Robert Sturm

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 Model of Particle Clearance in Human Bronchial Airways

A stochastic bronchial clearance model, based on a stochastic morphometric model of the human bronchial tree, has been developed, which simulates the combined action of fast and slow bronchial clearance mechanisms by Monte Carlo methods. To model fast bronchial clearance, mucus velocities in individual airways were based on a correlation between mucus velocity and airway diameter, considering conservation of mucus flow. In addition, mucus transport was assumed to be delayed at bronchial bifurcation zones. The size dependence of the slow bronchial clearance phase was considered by a linear relationship between the slow bronchial clearance fraction, f(s), and the geometric particle diameter, derived from bolus inhalation experiments. Potential variations of f(s) from proximal to distal airway generations were simulated by five different scenarios, which allocated slow bronchial clearance to successively peripheral bronchial regions. Alveolar clearance, which contributes only to longterm particle retention, was modeled by transfer rates supplied by the ICRP respiratory tract model. To test the different components of the clearance model, modeling predictions were compared with experimental retention data from bolus inhalation experiments, using various particle sizes and bolus front depths, as well as from slow inhalation experiments, with a flow rate of only 0.045 L sec(-1). The overall good agreement between modeling results and experimental data indicate that the present model correctly predicts bronchial clearance, suggesting that slow bronchial clearance mechanisms are most effective in smaller bronchial airways.

Stability of zircon in a low-grade ultramylonite and its utility for chemical mass balancing: the shear zone at Miéville, Switzerland

At Mieville, Switzerland, granitic basement rocks of the Aiguilles Rouges Massif are cut by a subvertical shear zone. The Variscan shearing event produced a low-grade ultramylonite zone, which is up to 50 m wide and several kilometers long. Investigations of accessory zircons from the undeformed wall rock and from the most highly deformed ultramylonite show only minor alterations and mechanical damage of zircon crystals even in an extreme state of deformation. This outstanding stability of zircon allows one to consider the element Zr as immobile and therefore to use it as a passive marker for calculations of mass and volume changes during deformation processes. Application of this method confirms that the deformation at Mieville proceeded under simple shear, constant volume, and isochemical conditions. This is in agreement with the results of classical geochemical mass balancing. In addition, uncertainties inherent in the geochemical approach can be minimized by the new method.

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.

Semi-Empirical Stochastic Model of Aerosol Bolus Dispersion in the Human Lung

Aerosol bolus dispersion, that is, the broadening of an inhaled narrow aerosol bolus upon exhalation, was simulated by Monte Carlo methods using a stochastic, asymmetric morphometric model of the human lung. Physical mechanisms considered to contribute to bolus dispersion were () axial diffusion in conductive airways, approximated by effective diffusivities, () convective mixing at airway bifurcation sites, () differences in inspiratory and expiratory velocity profiles, () mixing with residual air in alveoli, and () inhomogeneous ventilation of the lung lobes due to asymmetric flow spitting at bifurcations and asymmetric and asynchronous filling of the five lung lobes. Theoretical predictions of the bolus dispersion model were compared to experimental data for 79 healthy volunteers, which provide detailed information on statistical bolus parameters (half-width, standard deviation, skewness, and mode shift) and total bolus deposition as a function of the depth of bolus penetration into the airway system. Predicted bolus dispersion and deposition data show excellent agreement with the published experimental data, suggesting that axial diffusion in conductive airways and convective mixing in alveoli, resulting in irreversible particle transport, are the major determinants of bolus dispersion. The variability and asymmetry of the branching airway network, leading to asymmetric flow splitting at airway bifurcations, greatly enhances the effect of irreversibility and the resulting dispersion of the inhaled bolus.

Theoretical models for dynamic shape factors and lung deposition of small particle aggregates originating from combustion processes.

A theoretical model was developed which allows the generation of irregularly shaped aggregate particles due to the stepwise joining of spherical components with variable diameters. The mathematical approach is mainly thought to act as a supporting tool for the simulation of the transport and deposition behaviour of combustion aerosols in the atmosphere and the human respiratory tract. In combination with aggregate construction essential particle parameters (dynamic shape factor χ, aerodynamic diameter d(ae)) are computed using the model. As a main result of aggregate generation, an increasing particle size, expressed by an increasing number of spherical components, leads to an enhancement of χ and d(ae), whereby values of the first parameter range from 2 to 70. Deposition of small aggregates (sizes between 2 and 200nm) in the human respiratory tract is commonly marked by high rates of bronchial particle accumulation (40-60%) and declined rates of extrathoracic (20-30%) and alveolar accumulation (2-15%). Concerning aggregate deposition by airway generation, increased cluster size causes a significant decrease of particle accumulation in the proximal airways, whilst accumulation in the intermediate to distal airways is dramatically enhanced. The model was validated using experimental deposition data of tobacco smoke. An excellent correspondence between experimental and theoretical results was found.

SHEARCALC—a computer program for the calculation of volume change and mass transfer in a ductile shear zone☆

Abstract SHEARCALC was created to automate mass balance calculations in an alteration zone. The program can be most successfully applied to ductile shear zones, where an undeformed wall rock is transformed into a fine-grained mylonite via several protomylonitic stages. The program was written in Visual Basic 6.0 and offers numerous features typical for Windows™ applications to increase the user friendliness. SHEARCALC consists of an input part for entering sample names, specific weights and chemical data of the investigated rocks as well as for selecting immobile elements and scaling factors for an appropriate display of the data in the isocon diagram. In the calculation part, the slope of the isocon and related volume changes between two specific stages of alteration are computed. Additionally, gains and losses of the main elements during deformation are expressed by respective mass transfer equations. As a special feature, SHEARCALC contains an extensive diagram section, where the user can select between three chart types. Besides the classical isocon diagram, mass changes of elements are also displayed in specific two- or three-dimensional bar charts. Element behaviour along a transsect through the shear zone is documented by two- or three-dimensional profile graphs. SHEARCALC is a stand-alone application adapted to modern Windows™ operating systems and therefore differs from many available programs in the geoscience which only run in DOS mode.

A three-dimensional model of tracheobronchial particle distribution during mucociliary clearance in the human respiratory tract

Although theoretical approaches to tracheobronchial (TB) clearance have been continuously refined during the past decades, questions concerning the exact course of particle removal from the TB tree have been largely remained unsolved. In order to clarify this problem, three-dimensional patterns of mucociliary particle clearance have to be generated at pre-defined time points after particle exposure. Here, we present a mathematical method for the generation of respective clearance patterns. Three-dimensional transport paths of inhaled particles as well as spatial deposition patterns were generated by determining spatial information of all airway tubes passed by the particles and the particle deposition sites. Three-dimensional data were converted to a coordinate system, within which the trachea represented the z-axis. Visualization of stored data was realized with the help of a freely available program code that is specialized in processing huge data sets. Mucociliary clearance of deposited particular mass was computed by assuming (1) an interrelationship between mucus velocity and airway caliber and (2) an average tracheal mucus velocity of 5.5mm min(-1). Position of cleared particles within the spatial TB tree was determined at t=0 h (immediately after exposure), t=12 h and t=24 h. Spatial patterns of mucociliary clearance were computed for particles with a uniform geometric diameter of 5μm and a density of 1g cm(-3). Inhalation of the aerosol loaded with those particles took place under sitting breathing conditions (breathing frequency: 15min(-1), tidal volume: 750 ml). As demonstrated by the generated clearance patterns, mucociliary transport of 5μm particles is completed after 30 h. Within the first 12 h following aerosol exposure, about 75% of the initially deposited particular mass is removed from the TB tree. After 24 h, 95% of the particles have been cleared. Clearance patterns are characterized by a successive transition of maximal particle concentrations towards more proximal airway generations. For 0.1μm particles and 1μm particles clearance times are significantly prolonged, whilst 10μm particles are even faster removed from the TB tree than the 5μm particles. Based on the results of this study the time span between initial deposition of particular matter and complete evacuation of deposited particles ranges from several hours to some days and depends on (1) the preferential deposition site of the inhaled material and (2) the mean mucus velocities in the bronchial airway generations.

Theoretical approach to the hit probability of lung‐cancer‐sensitive epithelial cells by mineral fibers with various aspect ratios

Background:  Inhalation of fibers may lead to the damage and, as a further consequence, to the malignant transformation of specific (most of all non‐ciliated) cells of the bronchial and bronchiolar airway epithelium. In order to accurately estimate the cancer risk induced by inhaled fibers, hit probabilities of non‐ciliated (secretory) cells by mineral fibers (asbestos and chrysotile) were computed.

Morphology and development of the female accessory sex glands in the cricket Teleogryllus commodus (Saltatoria: Ensifera: Gryllidae)

Summary In females of the cricket Teleogryllus commodus Walker the paired accessory sex glands are characterized by an irregular shape due to numerous ramifications of various length. Each gland consists of a basal, middle, and apical region within which the epithelium is uniformly built up by an inner cuticular intima, one layer of gland cells with basal-situated nuclei, and a basal lamina. In the direct vicinity of the glands orifice, the epithelium is surrounded by a coat of longitudinal and circular muscle fibres which control the delivery of the secretory material into the genital chamber. In all three regions of the gland, the cuticular intima is marked by hair-like processes of unknown function which are mainly oriented in the direction of the orifice. As a special feature the intima does not show any channel-like structures or breaks facilitating the transport of secretory material into the lumen of the gland. Additionally, the cuticular layer is folded into the gland cell sporadically and thinned out considerably at those regions. In the apical and middle region of each gland the basal cell membrane shows numerous in-foldings forming a widespread lacunar system. The secretory activity of the gland cells starts 5–6 days after adult moult. The produced material is supposed to permeate the cuticular mainly at those regions where its thickness is reduced to a minimum. Regarding the development of the accessory glands, morphological changes caused by an increasing volume of the gland cells as well as ultrastructural alterations due to an augmentation of the compartments important for secretory activity are observed.