Weibel A model

TABLE S.S Representative Conducting Airway Dimensions Based on the Weibel A Model... 

Kim et al. developed a lung model based on the Weibel-A model in which they decreased airway diameter by 25 or 40% in both the peripheral and central airways (102). Then they calculated the increases in resistance and deposition. Their results are presented in Fig. 14A and B. The upper graph represents the situation after a diameter reduction of 25%, the lower one after a 40% reduction. It is clear from the graphs that there is no simple one-to-one relationship between the increase in resistance and deposition. This is to be expected, because resistance relates to airway diameter raised to the fourth power, while deposition does not. Nevertheless, from both graphs, it is clear that the model predicts that as resistance increases, the increase in deposition will occur mainly in the larger airways (generations 0-7). Deposition in generations 8-16 will be less affected by the inaease in resistance. 

Most dosimetry models have incorporated the so-called Weibel A airway dimensions (Weibel, 1963) in order to calculate aerosol deposition, clearance and the density of alpha-decays per unit surface... 

Both the Weibel A and Yeh-Schum models need to be reduced in scale to represent adult human lung at a normal level of inflation corresponding to 3000 ml functional residual capacity (FRC) (Yu and Diu, 1982). Partial scaling has been included in some dosimetric models (NEA, 1983 James, 1984) but not in others. In all cases the airway sizes used to represent adult lung correspond to a higher level of inflation than the standard FRC, leading to general but relatively small underestimates of bronchial dose. 

The volumes and surface areas of airways in each generation that result from scaling the Weibel A, Yeh-Schum and UCI lung models to the standard FRC (Yu and Diu, 1982), are shown in Figure 3. The residual differences in airway size are appreciable, but there is no overriding reason to prefer a particular model. Dosimetric results are therefore evaluated below for all three. 

Figure 3. Volumes and surface areas of airways in each bronchial generation of the Weibel A, Yeh-Schum and UCI lung models, with total volumes 2V and areas 2A.

Dosimetry. Dosimetry for inhaled Rn-d particles has made significant advances over the past twenty years. Lung modelling, based initially to a large extent on the WEIBEL A -symmetrical lung model, has been... 

Several investigators have modeled deposition within the Inng as a function of particle size. Gerrity related particle size and regional deposition on a per airway generation basis, as shown in Fig. 4 (15). His calculations took into account the Landahl equations (9) and the Weibel-A lung model (16). This model... 

This trumpet model was originally introduced by Scherer et al. (141) for simulations of intrapulmonary gas transport and is based on a morphometric data set proposed by Weibel (5). In Weibel s model, the structural parameters of each airway generation are described by average values, so that all airways of a given generation are identical, as are all pathways leading to a specific airway generation. The model is, therefore, termed symmetrical or deterministic. ... 

In the present study the bronchial morphometry of Yeh and Schum (1980) is utilized instead of the Weibel model. This is a more accurate description of the bronchial airway lengths, diameters and branching pattern. It does not assume dichotomous branching and therefore does not suffer from the problem of the artificially high surface area leading to low alpha dose in the more distal airways common to other models of the human airways. 

Bakd et al. theoretically analyzed simultaneous gas flow and diffusion in Weibel s symmetric model. Th applied a time-varying flow with simultaneous longitudinal diffusion and concluded that convective mixing is much less important than mixing induced by molecular diffusion. 

The Henry s law constant in water was used in the McJilton et al. uptake model to determine the equilibrium concentration of ozone and sulfur dioxide at the surface of a simulated mucus film along the airways in Weibel s symmetric model.It is also used to determine the concentration of absorbed gas at the surface of the mucus when the pollutant gas undergoes a homogeneous or heterogeneous chemical reaction within the mucus layer. 

Weibel D B etal., 2005b, Modeling the Anodic Half-Cell of a Low-Temperature Coal Fuel Cell. Angewandte Chemie International Edition, 44, 5682-5686. 

The nature of particle deposition forces and their relationship to aerodynamic particle size have been the subject of many studies and reports. A variety of models for aerosol deposition in the respiratory tract have been proposed. The most notable are those of Findeisen [80], Landahl [53,81], and Weibel [1],... 

Yu and Diu (1982) used four different anatomical models to determine regional deposition in nose breathers. The anatomical models employed were those of Weibel (1963), Olson et al. (1970), Hansen and Ampaya (1975) and Yeh and Schum (1980). All regional deposition estimates were within a factor of 2, thus demonstrating reasonable agreement (Table 27.4). 

Giithenke A, Chatterjee D, Weibel M, Krutzsch B, Koci P, Marek M, Nova I, Tronconi E (2008) Current status of modeling lean exhaust gas aftertieatment catalysts. Advances in Chemical Engineering 33 103-211... 

Chatterjee D, Kocr P, SchmeiBer V, Marek M, Weibel M, Krutzsch B (2010) Modelling of a combined NOx storage and NH3-SCR catalytic system for Diesel exhaust gas aftertreatment. Catalysis Today 151 395-409... 

Nova I, Colombo M, Tronconi E, Schmeisser V, Weibel M (2011) The NH3 Inhibition Effect in the Standard SCR Reaction over a Commercial Fe-zeolite Catalyst for Diesel Exhaust Aftertreatment An Experimental and Modeling Study. SAE International Journal of Engines 4 (1) 1822-1838... 

Zukerman R, Vradman L, Herskowitz M, Liverts E, Liverts M, Massner A, Weibel M, Brilhac JF, Blakeman PG, Peace LF (2009) Modeling and simulation of a smart catalytic converter combining NOx storage, ammonia production and SCR. Chem. Eng. J. 155 419-426... 

Grossale A, Nova I, Tronconi E, (Thatterjee D, Weibel M (2009) NH3-N0/N02 SCR for Diesel Exhausts Afteitreatment Reactivity, Mechanism and Kinetic Modelling of Commercial Fe- and Cu-Promoted Zeolite Catalysts. Topics in Catalysis, 52, 1837-1841... 

Weibel and Raabe et al. have shown that the structure of human bronchial airways can be approximated as a network of repeatedly bifurcating tubes. The bifurcations are generally asymmetric. In most computer models, however, symmetric conditions are assumed. 

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