J. Biomedical Science and Engineering, 2011, 4, 10-17
doi:10.4236/jbise.2011.41002 Published Online January 2011 (http://www.SciRP.org/journal/jbise/
JBiSE
).
Published Online January 2011 in SciRes. http://www.scirp.org/journal/JBiSE
Effect of off-axis cell orientation on mechanical properties in
smooth muscle tissue
P. A. Sarma1,2, Ramana M. Pidaparti2,3, Richard A. Meiss4
1Department of Mathematics, Southern West Virginia Community and Technical College, Logan, USA;
2Previously at the Department of Mechanical Engineering, Purdue School of Engineering and Technology, IUPUI, Indianapolis,
USA;
3Department of Mechanical Engineering, Virginia Commonwealth University, Richmond, USA;
4Department of OB/GYN, IU School of Medicine, Indiana University Medical Center, Indianapolis, USA.
Received August 18 2010; revised September 5 2010; accepted 9 September 2010.
ABSTRACT
The cell alignment in a smooth muscle tissue plays a
significant role in determining its mechanical proper-
ties. The off-axis cell orientation “θ” not only effects
the shortening strain but also modifies the shear
stress relationship significantly. Both experiments
and finite element analysis were carried out on a
tracheal smooth muscle strip to study how the cell
alignment in smooth muscle affects the shear stiffness
and shear stresses as well as deformation. A simple
model for shear stiffness is derived using the data
from experiments. Shear stiffness results obtained
from the model indicate that the muscle shear stiff-
ness values increase non-linearly with strain and with
higher off-axis alignment of cells. Results of deforma-
tion and shear stresses obtained from finite element
analysis indicate that the maximum shear stress val-
ues of tracheal smooth muscle tissue at 45% of strain
are 2.5 times the corresponding values at 20% of
strain for all three off-axis cell orientation values θ =
15˚, 30˚ and 45˚.
Keywords: Smooth Muscle; Shear Stress; Finite
Element Model; Cell Orientation; Shortening Strain
1. INTRODUCTION
Smooth muscle tissue is an important part of any vascu-
lar system and the study of its mechanical properties has
applications in organs like intestines, blood vessels, di-
gestive tract, uterus and similar organs. Usually the
smooth muscle tissue is arranged in circular and longitu-
dinal layers that act antagonistically to shorten or
lengthen and thus constrict or expand the volume of the
organ. The muscle cells usually run parallel and are
densely populated in an irregular manner. The mechani-
cal properties of the tissue, such as force development,
shortening and axial stiffness changes are due to the
various cell activities within the tissue.
Specific architectural features of the tissue, such as
the alignment of the cells along the major axis of the
tissue strip, can also have significant effects on the me-
chanical properties. Several authors [1-4] investigated
the axial stiffness of smooth muscle tissue and its varia-
tions with shortening length. Recently it has been shown
that when the cells are not aligned along the major axis,
the axial stiffness of the tissue is lower [5,6]. There have
been no further studies in the literature reporting the
shear stiffness for isolated smooth muscle tissues.
Meiss and Pidaparti [5,6], in their study on the me-
chanical effects of off-axis cell orientation in a smooth
muscle strip, have reported that the cell alignment in a
smooth muscle tissue has a significant role in determin-
ing its length tension behavior and the isometric forces
that it could generate. They further showed that the
shortening capacity of the off-axis strip was greatly di-
minished, and the isometric force decreased much more
rapidly with decreasing length. The effects of internal
radial constraints based on tissue architecture were not
significant at the lengths in question, nor could they ex-
plain the effects of off-axis cell orientation. Meiss and
Pidaparti also noted that the shortening capacity and
isometric force developed in the smooth muscle strip
depended on its off-axis cellular orientation angle and
that the relative stiffness increased with decreasing
length much more than in the on-axis strip. This suggests
that cells in these strips may have been free to move to a
lower position on their intrinsic length-tension curves,
although other possibilities, as reported here, were not
ruled out.
It is usually difficult to conduct mechanical experi-
ments on off-axis strips, especially in dissecting an iso-

P. A. Sarma et al. / J. Biomedical Science and Engineering 4 (2011) 10-17
11
lated smooth muscle at a particular orientation. In this
study, we investigate how the alignment of smooth mus-
cle cells affects the shear stiffness of a tracheal smooth
muscle strip through a simple model derived from ex-
periments. In addition, the effects of off-axis cell orien-
tation on shear stresses are investigated through a finite
element analysis. The results of Von-mises stress and
maximum shear stress values of the tissue are obtained
and presented as functions of shortening strain and
off-axis cell orientation θ.
2. MATERIALS AND METHODS
2.1. Experiments
2.1.1. Muscle Preparations
All of the experiments were carried out on isolated strips
of tracheal muscle from mongrel dogs. The animals were
anaesthetised with pentobarbital sodium. Segments of
100- to 150-mm-long extrathoracic trachea were quickly
removed and placed in physiological saline solutions of
the following millimolar compositions: 125 NaCl, 4.7
KC1, 2.5 CaC12, 1.2 MgSO4, 15.5 NaHCO3, 1.2 KH2PO4,
and 11.5 glucose. The solutions were bubbled through-
out the experiment with 95% O2, and 5% CO2 to main-
tain a physiological pH. As shown in Figure 1, the car-
tilaginous rings of the trachea were cut at both sides, and
the preparation was pinned out in a dissecting dish. The
muscle area was cleaned of epithelial and adventitial
tissue. The muscle of the canine trachea consists of par-
allel bundles of muscle tissue with axially oriented cells.
Small strips of muscle tissue (~0.75 mm diameter and
8-12 mm long) were cut from the muscle sheet, follow-
ing the natural division of the tissue into discrete fiber
bundles. These strips are termed ‘on-axis’. To prepare
‘off-axis strips’, lengths of black thread were stretched
across the tissue to mark the normal orientation and the
desired off-axis angle (30˚ in this case). The tissue was
pinned to the dissecting dish along the thread guides so
that it would not be distorted during the dissection. Us-
ing the angle thread as a guide, a strip similar to the con-
trol strip was dissected. To ensure a low-compliance
Figure 1. Dissection of off-axis tracheal muscle strips. A section of trachea approximately 30 mm long
was removed from the excised organ. The cartilaginous rings were cut along both sides of the cylinder,
and the posterior portion, containing the tracheal muscle sheet, was pinned down (as shown above) in a
dissecting dish and stretched slightly to extend the fiber bundles. The On-Axis strip was cut from the
muscle sheet parallel to the orientation of the fiber bundles. The Off-Axis strip was cut across the muscle
sheet at a 30 degree angle to the axis of the fiber bundles. This produced a strip with cells oriented at 30
degrees with respect to the long axis of the strip. The typical orientation of a cell within the tissue is
shown at the right.

P. A. Sarma et al. / J. Biomedical Science and Engineering 4 (2011) 10-17
12
attachment to the experimental apparatus, the ends of all
strips were clamped in aluminum foil cylinders as pre-
viously described [2]. Direct measurement of total sys-
tem compliance, including that of the force transducer
and all other mechanical components, gave a value of
0.93 µ/mN, equivalent to <0.5% of the muscle length at
maximal force (e.g., 50 mN) at optimum length (Lo) (e.g.,
10 mm).
After mounting the tissue to the extension arms of the
apparatus, it was extended by adjusting the position of
the force transducer until a small force (~1-2% of the
anticipated maximum) was recorded. This length was
designated the rest length (Lr) and was approximately
10% less than Lo. This procedure was followed because
the experimental protocols required that passive force be
kept to a minimum. After mounting the tissue, the mus-
cle bath, borne on a rack-and-pinion assembly, was ele-
vated to immerse the muscle in circulating, tempera-
ture-controlled, and oxygenated physiological saline
solution. Muscles were stimulated by using platinum
electrodes along either side of the tissue, with supra-
maximal voltage pulses of alternating polarity at a fre-
quency and voltage previously determined to produce
the maximum mechanical response.
2.1.2. Mechanical Instrumentation
All experimental contractions were made in a digitally-
controlled force-clamp servo system [2]. This system
was capable of producing both isometric (length- con-
trolled) and isotonic (force-controlled) conditions and of
switching rapidly between them under manual or com-
puter control. In addition, special conditions of length or
force (i.e., length vibrations or rapid force steps) could
be imposed. The continuous measurement of dynamic
stiffness was performed as previously described, by ap-
plying a very small (<0.5% Lr) sinusoidal length oscilla-
tion (usually at 80 Hz) to one end of the preparation and
recording and analyzing the resulting force oscillation.
These oscillations, superimposed on the length and force
traces, were removed and quantified by a digitally-
controlled set of bandpass, notch, and low-pass filters.
Force, length, and stiffness data were digitized and
stored in computer memory for subsequent analysis.
2.2. Shear Stiffness Model
In this study, we developed a simple analytical model to
predict the shear stiffness (resistance to off-axis loads or
off-axis cells) of tracheal smooth muscle tissue as it is
difficult to measure this stiffness experimentally. It was
assumed that the off-axis smooth muscle tissue follows a
similar behavior model to bone and other fiber-reinforced
composites [7,8]. In addition, based on the architecture
of the smooth muscle strip, it was further assumed that
the tissue has negligible resistance in the transverse di-
rection compared to the longitudinal direction of the strip.
The off-axis stiffness coefficient (Eθ) for the smooth
muscle tissue was defined as
4
22
2
1cos 1cos sin
xy
xxxy xx
EE GE










(1)
where θ is the angular orientation with respect to the
long axis (on-axis) of the tissue strip, Exx is the stiffness
in the on-axis (axial) direction, Gxy is the shear stiffness,
and νxy is the Poisson ratio. The shear stiffness, Gxy as a
function of the shortening strain ε can be estimated by
knowing the on-axis stiffness (Exx) and measuring the
off-axis stiffness (Eθ) for a particular orientation of the
smooth muscle strip. A Poisson’s ratio of 0.45 was as-
sumed in the model, as there are no data available in the
literature. Rearranging the Eq.1, the shear stiffness is
given by
 
4
22
11cos1
,,, cos sin
xy xx
GEE


 








(2)
We used force–length experimental data for angular ori-
entations θ = 11° and 30°, and derived the expression for
shear stiffness, Gxy.
2.3. Finite Element Simulation
A smooth muscle tissue strip consisting of cells embed-
ded in a tissue matrix, is assumed to be a cylinder of
length 1mm and a radius of 0.175 mm. We further as-
sume that it contains a single cylindrical cell of length
0.5 mm and radius 0.07 mm aligned at an off-axis orien-
tation θ to the major axis. This smooth muscle cell-tissue
strip is modeled as 3D solid with SOLID-175 finite ele-
ments using ANSYS-6.1 commercial software [9]. The
final finite element model of smooth muscle cell-tissue
cylinder consisted of 16482 SOLID-175 elements and
23828 nodes.
The material properties for the finite element model
were assumed to be isotropic for both tissue and cell.
The Young’s modulus values are in the range (E = 1 ×
104 to 1 × 107) for cell and tissue. Further, a value of
0.44 for Poisson ratio was used for the material. The
boundary conditions imposed were similar to those used
in medical experiments, i.e., the smooth muscle is
clamped at one end and at the other end, a constant
compressive force (in the form of uniform displacement
is distributed over the cross-section). Several structural
analysis runs were carried out to study the effect of
Von-mises stress for various displacements and off-axis
cell orientations. The results are discussed in detail in the
next section.

P. A. Sarma et al. / J. Biomedical Science and Engineering 4 (2011) 10-17
13
3. RESULTS AND DISCUSSION
Shear stiffness Gxy(θ) is estimated using Eq.2 and the
derived results from the experimental data for the
on-axis stiffness Exx (θ = 0˚). Figure 2 depicts the be-
havior of shear stiffness as a function of shortening
strain and off-axis cell orientation (θ). It can be seen
from Figure 2 that the shear stiffness values decreased
with increasing shortening strain, and this decrease in
shear stiffness values increased with higher off-axis cell
orientations. For example, there was a 120% shear stiff-
ness reduction for 20% shortening when the cells were
oriented at 30˚. But at lower off-axis cell orientations,
the stiffness reduction was much less. Also, the initial
shear stiffness values for 19.5˚ and 30˚ off-axis cell ori-
entations was about 2.2 and 4.7 times higher than those
of the stiffness values at 11˚ off-axis cell orientation.
There was a non-linear behavior of shear stiffness with
off-axis orientation and this non-linear behavior in-
creased with higher off-axis cell orientation.
Figure 3 shows the deformation of the cell oriented at
30° under shortening strains of 5%, 35% and 50%, re-
spectively. It can be seen from Figure 3 that the cell
deformation as well as the initial cell orientation changes
as the shortening strain increases. It has been observed
that the cell reorients by about two times the initial ori-
entation under 50% shortening. Figure 4 shows the cut
section views of undeformed and deformed cell-tissue
model for a cell oriented at 30˚ under shortening strain
of 45%. It can be seen from Figure 4 that once again a
substantial amount of cell reorientation takes place. It
should be noted that the change in initial cell orientation
with shortening strain should be considered for a realis-
tic analysis in order to see how it affects the shear
stresses.
The deformed shapes of the cell for various shortening
strains were determined as a function of off-axis angles.
Figure 5 shows the results of both undeformed and de-
formed cells oriented at 0˚, 30˚, and 45˚ under shorten-
ing strains of 20% (Figure 5 left) and 45% (Figure 5
right). From the results of Von-Mises stresses presented
in Figure 5, it can be seen that, both the deformation and
stresses increase with increasing cell orientation and also
with increasing strain. These results indicate that, in
general, the cell is displaced from its initial position with
angle shift depending on the strain applied and off-axis
angle orientation θ.
The effect of off-axis cell orientation and shortening
strain on maximum shear stress is shown in Figure 6. It
is evident from Figure 6, that the maximum shear stress
values of the tissue at 45% strain are 2.5 times the cor-
responding values at 20% strain for off-axis orientation
values θ = 15˚, 30˚ and 45˚. In general, the results pre-
sented in Figures 5 and 6 illustrate the effect of cell ori-
entation and shortening strains on shear stresses and
deformation.
Figure 2. Shear stiffness-strain behavior predicted for off-axis cell orientations of θ = 11°, 19.5° and 30° in a
smooth muscle tissue.

P. A. Sarma et al. / J. Biomedical Science and Engineering 4 (2011) 10-17
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P. A. Sarma et al. / J. Biomedical Science and Engineering 4 (2011) 10-17
15
Figure 3. Cut section view of the deformation for a cell oriented at 30˚ under shortening strains of 5%, 35%
and 50%.
Figure 4. Cut section view of the undeformed and deformed cell-tissue model for a cell oriented at 30˚ under
shortening strain of 45%.

P. A. Sarma et al. / J. Biomedical Science and Engineering 4 (2011) 10-17
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Figure 5. Deformed and undeformed cell shapes along with Von-Mises stresses at strains of 20% (left) and 45% (right).

P. A. Sarma et al. / J. Biomedical Science and Engineering 4 (2011) 10-17
17
Figure 6. Effect of off-axis cell orientation and shortening strain on maximum shear stress.
4. CONCLUSIONS
This study investigated how the alignment of smooth
muscle cells affects the shear stiffness of a tracheal smooth
muscle strip through a simple model derived from ex-
periments. Also, finite element analysis was carried out
to study the effect of off-axis cell orientation on defor-
mation and shear stresses. Shear stiffness results ob-
tained from the model indicate that the muscle shear
stiffness values increase non-linearly with increasing
value of strain and with higher off-axis alignment of
cells. One limitation of the model is that it does not take
into account interactions between active and passive
tissue components. Results of Von-mises stresses ob-
tained indicate that the maximum shear stress values of
tracheal smooth muscle increase with increasing values
of shortening strain for each off-axis cell orientation.
The authors thank the U. S. National Science Foundation for support-
ing this work through a grant IBN–9904610.
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