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TECHNICAL PAPERS: Fluids/Heat/Transport

Two Mathematical Models for Predicting Dispersion of Particles in the Human Lung

[+] Author and Article Information
G. H. Ganser, I. Christie

Department of Mathematics,  West Virginia University, P.O. Box 6310, Morgantown, WV 26506

M. A. McCawley

Department of Civil and Environmental Engineering,  West Virginia University, P.O. Box 6103, Morgantown, WV 26506

J Biomech Eng 129(1), 51-57 (Jun 30, 2006) (7 pages) doi:10.1115/1.2401183 History: Received December 05, 2005; Revised June 30, 2006

The dispersion of particles in the human lung is modeled as a series of virtual mixing tanks. Using the experimental results of Scherer (1975, J. Appl. Physiol., 38(4), pp. 719–723) for a five-generation glass lung model, it is shown that each generation of the glass lung behaves like an independent virtual mixing tank. The corresponding resident time distribution is shown to have a variance approximately equal to the square of the average time a particle spends in the generation. By assuming that each generation of the human lung behaves as an independent virtual mixing tank, the realistic lung data provided by Weibel (1963, Morphometry of the Human Lung, Spinger-Verlag, New York) are used to validate this assumption in two ways. First, the half-width of the exhaled particle concentration profile is obtained. Second, a system of differential equations, with the concentration of particles in each mixing tank as its solution, is derived and solved numerically. This gives the exhaled concentration profile. Both techniques yield similar results to each other, and both give excellent agreement with the experimental data. The virtual mixing tank approach allows the complex mixing that occurs in the branching pathways of the lung to be more simply modeled. The model, thereby derived, is simple to change and could lead to enhancements in the understanding of the underlying processes contributing to the ventilation of the lung in health and disease.

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Copyright © 2007 by American Society of Mechanical Engineers
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Figures

Grahic Jump Location
Figure 1

(a) Tank system used to model the lung: The first in last out (FILO) model. (b) Tank system used to model the lung: The symmetrical model.

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Figure 2

Three complete inhalation∕exhalation cycles for a flow rate of 500cc∕s and a bolus volume of 100cc, for a single, typical, asymptomatic male age 45years, height 172cm. The three graphs correspond to the different volumes of penetration, 301, 405.1, and 605.7cc, and tidal volumes of 1000, 1100, and 1300cc. Each graph has a peak on the left showing the inhaled concentration. The jagged curve on the right is from the experiment, and the smooth curve is from the model.

Grahic Jump Location
Figure 3

Comparison of models (solid and broken lines) and experimental results (circles) for a flow rate of 500cc∕s, tidal volume of 1000cc, and a bolus of volume 100cc for a single, typical, asymptomatic male age 44years, height 175cm. σH* is given by Eq. 13 and σH=2ln2σH*. FILO is calculated using Eqs. 14,15,16,17,18.

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