Fluid-dynamic optimality in the generation-averaged length-to-diameter ratio of the human bronchial tree

Lee, Jinwon; Kang, Min Yeong; Yang, Hoe J.; Lee, Eugene

doi:10.1007/s11517-007-0232-8

Cited by 16 publications

(16 citation statements)

References 15 publications

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“…Bronchial tree asymmetry explains airway diameters in any branching level and can determine air flux in the lung (Horsfield;Majumdar et al, 2005;Lee et al, 2007).…”

Section: Discussionmentioning

confidence: 99%

Bronchial tree Architecture in Mammals of Diverse Body Mass

Monteiro

Smith

2014

Int. J. Morphol.

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SUMMARY:The anatomy of mammal's lung air space constitutes the bronchial tree which disposition is associated to air flux dynamics. Casts obtained from human, pig and rat lungs were studied to analyze possible differences of the bronchial tree architecture in mammals with diverse dimensions and posture. Air spaces were filled with polymers through trachea followed by acid corrosion. Tracheal and main bronchial division's diameters were measured to relate with body mass using allometry. The results revealed a dichotomic bronchial branching pattern in the human casts and a monopodial pattern in animals. In allometric relationship trachea was larger in rats, then pigs and lastly in humans, differences were statistically significant, the same occurs in right bronchus, as in the left bronchus there was no difference between rat and pig. The linear relationship between the human tracheal diameters was 1.2 times larger than the pig and 6.7 times larger than the rat; the pig tracheal diameter was 5.6 times larger than the rat. Quadruped position of the pig and rat is linked to a horizontal air way while the erect position, biped in human, correspond to a vertical air way. A big mammal shows less respiratory frequency than small mammals. Mammals with small, medium and high body mass allied to diverse posture and habits was compared revealing morphological differences in the bronchial trees as different allometric correlations between quadruped animals and human biped.

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“…Bronchial tree asymmetry explains airway diameters in any branching level and can determine air flux in the lung (Horsfield;Majumdar et al, 2005;Lee et al, 2007).…”

Section: Discussionmentioning

confidence: 99%

Bronchial tree Architecture in Mammals of Diverse Body Mass

Monteiro

Smith

2014

Int. J. Morphol.

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“…(1), DV and DP AE Q, need to be expressed in terms of h and other variables which remain unchanged by a variation of h. In the lung airways l is not independent of d and h but is related to them by an optimality rule in the generationaverage sense 7,8 and Q is strongly dependent on d. 2,4,10 The relationships between morphometric parameters are all taken into the equation, leaving h the only free variable, then Eq. 1 is differentiated with respect to h to find the optimum branch angle.…”

Section: Formulation Of the Optimizationmentioning

confidence: 99%

“…Details of flow transition through a tube branch are very complicated, and the characteristics of pressure loss in a tube branch are not well formulated yet in laminar flow conditions, unlike in turbulent flow conditions. So the simplest possible form proper for optimization will be used for the pressure loss in this study, following the successful formulation of Lee et al 8 for the optimum l/d where the addition of the branching loss played a central role.…”

Section: Formula For the Pressure Loss In A Branched Tube Under Laminmentioning

confidence: 99%

“…2 The l/d ratio of 3.0-3.5 could be successfully predicted recently when the pressure loss due to branching was included in addition to the Poiseuille loss. 7,8 As to the branching angle, Murray 10 and Horsfield and Cumming 1 used the condition of minimum work or minimum volume, respectively, to obtain a formula for the optimum branching angle as a function of d/d 0 alone, resulting in a single value of 37°28¢ (=cos -1 (2 -1/3 )) at the optimum d/d 0 = 0.794. Zamir 16 obtained equations for the optimum branch angle based on minimum surface area, volume, drag force or power as functions of d/d 0 and flow rate ratio at bifurcation.…”

Section: Introductionmentioning

confidence: 99%

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Optimality in the Variation of Average Branching Angle with Generation in the Human Bronchial Tree

et al. 2008

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In the human bronchial tree the branching angle becomes larger with generation or for the smaller branches. Previous theories based on single parameter optimization have not been successful at all in predicting the consistent increasing trend of branching angle with continued bifurcation. In this study a new theory for the optimality of the branching angle is proposed, which is based on the optimization between dual competing performances, the maximum space-filling capability at the expense of minimum energy loss. A large-angle branching gives an effect of delivering air into a new direction away from the preceding airways. It then has an effect of utilizing the lung volume with better uniformity, but at the same time inevitably requires a high pressure loss. It is shown in this paper that the ever increasing branching angle with generation can be well explained as the optimum branching structure where the dual opposing performance of space filling and pressure loss is optimized. In estimating the pressure loss, branching loss is considered in addition to the Poiseuille loss. Change of predicted optimum branching angle with generation shows an excellent agreement with the observed data found in the human conducting airways.

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“…for mass or heat transfer in various solar systems [1], heat exchangers [2], blade machines, fuel cells [3,4] etc. The issue of unsteady phenomena is also reflected in areas, which seem to be distant from engineering practice at first sight, such us blood flow in cardiovascular system [5,6,7,8,9] or air flow in the respiratory system [10].…”

Section: Introductionmentioning

confidence: 99%

Method for the evaluation of minor losses in pulsatile laminar fluid flow

Netřebská

Matěcha

Schmirler

et al. 2014

EPJ Web of Conferences

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Abstract. This article focuses on description and evaluation of the size of the minor losses in pulsatile laminar flow. It describes a method for determination of minor losses with respect to the phase delay between pressure waveforms and flow waveforms. The whole evaluation method is presented on the example of minor loss in the sharp 90° bend in the channel with constant square cross-section in pulsatile laminar flow of an incompressible Newtonian fluid. For this example, the minor loss coefficient is expressed depending on the dimensionless flow parameters. Total minor loss was calculated numerically. An analytical solution was used for quantification of the head loss in the developed laminar flow in the straight channel. Unsteady flow conditions were controlled by the sinusoidal flow.

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Fluid-dynamic optimality in the generation-averaged length-to-diameter ratio of the human bronchial tree

Cited by 16 publications

References 15 publications

Bronchial tree Architecture in Mammals of Diverse Body Mass

Bronchial tree Architecture in Mammals of Diverse Body Mass

Optimality in the Variation of Average Branching Angle with Generation in the Human Bronchial Tree

Method for the evaluation of minor losses in pulsatile laminar fluid flow

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