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In the study presented here deposition of spheres and nonspherical particles with various aspect ratios (0.01–100) in the human respiratory tract was theoretically modeled. Shape of the nonspherical particles was considered by the application of the latest aerodynamic diameter concepts. Particle deposition was predicted by using a stochastic model of the lung geometry and simulating particle transport trajectories according to the random-walk algorithm. Concerning fibers total deposition is significantly enhanced with respect to that of spheres for

The shape of aerosol particles may be regarded as a determinant which affects well-known phenomena such as dry deposition, cloud scavenging, and deposition in the human respiratory tract. The majority of aerosol particles occurring in the atmosphere deviates significantly from ideal spherical shape. This category of nonspherical particles among other includes fibers, disk- or platelet-shaped particulate structures, and various kinds of agglomerates. Fibers are defined as elongated particles with an aspect ratio, that is, a ratio of the length to the diameter, greater than three [

Diagram with particle length plotted against cylindrical particle diameter. While for fibers with cylindric or rod-like shapes aspect ratio

Theoretical approaches to the deposition of nonspherical particles in the human respiratory tract are mainly based on the concept of the aerodynamic diameter which represents the diameter of a unit-density sphere with identical settling velocity as the particle of interest. For ^{−1}) alveolar deposition of fibers with aspect ratios smaller than ten is similar to that of spheres but also remains appreciable for longer fibers [

The objectives of the study presented here are two-fold. In a preceding theoretical part, the mathematical background necessary for the simulation of nonspherical particle deposition in the human respiratory tract is introduced. Main interest is focused on the computation of appropriate dynamic shape factors and resulting aerodynamic diameters of fibers and disks with different aspect ratios. In a modelling part following the theoretical remarks, the aerodynamic diameter concept is applied to a stochastic particle transport and deposition model [

As already outlined in the preceding section, the simulation of nonspherical particle deposition in the lung, which is in the centre of interest in this work, is based on the concept of aerodynamic diameters. In general, the aerodynamic diameter, ^{−3}) of the particle, unit density (=1 g cm^{−3}), the Cunningham slip correction factor for a particle with diameter ^{3}/mol K), ^{23}), ^{−4} Pa·s or 0.18 cP (centipoise).

Dynamic shape factors of nonspherical particles, using the definition of the coefficients outlined in (

Coefficients | Fibers | Oblate disks | ||

8 | 8 | 4 | 4 | |

3 | 1 | 3 | 1 | |

− | − | |||

Arccos | Arccos |

The stochastic deposition model used in this context was introduced and described in detail by Koblinger and Hofmann [

In the stochastic deposition model, three main particle deposition forces, namely, inertial impaction, gravitational settling, and Brownian diffusion are distinguished. Corrected diameters for anisometric particles introduced in (^{−2}), the aerodynamic diameter of the particle of interest, the angle of a given airway tube axis relative to the direction of gravity, and the flow velocity in the airway tube. Deposition probability caused by Brownian diffusion is defined by the formula

As demonstrated by (

Normalised mobilities

The calculated diameters

Aerodynamic diameters of nonspherical particles with various aspect ratios

Fibers | Disks, platelets | |||||

0.01 | 0.0151 | 0.0176 | 0.0185 | 0.0070 | 0.0039 | 0.0011 |

0.02 | 0.0303 | 0.0354 | 0.0384 | 0.0139 | 0.0079 | 0.0021 |

0.05 | 0.0762 | 0.0902 | 0.1053 | 0.0349 | 0.0198 | 0.0053 |

0.10 | 0.1532 | 0.1850 | 0.2271 | 0.0700 | 0.0399 | 0.0108 |

0.20 | 0.3083 | 0.3786 | 0.4786 | 0.1409 | 0.0808 | 0.0219 |

0.50 | 0.7750 | 0.9635 | 1.2425 | 0.3556 | 0.2077 | 0.0571 |

1.00 | 1.5536 | 1.9406 | 2.5215 | 0.7144 | 0.4235 | 0.1209 |

2.00 | 3.1112 | 3.8964 | 5.0826 | 1.4326 | 0.8569 | 0.2564 |

5.00 | 7.7844 | 9.7654 | 12.768 | 3.5882 | 2.1601 | 0.6732 |

10.0 | 15.573 | 19.547 | 25.579 | 7.1812 | 4.3338 | 1.3731 |

Results of the computations of nonspherical unit-density particle deposition in the human respiratory tract under light-work breathing conditions [

Total deposition of fibers (a) and platelets (b) with different aspect ratios in the human respiratory tract assuming light work-breathing conditions [

Regional, that is, extrathoracic (ET), bronchial (BB), and bronchiolar/alveolar (bb + ALV), deposition of spheres (

Generation-by-generation deposition of spheres (

Interesting results are also obtained regarding the regional deposition of nonspherical particles, whereby for the computations, three lung regions, namely, the extrathoracic region (ET), the bronchi (BB), and the bronchioli/alveoli (bb + ALV) were distinguished. Simulations were conducted for three different particle sizes to cover a wider range of natural aerosols (Figure

The relative particle deposition per airway generation providing some information on local deposition phenomena is illustrated in Figure

To account for possible health effects due to nonspherical particle deposition in the lungs, regional, that is, extrathoracic, tracheal, bronchial, and bronchiolar/alveolar, deposition of spheres and anisometric particles with various geometric dimensions was computed as a function of the widely used mathematical term ^{4} cm^{3}·min^{−1} (breathing conditions during sleep [^{5} cm^{3}·min^{−1} (breathing condition during heavy work [^{−3} to 10^{1} ^{2}·cm^{3}·min^{−1} but becomes highly significant for ^{2}·cm^{3}·min^{−1}. In the case of ^{3} ^{2}·cm^{3}·min^{−1} due to, for example, an increase of the breathing frequency or an enhancement of the aerodynamic particle diameter deposition continuously approaches 100% (Figure ^{2} ^{2}·cm^{3}·min^{−1}. Another remarkably smaller deposition peak is located at very low values for ^{−3 }^{2}·cm^{3}·min^{−1}), underlining the significance of Brownian diffusion as a main deposition mechanism in the tracheal airway tube (Figure ^{2}·cm^{3}·min^{−1} and ^{2}·cm^{3}·min^{−1}. Differences between the two parts of the respiratory tract chiefly concern the amount of deposited material which in the bronchi is about 10 times higher than in the trachea (Figure ^{−2} to 10^{1} ^{2}·cm^{3}·min^{−1}. While for lower values of ^{2}·cm^{3}·min^{−1}, it may be evaluated as negligible (Figure

Dependence of extrathoracic (a), tracheal (b), bronchial (c), and bronchiolar/alveolar (d) deposition in the human respiratory tract on

Since environmental aerosols mainly contain particles that deviate from ideal spherical shape, detailed knowledge concerning the deposition of such nonspherical particulate matter in the human lungs represents an important basis in modern pulmology. In the past, theoretical description of the transport and deposition of anisometric particles in the human respiratory tract has chiefly been conducted by using the aerodynamic diameter concept [

Regarding total particle deposition in the human respiratory tract, fibers and oblate disks exhibit partly significant characteristics (Figure

Comparison between experimental [^{−1}, fiber length: 10–20 ^{−1}, fiber length: 60–70

Unfortunately, any comparison of the results generated in this study with calculations derived from numerical simulation methods using either the Lagrangian-Eulerian technique or DNS is not possible because numerical models are not able to define appropriate anisometric particles hitherto. In future models the effect of fibrosis generation due to enhanced alveolar deposition of dust particles and fibers will be considered more in detail.

Summing up the results of fiber and disk deposition in different lung regions and airway generations, preferred deposition sites of anisometric particles are the airway tubes and, depending upon particle size, also the alveoli. From these findings, it can be concluded that these particle classes may represent tremendous occupational hazards, especially if they are attached with radioactive elements or heavy metals [