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In this paper we present a general procedure for designing higher strong order methods for linear Itô stochastic differential equations on matrix Lie groups and illustrate this strategy with two novel schemes that have a strong convergence order of 1.5. Based on the Runge–Kutta–Munthe–Kaas (RKMK) method for ordinary differential equations on Lie groups, we present a stochastic version of this scheme and derive a condition such that the stochastic RKMK has the same strong convergence order as the underlying stochastic Runge–Kutta method. Further, we show how our higher order schemes can be applied in a mechanical engineering as well as in a financial mathematics setting.

To develop a stochastic five-lobe lung model and to compute particle deposition fractions in the five lobes, considering anatomical as well as ventilatory asymmetry.The stochastic five-lobe lung model was derived from an existing stochastic model for the whole lung, which implicitly contains information on the lobar airway structure. Differences in lobar ventilation and sequential filling of individual lobes were simulated by a stochastic lobar ventilation model. Deposition fractions of inhaled unit density particles in the five lobes were calculated by an updated version of the Monte Carlo deposition code Inhalation, Deposition, and Exhalation of Aerosols in the Lung (IDEAL).Simulations for defined exposure and breathing conditions revealed that the two lower lobes receive higher deposition and the two upper lobes lower deposition, compared to the average deposition for the whole lung. The resulting inter-lobar distribution of deposition fractions indicated that the non-uniform lung morphometry is the dominating effect, while non-uniform ventilation only slightly enhances the lobar differences. The relation between average lobe-specific deposition fractions and corresponding average values for the whole lung allowed the calculation of lobe-specific deposition weighting factors.Comparison with limited deposition measurements for upper

Electronic cigarette (EC) aerosols are typically composed of a mixture of nicotine, glycerine (VG), propylene glycol (PG), water, acidic stabilizers and a variety of flavors. Inhalation of e-cigarette aerosols is characterized by a continuous modification of particle diameters, concentrations, composition and phase changes, and smoker-specific inhalation conditions, i.e. puffing, mouthhold and bolus inhalation. The dynamic changes of inhaled e-cigarette droplets in the lungs due to coagulation, conductive heat and diffusive heat/convective vapor transport and particle phase chemistry are described by the Aerosol Dynamics in Containment (ADiC) model. For the simulation of the variability of inhaled particle and vapor deposition, the ADiC model is coupled with the IDEAL Monte Carlo code, which is based on a stochastic, asymmetric airway model of the human lung. We refer to the coupled model as "IDEAL/ADIC_v1.0". In this study, two different ecigarettes were compared, one without any acid ("no acid") and the other one with an acidic regulator (benzoic acid) to establish an initial pH level of about 7 ("lower pH"). Corresponding deposition patterns among human airways comprise total and compound-specific number and mass deposition fractions, distinguishing between inhalation and exhalation phases and condensed and vapor phases. Note that the inhaled EC aerosol is significantly modified in the oral cavity prior to inhalation into the lungs. Computed deposition fractions demonstrate that total particle mass is preferentially deposited in the alveolar region of the lung during inhalation. While nicotine deposits prevalently in the condensed phase for the "lower pH" case, vapor phase deposition is dominating the "no acid" case. The significant statistical fluctuations of the particle and vapor deposition patterns illustrate the inherent anatomical variability of the human lung structure.

The purpose of the present work is the implementation of the aerosol dynamics model ADiC, specifically its heat/vapor transport and phase transition components, into the stochastic lung deposition model IDEAL. The combined ADiC/IDEAL model allows the simultaneous calculation of relative humidity, hygroscopic growth and deposition of inhaled NaCl aerosols in individual airways of the human lung along randomly selected particle paths and randomly selected times during the inhalation phase. Hygroscopic growth decreases deposition of submicron particles compared to hydrophobic particles with equivalent diameters due to a less efficient diffusion mechanism, while the more efficient impaction and sedimentation mechanisms increase total deposition for micrometer particles. Due to the variability and asymmetry of the human airway system, individual trajectories of inhaled particles are associated with individual growth factors. For a realistic breathing scenario, particles are inhaled at different times during the inspiratory phase and hence experience individual growth factors, thereby further enhancing the variability of individual growth factors and resulting deposition patterns. While nanometer particles adopt their equilibrium growth factor value already within the mouth and pharynx/larynx during the inspiratory phase, micrometer particles approach this value at the end of inspiration, thus further increasing in size during the exhalation phase. In summary, individual hygroscopic growth factors vary for different paths and different inhalation times. For model validation purposes, theoretical predictions were compared with human experimental deposition data and previous hygroscopic growth model simulations for total deposition of ultrafine and micrometer-sized NaCl particles.

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.

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.

The transfer of radon from thermal water via the skin to different human organs in radon therapy can experimentally be determined by measuring the radon activity concentration in the exhaled air. In this study, six volunteers were exposed to radon-rich thermal water in a bathtub, comprising eleven measurements. Exhaled activity concentrations were measured intermittently during the 20 min bathing and 20 min resting phases. Upon entering the bathtub, the radon activity concentration in the exhaled breath increased almost linearly with time, reaching its maximum value at the end of the exposure, and then decreased exponentially with time in the subsequent resting phase. Although for all individuals the time-dependence of exhaled radon activity was similar during bathing and resting, significant inter-subject variations could be observed, which may be attributed to individual respiratory parameters and body characteristics. The simulation of the transport of radon through the skin, its distribution among the organs, and the subsequent exhalation via the lungs were based on the biokinetic model of Leggett and co-workers, extended by a skin and a subcutaneous fat compartment. The coupled linear differential equations describing the radon activity concentrations in different organs as a function of time were solved numerically with the program package Mathcad. An agreement between model simulations and experimental results could only be achieved by expressing the skin permeability coefficient and the arterial blood flow rates as a function of the water temperature and the swelling of the skin.

The Aerosol Dynamics in Containments (ADiC) model describes the dynamic changes of inhaled cigarette smoke droplets during puffing, mouth-hold, and inspiration and expiration, considering coagulation, phase transition, conductive heat and diffusive/convective vapor transport, and dilution/mixing. The ADiC model has been implemented into a single path representation of the stochastic lung dosimetry model IDEAL to compute particulate phase deposition as well as vapor phase deposition in the airway generations of the human lung. In the present study, the ADiC model has been applied to the inhalation of combustible and electronic cigarette aerosols. Aerosol dynamics processes significantly influence the physical properties of particle and vapor phase in the human respiratory tract: (i) number reduction of inhaled aerosol particles is caused primarily by coagulation and less by deposition for both aerosols; (ii) hygroscopic growth rates are higher for e-cigarettes than for combustible cigarettes; (iii) the effect of particle growth on deposition leads to a lower total deposition in the case of cigarette smoke particles and a higher total deposition in the case of e-cigarette droplets relative to their initial size distributions; and, (iv) most of the nicotine is deposited by the vapor phase for both aerosols.

The mouse lung has become increasingly important as a surrogate of the human lung for inhalation risk assessment. The main structural difference between the two lungs is that the airway branching of the human lung is relatively symmetric, while that of the mouse lung is distinctly asymmetric or monopodial. The objectives of this study were to develop a stochastic, asymmetric particle deposition model for the Balb/c mouse and to compare predicted deposition patterns with those in the human lung. The asymmetric bronchial airway geometry of the Balb/c mouse was based on a statistical analysis of several lung casts, while, in the absence of pertinent data, the asymmetric acinar airway geometry was represented by an allometrically scaled-down version of the rat acinar region, assuming structural similarity. Deposition of inhaled particles in nasal, bronchial and acinar airways for mouse-specific breathing conditions was computed with the Monte Carlo deposition model IDEAL-mouse. While total deposition for submicron particles decreases with increasing diameter in a fashion similar to that in the human lung, the effect of inhalability and nasal pre-filtration significantly reduces total deposition in the mouse lung for particles with diameters greater than about 3 μm. The most notable difference between submicron particle deposition in the mouse and human airways is the shift of the deposition distribution from distal airway generations in the human lung to upper airway generations in the mouse lung. However, if plotted as a function of airway diameter, both deposition distributions are quite similar, indicating that airway diameter may be a more appropriate morphometric parameter for extrapolation purposes than airway generation.

In the Gastein valley, numerous facilities use radon for the treatment of various diseases either by exposure to radon in air or in radon rich thermal water. In this study, six test persons were exposed to radon thermal water in a bathtub and the time-dependent radon activity concentration in the exhaled air was recorded. At temperatures between 38°C and 40°C, the radon activity concentration in the water was about 900 kBq/m3 in a total volume of 600 l, where the patients were exposed for 20 min, while continuously sampling the exhaled air during the bathing and 20 min thereafter. After entering the bath, the exhaled radon activity concentration rapidly increased, reaching some kind of saturation after 20 min exposure. The radon activity concentration in the exhaled air was about 8000 Bq/m3 at the maximum, with higher concentrations for male test persons. The total radon transfer from water to the exhaled air was between 480 and 1000 Bq, which is equivalent to 0.08% and 0.2% of the radon in the water.

Inhaled hygroscopic aerosols will absorb water vapor from the warm and humid air of the human lung, thus growing in size and consequently changing their deposition properties.The objectives of the present study are to study the effect of a stochastic lung structure on individual particle growth and related deposition patterns and to predict local deposition patterns for different hygroscopic aerosols.The hygroscopic particle growth model proposed by Ferron et al. has been implemented into the stochastic asymmetric lung deposition model IDEAL. Deposition patterns were calculated for sodium chloride (NaCl), cobalt chloride (CoCl2 · 6H2O), and zinc sulfate (ZnSO4 · 7H2O) aerosols, representing high, medium and low hygroscopic growth factors.Hygroscopic growth decreases deposition of submicron particles compared to hydrophobic particles with equivalent diameters due to a less efficient diffusion mechanism, while the more efficient impaction and sedimentation mechanisms increase total deposition for micron-sized particles. Due to the variability and asymmetry of the human airway system, individual trajectories of inhaled particles are associated with individual growth factors, thereby enhancing the variability of the resulting deposition patterns.Comparisons of model predictions with several experimental data for ultrafine and micrometer-sized particles indicate good agreement, considering intersubject variations of morphometric parameters as well as differences between experimental conditions and modeling assumptions.

The primary objectives of the present study were to mathematically describe particle coagulation within the human respiratory tract and to analyze its impact on local particle deposition patterns for high concentrations of inhaled cigarette smoke particles. Coagulation mechanisms simulated were thermal motion, gravitational settling, laminar shear, turbulences, electrical charges, and inertial effects at airway bifurcations. To implement concentration dependent coagulation processes, the Lagrangian random walk deposition model IDEAL, simulating the paths of an individual particle, was modified by tracking the random path of an elemental air volume containing the full size distribution, thus adding an Eulerian element to the Lagrangian random path model. In this combined Lagrangian/Eulerian deposition model, the initial size distribution is continuously modified by coagulation, hygroscopic growth and deposition. For the specific inhalation conditions and the cigarette smoke size distribution assumed in this study, thermal diffusion is by far the greatest source of coagulation, with a minor contribution of laminar shear in peripheral airway generations. Number deposition, which comprises the loss of inhaled particles not only by deposition but also by coagulation, and mass deposition fractions were computed for different puff and breath-hold scenarios as a function of lung generation numbers. The main reduction of the number of inhaled particles in the respiratory tract occurs in the mouth due to coagulation, accompanied by a significant shift of the size distribution to larger particle diameters. In the lung, particle loss is caused primarily by deposition due to diffusion with a preferential deposition of smaller particle diameters. In the size range from about 250 to 500 nm, the number concentration of particles in the exhaled air is higher than that in the inhaled air, indicating that the production of particles in this size range by coagulation is greater than the loss by coagulation to larger sizes and deposition.

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.

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.

We consider stochastic Runge-Kutta methods for Ito stochastic ordinary differential equations, and study their mean-square convergence properties for problems with small multiplicative noise or additive noise. First we present schemes where the drift part is approximated by well-known methods for deterministic ordinary differential equations, and a Maruyama term is used to discretize the diffusion. Further, we suggest improving the discretization of the diffusion part by taking into account also mixed classical-stochastic integrals, and we present a suitable class of fully derivative-free methods. We show that the relation of the applied step-sizes to the smallness of the noise is essential to decide whether the new methods are worth the effort. Simulation results illustrate the theoretical findings.

Total deposition of petrol and diesel combustion aerosols and environmental tobacco smoke (ETS) particles in the human respiratory tract for nasal breathing conditions was computed for 14 nonsmoking volunteers, considering the specific pulmonary function parameters of each volunteer and the specific size distribution for each inhalation experiment. Theoretical predictions were 34.6% for petrol smoke, 24.0% for diesel smoke, and 18.5% for ETS particles. Compared to the experimental results, predicted deposition values were consistently smaller than the measured data (41.4% for petrol smoke, 29.6% for diesel smoke, and 36.2% for ETS particles). The apparent discrepancy between experimental data on total deposition and modeling results may be reconciled by considering the nonspherical shape of the test aerosols by diameter-dependent dynamic shape factors to account for differences between mobility-equivalent and volume-equivalent or thermodynamic diameters. While the application of dynamic shape factors is able to explain the observed differences for petrol and diesel combustion particles, additional mechanisms may be required for ETS particle deposition, such as the size reduction upon inspiration by evaporation of volatile compounds and/or condensation-induced restructuring, and, possibly, electrical charge effects.

The paper consists of two parts. In the first part of the paper, we proposed a procedure to estimate local errors of low order methods applied to solve initial value problems in ordinary differential equations (ODEs) and index-1 differential-algebraic equations (DAEs). Based on the idea of Defect Correction we developed local error estimates for the case when the problem data is only moderately smooth, which is typically the case in stochastic differential equations. In this second part, we will consider the estimation of local errors in context of mean-square convergent methods for stochastic differential equations (SDEs) with small noise and index-1 stochastic differential-algebraic equations (SDAEs). Numerical experiments illustrate the performance of the mesh adaptation based on the local error estimation developed in this paper.

Endosialin (Tem1) has been identified by two independent experimental approaches as an antigen of tumor-associated endothelial cells, and it has been claimed to be the most abundantly expressed tumor endothelial antigen, making it a prime candidate for vascular targeting purposes. Recent experiments have challenged the endothelial expression of endosialin and suggested an expression by activated fibroblasts and pericytes. Thus, clarification of the controversial cellular expression of endosialin is critically important for an understanding of its role during tumor progression and its validation as a potential therapeutic target. We have therefore performed extensive expression profiling analyses of endosialin. The experiments unambiguously demonstrate that endosialin is expressed by tumor-associated myofibroblasts and mural cells and not by endothelial cells. Endosialin expression is barely detectable in normal human tissues with moderate expression only detectable in the stroma of the colon and the prostate. Corresponding cellular experiments confirmed endosialin expression by mesenchymal cells and indicated that it may in fact be a marker of mesenchymal stem cells. Silencing endosialin expression in fibroblasts strongly inhibited migration and proliferation. Collectively, the experiments validate endosialin as a marker of tumor-associated myofibroblasts and tumor vessel-associated mural cells. The data warrant further functional analysis of endosialin during tumor progression and its exploitation as marker of tumor vessel-associated mural cells, expression of which may reflect the non-normalized phenotype of the tumor vasculature.

In this article the numerical approximation of solutions of Ito stochastic delay differential equations is considered. We construct stochastic linear multi-step Maruyama methods and develop the fundamental numerical analysis concerning their 𝕃 p -consistency, numerical 𝕃 p -stability and 𝕃 p -convergence. For the special case of two-step Maruyama schemes we derive conditions guaranteeing their mean-square consistency.

In order to investigate the degree of dose uncertainty produced by different models, three dosimetry models were compared with each other, representing different classes of models: (i) The RADEP/IMBA model based on the ICRP Human Respiratory Tract Model, a deterministic regional compartment model, (ii) the RADOS model, a deterministic airway generation model and (iii) the IDEAL dosimetry model, a stochastic airway generation model. The outputs of the three models for defined mining exposure conditions were compared at three different levels: deposition fractions for attached and unattached radon progeny; nuclear transformations, reflecting the combined effect of deposition and clearance; and resulting cellular doses. Resulting dose exposure conversion factors ranged from 7.8 (median) mSv/WLM (IDEAL) to 11.8 mSv/WLM (RADEP/IMBA), with 8.3 mSv/WLM (RADOS) as an intermediate value. Despite methodological and computational differences between the three models, resulting dose conversion factors do not appreciably differ from each other, although predictions by the two generation models are consistently smaller than that for the RADEP/IMBA model.

For radiation protection purposes, the relative contributions of bronchial (BB), bronchiolar (bb) and alveolar-interstitial (AI) doses to lung cancer risk are represented by their corresponding apportionment factors. The current assumption of equal apportionment factors can be tested by comparing different radon and thoron progeny exposures, which produce different regional dose distributions, with the pathologically observed regional cancer distributions: (1) radon progeny inhalation, (2) thoron progeny inhalation, (3) thoron and thoron progeny exhalation (Thorotrast patients) and (4) RP inhalation in rats, and cigarette smoke inhalation as smoking is the dominant cause of lung cancer. Comparison with the pathologically observed regional cancer distributions suggests (1) a smaller apportionment factor for the AI region as compared with BB and bb regions and (2) a higher value for the BB region relative to that for the bb region.

Sensitive basal and secretory cells receive a wide range of doses in human bronchial and bronchiolar airways. Variations of cellular doses arise from the location of target cells in the bronchial epithelium of a given airway and the asymmetry and variability of airway dimensions of the lung among airways in a given airway generation and among bronchial and bronchiolar airway generations. To derive a single value for the average lung dose which can be related to epidemiologically observed lung cancer risk, appropriate weighting scenarios have to be applied. Potential biological weighting parameters are the relative frequency of target cells, the number of progenitor cells, the contribution of dose enhancement at airway bifurcations, the promotional effect of cigarette smoking and, finally, the application of appropriate regional apportionment factors. Depending on the choice of weighting parameters, detriment-weighted average lung doses can vary by a factor of up to 4 for given radon progeny exposure conditions.

The paper consists of two parts. In the first part, we propose a procedure to estimate local errors of low order methods applied to solve initial value problems in ordinary differential equations (ODEs) and index 1 differential-algebraic equations (DAEs). Based on the idea of defect correction we develop local error estimates for the case when the problem data is only moderately smooth. Numerical experiments illustrate the performance of the mesh adaptation based on the error estimation developed in this paper. In the second part of the paper, we will consider the estimation of local errors in context of stochastic differential equations with small noise.

We deal with linear multi-step methods for SDEs and study when the numerical approximation shares asymptotic properties in the mean-square sense of the exact solution. As in deterministic numerical analysis we use a linear time-invariant test equation and perform a linear stability analysis. Standard approaches used either to analyse deterministic multi-step methods or stochastic one-step methods do not carry over to stochastic multi-step schemes. In order to obtain sufficient conditions for asymptotic mean-square stability of stochastic linear two-step-Maruyama methods we construct and apply Lyapunov-type functionals. In particular we study the asymptotic mean-square stability of stochastic counterparts of two-step Adams–Bashforth- and Adams–Moulton-methods, the Milne–Simpson method and the BDF method.

We consider linear multi-step methods for stochastic differential equations and present a theorem ensuring their numerical stability and strong convergence. We use this to study the properties of two-step schemes for stochastic differential equations with small noise. (© 2004 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

This paper deals with periodic index-2 differential algebraic equations and the question whether a periodic solution is stable in the sense of Lyapunov. As the main result, a stability criterion is proved. This criterion is formulated in terms of the original data so that it may be used in practical computations.

Cave therapy is an efficient therapeutic method to cure asthma, but the exact healing effect has not yet been clarified. This study was motivated by the basic assumption that aerosols may play a key role in cave therapy. Aerosol particles were collected in a therapeutic cave in Budapest, Hungary (Szemlohegyi cave) at different locations arranged for the therapeutic treatment. Samples were further analysed by EPMA and XRF for chemical composition and morphology, determining the particle number distribution and classifying them according to their elemental composition. Three particle classes were determined based on major element concentrations: aluminosilicate, quartz and calcium carbonate. The combination of single-particle EPMA and XRF resulted in relevant chemical information that could be used further for lung deposition modelling, namely the diameter and the number distribution to calculate the deposition probability, and the concentration of the element within a particle class necessary for the estimation of the deposited dose. The final results for the health effect study are the deposition efficiencies and deposition patterns of inhaled cave aerosols. The results of the stochastic deposition model showed that roughly 41% of the inhaled particles are deposited in the lung. From this amount, around 39% are deposited within airway generations 6–15, which is the most infected area in an asthmatic lung. The explanation of the healing effects might be based on the presented dose calculations. Copyright © 2002 John Wiley & Sons, Ltd.

Elemental composition and mass size distribution of cave aerosols were determined by PIXE on seven-stage cascade impactor samples collected in two different sites of the Szemlőhegy-cave, a speleotherapeutic cave situated below Budapest, Hungary. In addition, individual particle analysis was also performed on about 450 aerosol particles. Significant differences were found between the two sampling sites and also in comparison with the external air in both the size distribution and in the composition of the aerosol. On the basis of the obtained data a stochastic lung deposition model was used to calculate total and regional deposition efficiencies of the different types of particles along the human respiratory system. One can conclude that the extrathoracic deposition is quite significant and its role increasing with increasing respiratory minute volume. The regional thoracic deposition is not very sensitive to the size distribution and it has a maximum around the 15–20th airway generations.

The computation of cellular doses requires the development of four interrelated models: (i) morphometric models of the human airway system; (ii) models for radon progeny deposition in bronchial airways; (iii) models for particle clearance in bronchial airways; and (iv) dosimetric models for energy deposition in sensitive target cells in bronchial epithelium. This study focuses on the effects of different modeling concepts and mechanisms resulting to cellular doses for each of the above model categories rather than on parameter variations. For example, several morphometric lung models have been published which differ in terms of airway structure and lung volume, thereby affecting the particle deposition efficiencies. Likewise, different mechanisms of particle clearance in bronchial airways have been proposed, such as fast mucociliary clearance and a slow macrophage-mediated clearance. The present comparison of a variety of modeling concepts suggests that the choice of specific modeling assumptions is as important for dose calculations as the choice of proper parameter values. Since some of the models and mechanisms analysed in the present study differ from those employed in the recent ICRP model, dose estimates will consequently differ from ICRP predictions. Indeed, the dosimetry model presented here predicts a weighted effective dose of 7.6 (6.2) mSv/WLM for indoor exposure conditions, as compared to 14.5 mSv/WLM based on the ICRP model. Thus, considering the inherent uncertainties in modeling assumptions and epidemiological analysis, dosimetric estimates do not differ appreciably from the epidemiologically derived dose convention of about 4 mSv/WLM.

The morphological variability in human lungs was simulated by 10 multiple-path lung models, generated on the basis of probability distributions and correlations of airway parameters provided by the stochastic lung model of Koblinger and Hofmann (Phys. Med. Biol. 30 (1985) 541). Total, regional and generation-per-generation deposition was computed for particle sizes in the range of 0.01– 10 μm under resting breathing conditions. Our calculations suggest that structural and volumetric differences of lung morphologies among different individuals are primarily responsible for the experimentally observed intersubject variability in total and regional deposition under controlled breathing conditions. Individual differences in deposition among single airways can be substantially larger than those in total and regional deposition. Furthermore, variations are most pronounced for small (0.01 μm ) and large (10 μm ) particles.

Elemental mass size distributions were experimentally determined in atmospheric aerosols collected at four different locations in Budapest, Hungary, comprising a urban background site, two downtown sites and a road tunnel. Based on these distributions, deposition fractions for the various elements in the respiratory system were calculated for a healthy Caucasian adult male, female and 5-year-old child under sitting breathing conditions by a stochastic lung deposition model. The highest deposition values were observed in the extrathoracic region regardless of subject's age and gender, and chemical species and size distributions. Deposition in the tracheobronchial tree and acinar region was much smaller than that in the extrathoracic region. Variations in the deposition fractions due to differences in the size distributions were really significant only in the extrathoracic region. Surprisingly, the different size distributions yielded similar depositions in the thoracic region for a given gender as far as the shape of the deposition curve and the total amount are concerned. Regional deposition fractions were compared for the male, female and child, and for various size distributions (sampling location) and elements.

Local stability of periodic solutions is established by means of a Floquet theory for index-1 differential algebraic equations. Linear differential algebraic equations with periodic coefficients are considered in detail, and a natural notion of the monodromy matrix is obtained that generalizes the well-known theory for regular ordinary differential equations.

Deposition fractions of inhaled particles predicted by different computational models vary with respect to physical and biological factors and mathematical modeling techniques. These models must be validated by comparison with available experimental data. Experimental data supplied by different deposition studies with surrogate airway models or lung casts were used in this study to evaluate the stochastic deposition model Inhalation, Deposition and Exhalation of Aerosols in the Lung at the airway generation level. Furthermore, different analytical equations derived for the three major deposition mechanisms, diffusion, impaction, and sedimentation, were applied to different cast or airway models to quantify their effect on calculated particle deposition fractions. The experimental results for ultrafine particles (0.00175 and 0.01) were found to be in close agreement with the stochastic model predictions; however, for coarse particles (3 and 8 mm), experimental deposition fractions became higher with increasing flow rate. An overall fair agreement among the calculated deposition fractions for the different cast geometries was found. However, alternative deposition equations resulted in up to 300% variation in predicted deposition fractions, although all equations predicted the same trends as functions of particle diameter and breathing conditions. From this comparative study, it can be concluded that structural differences in lung morphologies among different individuals are responsible for the apparent variability in particle deposition in each generation. The use of different deposition equations yields varying deposition results caused primarily by (i) different lung morphometries employed in their derivation and the choice of the central bifurcation zone geometry, (ii) the assumption of specific flow profiles, and (iii) different methods used in the derivation of these equations.

The current version of the stochastic lung dosimetry model IDEAL-DOSE considers deposition in the whole tracheobronchial (TB) and alveolar airway system, while clearance is restricted to TB airways. For the investigation of doses produced by inhaled long-lived radionuclides (LLR) together with short-lived radon progeny, alveolar clearance has to be considered. Thus, present dose calculations are based on the average transport rates proposed for the revision of the ICRP human respiratory tract model. The results obtained indicate that LLR cleared from the alveolar region can deliver up to two to six times higher doses to the TB region when compared with the doses from directly deposited particles. Comparison of LLR doses with those of short-lived radon progeny indicates that LLR in uranium mines can deliver up to 5 % of the doses predicted for the short-lived radon daughters.

Noise in electronic components is a random phenomenon that can adversely affect the desired operation of a circuit. Transient noise analysis is designed to consider noise effects in circuit simulation. Taking noise into account by means of Gaussian white noise currents, mathematical modelling leads to stochastic differential algebraic equations (SDAEs) with a large number of small noise sources. Their simulation requires an efficient numerical time integration by mean-square convergent numerical methods. As efficient approaches for their integration we discuss adaptive linear multi-step methods, together with a new step-size and path selection control strategy. Numerical experiments on industrial real-life applications illustrate the theoretical findings.

Cigarette smoking may, change the morphological and physiological parameters of file lung. Thus file 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 or inhaled radon progeny to the risk of lung cancer in smokers, May be higher than currently, assumed on the basis of NS doses.

Transient noise analysis means time domain simulation of noisy electronic circuits. We consider mathematical models where the noise is taken into account by means of sources of Gaussian white noise that are added to the deterministic network equations, leading to systems of stochastic differential algebraic equations (SDAEs). A crucial property of the arising SDAEs is the large number of small noise sources that are included. As efficient means of their integration we discuss adaptive linear multi-step methods, in particular stochastic analogues of the trapezoidal rule and the two-step backward differentiation formula, together with a new step-size control strategy. Test results including real-life problems illustrate the performance of the presented methods.

Stochastic differential algebraic equations (SDAEs) arise as a mathematical model for electrical network equations that are influenced by additional sources of Gaussian white noise. In this paper we discuss adaptive linear multistep methods for the numerical integration of SDAEs, in particular stochastic analogues of the trapezoidal rule and the two-step backward differentiation formula, together with a new step-size control strategy. Test results illustrate the performance of the presented methods.

Deposition fractions in human airway generations were computed with a stochastic deposition model, which is based on a randomly, asymmetrically dividing lung morphology, applying Monte Carlo techniques. Corresponding uncorrelated surface deposition densities were obtained by dividing the average deposition fraction in a given generation by the average total surface area of that generation. In order to consider the statistical correlation between deposition probability and linear airway dimensions in each airway, correlated surface deposition densities were calculated by dividing the deposition fraction in a randomly selected bronchial or acinar airway by the surface area of that airway and by the total number of bronchial or acinar airways in that generation. Average surface deposition densities are relatively constant throughout bronchial airway generations, while average acinar surface deposition densities exhibit a distinct decrease with rising penetration into the acinar region. Due to the correlation between deposition fraction and surface area in a given airway generation, average correlated surface deposition densities are consistently higher than average uncorrelated densities, particularly in the acinar region, where differences can be as high as a few orders of magnitude. Already significant statistical fluctuations of the deposition fractions in individual airway generations are even exacerbated for surface deposition densities, with coefficients of variation about twice as high as for correlated deposition fractions.

Spherical monodisperse ferromagnetic iron oxide particles of 1.9-microm geometric and 4.2-microm aerodynamic diameter were inhaled by 13 healthy nonsmoking subjects using the shallow bolus technique. The bolus width was 100 ml, and the penetration front depth was 150 +/- 27 ml. The mean flow rate during inhalation and exhalation was 250 ml/s. The Fowler dead space and the phase 1 dead space of the airways were 282 +/- 49 and 164 +/- 34 ml, respectively. Deposition was below 20% without breath holding and 51 +/- 8% after an 8-s breath-holding time. We attempted to confine the bolus deposition to the bronchial airways by limiting the bolus front depth to the phase 1 dead space volume. Particle retention was measured by the magnetopneumographic method over a period of 9 mo. Particle clearance from the airways showed a fast and a slow phase; 49 +/- 9% followed the fast phase with a mean half-time of 3.0 +/- 1.6 h and characterized the mucociliary clearance. The remaining fraction was cleared slowly with a half-time of 109 +/- 78 days. The slow clearance phase was comparable to clearance measurements from the lung periphery of healthy nonsmokers, which allowed macrophage-dependent clearance mechanisms of the slow cleared fraction to be taken into account. Despite the fact that part of the slowly cleared particles may originate from peripheral deposition, the data demonstrate that mucociliary clearance does not remove all particles deposited in the airways and that a significant fraction undergoes long-term retention mechanisms, the origin of which is still under discussion.

In this paper we describe how stochastic differential-algebraic equations (SDAEs) arise as a mathematical model for network equations that are influenced by additional sources of Gaussian white noise. We give the necessary analytical theory for the existence and uniqueness of strong solutions, provided that the systems have noise-free constraints and are uniformly of DAE-index 1. We express these conditions in terms of the network-topology for reasons of use within a circuit simulator. In the second part we analyze discretization methods. Due to the differential-algebraic structure, implicit methods will be necessary. By the examples of the drift-implicit Euler and Milstein schemes we show how drift-implicit schemes for SDEs can be adapted to become directly applicable to stochastic DAEs and prove that the convergence properties of these methods known for SDEs are preserved. For illustration we apply the drift-implicit Euler scheme to an oscillator circuit.