Diameter-based analysis of the branching geometry of four mammalian bronchial trees

Phillips, C. G.; Kaye, S

doi:10.1016/0034-5687(95)00056-9

Cited by 62 publications

(53 citation statements)

References 15 publications

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“…Length to diameter ratio was appreciably larger for small d/d p indicating that length, compared to diameter, of strictly minor daughter is larger than that of major daughter. Previous studies (Phalen et al, 1978;Phillips and Kaye, 1995) show that the length to diameter ratio of the minor daughter is clearly larger than that of the major one, which agrees with our results (Fig. 8).…”

Section: Diameter-based Analysissupporting

confidence: 94%

“…For some geometric parameters, diameter-based analysis (Phillips and Kaye, 1995) is more useful than generation-based analysis to describe monopodial branching patterns in rat airways. Asymmetric branching features such as ratio of daughter diameters and ratio of daughter branching angles are essential for modeling monopodial architecture.…”

Section: Diameter-based Analysismentioning

confidence: 99%

“…Table 3 shows the number of generations (NG) to reach an airway as a function of diameter range. Number of generations to reach 0.35 mm, which will be close to terminal bronchioles (Phillips and Kaye, 1995), ranges from 6 to 33, which indicates that global architecture of rat airways is highly asymmetric. Intrasubject variance of NG to reach around 0.35 mm is less than 1.…”

Section: Correlation Between Geometry Parametersmentioning

confidence: 99%

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Pulmonary Architecture in the Conducting Regions of Six Rats

Lee

Fanucchi

Plopper

et al. 2008

The Anatomical Record

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Rats are widely used for studies of pulmonary toxicology and lung disease. Several studies suggest nominal geometric parameters describing the architecture of the rat airway. However, intersubject variance has never been reported due to the huge effort and time to take these manual measurements. In this study, we present statistics of the branching pattern of six healthy male Sprague Dawley rats by automatically analyzing computed tomography images of silicon casts of their airways. Details of branching characteristics and also intersubject variance are presented. In addition, this study shows that mean and standard deviation of many geometric parameters insufficiently represent pulmonary architecture because some, such as diameter-asymmetry, are not normally distributed. Detailed statistics including inter-and intrasubject variance and distribution of the geometric parameters will aid in constructing more realistic airway models for particle transport and studies of normal and abnormal respiratory physiology. Anat Rec,

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Section: Diameter-based Analysissupporting

confidence: 94%

Section: Diameter-based Analysismentioning

confidence: 99%

Section: Correlation Between Geometry Parametersmentioning

confidence: 99%

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Pulmonary Architecture in the Conducting Regions of Six Rats

Lee

Fanucchi

Plopper

et al. 2008

The Anatomical Record

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“…We will explicitly study the dependence of the radii of the bifurcated vessels on the radius of the parent vessel, thus allowing a more direct comparison with theoretical models. We show that important aspects of previous observations [11] for the human bronchial tree, not predicted by the theoretical models, are more general than has been previously noticed. In particular, we find qualitatively similar behavior for dog arterial and bronchial trees, and lamb fetal and neonatal arterial trees.…”

supporting

confidence: 52%

Scale Dependence of Branching in Arterial and Bronchial Trees

2006

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Although models of branching in arterial and bronchial trees often predict a dependence of bifurcation parameters on the scale of the bifurcating vessels, direct verifications of this dependence by comparison with data are uncommon. We compare measurements of bifurcation parameters of airways and arterial trees of different mammals as a function of scale to general features predicted by theoretical models based on minimization of pumping power and network volume. We find that the size dependence is more complex than existing theories based solely on energy and volume minimization, and suggest additional factors that may govern the branching at different scales.The potential factors determining the parameters at bifurcations in the arterial and bronchial trees of mammals have lately received attention. Most notably, these local bifurcation characteristics have been proposed to determine allometric scaling laws for biologically important variables (see [1, 2] and [3]). It has been suggested that arterial and bronchial trees follow a pattern that minimizes a combination of pumping power and the total volume of the tree (see for example [1]-[6]). If the flow is assumed to be Poiseuille (resistance proportional to the inverse fourth power of the vessel radius) on all scales, self-similar branching results, i.e., the branching parameters do not depend on the scale. However, it has been argued [1] that, due to the fact that the blood flow is pulsatile [8,9], arterial trees determined by optimization have branching parameters that depend on the scale (the form of this dependence is discussed below). As a direct test of these theories and their assumptions, we compare in this Letter experimental measurements of the scale dependence of the branching parameters with the predictions of theoretical models. Many studies of bifurcation parameters rely on ordering schemes [10] which do not directly consider the dependence of the bifurcation parameters on the scale, and thus are not appropriate for our particular purpose. We will explicitly study the dependence of the radii of the bifurcated vessels on the radius of the parent vessel, thus allowing a more direct comparison with theoretical models. We show that important aspects of previous observations [11] for the human bronchial tree, not predicted by the theoretical models, are more general than has been previously noticed. In particular, we find qualitatively similar behavior for dog arterial and bronchial trees, and lamb fetal and neonatal arterial trees. Our results suggest that, in addition to minimizing pumping power and network volume, there might be other important factors determining the * Electronic address: juanga@math.umd.edu branching in the arterial and bronchial trees.Arterial and bronchial trees start with a tree root (a parent vessel) that divides into two (daughter) vessels, and these in turn subdivide in a similar fashion, continuing until a certain approximate value of the radius is attained (in the case of arterial trees, the capillary radius). At a partic...

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“…This main lateral-branching pattern points out the fractal 3D asymmetrically branching structure, which other models have been unable to because they only focused on each individual branching node or branch segment between adjacent nodes based on the mother-daughter pattern. We believe that this main lateral-branching pattern in the monopodial branching airways must play an important functional role in preferential distribution of ventilation to peripheral regions of the lung, especially during higher inspiratory flow rates, because the approximately straight monopodial main trunk in this airway arrangement may support an optimal internal flow for faster convective gas transport with less energy dissipation during high-airflow ventilation (3,12). Thus homogeneous and synchronous gas exchange can be achieved in the whole lung in the narrow, cone-shaped, canine chest, especially during the heavy breathing demands associated with either chase or escape activities.…”

Section: Discussionmentioning

confidence: 99%

Fractal branching pattern of the monopodial canine airway

Wang¹,

Kraman²

2004

Journal of Applied Physiology

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Unlike the human lung, monopodial canine airway branching follows an irregular dichotomized pattern with fractal features. We studied three canine airway molds and found a self-similarity feature from macro- to microscopic scales, which formed a fractal set up to seven scales in the airways. At each fractal scale, lateral branches evenly lined up along an approximately straight main trunk to form three to four two-dimensional structures, and each lateral branch was the monopodial main trunk of the next fractal scale. We defined this pattern as the fractal main lateral-branching pattern, which exhibited similar structures from macro- to microscopic scales, including lobes, sublobes, sub-sublobes, etc. We speculate that it, rather than a mother-daughter pattern, could better describe the actual asymmetrical architecture of the monopodial canine airway.

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Diameter-based analysis of the branching geometry of four mammalian bronchial trees

Cited by 62 publications

References 15 publications

Pulmonary Architecture in the Conducting Regions of Six Rats

Pulmonary Architecture in the Conducting Regions of Six Rats

Scale Dependence of Branching in Arterial and Bronchial Trees

Fractal branching pattern of the monopodial canine airway

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