Low Reynolds number airflow in the pulmonary acinus and aerosol particle kinetics therein are significantly conditioned by the nature of the tidal motion of alveolar duct geometry. At least two components of the ductal structure are known to exhibit stress-strain hysteresis: smooth muscle within the alveolar entrance rings, and surfactant at the air-tissue interface. We hypothesize that the geometric hysteresis of the alveolar duct is largely determined by the interaction of the amount of smooth muscle and connective tissue in ductal rings, septal tissue properties, and surface tension-surface area characteristics of surfactant. To test this hypothesis, we have extended the well-known structural model of the alveolar duct by Wilson and Bachofen (1982, “A Model for Mechanical Structure of the Alveolar Duct,” J. Appl. Physiol. 52(4), pp. 1064–1070) by adding realistic elastic and hysteretic properties of (1) the alveolar entrance ring, (2) septal tissue, and (3) surfactant. With realistic values for tissue and surface properties, we conclude that: (1) there is a significant, and underappreciated, amount of geometric hysteresis in alveolar ductal architecture; and (2) the contribution of smooth muscle and surfactant to geometric hysteresis are of opposite senses, tending toward cancellation. Quantitatively, the geometric hysteresis found experimentally by Miki et al. (1993, “Geometric Hysteresis in Pulmonary Surface-to-Volume Ratio during Tidal Breathing,” J. Appl. Physiol. 75(4), pp. 1630–1636) is consistent with little or no smooth muscle tone in anesthetized rabbits in control conditions, and with substantial smooth muscle activation following methacholine challenge. The observed local hysteretic boundary motion of the acinar duct would result in irreversible acinar flow fields, which might be important mechanistic contributors to aerosol mixing and deposition deep in the lung.

References

References
1.
Tsuda
,
A.
,
Laine-Pearson
,
F. E.
, and
Hydon
,
P. E.
, 2011a, “
Why Chaotic Mixing of Particles is Inevitable in the Deep Lung
,”
J. Theor. Biol.
286
, pp.
57
66
.
2.
Tsuda
,
A.
,
Henry
,
F. S.
, and
Butler
,
J. P.
, 1995, “
Chaotic Mixing of Alveolated Duct Flow in Rhythmically Expanding Pulmonary Acinus
,”
J. Appl. Physiol.
,
79
(
3
), pp.
1055
1063
.
3.
Henry
,
F. S.
,
Butler
,
J. P.
, and
Tsuda
,
A.
, 2002, “
Kinematically Irreversible Flow and Aerosol Transport in the Pulmonary Acinus: A Departure from Classical Dispersive Transport
,”
J. Appl. Physiol.
,
92
, pp.
835
845
.
4.
Henry
,
F. S.
,
Laine-Pearson
,
F. E.
, and
Tsuda
,
A.
, 2009, “
Hamiltonian Chaos in a Model Alveolus
,”
ASME J. Biomech. Eng.
,
131
(
1
), pp.
011006
.
5.
Haber
,
S.
,
Butler
,
J. P.
,
Brenner
,
H.
,
Emanuel
,
I.
, and
Tsuda
,
A.
, 2000, “
Flow Field in Self-Similar Expansion on a Pulmonary Alveolus during Rhythmical Breathing
,”
J. Fluid Mech.
,
405
, pp.
243
268
.
6.
Haber
,
S.
,
Yitzhak
,
D.
, and
Tsuda
,
A.
, 2003, “
Gravitational Deposition in a Rhythmically Expanding and Contracting Alveolus
,”
J. Appl. Physiol.
,
95
, pp.
657
671
.
7.
Haber
,
S.
, and
Tsuda
,
A.
, 2006, “
Cyclic Model for Particle Motion in the Pulmonary Acinus
,”
J. Fluid Mech.
,
567
, pp.
157
184
.
8.
Ardila
,
R.
,
Horie
,
Y.
, and
Hildebrandt
,
J.
, 1974, “
Macroscopic Isotropy of Lung Expansion
,”
Respir. Physiol.
,
20
, pp.
105
115
.
9.
Gil
,
J.
, and
Weibel
,
E. R.
, 1972, “
Morphological STUDY of Pressure-Volume Hysteresis in Rat Lungs Fixed by Vascular Perfusion
,”
Respir. Physiol.
,
15
, pp.
190
213
.
10.
Gil
,
J.
,
Bachofen
,
H.
,
Gehr
,
P.
, and
Weibel
,
E. R.
, 1979, “
Alveolar Volume-Surface Area Relation in Air- and Saline-Filled Lungs Fixed by Vascular Perfusion
,”
J. Appl. Physiol. Respir., Environ. Excercise Physiol.
,
47
(
5
), pp.
990
1001
.
11.
Miki
,
H.
,
Butler
,
J. P.
,
Roger
,
R. A.
, and
Lehr
,
J. L.
, 1993, “
Geometric Hysteresis in Pulmonary Surface–to-Volume Ratio during Tidal Breathing
,”
J. Appl. Physiol.
,
75
(
4
), pp.
1630
1636
.
12.
Weibel
,
E. R.
, and
Gil
,
J.
, 1977, “
Alveolar Structure-Function Relationships
,”
Bioengineering Aspects of the Lung
,
J. B.
West
, ed.,
Marcel Dekker
,
New York
.
13.
Weibel
,
E. R.
, 1986, “
Functional Morphology of Lung Parenchyma
,”
Handbook of Physiology, The Respiratory System
,
A. P.
Fishman
, ed., Sec. 3, Vol.
III
, Chap. 8,
American Physiological Society
,
Bethesda, MD
, pp.
89
111
.
14.
Butler
,
J. P.
, and
Tsuda
,
A.
, 2005, “
Logistic Trajectory Maps and Aerosol Mixing due to Asynchronous Flow at Airway Bifurcations
,”
Respir. Physiol. Neurobiol.
,
148
, pp.
195
206
.
15.
Tsuda
,
A.
,
Otani
,
Y.
, and
Butler
,
J. P.
, 1999, “
Acinar Flow Irreversibility Caused by Boundary Perturbation of Reversible Alveolar Wall Motion
,”
J. Appl. Physiol.
,
86
(
3
), pp.
977
984
.
16.
Tsuda
,
A.
,
Rogers
,
R. A.
,
Hydon
,
P. E.
, and
Butler
,
J. P.
, 2002, “
Chaotic Mixing Deep in the Lung
,”
Proc. Natl. Acad. Sci. U.S.A.
,
99
, pp.
10173
10178
.
17.
Tsuda
,
A.
,
Henry
,
F. S.
, and
Butler
,
J. P.
, 2008, “
Gas and Aerosol Mixing in the Acinus
,”
Respir. Physiol. Neurobiol.
,
163
(
1–3
), pp.
139
149
.
18.
Tsuda
,
A.
,
Henry
,
F. S.
, and
Butler
,
J. P.
, 2011, “
Particle Transport and Deposition
,” Comprehensive Physiology,
J.
Fredberg
,
G.
Sieck
, and
W.
Gerthoffer
, eds.,
Amer. Physiol. Soc.
, in press.
19.
Wilson
,
T. A.
, and
Bachofen
,
H.
, 1982, “
A Model for Mechanical Structure of Alveolar Duct
,”
J. Appl. Physiol., Respir. Environ. Excercise Physiol.
,
52
(
4
), pp.
1064
1070
.
20.
Ingenito
,
E. P.
,
Mark
,
L.
,
Morris
,
J.
,
Espinosa
,
F. F.
,
Kamm
,
R. D.
, and
Johnson
,
M.
, 1999, “
Biophysical Characterization and Modeling of Lung Surfactant Components
,”
J. Appl. Physiol.
,
86
(
5
), pp.
1702
1714
.
21.
Sasaki
,
H.
, and
Hoppin
,
F. G.
, Jr.
, 1979, “
Hysteresis of Contracted Airway Smooth Muscle
,”
J. Appl. Physiol.: Respir. Environ. Exercise Physiol.
,
47
(
6
), pp.
1251
1262
.
22.
Oldmixon
,
E. H.
,
Butler
,
J. P.
, and
Hoppin
,
F. G.
, Jr.
, 1989, “
Lengths and Topology of Alveolar Septal Borders
,”
J. Appl. Physiol.
,
67
(
5
), pp.
1930
1940
.
23.
Oldmixon
,
E. H.
, and
Hoppin
,
F. G.
, Jr.
, 1989, “
Distribution of Elastin and Collagen in Canine Lung Alveolar Parenchyma
,”
J. Appl. Physiol.
,
67
(
5
), pp.
1941
1949
.
24.
Oldmixon
,
E. H.
,
Carlsson
,
K.
,
Kuhn
,
C.
III.
,
Butler
,
J. P.
, and
Hoppin
,
F. G.
, Jr.
, 2001, “
α-Actin: Disposition, Quantities, and Estimated Effects on Lung Recoil and Compliance
,”
J. Appl. Physiol.
,
91
, pp.
459
473
.
25.
Suki
,
B.
,
Barabási
,
A. L.
, and
Lutchen
,
K. R.
, 1994, “
Lung Tissue Viscoelasticity: A Mathematical Framework and its Molecular Basis
,”
J. Appl. Physiol.
,
76
(
6
), pp.
2749
2759
.
26.
Yuan
,
H.
,
Westwick
,
D. T.
,
Ingenito
,
E. P.
,
Lutchen
,
K. R.
, and
Suki
,
B.
, 1999, “
Parametric and Nonparametric Nonlinear System Identification of Lung Tissue Strip Mechanics
,”
Ann. Biomed. Eng.
,
27
(
4
), pp.
548
562
.
27.
Gunst
,
S. J.
, 1983, “
Contractile Force of Canine Airway Smooth Muscle during Cyclical Length Changes
,”
J. Appl. Physiol.: Respir. Environ. Exercise Physiol.
,
55
(
3
), pp.
759
769
.
28.
Shen
,
H. M.
,
Wu
,
F.
,
Tepper
,
R. S.
, and
Gunst
,
S. J.
, 1997, “
Mechanisms for the Mechanical Response of Airway Smooth Muscle to Length Oscillation
,”
J. Appl. Physiol.
,
83
(
3
), pp.
731
738
.
29.
Fukaya
,
H.
,
Martin
,
C. J.
,
Young
,
A. C.
, and
Katsura
,
S.
, 1968, “
Mechanical Properties of Alveolar Walls
,”
J. Appl. Physiol.
,
25
(
6
), pp.
689
695
.
30.
Hildebrandt
,
J.
,
Fukaya
,
H.
, and
Martin
,
C. J.
, 1969, “
Stress-Strain Relations of Tissue Sheets Undergoing Uniform Two-Dimensional Stretch
,”
J. Appl. Physiol.
,
27
(
5
), pp.
758
762
.
31.
Lee
,
C. G.
, and
Hoppin
,
F. G.
, Jr.
, 1972, “
Lung Elasticity
,”
Biomechanics – Its Foundations and Objectives
,
Y. C.
Fung
,
N.
Perrone
, and
M.
Anliker
, eds.,
Prentice-Hall
,
Englewood Cliffs
, pp.
317
335
.
32.
Krueger
,
M. A.
, and
Gaver
,
D. P.
III.
, 2000, “
A Theoretical Model of Pulmonary Surfactant Multilayer Collapse under Oscillating Area Conditions
,”
J. Colloid Interface Sci.
,
229
, pp.
335
364
.
33.
Schurch
,
S.
,
Bachofen
,
H.
, and
Possmayer
,
F.
, 2001, “
Surface Activity In Situ, in vivo, and in Captive Bubble Surfactometer
,”
Comp. Biochem. Physiol.
, Part A,
129
, pp.
195
207
.
34.
Smith
,
J. C.
, and
Stamenovic
,
D.
, 1986, “
Surface Forces in Lungs. I. Alveolar Surface Tension-Lung Volume Relationships
,”
J. Appl. Physiol.
,
60
(
4
), pp.
1341
1350
.
35.
Wilson
,
T. A.
, 1982, “
Surface Tension-Surface Area Curves Calculated from Pressure-Volume Loops
,”
J. Appl. Physiol.: Respir. Environ. Exercise. Physiol.
,
53
(
6
), pp.
1512
1520
.
36.
Bachofen
,
H. P.
, and
Schurch
,
H.
, 2001, “
Alveolar Surface Forces and Lung Architecture
,”
Comp. Biochem. Physiol., Part A
,
129
, pp.
183
193
.
37.
Bachofen
,
H. P.
,
Gehr
,
P.
, and
Weibel
,
E. R.
, 1979, “
Alterations of Mechanical Properties and Morphology in Excised Rabbit Lungs Rinsed with Detergent
,”
J. Appl. Physiol. Respir. Environ. Exercise. Physiol.
,
47
, pp.
1002
1010
.
38.
Sakai
,
H.
,
Ingenito
,
E. P.
,
Mora
,
R.
,
Abbay
,
S.
,
Cavalcante
,
F. S.
,
Lutchen
,
K. R.
, and
Suki
,
B.
, 2001, “
Hysteresivity of the Lung and Tissue Strip in the Normal Rat: Effects of Heterogeneities
,”
J. Appl. Physiol.
,
91
, pp.
737
747
.
39.
Schürch
,
S.
,
Bachofen
,
H. P.
,
Goerke
,
J.
,
Green
,
F.
, 1992, “
Surface Properties of Rat Pulmonary Surfactant Studied with the Captive Bubble Method: Adsorption, Hysteresis, Stability
,”
Biochim. Biophys. Acta
,
1103
, pp.
127
136
.
40.
Denny
,
E.
, and
Schroter
,
R. C.
, 2000, “
Viscolelastic Behavior of a Lung Alveolar Duct Model
,”
J. Biomech. Eng. Trans. ASME
,
122
, pp.
143
151
.
41.
Bathe
,
K. J.
, 1996,
Finite Element Procedures
,
Prentice-Hall
,
Englewood Cliffs
.
42.
Kojic
,
M.
, and
Bathe
,
K. J.
, 2005,
Inelastic Analysis of Solids and Structures
,
Springer
,
Berlin
.
43.
Kojic
,
M.
,
Filipovic
,
N.
,
Stojanovic
,
B.
, and
Kojic
,
N.
, 2008,
Computer Modeling in Bioengineering – Theoretical Background, Examples and Software
,
J. Wiley and Sons
,
Chichester
.
44.
Kojic
,
M.
,
Slavkovic
,
R.
,
Zivkovic
,
M.
,
Grujovic
,
N.
, and
Filipovic
,
N.
, 1998,
PAK- Finite Element Program for Linear and Nonlinear Analysis
,
Mechanical Engineering Dept. University of Kragujevac
,
Kragujevac, Serbia
.
45.
Kojic
,
M.
,
Vlastelica
,
I.
,
Stojanovic
,
B.
,
Rankovic
,
V.
, and
Tsuda
,
A.
, 2006, “
Stress Integration Procedures for a Biaxial Isotropic Material Model of Biological Membranes and Hysteretic Models of Muscle Fibers and Surfactant
,”
Int. J. Numer. Methods Eng.
,
68
, pp.
893
909
.
46.
Bachofen
,
H.
, and
Hildebrandt
,
J.
, 1971, “
Area Analysis of Pressure-Volume Hysteresis in Mammalian Lungs
,”
J. Appl. Physiol.
,
30
(
4
), pp.
493
497
.
47.
Fredberg
,
J. J.
, and
Stamenovic
,
D.
, 1989, “
On the Imperfect Elasticity of Lung Tissue
,”
J. Appl. Physiol.
,
67
(
6
), pp.
2408
2419
.
48.
Fung
,
Y. C.
, 1990,
Biomechanics – Motion, Flow, Stress, and Growth
,
Springer-Verlag
,
New York
.
49.
Budiansky
,
B.
, and
Kimmel
,
E.
, 1987, “
Elastic Moduli in Lungs
,”
J. Appl. Mech. Trans. ASME
,
54
, pp.
351
358
.
50.
Dale
,
P. J.
,
Matthews
,
F. L.
, and
Shroter
,
R. C.
, 1980, “
Finite Element Analysis of Lung Alveolus
,”
J. Biomech.
,
13
, pp.
865
873
.
51.
Denny
,
E.
, and
Schroter
,
R. C.
, 1995, “
The Mechanical Behavior of Mammalian Lung Alveolar Duct Model
,”
J. Biomech. Eng. Trans. ASME
,
117
, pp.
254
261
.
52.
Denny
,
E.
, and
Schroter
,
R. C.
, 1997, “
Relationships between Alveolar Size and Fibre Distribution in a Mammalian Lung Alveolar Duct Model
,”
J. Biomech. Eng. Trans. ASME
,
119
, pp.
289
297
.
53.
Denny
,
E.
, and,
Schroter
,
R. C.
, 2006, “
A Model of Non-Uniform Lung Parenchyma Distortion
,”
J. Biomech.
,
39
, pp.
652
663
.
54.
Kimmel
,
E.
, and
Budiansky
,
B.
, 1990, “
Surface Tension and the Dodecahedron Model for Lung Elasticity
,”
J. Biomed. Eng. Trans. ASME
,
112
, pp.
160
167
.
55.
Kowe
,
R.
,
Schroter
,
R. C.
,
Matthews
,
F. L.
,
Hitchings
,
D. L.
, 1986, “
Analysis of Elastic and Surface Tension Effects in the Lung Alveolus using Finite Element Methods
,”
J. Biomech.
,
19
(
7
), pp.
541
549
.
56.
Dickie
,
R.
,
Wang
,
Y. T.
,
Butler
,
J. P.
,
Schulz
,
H.
, and
Tsuda
,
A.
, 2008, “
Distribution and Quantity of Contractile Tissue in Postnatal Development of Rat Alveolar Interstitium
,”
Anat. Rec.: Adv. Integrative Anat. Evol. Biol.
,
291
(
1
), pp.
83
93
.
57.
Stamenovic
,
D.
, and
Smith
,
J. C.
, 1986, “
Surface Forces in Lungs. II. Microstructural Mechanics and Lung Stability
,”
J. Appl. Physiol.
,
60
(
4
), pp.
1351
1357
.
58.
Mijailovic
,
S.
, 2003, private communication.
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