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.