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Optimal Plating System for a 45-Degree Tibia Fracture Eliezer Alvarado, Zaid Haddadin, Neetal Kumar
Group #4
Cell Mechanics
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Introduction
Bone fractures occur due to high trauma causing the bone material to fail or
weaken to a point where it breaks. The most common remedy is internal fixation. Internal
fixation is the usage of plates and screws to aid in the healing of the bone fracture. The
plates and screws are usually added in an open surgery of the bone, which is called open
reduction. This entire process is referred to as Open Reduction Internal Fixation or ORIF.
There is another remedy know as external fixation where the screws and plates are done
outside of the leg to where it is visible and tangible.
There have been several plate designs over the course of the century that was
considered the standard. But the thing about the standard is that there only a few changes.
The general standard is usually a really long plate with holes in which screws can go
through. The changes are usually tied into the physiological aspects of the bone and the
plate itself. For instances, bone to plate contact usually leads to necrosis, in effect, bone
loss as well; this is known as Osteonecrosis. Avascular necrosis, or Osteonecrosis, occurs
due to the external pressure added by the internal fixation. This pressure blocks blood
vessels from functioning resulting in loss of oxygen. A loss of oxygen results in hypoxia,
which is where the partial pressure of oxygen is reduce to less than 10 mm.
Hematopoietic stem cells are the most vulnerable to this effect so they are first to go. And
then if there is still a lack of oxygen after 5 days, bone marrow cells begin die. To
preform internal fixation, properties of the plate has to be considered in order to design a
plate.
There are two major characteristics that need to be analyzing before designing a
plate. They are the size and material. The size refers to the length and width as well as the
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thickness. The length and width is crucial to minimize; if there is a bigger area that is
attached to the bone, there will be more bone contact which results in more pressure that
adds into possible bone deterioration. The material is crucial in that in need to sustain not
only the stress from the fracture but applied forces as well. If a material is too brittle, then
it under normal conditions the plate will crack thus leading into an infection. Moreover, if
the point of failure is low then the material would not be any good due to the high
possibility of the plate failing to sustain the stresses.
Screws
In this case, screws will used so we will analyze the different type of screws.
Screws can vary by where it is positioned, the pitch of the threads, and the dimensions of
the screw. A lag screw is where a screw is inserted at an angle that is not perpendicular
to the surface of the bone. This aids in the compression between the fractures of the two
bones. Another screw is the cannulated screw, which has a hollow shaft and the threads
are at the end only. A lag screw is defined by its position whereas cannulated screw is
defined by the properties of the screw. Having a combination of these screws can be
useful as both have different functions.
By modeling a tibia bone, we needed a program to apply forces to identify the
stress, strain, and deformation before and after the fracture and the plate. We used the
Static Structure on ANSYS workbench. This gave use stress, strain, and deformation
values with great detail. The forces applied where as follows:
Axial: 1500 N
Bending: 20 N
Torque: 50 Nm
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The axial load value came from how much an average person weighs. The
bending load came from the average possible load a fracture leg might endure while
walking. The torque came from research paper that suggests that 50 Nm was the best
value. The fixed support is applied to the face opposite from where the axial load is
applied.
For Meshing, the automatic method was selected with the addition of changing
the fixed face values to 2.0 mm for max size and max face size. This gives us the most
nodes without crashing the computer.
Design Z
I initially chose this design because I though that having extensive 180 degree
coverage would provide strong support over the fracture. However this did not seem to be
the case. I also thought that angling the two center screws perpendicular to each other
would also help in stabilizing the fracture. Although the principle strain of the combined
forces shows that the screws had minimal strain on them, meaning that the bone was left to
take most of the force.
The Z design uses titanium alloy for both the screws and the plate. Titanium alloy
(Ti-6Al-4V) has a Young’s Modulus of 110 GPa and a Poisson ratio of .31. The advantages of
using titanium for the design are its high degree of biocompatibility, and poor shear
strength. This is great compared to other metals which are also used in fracture repair, such
as Cobalt-Chromium which is known to be toxic. Titanium alloy also has a much lower
Young’s Modulus than Cobalt-Chromium which is at 200 GPa. However a con of using
titanium is that it has poor wear characteristics.
The Z design consists of a single plate roughly 5 inches in length with center 2.5
inches providing 180 degree cover on bone and the rest of plate covering 90 degrees of the
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bone. Overall the plate has 6 cortical 3.5 mm diameter screws holding it to the bone. 4 are
place down the center of the plate while two are angled 90 degrees towards each other on
the center, as shown in the following figures.
The screws are placed perpendicular to each other in an attempt to reduce stress on
the fractured tibia. However this does not seem to be the case. When combined forces are
applied much of the principle strain is on the bone rather than on the plate. This is noted by
the dark blue regions on the plate while the lighter shade of blue indicated a higher value of
principle stress. This is shown in the following figure.
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When the combined principle stress was measured the forces were spread evenly
across the bone, plate and screws, except the edges of the plate, which had the most stress.
The bone with this plate design experienced a maximum principle stress of 9.967e6 Pa. This
is greatly reduced from the base bone (without fracture), which had a maximum combined
principle stress of 2.61e8 Pa.
Pros of this plate design is that it is made up of titanium, alloy which is
biocompatible, and. The Cons are that such a wide angle of coverage is not optimal. The
extensive contact between plate and bone is known to cause cellular death in the bone after
a while. The size of the plate is also large, meaning that the surgery would be highly
invasive, requiring a large part of the lower leg be cut open in order to be able to screw in
the plate. This can also cause discomfort in the patient and even restrict movement
depending on how close to the joints the fracture.
There are several ways to possibly improve on the design of this plate in order to
make it a more viable option for clinical use. One would be to reduce the length and
thickness of the plate. Reducing the plate’s length by one inch would make the plate roughly
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20% less massive. This change is in size would still cover and support the fracture but
would give patients an increased range of motion in there joints versus having the larger
size. Adding a lagging screw, which is longer than the rest of the cortical screws in the
center of the plate, may provide more support. A lagging screw would hold fracture more
tightly in place as well as help alleviate the bone by allowing the plate and screws to bear
more.
Design E
When we had to come up with a design during class, I saw that everyone was a
really long plate with nails perpendicular to the surface. So I thought why not simply
make the screw perpendicular to the fracture line considering that it is an oblique
fractured line. Moreover, the other designs that I spectated were one sided so I decided to
put two. As a result of having two plates, I decided to have smaller areas for each plate to
minimize bone contact with the plates. I realized that simply having two screws, one on
each plate, would be unstable under bending loads, so I try to compensate by adding two
perpendicular screws on each plate. That is, perpendicular to the plate rather than the
fracture line.
For the plate, I used titanium alloy Ti-6-Al-4-V, which is a biocompatible
material widely, used in orthopedics. This material can sustain intense chemical
reactions, as it is immune to acidic reactions. As for my screws, I decided to be different
and use Ultra High Molecular Weight Polyethylene. Through some research, I found this
material to be soft and delicate yet extremely strong. I figure this would be best for the
tibia since the soft material will be easy when inserted. When testing with forces and
such, the material maintains its structure and properties, meaning that this material was
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able to endure/sustain through the different loads/forces. I used the standard cortical
screw with a 3.5mm thread diameter with a high pitch. The higher the pitch the more the
threads, the more threads the harder it will be for the screw to come out. With the stress
values reducing by half of that of a regular tibia, this model is significantly better than
that of a regular standing tibia, in theory.
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Figure Set X – These are the forces for my design in the order of MP Strain, MP Stress,
Total Deformation, and Vector Principal Stress
For all the forces applied, my design is strong enough to sustain the values below
the median value. Moreover, the Vector Principal Stresses show how the forces are
distributed across the tibia. This is good because original in the base model, the forces are
also distributed across the tibia. This design is good overall with almost no exception.
Due note, that all the stresses and strain were exceptionally higher at the edges of the
plate.
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Design N
This design was chosen because of how much support a sleeve gives to a fracture.
Because a sleeve would not be easy for a surgeon to place around the fracture, this design
would help make it a bit easier to place
around the bone. This design is two
separate plates that fit into each other like
Lego pieces. It is designed to where screw
holes line up when the two plates are
aligned. All the surgeon has to do in the
procedure is place the two plates around
the fracture to where they snap into place
and drill in the screws. Figures 1 and 2
show two different views of the places
going around the bone. Figure 1 displays
how the plates would “lock” into one
another by showing they would fit into
one another. Figure 2 shows how the
screws would go into the bone and their
distances from the fracture. The material
chosen for this design is titanium alloy
(Young’s Modulus of 110 GPa and a Poisson ratio of .31) because its stability and
biocompatibility. The dimensions for this design were 0.5 mm in thickness and 100 mm
in length. The thickness of the plate was chosen because a thicker plate would be too
Figure 1: Cross Sectional View of Design N
Figure 2: Sliced view of Design N with fracture, plates and screws.
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bulky for the fracture and difficult for the surgeon to work with. The length was set to
where the plate covered the entire fracture so that a screw can be placed both above and
below the fracture as seen in Figure 2. Screws were placed at equal distances apart from
each other and mirrored onto the other plate. This is so stresses and strains would be
distributed equally onto the screws.
Results
The following loads were applied to the structure: Axial (1500 N), Bending (20 N)
Torsion (50 Nm), and all forces combined with a fixed support at the base. Maximum
principle stress, maximum principle strain, total deformation, and vector principal stress
were calculated with these forces.
Layout of pictures in collages:
Torsion Moment
Bending Axial
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Figure 3: Total deformation that occurred with Torsion, Combined forces, Bending force, and axial
force.
Table 1: Max and Median values of forces applied to the system.
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Figure 4: Max Stress of torsion, axial, bending, and combined forces
Table 2: Values for Max stress that occurred with axial, bending, torsion, and combined forces.
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Figure 5: Max strain that occurred with torsion, bending, axial, and combined forces.
Table 3: Values of max strain that occur with bending, axial, torsion, and combined forces.
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Figure 6: Vector Principle Stresses with axial bending, torsion, and combined forces.
Figure 7: Zoomed in view of vector principle stresses.
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In conclusion, the design worked well in distributing stress and strain because it
provided support on both sides of the fracture. The stress and strain occurred only on the
plates and screws, and none on the bone. However, the value of total deformation is very
high. This would cause major discomfort to the patient and also increase time to heal.
This design would be that it is also more invasive because it goes all the way around the
bone. This could cause more damage to tendons and ligaments than the current plating
system used. One final flaw of this design is that it only accommodates to one size,
current plating systems don’t go around the bone so two plates of any size can be added
to the fracture. Not every person has the same tibia bone diameter, so the diameter of the
plates would have to be adjusted per patient. It would be better to reduce the amount of
coverage on the bone that a plating system does on a fracture to help increase healing
time.
Design ZEN
We wanted to be different and thought about a way to combine Neetal’s Design as
well as Eliezer’s Design. By combing the two, we establish rigidity and endurance in our
plating.
The materials are the same as in Design E, but the plating is a helical formation.
The concept of DNA having a strong structure inspired us to apply a biological entity to
our biological and mechanical problem. There are two lag screws like in Design E but
with a total of 7 more perpendicular screws.
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Using the physical model rather than ANSYS to test this design, we discovered
that this design can withhold more and more stress and strain with more perpendicular
screws.
Cortical threaded screws were used for the final design of the model
with 4.5 mm threads.
Using an actual threaded screw made it difficult for ANSYS to
compute. Each thread was considering a body which made
computation 90x more difficult as there were a total of 9 screws. It
would have been better to use a simple rode for this demonstration but we all thought that
a physical model test was more realistic. We applied all the forces that were applied in
ANSYS over 10 times to see if it would break, but it did not.