Numerical Modeling of Steady Inspiratory Airflow Through a Three-Generation Model of the Human Central Airways

Abstract

Two-dimensional steady inspiratory airflow through a three-generation model of the human central airways is numerically investigated, with dimensions corresponding to those encountered in the fifth to seventh generations of the Weibel's model. Wall curvatures are added at the outer walls of the junctions for physiological purposes. Computations are carried out for Reynolds numbers in the mother branch ranging from 200 to 1200, which correspond to mouth air breathing at flow rates ranging from 0.27 to 1.63 liters per second. The difficulty of generating grids in a so complex configuration is overcome using a nonoverlapping multiblock technique. Simulations demonstrate the existence of separation regions whose number, location, and size strongly depend on the Reynolds number. Consequently, four different flow configurations are detected. Velocity profiles downstream of the bifurcations are shown to be highly skewed, thus leading to an important unbalance in the flow distribution between the medial and lateral branches of the model. These results confirm the observations of Snyder et al. and Tsuda et al. and suggest that a resistance model of flow partitioning based on Kirchhoff's laws is inadequate to simulate the flow behavior accurately within the airways. When plotted in a Moody diagram, airway resistance throughout the model is shown to fit with a linear relation of slope -0.61. This is qualitatively in good agreement with the experimental investigations of Pedley et al, and Slutsky et al.

Multi-branching flows from one mother tube to many daughters or to a network

“…Several theoretical conjectures remain largely untested, while direct computation has only given solutions either accurately over a few generations or with limited detail over more generations (see Hademenos et al 1996;Pries et al 1998;Goldman & Popel 2000;Smith & Jones 2003). Related branching or network studies have been conducted with some success by Handa et al (1993), Miyasaka et al (1993), Pedley et al (1994), Gatlin et al (1995), Young et al (1996), Gao et al (1997), Hademenos & Massoud (1997), Wilquem & Degrez (1997), Zhai et al (1997), Pries et al (1998), Brada & Kitchen (2000), Kassab et al (2000), Lorthois et al (2000), McEvoy et al (2000), Cassidy et al (2001) and Comer et al (2001). The presence of an arteriovenous malformation in a cranial system eventually requires study of the application of type I within the wider framework of an application similar to type II.…”

Interplay between Geometry and Flow Distribution in an Airway Tree

“…Unambiguous experimental and numerical evidences of inertial effects have been observed in several studies on flow though branched structures, with special emphasis on the bronchial tree [2][3][4][5][6][7][8][9][10][11][12][13][14]. Such phenomena exists in real lungs but they are more simple to study in a symmetric geometry [15,16].…”

Finite element analysis of particle motion in steady inspiratory airflow

“…As for the inhaled air, we consider that the air speed is not so high as to permit avoiding the need to choose an appropriate, if any, turbulence model for the airflow. Like many previous investigations, such as some of them in [1][2][3][4][5][6][7], the flow is investigated in a domain of two dimensions to facilitate the analysis. As with the conventional gas-solid two-phase flow analyses, we assume that the gas and solid phases have complementary regions.…”

“…The problem, known as the Weibel model of the human central airway, has been considered by Wilquem and Degrez [1]. The domain, schematically shown in Fig.…”

“…These airways have different diameters, ranging from 18 mm for the trachea to 0.4 mm for other posterior branchea [1]. Besides difficulties with geometrical complexities and equation nonlinearities in the numerical simulation, this system is physiologically very complex.…”