The dispersion of particles in the human lung is modeled as a series of virtual mixing tanks. Using the experimental results of Scherer et al. (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.

1.
Scherer
,
P. W.
,
Shendalman
,
L. H.
,
Greene
,
N. M.
, and
Bouhuys
,
A.
, 1975, “
A Measurement of Axial Diffusivities in a Model of the Bronchial Airways
,”
J. Appl. Physiol.
0021-8987,
38
(
4
), pp.
719
723
.
2.
Rainey
,
R. H.
, 1967, “
Natural Displacement of Pollution From the Great Lakes
,”
Science
0036-8075,
155
(
3767
), pp.
1242
1243
.
3.
McCawley
,
M.
,
Abrons
,
H.
, and
Lippmann
,
M.
, 1988, “
Modelling an Aerosol Dispersion Test for Detecting Early Airway Changes
,”
Ann. Occup. Hyg.
0003-4878
32
(Suppl. 1), pp.
81
89
.
4.
Nauman
,
E. B.
, and
Buffham
,
B. A.
, 1983,
Mixing in Continuous Flow Systems
Wiley
,
New York
.
5.
Paiva
,
M.
, 1973, “
Gas Transport in the Human Lung
,”
J. Appl. Physiol.
0021-8987,
35
, pp.
401
410
.
6.
Ultman
,
J. S.
, 1985, “
Gas Transport in the Conductive Airways
,” in
L. A.
Engel
and
M.
Paiva
, eds.,
Gas Mixing and Distribution in the Lung
,
Marcel Dekker
,
New York
.
7.
Weibel
,
E. R.
, 1963,
Morphometry of the Human Lung
,
Springer-Verlag
,
New York
.
8.
Taylor
,
G. I.
, 1953, “
Dispersion of Soluble Matter in Solvent Flowing Slowly Through a Tube
,”
Proc. R. Soc. London, Ser. A
1364-5021,
219
, pp.
186
203
.
9.
Taylor
,
G. I.
, 1954, “
The Dispersion of Matter in Turbulent Flow Through a Pipe
,”
Proc. R. Soc. London, Ser. A
1364-5021,
223
, pp.
446
468
.
10.
Darquenne
,
C.
, and
Paiva
,
M.
, 1994, “
One-Dimensional Simulation of Aerosol Transport and Deposition in the Human Lung
,”
J. Appl. Physiol.
8750-7587,
77
(
6
), pp.
2889
2898
.
11.
Tennekes
,
H.
, and
Lumley
,
J. L.
, 1971,
A First Course in Turbulence
,
MIT
,
Cambridge, MA.
12.
Khandare
,
P.
,
McCawley
,
M.
, and
Zondlo
,
J.
, 1994, “
Validation of the Mixed Tank Reactor Model Used to Model Aerosol Dispersion in the Lung
,”
Ann. Occup. Hyg.
0003-4878
38
(Suppl. 1), pp.
151
158
.
13.
Edwards
,
D. A.
, 1994, “
A General Theory of the Macrotransport of Nondepositing Particles in the Lung by Convective Dispersion
,”
J. Aerosol Sci.
0021-8502,
25
(
3
), pp.
543
565
.
14.
Altshuler
,
B.
,
Palmes
,
E. D.
,
Yarmus
,
L.
, and
Nelson
,
N.
, 1959, “
Intrapulmonary Mixing of Gases Studied With Aerosols
,”
J. Appl. Physiol.
0021-8987,
14
, pp.
321
327
.
15.
McCawley
,
M.
, and
Lippmann
,
M.
, 1984, “
An Aerosol Dispersion Test: Comparison of Results From Smokers and Non-Smokers
,” in
B. Y. H.
Liu
,
D. Y. H.
Piu
, and
H. J.
Fissan
, eds.,
Aerosols
,
Elsevier
,
New York
, pp.
1007
1010
.
16.
Blanchard
,
J. D.
, 1996, “
Aerosol Bolus Dispersion and Aerosol-Derived Airway Morphometry: Assessment of Lung Pathology and Response to Therapy, Part I
,”
J. Aerosol Med.
,
9
, pp.
183
201
.
You do not currently have access to this content.