Morphometry and strain distribution in guinea pig duodenum
with reference to the zero-stress state
H.
Gregersen1,2,
G.
Kassab1,
E.
Pallencaoe1,
C.
Lee1,
S.
Chien1,3,
R.
Skalak
,2,3, and
Y. C.
Fung1,3
1 Department of Bioengineering,
3 Institute for Biomedical
Engineering, and 2 Institute of
Mechanics and Materials, University of California, San Diego, La Jolla,
California 92093-0404
 |
ABSTRACT |
The aim of the present study is to determine the
distribution of residual circumferential strains along the duodenum in
anesthetized guinea pigs. A silicone elastomer was allowed to harden in
the duodenal lumen under a pressure of 0.7 kPa. The duodenum was
excised with the cast and photographed. The zero-stress state was
obtained by cutting rings of duodenum radially. The geometric
configuration at the zero-stress state is of fundamental importance,
because it is the basic state with respect to which the physical
stresses and strains are defined. A basic piece of information is the
way the tangent vector rotates from one end of the circumference
to the other. In the duodenum at zero-stress state, the total rotation of the tangent from one tip to the other is
500 to
850°, with the lowest absolute value in the proximal
duodenum. In other words, the duodenum usually turns itself inside out
on changing from a loaded state to the zero-stress state. The serosal
circumference, the duodenal wall thickness, and the ratio of wall
thickness to mucosal circumference decreased in the distal direction.
In the pressurized state, the serosal Cauchy strain was tensile and
increased in the distal direction; the mucosal Cauchy strain was
compressive in the proximal half of the duodenum and tensile in the
distal half. The large circumferential residual strains must be taken into account in a study of physiological problems in which the stresses
and strains are important, e.g., the bolus transport function.
biomechanics; mucosal compression; residual strain; small
intestine; tangent rotation angle
 |
INTRODUCTION |
THE FUNCTION OF THE DUODENUM is mechanical
to a large degree. Contents received from the stomach are propelled
further down the intestine and mixed with secreted fluids to digest and
absorb the food constituents. Data in the literature pertaining to the mechanical aspects of duodenal function are concerned with the contraction patterns (4, 16, 22), the length-tension relationship in
circular and longitudinal tissue strips (32), fluid mechanics (29), and
the compliance and the stress-strain relationship of the walls (26).
However, the constitutive equation, which is the mathematical
description of the relationship between physical stresses and strains
in three dimensions, is basically unknown. The three-dimensional
distribution of stress and strain in the duodenum and the effect of
stress and strain on the biology of the mucosa, submucosa, and
longitudinal and circumferential muscles have not been studied in
detail. It is the objective of this study to make a beginning. For this
purpose, the overall scheme must be briefly described. Because the
active contraction of the muscles is the most important feature of the
peristaltic movement of the duodenum, the method of handling the
muscles must be described first. We shall use the "three-element
model" of Nobel Laureate A. V. Hill from 1939. The model considers
the tissue to be composed of a "contractile element" connected
with a "series elastic element" to describe the active
contraction of the muscle and a "parallel element" to describe
the connective tissue. This model has been applied extensively to the
mechanics of the heart, lung, blood vessels, and kidney. No competing
model had better success. With regard to the duodenum, we consider the
mucosa, the submucosa, and the quiescent muscles as parallel
elements, whereas the contractile and series elastic
elements belong to the active muscles. Continuum mechanics will link
all the elements together. This study deals with the parallel elements
exclusively.
Strain describes the mechanical deformation of a material. In
biomechanics, strains express dimensionless fractional changes in
dimensions and are related to stresses. In a distensible biologic tube
like the duodenum, the principal strain of interest is the circumferential strain. To compute the strains under physiological or
pathophysiological conditions, one must know the configuration at which
the stress is zero. In recent years, it has become evident that in
blood vessels, airways, and the heart wall the zero-stress state is
very different from the no-load state, in which all the external loads
are removed. A simple way to approach the zero-stress state is to cut
the organ under study transversely into a series of short ring-shaped
segments and then to cut each ring once radially (5, 6, 27), causing it
to open into a sector (Fig.
1B). The
closed ring with zero transmural pressure is the no-load state (Fig.
1A), but it may have locked-in
stresses called residual stresses in this state. These residual
stresses can be characterized by an opening angle (Fig.
1B). The strain differences between the zero-stress state and the no-load state are called the residual strains. Current literature on the zero-stress state contains data on
the opening angles of systemic and pulmonary arteries of normal,
hypertensive, and diabetic rats (8, 9, 12, 17), normal systemic
arteries of pigs and rabbits (12, 28), systemic veins of rats (30), the
left ventricle of rats (21), and the trachea of pigs and dogs (13).
This listing of references for these organs is not comprehensive, but
we are not aware of any such study aimed specifically at the
gastrointestinal (GI) tract. We found that the duodenum has a greater
opening angle than any other organs known today (see below).

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Fig. 1.
A: no-load state. Dashed lines, radial
cuts to obtain zero-stress states as shown in
B and
C. B:
definition of zero-stress state. Traditionally, zero-stress state is
characterized by an opening angle ( ) defined as the angle subtended
by 2 radii drawn from the midpoint of the inner wall to the inner tips
of the 2 ends of the specimen in zero-stress state. The tangent
rotation angle, which was used in this study, is denoted by .
C: 3 pieces of a ring produced by 3 radial cuts. It is assumed that the tangent rotation angle turns
segments inside out, as indicated by labels M (mucosa) and S (serosa).
Angles subtended by tangents to each end of the 3 pieces are added
together (see Fig. 3).
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We measured the circumferential strains with respect to the zero-stress
state in the guinea pig duodenum and correlated these measurements with
morphometric data. New experimental data obtained here allow the
computation of the circumferential strain directly, taking the residual
strains into account without invoking the unknown constitutive
equation. In blood vessels the zero-stress state can be obtained by one
radial cut and can be characterized by an opening angle. In the
duodenum we found that the same method did not work. Cutting of the
duodenum required elaborate preparation, and the measurement of the
opening angle, which in the duodenum is much larger than 360°, was
difficult. Consequently, a tangent rotation angle is introduced,
instead of the traditional opening angle, as a measure of the residual
strain. The mucosal layer is shown to be under compression in the
circumferential direction in the resting state and at low pressures. A
large variation along the length of the duodenum is demonstrated for
most of the biomechanical and morphometric parameters.
The effect of the zero-stress state on physiology may not be obvious
until the full Hill's model is analyzed. It is clear, however, that it
is a fundamental feature of the parallel element. The function of the
contractile element depends on the parallel element. For example, the
length of the muscle cell depends on the strain of the parallel
element; hence, whether the muscle can achieve the optimum length of
the length-tension relationship for its contraction depends on the
zero-stress state of the parallel element in principle.
 |
MATERIALS AND METHODS |
Seven guinea pigs (Cavia porcellus,
800 g) of both sexes were used in this study. The experiments were
carried out in accordance with the guidelines of the American
Physiological Society and had been approved by the Animal Subject
Committee of the University of California, San Diego. The animals were
anesthetized with ketamine (25 mg/kg im) and xylazine (0.25 mg/kg im).
Atropine, a muscarinic receptor blocker, was administered
intramuscularly before surgery. After the attainment of surgical
anesthesia, a short midline abdominal incision was performed, and a
small incision was made in the proximal part of the jejunum. A soft
polyvinylchloride (PVC) tube (4.8 mm OD, 3.2 mm ID) was inserted in the
proximal direction and fixed by ligation without damaging the adjacent
vessels. Care was taken not to ligate the duodenal blood vessels. A
small incision was then made in the stomach, and a soft PVC catheter
(2.4 mm OD, 1.3 mm ID) was inserted and gently guided through the
pylorus into the duodenal bulb. A small incision was made in the
mesenterium, and the pylorus was ligated without affecting the adjacent
blood vessels. At this point the gallbladder was punctured to empty its
contents, since pilot studies showed that bile would otherwise flow
from the bile tract into the duodenum and interfere with the hardening
of the silicone elastomer. The stomach tube was connected to a fluid
container, and the duodenal lumen was perfused under low pressure
(inlet pressure of ~0.5 kPa) with calcium-free Krebs solution
containing 6% dextran and 2 mM ethylene glycol-bis(
-aminoethyl ether)-N,N,N',N'-tetraacetic
acid (EGTA) to clear the lumen of its contents and to relax the smooth
muscles. No further contractile activity was observed in the duodenum
in situ and ex situ in the organ bath (see below). After ~10 min the
Krebs solution was replaced with 30 ml of a catalyzed silicone
elastomer solution (Microfil CP-101, Flow Tek, Boulder, CO) at an inlet
pressure of 0.7 kPa. The use of silicone elastomer makes it possible to
reconstruct organ geometry (15). After perfusion for 5 min the outlet
from the proximal jejunum was clamped. The silicone elastomer was
catalyzed with 5% tin octate and 25% ethyl silicate (15) to harden in ~20 min. After hardening of the cast, the whole duodenum, including its mesenterium, the cast, and the most adjacent part of the catheters, was quickly dissected free and immersed in an organ bath containing the
Krebs solution with dextran and EGTA aerated with 95%
O2-5% CO2 at pH 7.4 and room
temperature. Within a short time, the duodenal surface was cleaned and
dissected free of the mesenterium, and the free ends of the tubing were
cut. Figure 2 shows the isolated duodenum
with the cast inside. At this time, the duodenum with the cast inside
was cut into approximately seven smaller samples. These cuts were made
transversely through the structure in specific locations, so that the
individual samples were straight. This facilitated photographing the
samples from two directions corresponding to the major and minor
diameters of the duodenum with the cast (loaded-state serosal
diameters), the cast itself (loaded-state mucosal diameters), and the
duodenum without the cast inside (no-load state). The duodenum in its
no-load state and the cast were approximately equal in length, showing
that longitudinal strain in the loaded state was negligible.
Unfortunately, the no-load state of the samples could not be evaluated
further, since the sections tended to twist and did not conform to any
simple geometric shape. At this stage, two to four short rings from
each specimen were cut radially to obtain the zero-stress state. The
axial locations of these rings were noted. The width (1-2 mm) was
chosen on the basis of pilot experiments (shorter rings tend to curl,
and wider rings heel in the longitudinal direction to impede movement
in the circumferential direction).

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Fig. 2.
Photograph of isolated duodenal segment with cast inside. Proximal end
(duodenal bulb) is located adjacent to scale.
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Characterization of the zero-stress state.
The traditional method for characterizing the zero-stress state is
based on measurement of the opening angle (Fig.
1B in Ref. 5) denoted by
and
defined as the angle subtended by two radii drawn from the midpoint of
the inner wall to the inner tips of two ends of the specimen in the
zero-stress state. When this method is applied to the duodenal
specimens, one has to follow the tips as they open. When a section
becomes completely inside out, the opening angle is 360°. The
duodenum often has
> 360° at zero-stress state. In fact, most
rings turned the mucosa to the outside even before the first radial
cut, indicating large compressive forces in the mucosa in the no-load
state. This can be prevented by taking longer segments. For short
rings, however, it was not possible to obtain valid data on the no-load
state, and the strain data in this study are therefore limited to the
zero-stress and the loaded state. When the opening angle is 360°,
the cut ends come in contact again after an inside-out deformation. For
> 360°, it is simpler to make two to three cuts in each
circumference to establish the zero-stress state. In this case, it is
easier to use the tangent rotation angle, denoted by
in Fig.
1B, to describe the zero-stress state.
To define
, one fixes a point on the outer rim of the cross section,
such as point 0 in Fig. 1A, and measures the length of the
outer rim s from the
origin 0 and uses
s as a curvilinear coordinate along
the rim. Define a unit tangent vector
T on the outer rim. As
s increases, the tangent rotates. For
a complete circle, the tangent rotates 360° when
s returns to the origin. When a
section opens, the total angle of rotation from one tip to the other is
<360°. The angle of rotation can be measured in segments. If the
specimen is cut radially in three places to produce three
nonoverlapping pieces, as shown in Fig.
1C, and the tangents of the segments
rotate by angles
a,
b, and
c, then the total angle of
rotation of the whole specimen is
=
a +
b +
c. This resultant value of
is independent of where the cuts are made in the original ring and does
not require the original or final shapes to be circular (see
APPENDIX in Ref. 31). The tangent
rotation angle and the mucosal and serosal edge lengths in the
zero-stress state were measured from photographs of the cut-open
specimens. The photographs were taken when steady state was reached 30 min after the radial cuts to allow the viscoelastic phase to subside.
The geometry of the duodenum at the zero-stress state can also be
characterized by the angle between the last tangent of the tip and the
first tangent of the tip,
(Fig.
1B).
may be called the angle
between the tip tangents. Clearly,
= 2
. We use all
three measures,
,
, and
, to characterize the zero-stress state. Figure 3 depicts the relationship
between the zero-stress state and measurements of
,
, and
.

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Fig. 3.
Manner whereby opening angle ( ), tangent rotation ( ), and angle
between tip tangents ( ) change with opening of a cut specimen.
Mucosa and serosa are labeled m and s, respectively.
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Data analysis.
The length of the duodenum, as well as the length of the cranial,
descending, transverse, and ascending sections of the duodenum according to the classification by Cooper and Schiller (3), varied
considerably among animals. This necessitated normalization of data
within appropriate subdivisions of the duodenum. In this study we found
that it was fairly easy to identify the proximal and distal ends of the
duodenum as well as two intermediate locations corresponding to major
duodenal bends (Fig. 4). Therefore, the duodenum was subdivided into proximal, middle, and distal segments in
this study (Fig. 4). The lengths of these segments are given in Table
1. Because of the large variation in length
among the three segments and among animals, the data were normalized in terms of a local dimensionless curvilinear coordinate, with the orad
and aborad ends of each segment assigned 0% and 100%, respectively. Consequently, the 100% location in the proximal segment is identical to the 0% location in the middle segment, and so on. Because it was
only possible to obtain rings at exactly the 0% and 100% locations, the intermediate data points were allocated to 25% intervals. This
interval was selected because larger intervals give a poorer resolution
and smaller intervals would contain too few data in a given segment.

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Fig. 4.
Schematic drawing showing subdivision of duodenum into 3 segments:
proximal (P), middle (M), and distal (D). Four solid lines indicate
proximal and distal ends of duodenum and 2 major bends used as
landmarks. Circles, insertion holes for proximal and distal catheters.
Table 1 gives data on length of whole duodenum and segments determined
experimentally in this study.
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The morphometric data were measured from the photographs of the
segments in the zero-stress and no-load states. The negatives were
illuminated and displayed on a separate monitor using frame-grabbing software. The measurements were done using Optimas software. The resolution was 0.17° and 0.01 mm for angle and length measurements, respectively. The loaded-state data were measured on the photographs of
the duodenum with the cast (data on the outer wall of the serosa) and
of the cast itself (data on the inner wall of the mucosa). Measurements
were done at locations corresponding precisely to the locations where
the rings were cut out. The cross sections were not exactly round. The
photographs allowed measurements of the major
(Dma) and minor
(Dmi) diameters
of the cross section of the loaded state. If one could assume the cross
section to be elliptical, then it is possible to compute the
circumferences of the mucosa and serosa,
Cl mucosa
and
Cl serosa,
respectively. The exact formula is
|
(1)
|
where
E(k)
is the complete elliptical integral of the second kind and
k is a parameter defined by
|
(2)
|
If
the ratio
Dmi/Dma
is very close to 1, then Eq. 1 may be
approximated by
|
(3)
|
For
example, if
Dma/Dmi = 1.15, then the
Cl calculated by
Eq. 3 is 0.12% of that given by
Eq. 1. The use of Eq. 3 involves two assumptions:
1) that the cross section is
elliptical and 2) that
Dmi/Dma
is quite close to 1. To test these assumptions, we sliced the casts.
From photographs of these slices, we measured Dma,
Dmi, and
Cl. Figure
5 shows the circumference of the cast slices measured directly from photographs and the circumference computed from measurements of the major and minor radii from the same
photographs using Eq. 3. The
regression line of Fig. 5 can be expressed in the form
|
(4)
|
where
A and
B are empirical constants, 1.17 and
0.297 mm, respectively. The correlation coefficient was 0.98. We may
regard Eq. 4 as an improvement of
Eqs. 1 and 3 for a duodenum with a cross section
that is not exactly elliptical and
Dma/Dmi
not equal to 1. The serosal circumferences also needed correction and
were calculated on the basis of Eq. 4
and the wall thickness. First, the mean wall thickness
(h) in the loaded state was
calculated as
|
(5)
|
where
OD and ID denote the outer (serosal) and inner (mucosal) diameters,
respectively. The serosal circumference based on the correction factor
was computed as
|
(6)
|
To
assess the physiological significance of the tangent rotation angle and
the strains, the circumferences at zero-stress and homeostatic
conditions must be measured on the same duodenal specimens to obtain
the desired accuracy. The tangent rotation angle (or the opening angle
when applicable) is a measure of the residual strain (7, 8). The strain
at the loaded state is called homeostatic strain. For a continuum
subjected to finite deformation, strains can be defined in several
different ways in relation to the deformation gradient (7). The Cauchy
strain
, relative to the zero-stress state, is
|
(7)
|
where
subscripts l and z refer to the loaded and zero-stress states,
respectively. The Cauchy strain is especially useful in linearized
theory of elasticity, which is valid when
is infinitesimal. For
finite deformation, the strain defined by Green is more conveniently related to stress (7). Green's strain in the circumferential direction
of the duodenum is
|
(8)
|
Thus,
from the circumferential lengths at the zero-stress state and the
loaded state, we can obtain the circumferential strain at the mucosal
and serosal surfaces in the sense of Cauchy or in the sense of Green.

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Fig. 5.
Correction factor for mucosal circumference measurements. Circumference
of cast slices was measured directly from photographs
(y data) and also computed from measurements of
major and minor radii from the same photographs
(x data). Because measured and
computed circumferences were not identical, a correction factor was
introduced in all other experiments on the basis of linear relationship
(y = 1.17x + 0.297, r = 0.98) found in these
experiments by least-squares fitting (solid line). Dashed line, line of
identity between x and
y.
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The data are representative of a normal distribution, and accordingly
the results are expressed as means ± SE. Student's
t-test and analysis of variance were
used to detect differences along the length of the duodenum and between
groups of data. Spearman's correlation test was used to investigate
association between variables. The results were regarded as significant
if P < 0.05.
 |
RESULTS |
Figure 6 depicts a cross-sectional view of
a specimen from the most proximal part of the duodenum cut into two
pieces to obtain the zero-stress state. On reduction of the no-load
state to the zero-stress state by cutting the ring, the two pieces
expanded themselves into a configuration with a tangent rotation angle of about
640°. The pieces literally turned inside out. The
outside of each specimen represents the mucosa and the inside the
serosa.

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Fig. 6.
Photograph of specimen from proximal duodenum in zero-stress state. In
this case, 2 radial cuts were made. Rings located more distally in
duodenum required 3 radial cuts to obtain zero-stress state. The inside
of these pieces corresponds to the serosa. Diameter of photograph view
is 12 mm.
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The ratio
Dma/Dmi
of the duodenum in the loaded state was ~1-1.15 without
significant axial variations. The distribution of the mucosal and
serosal circumferences in the zero-stress state and the loaded state
and the wall thickness as a function of the axial location in the
proximal, middle, and distal segments of the duodenum are shown in Fig.
7. The mean and standard error of the
variables are functions of the normalized distance within each segment.
A point labeled 26-50% means that this point is located at
26-50% of the length of that particular segment of the duodenum
from the proximal end.

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Fig. 7.
Mucosal ( ) and serosal ( ) circumferences in zero-stress state
(A) and in loaded state
(B) and wall thickness
(C) as functions of axial location
in proximal, middle, and distal segments of duodenum. Values are
means ± SE based on 5-7 observations in each
interval (except for 76-99% interval in proximal segment, where
n = 3).
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Because the duodenal specimens turned inside out, the mucosal
circumferences were larger than the serosal circumferences in the
zero-stress state. The serosal circumference was largest in the
proximal duodenum and decreased in the distal direction
(F = 4.1, P < 0.001), whereas the mucosal
circumference showed only borderline significance in the axial
direction (F = 1.6; 0.10 > P > 0.05). In the loaded state the
serosal circumference was ~20-25 mm in the duodenum with little
axial variation (F = 1.6, P > 0.10). The mucosal circumference
was ~12-18 mm in the loaded state with no axial variation
(F = 1.2, P > 0.2). However, examination of
juxtaposed locations revealed some significant differences; e.g., the
data point at the duodenal bend between the middle and the distal
segments of the duodenum was significantly higher than the data point
immediately distal to it (P < 0.05).
The wall thickness in the proximal duodenum was approximately twice
that in more distal parts (F = 3.8, P < 0.001).
The distribution of the tangent rotation angle in the zero-stress
state, the mucosal and serosal strains, and the wall
thickness-to-mucosal circumference ratio as functions of the axial
location in the proximal, middle, and distal segments of the duodenum
are shown in Fig. 8. The absolute value of
the tangent rotation angle was lower in the proximal duodenum than in
more distal parts (F = 3.8, P < 0.001). The lowest absolute
value of 537 ± 28° was found in the first 25% of the proximal
segment. The highest absolute values of ~850° were found close to
the major bends and most distal in the duodenum. In the loaded state
the serosal Cauchy strain was tensile with values of ~1 in the
proximal part and a significant increase toward the distal direction
(F = 3.0, P < 0.005). The mucosal Cauchy
strain was compressive in the proximal half of the duodenum, with
values of approximately
0.1 to
0.4, whereas it was
between 0.05 and 0.4 in the distal half. Figure 8 depicts both
Cauchy and Green strains. Statistically significant axial variation was
found (F = 2.6, P < 0.01). The
wall thickness-to-mucosal circumference ratio also varied in the
axial direction (F = 4.0, P < 0.001), with the highest
values in the proximal segment of the duodenum.

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Fig. 8.
Tangent rotation angle (A), mucosal
Cauchy ( ) and Green ( ) strains and serosal Cauchy ( ) and Green
( ) strains (B), and wall
thickness (WT)-to-mucosal circumference ratio
(C) as functions of axial location
in proximal, middle, and distal segments of duodenum. Values are means ± SE. See Fig. 7 legend for number of observations. All strains are
in circumferential direction.
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The tangent rotation angle did not correlate directly with the Cauchy
strains at 7 cmH2O or directly
with any other morphometric parameters. These variables are tied
together by mechanics, which can be validated after the stress-strain
relationship is determined. The mucosal and serosal strains were
negatively related to the wall thickness
(r =
0.63,
P < 0.01 and
r =
0.31,
P < 0.01, respectively). Because the
wall thickness-to-mucosal circumference ratio is a determinant of the
wall stress, the correlation between this ratio and mucosal strain was
studied, and a significant correlation was found
(r =
0.77,
P < 0.01).
 |
DISCUSSION |
The major function of the duodenum is to transport gastric
contents further down the intestine and to mix the contents with secreted fluids to break down and absorb the food constituents. The
evaluation of duodenal mechanical function traditionally has focused on
the peristaltic contraction patterns and the bolus transport that
results from the sequence of duodenal muscle contraction and relaxation
and gastric emptying (4, 18, 22). It is well known that a number of
factors such as the volume and viscosity of the bolus and the pressures
generated by the peristaltic contractions determine the transport
function of the duodenum. Classic biomechanical theory on the transport
of fluid boli in distensible tubes indicates the importance of
considering the geometry and elasticity of the organ under study.
Furthermore, the wall of the GI tract is stretched passively in the
vicinity of a bolus (25), indicating that the luminal dimension, the
function of the contractile element, and the elastic properties of the
duodenum in the low stress range determine the resistance to flow. To
compute the stress and strain in tissue and muscle under physiological
or pathophysiological conditions, one must know the configuration when
the stress is zero. It is well recognized that in the blood vessels,
the heart, and the airways the zero-stress state is different from the
no-load state, where all the external loads are removed but the organ is intact (8, 9, 12, 13, 17, 21, 28, 30). To the best of our knowledge,
previous studies of duodenal distensibility have not considered the
zero-stress state. This study was confined to the analysis of strain,
since stress analysis requires the stress-strain relationship
(constitutive equation), which has not been determined for the
duodenum. The strain analysis was based on experimental measurements of
the duodenal geometry in the zero-stress and loaded states and was
simplified by assuming elliptical geometry with an empirical
correction. The whole length of the duodenum is not necessarily in the
same horizontal plane, and therefore the applied hydrostatic pressure
will vary slightly along the length. The difference in hydrostatic
pressure will be at most 0.5-1
cmH2O, i.e., <15% of the
applied pressure. Furthermore, because the surrounding tissues have an
approximate density of that of the silicone elastomer, the transmural
pressure likely did not vary significantly along the duodenal length.
A detailed biomechanical analysis of GI physiology requires a complete
data base on GI geometry. The present study constitutes the first
attempt to reconstruct the geometry of the entire duodenum at
zero-stress level and a specified pressurized condition. Some basic
morphometric data are presented. Previous studies have mainly been
descriptive. Gabella (10) described characteristics of the whole guinea
pig GI tract. This provided important data on differences in
histomorphology along the small intestine, but unfortunately only one
data point was from the duodenum. In this study we obtained a good
resolution for the entire duodenum and avoided the tissue shrinkage
from the use of fixative by making optical measurements with in vivo
casting. Gabella (10) found a decrease in wall thickness from the
duodenum to the terminal ileum. Our results on the decrease in duodenal
wall thickness toward the distal direction are thus in line with those
of Gabella (10).
A principal result of the present study is the clear demonstration of
the presence of large residual strains in the duodenum and a gradient
of this parameter along the length of the duodenum. The large residual
strain, due to the difference between the "no-load" state and the
"zero-stress" state, is an inherent property of the duodenum. It
can be influenced by the duodenal smooth muscles. In the present
determination, we have made every possible effort to abolish muscle
contractile activity by using a calcium-free medium containing EGTA to
chelate intracellular calcium stores under otherwise physiological
experimental conditions. The absence of the smooth muscle activity was
consistent with the observation that whereas duodenal muscle
contractions are mainly phasic, we did not see any contractile activity
during the studies. The residual strain in the mucosa and submucosa was
found to be compressive in the circumferential direction. The mucosa,
of course, is not a smooth solid layer, since the villi are physically
connected only via the base to the submucosal layer. The villi are, to
a small degree, free to move away from each other, allowing fluids to
move between the villi: more movement if the circumferential strain is
tensile, less if the strain is compressive. Mucosal cell edema was
avoided by using a Krebs solution containing high-molecular-weight dextran. We have observed that the duodenum springs open when cut
longitudinally in vivo; thus it is very unlikely that our observations
were caused by fluid movements. To further elucidate whether volume was
conserved, we analyzed a few of the best no-load-state photographs and
compared the whole wall cross section from the no-load state with that
from the zero-stress state. This analysis revealed no difference in
cross section between the no-load and the zero-stress state, indicating
that volume was indeed conserved in these experiments. Thus we believe
that the mucosa in the no-load state was under compression.
Because a large residual strain was observed in the duodenum, we may
speculate about the function of this prestress. Prestressing the
duodenum may be nature's way of efficiently resisting luminal pressures in a manner similar to the prestressing of gun barrels and
other mechanical devices. For arteries, it has been demonstrated that
residual stress reduces the stress concentration at the inner wall of
the artery at normal blood pressure (2). The present data also
demonstrate that the prestressing effect causes compressive mucosal
strains in the proximal duodenum at a physiological pressure of 0.7 kPa
and in the mucosa of the whole duodenum at resting conditions. Thus the
compressed mucosa may be better protected against injury from the flow
of luminal contents than the uncompressed mucosa would otherwise be.
These protection mechanisms could be important when unphysiologically
high pressures are reached, e.g., in mechanical obstruction. The
residual strain affects the whole stress and strain distribution, since
large errors in strain calculation will result from ignoring the
residual strain. Because peristaltic bolus transport bulges out the
intestinal wall in the vicinity of the bolus (1, 25), the residual
strain would likely influence the resistance to bolus flow under normal
conditions.
It is worthwhile to notice that the duodenum differs from the blood
vessels, trachea, bronchi, and esophagus in the sense that the residual
strain is much larger and the wall is thinner. This study opens many
new interesting questions, some of them hypothetical because of the
lack of precise data. Because residual strains exist, the duodenal
mucosa will inevitably be under compressive stresses and strain in the
no-load condition, i.e., where the transmural pressure is zero. In
phases I and II of the interdigestive state, the small intestine is at
the no-load condition most of the time, since phasic contractions are
only infrequently present (16). We may ask therefore if there could be
functions of mucosal compression other than those mentioned above. It
is well known that the mucosa in the small intestine is one of the
tissues with the fastest turnover rate (14). The fast growth on the
mucosal surface could easily cause mucosal compression and by itself
explain the large residual strains found in this study. We know from
studies on the intestine and other organs that mechanical stresses are factors regulating gene expression and growth (9; unpublished observations). A well-known example is the cardiac hypertrophy caused
by hypertension. In bone, Wolff's law indicates that stress can induce
bone hypertrophy. In other words, the magnitude of compression may
affect the rate of growth and vice versa. Absorption of luminal
contents may theoretically also be affected by the compression. It is
well known that a gradient in the height of the mucosal villi exists
along the small intestine, with the highest villi found in the proximal
duodenum (10), and that small intestinal absorption depends on the
luminal pressure (19). Thus there may exist a correlation between the
residual strain gradient and the gradient in the height of the villi.
These interesting aspects of small intestinal function certainly need
attention in future studies. Other important questions pertain to the
function of the mechanoreceptors (nerve endings of the sensory afferent
nerves) in the intestinal wall. Previous studies have shown that the
receptors are located in the submucosa and in the muscle layers and
that the receptors can be classified on the basis of their thresholds to pressure (24). From this study, we learn that a gradient in strain
exists from the mucosa to the serosa of the wall under physiological
conditions; hence, the mechanoreceptors from the different layers are
exposed to different strains. This suggests that the receptors from
different locations in the wall may have different zero settings and
respond differently to the same stimuli because of the variation in the
magnitudes of tensile stresses and strain during distension and in the
magnitudes of compressive stresses and strain during muscle
contraction. A difference in the responses of mucosal and muscle
receptors to stimuli has been observed (11). Furthermore, the present
results emphasize the importance of studying the receptor kinematics by
using experimental models on the intact organ close to the in vivo
conditions. Yuan et al. (33) studied the effect of mucosal compression
on the peristaltic reflex. Compression was found to stimulate the
reflex, but unfortunately the experiments were performed on excised
flat sheets of tissue.
The most important future work is to complete Hill's three-element
model so that we can understand the interaction between the parallel
element and the contractile element. Further work is also needed to
determine how the residual strains affect responses to physical and
chemical stimulations in pathophysiological states and to determine
whether species variations exist. Because the duodenum is essentially a
muscular tube, alteration of the activity of the smooth muscle cells by
agents acting on the muscles directly or on their innervation will
change the zero-stress state of this organ. Hence, the effects of these
agents on the duodenum and other parts of the small intestine need to
be investigated to accurately model the normal bolus transport and
pathological situations of blockage or disease.
Mathematical discussion.
The opening angle is defined as the angle between two radius vectors
connecting the midpoint of the inner wall to the inner tips of the
ends. Designated
, its measurement focuses attention only on these
two vectors and disregards the shape of the curve. It gives no
information on the curvature of the wall.
The tangent vector T is a unit vector
field associated with any space curve. If
s is a curvilinear coordinate of
points on the curve, with significance of length measured along the
curve from an origin on the curve, then the angle between
T(s) and
T(o)
is the angle of the tangent between s
and o. The derivative of rotation
dT(s)/ds
is the curvature of the curve, which is a quantity of major importance
in the mechanics of the curve representing a shell.
The angle between the tangents at the tips is the angle between
T(c)
and T(o),
where c is the circumference. It is
the integral of the curvature from s = o to
s = c. Writing
for the angle of
rotation of the tangent from s = o to
s = c and
for the angle between the tip tangents, we have
or
The change in
,
,
and
with the opening of a cut specimen is shown in Fig. 3.
Concluding remarks.
Measurements of the tangent rotation angles in the guinea pig duodenum
at the zero-stress state show substantial residual strains and stresses
in the duodenum, an organ that experiences low luminal pressures in
resting conditions. Several radial cuts are needed to allow measurement
of the residual strain in a segment. The tangent rotation angle is very
large and varies along the length of the duodenum. The residual strain
affects the strain distribution in the duodenum under resting
conditions and influences the stress-strain distribution in the
duodenum during bolus transport. It could potentially affect mucosal
growth and absorption. Data on the zero-stress state in the duodenum
have physiological and clinical relevance, since the biomechanical and
morphological properties affect flow, and they change in various
diseases of the GI tract, e.g., in mechanical obstruction of the small
intestine, in diabetes, and after partial resection of the small
intestine (20, 23).
The work to be done next is quite clear: the constitutive equations,
i.e., the three-dimensional stress-strain relationships of the duodenal
tissues, must be determined. With the constitutive equations, the
distribution of physical stresses and strains in the duodenum in vivo
and the function of bolus transport and fluid movement in the intestine
can be analyzed by methods of continuum mechanics. The analytic results
will relate the stress and function of the duodenum with the duodenal
structure represented by the geometric parameters, such as the
circumferential length, wall thickness, and tangent rotation angle,
presented here. Actually, the job of determining the constitutive
equations is not as daunting as it seems, because the mathematical form
of most soft tissues is known (6, 7), including the vascular smooth
muscles of the arterioles (6a). If the hypothesis that the constitutive
equations of the duodenal tissues are similar to those of other soft
tissues can be confirmed, then it remains only to identify the
mathematical constants of the duodenal tissues. Instruments are
available, and this task is being pursued in our laboratory.
 |
ACKNOWLEDGEMENTS |
H. Gregersen was supported by the Danish Medical Research
Association, the Karen Elise Jensens Foundation, and the University of
Aarhus (Aarhus, Denmark).
 |
FOOTNOTES |
Deceased 17 August 1997.
H. Gregersen was on leave from the University of Aarhus.
Address for reprint requests: H. Gregersen, Institute of Experimental
Clinical Research, Skejby University Hospital, Brendstrupgaardsvej,
DK-8200 Aarhus N, Denmark.
Received 9 October 1996; accepted in final form 24 June 1997.
 |
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