The human respiratory tract is a complex, asymmetrical, tree-like system of tubular structures, optimized for the transport and distribution of respiratory gases. The objective of this study is to use a computerized lung model to study the effect of lung morphometry on the airway deposition of inhaled particles.
Material and methods: We used a stochastic lung model to simulate the total and regional deposition of 0.01-10 µm particles through oral breathing in sitting condition. The effect of lung morphometry was examined using the same model with a modified algorithm to create a fully symmetrical lung geometry. The results were compared using Student's t test and a p value <0.05 was considered to be statistically significant.
Results: Total deposition curves show the same trend in the deposition of particles, but absolute deposition values show significant differences, especially for particles larger than 1 µm. While extrathoracic deposition is similar for both models, the effect of different airway geometries becomes clearly visible in the bronchial and acinar regions.
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Conclusions: Our study shows that the deposition of inhaled particles is highly dependent on particle size, but also on the lung geometry the models are built on. Using a symmetrical lung geometry yields significantly different deposition values in the bronchial and acinar regions of the airways, compared with a realistic, asymmetrical, stochastic model.
Keywords: airways, morphometry, modelling, stochastic, symmetric
The human respiratory tract can be described as a complex system of cylindrical tubes, optimized for the transport of respiratory gases. From a geometrical point of view, the airways assume a tree-like structure, with branches that try to fill efficiently the space they are in, i.e. the thoracic cavity. The way the respiratory tract is optimized for gas transport, while respecting a set of biological, physiological and physical rules, represents a careful balance of design and function. One of the most interesting characteristic of this tree-like structure is its asymmetry: each branch gives birth to two (or sometimes more) daughter branches with different lengths, diameters and branching angles.
The deposition of inhaled particles in the human airways has great implications in the assessment of risks associated with the exposure to infectious agents, toxic, radioactive or allergenic substances from the ambient air, but also in the refinement of therapeutic aerosols used in the treatment of chronic respiratory diseases.
Due to the fact that because of ethical considerations and technical limitations experimental data is limited, currently the most widespread method to study the airway deposition of inhaled particles is to use computerized lung models, which can simulate the transport and deposition characteristics of a wide range of particles in a large number of respiratory conditions. The main differences between these models concern the lung geometry and the modelling technique used to carry out the simulations.
The objective of this study is to use a computerized lung model to study the effect of lung morphometry on the airway deposition of inhaled particles.
Material and methods
The deposition of inhaled particles was modelled using a new version of the stochastic lung model developed by Koblinger and Hofmann [1,2], Hofmann and Koblinger [3,4]. The model uses a stochastic asymmetric lung structure, based on the statistical analysis of measured data, and the airways are modelled by a sequence of Y-shaped bifurcation units, consisting of a parent tube and two asymmetrically dividing daughter airways. The geometric properties of the daughter branches (diameter, length, branching angle, gravity angle) and particle trajectories are selected randomly for each airway segment, thus all paths of the inhaled particles are different from each other.
In order to investigate the effect of lung morphometry, we created a symmetrical, one-path model by modifying the algorithm selecting the morphometric parameters of the airways in which the simulations are carried out. In this symmetrical model, each airway in one airway generation has identical linear dimensions and branches symmetrically into two identical daughter airways.
All simulations were carried out for a healthy, adult male subject, for oral breathing, in sitting condition. The respiratory parameters included a 750 ml tidal volume, a 3300 ml functional residual capacity and a 5 second long symmetrical breathing cycle. These specific parameters were obtained from the ICRP66 publication .
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We modelled the deposition of unit density (1 g/cm3) particles with diameters between 0.01 and 10 µm, namely particles of 0,01 µm, 0,02 µm, 0,05 µm, 0,1 µm, 0,2 µm, 0,5 µm, 1 µm, 2 µm, 5 µm and 10 µm in diameter. The simulations were carried out for one complete breathing cycle using 100,000 particles, and we assumed the particles are inhaled uniformly during inhalation.
Through the simulations the respiratory tract was divided into three distinct regions: the upper airways, or the extrathoracic region (the oral and nasal cavity, the larynx and the pharynx), a bronchial region (generations 0-16) and an acinar region (generations 17-23). The last two regions form the lower airways.
The stochastic model calculates the deposition probability of each inhaled particle for each bifurcation unit. Simulation results are presented as deposited fractions (the ratio of deposited particles and the total number of inhaled particles) for total, regional, generational and lobar deposition. Data processing and statistical analysis were performed using Microsoft Excel 2007. We used Student's t test to compare the results, and a p level of <0.05 was considered to be statistically significant.
Total deposition values obtained with the asymmetrical vs. the symmetrical models are depicted in Figure 1. Deposition in the upper airways is presented in Figure 2, while deposition in the bronchial and acinar regions are presented in Figure 3 and 4, respectively.
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According to Hofmann, modelling particle deposition in the human lung is an attempt to solve a physical problem in a biological system by applying mathematical methods . Particle deposition is influenced by biological factors, such as lung morphometry or respiratory parameters, but also physical factors, such as fluid dynamics, particle properties or deposition mechanisms. Although it has been proved that the deposition of inhaled particles shows significant variations through various breathing conditions [7,5,8-12], this study focuses on the effect of lung geometry. The simulations were carried out for a wide range of particle diameters. The size of the particles determines the dominant deposition mechanism and the lung regions where deposition are characteristic, thus deposition mechanisms will also be discussed.
The three main deposition mechanisms are Brownian diffusion, gravitational sedimentation and inertial impaction. The magnitude of each deposition mechanism varies with parameters of particles, lung morphometry and breathing method . Particles larger than 1 µm deposit in the upper airways and the central airways through impaction, due to their large size and the high flow velocity in these regions. Smaller particles on the other hand reach the distal areas of the airways, even the alveoli, where the velocity of the air is reduced, and they may deposit there dominantly by sedimentation and diffusion. Diffusion efficiently may affect deposition of particles smaller than 0.1 µm.
The intricate relation of particle size and deposition mechanisms yields the typical U-shaped deposition curve of total deposition, presented in Figure 1. While the curves show similar deposition trends for the two models - the symmetric model returning slightly higher deposition values for submicron particles -, the differences become much more visible for particles larger than 1 µm, the deposited fractions predicted by the asymmetric model being almost four times higher in the case of 2 µm particles (p<0.001) and more than three times higher in the case of 5 µm particles (p<0.001). In the case of the symmetric model, the majority of these particles leaves the respiratory tract during exhalation without deposition.
The extrathoracic deposition values (Figure 2) show the filtering effect of the upper airways for 10 µm particles, especially in the case of the symmetric model, where more than 90% of the predicted deposition occured in this region. The symmetrical model predicted slightly higher deposited fractions for almost all particle sizes (p<0.001), but the differences disappear gradually as particle size increases, being negligible for 5 µm and 10 µm particles.
As the morphometric differences between the two models only affect the lung airways, the effect of airway geometry on regional deposition becomes significant in the bronchial and acinar regions (Figures 3 and 4). The bronchial deposition curve obtained with the asymmetric model is similar to the total deposition curve. Deposition values of submicron particles predicted by the symmetric model are consistently higher in this area, being approximately twice as large for 0.02-0.1 µm particles, compared with the asymmetric model (p<0.001). For particles larger than 1 µm the deposition values predicted by the symmetric model are considerably lower (p<0.001), especially for particles in the 5-10 µm size range. These differences reach a factor of almost ten in the case of 5 µm particles (21.6% vs. 2.86%, p<0.001).
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In the acinar region the deposition curve predicted by the asymmetric model assumes a saddle-like shape with two peaks at 0.02 µm and 5 µm particles. The deposited fractions predicted by the symmetric model are lower for the majority of particle sizes (p<0.001), with the exception of particles with diameters between 0.2-0.5 µm.
While it is rather difficult to compare the results with similar studies, due to the wide range of models and parameters these studies employ, all studies seem to agree that the deposition curves follow the same trend depending on the size of the particles, regardless of lung geometry and modelling technique. In a study by Hofmann , several types of lung models were compared, using the same set of modelling parameters, which were very similar to the ones used in our study: particle size 0.001-10 µm, nose breathing in resting, tidal volume 750 ml, functional residual capacity 3300 ml and a 5 second long breathing cycle. This study found that total and regional deposition curves were similar in all cases, and while there were differences in the absolute values, all deposition fractions were within a range of ±10%. The same study also reports that deposition calculations using different deposition equations in a given lung model or different morphometric lung models with the same deposition equations indicate that deposition fractions are affected by the selection of a specific lung model and a specific set of deposition equations, but all models predict the same trends as functions of particle diameter and breathing parameters . Although there are certain differences between this comparison and our study (nose breathing vs. mouth breathing, and the inclusion of particles smaller than 0.01 µm), our results obtained with the asymmetrical model are in good agreement with this study. Other studies [13-15] report considerable differences in regional deposition values, when comparing results obtained with models using different lung geometries. We consider that the differences in regional, but also total deposition values observed in our study can be attributed to the different lung geometries and particle trajectories used by the two models. Further studies are needed to assess the cumulated effect of different lung geometries and breathing conditions on the deposition of the inhaled particles.
Lung models are currently used to assess the health risks associated with the inhalation of toxic, radioactive or allergenic substances from the ambient air [16-19], playing an important role also in cancer related research, where they have the potential to clarify why certain types of cancer develop predominantly in certain areas of the airways [20,21]. Simulation models are also used to evaluate the efficiency of aerosols in the treatment of chronic respiratory diseases such as asthma bronchiale , but also in systemic diseases such as diabetes  or cancer [23-25]. While obstructive respiratory diseases require the medication to transport into the bronchial region, drugs intended for systemic use need to reach the alveoli, where they can enter the blood stream. In these conditions, it is extremely important to use an anatomically correct representation of the airways in simulation models. Many of the models currently used imply an idealized, symmetrical lung structure, to reduce computational resources [26,5], but their simplicity also means that they cannot be used for the prediction of realistic deposition patterns in asymmetric and variable lung structures . Numerical models on the other hand involve computational fluid and particle dynamics (CFPD) calculations, using highly realistic three-dimensional geometries, but their high computational needs limit them to only a several consecutive airway generations, therefore these models can only be used on a local scale [27-30]. In these conditions, whole lung models that use an asymmetrical lung geometry present a clear advantage over symmetrical models. The stochastic lung model used in our study applies the most realistic lung structure presently available in terms of dimensional variability and branching asymmetry, being also able to quantify the distributions of deposition fractions due to intra- and inter-subject variability .
Our study shows that the deposition of inhaled particles is highly dependent on particle size, but also on the lung geometry the models are built on. Using a symmetrical lung geometry yields significantly different deposition values in the bronchial and acinar regions of the airways, compared with an asymmetrical, stochastic model.