Relation between diameter and flow in branches of the bronchial tree

Two methods are described for calculating the value of the exponentx in the equation flow =k×diameter ^x , as pertaining to a branch of the bronchial tree. In the lungs from three humans, two dogs, one hamster, and one rat mean values ofx between 2.419 and 2.903 were found. They lie within the range of 2.333 to 3.0 predicted by the analysis of Uylings (Bull. Math. Biol. 39, 501–519, 1977).     

Dynamic model of the bronchial tree

We present a distributed model of the bronchial tree which simulates the global dynamic characteristics of the lung. Local mechanical characteristics of each airway are represented by RCL circuits and parameters of the electrical components are determined from local physiological data. The bronchi geometry is described by Weibel's symmetric model, the flow in each airway is assumed laminar and mixing effects at the bifurcations are neglected; the transpulmonary pressure is assumed to be sinusoidal. In simulations of quiet breathing the resistance to airflow is found to be dominant, the flow amplitude decreasing as breathing frequency increases, but remaining almost constant in all the generations. Simulations of ventilation through obstructed lungs show frequency dependence of the dynamic characteristics in very compliant lungs. The global resistance to airflow and the dynamic compliance of the bronchi decrease as the forced oscillation frequency increases in a pattern similar to in vivo measurements in diseased lungs. This may be an outcome of the RCL properties of the network rather than due to uneven distribution of mechanical properties of the lung.     

Various reduced-order surrogate models for fluid flow and mass transfer in human bronchial tree

Biomechanics and Modeling in Mechanobiology - The bronchial tree plays a main role in the human respiratory system because the air distribution throughout the lungs and gas exchange with blood...     

Patterns of pollen flow in a dense population of the insect-pollinated canopy tree species Castanopsis sieboldii

Insect pollinations of tree species with high-density populations have rarely been studied. Since the density of adults can affect effective pollen dispersal, short-distance pollination, even by insects, may frequently occur in high-density populations. To test this prediction, we investigated pollination patterns in a high-density population of the insect-pollinated canopy tree species Castanopsis sieboldii by paternity analysis using genotypes at 8 microsatellite loci of 145 adult trees and 439 seeds from 11 seed parents in a 4-ha plot. We then explored their genetic effects on the population by calculating other population genetics parameters. Although C. sieboldii has high potential for long-distance dispersal of pollen (as indicated by a fat-tailed dispersal kernel), the cumulative pollination at the local scale was spatially limited and strongly dependent on the distance between parents due to the high density of adults. Genetic diversity estimates for pollen pools accepted by each seed parent converged on a maximum as the effective number of pollen parents increased. The genetic diversity of pollen pool bulked over all the seed parents from inside the plot did not differ from that of the total pollen pools. Therefore, although pollen flow from distant pollen parents may help to maintain the genetic diversity of offspring, pollen parents neighboring seed parents may be the main contributors to the genetic diversity of the offspring at the seed stage.     

Beyond the principle of similitude: renormalization in the bronchial tree

The average dimensions (diameter, length, and volume) of the airways in the mammalian bronchial tree, long thought to be exponential functions of the generation number, are shown to be power laws in generation number modulated by a harmonic variation. These data are satisfactorily described by means of a functional scaling relation--renormalization group property--between successive generations for the average variable of interest. This type of scaling may provide a mechanism for the morphogenesis of complex but highly stable structures.     

Heterogeneity in the effects of epithelium removal in the canine bronchial tree

The effect of removing the airway epithelium on the responses of canine airways of decreasing diameter to contractile and relaxing agonists was explored. Three orders of canine bronchus were studied: second order (lobar bronchus), third order (segmental bronchus), and fourth order (subsegmental bronchus). Paired rings of tissue, with and without epithelium, were placed in organ chambers in physiological salt solution gassed with 95% O2-5% CO2 and maintained at 37 degrees C. For second- and third-order bronchi, epithelium removal caused significant left-ward shifts of the concentration-effect curves for 5-hydroxytryptamine, histamine, and acetylcholine. In fourth-order bronchi, there was no significant shift for any of the contractile agonists. Isoproterenol (during contractions evoked by acetylcholine) induced concentration-dependent relaxations that were significantly greater in bronchi with than in those without epithelium. This effect was most prominent in fourth-order bronchi. These results suggest that 1) the canine airway epithelium releases a relaxing factor, 2) in larger airways the major effect is reduction of contractile responses, and 3) in smaller airways the major effect is enhancement of relaxing responses.     

Computer simulation of the geometry of the human bronchial tree

Some morphological features of the human bronchial tree were simulated by computergenerated trees. The trees were ordered by the methods of Horsfield and Strahler. Delta, the difference between the Horsfield orders of the two branches at a bifurcation, was determined by pseudorandom numbers generated according to a distribution of probabilities defined on input. By trial and error a distribution was found which resulted in trees being generated with average Strahler order branching ratios of 2.82, similar to a real bronchial tree. Branching angles and length ratio could also be defined on input. By varying these input parameters it was found that the form of the tree was quite sensitive to them, and that by a suitable choice the intrasegmental part of the bronchial tree could be simulated. It is concluded that branching ratio, length ratio, mean branching angles and distribution of delta are controlled within tight limits in the bronchial tree, and this may support the concept of optimal design.     

Viscous energy dissipation in a model of the human bronchial tree

The viscous energy dissipation in a two generation model of the human bronchial tree is determined from inspiratory velocity and static pressure data obtained for large Reynolds numbers (10⁴ < Re < 10⁵). This dissipation is found to be an increasing function of both Re and distance downstream from the inlet of the model. The ratio of the dissipation in the model to the energy dissipation in an equivalent straight pipe system is determined. This ratio, Z^*, for the model is compared to values in the literature for lower (laminar) Re. There is more dissipation in the branched model than in a straight pipe (Z^* > 1) and turbulence keeps Z^* at roughly a fixed value for large Reynolds numbers (10⁴ < Re < 10⁵). Z^* values for curved pipes are also compared to the branching system values. It is found that the energy dissipation for the branched model behaves similarly to that in curved pipes.     

A three-dimensional model of the upper tracheobronchial tree

A new model of the upper tracheobronchial tree is proposed to account for the three-dimensional nature of the airway system. In addition to the tube length, the tube diameter, and the branching angle, the model includes information on the orientation angle of each tube relative to its parent tube. The orientation angle, defined as the angle between two successive bifurcations, is useful for calculating the gravitational inclination of each tube. The information on orientation angle is further used to construct a binary coding system for identifying individual tubes in the airway tree. The proposed model is asymmetrical, but the same principles can be readily used to construct a symmetrical one.     

Aspiration biopsy cytology of adenocarcinoid tumor of the bronchial tree

Aspirated material from two cases of histologically and ultrastructurally confirmed adenocarcinoid tumor of the lung was evaluated. In one case, columnar and cuboidal cells with ill-defined cytoplasm and round or oval nuclei were seen in large sheets and syncytiumlike clusters with focal glandular arrangement. In the other case, spindle-shaped and columnar cells with ovoid nuclei and ill-defined cytoplasm were seen singly and in loose clusters. Fragments of tumor epithelium with nuclei arranged in pseudo-stratified pattern were noted. Staining of tumor cells by the Grimelius technique demonstrated numerous intracytoplasmic brown-black granules. The cytologic differential diagnosis between adenocarcinoid tumor and other primary and metastatic adenocarcinomas of the lung is briefly discussed.