A model for the mechanical properties of an alveolar duct is analyzed using the finite element method. Its geometry comprises an assemblage of truncated octahedral alveoli surrounding a longitudinal air duct. The amounts and distributions of elastin and collagen fiber bundles, modeled by separate stress-strain laws, are based upon published data for dogs. The surface tension of the air-liquid interface is modeled using an area-dependent relationship. Pressure-volume curves are computed that compare well with experimental data for both saline-filled and air-filled lungs. Pressure-volume curves of the separate elastin and collagen fiber contributions are similar in form to the behavior of saline-filled lungs treated with either elastase or collagenase. A comparison with our earlier model, based upon a single alveolus, shows the duct to have a behavior closer to reported experimental data.

1.
Bachofen
H.
,
Hildebrant
J.
, and
Bachofen
M.
,
1970
, “
Pressure-Volume Curves of Air and Liquid Filled Excised Lungs-Surface Tension in situ
,”
J. Appl. Physiol.
, Vol.
29
, pp.
422
431
.
2.
Carton
R. W.
,
Dianauskas
J.
, and
Clark
J. W.
,
1962
, “
Elastin Properties of Single Elastic Fibers
,”
J. Appl. Physiol.
, Vol.
17
, pp.
547
551
.
3.
Clements
J. A.
,
Brown
E. S.
, and
Johnson
R. P.
,
1958
, “
Pulmonary Surface Tension and Mucus Lining of the Lungs
,”
J. Appl. Physiol.
, Vol.
12
, pp.
262
268
.
4.
Dale
P. J.
,
Mathews
F. L.
, and
Schroter
R. C.
,
1980
, “
Finite Element Analysis of Lung Parenchyma
,”
J. of Biomech.
, Vol.
13
, pp.
865
873
.
5.
Frankus
A.
, and
Lee
G. C.
,
1974
, “
A Theory for Distortion of Lung Parenchyma Based on Alveolar Membrane Properties
,”
J. of Biomech.
, Vol.
7
, pp.
101
107
.
6.
Fukaya
H.
,
Martin
C. J.
,
Young
A. C.
, and
Katsura
S.
,
1968
, “
Mechanical Properties of Alveolar Walls
,”
J. Appl. Physiol.
, Vol.
25
, pp.
689
696
.
7.
Fung, Y. C., 1981, Biomechanics: Mechanical Properties of Living Tissues, Springer-Verlag, New York.
8.
Fung
Y. C.
,
1988
, “
A Model of the Lung Structure and its Validation
,”
J. Appl. Physiol.
, Vol.
64
, pp.
2132
2141
.
9.
Fung, Y. C., 1990, Biomechanics: Motion, Flow, Stress and Growth, Springer-Verlag, New York.
10.
Glaister
D. H.
,
Schroter
R. C.
,
Sudlow
M. F.
, and
Milic-Emili
J.
,
1973
, “
Bulk Elastic Properties of Exercised Lungs and the Effect of a Transpulmonary Pressure Gradient
,”
Respir. Physiol.
, Vol.
17
, pp.
347
364
.
11.
Hoppin, F. G., and Hidlebrant, J., 1977, “Mechanical Properties of the Lung,” Bioengineering Aspects of the Lung, West, J. B., ed. Marcel Dekker, New York.
12.
Karakaplan
A. D.
,
Bieniek
M. P.
, and
Skalak
R.
,
1980
, “
A Mathematical Model of Lung Parenchyma
,”
ASME JOURNAL OF BIOMECHANICAL ENGINEERING
, Vol.
102
, pp.
124
136
.
13.
Karlinsky
J. B.
,
Snider
G. L.
,
Franzblau
C.
,
Stone
P. J.
, and
Hoppin
F. G.
,
1976
, “
In Vitro Effects of Elastase and Collagenase on Mechanical Properties of Hamster Lungs
,”
Am. Rev. Respir. Dis.
, Vol.
113
, pp.
769
777
.
14.
Kimmel
E.
,
Kamm
R. D.
, and
Shapiro
A. H.
,
1987
, “
A Cellular Model of Lung Elasticity
.”
ASME JOURNAL OF BIOMECHANICAL ENGINEERING
, Vol.
109
, pp.
126
131
.
15.
Kimmel
E.
, and
Budiansky
B.
,
1990
, “
Surface Tension and the Dodecahedron Model for Lung Elasticity
,”
ASME JOURNAL OF BIOMECHANICAL ENGINEERING
, Vol.
112
, pp.
160
167
.
16.
Kowe
R.
,
Schroter
R. C.
,
Mathews
F. L.
, and
Hitchings
D.
,
1986
, “
Analysis of Elastic and Surface Tension Effects in Lung Alveolus using Finite Element Methods
,”
J. of Biomech.
, Vol.
19
, pp.
541
549
.
17.
Kowe, R., Hitchings, D., Mathews, F. L., and Schroter, R. C., 1988, “Finite Element Model of Alveoli and Ducts,” Proceedings World Congress on Medical Physics and Biomedical Engng, San Antonio, Texas.
18.
Lum
H.
, and
Mitzner
W.
,
1987
, “
A Species Comparison of Alveolar Size and Surface Forces
,”
J. Appl. Physiol.
, Vol.
62
, pp.
1865
1871
.
19.
Matsuda
M.
,
Fung
Y. C.
, and
Sobin
S. S.
,
1987
, “
Collagen and Elastin Fibers in Human Pulmonary Alveolar Mouths and Ducts
,”
J. Appl. Physiol.
, Vol.
63
, pp.
1185
1194
.
20.
Mercer
R. R.
, and
Crapo
J. D.
,
1987
, “
Three-Dimensional Reconstruction of the Rat Acinus
,”
J. Appl. Physiol.
, Vol.
63
, pp.
785
794
.
21.
Mercer
R. R.
, and
Crapo
J. D.
,
1990
, “
Spatial Distribution of Collagen and Elastin Fibers in the Lungs
,”
J. Appl. Physiol.
, Vol.
69
, pp.
756
765
.
22.
Mercer
R. R.
, and
Crapo
J. D.
,
1992
, “
Structural Changes in Elastic Fibers After Pancreatic Elastase Administration in Hamsters
,”
J. Appl. Physiol.
, Vol.
72
, pp.
1473
1479
.
23.
Oldmixon
E. H.
, and
Hoppin
F. G.
,
1984
, “
Comparison of Amounts of Collagen and Elastin in Pleura and Parenchyma of Dog Lung
,”
J. Appl. Physiol.
, Vol.
56
, pp.
1383
1388
.
24.
Oldmixon
E. H.
,
Butler
J. P.
, and
Hoppin
F. G.
,
1988
, “
Dihedral Angles Between Alveolar Septa
,”
J. Appl. Physiol.
, Vol.
64
, pp.
299
307
.
25.
Olmixon
E. H.
,
Butler
J. P.
and
Hoppin
F. G.
,
1989
, “
Lengths and Topology of Alveolar Septal Borders
,”
J. Appl. Physiol.
, Vol.
67
, pp.
1930
1940
.
26.
Oldmixon
E. H.
, and
Hoppin
F. G.
,
1989
, “
Distribution of Elastin and Collagen in Canine Lung Alveolar Parenchyma
,”
J. Appl. Physiol.
, Vol.
67
, pp.
1941
1949
.
27.
Scarpelli
E. M.
,
Clutario
B. C.
, and
Taylor
F. A.
,
1967
, “
Preliminary Identification of the Lung Surfactant System
,”
J. Appl. Physiol.
, Vol.
6
, pp.
880
886
.
28.
Schu¨rch
S.
,
Bachofen
H.
,
Goerke
J.
, and
Possmayer
F.
,
1989
, “
A Captive Bubble Method Reproduces the in Situ Behaviour of Lung Surfactant Molecules
,”
J. Appl. Physiol.
, Vol.
67
, pp.
2389
2396
.
29.
Sobin
S. S.
,
Fung
Y. C.
, and
Tremer
H. M.
,
1988
, “
Collagen and Elastin Fibers in Human Pulmonary Alveolar Walls
,”
J. Appl. Physiol.
, Vol.
64
, pp.
1659
1675
.
30.
Stromberg
D. D.
, and
Wiederhelm
C. A.
,
1969
, “
Viscoelastic Description of a Collagenous Tissue in Simple Elongation
,”
J. Appl. Physiol.
, Vol.
26
, pp.
857
862
.
31.
Suzuki
S.
,
Butler
J. P.
,
Oldmixon
E. B.
, and
Hoppin
F. G.
,
1985
, “
Light Scattering by Lungs Correlates with Stereological Measurements
,”
J. Appl. Physiol.
, Vol.
58
, pp.
97
104
.
32.
Vawter
D. L.
,
Fung
Y. C.
, and
West
J. B.
,
1978
, “
Elasticity of Exercised Dog Lung Parenchyma
,”
J. Appl. Physiol.
, Vol.
45
, pp.
261
269
.
33.
Wilson
T. A.
, and
Bachofen
H.
,
1982
, “
A Model for Mechanical Structure of the Alveolar Duct
,”
J. Appl. Physiol.
, Vol.
52
, pp.
1064
1070
.
34.
Wilson
T. A.
,
1982
, “
Surface Tension-Surface Area Curves Calculated from Presure-Volume Loops
,”
J. Appl. Physiol.
, Vol.
53
, pp.
1512
1520
.
35.
Yager
D.
,
Feldman
H.
, and
Fung
Y. C.
,
1992
, “
Microscopic vs. Macroscopic Deformation of the Pulmonary Alveolar Duct
,”
J. Appl. Physiol.
, Vol.
72
, pp.
1348
1354
.
This content is only available via PDF.
You do not currently have access to this content.