Effect of off-axis cell orientation on mechanical properties in smooth muscle tissue

doi:10.4236/jbise.2011.41002

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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.

Email: [email protected], [email protected]

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

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

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

1cos 1cos sin

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

 

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

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

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

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

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.

REFERENCES

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[3] Meiss, R.A. (2001) Shortening-dependent stiffness of

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5. ACKNOWLEDGEMENTS

[8] Jones, R.M. (1975) Mechanics of composite materials.

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[9] ANSYS 6.1 (2001) Finite element software. Pittsburgh,

PA.

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