The function of the esophagus is mechanical. To understand the function, it is necessary to know how the stress and strain in the esophagus can be computed, and how to determine the stress-strain relationship of the wall materials. The present article is devoted to the issue of determining the incremental elastic moduli in the layers of the esophagus under homeostatic conditions. The esophagus is treated as a two-layered structure consisting of an inner collagen-rich submucosa layer and an outer muscle layer. We adopt a theory based on small perturbation experiments at homeostatic conditions for determination of incremental moduli in circumferential, axial, and cross directions in the two layers. The experiments are inflation, axial stretching, circumferential bending, and axial bending. The analysis takes advantage of knowing the esophageal zero-stress state (an open sector with an opening angle of 59.4±13.2deg). The neutral axis was located 27%±1.9%away from the mucosal surface. It is demonstrated that under homeostatic conditions, the incremental moduli are layer and direction dependent. The incremental modulus is the highest in the axial direction. Furthermore, the axial moduli for the two layers are similar, whereas in the circumferential direction, the incremental modulus is a factor of 6 higher in the mucosa-submucosa layer compared to the muscle layer. Hence, the esophagus has to be treated as a composite, anisotropic body. With this additional information, we can then look forward to a vision of truly understanding the mechanical events of the esophagus.

1.
Lu
,
X.
,
Pandit
,
A.
, and
Kassab
,
G. S.
, 2004, “
Biaxial Incremental Homeostatic Elastic Moduli of Coronary Artery: Two-Layer Model
,”
Am. J. Physiol. Heart Circ. Physiol.
0363-6135,
287
(
4
), pp.
H1663
H1669
.
2.
Frokjaer
,
J. B.
,
Andersen
,
S. D.
,
Lundbye-Christensen
,
S.
,
Funch-Jensen
,
P.
,
Drewes
,
A. M.
, and
Gregersen
,
H.
, 2006, “
Sensation and Distribution of Stress and Deformation in the Human Oesophagus
,”
Neurogastroenterol Motil
1350-1925,
18
(
2
), pp.
104
114
.
3.
Kassab
,
G. S.
, and
Navia
,
J. A.
, 2006, “
Biomechanical Considerations in the Design of Graft: The Homeostasis Hypothesis
,”
Annu. Rev. Biomed. Eng.
1523-9829,
8
, pp.
499
535
.
4.
Gleason
,
R. L.
,
Wilson
,
E.
, and
Humphrey
,
J. D.
, 2006, “
Biaxial Biomechanical Adaptations of Mouse Carotid Arteries Cultured at Altered Axial Extension
,”
J. Biomech.
0021-9290,
40
(
4
), pp.
766
776
.
5.
Liao
,
D.
,
Cassin
,
J.
,
Zhao
,
J.
, and
Gregersen
,
H.
, 2006, “
The Geometric Configuration and Morphometry of the Rabbit Oesophagus During Luminal Pressure Loading
,”
Physiol. Meas
0967-3334,
27
(
8
), pp.
703
711
.
6.
Yang
,
J.
,
Zhao
,
J.
,
Liao
,
D.
, and
Gregersen
,
H.
, 2006, “
Biomechanical Properties of the Layered Oesophagus and its Remodelling in Experimental Type-1 Diabetes
,”
J. Biomech.
0021-9290,
39
(
5
), pp.
894
904
.
7.
Fan
,
Y.
,
Zhao
,
J.
,
Liao
,
D.
, and
Gregersen
,
H.
, 2005, “
The Effect of Digestion of Collagen and Elastin on Histomorphometry and the Zero-Stress State in Rat Esophagus
,”
Dig. Dis. Sci.
0163-2116,
50
(
8
), pp.
1497
505
.
8.
Fan
,
Y.
,
Gregersen
,
H.
, and
Kassab
,
G. S.
, 2004, “
A Two-Layered Mechanical Model of the Rat Esophagus. Experiment and Theory
,”
Biomed. Eng. Online
1475-925X,
40
, pp.
1
9
.
9.
Liao
,
D.
,
Zhao
,
J.
,
Fan
,
Y.
, and
Gregersen
,
H.
, 2004, “
Two-Layered Quasi-3D Finite Element Model of the Oesophagus
,”
Med. Eng. Phys.
1350-4533,
26
(
7
), pp.
535
543
.
10.
Liao
,
D.
,
Fan
,
Y.
,
Zeng
,
Y.
, and
Gregersen
,
H.
, 2003, “
Stress Distribution in the Layered Wall of the Rat Oesophagus
,”
Med. Eng. Phys.
1350-4533,
25
(
9
), pp.
731
8
.
11.
Gregersen
,
H.
,
Lee
,
T. C.
,
Chien
,
S.
,
Skalak
,
R.
, and
Fung
,
Y. C.
, 1999, “
Strain Distribution in the Layered Wall of the Esophagus
,”
ASME J. Biomech. Eng.
0148-0731,
121
, pp.
442
448
.
12.
Fung
,
Y. C.
, and
Liu
,
S. Q.
, 1995, “
Determination of the Mechanical Properties of the Different Layers of Blood Vessel In Vivo
,”
Proc. Natl. Acad. Sci. U.S.A.
0027-8424,
92
, pp.
2169
2173
.
13.
Gregersen
,
H.
, 2002,
Biomechanics of the Gastrointestinal Tract
,
Springer
,
London
.
14.
Yang
,
J.
,
Zhao
,
J.
,
Zeng
,
Y.
, and
Gregersen
,
H.
, 2004, “
Biomechanical Properties of the Rat Oesophagus in Experimental Type-1 Diabetes
,”
Neurogastroenterol Motil
1350-1925,
16
(
2
), pp.
195
203
.
15.
Fung
,
Y. C.
,
Liu
,
S. Q.
, and
Zhou
,
J. B.
, 1993, “
Remodeling of the Constitutive Equation While a Blood Vessel Remodels Itself Under Stress
,”
ASME J. Biomech. Eng.
0148-0731,
115
, pp.
1670
1676
.
16.
Fung
,
Y. C.
, 1993,
Biomechanics: Mechanical Properties of Living Tissues
,
Springer-Verlag
,
New York
,
2nd ed.
, pp.
350
351
.
17.
Chuong
,
C. J.
, and
Fung
,
Y. C.
, 1986, “
On Residual Stress in Arteries
,”
ASME J. Biomech. Eng.
0148-0731,
108
, pp.
189
192
.
18.
Liu
,
S. Q.
, and
Fung
,
Y. C.
, 1988, “
Zero-Stress State of Arteries
,”
ASME J. Biomech. Eng.
0148-0731,
110
, pp.
82
84
.
19.
Siegle
,
M. L.
, and
Ehrlein
,
H. J.
, 1989, “
Effects of Various Agents on Ileal Postprandial Motor Patterns and Transit of Chyme in Dogs
,”
Am. J. Physiol.
0002-9513,
257
, pp.
G698
G703
.
20.
Christensen
,
J.
,
Freeman
,
B. W.
, and
Miller
,
J. K.
, 1973, “
Some Physiological Characteristics of the Esophagogastric Junction in the Opossum
,”
Gastroenterology
0016-5085,
64
, pp.
1119
1125
.
21.
Wareham
,
A. C.
, and
Whitmore
,
I.
, 1982, “
A Comparison of the Mechanical Properties of Oesophageal Striated Muscle With Skeletal Muscles of the Guinea Pig
,”
Pfluegers Arch.
0031-6768,
395
, pp.
312
317
.
22.
Gregersen
,
H.
,
Giversen
,
I. M.
,
Rasmussen
,
L. M.
, and
Tøttrup
,
A.
, 1992, “
Biomechanical Wall Properties and Collagen Content in the Partially Obstructed Opossum Esophagus
,”
Gastroenterology
0016-5085,
103
, pp.
1547
1551
.
23.
Vinter-Jensen
,
L.
,
Juhl
,
C. O.
, and
Gregersen
,
H.
, 1994, “
Regional Differences in Passive Elastic Wall Properties of the Esophagus: An Impedance Planimetric Study in Pigs
,”
Neurogastroenterol Motil
1350-1925,
6
, pp.
233
238
.
24.
Gregersen
,
H.
, and
Kassab
,
G. S.
, 1996, “
Biomechanics of the Gastrointestinal Tract
,”
Neurogastroenterol Motil
1350-1925,
8
, pp.
277
297
.
25.
Fung
,
Y. C.
, and
Liu
,
S. Q.
, 1989, “
Changes of Residual Strains in Arteries Due to Hypertrophy Caused by Aortic Constriction
,”
Circ. Res.
0009-7330,
65
, pp.
1340
1349
.
26.
Fung
,
Y. C.
, and
Liu
,
S. Q.
, 1991, “
Changes of the Zero-Stress State of Rat Pulmonary Arteries in Hypoxic Hypertension
,”
J. Appl. Physiol.
8750-7587,
70
, pp.
2455
2470
.
27.
Liu
,
S. Q.
, and
Fung
,
Y. C.
, 1989, “
Relationship Between Hypertension, Hypertrophy, and Opening Angle of Zero-Stress State of Arteries Following Aortic Constriction
,”
ASME J. Biomech. Eng.
0148-0731,
111
, pp.
325
335
.
28.
Han
,
H. C.
, and
Fung
,
Y. C.
, 1991, “
Species Difference of the Zero-Stress State of Aorta: Pig vs. Rat
,”
ASME J. Biomech. Eng.
0148-0731,
113
, pp.
446
451
.
29.
Han
,
H. C.
, and
Fung
,
Y. C.
, 1988, “
Residual Strains in Porcine and Canine Trachea
,”
J. Biomech.
0021-9290,
24
, pp.
307
315
.
30.
Omens
,
J. H.
, 1988, “
Left Ventricular Strain in the No-Load State Due to the Existence of Residual Stress
,” Ph. D. thesis. University of California, San Diego.
31.
Omens
,
J. H.
, and
Fung
,
Y. C.
, 1990, “
Residual Strain in the Rat Left Ventricle
,”
Circ. Res.
0009-7330,
66
, pp.
37
45
.
32.
Vaishnav
,
R. N.
, and
Vossoughi
,
J.
, 1987, “
Residual Stress and Strain—in Aortic Segments
,”
J. Biomech.
0021-9290,
20
, pp.
235
239
.
33.
Vossoughi
,
J.
,
Weizsacker
,
H. E.
, and
Vaishnav
,
R. N.
, 1985, “
Variation of Aortic Geometry in Various Animal Species
,”
Biomed. Tech.
0013-5585,
30
, pp.
48
54
.
34.
Xie
,
J. P.
,
Liu
,
S. Q.
,
Yang
,
R. F.
, and
Fung
,
Y. C.
, 1991, “
The Zero-Stress State of Rat Veins and Vena Cava
,”
ASME J. Biomech. Eng.
0148-0731,
113
, pp.
36
41
.
35.
Ravinder
,
K. M.
,
Ren
,
J.
,
McCallum
,
R. W.
,
Shaffer
,
H. A.
, and
Sluss
,
J.
, 1990, “
Modulation of Feline Oesophageal Contractions by Bolus Volume and Outflow Obstruction
,”
Am. J. Physiol.
0002-9513,
258
, pp.
G208
G215
.
36.
Xie
,
J. P.
,
Zhou
,
J. B.
, and
Fung
,
Y. C.
, 1995, “
Bending of Blood Vessel Wall: Stress-Strain Laws of the Intima-Media and Adventitial Layers
,”
ASME J. Biomech. Eng.
0148-0731,
117
, pp.
136
145
.
37.
Yu
,
Q. L.
,
Zhou
,
J. B.
, and
Fung
,
Y. C.
, 1993, “
Neutral Axis Location in Bending and Young’s Modulus of Different Layers of Arterial Wall
,”
Am. J. Physiol.
0002-9513,
265
, pp.
H52
H60
.
38.
Berry
,
J.
,
Rachev
,
A.
,
Moore
, Jr.,
J. E.
, and
Meister
,
J. L.
, 1992, “
Analysis of the Effect of a Non-Circular Two-Layer Stress-Free State on Arterial Wall Stress
,”
Proceedings of the IEEE EMBS
, pp.
65
66
.
39.
Demiray
,
H.
, and
Vito
,
R. P.
, 1991, “
A Layered Cylindrical Shell Model for an Aorta
,”
Int. J. Eng. Sci.
0020-7225,
29
, pp.
47
54
.
40.
Maltzahn
,
W. W. V.
,
Besdo
,
D.
, and
Wiemer
,
W.
, 1981, “
Elastic Properties of Arteries. A Nonlinear Two-Layer Cylindrical Model
,”
J. Biomech.
0021-9290,
14
, pp.
389
397
.
41.
Maltzahn
,
W. W. V.
,
Warringar
,
R. G.
, and
Keitzer
,
W. F.
, 1984, “
Experimental Measurement of Soft Elastic Properties of Media and Adventitia of Bovine Carotid Arteries
,”
J. Biomech.
0021-9290,
17
, pp.
839
848
.
42.
Rachev
,
A.
, 1997, “
Theoretical Study of the Effect of Stress-Dependent Remodeling on Arterial Geometry Under Hypertensive Conditions
,”
J. Biomech.
0021-9290,
30
, pp.
819
827
.
You do not currently have access to this content.