Zero-stress state of intra- and extraparenchymal airways from human, pig, rabbit, and sheep lung.

Alterations in airway wall anatomic properties and the consequential effects on airway narrowing have been assessed by use of computational models. In these models, it is generally assumed that at zero transmural pressure the airway wall exists in a zero-stress state. Many studies have shown that this is often not the case, as evidenced by a nonzero opening angle. In this study, we measured the opening angle of airway rings at zero transmural pressure to test this assumption. The airway tree was dissected from human, pig, sheep, and rabbit lungs. Airways were excised from the tree, and the opening angle was measured. There were obvious species and regional differences in opening angle. Rabbit airways from both extraparenchymal and intraparenchymal sites exhibited marked opening angles (7-82 degrees). Extraparenchymal airways from sheep had large opening angles (up to 50 degrees), but ovine intraparenchymal airways had small opening angles. Measurable opening angles were rarely observed in human and porcine airways of any size. The assumption of a stable zero-stress state at zero transmural pressure is therefore valid for human and porcine, but not rabbit and sheep, airways.     

Anatomically based finite element models of the human pulmonary arterial and venous trees including supernumerary vessels.

Studies of the origin of pulmonary blood flow heterogeneity have highlighted the significant role of vessel branching structure on flow distribution. To enable more detailed investigation of structure-function relationships in the pulmonary circulation, an anatomically based finite element model of the arterial and venous networks has been developed to more accurately reflect the geometry found in vivo. Geometric models of the arterial and venous tree structures are created using a combination of multidetector row X-ray computed tomography imaging to define around 2,500 vessels from each tree, a volume-filling branching algorithm to generate the remaining accompanying conducting vessels, and an empirically based algorithm to generate the supernumerary vessel geometry. The explicit generation of supernumerary vessels is a unique feature of the computational model. Analysis of branching properties and geometric parameters demonstrates close correlation between the model geometry and anatomical measures of human pulmonary blood vessels. A total of 12 Strahler orders for the arterial system and 10 Strahler orders for the venous system are generated, down to the equivalent level of the terminal bronchioles in the bronchial tree. A simple Poiseuille flow solution, assuming rigid vessels, is obtained within the arterial geometry of the left lung, demonstrating a large amount of heterogeneity in the flow distribution, especially with inclusion of supernumerary vessels. This model has been constructed to accurately represent available morphometric data derived from the complex asymmetric branching structure of the human pulmonary vasculature in a form that will be suitable for application in functional simulations.     

Understanding the contribution of native tracheobronchial structure to lung function: CT assessment of airway morphology in never smokers

Background

Computed tomographic (CT) airway lumen narrowing is associated with lower lung function. Although volumetric CT measures of airways (wall volume [WV] and lumen volume [LV]) compared to cross sectional measures can more accurately reflect bronchial morphology, data of their use in never smokers is scarce. We hypothesize that native tracheobronchial tree morphology as assessed by volumetric CT metrics play a significant role in determining lung function in normal subjects. We aimed to assess the relationships between airway size, the projected branching generation number (BGN) to reach airways of <2mm lumen diameter –the site for airflow obstruction in smokers- and measures of lung function including forced expiratory volume in 1 second (FEV₁) and forced expiratory flow between 25% and 75% of vital capacity (FEF 25–75).

Methods

We assessed WV and LV of segmental and subsegmental airways from six bronchial paths as well as lung volume on CT scans from 106 never smokers. We calculated the lumen area ratio of the subsegmental to segmental airways and estimated the projected BGN to reach a <2mm-lumen-diameter airway assuming a dichotomized tracheobronchial tree model. Regression analysis was used to assess the relationships between airway size, BGN, FEF 25–75, and FEV₁.

Results

We found that in models adjusted for demographics, LV and WV of segmental and subsegmental airways were directly related to FEV₁ (P <0.05 for all the models). In adjusted models for age, sex, race, LV and lung volume or height, the projected BGN was directly associated with FEF 25–75 and FEV₁ (P = 0.001) where subjects with lower FEV₁ had fewer calculated branch generations between the subsegmental bronchus and small airways. There was no association between airway lumen area ratio and lung volume.

Conclusion

We conclude that in never smokers, those with smaller central airways had lower airflow and those with lower airflow had less parallel airway pathways independent of lung size. These findings suggest that variability in the structure of the tracheobronchial tree may influence the risk of developing clinically relevant smoking related airway obstruction.

Electronic supplementary material

The online version of this article (doi:10.1186/s12931-015-0181-y) contains supplementary material, which is available to authorized users.     

Automatic construction of subject-specific human airway geometry including trifurcations based on a CT-segmented airway skeleton and surface

We propose a method to construct three-dimensional airway geometric models based on airway skeletons, or centerlines (CLs). Given a CT-segmented airway skeleton and surface, the proposed CL-based method automatically constructs subject-specific models that contain anatomical information regarding branches, include bifurcations and trifurcations, and extend from the trachea to terminal bronchioles. The resulting model can be anatomically realistic with the assistance of an image-based surface; alternatively a model with an idealized skeleton and/or branch diameters is also possible. This method systematically identifies and classifies trifurcations to successfully construct the models, which also provides the number and type of trifurcations for the analysis of the airways from an anatomical point of view. We applied this method to 16 normal and 16 severe asthmatic subjects using their computed tomography images. The average distance between the surface of the model and the image-based surface was 11 % of the average voxel size of the image. The four most frequent locations of trifurcations were the left upper division bronchus, left lower lobar bronchus, right upper lobar bronchus, and right intermediate bronchus. The proposed method automatically constructed accurate subject-specific three-dimensional airway geometric models that contain anatomical information regarding branches using airway skeleton, diameters, and image-based surface geometry. The proposed method can construct (i) geometry automatically for population-based studies, (ii) trifurcations to retain the original airway topology, (iii) geometry that can be used for automatic generation of computational fluid dynamics meshes, and (iv) geometry based only on a skeleton and diameters for idealized branches.     

Development and Analysis of Patient-Based Complete Conducting Airways Models

The analysis of high-resolution computed tomography (CT) images of the lung is dependent on inter-subject differences in airway geometry. The application of computational models in understanding the significance of these differences has previously been shown to be a useful tool in biomedical research. Studies using image-based geometries alone are limited to the analysis of the central airways, down to generation 6–10, as other airways are not visible on high-resolution CT. However, airways distal to this, often termed the small airways, are known to play a crucial role in common airway diseases such as asthma and chronic obstructive pulmonary disease (COPD). Other studies have incorporated an algorithmic approach to extrapolate CT segmented airways in order to obtain a complete conducting airway tree down to the level of the acinus. These models have typically been used for mechanistic studies, but also have the potential to be used in a patient-specific setting. In the current study, an image analysis and modelling pipeline was developed and applied to a number of healthy (n = 11) and asthmatic (n = 24) CT patient scans to produce complete patient-based airway models to the acinar level (mean terminal generation 15.8 ± 0.47). The resulting models are analysed in terms of morphometric properties and seen to be consistent with previous work. A number of global clinical lung function measures are compared to resistance predictions in the models to assess their suitability for use in a patient-specific setting. We show a significant difference (p < 0.01) in airways resistance at all tested flow rates in complete airway trees built using CT data from severe asthmatics (GINA 3–5) versus healthy subjects. Further, model predictions of airways resistance at all flow rates are shown to correlate with patient forced expiratory volume in one second (FEV1) (Spearman ρ = −0.65, p < 0.001) and, at low flow rates (0.00017 L/s), FEV1 over forced vital capacity (FEV1/FVC) (ρ = −0.58, p < 0.001). We conclude that the pipeline and anatomical models can be used directly in mechanistic modelling studies and can form the basis for future patient-based modelling studies.     

Computational model of airflow in upper 17 generations of human respiratory tract

Computational fluid dynamics (CFD) studies of airflow in a digital reference model of the 17-generation airway (bronchial tree) were accomplished using the FLUENT computational code, based on the anatomical model by Schmidt et al. [2004. A digital reference model of the human bronchial tree. Computerized Medical Imaging and Graphics 28, 203-211]. The lung model consists of 6.744 x 10(6) unstructured tetrahedral computational cells. A steady-state airflow rate of 28.3L/min was used to simulate the transient turbulent flow regime using a large eddy simulation (LES) turbulence model. This CFD mesh represents the anatomically realistic asymmetrical branching pattern of the larger airways. It is demonstrated that the nature of the secondary vortical flows, which develop in such asymmetric airways, varies with the specific anatomical characteristics of the branching conduits.     

Analysis of bronchial mechanics and density dependence of maximal expiratory flow

The computational model for expiratory flow in humans of Lambert and associates (J. Appl. Physiol. Respirat. Environ. Exercise Physiol. 52: 44-56, 1982) was used to investigate the effect of bronchial constrictions in three airway zones on the density dependence of maximal expiratory flow. It was found that constriction of the peripheral airways (less than 2 mm diam) reduced density dependence and increased the volume of isoflow. Constriction of the larger intraparenchymal airways resulted in increased density dependence at low lung volumes and essentially normal values at other volumes. The volume of isoflow was reduced. Extraparenchymal (but intrathoracic) airway constriction caused no change in the volume of isoflow but caused increased density dependence at the higher lung volumes. It was shown that in these model simulations the addition of extraparenchymal constriction to intraparenchymal constriction causes essentially no changes in density dependence. An increased volume of isoflow and significantly decreased density dependence at 50 and 25% vital capacity were produced by simulated constrictions only in the peripheral airways.     

Airway branching morphology of mature and immature rabbit lungs.

The scheme of Horsfield et al. for describing the pulmonary airway tree (J Appl Physiol 52: 21-26, 1982) catalogs each airway according to its order and the difference in order of its two daughters (denoted Delta). Although this scheme captures the natural asymmetry in the airway tree, it is still deterministic, because it assumes that all airways of a given order are the same; yet such variability is extremely important in determining the overall behavior of the lungs. We therefore analyzed complete lung lobes from three mature and two immature rabbits and determined the Horsfield order and Delta of every airway down to the terminal bronchioles. We also measured the diameter of each airway. This allowed us to determine the average structure of the rabbit airway tree, the variation about this average, and also how the structures of mature and immature airway trees compare. We found some variation in branching asymmetry and airway diameter at a given order between animals but no evidence of systematic differences in structure between mature and immature lungs. We found evidence of a difference in the branching structure of the peripheral vs. the central part of the airway tree (the break point being around order 20). We also determined the nature of the variation in Delta and diameter as a function of order, which should be valuable for the development of computer models seeking to encapsulate the naturally occurring regional variation in airway geometry in the normal rabbit lung.     

Heterogeneous airway tone in asthmatic subjects.

We examined the effect of volume history on the dynamic relationship between airways and lung parenchyma (relative hysteresis) in 20 asthmatic subjects. The acoustic reflection technique was employed to evaluate changes in airway cross-sectional areas during a slow continuous expiration from total lung capacity to residual volume and inspiration back to total lung capacity. Lung volume was measured continuously during this quasi-static maneuver. We studied three anatomic airway segments: extra- and intrathoracic tracheal and main bronchial segments. Plots of airway area vs. lung volume were obtained for each segment to assess the relative magnitude and direction of the airway and parenchymal hysteresis. We also performed maximal expiratory flow-volume and partial expiratory flow-volume curves and calculated the ratio of maximal to partial flow rates (M/P) at 30% of the vital capacity. We found that 10 subjects (group I) showed a significant predominance of airway over parenchymal hysteresis (P < 0.005) at the extra- and intrathoracic tracheal and main bronchial segments; these subjects had high M/P ratios [1.53 +/- 0.27 (SD)]. The other 10 subjects (group II) showed similar airway and parenchymal hysteresis for all three segments and significantly lower M/P ratios (1.16 +/- 0.20, P < 0.01). We conclude that the effect of volume history on the relative hysteresis of airway and lung parenchyma and M/P ratio at 30% of vital capacity in nonprovoked asthmatic subjects is variable. We suggest that our findings may result from heterogeneous airway tone in asthmatic subjects.     

Simultaneous diffusion and convection in single breath lung washout

Two mathematical models of pulmonary single breath gas washout (one analytic, one numerical) are developed and their predictions compared with experimental data on human subjects. Weibel's 23 generation symmetric anatomical model is used as a guide to bronchial tree geometry. Experimental plots of nitrogen concentration versus volume expired, dead space versus breath holding time, and dead space versus tidal volume are compared with plots predicted by the models. Agreement is good. A plot of nitrogen concentration in the airways as predicted by the numerical model at different times during inhalation and exhalation of a single breath of oxygen is shown. Model predictions for changes in dead space with changes in washout gas and expiratory flow rate are discussed. Use of the analytic model for obtaining average values of the path length from mouth to alveoli in a given subject is discussed. To the extent of their agreement with experiment, the models provide a sound physical basis for the correlation of airway structure and function.     

Model of forced expiratory flows and airway geometry in infants.

Early measurements of autopsied lungs from infants, children, and adults suggested that the ratio of peripheral to central airway resistance was higher in infants than older children and adults. Recent measurements of forced expiration suggest that infants have high flows relative to lung volume. We employed a computational model of forced expiratory flow along with physiological and anatomic data to evaluate whether the infant lung is a uniformly scaled-down version of the adult lung. First, we uniformly scaled an existing computational model of adult forced expiration to estimate forced expiratory flows (FEF) and density dependence for an 18-mo-old infant. The values obtained for FEF and density dependence were significantly lower than those reported for healthy 18-mo-old infants. Next, we modified the model for the infant lung to reproduce standard indexes of expiratory flow [forced expiratory volume in 0.5 s (FEV(0.5)), FEFs after exhalation of 50 and 75% forced vital capacity, FEF between 25 and 75% expired volume] for this age group. The airway sizes obtained for the infant lung model that produced accurate physiological measurements were similar to anatomic data available for this age and larger than those in the scaled model. Our findings indicate that the airways in the infant lung model differ from those in the scaled model, i.e., middle and peripheral airway sizes are larger than result from uniform downscaling of the adult lung model. We show that the infant lung model can be made to reproduce individual flow-volume curves by adjusting lumen area generation by generation.     

Emergence of matched airway and vascular trees from fractal rules

The bronchial, arterial, and venous trees of the lung are complex interwoven structures. Their geometries are created during fetal development through common processes of branching morphogenesis. Insights from fractal geometry suggest that these extensively arborizing trees may be created through simple recursive rules. Mathematical models of Turing have demonstrated how only a few proteins could interact to direct this branching morphogenesis. Development of the airway and vascular trees could, therefore, be considered an example of emergent behavior as complex structures are created from the interaction of only a few processes. However, unlike inanimate emergent structures, the geometries of the airway and vascular trees are highly stereotyped. This review will integrate the concepts of emergence, fractals, and evolution to demonstrate how the complex branching geometries of the airway and vascular trees are ideally suited for gas exchange in the lung. The review will also speculate on how the heterogeneity of blood flow and ventilation created by the vascular and airway trees is overcome through their coordinated construction during fetal development.     

Distribution of airway narrowing responses across generations and at branching points,assessed in vitro by anatomical optical coherence tomography

Background

Previous histological and imaging studies have shown the presence of variability in the degree of bronchoconstriction of airways sampled at different locations in the lung (i.e., heterogeneity). Heterogeneity can occur at different airway generations and at branching points in the bronchial tree. Whilst heterogeneity has been detected by previous experimental approaches, its spatial relationship either within or between airways is unknown.

Methods

In this study, distribution of airway narrowing responses across a portion of the porcine bronchial tree was determined in vitro. The portion comprised contiguous airways spanning bronchial generations (#3-11), including the associated side branches. We used a recent optical imaging technique, anatomical optical coherence tomography, to image the bronchial tree in three dimensions. Bronchoconstriction was produced by carbachol administered to either the adventitial or luminal surface of the airway. Luminal cross sectional area was measured before and at different time points after constriction to carbachol and airway narrowing calculated from the percent decrease in luminal cross sectional area.

Results

When administered to the adventitial surface, the degree of airway narrowing was progressively increased from proximal to distal generations (r = 0.80 to 0.98, P < 0.05 to 0.001). This ''serial heterogeneity'' was also apparent when carbachol was administered via the lumen, though it was less pronounced. In contrast, airway narrowing was not different at side branches, and was uniform both in the parent and daughter airways.

Conclusions

Our findings demonstrate that the bronchial tree expresses intrinsic serial heterogeneity, such that narrowing increases from proximal to distal airways, a relationship that is influenced by the route of drug administration but not by structural variations accompanying branching sites.     

Contribution of tree structures in the lung to lung elastic recoil

The direct contribution of forces in tree structures in the lung to lung recoil pressure and changes in recoil pressure induced by alterations of the forces are analyzed. The analysis distinguishes the contributions of axial and circumferential tensions in the trees and indicates that only axial tensions directly contribute to static recoil. This contribution is derived from analysis of the axial forces transmitted across a random plane transecting the lung. The change in recoil pressure induced by changes in axial tension is similarly derived. Alterations of circumferential tensions in the trees indirectly change recoil by causing nonuniform deformations of the surrounding lung parenchyma, and a continuum elasticity solution for the stress induced by the deformations is derived. Sample calculations are presented for the airway tree based on available data on airway morphometric and mechanical properties. The increase in recoil pressure accompanying increases in axial and circumferential tensions with contraction of airway smooth muscle is also analyzed. The calculations indicate that axial stresses in the airway tree out to bronchioles directly contribute only a small fraction of the static recoil pressure. However, it is found that contraction of smooth muscle in these airways can increase recoil pressure appreciably (10-20%), mainly by the deformation of the parenchyma with increases in circumferential tension in smaller airways. The results indicate that the geometric and mechanical properties of the airway tree are such that only peripheral elements of the tree can substantially affect the elastic properties of the lung. The possible contributions of vascular trees for which data on mechanical and morphometric properties are more limited are also discussed.     

Activation of smooth muscle in the airway wall, force production, and airway narrowing.

Airway narrowing depends on smooth muscle force production and muscle shortening, but the structural and geometric properties exhibited by individual generations of the bronchial tree largely determine the extent and characteristics of airway narrowing. Properties of major importance include the nature and integrity of the epithelium, the structural and mechanical properties of the airway wall, as well as airway diameter. The influence of these properties on airway narrowing measured as flow or flow resistance in large and small diameter segments of airways from pig lung is described using a novel preparation, the perfused bronchial segment.     

Pressure oscillation delivery to the lung: Computer simulation of neonatal breathing parameters

Preterm newborn infants may develop respiratory distress syndrome (RDS) due to functional and structural immaturity. A lack of surfactant promotes collapse of alveolar regions and airways such that newborns with RDS are subject to increased inspiratory effort and non-homogeneous ventilation. Pressure oscillation has been incorporated into one form of RDS treatment; however, how far it reaches various parts of the lung is still questionable. Since in-vivo measurement is very difficult if not impossible, mathematical modeling may be used as one way of assessment. Whereas many models of the respiratory system have been developed for adults, the neonatal lung remains essentially ill-described in mathematical models. A mathematical model is developed, which represents the first few generations of the tracheo-bronchial tree and the 5 lobes that make up the premature ovine lung. The elements of the model are derived using the lumped parameter approach and formulated in Simulink? within the Matlab? environment. The respiratory parameters at the airway opening compare well with those measured from experiments. The model demonstrates the ability to predict pressures, flows and volumes in the alveolar regions of a premature ovine lung.     

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-μm 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.     

Angles of branching and diameters of branches in the human bronchial tree

The principle of minimal work requires that the conducting airways of the human lung should have a maximum radius for minimal resistance to gas flow. At the same time there is a requirement that the airways should have a minimal volume for economy of space. These two opposing requirements have been investigated mathematically, and a method for calculating the angle of branching which produces minimal volume has been derived. The relationship of the radii of the parent and daughter branches to produce minimal resistance has been similarly defined. By measurement of a bronchial cast from a human lung the extent to which the predicted optimum structure is realized in practice has been shown. The change in structure associated with change of function at the transition from conducting airway to diffusion zone has been demonstrated.     

Changes in airway length after unilateral pneumonectomy in weanling ferrets

We have previously shown that airway cross-sectional area increases 15-20% after pneumonectomy in weanling ferrets by measuring bronchial casts. We have now reanalyzed these same casts to quantitate changes in airway length after pneumonectomy. In each cast the distance from each of 120 airways to the terminal bronchiole along its axial pathway was measured. The relationship between the logarithm of this distance and that of the fraction of the lobe subtended by an airway could be described by a quadratic equation with a correlation coefficient greater than 0.85. Subsegmental and more distal airways of postpneumonectomy animals were 33-47% longer than those of controls. Overall the main axial pathway of airways in the left lower lobes was 12% longer in operated animals, but this increase was primarily accounted for by an increase in the length of the more peripheral airways. Central airways were little if any longer in operated animals. After pneumonectomy in weanling ferrets, subsegmental and peripheral airway lengths increase to a greater degree than lung volume and airway cross-sectional area, whereas central airway lengths increase to a lesser extent if at all. The mechanisms responsible for this difference between central and intralobar compensatory airway growth are unknown.