Mechanical response of uterine tissue under the influence of hemostatic clips: A non-linear finite-element approach

doi:10.4236/jbise.2013.612A004

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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: *[email protected]

Received 30 September 2013; revised 28 October 2013; accepted 14 November 2013

which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

ABSTRACT

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-

quired.

Keywords: Medical Device Design; Hemostasis; Finite

Element Modeling; Tissue Modeling; Myometrial Tissue

1. INTRODUCTION

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.

OPEN ACCESS

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. MATERIALS AND METHODS

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:

iij





, (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

tissue

Figure 1. Axisymmetric geometry used to model the clamping of uterine tissue.

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.

Contact

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].

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,



123

iii i













1J

(2)

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],









 (3)

where



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

tissue.

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

purposes.

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

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

model.

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. RESULTS

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

(cm)

Indenter Width

(mm)

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

(cm)

Indenter Width

(mm)

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

M. A. Nicosia et al. / J. Biomedical Science and Engineering 6 (2013) 21-28

0.0E+00

2.5E+06

5.0E+06

7.5E+06

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.

0.E+00

5.E+05

1.E+06

2.E+06

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.

OPEN ACCESS

4. DISCUSSION

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).

120

160

200

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

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.

5. ACKNOWLEDGEMENTS

This study was funded by ZSX Medical and Ben Franklin Technology

Partners of Southeastern PA.

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