J. Biomedical Science and Engineering, 2013, 6, 21-28 JBiSE
http://dx.doi.org/10.4236/jbise.2013.612A004 Published Online December 2013 (http://www.scirp.org/journal/jbise/)
Mechanical response of uterine tissue under the influence
of hemostatic clips: A non-linear finite-element approach
Mark A. Nicosia1*, Donald A. Wood1, Daniel Mazzucco2
1Department of Mechanical Engineering, Widener University, Chester, USA
2ZSX Medical, LLC., King of Prussia, usa
Email: *manicosia@widener.edu
Received 30 September 2013; revised 28 October 2013; accepted 14 November 2013
Copyright © 2013 Mark A. Nicosia et al. This is an open access article distributed under the Creative Commons Attribution License,
which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
A modeling strategy to predict the ability of surgical
clips to achieve mechanical hemostasis when applied
to the cut edge of a thick and muscular tissue is pre-
sented in this work. Although such a model may have
broad utility in the design of hemostatic clips and oth-
er surgical and wound closure applications, our par-
ticular focus was on uterine closure following a Cesa-
rean delivery. Mechanical closure of a blood vessel,
which is the first step in the hemostatic process, is
established when the compressive forces on the outer
surface of a blood vessel are sufficient to overcome
the local blood pressure and collapse the vessel. For
thick tissue, forces applied to the tissue surface set up
a stress distribution within the tissue that, if sufficient
to mechanically close all vessels, will lead to cessation
of local blood flow. The fo cus of the current work was
on utilization of a planar and nonlinear finite element
model to predict the pressure distribution within ute-
rine tissue under the influence of hemostatic clips.
After experimental model validation with a polymer
tissue phantom, design curves were numerically de-
veloped, which consisted of the clip force necessary to
achieve hemostasis for a given thickness tissue as well
as the resulting deformed tissue thickness. Such
curves could form the basis for a preliminary clip
design, which would provide initial design guidance
before more expensive experimental studies were re-
Keywords: Medical Device Design; Hemostasis; Finite
Element Modeling; Tissue Modeling; Myometrial Tissue
Computer simulations are routinely used to aid in the
design and development of engineered products. Typical
computational models consider stress analysis to predict
material failure, fluid dynamics to predict fluid shear
stress imposed on structures, or heat transfer to predict
temperature distributions. Application of simulations to
medical device design is complicated by many factors,
such as uncertainty in tissue material properties and ge-
ometry due to physiological variation [1], nonlinear con-
stitutive models [2], and the presence of non-traditional
or multi-physics effects (e.g., muscle contraction, blood
flow within tissue, and fluid-structure interaction). The
focus of the current work is to model via a nonlinear fi-
nite element formulation the mechanical interaction be-
tween hemostatic clips and uterine tissue in closure ap-
plications during cesarean delivery, furnishing useful
indications for clip design.
During cesarean deliveries, which account for appro-
ximately 32% of births in the United States [3], the baby
is delivered through incisions in the uterus and abdomen
rather than vaginally. Once the baby and placenta have
been delivered, the surgeon sutures the incisions closed,
starting with the uterine wall and working outward to-
wards the body surface. There are both short-term and
long-term risks associated with cesarean delivery, in-
cluding hemorrhage, injury to urogenital and gastrointes-
tinal organs, and uterine complications affecting subse-
quent pregnancies. In addition, the formation of adhe-
sions, common after pelvic surgery, is considered to be a
leading cause of infertility [4]. A surgical closure device
that reduces these risks would be of great value.
Hemostatic clips are an alternative to sutures for sur-
gical closure, such as the Raney clip used on the scalp.
Mechanically, clips and sutures both apply compressive
forces to the tissue to occlude transected vessels and stop
blood flow; they differ in that clips which do not pene-
trate the tissue, but rather apply a force to the surface of
the tissue and rely on internal compressive stress within
the tissue for vessel closure. This lack of penetration of
*Corresponding author.
M. A. Nicosia et al. / J. Biomedical Science and Engineering 6 (2013) 21-28
clips rela- tive to sutures may decrease tissue damage by
applying a smaller, more uniform stress to the tissue sur-
face. In ad- dition, with the development of a specialized
application tool, clips may be faster to apply than sutures,
thereby limiting blood loss.
A key design constraint in developing such clips is that
the force applied to the tissue surface generates sufficient
internal pressure throughout the tissue thickness to main-
tain vessel closure throughout the tissue. This is particu-
larly challenging for thick tissue, such as myometrium,
which can be as thick as 1.5 cm at the time of delivery
[5]. The focus of the current work is to model via a
nonlinear finite element formulation the mechanical in-
teraction between hemostatic clips and uterine tissue in
closure applications during caesarean delivery, furnish-
ing useful indications for clip design.
2.1. Geometric Model
To apply the hemostatic clip, the cut edges of the tissue
(tissue shown in grey in Figure 1) would be drawn to-
gether and everted, and the clip placed on the exterior
surface of the organ. Contact between the clip and the
tissue is depicted two-dimensionally in Figure 1. The
two portions of the clip that come in contact with the
tissue are labeled “indenters.” Tissue thickness is given
by t and indenter width by w. The indenters come in
contact with the tissue at a distance d from the edge and
apply a load compressing the tissue between them. The
distance d was set at 1 cm, which is based on the dimen-
sions of the simulated clip. Simulations were run for in-
denter widths of 2 mm and 5 mm, and tissue thicknesses
of 1.5 cm and 2 cm.
2.2. Theoreti cal Background
To predict whether a given stress distribution would be
sufficient for hemostasis, recall that the components of
the traction vector ti (force per unit area) on a surface
within a material are given by:
, (1)
where σij are the components of the Cauchy stress, nj are
the components of the unit outward normal of the surface,
and summation over repeated indices is implied. Our
working assumption is that if the compressive traction on
the surface of a blood vessel exceeds the internal pres-
sure (i.e., local blood pressure), the vessel will collapse.
In this work, the pressure to induce collapse was set at
200 mmHg. This assumption ignores two important ef-
fects—pressure drop within a vessel due to blood flow
and the presence of passive or active elastic tension
within the wall of the vessel [6]. Either effect, however,
would serve to decrease the external pressure required
for vessel occlusion. Pressure drop due to flow would
reduce the internal pressure while muscle tension would
be in the same direction as external pressure and thus
work towards vessel occlusion. Thus, estimates based on
this model will be conservative, which is appropriate
from the perspective of design (i.e., the model creates an
additional safety factor).
From elementary solid mechanics (e.g., [7]), the three
principal stresses at a point (denoted σ1, σ2 and σ3) con-
tain the maximum and minimum values for any coordi-
nate system passing through the point. This implies that
the minimum principal stress (i.e., negative stress with
largest magnitude) is a coordinate-independent measure
of compressive stress within the tissue.
2.3. Finite Element Simulations
Abaqus finite element software (Simulia, Providence, RI)
was used to create a two-dimensional (plane strain) finite
element model based on the geometry described previ-
ously. Bilinear quadrilateral elements were used, and
t t
indenter modeling
clip face
interior of organ
cut edges of
Figure 1. Axisymmetric geometry used to model the clamping of uterine tissue.
Copyright © 2013 SciRes. OPEN ACCESS
M. A. Nicosia et al. / J. Biomedical Science and Engineering 6 (2013) 21-28 23
large deformation effects were included to account for
the compliant nature of muscle tissue. A Newton-Rhap-
son method was used to solve the nonlinear equations.
The far ends of each piece of tissue, which represent the
continuing uterine tissue, were fixed in all directions.
The indenters were constrained to only move in the x1
direction, and they were also prevented from rotating in
the x1 x2 plane. Boundary conditions depicted in Fig-
ure 2 were applied to the model.
Contact was established between each indenter and its
respective piece of tissue, as well as between the two
pieces of tissue. Because the interface between the two
pieces of tissue would be moist and well lubricated, this
contact was defined as frictionless. The contact between
the indenters and tissue was given a coefficient of fric-
tion of 0.9. Although the actual coefficient of friction
between these parts is not known and depends on the
geometry of the indenter face, a sensitivity study showed
a variation of less than 1% over a range of 0.3 to 0.9
(data not shown).
The force applied by the clips to the tissue was simu-
lated by applying a concentrated force at the center of
each indenter (Figure 2). Because of the 2D plane-strain
approximation, this force corresponds to the force per
unit depth of the clip (depth refers to the dimension run-
ning into the page). In other words, the area of the clip
contacting the tissue would be equal to depth × width.
2.4. Material Model for Myometrial Tissue
Uterine tissue was treated as an isotropic, incompressible,
hyperelastic material. Uterine tissue is generally isotropic,
with muscle fibers oriented in the circumferential, longi-
tudinal, and diagonal directions. Since our loading is
perpendicular to these fiber directions, an isotropic mo-
del is a reasonable approximation. In addition, although
muscle often displays viscoelastic characteristics [8], the
current study focused on the steady-state stress distribu-
tion, so viscous effects were not included. Given that
compression was the primary loading mechanism for the
clips under consideration, a constitutive model for uter-
ine tissue was developed based on data in the literature
describing primarily the compressive mechanical proper-
ties of human myometrium [9]. That study showed a
large variability in stress-strain behavior between sam-
ples. To account for this variability, three representative
curves were created and used for analysis—high, me-
dium, and low stiffness (Figure 3). Each loading case
was run for all three material models.
Frictionless Contact
Ends Fixed
Figure 2. Boundary and loading conditions for finite element simulation.
Figure 3. Three different stress-strain curves used to model the nonlinear elasticity of
uterine tissue in this study. Data taken from [9].
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M. A. Nicosia et al. / J. Biomedical Science and Engineering 6 (2013) 21-28
Each stress-strain curve was fit to a 3rd order Ogden
hyperelastic model within Abaqus, and these models
were used throughout the simulations. The formulation
of the Ogden strain energy function that was used is
given by,
iii i
where 1/3
are the deviatoric principal stretches,
J is the determinant of the deformation gradient tensor,
is the elastic volume ratio (equal to J for isothermal
problems such as assumed in the current work) and
Di are material parameters. Values for these coefficients
are provided below in Table 1.
Although muscle tissue is essentially incompressible
[10], this constraint is difficult to enforce exactly in a
plane strain setting. Numerically, incompressibility is
usually implemented by including a volume dilatation
term with a large but finite bulk modulus in the strain
energy function [the last term in Equation (2), above]. In
the current work, the material parameter governing com-
pressibility, Di is parameterized in terms of the Poisson
ratio, ν (a Poisson ratio tending to 0.5 corresponds to
incompressibility). The relationship among the Ogden
material properties and the Poisson ratio is given by [11],
i =
1 +
2 +
3 and K is the bulk modulus.
A sensitivity study showed that running our simulation
for values of ν between 0.495 and 0.4995 led to a coeffi-
cient of variation of less than 1% in the minimum com-
pressive stress (data not shown). A value of ν = 0.499
was used in all simulations. Finally, the indenters were
modeled as rigid bodies, so no material properties were
associated with them.
2.5. Simulations
The simulation focused on the effects of two variables on
internal tissue pressure: the width of the indenter face (2
mm and 5 mm) and tissue thickness (1.5 cm and 2 cm).
Table 1. Material parameters for Ogden material model fit from
Reference [9].
i have dimensions of dynes/cm2,
i are unitless.
High Mid Low
1 3,135,789 13,814 52,338
2 3,064,710 80,456 145,693
3 193,610 12.3 38,515
1 6.10 2.84 4.33
2 6.39 9.23 8.22
3 4.28 12.56 4.60
The load applied to the indenter was incremented from 1
N to 20 N for each case. In addition, the variability in
uterine material properties was accounted for by running
three simulations for each combination of indenter height
and tissue thickness. Each simulation represented a dif-
ferent set of uterine material properties (high, middle,
and low stiffness) as in Figure 3.
2.6. Data Analysis
As mentioned previously (Theoretical Background sec-
tion), the most negative value among the three principal
stresses (i.e., the minimum principal stress) at a point in
the tissue corresponds to the maximum compressive
stress at that location (of course, it is possible in general
to have a case in which all three principal stresses are
positive, such as tri-axial stretching, but that was not the
case in this simulation). Minimum principal stress data
were collected within the band of elements between the
indenters, as this is where compressive loads would be
felt. The location which corresponds to the smallest
magnitude of these minimum principal stresses would be
experiencing the lowest compressive load, and thus ap-
ply the smallest compressive load to close blood vessels
in the area. This value will be referred to as the minimum
compressive stress. When the minimum compressive
stress exceeds local blood pressure, it is predicted that
hemostasis will be achieved through the thickness of the
From these data, a series of design curves were gener-
ated relating the minimum compressive stress to the
range of tissue material properties, indenter width, and
tissue thickness as a function of the load applied to the
indenter. In addition, the final distance between the in-
denter faces was quantified; this distance is a measure of
the deformed tissue thickness, and is valuable for design
2.7. Model Validation
To validate the numerical model, an experiment was set
up mimicking the physical system (Figure 4). Sylgard
527 dielectric gel (Dow Corning, Midland, MI), cast into
a disc (12 cm radius, 2 cm thickness), was used as a tis-
sue analog [12]. The gel disc was placed on a lubricated,
rigid base. A stainless steel indenter was custom-fabric-
cated (2 inch diameter with 0.25 inch radius rounded
edge) and attached in series with a 300-lb load cell
(Omega Engineering, Stamford, CT) to a screw-driven
load frame via a custom-made carriage. Force-sensitive
resistors (Tekscan, Inc, Boston, MA) were used to meas-
ure contact pressure between the bottom of the gel disc
and the rigid support. One sensor was placed directly
under the indenter and another at 2 cm away from the
indenter. All sensors were calibrated before each trial. In
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M. A. Nicosia et al. / J. Biomedical Science and Engineering 6 (2013) 21-28 25
a given trial, a given displacement was applied to the
carriage while the indenter force and contact pressure
were measured. Both pressure sensor and load cell data
were collected using a digital data acquisition system
(National Instruments, Austin, TX).
Prior to the indentation tests, an unconfined compres-
sion test was performed on smaller gel discs (4.5 cm di-
ameter) to quantify the material properties of the gel. In
these experiments, the indenter was replaced with a lu-
bricated flat metal plate. The gel material was fit to a
Neo-Hookean material model (
= 78,192 dynes/cm2, ν =
0.499). Note that although the material model is slightly
different from the one used for the tissue, the one-pa-
rameter Ogden model is equivalent to a Neo-Hookean
An axisymmetric finite element mesh was created of
the gel and indenter (Figure 5). The same element for-
mulation and solution method as described for the myo-
metrial tissue model was used in this model. A dis-
placement boundary condition was applied to the in-
denter and frictionless contact was enforced at the
boundary between the gel and the rigid base. The reac-
tion force of the indenter and the base contact pressure
were computed and compared to experimental values for
the same indenter displacement. Accurate prediction of
the base contact pressure for the tissue-like material will
be used as verification of the prediction of compressive
stresses within simulated myometrial tissue.
Pressur e Sensors
Load Cell
Gel Disc
Ind enter
Figure 4. Experimental apparatus used for validation of com-
puter model.
Figure 5. Axisymmetric finite element mesh of gel and in-
denter used for validation.
3.1. Valid ati on Model
Before considering the myometrial tissue model, the
validation model was first studied. For both indenter
force and surface pressure, comparison between experi-
mental results and simulations of the gel disc was excel-
lent (Figures 6 and 7).
3.2. Myometrial Model
In general, the simulated uterine tissue showed a charac-
teristic stress distribution during compression by the in-
denters, as shown in Figure 8 for 1.5 cm thickness tissue,
a 2 mm indenter face. As expected, the deformation was
significant, given the very compliant nature of muscle
tissue. The minimum principal stress (i.e., largest com-
pressive stress) was centered between the indenters;
stress decreased in magnitude towards the indenter edge,
where the tissue is in tension as it wraps around the
curved portion of the indenter.
Based on the full set of simulation results, design
curves were created relating indenter force to the mini-
mum compressive tissue stress between the indenters. A
representative set of curves is shown in Figure 9 for a
tissue thickness of 2 cm, an indenter width of 5 mm, and
all three myometrial material models. Table 2 summa-
rizes the results of the force data. The third column
shows the range of forces required per cm of clip width
to achieve hemostasis accounting for both high and low
stress-strain curves.
The deformed tissue thickness at the hemostatic load
for each condition is shown in Table 3. The range of
values for each thickness and width represents the thick-
ness at the load required for hemostasis for low and high
Table 2. Force per unit depth of clip required to achieve hemo-
stasis. The values corresponding to low and high tissue stiffness
tissue are presented.
Tissue Thickness
Indenter Width
Force Range Required
for Hemostasis (N/cm)
2 2.8 - 3.5
1.5 5 3 - 4
2 3.8 - 5
2 5 4 - 5.4
Table 3. Deformed tissue thickness of each sample at hemo-
static load. The values corresponding to low and high tissue
stiffness tissue are presented.
Tissue Thickness
Indenter Width
Tissue thickness at
hemostatic load (cm)
2 0.50 - 1.17
1.5 5 0.54 - 1.19
2 0.63 - 1.54
2 5 0.69 - 1.57
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M. A. Nicosia et al. / J. Biomedical Science and Engineering 6 (2013) 21-28
Copyright © 2013 SciRes.
00.25 0.5 0.751
IndentorForce (Dy ne)
Indente r Displa ceme nt (cm)
FEA Data
Test Data
Figure 6. Comparison of indenter force vs. displacement curve for simulation and experiment,
showing excellent agreement.
00.25 0.50.751
Pressure (dynes/sq cm)
Indenter Displacement (cm)
C entr al Sens or ( FEA)
C entr al Sens or ( Exp)
Out er Sens or ( FEA)
Out er Sens or ( Exp)
Figure 7. Comparison of contact pressure for simulation and experiment, showing excellent agree-
ment. The central sensor was located directly under the indenter and the outer sensor was 2 cm out
from center of the indenter.
stiffness curves at each tissue width and indenter width.
Note that the large range in strains, due to the non-linear
stiffness of the tissue. For example, for the 1.5 cm tissue
and 2 mm indenter face, tissue compressed to 33% of its
original thickness for the high compliance tissue while
only deforming to 80% of the original thickness for the
low-compliance curve.
The goal of this work was to develop, validate, and apply
a framework to utilize finite element modeling in the
design of hemostatic clips for surgical closure applica-
tions. Surgical closure techniques aim to mechanically
facilitate apposition of cut edges of tissue to promote
wound healing, while stopping blood flow to allow he-
mostasis to occur. The central issue addressed in this
work was the ability of a hemostatic clip applied at the
surface of a thick and muscular organ to provide suffi-
cient internal pressure to achieve mechanical hemostasis
throughout the tissue. Although the particular focus was
on uterine tissue at full-term pregnancy, the work is
broadly applicable to surgical closure of other thick-
walled organs.
The guiding principle underlying the analysis is that if
the compressive stress acting on a blood vessel within a
tissue exceeds local blood pressure, the vessel will col-
lapse and blood flow will be halted in that particular
vessel. If the compressive stress throughout the entire
thickness of the tissue exceeds local blood pressure, then
bleeding should be stopped, allowing the clotting process
to begin.
To predict the distribution of compressive stress within
the tissue, we utilized the finite element method. The
finite element method breaks the domain into small ele-
ments, over which the equations of mechanics are solved,
ielding the stress distribution over the entire domain. y
M. A. Nicosia et al. / J. Biomedical Science and Engineering 6 (2013) 21-28 27
Figure 8. Distribution of minimum principal stress (dynes/cm2) for representative load case
(1.5 cm tissue thickness; 2 mm indenter, mid-level material model).
0510 15
Minimum Comp. Stress between
Indenter s (kPa)
Force (N) Applie d to Indento r sper cm of Clip Length
High Curve
Mid Curve
Low Curve
Design Poin
Figure 9. Magnitude of minimum compressive stress between indenters (2 mm tissue thickness; 5
mm indenter width).
From basic continuum mechanics, the state of stress can
be represented in a coordinate-invariant manner through
the three principal stresses, which are the eigenvalues of
the stress tensor. Furthermore, the minimum value of the
principal stress components represents the maximum
compressive stress at a point in the tissue. The condition
for hemostasis was that the maximum compressive stress
must exceed the local blood pressure through the entire
tissue thickness (i.e., the minimum value of the maximum
compressive stress exceeding local blood pressure
throughout the tissue). Based on the considerations
above, design curves were developed which related tis-
sue thickness, tissue material properties, and applied load
to achieve hemostasis.
The design curves were intended to aid in clip design
by estimating whether a given clip design would achieve
hemostasis in advance of any physical testing. To illus-
trate one possible scenario, it should consider a candidate
clip design that utilized elastic deformation to provide
clamping force, such as in a spring-loaded clamp. In such
a case, the clip would first be opened, allowing it to be
placed on the tissue. The tissue would in turn deform
under the pressure applied by the clip, and the system
would come to a state of equilibrium. The magnitude of
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M. A. Nicosia et al. / J. Biomedical Science and Engineering 6 (2013) 21-28
the clamping force applied by the clip in this equilibrium
state would depend upon the final deformed thickness of
the tissue. Knowledge of the force-deflection characteri-
stics of the tissue (i.e., the final deformed tissue thick-
ness in response to a given clip force) would provide
valuable information in designing the clip. This clamping
force would then be compared to the force required for
hemostasis to see if the design is viable.
One of the challenges in utilizing computational mod-
eling as a design tool for medical devices is the inherent
uncertainty in physiological systems, both with respect to
tissue constitutive models as well as geometry. In general,
mechanical property data for human subjects are often
scarce and may show considerable variations among in-
dividuals (see Figure 3). In addition, geometric parame-
ters such as tissue thickness may vary between individu-
als, or even within an individual for different parts of the
organ or for different times. This is particularly relevant
in the current application, cesarean delivery, due to the
rapid post-delivery changes in uterine thickness and ge-
ometry. Our approach was to estimate upper and lower
bounds for both thickness and material properties. Simu-
lations were carried out between these bounds, and
ranges for hemostatic force were provided, rather than a
single value.
Several simplifications were utilized in this work that
could potentially impact the results. The geometric
model utilized was strictly two-dimensional, which ne-
cessitated neglecting three-dimensional effects. One such
three-dimensional effect relates to the use of multiple
clips to close an incision. Even if interlocking clips were
used, the pressure between clips may fall below the
hemostatic limit even if the pressure directly under the
clip is sufficient. This issue can be handled with tightly-
spaced clips and a reasonable factor of safety. Another
three-dimensional effect relates to the clip-face geometry.
In this work, the faces of each clip were modeled as
smooth, whereas they will most likely be textured or
serrated to grip the tissue without slipping. The complex
stress distribution associated with such a face will be a
local effect and will not affect the overall stress distribu-
tion away from the clip, according to St. Venant’s Princi-
ple [7]. Finally, uterine tissue was modeled to be isotro-
pic, while muscle tissue is known to be anisotropic.
However, in this case, the load is applied perpendicular
to the fiber direction (normal to the surface), so it is rea-
sonable to ignore anisotropy.
This work focused specifically on closure of a full-
term pregnant uterus; the development of hemostatic
clips as an alternative to sutures for closure as a part of
cesarean delivery has the potential to improve patient
outcomes. However, the general methodology is applica-
ble to a number of thick-walled organs, and has demon-
strated that computational modeling can provide valuable
information to aid in implant design, potentially improv-
ing the efficiency of the design process.
This study was funded by ZSX Medical and Ben Franklin Technology
Partners of Southeastern PA.
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