposition in the human respiratory tract: differences between experimental and theoretical approaches

Total deposition of environmental tobacco smoke (ETS) particles was measured in a group of 15 nonsmokers who inhaled ETS of count median diameter of 0.2 microm and geometric standard deviation of 1.6. A total deposition of 56.0 +/- 15.9% was observed for nasal breathing and 48.7 +/- 11.5% for oral breathing. In contrast, our stochastic deposition model predicted a total deposition of only 17.9% (male) and 15.7% (female) for nose breathing, and 13.4% (male) and 10.7% (female) for mouth breathing, if based on standard breathing conditions. Consideration of individual lung volumes and breathing parameters for each volunteer resulted in total deposition values of 16.9 +/- 2.2% for nose breathing and 12.1 +/- 2.1% for mouth breathing. The apparent discrepancy between experiment and modeling suggests that either single ETS particles increase substantially in size upon inhalation (up to an order of magnitude) and/or additional physical mechanisms must be invoked that are acting specifically upon ETS particles: (1) hygroscopic growth of ETS particles does not exceed 20-30%; (2) number concentrations in the ETS experiments (3.8 x 10(4), to 1.3 x 10(5) cm(-3)) are too low to increase particle size by coagulation; (3) cast experiments indicate that electrical charge (image forces) may play an important role, but theory predicts only an increase of 20-60%; and (4) cloud settling is unlikely to be a significant factor at such low number concentrations. In conclusion, estimates of the magnitudes of these potential effects demonstrate that none of these mechanisms alone can be responsible for the significantly higher total ETS deposition observed in the experiments. This suggests that a combination of all these mechanisms may be necessary to reconcile experimental and theoretical ETS deposition data, the most likely candidates being image forces and hygroscopic growth.

Characterization of the laryngeal jet using phase Doppler interferometry

The purpose of this study was to characterize the effects of the laryngeal jet on inhalation air flows in the trachea, and to extend these ideas to further an understanding of aerosol deposition in this region. Phase Doppler Interferometry was used to characterize axial velocity and turbulence intensity contours in the tracheal section of a cadaver-based larynx-trachea model. An array of 30 measurements was made at each of 6 downstream planes within the tracheal portion of the model (immediately downstream of the larynx, and at 0.5, 1, 2, 3, and 4 diameters further downstream). The flow was characterized for steady state flow at three Reynolds numbers (1250, 1700, and 2800). The Re = 1250 case approximates the inhalation of a 6-year-old child. Reverse flows with significant velocities were noted in the anterior trachea within one diameter downstream of the larynx, for all three flow cases. The cross sectional area of the reverse flow regions was larger for the lower Reynolds number cases. These reverse flows are a consequence of the nearly triangular shape of the lumen between the vocal folds in the larynx and constitute a potential deposition mechanism. High levels of axial turbulence intensity were noted near the anterior/left tracheal walls within one diameter downstream of the larynx. This indicates the potential for deposition due to turbulence in this region. Turbulence levels were still significant after four downstream diameters, indicating the potential for turbulent deposition at positions further downstream, including the bronchial tree where passage diameters are smaller. Contrary to expectations, turbulence levels were approximately 20% higher for the Re = 1250 case compared to the Re = 2800 at the furthest downstream locations (with 99% confidence). This is likely due to the complex nature of the confined jet flow.

Theoretical relationship of lung deposition to the fine particle fraction of inhalation aerosols

Pharmaceutical inhalation aerosols intended to deliver drugs to the lungs may be sampled by inertial devices, that divide particle distributions into pre-calibrated diameters. A characteristic particle diameter (D50) is prescribed, below which the aerosol mass is designated the 'respirable fraction'. The following studies compare designated respirable fractions with predicted lower lung deposition. Designated respirable fractions (% of particulate matter < 6.4 microns or alternatively < 9.8 microns) of 30, 40 and 50% were selected to represent typical inhalation aerosols. The compendial inertial samplers used to aerodynamically characterize the particle size of pharmaceutical aerosols operate at approximately 30 or 60 l/min. These values were selected as the volumetric flow rates (Qv) for a mathematical model of lung deposition. The model was employed to predict the lung deposition of particle size distributions giving rise to each designated respirable fraction. Nominal tidal volumes (Tv) of 500 and 1622 ml were adopted at appropriate breathing frequencies to accommodate the designated Qv. Predicted lung depositions (+/- range due to particle size) of 1.4 +/- 0.6%, at a respirable fraction of 30% (Qv = 60 l/min, Tv = 500 ml, D50 = 9.8 microns), and 20.9 +/- 3.6%, at a respirable fraction of 50% (Qv = 30 l/min., Tv = 1622 ml, D50 = 6.4 microns) illustrate the range of results obtained. Under well defined conditions there appeared to be a qualitative correlation between respirable fraction and predicted lower lung deposition. However, this was influenced by the aerosol particle size distribution and breathing parameters.

Mathematical model for the selective deposition of inhaled pharmaceuticals

To accurately assess the potential therapeutic effects of airborne drugs, the deposition sites of inhaled particles must be known. Herein, an original theory is presented for physiologically based pharmacokinetic modeling and related prophylaxis of airway diseases. The mathematical model describes the behavior and fate of particles in the lungs of adult human subjects under various breathing conditions. Their deposition patterns are calculated via superposition of the separate but not independent processes of inertial impaction, sedimentation, and diffusion. The related computer code is designed to calculate total and compartmental (tracheobronchial and pulmonary) distributions of inhaled aerosols. In this manuscript, the model is first tested via comparisons of predicted deposition patterns with laboratory data from human inhalation exposure experiments and then it is applied to determine which factors most influence the dosimetry of inhaled particles. In this format, deposition patterns are explicitly related to particle characteristics, ventilatory parameters, and intersubject variabilities of lung morphologies. The dosimetric model was developed to improve the efficacy of aerosol therapy via the selective deposition of inhaled pharmaceuticals at prescribed lung locations to elicit optimum effects.

Use of analytically defined estimates of aerosol respirable fraction to predict lung deposition patterns

Analytical estimates of the respirable fractions on inhaled pharmaceutical aerosols are obtained by inertial sampling techniques. The respirable fraction may be defined as that portion of the particle size distribution less than a designated diameter. The diameter size below which particles were considered respirable in these studies was 6.4 microns. In clinical practice, a variety of particle size distributions may be related to a single respirable fraction. Herein, three respirable fractions were each defined by six particle size distributions. The deposition patterns of aerosols exhibiting these particle size characteristics were examined in a mathematical model. The analytically defined respirable fractions were compared with predicted lung deposition values. Under clearly defined breathing conditions, there is a correlation between the nominal respirable fraction and deposition. However, it was concluded that the variations which occur in breathing parameters within patient populations may not allow a single analytically derived respirable fraction to be appropriate for all individual subjects.

Airway structure variability in the Long-Evans rat lung

Mathematical models used to study deposition of inhaled toxicants require morphometric data to represent the tracheobronchial airways of laboratory animals. Because of the difficulty and cost of obtaining detailed measurements, morphometric models are generally based on measurements from a small number of specimens. To determine the degree of interanimal variability among laboratory animals of the same strain and size, lengths and diameters of the same 200 airways were measured in solid casts in each of 10 male Long-Evans rats. Intraanimal variability was substantially greater than interanimal variability for airway lengths and diameters. Intraanimal variability was reduced when the airways were grouped so that airway generations were adjusted for lobar position. The study results suggest that detailed measurements of the conducting airways in a small number of casts with summarization techniques that retain lobar information will provide a less variable estimate of lung geometry than a smaller number of measurements made in several casts.