# Experimental and Numerical Modeling of Screws Used for Rigid Internal Fixation of Mandibular Fractures

Authors: Naresh Chaudhary; Scott T. Lovald; Jon Wagner; Tariq Khraishi; Bret Baack
Journal: Modelling and Simulation in Engineering
 (2008)

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## Abstract

Experimental and numerical methods are used to explore the stresses generated around bone screws used in rigid internal fixation of mandibular fractures. These results are intended to aid in decisions concerning both the design and the use of these bone screws. A finite element (FE) model of a human mandible is created with a fixated fracture in the parasymphyseal region. The mandibular model is anatomically loaded, and the forces exerted by the fixation plate onto the simplified screws are obtained and transferred to another finite element submodel of a screw implant embedded in a trilaminate block with material properties of cortical and cancellous bone. The stress in the bone surrounding the screw implant is obtained and compared for different screw configurations. The submodel analyses are further compared to and validated with simple axial experimental and numerical screw pull-out models. Results of the screw FE analysis (FEA) submodel show that a unicortical screw of 2.6 mm major diameter and 1.0 mm pitch will cause less bone damage than a bicortical screw of 2.3 mm major diameter and 1.0 mm pitch. The results of this study suggest that bicortical drilling can be avoided by using screws of a larger major diameter.


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## Body

## 1. Introduction

Failure of bone
screws used for fracture  fixation in trauma surgeries is a significant problem
that has been examined  previously. Rigid
internal fixation (RIF) of mandibular
fractures has been a focus of studies on screw performance due to the
mandible’s load bearing function and the rate of complication seen with these
types of surgery. Screw failure in
mandibular bone is undesirable as any movement of the mandible in the presence
of a foreign body can lead to infection. Tada [1] stated that inappropriate loading can cause excessive stress in
the bone around a foreign implant and may result in bone resorption. Screw loosening not only increases the chance
of infection at the screw failure site but creates a less stable environment
for fracture healing. Murthy [2] and
Gabrielli [3] have both stated that stability in the fracture region can aid in
defending against infection. Infection
reduces oxygenation to the fracture site creating an environment more conducive
to fibrous union than bone deposition. The result of this activity is that infection leads to more serious
complications including debilitating pain, malunion, nonunion, chronic
osteomyelitis, and acquired skeletal deformities [4]. Complications of this nature can in some cases
require a second surgery.The most pertinent
metric to measure the success of a bone screw has traditionally been the
pullout or holding strength of the screw when seated in bone [5]. In such mechanical assemblies, there will be
some sort of internally and/or externally generated forces on these screws that
can encourage failure of either the screw or the surrounding bone. Each bone screw has design parameters that
may affect the likelihood of screw implant failure. One of the most important considerations is
the decision to use bicortical or unicortical fixation. Bicortical fixation utilizes longer screws
that are seated within both the buccal and lingual cortices while unicortical
fixation uses shorter screws that are seated only in the buccal section of
cortical bone. Utilization of bicortical
screws stems from the common belief that a bicortically drilled screw can
sustain a stronger load before failure. However, a bicortical fixation also means longer surgical times and
increased chance of complications due to higher probability of interference
with the dental segment and the inferior alveolar nerve. Unicortical fixations, onthe other hand, are less
time consuming and avoid interference with the dental segment and the inferior alveolar nerve. It is important to have
an understanding of the effect of screw length, as well as other design
parameters, for a surgeon to make a judicious decision of the level of
intrusion necessary to safely fixate a mandibular fracture.Previous research
has yielded many insightful observations into the modes of bone screw failure
and the effect of certain design parameters for different types of bone
screws. Skinner [6] compared four
different types of screws used in transpedicular screw fixation. They observed
an increase in the pull-out strength due to an increase in the screw diameter
and an increase in displacement before failure resulting from an increase in the screw pitch. Complete failure
occurred when a sharp-threaded screw was pulled out one whole pitch distance,
an observation also reported by Ryken [7] using cervical plate screws. Another study by Ryken [8] suggested that
bicortical screw insertion provides more holding than unicortical insertion
while also finding a direct correlation between the bone mineral density (BMD)
of the surrounding bone and the screw pull-out strength. Using Casper cervical screws, Maiman [9] observed that cancellous bone remained on screw
threads after failure, but that posterior cortical penetration does not improve
pull-out strength. With regard to
smaller screws used in mandibular and maxilla fracture fixation, Boyle [10]
suggested that 2.7 mm diameter screws do not have an advantage over 2.0 mm
screws when seated in thin porcine rib, while at least three self-tapping
threads should be used for maximum retention. A similar conclusion was also
reached by Phillips [11]. Although a
wealth of information exists on screw pull-out studies, there have been no
studies that have completed a thorough analysis of screws used in mandibular fracture repair. To the authors’ knowledge, this would be the first such
study.The first focus of
the current study is to perform screw pull-out using mandibular bone screws in
a trilaminate block with sections representing material properties closely
resembling two sections/layers of cortical bone sandwiching a section of
cancellous bone. This provides a more
realistic determination of the effect of bone screw design parameters than
using a single layer of continuous material. Screws will be experimentally pulled out of the trilaminate block to
observe actual modes of screw failure before a FE model will simulate the experimental testing. The FE model gives
flexibility towards discovering the effects of different design parameters on
the pull-out strength. This is the first
known correlated attempt to perform both experimental and simulated screw
pull-out testing on a trilaminate material closely resembling layers of
cortical and cancellous bone.While both
experimental testing and finite element analysis of screw loading and failure
have received some attention, the natural loading on mandibular implant screws
during masticationhas not yet been
reported. Previous studies have shown that FEA of screw pull-out testing can be both validated by experiment,
andit is a useful
design tool when looking at stress and strain generated around screw implants
[1]. The value of these studies has so far been limited by the generally unknown forces on the screws implants in actual patients.Recently, work by
Cox [12],Fernández [13], Wagner [14], and Lovald [15, 16] has shown that finite
element analysis (FEA) of the entire mandible can mimic natural human loading
on a fractured mandible andcan determine the stress and strain fields within the bone and implant devices as well as the forces generated on the screw implants.
Given the size and complexity of these models, simplifications are often required in representing the bone screws.
Wagner and Cox neglected the screws, bonding the plate directly to mandibular bone. Lovald used cylinders
in place of threaded screws. While these
models were able to determine stress in the fixation plate and fracture
mobility, they did not yield accurate results pertaining to the stresses in
cortical and cancellous bone emanating from a threaded screw.The second focus
of the current study enhances work on both studies of screw pull-out FEA and
mandibular fracture fixation FEA by translating three-dimensional forces from a
mandibular FE model to a screw FE submodel considering bone screw embedded in a
trilaminate bone material. The
comparison will use von Mises stress in the cortical bone surrounding the
screws. Stress in the bone surrounding
the seated screw can lead to screw failure and the complications described
previously. Von Misescriterion was chosen in
order to be consistent with prior studies of similar nature [1, 12–15]. Using the boundary conditions from the
mandibular FEA model, the effect of certain screw design parameters, including
bicortical versus unicortical fixation, will once again be explored. To simplify the second part of this study,
parameters determined optimal during the first part of the study will be
used. Design parameter analysis will be
focused on four configurations with differing screw lengths, pitches, and major
diameters.


## 2. Materials and Methods

The current study has three components:(i)
validation
and design parameter analysis of experimental and numerical screw pull-out
from a trilaminate block with properties of cortical and cancellous bone;(ii)
determination
of forces applied to screw implants during natural human loading using FEA
of a fractured and fixated human mandible;(iii)
application
of the determined forces in component (ii) to a numerical analysis submodel
of a screw embedded in a trilaminate block from component (i).The methods section is broken into the three respective subsections.


### 2.1. Experimental and Numerical Analysis of Screw Pull-out

#### 2.1.1. Experimental Screw Pull-out

The experimental tests were done using bone
screws embedded in a trilaminate standard polyurethane block. The polyurethane
block has two outer cortical layers and a middle cancellous layer, each 3.0 mm
thick, mimicking mandibular bone. The
material properties of these layers were synthesized to closely match
mandibular bone properties (Pacific Research Laboratories, Inc., Vashon,Wash, USA). The dimensions of the block for all
experiments are15mm×15mm×9mm. Apart from having realistic material properties, these “artificial bone”
samples are less expensive, exhibit homogenous properties over a layer, and are
easy to manipulate for experiment.After drilling a pilot hole, titanium self-tapping
screws were inserted either completely for bicortical seating, or up to the
cancellous layer for unicortical seating. Self-tapping screws eliminate the
separate tapping requirement for surgical screw insertion. The self-tapping screws are provided by the
Leibinger Micro Implants (Stryker Corporation, Kalamazoo,Mich,
USA).The pull-out experiments were carried out on
an Instron machine (4400R controller model). Figure1(a) shows the experimental
setup. The specimen is held by clamps in
a specially designed vise. The screw is
held in a jig such that the screw head rests on the seat provided in the
jig. This jig is mounted on the
stationary end, which is the Instron machine’s upper crossbar. The lower
crossbar of the Instron, to which the vise is attached, is then gradually
pulled down at a speed of 5 mm/min till the screw disengages completely from
the block. Computer data acquisition recorded all the forces and displacements
during the testing.(a) Experimental setup for the pull-out tests, (b) typical specimen after
cylindrical failure with material trapped between screw threads, (c) pull-out
specimen with vertical cracks, and (d) pull-out specimen with diagonal cracks.
(a)(b)(c)(d)


#### 2.1.2. Polishing of the Experimental Specimen

The failure of the
screw-bone interface is hypothesized to start long before the screw is
completely pulled out of the block. Therefore, to verify the hypothesis, it is
important to do a micro examination of bone damage at loads well below the
maximum pull-out load encountered. This is done by taking partially pulled
specimen and grinding them finely for examination under a high-resolution
microscope. Using the mean failure load data from the pull-out experiments,
different polished samples were obtained at different loads. A specimen was
then ground on various abrasive grits, rough to fine, till the specimen was
sectioned in half.


#### 2.1.3. Numerical Analysis of Screw Pull-out

2.1.3.1. Geometry Creation
The 3D CAD
modeling system Pro/ENGINEER Wildfire (PTC, Needham, Mass, USA) was used to build a
model of a trilaminate mandibular bone specimen with an embedded screw
implant. Finite element analysis (FEA)
of a simulated screw pull-out process was carried out using the Pro/Mechanica software,
which is companion software to Pro/ENGINEER Wildfire. Geometrical data for the screwswas provided by the
Stryker-Leibinger Corp. (Kalamazoo,Mich, USA).
To simplify the model, the trilaminate bone specimen is modeled as a
cuboid (Figure2). The trilaminate
block is modeled as a 15mm×15mm square with three 3 mm thick layers of
outer cortical bone and inner cancellous bone.
These layers are perfectly bonded to one another. Aluminum clamps of dimensions 15.0mm×3.5mm×2.0m were placed on the top edges of the block to mimic the experimental
vise. The screw hole in the block is a
direct replica of the screw geometry to facilitate CAD assembly. Titanium screws were inserted into the
drilled blocks and assumedto be perfectly bonded to the block material.Figure 2
The Pro/E 3D assembly for the screw-pull out finite element analysis.2.1.3.2. Material Properties
All materials are assumed to be linear elastic and isotropic. The material properties were taken directly
from the respective manufacturers of the bone screws and the synthetic
trilaminate block material. Table1
gives the material properties used in the screw pull-out FEA.Table 1
Material properties used in the numerical
analysis of the screw pull-out.
Material properties for screw pull-out
FEAElastic modulus (Gpa)Poisson's ratioBone screw113.8000.342Cortical block layer1.1900.300Cancellous block layer0.2670.300Aluminum clamps69.0000.3002.1.3.3. Boundary Conditions
The boundary
conditions for the numerical analysis are meant to mimic the experiment. The top face of the screw was constrained
from movement in all directions. A
constant force of 600N is applied upon the top sides of the aluminum clamps in
a downward direction.
The model was solved numerically for various
parameters to study the effects of screw pitch, major diameter, and thread depth on the pull-out strength. The parameter values are as follows: major diameter: 2.0, 2.3, and 2.6 mm; pitch:
1.0, 1.2, and 1.4 mm; thread depth: 0.2, 0.3, and 0.4 mm. Each of these parameters was varied during
the study using baseline values of 2.3 mm for the major diameter, 1.0 mm for
the pitch, and 0.3 mm for the thread depth.


### 2.2. FEA of a Fractured Mandible

#### 2.2.1. Mandibular FEA Geometry Creation

Computerized tomography
scans of a 22-year-old male were obtained from a Siemens Somatone Sensations
Multislice Scanner. The patient had full
dentition and normal occlusion. The
scans were imported into Mimics 7.3 (Materialise, Ann Arbor,
Mich, USA)
where thresholding and editing functions were used to create entities for
cortical bone, cancellous bone, and the dental segment. Initial graphics exchange specification
(IGES) curves were approximated around the volumes and imported into ANSYS
8.0. Volumes were created and
subsequently bonded in the symphysis, parasymphysis, body, angle, ramus,
coronoid, and condyle regions using their respective IGES curves.The volumes
created were meshed using tetrahedral-shaped solid elements. The final mesh of the mandible with hardware
consisted of 67 434 elements and 107 352 nodes. Mesh
refinement was used in the plate, screws, fracture region, and the surrounding
cortical and cancellous regions until convergence of all pertinent measures was
established. A consistent mesh size was used in all
analyses. Geometric information from the
finite element model was compared to the original CT scan data to ensure model validity. Furthermore, loadings similar to previous studies were mimicked in order to validate stress results. CAD model verification for this study was
detailed in Chaudhary [17] and Lovald [15, 18].The fracture was simulated
as a 2 mm thick linear fracture in the parasymphyseal region. The symphysis of the mandible is the region
of the junction of the two symmetrical halves near the sagittal plane. Geometrical data for the plate was provided
by the Stryker-Leibinger Corp. (Kalamazoo, Mich,USA). The plate analyzed is the 3D Matrix4×2 Hole
Mini Plate. There is a small amount of
clearance between the modeled plate and bone, as in clinical situations. Unicortical screw fixation was used on the
superior border while bicortical fixation was used on the inferior border. Screws were simulated as solid cylinders with
a diameter of 2.3 mm that were inserted and bonded into the bone material.


#### 2.2.2. Material Properties

The finite element (FE)
model of the dentate mandible consists of the following materials: cortical
bone, cancellous bone, and dental segment (dentin, enamel, and periodontal
ligament). Coordinate systems and
orthotropic properties for cortical bone only were designated in each of 12
mandibular volumes created and mentioned previously. Table2 gives the material properties for the
mandibular FEA. The orthotropic
cortical bone values were taken from a study by Schwartz-Dabney and Dechow
[19]. Isotropic properties for
cancellous bone were taken from [13].
The properties for dentin were taken from another finite element study [20],
and they correlate
well with a study by Craig and Peyton [21].  In the current study, only material properties for dentin are modeled in the
dental segment due to its high modulus of elasticity. The fracture region was given properties of
initial connective tissue [22] (Young’s modulus of 3 MPa and Poisson’s ratio of
0.4). The properties of titanium plates
and screws were taken from another FE study of mandibular angle fractures [12].Table 2
Material properties used in FEA of the
mandible. Orthotropic properties were
used for cortical bone, while isotropic properties were used for cancellous
bone, dentin, and the titanium plate.
Thex-direction is along the length of the mandible, the y-direction is
normal to the bone plane, and the z-direction is their cross product.
Material
propertiesSymphysisParasymphysisAngleRamusCondyleCoronoidCancellousDentinTitaniumEx (MPa)20 49221 72823 79324 60723 50028 0007 93017 600110 000Ey (MPa)12 09212 70012 75712 97112 65014 0007 93017 600110 000Ez (MPa)16 35017 82819 01418 35717 85017 5007 93017 600110 000νxy0.430.450.410.380.320.280.30.340.34νyz0.220.20.220.230.250.280.30.340.34νxz0.340.340.30.280.240.230.30.340.34Gxy (MPa)5 3175 5335 4935 3865 5005 7503 0506 56741 045Gyz (MPa)4 8255 0834 9865 0145 1505 3003 0506 56741 045Gxz (MPa)6 9087 4507 5797 4077 1507 1503 0506 56741 045


### 2.2.3. Boundary Conditions

The bite force used in this
FEA was a unilateral molar clench.
Muscle force vectors that were experimentally derived for that specific
bite are distributed around the mandible.
Each force has a direction, area of attachment, and magnitude. The magnitude and direction of muscle forces
during the simulated bite were obtained from Korioth et al. [20] and are detailed in Lovald et al. [15]. The data from this
reference pertains to the bite of a healthy adult with an intact mandible. It is estimated that the bite force of a
patient with a fractured mandible is 60% of that of a healthy adult [23]. The bite force data was modified accordingly
in this study. The muscle attachment
areas on the mandible were obtained from [24].
Both condyles and the occlusal surface of the right first molar are
restrained from movement in all directions.
Figure 3 shows the meshed mandibular model.Figure 3
Meshed mandibular model showing a parasymphyseal fracture, fixation plates and screws,
and different material regions for orthotropic material properties.


### 2.3. Submodel FEA of a Threaded Screw

#### 2.3.1. Geometry Creation

Geometry used in the screw FEA submodel is nearly identical to that
described in Section 2.1.3.1. To simplify the
modeling, the aluminum clamps were not modeled.


#### 2.3.2. Material Properties

The material properties in the screw FEA submodel
are identical to those of the mandibular FEA from Section2.2. The outer layers of the trilaminate block are
assumedto be orthotropic and are taken directly from the material properties of the
parasymphyseal region from the mandibular FEA.
To the authors’ knowledge, this is the first FE study of screw pull-out
using orthotropic cortical bone properties.
The inner section of the trilaminate block was assumedto be isotropic andwas given material
properties of cancellous bone. The screw
implant was given material properties of titanium. All material properties for the screw FEA
submodel are given in Table 2.


#### 2.3.3. Boundary Conditions

Thesubmodel trilaminate block was restrained from movement
in three directions on its four sides. A
force, obtained from the mandibular FEA in Section2.2, was applied to the top
surface of the screw implant (Figure 4). The force of the particular screw which showed the highest magnitude in
the mandibular FEA was the only force applied to the screw FEA submodel. The same constitutive equations as in Sections
2.1.3.2 and 2.2.2 apply also here to the screw pull-out submodeling.Figure 4
The 3D Pro/E assembly with boundary
conditions. The bone layers are treated as orthotropic.This screw FEA submodel setup was utilized to compare different screw design configurations. Table3 shows the configurations for each
analysis. The bicortical screw
configuration was considered the base analysis.
The other configurations were analyzed to compare with the bicortical
screw configuration. A thread depth of
0.3 mm was held constant throughout all analyses. All screw parameter configurations are
commercially available.Table 3
Different screw configurations used in the FEA
screw submodel.
FixationMajor diameter (mm)Pitch (mm)Bicortical2.31.0Unicortical2.31.0Unicortical2.31.2Unicortical2.61.0


## 2.1. Experimental and Numerical Analysis of Screw Pull-out

### 2.1.1. Experimental Screw Pull-out

The experimental tests were done using bone
screws embedded in a trilaminate standard polyurethane block. The polyurethane
block has two outer cortical layers and a middle cancellous layer, each 3.0 mm
thick, mimicking mandibular bone. The
material properties of these layers were synthesized to closely match
mandibular bone properties (Pacific Research Laboratories, Inc., Vashon,Wash, USA). The dimensions of the block for all
experiments are15mm×15mm×9mm. Apart from having realistic material properties, these “artificial bone”
samples are less expensive, exhibit homogenous properties over a layer, and are
easy to manipulate for experiment.After drilling a pilot hole, titanium self-tapping
screws were inserted either completely for bicortical seating, or up to the
cancellous layer for unicortical seating. Self-tapping screws eliminate the
separate tapping requirement for surgical screw insertion. The self-tapping screws are provided by the
Leibinger Micro Implants (Stryker Corporation, Kalamazoo,Mich,
USA).The pull-out experiments were carried out on
an Instron machine (4400R controller model). Figure1(a) shows the experimental
setup. The specimen is held by clamps in
a specially designed vise. The screw is
held in a jig such that the screw head rests on the seat provided in the
jig. This jig is mounted on the
stationary end, which is the Instron machine’s upper crossbar. The lower
crossbar of the Instron, to which the vise is attached, is then gradually
pulled down at a speed of 5 mm/min till the screw disengages completely from
the block. Computer data acquisition recorded all the forces and displacements
during the testing.(a) Experimental setup for the pull-out tests, (b) typical specimen after
cylindrical failure with material trapped between screw threads, (c) pull-out
specimen with vertical cracks, and (d) pull-out specimen with diagonal cracks.
(a)(b)(c)(d)


### 2.1.2. Polishing of the Experimental Specimen

The failure of the
screw-bone interface is hypothesized to start long before the screw is
completely pulled out of the block. Therefore, to verify the hypothesis, it is
important to do a micro examination of bone damage at loads well below the
maximum pull-out load encountered. This is done by taking partially pulled
specimen and grinding them finely for examination under a high-resolution
microscope. Using the mean failure load data from the pull-out experiments,
different polished samples were obtained at different loads. A specimen was
then ground on various abrasive grits, rough to fine, till the specimen was
sectioned in half.


### 2.1.3. Numerical Analysis of Screw Pull-out

2.1.3.1. Geometry Creation
The 3D CAD
modeling system Pro/ENGINEER Wildfire (PTC, Needham, Mass, USA) was used to build a
model of a trilaminate mandibular bone specimen with an embedded screw
implant. Finite element analysis (FEA)
of a simulated screw pull-out process was carried out using the Pro/Mechanica software,
which is companion software to Pro/ENGINEER Wildfire. Geometrical data for the screwswas provided by the
Stryker-Leibinger Corp. (Kalamazoo,Mich, USA).
To simplify the model, the trilaminate bone specimen is modeled as a
cuboid (Figure2). The trilaminate
block is modeled as a 15mm×15mm square with three 3 mm thick layers of
outer cortical bone and inner cancellous bone.
These layers are perfectly bonded to one another. Aluminum clamps of dimensions 15.0mm×3.5mm×2.0m were placed on the top edges of the block to mimic the experimental
vise. The screw hole in the block is a
direct replica of the screw geometry to facilitate CAD assembly. Titanium screws were inserted into the
drilled blocks and assumedto be perfectly bonded to the block material.Figure 2
The Pro/E 3D assembly for the screw-pull out finite element analysis.2.1.3.2. Material Properties
All materials are assumed to be linear elastic and isotropic. The material properties were taken directly
from the respective manufacturers of the bone screws and the synthetic
trilaminate block material. Table1
gives the material properties used in the screw pull-out FEA.Table 1
Material properties used in the numerical
analysis of the screw pull-out.
Material properties for screw pull-out
FEAElastic modulus (Gpa)Poisson's ratioBone screw113.8000.342Cortical block layer1.1900.300Cancellous block layer0.2670.300Aluminum clamps69.0000.3002.1.3.3. Boundary Conditions
The boundary
conditions for the numerical analysis are meant to mimic the experiment. The top face of the screw was constrained
from movement in all directions. A
constant force of 600N is applied upon the top sides of the aluminum clamps in
a downward direction.
The model was solved numerically for various
parameters to study the effects of screw pitch, major diameter, and thread depth on the pull-out strength. The parameter values are as follows: major diameter: 2.0, 2.3, and 2.6 mm; pitch:
1.0, 1.2, and 1.4 mm; thread depth: 0.2, 0.3, and 0.4 mm. Each of these parameters was varied during
the study using baseline values of 2.3 mm for the major diameter, 1.0 mm for
the pitch, and 0.3 mm for the thread depth.


## 2.1.1. Experimental Screw Pull-out

The experimental tests were done using bone
screws embedded in a trilaminate standard polyurethane block. The polyurethane
block has two outer cortical layers and a middle cancellous layer, each 3.0 mm
thick, mimicking mandibular bone. The
material properties of these layers were synthesized to closely match
mandibular bone properties (Pacific Research Laboratories, Inc., Vashon,Wash, USA). The dimensions of the block for all
experiments are15mm×15mm×9mm. Apart from having realistic material properties, these “artificial bone”
samples are less expensive, exhibit homogenous properties over a layer, and are
easy to manipulate for experiment.After drilling a pilot hole, titanium self-tapping
screws were inserted either completely for bicortical seating, or up to the
cancellous layer for unicortical seating. Self-tapping screws eliminate the
separate tapping requirement for surgical screw insertion. The self-tapping screws are provided by the
Leibinger Micro Implants (Stryker Corporation, Kalamazoo,Mich,
USA).The pull-out experiments were carried out on
an Instron machine (4400R controller model). Figure1(a) shows the experimental
setup. The specimen is held by clamps in
a specially designed vise. The screw is
held in a jig such that the screw head rests on the seat provided in the
jig. This jig is mounted on the
stationary end, which is the Instron machine’s upper crossbar. The lower
crossbar of the Instron, to which the vise is attached, is then gradually
pulled down at a speed of 5 mm/min till the screw disengages completely from
the block. Computer data acquisition recorded all the forces and displacements
during the testing.(a) Experimental setup for the pull-out tests, (b) typical specimen after
cylindrical failure with material trapped between screw threads, (c) pull-out
specimen with vertical cracks, and (d) pull-out specimen with diagonal cracks.
(a)(b)(c)(d)


## 2.1.2. Polishing of the Experimental Specimen

The failure of the
screw-bone interface is hypothesized to start long before the screw is
completely pulled out of the block. Therefore, to verify the hypothesis, it is
important to do a micro examination of bone damage at loads well below the
maximum pull-out load encountered. This is done by taking partially pulled
specimen and grinding them finely for examination under a high-resolution
microscope. Using the mean failure load data from the pull-out experiments,
different polished samples were obtained at different loads. A specimen was
then ground on various abrasive grits, rough to fine, till the specimen was
sectioned in half.


## 2.1.3. Numerical Analysis of Screw Pull-out

2.1.3.1. Geometry Creation
The 3D CAD
modeling system Pro/ENGINEER Wildfire (PTC, Needham, Mass, USA) was used to build a
model of a trilaminate mandibular bone specimen with an embedded screw
implant. Finite element analysis (FEA)
of a simulated screw pull-out process was carried out using the Pro/Mechanica software,
which is companion software to Pro/ENGINEER Wildfire. Geometrical data for the screwswas provided by the
Stryker-Leibinger Corp. (Kalamazoo,Mich, USA).
To simplify the model, the trilaminate bone specimen is modeled as a
cuboid (Figure2). The trilaminate
block is modeled as a 15mm×15mm square with three 3 mm thick layers of
outer cortical bone and inner cancellous bone.
These layers are perfectly bonded to one another. Aluminum clamps of dimensions 15.0mm×3.5mm×2.0m were placed on the top edges of the block to mimic the experimental
vise. The screw hole in the block is a
direct replica of the screw geometry to facilitate CAD assembly. Titanium screws were inserted into the
drilled blocks and assumedto be perfectly bonded to the block material.Figure 2
The Pro/E 3D assembly for the screw-pull out finite element analysis.2.1.3.2. Material Properties
All materials are assumed to be linear elastic and isotropic. The material properties were taken directly
from the respective manufacturers of the bone screws and the synthetic
trilaminate block material. Table1
gives the material properties used in the screw pull-out FEA.Table 1
Material properties used in the numerical
analysis of the screw pull-out.
Material properties for screw pull-out
FEAElastic modulus (Gpa)Poisson's ratioBone screw113.8000.342Cortical block layer1.1900.300Cancellous block layer0.2670.300Aluminum clamps69.0000.3002.1.3.3. Boundary Conditions
The boundary
conditions for the numerical analysis are meant to mimic the experiment. The top face of the screw was constrained
from movement in all directions. A
constant force of 600N is applied upon the top sides of the aluminum clamps in
a downward direction.
The model was solved numerically for various
parameters to study the effects of screw pitch, major diameter, and thread depth on the pull-out strength. The parameter values are as follows: major diameter: 2.0, 2.3, and 2.6 mm; pitch:
1.0, 1.2, and 1.4 mm; thread depth: 0.2, 0.3, and 0.4 mm. Each of these parameters was varied during
the study using baseline values of 2.3 mm for the major diameter, 1.0 mm for
the pitch, and 0.3 mm for the thread depth.


## 2.2. FEA of a Fractured Mandible

### 2.2.1. Mandibular FEA Geometry Creation

Computerized tomography
scans of a 22-year-old male were obtained from a Siemens Somatone Sensations
Multislice Scanner. The patient had full
dentition and normal occlusion. The
scans were imported into Mimics 7.3 (Materialise, Ann Arbor,
Mich, USA)
where thresholding and editing functions were used to create entities for
cortical bone, cancellous bone, and the dental segment. Initial graphics exchange specification
(IGES) curves were approximated around the volumes and imported into ANSYS
8.0. Volumes were created and
subsequently bonded in the symphysis, parasymphysis, body, angle, ramus,
coronoid, and condyle regions using their respective IGES curves.The volumes
created were meshed using tetrahedral-shaped solid elements. The final mesh of the mandible with hardware
consisted of 67 434 elements and 107 352 nodes. Mesh
refinement was used in the plate, screws, fracture region, and the surrounding
cortical and cancellous regions until convergence of all pertinent measures was
established. A consistent mesh size was used in all
analyses. Geometric information from the
finite element model was compared to the original CT scan data to ensure model validity. Furthermore, loadings similar to previous studies were mimicked in order to validate stress results. CAD model verification for this study was
detailed in Chaudhary [17] and Lovald [15, 18].The fracture was simulated
as a 2 mm thick linear fracture in the parasymphyseal region. The symphysis of the mandible is the region
of the junction of the two symmetrical halves near the sagittal plane. Geometrical data for the plate was provided
by the Stryker-Leibinger Corp. (Kalamazoo, Mich,USA). The plate analyzed is the 3D Matrix4×2 Hole
Mini Plate. There is a small amount of
clearance between the modeled plate and bone, as in clinical situations. Unicortical screw fixation was used on the
superior border while bicortical fixation was used on the inferior border. Screws were simulated as solid cylinders with
a diameter of 2.3 mm that were inserted and bonded into the bone material.


### 2.2.2. Material Properties

The finite element (FE)
model of the dentate mandible consists of the following materials: cortical
bone, cancellous bone, and dental segment (dentin, enamel, and periodontal
ligament). Coordinate systems and
orthotropic properties for cortical bone only were designated in each of 12
mandibular volumes created and mentioned previously. Table2 gives the material properties for the
mandibular FEA. The orthotropic
cortical bone values were taken from a study by Schwartz-Dabney and Dechow
[19]. Isotropic properties for
cancellous bone were taken from [13].
The properties for dentin were taken from another finite element study [20],
and they correlate
well with a study by Craig and Peyton [21].  In the current study, only material properties for dentin are modeled in the
dental segment due to its high modulus of elasticity. The fracture region was given properties of
initial connective tissue [22] (Young’s modulus of 3 MPa and Poisson’s ratio of
0.4). The properties of titanium plates
and screws were taken from another FE study of mandibular angle fractures [12].Table 2
Material properties used in FEA of the
mandible. Orthotropic properties were
used for cortical bone, while isotropic properties were used for cancellous
bone, dentin, and the titanium plate.
Thex-direction is along the length of the mandible, the y-direction is
normal to the bone plane, and the z-direction is their cross product.
Material
propertiesSymphysisParasymphysisAngleRamusCondyleCoronoidCancellousDentinTitaniumEx (MPa)20 49221 72823 79324 60723 50028 0007 93017 600110 000Ey (MPa)12 09212 70012 75712 97112 65014 0007 93017 600110 000Ez (MPa)16 35017 82819 01418 35717 85017 5007 93017 600110 000νxy0.430.450.410.380.320.280.30.340.34νyz0.220.20.220.230.250.280.30.340.34νxz0.340.340.30.280.240.230.30.340.34Gxy (MPa)5 3175 5335 4935 3865 5005 7503 0506 56741 045Gyz (MPa)4 8255 0834 9865 0145 1505 3003 0506 56741 045Gxz (MPa)6 9087 4507 5797 4077 1507 1503 0506 56741 045


## 2.2.1. Mandibular FEA Geometry Creation

Computerized tomography
scans of a 22-year-old male were obtained from a Siemens Somatone Sensations
Multislice Scanner. The patient had full
dentition and normal occlusion. The
scans were imported into Mimics 7.3 (Materialise, Ann Arbor,
Mich, USA)
where thresholding and editing functions were used to create entities for
cortical bone, cancellous bone, and the dental segment. Initial graphics exchange specification
(IGES) curves were approximated around the volumes and imported into ANSYS
8.0. Volumes were created and
subsequently bonded in the symphysis, parasymphysis, body, angle, ramus,
coronoid, and condyle regions using their respective IGES curves.The volumes
created were meshed using tetrahedral-shaped solid elements. The final mesh of the mandible with hardware
consisted of 67 434 elements and 107 352 nodes. Mesh
refinement was used in the plate, screws, fracture region, and the surrounding
cortical and cancellous regions until convergence of all pertinent measures was
established. A consistent mesh size was used in all
analyses. Geometric information from the
finite element model was compared to the original CT scan data to ensure model validity. Furthermore, loadings similar to previous studies were mimicked in order to validate stress results. CAD model verification for this study was
detailed in Chaudhary [17] and Lovald [15, 18].The fracture was simulated
as a 2 mm thick linear fracture in the parasymphyseal region. The symphysis of the mandible is the region
of the junction of the two symmetrical halves near the sagittal plane. Geometrical data for the plate was provided
by the Stryker-Leibinger Corp. (Kalamazoo, Mich,USA). The plate analyzed is the 3D Matrix4×2 Hole
Mini Plate. There is a small amount of
clearance between the modeled plate and bone, as in clinical situations. Unicortical screw fixation was used on the
superior border while bicortical fixation was used on the inferior border. Screws were simulated as solid cylinders with
a diameter of 2.3 mm that were inserted and bonded into the bone material.


## 2.2.2. Material Properties

The finite element (FE)
model of the dentate mandible consists of the following materials: cortical
bone, cancellous bone, and dental segment (dentin, enamel, and periodontal
ligament). Coordinate systems and
orthotropic properties for cortical bone only were designated in each of 12
mandibular volumes created and mentioned previously. Table2 gives the material properties for the
mandibular FEA. The orthotropic
cortical bone values were taken from a study by Schwartz-Dabney and Dechow
[19]. Isotropic properties for
cancellous bone were taken from [13].
The properties for dentin were taken from another finite element study [20],
and they correlate
well with a study by Craig and Peyton [21].  In the current study, only material properties for dentin are modeled in the
dental segment due to its high modulus of elasticity. The fracture region was given properties of
initial connective tissue [22] (Young’s modulus of 3 MPa and Poisson’s ratio of
0.4). The properties of titanium plates
and screws were taken from another FE study of mandibular angle fractures [12].Table 2
Material properties used in FEA of the
mandible. Orthotropic properties were
used for cortical bone, while isotropic properties were used for cancellous
bone, dentin, and the titanium plate.
Thex-direction is along the length of the mandible, the y-direction is
normal to the bone plane, and the z-direction is their cross product.
Material
propertiesSymphysisParasymphysisAngleRamusCondyleCoronoidCancellousDentinTitaniumEx (MPa)20 49221 72823 79324 60723 50028 0007 93017 600110 000Ey (MPa)12 09212 70012 75712 97112 65014 0007 93017 600110 000Ez (MPa)16 35017 82819 01418 35717 85017 5007 93017 600110 000νxy0.430.450.410.380.320.280.30.340.34νyz0.220.20.220.230.250.280.30.340.34νxz0.340.340.30.280.240.230.30.340.34Gxy (MPa)5 3175 5335 4935 3865 5005 7503 0506 56741 045Gyz (MPa)4 8255 0834 9865 0145 1505 3003 0506 56741 045Gxz (MPa)6 9087 4507 5797 4077 1507 1503 0506 56741 045


## 2.2.3. Boundary Conditions

The bite force used in this
FEA was a unilateral molar clench.
Muscle force vectors that were experimentally derived for that specific
bite are distributed around the mandible.
Each force has a direction, area of attachment, and magnitude. The magnitude and direction of muscle forces
during the simulated bite were obtained from Korioth et al. [20] and are detailed in Lovald et al. [15]. The data from this
reference pertains to the bite of a healthy adult with an intact mandible. It is estimated that the bite force of a
patient with a fractured mandible is 60% of that of a healthy adult [23]. The bite force data was modified accordingly
in this study. The muscle attachment
areas on the mandible were obtained from [24].
Both condyles and the occlusal surface of the right first molar are
restrained from movement in all directions.
Figure 3 shows the meshed mandibular model.Figure 3
Meshed mandibular model showing a parasymphyseal fracture, fixation plates and screws,
and different material regions for orthotropic material properties.


## 2.3. Submodel FEA of a Threaded Screw

### 2.3.1. Geometry Creation

Geometry used in the screw FEA submodel is nearly identical to that
described in Section 2.1.3.1. To simplify the
modeling, the aluminum clamps were not modeled.


### 2.3.2. Material Properties

The material properties in the screw FEA submodel
are identical to those of the mandibular FEA from Section2.2. The outer layers of the trilaminate block are
assumedto be orthotropic and are taken directly from the material properties of the
parasymphyseal region from the mandibular FEA.
To the authors’ knowledge, this is the first FE study of screw pull-out
using orthotropic cortical bone properties.
The inner section of the trilaminate block was assumedto be isotropic andwas given material
properties of cancellous bone. The screw
implant was given material properties of titanium. All material properties for the screw FEA
submodel are given in Table 2.


### 2.3.3. Boundary Conditions

Thesubmodel trilaminate block was restrained from movement
in three directions on its four sides. A
force, obtained from the mandibular FEA in Section2.2, was applied to the top
surface of the screw implant (Figure 4). The force of the particular screw which showed the highest magnitude in
the mandibular FEA was the only force applied to the screw FEA submodel. The same constitutive equations as in Sections
2.1.3.2 and 2.2.2 apply also here to the screw pull-out submodeling.Figure 4
The 3D Pro/E assembly with boundary
conditions. The bone layers are treated as orthotropic.This screw FEA submodel setup was utilized to compare different screw design configurations. Table3 shows the configurations for each
analysis. The bicortical screw
configuration was considered the base analysis.
The other configurations were analyzed to compare with the bicortical
screw configuration. A thread depth of
0.3 mm was held constant throughout all analyses. All screw parameter configurations are
commercially available.Table 3
Different screw configurations used in the FEA
screw submodel.
FixationMajor diameter (mm)Pitch (mm)Bicortical2.31.0Unicortical2.31.0Unicortical2.31.2Unicortical2.61.0


## 2.3.1. Geometry Creation

Geometry used in the screw FEA submodel is nearly identical to that
described in Section 2.1.3.1. To simplify the
modeling, the aluminum clamps were not modeled.


## 2.3.2. Material Properties

The material properties in the screw FEA submodel
are identical to those of the mandibular FEA from Section2.2. The outer layers of the trilaminate block are
assumedto be orthotropic and are taken directly from the material properties of the
parasymphyseal region from the mandibular FEA.
To the authors’ knowledge, this is the first FE study of screw pull-out
using orthotropic cortical bone properties.
The inner section of the trilaminate block was assumedto be isotropic andwas given material
properties of cancellous bone. The screw
implant was given material properties of titanium. All material properties for the screw FEA
submodel are given in Table 2.


## 2.3.3. Boundary Conditions

Thesubmodel trilaminate block was restrained from movement
in three directions on its four sides. A
force, obtained from the mandibular FEA in Section2.2, was applied to the top
surface of the screw implant (Figure 4). The force of the particular screw which showed the highest magnitude in
the mandibular FEA was the only force applied to the screw FEA submodel. The same constitutive equations as in Sections
2.1.3.2 and 2.2.2 apply also here to the screw pull-out submodeling.Figure 4
The 3D Pro/E assembly with boundary
conditions. The bone layers are treated as orthotropic.This screw FEA submodel setup was utilized to compare different screw design configurations. Table3 shows the configurations for each
analysis. The bicortical screw
configuration was considered the base analysis.
The other configurations were analyzed to compare with the bicortical
screw configuration. A thread depth of
0.3 mm was held constant throughout all analyses. All screw parameter configurations are
commercially available.Table 3
Different screw configurations used in the FEA
screw submodel.
FixationMajor diameter (mm)Pitch (mm)Bicortical2.31.0Unicortical2.31.0Unicortical2.31.2Unicortical2.61.0


## 3. Results

### 3.1. Experimental and Numerical Analysis of Screw Pull-out

#### 3.1.1. Experimental Screw Pull-out

The experimental results were dependent on how the screw exactly
failed. Three different modes of failure
were observed:(i)
cylindrical
failure (Figure 1(b)): in this scenario, the screw
pulls out from the block with a significant amount of material trapped
between the threads. Samples
showing this type of failure have an average pull-out force that is
greater than samples in the following scenarios. Samples with cylindrical
failure exhibit smooth load-displacement curves, with single maxima (i.e.,
the lower curve in Figure 5);(ii)
failure with vertical cracks(Figure 1(c)):
the block samples show cracks normal to the clamp faces. Wide vertical cracks appear on the top
surface of the block. Generally,
crackling sounds preceded and accompanied the failure. The cracking of this nature is thought
to be due to bending of the block. This assumption is supported by the
fact that these cracks were predominant when larger block sizes were used.
The curves in this case are jagged with multiple peaks (i.e., multiple
local maxima);(iii)
failure
with diagonal cracks (Figure 1(d)): these samples show cracks on
the top surface of the block that propagate from the circumference of the
screw to the corner of the clamp andthey are narrow in comparison to the vertical
cracks. The curves in this case are not seen to be as jagged as those of
the vertical crack.Figure 5
Graph
showing typical load-displacement curves for bicortical and unicortical
pull-outs. Results were taken for screws
with a 2.3 mm major diameter and a 1.0 mm pitch. Three different regions are denoted from
which specimens were taken for polishing.The experimental
load-displacement curves for the bicortical and unicortical screws show a very
consistent trend or characteristic shape for cylindrical type failure (similar
to the lower curve in Figure5). The curves
in Figure 5 were obtained using 2.3 mm major diameter screws with 1.0 mm
pitch. The curve can be divided into
three different regions. Region 1
represents a presumably elastic region. Region 2 is predicted to contain the start of plastic deformation through
the formation and growth of microcracks. Region 3 is the failure region with macrocracks clearly visible on the
surface of the block.The pull-out experiments were carried out with a sample size of 15
specimens for each of the unicortical and bicortical studies. Results for maximum load and maximum
displacement are shown in Table4.
Bicortical fixation is shown to have a higher pull-out strength than unicortical fixation,
similar to findings by various works on other types of surgical screws
[7, 8].Table 4
Load and displacement results for the screw pull-out
experiments.
MeanSt.
Dev.Bicortical
screwGlobal maximum load (N)975.0283.15Displacement (mm)1.610.20Unicortical
screwGlobal maximum load (N)372.9638.77Displacement (mm)0.960.24The mean displacement to failure in the case of unicortical pull-out was
approximately equal to the pitch of the screw used, similar to findings by
Ryken [7]. However, the study by Ryken
showed that bicortical screws had a mean displacement to failure greater than
unicortical screws by approximately 8%. This is in contrast to results from the
current study which shows about a 67% increase. Theses studies differed in thetested material, the
screw type/geometry, the pull-out rate, and the flex within the experimental
setup, which all can alter the pull-out force [25]. While Ryken focused on cervical plate screws,
the current study is deemed more appropriate pertaining to screws used in the
rigid fixation of mandibular fractures.


#### 3.1.2. Polishing

Five different samples, labeled S1, S2, S3, S4, and S5 (see Figure5),
were sectioned and polished to reveal their interior damage state. Specimen S1
showed no observed microdamage at magnification of 400X.S1 lies within an elastic region (Region1)
which exhibits linear behavior. Specimen
S2 was just past the elastic region but it was not associated with macro
surface cracks (Figure 6(a)). The image of
specimen S3 is shown in Figure 6(b).
Shearing of the cortical material can be seen near the top part of the
image. With increased load the screw is
slowly pulled out until the uppermost thread chips off the material (Figure
6(b)). For specimen S4, in addition to the
failure seen in S3, the bone undergoes microcracking (Figure 6(c)) at the thread
immediately inferior to the uppermost thread.Images of polished specimens showing the thread-block interface for the
following loads (clockwise from top-left): (a) 566.4N and magnification of 200X (specimen S2),
(b) 684.6N and magnification of 50X (specimen S3), (c) 783.9N and magnification
of 200X (specimen S4), and (d) 891.3N and magnification of 100X (specimen S5).At higher loads, near S5, microcracking also takes place in the lower
cortical layer as well (Figure6(d)). It is worthy to mention, from the polished
specimens, that crack formation always seems to start near the uppermost thread
in both the upper and lower cortical layers.


#### 3.1.3. Numerical Screw Pull-out

General stress
contours for all screws analyzed are first discussed. Figure7(a) shows a typical distribution of von
Mises stress in the block for the  numerical analysis using a load of 600N. Stress concentration occurs in the block
material immediately surrounding the screw threads with the highest stress
region observed near the top surface of the block. This finding is consistent
with another work by the authors in which 3D finite element modeling was
performed on a fractured mandible that was fixated with a common plating
configuration [15]. It is also
consistent with damage occurring near the top surface as found in the above
microscopic studies. In the current
work, the stress concentration on the top surface was found to be traversing in
a direction diagonal to the blockThis
was clear at higher loads and conforms to experimental observations as almost
all of the bicortical, and some of the unicortical specimens, failed with
diagonal surface cracks.Plots of von Mises stress (MPa) in a typical trilaminate block. The four views
shown are (clockwise from top-left): (a) isometric view, (b) diagonal section
view, (c) volumetric contours, and (d) section view.
(a)(b)(c)(d)Figures7(b) and
7(d) show plots depicting stress distribution along diagonal and frontal
sectional views. The stress is seen to concentrate along the screw-block
interface and in the general vicinity of the screw. Measurements suggest that inserted surgical
screws separated by a diameter or more would have little interaction between
their respective stress fields.Figure7(c) shows
a typical volumetric contour plot. The
plot shows only the material surrounding the screw that is stressed above a
certain threshold of von Mises stress. As mentioned in earlier sections, most
test failures occur in such a way that the screw comes off from the block with
cortical material entrapped between its threads. This type of failure was hence referred to as
“cylindrical failure”. Figures 7(b), 7(c),
and 7(d) show the screw surrounded by a cylindrical envelope of the block
material with the highest stress. This
is consistent with the experimentally observed cylindrical failures.Seven different parametric
cases were studied using the finite element model for both bicortical and
unicortical setups. Each case had a different combination of major diameter,
pitch, and thread depth. The base case
represents a major diameter of 2.3 mm, a pitch of 1.0 mm, and a screw depth of
0.3 mm. All of these base case numbers are standard for surgical screws (taken
with permission from Stryker Corporation, Kalamazoo,Mich,
USA). Note that every time a parameter (e.g., major
diameter) was varied, all other parameters were held constant (e.g., pitch and
screw depth). For a given case, von
Mises stresses are interrogated from the highest stress level, which occurs
near the top screw thread, down to a stress level, whichcompletely envelops the screw.
At this stress level, which we term the “envelope stress,” the stress at
any material point within this envelope will be equal or higher than this value
up to the maximum stress level near the uppermost thread. The envelope stress essentially describes the
weakest point before cylindrical failure, andit is used here to weigh the varying screw
parameters. A lower value of the
“envelope stress” is desirable when considering the different bone screws.The plots in Figure8 depict the effect of screw parameters of both bicortical
and unicortical screws on the screw envelope stress. Figure 8(a) shows the effect of the different
parameters on the unicortical pull-out.
The most optimal conditions pertaining to envelope stress were a larger
major diameter and a larger thread depth.
Interestingly, it was found that a small screw diameter also has a
desirable “envelope stress,” but it was associated with a higher stress measure
at the top surface when compared to the effect of other parameters. Change in screw pitch affected the envelope
stress less than the other screw parameters.Plots showing the “envelope stress” for unicortical and bicortical setups.
(a)(b)Figure8(b) shows the effects of various screw parameters on the pull-out
envelope stress of the bicortical samples.
Optimal conditions suggest a smaller pitch and a large major diameter. This is different than in the unicortical
results, where the pitch did not largely affect the stress. A deeper thread depth seems to have lower
“envelope stress,” but it was found to
have very high localized stress at the top surface of the block, again
differing from the unicortical screw results. A deeper thread depth appears to
be unfavorable in the bicortical case.
Similar to the unicortical sample conclusion, a large screw diameter has
a positive effect with a low stress value for the “envelope stress” plot.


### 3.2. Mandibular Finite Element Analysis

Results
for the forces transmitted upon mastication from the fixation plate to the
screw implant were obtained for the four screw implants most proximal to the
fracture (Table5). The x, y, and z axes
correspond to the orthotropic material axes described in Section 2.2.2, with
the positive y direction
corresponding to the pull-out direction (normal to the bone surface). A negative y direction refers to a “pushing in” of the screw  implant. Only the maximum “pulling out” force was
considered for the screw FEA submodel.Table 5
Force components (N) applied to the screw
implants by the fixation plate in FEA of a fractured and fixated mandible. Thex-direction is along the length of the
mandible, y is normal to the bone plane, and the z-direction is their cross
product.
Screw locationxyzSuperior
posterior medial55.3−13.239.4Superior
anterior medial−57.68.9−26.3Inferior
posterior medial−67.6−16.422.2Inferior
anterior medial51.021.8−30.0These results were
translated into relevant  loadings and applied to a threaded screw implant
submodel in order to compare the effect of different screw configurations on
stresses induced in the bone  in which they are seated. The study was undertaken to gather
information that will aid the  design and use of screw implants in rigid
internal fixation of mandibular fractures.
The results gathered are expected to be more relevant than linear screw
pull-out numerical analyses.The results of the mandibular FEA show the forces applied to the four
screw implants most proximal to the fracture.
The maximum pull-out force seen from the current mandibular FEA is 21.8N. This is considerably less than the
forces leading to failure in the experimental pull-out analyses. We see further that the transverse forces (in
thex and z directions) are the dominant loads upon screws used in the
fixation of mandibular fractures, which is contrary to all pull-out experiments in the literature focusing solely on the axial
direction.


### 3.3. Screw FEA Submodel

Results were obtained for von Mises stress in the bone surrounding the
screw implant for the screw FEA submodel.
Figure9 shows an isometric plot of the von Mises stress in the bone for
all four screw configurations analyzed.
The isometric plot shows only the material that is stressed beyond what
is considered the failure stress of the bone material. Frost suggested this failure stress is 60 MPa
[26]. The maximum error limit for all
numerical analyses was 2% of maximum principal stress.An isometric plot of the von Mises stress in
bone surrounding the 4 configurations of screw implants. The plot shows only stresses above a 60 MPa
threshold.
(a)(b)(c)(d)To simplify the comparison, the peak
von Mises stress was obtained from the analyses for the four different screw configurations under the described loading.
Table6 contains these peak stresses for the four screw configurations.Table 6
Peak von Mises stress in the bone surrounding
screw implants for the four different screw configurations.
FixationMajor diameter (mm)Pitch (mm)Peak von Mises Stress (MPa)Bicortical2.31.0147Unicortical2.31.0322Unicortical2.31.2226Unicortical2.61.0106Applying clinically relevant forces elucidates the true effect of screw
parameters on their fixation  capabilities for mandibular fractures. Like previous works, including previously in
this work, the highest stresses were located nearest to the cortical bone
surface, where the implant first enters the bone material [1, 15, 16]. Peak stress was the lowest in the unicortical
screw of 2.6 mm major diameter (Table 6).
This outperforms even the bicortically fixed screw configuration. Results from Figure 9 support this
conclusion. It is clearly shown that the
2.6 mm unicortical screw has the least amount of material that is above the
specified failure threshold. Based on
stress results, this evidence suggests that surgeons could avoid bicortical
drilling by using unicortical screws with a larger major diameter. This is fortunate as the likelihood of nerve
and dental segment interference can be significantly reduced without the need
to penetrate past the outer cortical shell of the mandibular corpus.Tada [1] reported that implant
length was a factor in analyses mimicking poor bone quality and pure axial
loading. While their study focused on
dental implants, loadings were similar in nature to those of experimental screw
testing. Less of an affect was seen in
bone modeled as having good quality and in analyses undergoing transverse
loading. Similarly Van Steenburgh [27]
found that the length did not affect the success rate in patients with good quality bone. The current study only considers bone of good
quality, and the loading applied here has a much higher transverse component
relative to the axial component. Both of these are conducive to results
unaffected by implant insertion length.
While the loading of the current study is considered more relevant than
previous works, the effect of bone quality on the results is not within the
current scope.Readers should be informed in
putting too much confidence into quantitative results from FE analyses of this
type. There is a large range of possible
inputs into mandibular FEA considering the different bone material properties,
bite force magnitudes, fracture locations, and jaw geometries among patients,
to name just a few variable patient parameters. Nonetheless, comparisons between different
screw configurations based on peak stress and the amount of material that is
predicted to fail given a failure stress threshold offer qualitative insight
that can aid both screw design and craniomaxillofacial surgical practice.


## 3.1. Experimental and Numerical Analysis of Screw Pull-out

### 3.1.1. Experimental Screw Pull-out

The experimental results were dependent on how the screw exactly
failed. Three different modes of failure
were observed:(i)
cylindrical
failure (Figure 1(b)): in this scenario, the screw
pulls out from the block with a significant amount of material trapped
between the threads. Samples
showing this type of failure have an average pull-out force that is
greater than samples in the following scenarios. Samples with cylindrical
failure exhibit smooth load-displacement curves, with single maxima (i.e.,
the lower curve in Figure 5);(ii)
failure with vertical cracks(Figure 1(c)):
the block samples show cracks normal to the clamp faces. Wide vertical cracks appear on the top
surface of the block. Generally,
crackling sounds preceded and accompanied the failure. The cracking of this nature is thought
to be due to bending of the block. This assumption is supported by the
fact that these cracks were predominant when larger block sizes were used.
The curves in this case are jagged with multiple peaks (i.e., multiple
local maxima);(iii)
failure
with diagonal cracks (Figure 1(d)): these samples show cracks on
the top surface of the block that propagate from the circumference of the
screw to the corner of the clamp andthey are narrow in comparison to the vertical
cracks. The curves in this case are not seen to be as jagged as those of
the vertical crack.Figure 5
Graph
showing typical load-displacement curves for bicortical and unicortical
pull-outs. Results were taken for screws
with a 2.3 mm major diameter and a 1.0 mm pitch. Three different regions are denoted from
which specimens were taken for polishing.The experimental
load-displacement curves for the bicortical and unicortical screws show a very
consistent trend or characteristic shape for cylindrical type failure (similar
to the lower curve in Figure5). The curves
in Figure 5 were obtained using 2.3 mm major diameter screws with 1.0 mm
pitch. The curve can be divided into
three different regions. Region 1
represents a presumably elastic region. Region 2 is predicted to contain the start of plastic deformation through
the formation and growth of microcracks. Region 3 is the failure region with macrocracks clearly visible on the
surface of the block.The pull-out experiments were carried out with a sample size of 15
specimens for each of the unicortical and bicortical studies. Results for maximum load and maximum
displacement are shown in Table4.
Bicortical fixation is shown to have a higher pull-out strength than unicortical fixation,
similar to findings by various works on other types of surgical screws
[7, 8].Table 4
Load and displacement results for the screw pull-out
experiments.
MeanSt.
Dev.Bicortical
screwGlobal maximum load (N)975.0283.15Displacement (mm)1.610.20Unicortical
screwGlobal maximum load (N)372.9638.77Displacement (mm)0.960.24The mean displacement to failure in the case of unicortical pull-out was
approximately equal to the pitch of the screw used, similar to findings by
Ryken [7]. However, the study by Ryken
showed that bicortical screws had a mean displacement to failure greater than
unicortical screws by approximately 8%. This is in contrast to results from the
current study which shows about a 67% increase. Theses studies differed in thetested material, the
screw type/geometry, the pull-out rate, and the flex within the experimental
setup, which all can alter the pull-out force [25]. While Ryken focused on cervical plate screws,
the current study is deemed more appropriate pertaining to screws used in the
rigid fixation of mandibular fractures.


### 3.1.2. Polishing

Five different samples, labeled S1, S2, S3, S4, and S5 (see Figure5),
were sectioned and polished to reveal their interior damage state. Specimen S1
showed no observed microdamage at magnification of 400X.S1 lies within an elastic region (Region1)
which exhibits linear behavior. Specimen
S2 was just past the elastic region but it was not associated with macro
surface cracks (Figure 6(a)). The image of
specimen S3 is shown in Figure 6(b).
Shearing of the cortical material can be seen near the top part of the
image. With increased load the screw is
slowly pulled out until the uppermost thread chips off the material (Figure
6(b)). For specimen S4, in addition to the
failure seen in S3, the bone undergoes microcracking (Figure 6(c)) at the thread
immediately inferior to the uppermost thread.Images of polished specimens showing the thread-block interface for the
following loads (clockwise from top-left): (a) 566.4N and magnification of 200X (specimen S2),
(b) 684.6N and magnification of 50X (specimen S3), (c) 783.9N and magnification
of 200X (specimen S4), and (d) 891.3N and magnification of 100X (specimen S5).At higher loads, near S5, microcracking also takes place in the lower
cortical layer as well (Figure6(d)). It is worthy to mention, from the polished
specimens, that crack formation always seems to start near the uppermost thread
in both the upper and lower cortical layers.


### 3.1.3. Numerical Screw Pull-out

General stress
contours for all screws analyzed are first discussed. Figure7(a) shows a typical distribution of von
Mises stress in the block for the  numerical analysis using a load of 600N. Stress concentration occurs in the block
material immediately surrounding the screw threads with the highest stress
region observed near the top surface of the block. This finding is consistent
with another work by the authors in which 3D finite element modeling was
performed on a fractured mandible that was fixated with a common plating
configuration [15]. It is also
consistent with damage occurring near the top surface as found in the above
microscopic studies. In the current
work, the stress concentration on the top surface was found to be traversing in
a direction diagonal to the blockThis
was clear at higher loads and conforms to experimental observations as almost
all of the bicortical, and some of the unicortical specimens, failed with
diagonal surface cracks.Plots of von Mises stress (MPa) in a typical trilaminate block. The four views
shown are (clockwise from top-left): (a) isometric view, (b) diagonal section
view, (c) volumetric contours, and (d) section view.
(a)(b)(c)(d)Figures7(b) and
7(d) show plots depicting stress distribution along diagonal and frontal
sectional views. The stress is seen to concentrate along the screw-block
interface and in the general vicinity of the screw. Measurements suggest that inserted surgical
screws separated by a diameter or more would have little interaction between
their respective stress fields.Figure7(c) shows
a typical volumetric contour plot. The
plot shows only the material surrounding the screw that is stressed above a
certain threshold of von Mises stress. As mentioned in earlier sections, most
test failures occur in such a way that the screw comes off from the block with
cortical material entrapped between its threads. This type of failure was hence referred to as
“cylindrical failure”. Figures 7(b), 7(c),
and 7(d) show the screw surrounded by a cylindrical envelope of the block
material with the highest stress. This
is consistent with the experimentally observed cylindrical failures.Seven different parametric
cases were studied using the finite element model for both bicortical and
unicortical setups. Each case had a different combination of major diameter,
pitch, and thread depth. The base case
represents a major diameter of 2.3 mm, a pitch of 1.0 mm, and a screw depth of
0.3 mm. All of these base case numbers are standard for surgical screws (taken
with permission from Stryker Corporation, Kalamazoo,Mich,
USA). Note that every time a parameter (e.g., major
diameter) was varied, all other parameters were held constant (e.g., pitch and
screw depth). For a given case, von
Mises stresses are interrogated from the highest stress level, which occurs
near the top screw thread, down to a stress level, whichcompletely envelops the screw.
At this stress level, which we term the “envelope stress,” the stress at
any material point within this envelope will be equal or higher than this value
up to the maximum stress level near the uppermost thread. The envelope stress essentially describes the
weakest point before cylindrical failure, andit is used here to weigh the varying screw
parameters. A lower value of the
“envelope stress” is desirable when considering the different bone screws.The plots in Figure8 depict the effect of screw parameters of both bicortical
and unicortical screws on the screw envelope stress. Figure 8(a) shows the effect of the different
parameters on the unicortical pull-out.
The most optimal conditions pertaining to envelope stress were a larger
major diameter and a larger thread depth.
Interestingly, it was found that a small screw diameter also has a
desirable “envelope stress,” but it was associated with a higher stress measure
at the top surface when compared to the effect of other parameters. Change in screw pitch affected the envelope
stress less than the other screw parameters.Plots showing the “envelope stress” for unicortical and bicortical setups.
(a)(b)Figure8(b) shows the effects of various screw parameters on the pull-out
envelope stress of the bicortical samples.
Optimal conditions suggest a smaller pitch and a large major diameter. This is different than in the unicortical
results, where the pitch did not largely affect the stress. A deeper thread depth seems to have lower
“envelope stress,” but it was found to
have very high localized stress at the top surface of the block, again
differing from the unicortical screw results. A deeper thread depth appears to
be unfavorable in the bicortical case.
Similar to the unicortical sample conclusion, a large screw diameter has
a positive effect with a low stress value for the “envelope stress” plot.


## 3.1.1. Experimental Screw Pull-out

The experimental results were dependent on how the screw exactly
failed. Three different modes of failure
were observed:(i)
cylindrical
failure (Figure 1(b)): in this scenario, the screw
pulls out from the block with a significant amount of material trapped
between the threads. Samples
showing this type of failure have an average pull-out force that is
greater than samples in the following scenarios. Samples with cylindrical
failure exhibit smooth load-displacement curves, with single maxima (i.e.,
the lower curve in Figure 5);(ii)
failure with vertical cracks(Figure 1(c)):
the block samples show cracks normal to the clamp faces. Wide vertical cracks appear on the top
surface of the block. Generally,
crackling sounds preceded and accompanied the failure. The cracking of this nature is thought
to be due to bending of the block. This assumption is supported by the
fact that these cracks were predominant when larger block sizes were used.
The curves in this case are jagged with multiple peaks (i.e., multiple
local maxima);(iii)
failure
with diagonal cracks (Figure 1(d)): these samples show cracks on
the top surface of the block that propagate from the circumference of the
screw to the corner of the clamp andthey are narrow in comparison to the vertical
cracks. The curves in this case are not seen to be as jagged as those of
the vertical crack.Figure 5
Graph
showing typical load-displacement curves for bicortical and unicortical
pull-outs. Results were taken for screws
with a 2.3 mm major diameter and a 1.0 mm pitch. Three different regions are denoted from
which specimens were taken for polishing.The experimental
load-displacement curves for the bicortical and unicortical screws show a very
consistent trend or characteristic shape for cylindrical type failure (similar
to the lower curve in Figure5). The curves
in Figure 5 were obtained using 2.3 mm major diameter screws with 1.0 mm
pitch. The curve can be divided into
three different regions. Region 1
represents a presumably elastic region. Region 2 is predicted to contain the start of plastic deformation through
the formation and growth of microcracks. Region 3 is the failure region with macrocracks clearly visible on the
surface of the block.The pull-out experiments were carried out with a sample size of 15
specimens for each of the unicortical and bicortical studies. Results for maximum load and maximum
displacement are shown in Table4.
Bicortical fixation is shown to have a higher pull-out strength than unicortical fixation,
similar to findings by various works on other types of surgical screws
[7, 8].Table 4
Load and displacement results for the screw pull-out
experiments.
MeanSt.
Dev.Bicortical
screwGlobal maximum load (N)975.0283.15Displacement (mm)1.610.20Unicortical
screwGlobal maximum load (N)372.9638.77Displacement (mm)0.960.24The mean displacement to failure in the case of unicortical pull-out was
approximately equal to the pitch of the screw used, similar to findings by
Ryken [7]. However, the study by Ryken
showed that bicortical screws had a mean displacement to failure greater than
unicortical screws by approximately 8%. This is in contrast to results from the
current study which shows about a 67% increase. Theses studies differed in thetested material, the
screw type/geometry, the pull-out rate, and the flex within the experimental
setup, which all can alter the pull-out force [25]. While Ryken focused on cervical plate screws,
the current study is deemed more appropriate pertaining to screws used in the
rigid fixation of mandibular fractures.


## 3.1.2. Polishing

Five different samples, labeled S1, S2, S3, S4, and S5 (see Figure5),
were sectioned and polished to reveal their interior damage state. Specimen S1
showed no observed microdamage at magnification of 400X.S1 lies within an elastic region (Region1)
which exhibits linear behavior. Specimen
S2 was just past the elastic region but it was not associated with macro
surface cracks (Figure 6(a)). The image of
specimen S3 is shown in Figure 6(b).
Shearing of the cortical material can be seen near the top part of the
image. With increased load the screw is
slowly pulled out until the uppermost thread chips off the material (Figure
6(b)). For specimen S4, in addition to the
failure seen in S3, the bone undergoes microcracking (Figure 6(c)) at the thread
immediately inferior to the uppermost thread.Images of polished specimens showing the thread-block interface for the
following loads (clockwise from top-left): (a) 566.4N and magnification of 200X (specimen S2),
(b) 684.6N and magnification of 50X (specimen S3), (c) 783.9N and magnification
of 200X (specimen S4), and (d) 891.3N and magnification of 100X (specimen S5).At higher loads, near S5, microcracking also takes place in the lower
cortical layer as well (Figure6(d)). It is worthy to mention, from the polished
specimens, that crack formation always seems to start near the uppermost thread
in both the upper and lower cortical layers.


## 3.1.3. Numerical Screw Pull-out

General stress
contours for all screws analyzed are first discussed. Figure7(a) shows a typical distribution of von
Mises stress in the block for the  numerical analysis using a load of 600N. Stress concentration occurs in the block
material immediately surrounding the screw threads with the highest stress
region observed near the top surface of the block. This finding is consistent
with another work by the authors in which 3D finite element modeling was
performed on a fractured mandible that was fixated with a common plating
configuration [15]. It is also
consistent with damage occurring near the top surface as found in the above
microscopic studies. In the current
work, the stress concentration on the top surface was found to be traversing in
a direction diagonal to the blockThis
was clear at higher loads and conforms to experimental observations as almost
all of the bicortical, and some of the unicortical specimens, failed with
diagonal surface cracks.Plots of von Mises stress (MPa) in a typical trilaminate block. The four views
shown are (clockwise from top-left): (a) isometric view, (b) diagonal section
view, (c) volumetric contours, and (d) section view.
(a)(b)(c)(d)Figures7(b) and
7(d) show plots depicting stress distribution along diagonal and frontal
sectional views. The stress is seen to concentrate along the screw-block
interface and in the general vicinity of the screw. Measurements suggest that inserted surgical
screws separated by a diameter or more would have little interaction between
their respective stress fields.Figure7(c) shows
a typical volumetric contour plot. The
plot shows only the material surrounding the screw that is stressed above a
certain threshold of von Mises stress. As mentioned in earlier sections, most
test failures occur in such a way that the screw comes off from the block with
cortical material entrapped between its threads. This type of failure was hence referred to as
“cylindrical failure”. Figures 7(b), 7(c),
and 7(d) show the screw surrounded by a cylindrical envelope of the block
material with the highest stress. This
is consistent with the experimentally observed cylindrical failures.Seven different parametric
cases were studied using the finite element model for both bicortical and
unicortical setups. Each case had a different combination of major diameter,
pitch, and thread depth. The base case
represents a major diameter of 2.3 mm, a pitch of 1.0 mm, and a screw depth of
0.3 mm. All of these base case numbers are standard for surgical screws (taken
with permission from Stryker Corporation, Kalamazoo,Mich,
USA). Note that every time a parameter (e.g., major
diameter) was varied, all other parameters were held constant (e.g., pitch and
screw depth). For a given case, von
Mises stresses are interrogated from the highest stress level, which occurs
near the top screw thread, down to a stress level, whichcompletely envelops the screw.
At this stress level, which we term the “envelope stress,” the stress at
any material point within this envelope will be equal or higher than this value
up to the maximum stress level near the uppermost thread. The envelope stress essentially describes the
weakest point before cylindrical failure, andit is used here to weigh the varying screw
parameters. A lower value of the
“envelope stress” is desirable when considering the different bone screws.The plots in Figure8 depict the effect of screw parameters of both bicortical
and unicortical screws on the screw envelope stress. Figure 8(a) shows the effect of the different
parameters on the unicortical pull-out.
The most optimal conditions pertaining to envelope stress were a larger
major diameter and a larger thread depth.
Interestingly, it was found that a small screw diameter also has a
desirable “envelope stress,” but it was associated with a higher stress measure
at the top surface when compared to the effect of other parameters. Change in screw pitch affected the envelope
stress less than the other screw parameters.Plots showing the “envelope stress” for unicortical and bicortical setups.
(a)(b)Figure8(b) shows the effects of various screw parameters on the pull-out
envelope stress of the bicortical samples.
Optimal conditions suggest a smaller pitch and a large major diameter. This is different than in the unicortical
results, where the pitch did not largely affect the stress. A deeper thread depth seems to have lower
“envelope stress,” but it was found to
have very high localized stress at the top surface of the block, again
differing from the unicortical screw results. A deeper thread depth appears to
be unfavorable in the bicortical case.
Similar to the unicortical sample conclusion, a large screw diameter has
a positive effect with a low stress value for the “envelope stress” plot.


## 3.2. Mandibular Finite Element Analysis

Results
for the forces transmitted upon mastication from the fixation plate to the
screw implant were obtained for the four screw implants most proximal to the
fracture (Table5). The x, y, and z axes
correspond to the orthotropic material axes described in Section 2.2.2, with
the positive y direction
corresponding to the pull-out direction (normal to the bone surface). A negative y direction refers to a “pushing in” of the screw  implant. Only the maximum “pulling out” force was
considered for the screw FEA submodel.Table 5
Force components (N) applied to the screw
implants by the fixation plate in FEA of a fractured and fixated mandible. Thex-direction is along the length of the
mandible, y is normal to the bone plane, and the z-direction is their cross
product.
Screw locationxyzSuperior
posterior medial55.3−13.239.4Superior
anterior medial−57.68.9−26.3Inferior
posterior medial−67.6−16.422.2Inferior
anterior medial51.021.8−30.0These results were
translated into relevant  loadings and applied to a threaded screw implant
submodel in order to compare the effect of different screw configurations on
stresses induced in the bone  in which they are seated. The study was undertaken to gather
information that will aid the  design and use of screw implants in rigid
internal fixation of mandibular fractures.
The results gathered are expected to be more relevant than linear screw
pull-out numerical analyses.The results of the mandibular FEA show the forces applied to the four
screw implants most proximal to the fracture.
The maximum pull-out force seen from the current mandibular FEA is 21.8N. This is considerably less than the
forces leading to failure in the experimental pull-out analyses. We see further that the transverse forces (in
thex and z directions) are the dominant loads upon screws used in the
fixation of mandibular fractures, which is contrary to all pull-out experiments in the literature focusing solely on the axial
direction.


## 3.3. Screw FEA Submodel

Results were obtained for von Mises stress in the bone surrounding the
screw implant for the screw FEA submodel.
Figure9 shows an isometric plot of the von Mises stress in the bone for
all four screw configurations analyzed.
The isometric plot shows only the material that is stressed beyond what
is considered the failure stress of the bone material. Frost suggested this failure stress is 60 MPa
[26]. The maximum error limit for all
numerical analyses was 2% of maximum principal stress.An isometric plot of the von Mises stress in
bone surrounding the 4 configurations of screw implants. The plot shows only stresses above a 60 MPa
threshold.
(a)(b)(c)(d)To simplify the comparison, the peak
von Mises stress was obtained from the analyses for the four different screw configurations under the described loading.
Table6 contains these peak stresses for the four screw configurations.Table 6
Peak von Mises stress in the bone surrounding
screw implants for the four different screw configurations.
FixationMajor diameter (mm)Pitch (mm)Peak von Mises Stress (MPa)Bicortical2.31.0147Unicortical2.31.0322Unicortical2.31.2226Unicortical2.61.0106Applying clinically relevant forces elucidates the true effect of screw
parameters on their fixation  capabilities for mandibular fractures. Like previous works, including previously in
this work, the highest stresses were located nearest to the cortical bone
surface, where the implant first enters the bone material [1, 15, 16]. Peak stress was the lowest in the unicortical
screw of 2.6 mm major diameter (Table 6).
This outperforms even the bicortically fixed screw configuration. Results from Figure 9 support this
conclusion. It is clearly shown that the
2.6 mm unicortical screw has the least amount of material that is above the
specified failure threshold. Based on
stress results, this evidence suggests that surgeons could avoid bicortical
drilling by using unicortical screws with a larger major diameter. This is fortunate as the likelihood of nerve
and dental segment interference can be significantly reduced without the need
to penetrate past the outer cortical shell of the mandibular corpus.Tada [1] reported that implant
length was a factor in analyses mimicking poor bone quality and pure axial
loading. While their study focused on
dental implants, loadings were similar in nature to those of experimental screw
testing. Less of an affect was seen in
bone modeled as having good quality and in analyses undergoing transverse
loading. Similarly Van Steenburgh [27]
found that the length did not affect the success rate in patients with good quality bone. The current study only considers bone of good
quality, and the loading applied here has a much higher transverse component
relative to the axial component. Both of these are conducive to results
unaffected by implant insertion length.
While the loading of the current study is considered more relevant than
previous works, the effect of bone quality on the results is not within the
current scope.Readers should be informed in
putting too much confidence into quantitative results from FE analyses of this
type. There is a large range of possible
inputs into mandibular FEA considering the different bone material properties,
bite force magnitudes, fracture locations, and jaw geometries among patients,
to name just a few variable patient parameters. Nonetheless, comparisons between different
screw configurations based on peak stress and the amount of material that is
predicted to fail given a failure stress threshold offer qualitative insight
that can aid both screw design and craniomaxillofacial surgical practice.


## 4. Conclusions

The current study used
experimental screw pull-out tests, finite element analysis (FEA) of detailed
screw pull-out models, and FEA of a fractured and fixated mandible to determine
the effect of bone screw design parameters on stresses generated in bone
surrounding screw implants used in patients treated with open reduction and
internal fixation (ORIF) of mandible fractures.
Results from the experimental and numerical screw pull out tests
correlated well. The parametric
numerical analyses gave differing conclusions pertaining to screw thread depth
and pitch for the unicortical and bicortical screws but concluded that the major diameter is
relevant in reducing high stress in the surrounding bone. Results of the mandibular FEA suggest that
transversely applied forces are dominant upon the implant. The screw FEA
submodel determined that there are lower stresses generated around a 2.6 mm
unicortical screw than those surrounding a 2.3 mm bicortical screw when
subjected to clinically relevant loading.
This suggests that better fixation can be achieved while avoiding
bicortical drilling by increasing the major diameter of unicortical bone screws
used in ORIF.



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*Source: 628120-2008-05-15.xml*