Stochastic model of particle clearance in human bronchial airways

Effects of spatial variation in dose delivery: what can we learn from radon-related lung cancer studies?

Exposure to radon progeny results in heterogeneous dose distributions in many different spatial scales. The aim of this review is to provide an overview on the state of the art in epidemiology, clinical observations, cell biology, dosimetry, and modelling related to radon exposure and its association with lung cancer, along with priorities for future research. Particular attention is paid on the effects of spatial variation in dose delivery within the organs, a factor not considered in radiation protection. It is concluded that a multidisciplinary approach is required to improve risk assessment and mechanistic understanding of carcinogenesis related to radon exposure. To achieve these goals, important steps would be to clarify whether radon can cause other diseases than lung cancer, and to investigate radon-related health risks in children or persons at young ages. Also, a better understanding of the combined effects of radon and smoking is needed, which can be achieved by integrating epidemiological, clinical, pathological, and molecular oncology data to obtain a radon-associated signature. While in vitro models derived from primary human bronchial epithelial cells can help to identify new and corroborate existing biomarkers, they also allow to study the effects of heterogeneous dose distributions including the effects of locally high doses. These novel approaches can provide valuable input and validation data for mathematical models for risk assessment. These models can be applied to quantitatively translate the knowledge obtained from radon exposure to other exposures resulting in heterogeneous dose distributions within an organ to support radiation protection in general.

Dosimetric Comparison of Exposure Pathways to Human Organs and Tissues in Radon Therapy

Three therapeutic applications are presently prescribed in the radon spas in Gastein, Austria: exposure to radon in a thermal bath, exposure to radon vapor in an exposure chamber (vapor bath), and exposure to radon in the thermal gallery, a former mine. The radiological exposure pathways to human organs and tissues in these therapeutic radon applications are inhalation of radon and radon progeny via the lungs, radon transfer from water or air through the skin, and radon-progeny deposition on the skin in water or air. The objectives of the present study were to calculate radon and radon-progeny doses for selected organs and tissues for the different exposure pathways and therapeutic applications. Doses incurred in red bone marrow, liver, kidneys, and Langerhans cells in the skin may be correlated with potential therapeutic benefits, while doses to the lungs and the basal cells of the skin indicate potential carcinogenic effects. The highest organ doses among the three therapeutic applications were produced in the thermal gallery by radon progeny via inhalation, with lung doses of 5.0 mSv, and attachment to the skin, with skin doses of 4.4 mSv, while the radon contribution was less significant. For comparison, the primary exposure pathways in the thermal bath are the radon uptake through the skin, with lung doses of 334 μSv, and the radon-progeny attachment to the skin, with skin doses of 216 μSv, while the inhalation route can safely be neglected.

A mechanistic framework for a priori pharmacokinetic predictions of orally inhaled drugs

The fate of orally inhaled drugs is determined by pulmonary pharmacokinetic processes such as particle deposition, pulmonary drug dissolution, and mucociliary clearance. Even though each single process has been systematically investigated, a quantitative understanding on the interaction of processes remains limited and therefore identifying optimal drug and formulation characteristics for orally inhaled drugs is still challenging. To investigate this complex interplay, the pulmonary processes can be integrated into mathematical models. However, existing modeling attempts considerably simplify these processes or are not systematically evaluated against (clinical) data. In this work, we developed a mathematical framework based on physiologically-structured population equations to integrate all relevant pulmonary processes mechanistically. A tailored numerical resolution strategy was chosen and the mechanistic model was evaluated systematically against data from different clinical studies. Without adapting the mechanistic model or estimating kinetic parameters based on individual study data, the developed model was able to predict simultaneously (i) lung retention profiles of inhaled insoluble particles, (ii) particle size-dependent pharmacokinetics of inhaled monodisperse particles, (iii) pharmacokinetic differences between inhaled fluticasone propionate and budesonide, as well as (iv) pharmacokinetic differences between healthy volunteers and asthmatic patients. Finally, to identify the most impactful optimization criteria for orally inhaled drugs, the developed mechanistic model was applied to investigate the impact of input parameters on both the pulmonary and systemic exposure. Interestingly, the solubility of the inhaled drug did not have any relevant impact on the local and systemic pharmacokinetics. Instead, the pulmonary dissolution rate, the particle size, the tissue affinity, and the systemic clearance were the most impactful potential optimization parameters. In the future, the developed prediction framework should be considered a powerful tool for identifying optimal drug and formulation characteristics.

The use of orally inhaled drugs for treating lung diseases is appealing since they have the potential for lung selectivity, i.e. high exposure at the site of action –the lung– without excessive side effects. However, the degree of lung selectivity depends on a large number of factors, including physiochemical properties of drug molecules, patient disease state, and inhalation devices. To predict the impact of these factors on drug exposure and thereby to understand the characteristics of an optimal drug for inhalation, we develop a predictive mathematical framework (a “pharmacokinetic model”). In contrast to previous approaches, our model allows combining knowledge from different sources appropriately and its predictions were able to adequately predict different sets of clinical data. Finally, we compare the impact of different factors and find that the most important factors are the size of the inhaled particles, the affinity of the drug to the lung tissue, as well as the rate of drug dissolution in the lung. In contrast to the common belief, the solubility of a drug in the lining fluids is not found to be relevant. These findings are important to understand how inhaled drugs should be designed to achieve best treatment results in patients.

Simulation of the effect of mucociliary clearance on the bronchial distribution of inhaled radon progenies and related cellular damage using a new deposition and clearance model for the lung

Most of the current dosimetry models of inhaled short-lived radon decay products assume uniform activity distributions along the bronchial airways. In reality, however, both deposition and clearance patterns of inhaled radon progenies are highly inhomogeneous. Consequently, a new deposition-clearance model has been developed that accounts for such inhomogeneities and applied together with biophysical models of cell death and cell transformation. The scope of this study was to apply this model which is based on computational fluid and particle dynamics methods, in an effort to reveal the effect of mucociliary clearance on the bronchial distribution of deposited radon progenies. Furthermore, the influence of mucociliary clearance on the spatial distribution of biological damage due to alpha-decay of the deposited radon progenies was also studied. The results obtained demonstrate that both deposition and clearance of inhaled radon progenies are highly non-uniform within a human airway bifurcation unit. Due to the topology of the carinal ridge, a slow clearance zone emerged in this region, which is the location where most of the radio-aerosols deposit. In spite of the slow mucus movement in this zone, the initial degree of inhomogeneity of the activity due to the nonuniform deposition decreased by a factor of about 3 by considering the effect of mucociliary clearance. In the peak of the airway bifurcation, the computed cell death and cell transformation probabilities were lower when considering deposition and clearance simultaneously, compared to the case when only deposition was considered. However, cellular damage remained clustered.

Regional Deposition: Deposition Models

Modeling particle deposition in the human lung requires information about the morphology of the lung in terms of simple geometric units, e.g., characterizing bronchial airways by straight cylindrical tubes. Five different regional deposition models are discussed in this section with respect to morphometric lung models and related mathematical modeling techniques: 1) one-dimensional cross-section or "trumpet" model, 2) deterministic symmetric generation or "single-path" model, 3) deterministic asymmetric generation or "multiple-path" model, 4) stochastic asymmetric generation or "multiple-path" model, and 5) single-path computational fluid and particle dynamics (CFPD) model. Current deposition models can predict the following regional deposition quantities relevant for the administration of medical aerosols: 1) regional bronchial and alveolar deposition, 2) generational lung deposition, 3) lobar deposition, 4) generational lobar deposition, and 5) generational surface deposition. Although deposition fractions predicted by the different models depend on the selection of a specific morphometric lung model and a specific set of analytical deposition equations, all models predict the same trends as functions of particle diameter and breathing parameters. In general, the overall agreement between the modeling predictions obtained by the various deposition models and the available experimental evidence indicates that current deposition models correctly predict regional and generational deposition.

CELLULAR DOSE DISTRIBUTIONS OF INHALED RADON PROGENY AMONG DIFFERENT LOBES OF THE HUMAN LUNG

Basal and secretory cell doses in the different lobes of the human lung following inhalation of short-lived radon progeny were calculated for a five-lobe asymmetric, stochastic lung model, considering the non-uniform ventilation of the lobes. Dose calculations for defined exposure conditions revealed that the upper lobes receive higher doses than the average bronchial dose for the whole lung, with the right upper lobe receiving the highest dose. The resulting inter-lobar distribution of cellular bronchial doses indicated that the non-uniform lung morphometry is the dominating factor, while non-uniform ventilation only slightly enhances the lobar differences. The comparison of average lobe-specific bronchial doses with the average bronchial dose for the whole lung allows the calculation of lobe-specific dose weighting factors, which can be used to convert average bronchial doses based on symmetric airway generation or bronchial compartment models to lobar bronchial doses.

The degree of inhomogeneity of the absorbed cell nucleus doses in the bronchial region of the human respiratory tract

Inhalation of short-lived radon progeny is an important cause of lung cancer. To characterize the absorbed doses in the bronchial region of the airways due to inhaled radon progeny, mostly regional lung deposition models, like the Human Respiratory Tract Model (HRTM) of the International Commission on Radiological Protection, are used. However, in this model the site specificity of radiation burden in the airways due to deposition and fast airway clearance of radon progeny is not described. Therefore, in the present study, the Radact version of the stochastic lung model was used to quantify the cellular radiation dose distribution at airway generation level and to simulate the kinetics of the deposited radon progeny resulting from the moving mucus layer. All simulations were performed assuming an isotope ratio typical for an average dwelling, and breathing mode characteristic of a healthy adult sitting man. The study demonstrates that the cell nuclei receiving high doses are non-uniformly distributed within the bronchial airway generations. The results revealed that the maximum of the radiation burden is at the first few bronchial airway generations of the respiratory tract, where most of the lung carcinomas of former uranium miners were found. Based on the results of the present simulations, it can be stated that regional lung models may not be fully adequate to describe the radiation burden due to radon progeny. A more realistic and precise calculation of the absorbed doses from the decay of radon progeny to the lung requires deposition and clearance to be simulated by realistic models of airway generations.

Theoretical and experimental approaches to the deposition and clearance of ultrafine carcinogens in the human respiratory tract

INTRODUCTION

  Although inhaled ultrafine particles (UFPs) represent serious lung burdens and are thus responsible for a remarkable number of respiratory diseases (including cancer), only limited information on their deposition and clearance in the lung compartments is available. The study presented here tries to overcome this deficit by using a detailed theoretical approach to UFP behavior in the lungs.

METHODS

  The deposition model used in this context is based upon a stochastic lung geometry and the generation of single-particle trajectories in the tracheobronchial tree according to the random walk algorithm. Simulation of UFP clearance is conducted with the help of a multi-compartment model that considers cellular/non-cellular sites of temporary particle storage as separate compartments.

RESULTS

  As predicted by the models and confirmed by experimental findings, deposition of UFPs by Brownian motion takes place in both the upper and lower compartments of the respiratory tract. Alveolar accumulation of particulate mass increases proportionally with the inhalative flow rate. Clearance of UFPs is chiefly dominated by slow mechanisms with respective half-times ranging from several days to months.

DISCUSSION

  Modeling of UFP behavior in the respiratory tract represents an appropriate tool for forthcoming medical studies on this particle class, but it needs to be subjected to further refinements. •  As outlined by this study, alveolar deposition of UFPs, correlating with a noticeable risk of malignant transformations and cancer development, is determined by a number of factors, including effective particle size and velocity of particle transport in the conducting airways. •  With the help of appropriately validated models, respective predictions on the pulmonary burdens of UFP after short-term or long-term exposure can be made. In the case of subjects suffering from bronchial and/or alveolar UFP overloads, respective clearance approaches may be applied to simulate particle removal scenarios.

Deposition and cellular interaction of cancer-inducing particles in the human respiratory tract: Theoretical approaches and experimental data

Inhaled particles that are deposited on the epithelial surface of the human respiratory tract (HRT) may act as serious health hazards, in the worst case inducing the development of various types of lung cancer. In the past, several particle types, such as asbestos fibers, hard wood dust and cigarette smoke were identified and classified as human carcinogens. Due to their different physical and chemical properties these particles are characterized by remarkable discrepancies concerning their transport, deposition, and epithelial interaction in the HRT. In order to continuously increase the knowledge on carcinogenic particle behavior in the HRT, theoretical models describing single stages of particulate action in the lung airways were developed over the last few decades. With the help of these mathematical approaches physical characteristics of aerosolized drugs as well as protocols of inhalative therapies for the treatment of lung diseases could be significantly optimized. In addition, new experimental setups for the enlightenment of possible mechanisms underlying particle-lung interaction were, among other things, founded upon the results of theoretical computations. This review summarizes the efforts and advances of theoretical lung modeling from the early 1970s till today, thereby mainly directing the attention to the simulation of carcinogenic particle behavior in the HRT.

Computer-aided generation and lung deposition modeling of nano-scale particle aggregates

The study sets its main focus on the introduction of a random-walk-based model for the generation of variably shaped particle aggregates consisting of a predefined number of spherical components. With the help of a well-defined algorithm, the user is enabled to select between isodimensional, chain-like and platelet-like aggregates, for which related aerodynamic parameters (dynamic shape factors, volume-equivalent diameters, aerodynamic diameters) are determined automatically. The theoretical approach for random aggregate construction is directly connected with the previously developed stochastic particle transport and deposition model. Thereby, individually shaped aggregates may be provided for each random-walk scenario taking place in the almost realistic lung structure. Preliminary application of the aggregate generation model was carried out by assuming single components with a constant diameter of 1 nm and unit-density (1 g cm^-3) and variably shaped aggregates consisting of 10, 100 and 1000 components. Inhalation of the aggregate-loaded aerosol into lungs of average size (FRC = 3300 mL) was supposed to take place under sitting, light-exercise and heavy-exercise conditions. Results obtained from deposition modeling clearly show that, independent of aggregate geometry, total deposition declines with increasing number of components included in the particulate construct, but experiences a continuous enhancement with rising inhalation flow rate. Among the predefined geometric categories, platelet-like aggregates are distinguished by lowest deposition and isodimensional clusters by highest. While isodimensional aggregates preferentially deposit in the extrathoracic and bronchial airways, chain-like and platelet-like aggregates exhibit a significantly increased tendency to hit the alveolar walls.

Bioaerosols in the lungs of subjects with different ages-Part 2: clearance modeling

BACKGROUND

The present contribution deals with theoretical aspects regarding biogenic particle clearance from various lung structures of probands with different ages (1, 5, 15, 20 y). With reference to part 1 of the study, particles varying in size and shape are subject to a detailed analysis. The main goal of the investigation consists in an increase of our knowledge concerning the clearance behaviour of bioparticles and its dependence upon various physiological and anatomical factors.

METHODS

Theoretical clearance of biogenic particles was subdivided into four main phases, namely fast bronchial clearance, slow bronchial clearance, fast alveolar clearance, and slow alveolar clearance. All of these phases were simulated by using a well validated stochastic modeling approach, where the main focus is set on the randomly varied particle mass transfer between main compartments of the human respiratory tract. Whilst effects of particle geometry on clearance were approximated by application of the projective-diameter concept, age dependence of the particle removal process was expressed by the experimentally proven relationship between bronchial mucus velocities and morphometry of the airway tree.

RESULTS

According to the results of the theoretical simulations efficiency of fast bronchial clearance, expressed by the 24-h-retention value, exhibits a negative correlation with proband's age, whereas the other clearance phases are characterized by a rather conservative behaviour among the different age categories. Highest clearance rates may be observed for very fine (<0.01 µm) and very coarse particles (>5 µm) preferentially deposited in the upper bronchial airways, whilst large particles accumulated in the alveoli may be stored there for several months to years.

CONCLUSIONS

The study comes to the conclusion that infants and children dispose of an enhanced bronchial clearance efficiency with respect to adolescents and adults, which results in a faster removal of particulate substances accumulated in the upper bronchial regions. Particles escaping from the natural filtering process in the upper airways and undergoing alveolar deposition are subject to identical clearance scenarios among the age groups and may represent remarkable health hazards.

A Macroscopic Model for Simulating the Mucociliary Clearance in a Bronchial Bifurcation: The Role of Surface Tension

The mucociliary clearance in the bronchial tree is the main mechanism by which the lungs clear themselves of deposited particulate matter. In this work, a macroscopic model of the clearance mechanism is proposed. Lubrication theory is applied for thin films with both surface tension effects and a moving wall boundary. The flow field is computed by the use of a finite-volume scheme on an unstructured grid that replicates a bronchial bifurcation. The carina in bronchial bifurcations is of special interest because it is a location of increased deposition of inhaled particles. In this study, the mucus flow is computed for different values of the surface tension. It is found that a minimal surface tension is necessary for efficiently removing the mucus while maintaining the mucus film thickness at physiological levels.

Local lung deposition of ultrafine particles in healthy adults: experimental results and theoretical predictions

BACKGROUND

Ultrafine particles (UFP) of biogenic and anthropogenic origin occur in high numbers in the ambient atmosphere. In addition, aerosols containing ultrafine powders are used for the inhalation therapy of various diseases. All these facts make it necessary to obtain comprehensive knowledge regarding the exact behavior of UFP in the respiratory tract.

METHODS

Theoretical simulations of local UFP deposition are based on previously conducted inhalation experiments, where particles with various sizes (0.04, 0.06, 0.08, and 0.10 µm) were administered to the respiratory tract by application of the aerosol bolus technique. By the sequential change of the lung penetration depth of the inspired bolus, different volumetric lung regions could be generated and particle deposition in these regions could be evaluated. The model presented in this contribution adopted all parameters used in the experiments. Besides the obligatory comparison between practical and theoretical data, also advanced modeling predictions including the effect of varying functional residual capacity (FRC) and respiratory flow rate were conducted.

RESULTS

Validation of the UFP deposition model shows that highest deposition fractions occur in those volumetric lung regions corresponding to the small and partly alveolated airways of the tracheobronchial tree. Particle deposition proximal to the trachea is increased in female probands with respect to male subjects. Decrease of both the FRC and the respiratory flow rate results in an enhancement of UFP deposition.

CONCLUSIONS

The study comes to the conclusion that deposition of UFP taken up via bolus inhalation is influenced by a multitude of factors, among which lung morphometry and breathing conditions play a superior role.

Total deposition of ultrafine particles in the lungs of healthy men and women: experimental and theoretical results

BACKGROUND

Inhaled ultrafine particles (UFP) may induce greater adverse respiratory effects than larger particles occurring in the ambient atmosphere. Due to this potential of UFP to act as triggers for diverse lung injuries medical as well as physical research has been increasingly focused on the exact deposition behavior of the particles in lungs of various probands. Main purpose of the present study was the presentation of experimental and theoretical data of total, regional, and local UFP deposition in the lungs of men and women.

METHODS

Both experiments and theoretical simulations were carried out by using particle sizes of 0.04, 0.06, 0.08, and 0.10 µm [number median diameters (NMD)]. Inhalation of UFP took place by application of predefined tidal volumes (500, 750, and 1,000 mL) and respiratory flow rates (150, 250, 375, and 500 mL·s(-1)). For male subjects a functional residual capacity (FRC) of 3,911±892 mL was measured, whereas female probands had a FRC of 3,314±547 mL. Theoretical predictions were based on (I) a stochastic model of the tracheobronchial tree; (II) particle transport computations according to a random walk algorithm; and (III) empirical formulae for the description of UFP deposition.

RESULTS

Total deposition fractions (TDF) are marked by a continuous diminution with increasing particle size. Whilst particles measuring 0.04 µm in size deposit in the respiratory tract by 40-70%, particles with a size of 0.10 µm exhibit deposition values ranging from 20% to 45%. Except for the largest particles studied here TDF of female probands are higher than those obtained for male probands. Differences between experimental and theoretical results are most significant for 0.10 µm particles, but never exceed 20%. Predictions of regional (extrathoracic, tracheobronchial, alveolar) UFP deposition show clearly that females tend to develop higher tracheobronchial and alveolar deposition fractions than males. This discrepancy is also confirmed by airway generation-specific deposition, which is permanently higher in women than in men.

CONCLUSIONS

From the experimental data and modeling predictions it can be concluded that females bear a slightly higher potential to develop lung insufficiencies after exposure to UFP than males. Besides higher deposition fractions occurring in female subjects, also total lung deposition dose is noticeably enhanced.

Bioaerosols in the lungs of subjects with different ages-part 1: deposition modeling

BACKGROUND

In this contribution the inhalation and deposition of bioaerosols including particles with various shapes and sizes were investigated for probands with different ages (1, 5, 15 and 20 y). The study should help to increase our knowledge with regard to the behavior of variably shaped and sized particles in lungs being subject to different developmental stages.

METHODS

Simulation of particle transport and deposition in single structures of the respiratory tract was conducted by using a stochastic model of the tracheobronchial tree and well-validated analytical and empirical deposition formulae. Possible effects of particle geometry on deposition were taken into consideration by application of the aerodynamic diameter concept. Age-dependent lung morphometry and breathing parameters were computed by using appropriate scaling factors.

RESULTS

Theoretical simulations came to the result that bioparticle deposition in infants and children clearly differs from that in adolescents and adults insofar as the amount of deposited mass exhibits a positive correlation with age. Nose breathing results in higher extrathoracic deposition rates than mouth breathing and, as a consequence of that, lower particle amounts are enabled to enter the lung structures after passing the nasal airways. Under sitting breathing conditions highest alveolar deposition rates were calculated for particles adopting aerodynamic diameters of 10 nm and 4 µm, respectively.

CONCLUSIONS

The study comes to the conclusion that bioparticles have a lower chance to reach the alveoli in infants' and children's lungs, but show a higher alveolar deposition probability in the lungs of adolescents and adults. Despite of this circumstance also young subjects may increasingly suffer from biogenic particle burden, when they are subject to a long-term exposure to certain bioaerosols.

Measurements of Deposition, Lung Surface Area and Lung Fluid for Simulation of Inhaled Compounds

Modern strategies in drug development employ in silico techniques in the design of compounds as well as estimations of pharmacokinetics, pharmacodynamics and toxicity parameters. The quality of the results depends on software algorithm, data library and input data. Compared to simulations of absorption, distribution, metabolism, excretion, and toxicity of oral drug compounds, relatively few studies report predictions of pharmacokinetics and pharmacodynamics of inhaled substances. For calculation of the drug concentration at the absorption site, the pulmonary epithelium, physiological parameters such as lung surface and distribution volume (lung lining fluid) have to be known. These parameters can only be determined by invasive techniques and by postmortem studies. Very different values have been reported in the literature. This review addresses the state of software programs for simulation of orally inhaled substances and focuses on problems in the determination of particle deposition, lung surface and of lung lining fluid. The different surface areas for deposition and for drug absorption are difficult to include directly into the simulations. As drug levels are influenced by multiple parameters the role of single parameters in the simulations cannot be identified easily.

Spatial visualization of theoretical nanoparticle deposition in the human respiratory tract

BACKGROUND

Although nanoparticles and their hazardous effects on human health are well elucidated meanwhile, inhalation and distribution of these materials in the human respiratory tract still represent partly enigmatic phenomena. Main objective of the present study was the detailed description of a mathematical method, with the help of which spatial distributions of nanoparticles deposited in the tracheobronchial tree may be visualized appropriately.

METHODS

The technique is founded on a stochastic model of the bronchial network, within which inhaled particles follow individual, randomly selected trajectories. The lengths of these random paths depend on the airway-specific deposition probabilities calculated for the particles and the duration of the breath cycle. Positions of the deposited material were determined by computation of the exact lengths of individual particle trajectories and the orientation of single path segments within a Cartesian coordinate system, where the z-direction corresponds with the trachea. For a better quantification of the particle distribution and its eventual comparison with experimental data particle coordinates were fitted into a voxel grid [1 voxel = (0.467 cm)(3)]. Particle deposition is chiefly controlled by diffusive processes, whereas deposition mechanisms associated with inertia or gravity play a subordinate role.

RESULTS

Deposition patterns were visualized for particles with sizes of 1, 10, and 100 nm. As clearly demonstrated by the results obtained from the modeling procedure, under normal breathing conditions 1-nm particles tend to deposit in the upper airways, whilst 10- and 100-nm particles are preferably accumulated in the airways of the central and peripheral lung. The particle dose deposited in the extrathoracic and thoracic airways within one breath cycle significantly declines with increasing particle size.

CONCLUSIONS

Based on the predictions presented in this study possible consequences of nanoparticle inhalation to the health of subjects increasingly exposed to these airborne materials were discussed.

A computer model for the simulation of nanoparticle deposition in the alveolar structures of the human lungs

BACKGROUND

According to epidemiological and experimental studies, inhalation of nanoparticles is commonly believed as a main trigger for several pulmonary dysfunctions and lung diseases. Concerning the transport and deposition of such nano-scale particles in the different structures of the human lungs, some essential questions are still in need of a clarification. Therefore, main objective of the study was the simulation of nanoparticle deposition in the alveolar region of the human respiratory tract (HRT).

METHODS

Respective factors describing the aerodynamic behavior of spherical and non-spherical particles in the inhaled air stream (i.e., Cunningham slip correction factors, dynamic shape factors, equivalent-volume diameters, aerodynamic diameters) were computed. Alveolar deposition of diverse nanomaterials according to several known mechanisms, among which Brownian diffusion and sedimentation play a superior role, was approximated by the use of empirical and analytical formulae. Deposition calculations were conducted with a currently developed program, termed NANODEP, which allows the variation of numerous input parameters with regard to particle geometry, lung morphometry, and aerosol inhalation.

RESULTS

Generally, alveolar deposition of nanoparticles concerned for this study varies between 0.1% and 12.4% during sitting breathing and between 2.0% and 20.1% during heavy-exercise breathing. Prolate particles (e.g., nanotubes) exhibit a significant increase in deposition, when their aspect ratio is enhanced. In contrast, deposition of oblate particles (e.g., nanoplatelets) is remarkably declined with any reduction of the aspect ratio.

CONCLUSIONS

The study clearly demonstrates that alveolar deposition of nanoparticles represents a topic certainly being of superior interest for physicists and respiratory physicians in future.

Theoretical models for the simulation of particle deposition and tracheobronchial clearance in lungs of patients with chronic bronchitis

INTRODUCTION

Based upon theoretical models particle deposition and clearance in human respiratory systems affected by chronic bronchitis can be approximated reliably. As a consequence of those hypothetical results, optimal frame conditions (e.g., inhalation time and volume, particle properties) for inhalation therapies can be determined.

METHODS

Simulation of particle deposition was conducted by modelling a partly or fully obstructed tracheobronchial architecture. Bronchitis-induced reductions of the airway calibres were computed by application of specific scaling factors. Three different scenarios of chronic bronchitis were modelled. Brownian motion, inertial impaction, interception, and gravitational settling were assumed as main deposition forces influencing inhaled particular mass. Tracheobronchial clearance was approximated by application of generation-specific mucus velocities as well as the consideration of a slow bronchial clearance phase, whose half-time varied between 5 and 20 days.

RESULTS

Under different breathing conditions (i.e., sitting and light-work breathing) deposition of submicron and µm-sized particles is significantly enhanced within the bronchial lung region, but also alveolar deposition becomes partly enhanced. By changing the inhalation conditions target sites of therapeutic aerosols may be reached with rather high accuracy. Based on the data of this modified models, particle retention in lung airways of patients suffering from chronic bronchitis may be noticeably prolonged, with 24-hour retention values being increased by up to 50%.

DISCUSSION AND CONCLUSIONS

As exhibited by the results, particle deposition behaviour in lungs affected by chronic bronchitis differs remarkably from that in healthy lungs. These theoretical finds are mostly supported by experimental data. Further, experimental and theoretical deposition results may be used for an estimation of the grade of disease. Tracheobronchial clearance reduces its efficiency with each progress of the disease which increases the probability of bacterial infections in the airways.

Theoretical deposition of nanotubes in the respiratory tract of children and adults

INTRODUCTION

Nanotubes are assumed to contribute to a significant exacerbation of asthma and to enhance the risk of profibrotic effects in lungs being affected by this injury. Therefore, deposition of nanotubes in the lungs of subjects with different ages was subject to a detailed theoretical investigation.

METHODS

Nanoparticle deposition was computed by application of well validated stochastic deposition model, including four main deposition forces (Brownian diffusion, inertial impaction, interception, gravitational settling). Nonspherical particle geometry was considered with the help of the aerodynamic diameter concept. Deposition was calculated for particles with diameters adopting values of 1, 10, and 100 nm as well as aspect ratios of 10, 50, and 100. Lungs of subjects with different ages were generated with the help of scaling factors and allometric functions. Inhalation was uniformly supposed to take place under non-strain conditions (sitting breathing conditions).

RESULTS

Total deposition of nanotubes is significantly increased with proceeding age, with deposition probability being negatively correlated with particle size (diameter and aspect ratio). Whilst extrathoracic deposition is subject to a slight decrease from infants to adults, bronchial/bronchiolar and alveolar depositions are exponentially increased.

DISCUSSION AND CONCLUSIONS

Due to an increase of nanotube deposition with proceeding age infants and children enjoy a certain protection from excessive particle exposure. This circumstance mostly reprieves their lungs from injuries induced by this sort of particles.

Nanotubes in the human respiratory tract - Deposition modeling

Deposition of inhaled single-wall carbon nanotubes (SWCNT) and multi-wall carbon nanotubes (MWCNT) in the respiratory tract was theoretically investigated for various age groups (infants, children, adolescents, and adults). Additionally, possible effects of the inhalative flow rate on nanotube deposition were simulated for adult lungs. Theoretical computations were based on the aerodynamic diameter concept and the assumption of particles being randomly transported through a stochastic (close-to-realistic) lung structure. Deposition of nanotubes was calculated by application of well validated empirical deposition formulae, thereby considering Browian motion, inertial impaction, interception, and sedimentation as main deposition mechanisms acting on the particles. Results of the simulations clearly show that for a given inhalation scenario (sitting breathing) total, bronchial, and acinar nanotube deposition increase with subject's age, whereas extrathoracic deposition is characterized by a decrease from younger to older subjects. According to the data provided by the model, MWCNT, whose aerodynamic diameters exceed those of SWCNT by one order of magnitude, are deposited in specific respiratory compartments to a lower extent than SWCNT. A change of the physical state from sitting to heavy work results in a common decline of bronchial and extrathoracic deposition of nanotubes. Total deposition is slightly increased for SWCNT and moderately decreased for MWCNT, whereas acinar deposition is significantly increased for SWCNT and decreased for MWCNT. Based on the results of this contribution it may be concluded that SWCNT bear a higher potential as health hazards than MWCNT, because they are accumulated in sensitive lung regions with higher doses than MWCNT.

Clearance of carbon nanotubes in the human respiratory tract-a theoretical approach

INTRODUCTION

Theoretical knowledge of carbon nanotube clearance in the human respiratory tract represents an essential contribution to the risk assessment of artificial airborne nanomaterials. Thus, single phases of nanotube clearance were simulated with the help of a theoretical model.

METHODS

In this study, clearance of single-walled carbon nanotubes (SWCNT) and multi-walled carbon nanotubes (MWCNT) was simulated by using a validated mathematical approach that includes all clearance mechanisms known hitherto. Fast mucociliary clearance is approximated by a steady-state steady-flow mucus model, whereas slow clearance mechanisms are modeled by definition of related clearance half-times.

RESULTS

Clearance may be subdivided into three phases, including fast bronchial clearance (mucociliary escalator), slow bronchial clearance (particle uptake by airway macrophages, transcytosis), and alveolar clearance (phagocytosis by alveolar macrophages, endocytosis by alveolar epithelium). According to the clearance model used in this study, mucociliary clearance is completed within the first 24 h after exposure, whereas slow bronchial clearance is characterized by a half-time of 5 d. Alveolar clearance is marked by half-times >100 d. As a result of their different deposition patterns, SWCNT and MWCNT show some discrepancies with regard to their clearance insofar as long SWCNT reside significantly longer in the lungs than MWCNT. This circumstance is among other expressed by higher 24-h, 10-d, and 100-d retentions computed for SWCNT compared to MWCNT.

DISCUSSION AND CONCLUSIONS

Due to their partly high residence times in distal lung regions, carbon nanotubes may bear the potential to act as triggers of inflammatory reactions or fibrotic modifications of the lung structure. Further they may also induce malignant transformations of lung cells, resulting in the development of lung tumours.

Theoretical models of carcinogenic particle deposition and clearance in children's lungs

INTRODUCTION

Deposition and clearance of carcinogenic particles in the lungs of subjects belonging to four different age groups (infants, children, adolescents, and adults) were theoretically investigated. The study is thought to contribute to the improvement of our knowledge concerning the behaviour of inhaled particles in lungs that may be attributed to different stages of development.

METHODS

Particle deposition and clearance were simulated by using a well established stochastic lung model, allowing the generation of nearly realistic scenarios. For the computation of particle deposition all main deposition forces were considered. Additionally, any influences on particle behaviour due to particle geometry were covered by using the aerodynamic diameter concept. Particle clearance was simulated by defining both a fast mucociliary clearance phase and a slow bronchial/alveolar clearance phase, the latter of which is based on previously published models and suggestions.

RESULTS

As clearly provided by the modelling computations, lung deposition of particles with aerodynamic diameters ranging from 1 nm to 10 µm may significantly differ between the studied age groups. Whilst in infants and children most particles are accumulated in the extrathoracic region and in the upper bronchi, in adolescents and adults high percentages of inhaled particular substances may also reach the lower bronchi and alveoli. Although mucus velocities are significantly lower in young subjects compared to the older ones, fast clearance is more efficient in small lungs due to the shorter clearance paths that have to be passed. Slow clearance is commonly characterized by insignificant discrepancies between the age groups.

CONCLUSIONS

From the study presented here it may be concluded that particle behaviour in infants' and children's lungs has to be regarded in a different light with respect to that in adolescents and adults. Although young subjects possess natural mechanisms of protecting their lungs from hazardous aerosols (e.g., expressed by breathing behaviour and lung size), they are much more sensitive to any particle exposure, since particle concentrations per lung tissue area may reach alarming values within a short period of inhalation.

Radioactivity and lung cancer-mathematical models of radionuclide deposition in the human lungs

The human respiratory tract is regarded as pathway for radionuclides and other hazardous airborne materials to enter the body. Radioactive particles inhaled and deposited in the lungs cause an irradiation of bronchial/alveolar tissues. At the worst, this results in a malignant cellular transformation and, as a consequence of that, the development of lung cancer. In general, naturally occurring radionuclides (e.g., (222)Rn, (40)K) are attached to so-called carrier aerosols. The aerodynamic diameters of such radioactively labeled particles generally vary between several nanometers (ultrafine particles) and few micrometers, whereby highest particle fractions adopt sizes around 100 nm. Theoretical simulations of radioactive particle deposition in the human lungs were based on a stochastic lung geometry and a particle transport/deposition model using the random-walk algorithm. Further a polydisperse carrier aerosol (diameter: 1 nm-10 µm, ρ ≈ 1 g cm(-3)) with irregularly shaped particles and the effect of breathing characteristics and certain respiratory parameters on the transport of radioactive particles to bronchial/alveolar tissues were considered. As clearly shown by the results of deposition modeling, distribution patterns of radiation doses mainly depend on the size of the carrier aerosol. Ultrafine (< 10 nm) and large (> 2 µm) aerosol particles are preferentially deposited in the extrathoracic and upper bronchial region, whereas aerosol particles with intermediate size (10 nm-2 µm) may penetrate to deeper lung regions, causing an enhanced damage of the alveolar tissue by the attached radionuclides.

An advanced stochastic model for mucociliary particle clearance in cystic fibrosis lungs

BACKGROUND

A mathematical model describing mucociliary clearance in cystic fibrosis (CF) patients and its development with progressing course of the disease was developed. The approach should support the prediction of the disease state on the basis of measured bronchial clearance efficiencies.

METHODS

The approach is based on the assumption of a steady-state steady-flow mucus transport through the tracheobronchial tree which enables the determination of airway generation-specific mucus velocities by using a measured tracheal mucus velocity and a realistic morphometric dataset of the human lung. Architecture of the tracheobronchial tree was approximated by a stochastic model, reflecting the intra-subject variability of geometric parameters within a given lung generation.

RESULTS

As predicted by the appropriately validated mathematical approach, mucociliary clearance efficiency in CF patients is partly significantly decreased with respect to healthy controls. 24-h retention of patients with mild CF (FEV(1) >70% of predicted) is reduced by 10% compared to healthy subjects, whilst 24-h retention of patients with moderate to severe CF (FEV(1) <70% of predicted) differs by 25% from that of the healthy controls. These discrepancies are further enhanced with continuation of the clearance process.

CONCLUSIONS

The theoretical results lead to the conclusion that CF patients have a higher risk of inhaled particle accumulation and related particle overload in specific lung compartments than healthy subjects.

Radon lung dosimetry models

Two different modelling approaches are currently used to calculate short-lived radon progeny doses to the lungs: the semi-empirical compartment model proposed by the International Commission on Radiological Protection and deterministic and stochastic airway generation models. The stochastic generation model IDEAL-DOSE simulates lung morphometry, transport, deposition and clearance of inhaled radionuclides, and cellular dosimetry by Monte Carlo methods. Specific dosimetric issues addressed in this paper are: (1) distributions of bronchial doses among and within bronchial airway generations; (2) relative contributions of radon progeny directly deposited in a given airway generation and those passing through from downstream generations to the bronchial dose in that generation; (3) distribution of bronchial doses among the five lobes of the human lung; (4) inhomogeneity of surface activities and resulting doses within bronchial airway bifurcations; (5) comparison of bronchial doses between non-smokers and smokers; (6) relative contributions of sensitive target cells in bronchial epithelium to lung cancer induction and (7) intra- and intersubject variations of bronchial doses.

Modeling intersubject variability of bronchial doses for inhaled radon progeny

The main sources of intersubject variations considered in the present study were: (1) size and structure of nasal and oral passages, affecting extrathoracic deposition and, in further consequence, the fraction of the inhaled activity reaching the bronchial region; (2) size and asymmetric branching of the human bronchial airway system, leading to variations of diameters, lengths, branching angles, etc.; (3) respiratory parameters, such as tidal volume, and breathing frequency; (4) mucociliary clearance rates; and (5) thickness of the bronchial epithelium and depth of target cells, related to airway diameters. For the calculation of deposition fractions, retained surface activities, and bronchial doses, parameter values were randomly selected from their corresponding probability density functions, derived from experimental data, by applying Monte Carlo methods. Bronchial doses, expressed in mGy WLM-1, were computed for specific mining conditions, i.e., for defined size distributions, unattached fractions, and physical activities. Resulting bronchial dose distributions could be approximated by lognormal distributions. Geometric standard deviations illustrating intersubject variations ranged from about 2 in the trachea to about 7 in peripheral bronchiolar airways. The major sources of the intersubject variability of bronchial doses for inhaled radon progeny are the asymmetry and variability of the linear airway dimensions, the filtering efficiency of the nasal passages, and the thickness of the bronchial epithelium, while fluctuations of the respiratory parameters and mucociliary clearance rates seem to compensate each other.

Lung dosimetry for inhaled radon progeny in smokers

Cigarette smoking may change the morphological and physiological parameters of the lung. Thus the primary objective of the present study was to investigate to what extent these smoke-induced changes can modify deposition, clearance and resulting doses of inhaled radon progeny relative to healthy non-smokers (NSs). Doses to sensitive bronchial target cells were computed for four categories of smokers: (1) Light, short-term (LST) smokers, (2) light, long-term (LLT) smokers, (3) heavy, short-term (HST) smokers and (4) heavy, long-term (HLT) smokers. Because of only small changes of morphological and physiological parameters, doses for the LST smokers hardly differed from those for NSs. For LLT and HST smokers, even a protective effect could be observed, caused by a thicker mucus layer and increased mucus velocities. Only in the case of HLT smokers were doses higher by about a factor of 2 than those for NSs, caused primarily by impaired mucociliary clearance, higher breathing frequency, reduced lung volume and airway obstructions. These higher doses suggest that the contribution of inhaled radon progeny to the risk of lung cancer in smokers may be higher than currently assumed on the basis of NS doses.

A theoretical approach to the deposition and clearance of fibers with variable size in the human respiratory tract

In the study presented here, a mathematical approach for the deposition and clearance of rigid and chemically stable fibers in the human respiratory tract (HRT) is described in detail. For the simulation of fiber transport and deposition in lung airways an advanced concept of the aerodynamic diameter is applied to a stochastic lung model with individual particle trajectories computed according to a random walk algorithm. Interception of fibrous material at airway bifurcations is considered by implementation of correction factors obtained from previously published numerical approaches to fiber deposition in short bronchial sequences. Fiber clearance is simulated on the basis of a multicompartment model, within which separate clearance scenarios are assumed for the alveolar, bronchiolar, and bronchial lung region and evacuation of fibrous material commonly takes place via the airway and extrathoracic path to the gastrointestinal tract (GIT) or via the transepithelial path to the lymph nodes and blood vessels. Deposition of fibrous particles in the HRT is controlled by the fiber aspect ratio beta in as much as particles with diameters <0.1 microm deposit less effectively with increasing beta, while larger particles exhibit a positive correlation between their deposition efficiencies and beta. A change from sitting to light-work breathing conditions causes only insignificant modifications of total fiber deposition in the HRT, whereas alveolar and, above all, tubular deposition of fibrous particles with a diameter >or=0.1 microm are affected remarkably. For these particles enhancement of the inhalative flow rate results in an increase of the extrathoracic and bronchial deposition fractions. Concerning the clearance of fibers from the HRT, 24-h retention is noticeably influenced by beta and, not less important, by the preferential deposition sites of the simulated particles. The significance of beta with respect to particle size may be regarded as similar to that determined for the deposition scenarios, while breathing conditions do not have a valuable effect on clearance.

Stochastic modeling predictions for the clearance of insoluble particles from the tracheobronchial tree of the human lung

Bronchial clearance of deposited particles was simulated using a stochastic model of the tracheobronchial tree. The clearance model introduced in this study considers (1) a continuous decrease of the mucus thickness from the trachea to the terminal bronchioles according to a linear or an exponential function, (2) the possibility of mucus discontinuities, which are mainly found in intermediate and distal airways of the tracheobronchial compartment, (3) mucus production in proximal airways, (4) a slow bronchial clearance phase due to the capture of a defined particle fraction f (s) in the periciliary sol phase, and (5) an eventual delay of the mucociliary transport at carinal ridges of airway bifurcations. Based on the concept of mucus volume conservation in single bifurcations, a reduction of the thickness of the mucus blanket from proximal to distal airways causes a significant increase of the mucus velocities in small ciliated airways compared to other stochastic modeling predictions assuming a constant thickness of the mucus layer throughout the conducting airways. This effect is further enhanced by the consideration of mucus discontinuities. In contrast, the ability of bronchial airways to produce a certain volume of mucus has a decreasing effect on the mucus velocities. In all generated clearance velocity models, mucociliary clearance is completely terminated within 24 h after exposure, consistent with the experimental evidence. Implementation of a slow bronchial clearance phase predicts a long-term retention fraction, which is fully cleared from the lung after several weeks. For 1-microm MMAD particles, 24-h retention varies between 0.42 and 0.52, in line with the suggestions of the ICRP. Mucus delay at carinal ridges only affects short-term clearance by increasing the retained particle fraction at a given time, while long-term retention is not influenced.