KECSKEMÉTI FŐISKOLA  

Design and simulation of the mechanical behavior using Finite Elements Methods of a hip prosthesis      

López Galbeño, Aitana   10/02/2015  

     

Project carried out under the supervision of Dr. Líska János. 1

Abstract   With more and more adults requiring total hip replacements, the need for bone saving implants is becoming increasingly more important. The main goal of this study was to computationally model a hip prosthesis after obtaining measurements through catalogs and reverse engineering and then to test it through simulations in order to compare it at different positions and with different materials. To conduct this study, the behavior of the bone, the different types of implants in existence and various types of joint replacements first needed to be studied. Models were then created with a Computer Aided Design (CAD) software, Inventor, and subsequent simulations were performed using the Ansys Workbench software. The aim of this study was to identify which safety factors were better for two different types of ceramic heads, to study the forces applied to the prosthesis and to determine the elastic Von-Mises coefficient strength in the prosthesis.                    

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INDEX 1.  

Bone  structure  ______________________________________________________   5   1.2.  

2.  

Fractured  bones   ______________________________________________________   7  

Implants  and  joint  replacements  _______________________________________   8   2.1.  History  of  artificial  joint  ___________________________________________________   8   2.1.1  Implant  materials  _____________________________________________________________  9  

2.2  Brief  types  of  prosthesis.  Total  hip  replacement.   ______________________________   10   2.3  Orthopedic  implants  in  the  hip  _____________________________________________   11   2.3.1  Biomechanical  study  in  a  health  joint   ____________________________________________  11   2.3.2  Hip  replacement  _____________________________________________________________  12   2.3.3  Biomaterials  ________________________________________________________________  13  

3.  The  prosthesis  of  this  study   ____________________________________________   15   3.1  Design  the  model  with  Reverse  Engineering  __________________________________   16   3.2  Design  of  the  prosthesis.  Material  and  shape  _________________________________   17   3.2.1  The  Acetabulum  _____________________________________________________________  17   3.2.2  Polyethylene  cup   ____________________________________________________________  19   3.2.3.  Femoral  component.  The  head  _________________________________________________  20   3.2.4.  Stem  ______________________________________________________________________  21   3.2.5  Assembly  ___________________________________________________________________  24  

3.3  Modeling  of  the  prosthesis  in  3D  with  CAD/CAM  programs  (Inventor)  _____________   27  

4.  Simulations  with  ANSYS  Workbench  _____________________________________   28   3.1  Static  structural   _________________________________________________________   29   3.1.1  Changing  the  materials  and  adding  the  specific  ones.  Engineering  Data.  _________________  29   3.1.2  Geometry.  Export  Geometry  from  the  CAD/CAM  program.  ___________________________  30   3.1.3  Model.  Surface  contacts,  meshing,  fixed  supports,  coordinate  system      and  forces.  ________  31             3.1.4  Experiments  ____________________________________________________________  35  

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6.  Conclusions   _________________________________________________________   49   7.  Bibliography   ________________________________________________________   50   Annex  I.  Planes  of  the  prosthesis  __________________________________________   52  

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1. Bone  structure  

Bones are constantly changing their structure to adapt to their environment and physical conditions. Bone is comprised of water, collagen, hydroxy-apatite mineral, proteoglycans, and non-collagenous proteins [1]. There are two types of bone that can be differentiated by porosity or apparent density. Cortical or compact bone is what lines the outer surface of most bones and it is characterized by low porosity. An example can be seen in Figure 1. Figure 2 shows highporosity or spongy bone known as trabecular bone. The section within bone that has no mineralized aspects is known as the medullar canal; this part houses the marrow, which is made up of blood vessels, nerves, and is the site where red blood cells as well as stem cells are formed [2]. Cortical bone's porosity typically ranges from 5-10% with an apparent density of approximately 1900 kg/m3. Looking at the structure of cortical bone in Figure 1, there are long tube-like columns running along the stress lines of the bone called osteons, the basic unit of structure of compact bone. Osteons are typically 200µm in diameter, 1cm long, and contain Haversian canals [2, 3]. They contain capillaries and nerves and serve as the structure that gives bone its stability. There are connecting tunnels that link osteons together known as Volkmann’s canal which also contain capillaries.

                           Figure 1.Cortical bone.

Figure 2.Trabecular and cortical bone.

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What makes trabecular bone so porous, with a porosity of 75-95%, is that its structure is made up of tiny struts and they arrange themselves to give support along stress lines that the bone experiences through everyday use. In older patients or patients with osteoporosis these struts become smaller due to the loss of bone mass and increase their chances of fracture.  

 

Figure 3.Compact Bone and spongy (cancellous bone).  

Both types of bone have two different types of bone tissue: woven and lamellar [4]. Woven tissue is a quick-forming, disorganized arrangement of bone. It is typically found at locations of fracture to quickly regain the structural integrity of that section of bone. Over time the second type of bone tissue is formed known as lamellar bone. This is a more organized bone that takes much longer to form. Lamellar bone forms layers, which creates a complex structure of collagen fibers and minerals. Because it is more organized less bone is required to maintain the same level of support (Figure 3).

 

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1.2. Fractured  bones  

To introduce the prosthesis of this study, the principal fractures that occur in bones must first be analyzed. Figure 4 shows a meaningful bone fracture. Traditional thinking concerning such bone quality and how it degrades with age has focused on the question of bone mass or bone mineral density as a predictor of such fracture risk. For developing a realistic understanding of how factors such as age, species, orientation, or location affect the fracture resistance of bone, it is critical to assess the importance of the various micro-structural features in determining the mechanical properties [5]. In short, the difficulty lies in determining the roles that the underlying micro-structural constituents, including their properties and their morphological arrangement, play in crack initiation, subsequent crack propagation and final unstable fracture and in separating these effects. Additionally, the role of fatigue, by repetitive cyclic loading or sustained static loading, on cortical bone failure will be reviewed. In all cases, the failure behavior of bone will be discussed, when possible, in light of the salient fracture and fatigue mechanisms involved [6].

 

Figure 4: Fractured bones.

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2. Implants  and  joint  replacements   Total joint replacement is widely regarded as the major achievement in orthopedic surgery in the 20th century. Arthroplasty, or the creation of a new joint, is the name given to the surgical treatment of degenerate joints aimed at the relief of pain and the restoration of movement. The age of the patient, the patient's expected activity levels and the extent of the patient's joint problems are among a long list of factors that the surgeon must consider in choosing an implant. Despite the concern over wear and osteolysis, it must be remembered that joint replacement is a highly successful treatment with few complications [7]. Compared to healthy, organic cartilage surfaces, which have a surface friction of nearly zero, the friction between these man-made bearing surfaces are hundreds of times higher. This friction subjects the implant components to wear that can limit the longevity of the joint replacement and induce inflammatory responses in the tissues surrounding the joint itself. Fundamental to replacing damaged joint surfaces with implants fabricated from manmade materials, then, is the requirement of producing a low-friction bearing to minimize surface wear, inflammation in surrounding tissues and possible loosening of the implant, resulting in the need for additional surgery [2].

2.1.  History  of  artificial  joint  

Artificial limbs have been used since early history to replace those lost to injury or disease, but this was typically only done for appendages. The first evidence of this comes from the Greeks 500 B.C. Medieval knights also had simple artificial limbs in order to improve their appearance. Over the years, the artificial limbs were increasingly replaced by artificial joints. An artificial joint must be implanted in the body and designed with the same shape and functionality as the connective tissue it replaces [2].

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The study of surgical joint replacement really progressed during the 1950s. Initial testing was done on patients whose joints were degenerated by disease, injury, or malformation. The replacement procedure was called total joint arthroplasty. Hip and knee replacements accounted for 80-90% of these operations. Arthroplasty was performed in 1951 and ten years later the first total hip replacement occurred taking into account that the materials used in hip replacement surgery should be designed to ensure that a patient's mobility was not hindered. Over the years, new technologies have been applied to create new hip replacement and artificial joints. Artificial joints are secured in place either by cement or by a relatively new process called bone ingrowths. Complications from replacement surgery include the loosening of the joint's components and infection, but both problems are fairly uncommon. While a return to normal functionality is not always possible with joint replacement, most patients realize some measure of enhanced mobility and pain relief. Research is ongoing to improve prosthetic materials such as surgical techniques [8].

2.1.1  Implant  materials  

In the 1960’s and 1970’s a number of materials were tried as bearing surfaces in joint arthroplasty, including Teflon and metallic alloys such as stainless steel and cobalt-chromium alloy. But through the 1980’s and much of the 1990’s, the preferred bearing combination was ultra high molecular weight polyethylene and cobalt-chromium [9]. Polyethylene results in a low amount of friction when bearing against a highly polished metallic surface. Today, metal-on-metal and ceramic-on-ceramic combinations are being considered as alternative bearing surfaces. The traditional type of replacement, which has been in use for many years, is a metal ball on a stem cemented into the femur and a plastic socket cemented into the pelvis. This is still the most commonly used type of hip. In older patient it is highly unlikely that it would need to be replaced within their lifetime. 9

2.2  Brief  types  of  prosthesis.  Total  hip  replacement.    

Depending on the issue of each patient, the different types of prosthesis need to be studied. For patients with severe arthritis total knee replacement surgery would be an option. When knee replacement surgery is performed, the cartilage of the knee joint is replaced with a metal and plastic implant. To improve the range of the motion at the shoulder joint, a total shoulder replacement can be a good option or the rotator cuff can be repaired. A variety of problems with the ankles and wrists require surgical treatment. Overuse injuries, rheumatoid arthritis, stress fractures and sprains can often be treated with surgery if more conservative treatment fails [2]. The type of prosthesis studied was the total hip replacement.

Total  hip  replacement  

This procedure involves removing the ball and socket of a joint with arthritis and inserting a new ball and socket to allow movement at the new joint. There are many types of total hip replacement implant options including the type of material (metal and ceramic), and how the implant is designed to work [2]. A total hip replacement is a surgical procedure whereby the diseased cartilage and bone of the hip joint is surgically replaced with artificial materials. The normal hip joint is a ball and socket joint. The socket is a "cup-shaped" component of the pelvis called the acetabulum. The ball is the head of the thighbone (femur). The metallic artificial ball and stem implanted during a total hip replacement are referred to as the "femoral prosthesis". Figure 5 shows the pieces for a total hip replacement [2].

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Figure 5.Total hip replacement.

2.3  Orthopedic  implants  in  the  hip  

2.3.1  Biomechanical  study  in  a  health  joint  

The normal hip joint, shown in Figure 6, is one of the most important joints in the human body. It allows us to walk, run and jump. It bears our body’s weight and the force of the strong muscles of the hip and leg. Yet the hip joint is also one of our most flexible joints and allows a greater range of motion.    

Figure 6.Hip joint.

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The hip joint is a ball-and-socket synovial joint formed between the acetabulum and the femur. The acetabulum forms the socket for the hip joint and the rounded head of the femur fits into the acetabulum and rotates. Hyaline cartilage also acts as a flexible shock absorber to prevent the collision of the bones during movement. Between the layers of hyaline cartilage, synovial membranes secrete watery synovial fluid to lubricate the joint capsule [2]. Surrounding the hip joint are many tough ligaments that prevent the dislocation of the joint. The strong muscles of the hip region also help to hold the hip joint together and prevent dislocation. Functionally, the hip joint enjoys a very high range of motion. The ball-and-socket structure of the joint allows the femur to rotate freely through a 360 degree circle. The femur may also rotate around its axis about 90 degrees at the hip joint. In addition to being flexible, each hip joint must be capable of supporting half of the body’s weight along with any other forces acting upon the body. During running and jumping, for example, the force of the body’s movements multiplies the force on the hip joint to many times the force exerted by the body’s weight [11]. The hip joint must be able to accommodate these extreme forces repeatedly during intense physical activities.

2.3.2  Hip  replacement  

The natural hip joint is a ball and socket joint which, with time, may wear out. When this happens the joint becomes steadily more painful and eventually a hip replacement is the only way to get rid of the pain and improve one's quality of life. Figure 7 shows a total hip replacement with the prosthesis attached to the bone. The aim of a hip replacement is to replace the worn out joint surfaces with new artificial surfaces and there are many different types of hip replacement available.

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Figure 7.Hip without prosthesis on the left and with prosthesis on the right.     2.3.3  Biomaterials  

Biomaterials are the man-made metallic, ceramic, or polymeric materials used for applications in the human body. Until recently, a biocompatible material was essentially thought one that would no harm [9].

2.3.2.1  Titanium  alloy    

Metals frequently are used in the body for orthopedic purposes where hard tissue (bony structures) must be repaired or replaced. The Titanium Alloy Ti6Al4V (Titanium alloy with 6% Aluminium and 4% vanadium by weight) may be considered in any biomedical application, particularly for implantable components, because of its biocompatibility, good fatigue strength, and low modulus. It could also be considered for any application where a combination of high strength, light weight, good corrosion resistance, and high toughness are required. Some typical applications where this alloy has been used successfully include joint replacements, bone fixation devices and surgical clips [9]. Ti6Al4V makes it particularly resistant to corrosion, which further justifies its use in biomedical applications such as implants and prostheses.

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2.3.2.2  Ceramics  

Ceramics offer excellent compressive yield, and thus are often used for such applications. Bioactive ceramics represent a different aspect of corrosion, because they are expected to transform into bony structures by gradually releasing their growing bone or tissue structure [9].

Alumina  

Alumina is one of the most cost effective and widely used materials in the family of engineering ceramics. The raw materials from which this high performance technical grade ceramic is made are readily available and reasonably priced; resulting in good value for the cost in fabricated alumina shapes [11]. With an excellent combination of properties and an attractive price, it is no surprise that fine grain technical grade alumina has a very wide range of applications.

Zirconium  Oxide  

Zirconium Oxide is an extremely refractory material. It offers chemical and corrosion inertness to temperatures well above the melting point of alumina. This material is similar to titanium in that it is considered a reactive metal [9]. As a result, Zirconium Oxide is very resistant to corrosive attack in most types of materials.

2.3.2.2  Polyethylene  

A wide variety of polymers are used in medicine as biomaterials. The Ultra High Molecular Weight Polyethylene (UHMWPE) was used in this study. The high molecular weight 14

makes it a very tough material, but results in less efficient packing of the chains into the crystal structure as evidenced by densities of less than high density polyethylene [10]. The high molecular weight makes it a very tough material, but results in less efficient packing of the chains into the crystal structure as evidenced by densities of less than high density polyethylene. Because of its outstanding toughness and its cut, wear and excellent chemical resistance, UHMWPE is used in a diverse range of applications.

3.  The  prosthesis  of  this  study    

The prosthesis to be designed is a standard prosthesis for a middle-aged person. Therefore it is a total prosthesis without cement, because the biological condition of the patient is reflected in the bone mineral. The bone is adhered to the prosthesis. The design of the hip prosthesis follows two kinds of relevant designs for the head and stem, one of them is the Monoblock where the head is fixed to the stem, and the other is the modular prosthesis where the head is separate from the stem. The prosthesis which will be studied is a modular prosthesis. Therefore the prosthesis consists of the following parts: •

The acetabulum, which fixes to the hip.

•

The polyethylene cup, which fixes to the cup.

•

The head, which replaces the femur head. This head rotates on polyethylene and is fixed through the 12-14 mm Morse Taper.

•

The stem, which is fixed to the femur.

Each of the parts of the total hip can be seen in Figure 8.  

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Figure 8.Total hip prosthesis.  

3.1  Design  the  model  with  Reverse  Engineering  

The main objective for the design of the prosthesis was to find a system very similar to the real joint in order to minimize the wear. Information from the different catalogs [13, 14, 15, 16 and 17] was used to obtain the measures of a standard prosthesis for a middle-aged person and reverse engineering was applied. Reverse engineering is only an analysis in order to deduce design features from products with little or no additional knowledge about the procedures involved in their original production. The elaboration of the model depends on the reverse engineering. The operating mode was evaluated, modified and improved after having analyzed previous prosthesis. Different alternatives were generated and depending on the result they were modified to produce a satisfactory result and were updated to resolve any issues and find the ultimate solution. For this prosthesis the stem had to be designed two times, because, as it can see in the next section, the first simulation of the first prototype of the prosthesis with a tiny neck failed and therefore had to be altered.

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After the experiments were conducted, taking into account the stress state of the healthy joint, the strength of cortical and trabecular bone, the points of maximum weight and the location in the space, the biomaterials, the shape and the fix method for modeling the 3D prosthesis were determined.  

3.2  Design  of  the  prosthesis.  Material  and  shape  

The properties of the materials had to be similar to those of the bones in the human body. The elasticity modulus of the biomaterials used for the implants also had to be very similar to human bones. If the Young's Modulus coefficient of the biomaterial is more than the modulus of the bone, the biomaterial undergoes re-absorption and the bone weakens [9]. Conversely, if the Modulus of the biomaterial is less, the bone can break.  

3.2.1  The  Acetabulum  

Titanium Alloy (Ti6Al4V) was used for made the acetabulum. Titanium has an excellent strength-to-weight ratio and an impressive resistance to corrosion. Therefore the hemispheric cup will be made from titanium (Ti6Al4V). The acetabulum has an exterior diameter Ø 58 mm and a thickness of 2 mm, as its shown Figure 9. The depth of the acetabulum exceeds the diameter of the semisphere polyethylene to prevent the polyethylene insert from falling out of place as it rotates in the natural motion of the bone.

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Figure 9.Cup with Ø 58mm and 2 mm of thickness.  

The cup is fixed to the bone with Ø 6.5 mm low profile titanium screws. This fix system consists of: 1. The top hole provides a viewing point to ascertain contact between the implant and the bone. 2. The three holes enable additional attachments to be made to the primary attachment using Ø 6.5 mm, as shows Figure 10, low profile titanium screws, to be used when the surgeon determines that an acceptable level of ‘pressfit’ stability has not been achieved.

 

Figure 10.Position of the three holes for the screws in the acetabulum.    

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3.2.2  Polyethylene  cup  

The material that was used in the polyethylene cup was ultra high molecular weight polyethylene (UHMWPE). UHMWPE is odorless, tasteless and nontoxic. It is highly resistant to corrosive chemicals, but it has extremely low moisture absorption and a very low coefficient of friction. Additionaly, it is self-lubricating, highly resistant to abrasion and, in some forms, is 15 times more resistant to abrasion than carbon steel [10]. The polyethylene insert has an exterior Ø 54mm and Figures 11 shows the piece. The polyethylene insert has 12 tabs in order to anchor it with the cup. Each tab is set to 30 degrees as shown in the Figure 12.

   

Figure 11.Insert of polyethylene with

Figure 12. Exceeds semi-sphere in the

         Ø 54mm of external diameter.

polyethylene for the head.  

     

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3.2.3.  Femoral  component.  The  head  

Ceramic Alumina and Zirconium Oxide were the materials used for the head. Although Alumina has been used in orthopedic surgery since the 1970s, the long-term clinical results of Zirconium Oxide have not been well documented [9]. Hips with these two different ceramics will be studied during the same period with the aim of comparing the two ceramics. Taking into account that the material of the implant will undergo compression and flexion, the material must be resistant to this type of effort and wear. It has been established that the size of the head is Ø 32mm. The recommendation from clinical studies is to use heads with diameters between 28 mm and 32 mm. The diameter of the head for this part optimizes wear resistance because with fewer diameters it would be more likely that the head would not fit well with the 12-14mm Morse taper and the polyethylene cup which would create the possibility of dislocation and also decrease the range of motion. Figure 13 demonstrates what would happen with a smaller-diameter head. Conversely, Figure 14 shows how the mechanism looks and functions with a head that is larger in diameter.

 

Figure 13.Head with smaller diameter.                                                      Figure 14.Head with higher diameter.      

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The femoral head has to be adapted to the internal diameter of the polyethylene insert previously chosen. Finally, Figure 15 shows the final model of the head made with the software Inventor.

.

 

Figure 15.The head.

3.2.4.  Stem  

The 12-14mm Morse Taper on the neck accommodates a complete selection of femoral heads with head center options from -3.5mm to 10.5 mm. The one in depicted in Figure 16 is of 10mm.

 

Figure 16. 12-14mm Morse Taper.

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The 12-14mm Morse Taper molds in order to combine properly with the head. The 12-14mm Morse Taper uses a tapered wedge fixation philosophy to maintain mediolateral stability. Made from titanium alloy, it is designed to be a bone-conserving implant femur by removing the head with a 45 degree incision. Figure 17 shows the 12-14mm Morse Taper with the top of the stem.

 

Figure 17. Taper showing the 12-14mm Morse taper.  

A good fit and fixation in the metaphysical area, which has been acquired due to a wide medial curvature that guarantees an excellent anatomical fit, is indispensable for the stability of the stem, as is shown in Figure 18.

 

Figure 18.Internal curvature in the stem.   22

The profile is characterized by the “V” shape in the proximal part that guarantees stability of the implant. This design provides a proximal distribution of the torsional strains, supporting flexional stresses through diaphysis. Figure 19 shows the lateral view of the stem and this form proves the maximum torsional stability achieved thanks to the rectangular section and a marked lateral flare. The tapered profile of the distal part is shown in Figure 20. This shape improves the adaptability to the most common bone morphologies and facilitates insertion of the stem in the canal avoiding irregular transfer of the load to the bone structure. This minimizes the undesired stress shielding and the point effect that is responsible for thigh pain.

         

Figure 19. Lateral view with “V” shape.

Figure 20.Tapered distal part.

 

The stem has a curved shape and trapezoidal cross section for maximum rotational stability, which needs to be 130 degree between the neck and the middle part of the stem, as shown in Figure 21, in order to prevent unnecessary changes to the implants.    

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Figure 21. Principal measures in the stem.    

The optimal neck-shaft angle to accurately restore the biomechanics of the hip joint was 130 degrees [14].

3.2.5  Assembly  

The socket was joined to the bone with low-profile round-head screws made from Ti6AL4V. The maximum angle was 15 degrees and with this angle the implant can be attached to the different areas of the bone offering a greater structural quality. The socket has an internal diameter groove to anchor the implant of the polyethylene cup. Figure 22 shows the assembly of each piece.

     

Figure 22. Assembly. Acetabulum and polyethylene cup.   24

There are twelve tabs on the surface of the cup and each one is separated by 30 degrees. The cup assembly with anti-rotational tab was inserted in the acetabulum.

 

Figure 23.System clips spaced 30 degrees.  

The system clips shown in Figure 23 were placed on the diameter groove of the metal cup to control rotation, resist inclination and luxation forces and offer greater versatility during insertion [13]. The polyethylene cup with the head are assembled to allow movement and rotation. Figure 24 shows the assembly between the head and the polyethylene cup.

 

Figure 24.Head assembly with the polyethylene cup.   25

Figure 25 shows the femoral stem, which accommodates both types of heads tested, the Ø 32 mm Alumina and Zirconium Oxide. The distal element of the implants has to be adjusted to the femur with a depth of 70 to 100 mm depending on the patient.

 

Figure 25. Stem for 32 mm head.

To conclude, the final model can be seen in the Figure 26.

 

Figure 26.Hip prosthesis. 26

The final coating between the bone and the prosthesis will be determined by the surgeon, depending of the specific patient. The surgeon will decide if the stem surface will be porous (covered with hydroxy-apatite) or not.  

3.3  Modeling  of  the  prosthesis  in  3D  with  CAD/CAM  programs  (Inventor)  

To carry out the modeling of the prosthesis, CAD software (Inventor) was used. This software facilitated the redesign and the production of the final prototype of this study. When the measures of the prosthesis were determined, the modeling was created using the aforementioned software. Normally a solid model consists of making a bi-dimensional plane of each element of the prosthesis and converting these planes into basic two-dimensional geometric shapes as shown in Figure 27. After that, solid pieces were made using the appropriate function provided by the software, which then allowed the creation of a 3D model.

 

Figure 27.Bi-dimensional plane of the head.  

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The solid model allows for the analysis of the different volume properties and materials used in the various tests conducted on the prosthesis. Figure 28 shows the three-dimensional model of the stem.

 

Figure 28.Three-dimensional model of the stem.    

The materials will ultimately be chosen using the software Ansys Workbench. This final model satisfies the expectations of the geometric parameters obtained by catalogs and by applying reverse engineering and it is therefore concluded that the final model of the prosthesis, after several modifications, was reliable. All the measures and the pieces can be seen in Annex I.

4.  Simulations  with  ANSYS  Workbench  

The starting point of this structural analysis came after various modifications and after having developed the desired 3D model of said structure using the Finite Element Model (FEM). For the study of this method the software Ansys Workbench was chosen because of its comfortable user interface and its specific and reliable results. With this software, it was possible to model the behavior of the hip prosthetic and all its components: a Titanium Alloy Ti6Al4V stem implant with a 12-14 mm Morse taper, a head made of two different materials and a socket lined with a polyethylene cup. All of these components were first simulated by fixing the 28

position of the stem within the model, meaning it was not physically attached to anything, but was unable to be moved. They were then tested a second time by attaching the stem to a bonelike supporting material made with polyethylene. If its taken into account that this study is part of a structural model, it is shown that the desired solution for the entire domain occurs in shifts, tensions and deformations. Because of this, to get the solutions the following things had to be considered: •

The deformations had to be compatible with the shifts.

•

The constitutive equations that establish a correct relationship between the tensions and the shifts had to be formulated. These represent the actual behavior of the material.

The analytic solution of the differential equations which satisfies the final equilibrium condition is very difficult to find or in some cases impossible. That is why the FEM is very useful in many cases, because it can reduce the expression into a simpler form.

3.1  Static  structural   3.1.1  Changing  the  materials  and  adding  the  specific  ones.  Engineering  Data.    

The first step in introducing the prosthetic is to introduce the different materials that have been used in Engineering Data. As it has been discussed, the stem and the cup have been designed with biocompatible Titanium Alloy Ti6Al4V, whose characteristics have been shown in the point before. In Workbench, Titanium Alloy has been chosen changing the specific characteristics in order to simulate the specific Titanium that was studied in the experiments. Two different heads were designed using two different types of ceramics, which were both created and then put into the Library of the project. These two materials were Zirconium Oxide ZO2 and Alumina Al2O3. 29

Finally, the polymer and the support, which simulate the bone, were composed of polyethylene, chosen this material from the Ansys Workbench library. Table 2 shows the most important mechanical properties of the materials that have been used in the simulation [9]. Material

Titanium Alloy

Easticity

Tensile strength

Poisson’s

Young’s Modulus

Density

modulus

Ultimate

ratio

(GPa)

(kg/m3)

E(GPa)

(Mpa)

113.8

950

0.342

110

4430

350

260.70

0.210

359

4000

200

711

0.320

220

6005

0.50

33

0.420

1.10

950

Ti6Al4V Ceramic Alumina Al2O3 Ceramic ZirconiOM ZO2 Polyethylene UHMWPE

Table 2.Mechanics properties of simulated materials.

3.1.2  Geometry.  Export  Geometry  from  the  CAD/CAM  program.    

The geometry of the different mechanics pieces has been exported to CAD in the parasolid format (.x_t), capable of maintaining its own geometric characteristics of the different pieces that have been created.

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                       3.1.3   Model.   Surface   contacts,   meshing,   fixed   supports,   coordinate   system       and   forces.     After exporting the geometry to CAD, the next step was the description of the boundary conditions with the definition and application of the charges, the mathematical method of meshing with the element size in each one was chosen paying close attention to the most important pieces. The articulation of the femoral bone with the pelvis usually gets fractured by the fatigue stresses to which it is subjected. For this reason, the Finite Element Method (FEM) is a powerful tool that can simulate the behavior of the hip implants against different types of stress and forces. Ansys Finite Element Analysis (FEA) program offers a variety of elements designed to treat cases of changing mechanical contact between the parts of an assembly or between the different parts of different faces of a single part. The contact application which is used in this study is surface to surface contact. The surface contacts have been bonded between themselves by the Boundary Conditions. The prosthetic consists of five different parts. In the prosthetic model, the different pieces, as well as the support were meshed in different ways. In order to decide how to apply the meshing, the different pieces were differentiated and simulated. All parts besides the 12-14 mm Morse Taper were designed by tetrahedral elements. The 12-14 mm Morse Taper was created by hexahedral divisions, because it is one of the most important pieces of the simulation and being a conical structure it was easy to mesh. Depending on the relevance of each piece the following sizes of meshing were selected as shown in Table 3.

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Piece

Mesh. Element Size (m)

Acetabulum

0,002

Polyethylene cup

0,001

Bone

0,005

Holes

0,0005

Face sizing (down-stem) Morse Taper Body sizing (up-stem) Head

0,004 0,001 0,002 0,001

Table 3. Different types of meshing in the structure.

Looking at the numbers in the Table 3, the support-bone is irrelevant in the solutions and the simulation, that’s why the element size of this piece is the biggest one. The head, the 12-14 mm Morse taper, and the implant polymer were created with a mesh of 1 ∙ 10!! m. With such a thin meshing, this part became the most important part of the study and it was essential to see the results from the simulations due to polymer wear, the safety factor and the changes that appeared between the two different ceramic materials of the head. The holes for the screws in the cup have an element size of5 ∙ 10!! m and finally the stem has an element size of 4 ∙ 10!! m. Figure 29 shows the most important meshing of the 3D Model. The stem has been made from two different types of meshing because the part of the stem closer to the 12-14mm Morse Taper has more significance and therefore needs to be studied more carefully.

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Figure 29. Meshing without bone. Different parts as shows Table 3.

Figures 30 and 31 shows the final meshing for all the structure with the bone with different perspectives.

Figures 30 and 31. Different position of the meshing in all the 3D Modeling.

Finally, Figure 32 shows the whole 3D model with the with 113706 nodes and 62809 elements.

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Figure 32.Total meshing. All view.

Four pairs of contact surfaces were created: one between the bone and the stem, the other between the stem and head, another between the head and the polymer and the last between the polymer and the acetabulum. During the experiments, an upward force was applied to the different materials that were tested in the head of the prosthetic. The maximum force of the test was 2300N, which was used with the materials considered most appropriate. The force was applied by uniformly distributing pressure on the top face of the acetabulum to represent the possible behaviors of the body relating to this part.

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          3.1.4  Experiments    

Model   without   bone,   fixing   the   stem   (first   model).   Applying   the   force   in   the   Z   axis.  Head  with  Alumina.  Prove  the  break  with  the  safety  factor.  

The first model tested was the one shown in Figure 33, with a point force of 1400N in the Z axis on the acetabulum. In this experiment no bone structure was used and the stem was the fixed support.

Figure 33.First model to analyze.

The simulation showed the break of the prosthesis in the in junction between the head and the 12-14mm Morse Taper, reaching a 0.81376 safety factor in the neck-head, having the maximum in the acetabulum zone. Figure 34 shows the safety factor in the entire model, where the conflict zone can be seen instantly.

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Figure 34. Safety Factor. All the structure.

Figure 35 and 36 are a zoom of the ceramic Alumina head, where the point of break can be seen in the inferior diameter of the head.

Figure 35.Alumina Head. Safety factor.

Figure 36.Alumina head. Safety factor.

Model  with  bone,  fixing  the  bone  (final  model).  Applying  the  force  in  the  Z  axis.   Head   with   Alumina.   Show   the   new   safety   factor   and   how   to   make   it   better   (with   chamfers  in  the  head  and  in  the  12-­‐14mm  Morse  taper).    

Taking into account the result that provided the first simulation, was carried out the restructuring of the piece where it failed, in the neck area where it was the 12-14 mm Morse 36

taper and the head of the prosthesis, changing the angle of this and also adding a support as a bone in the stem. The head and the stem were reestablished by the software Inventor, extending the stem at the top and finally reaching to the final result of the prosthesis, which they can be seen in Annex I. The final model was again analyzed and the safety factor was studied again. The restructured model successfully achieved not broken as it can be seen in the Figure 37 the safety factor in this test reached 1.3574.

Figure 37. Safety factor. Head without chamfer.

A trauma in the limb could produce a very severe impact between the 12-14mm Morse taper and the ceramic head and could reach a catastrophic failure resulting in an easy fracture of this piece, as it has been seen in the previous section. Despite all the benefits some laboratory studies have suggested about the classical Morse taper design with the stability around the implant, this study has shown that the use of neck-head connections by cylindrical morphology, specifically chamfering the 12-14 mm Morse taper and adapting the ceramic head to this new taper, gives the prosthesis a higher mechanical strength in the ceramic head which could contribute to a reduction in the incidence of injuries and fractures related to traumas. Therefore, the safety factor was tested by chamfering the 12-14mm Morse taper and adapting the head with 2mm chamfer using the final model.

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Figures 38 and 39 show the modified end pieces, which are the originals designed by Workbench Geometry area with a 2 mm chamfer added.

Figure 38. 12-14 mm Taper with chamfer.

Figure 39. Head with chamfer.

The size of the head and the neck also appears to influence the safety factor since the laboratory tests [18] and the clinical cases with fracture prosthetic heads [19,20] show a greater likelihood of breakage in those ceramic heads with a smaller diameter and a longer neck. Figures 40 and 41 show the final model and the result of the safety factor after simulating with the new pieces and the chamfer. This show two interesting things to consider: First, the safety factor has increased, reaching a value of 1.4808, and second, the safety factor is in an intermediate zone between the ceramic head and new 12-14mm taper, which demonstrates that accumulated tensions were avoided between these two new pieces.

Figure 40. New safety factor. Taper and head. 38

Figure 41. New safety factor. Head with chamfer.

Model   with   bone,   fixing   the   bone   (final   model).   Head   with   Alumina   and   with   Zirconium  Oxide.  Prove  the  better  safety  factor.    

With the new structured model the ceramic material of the head prosthesis was changed using Zirconium Oxide Instead of Alumina with the same force, 1400N, in the same direction and the same characteristics from previous experiments. It was decided to use ceramics heads throughout all the different tests as an alternative to metal heads (chromium-cobalt) since these materials are much harder than the others and they can be polished with a lower surface roughness than metal heads. The two types of ceramics are bioinert meaning the body is not being able to absorb them and therefore they don't produce any side reaction or allergy [9]. Reviewing the scientific literature it is found that the prevalence of broken ceramic heads is very low and when this does occur it does so predominately in hips with ceramic-ceramic pair friction [19] and especially in initial, primitive implants who had worse polished surface and larger, less homogeneous granules. However, this form of pair friction is especially uncommon

39

in this type of prosthesis. So, the normal one is as in the case which is being studied, using a pair friction made with ceramic-polyethylene. Figure 42 shows the results of the new safety factor with the ZO2 is 2.8162 and it is in an intermediate area of the 12-14 mm Morse taper, which is less important than in the edge of the surface head, which, as shown in previous results, is typically more vulnerable to breakage.

Figure 42. Safety factor with Zirconium Oxide.

The result is expected knowing the different characteristics of each different ceramic material. The zirconium oxide is harder and has a higher resistance to burst than the alumina but may undergo a phase transformation, since it is not a thermo-set material, which is probably as a result of its low heat conductivity. This defect is not very important since the zirconium oxide that is commonly used has a high chemical and dimensional stability and it has an excellent mechanical strength to the fracture toughness and the value of Young's modulus of the same order and magnitude as the steel alloys.

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Equivalent  Elastic  Strain  in  the  Polymer  with  the  different  types  of  ceramics  

The heads of alumina (Al2O3) and zirconia (ZrO2) have a high hardness and strength and those properties make them more resistant to scratches and less susceptible to abrasive wear. Conversely, they are brittle materials and the possibility of a fracture exists. Another important issue is the effect liquids have on this type of material. Ceramics are more hydrophilic, have less friction and lubricate easily, therefore they are suitable materials for coupling the polymeric parts of the prosthesis. Hip clinical studies and simulations indicate that the wear on the ceramic-polyethylene pairs is at least equivalent or less than the metalpolyethylene pairs[19]. In conclusion the two ceramics mentioned were considered in the study due to the polyethylene wear. The number, shape and size of the wear particles in the polyethylene depend on the methods and mechanisms that cause the wear, the stresses on the load surface, the movements and the polyethylene molecular orientation. The predominant wear mechanisms seem to be the micro-adhesion and the micro-abrasion. The damage caused by wear is predominantly eburnation, the pathologically increased bone density, and the scratches. The main thing that causes the wear in the polymeric piece is the development of osteolysis, a disease that damages the tissue of the skin and causes slackening of the bone structure near the hip, which requires revisionary surgery. Despite the low friction, polyethylene with ultra high molecular weight (UHMW) still increase the adhesive wear and abrasion wear and the secondary osteolytic response to the "disease of wear particles" is an issue in the medium and long term. It is estimated that the annual rate of wear for polyethylene is 0.10 mm per year, which is the limit for the prevention of the development of osteolysis-like symptoms. The adaptation and

41

removing of mobility at the interface between the outside surface of the polyethylene and the metal socket also help to prevent the wear and the osteolytic reaction. Taking this into account, Figures 43 and 44 show the result of the equivalent elastic strain with both the ceramic coupled and polyethylene pieces. The minimum with the Aluminia was 1.44 ∙ 10!! and with the Zirconium Oxide was 1.47 ∙ 10!! .

Figure 43. Equivalent Elastic Strain with Zirconium Oxide (ZrO2).

Figure 44. Equivalent Elastic Strain with Alumina (AlO2).

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Directional   (X,   Y,   Z)   and   total   deformations   with   both   types   of   ceramics   in   the   head.  Equivalent  (von-­‐Mises)  Stress.  

In this section the total deformation of both types of ceramic materials in the head of the prosthesis tested with a 1400N force at the three main directions in the Z axis can be seen for both cases. Figures 45 and 46 show the total deformation where the force has been applied.

Figure 45. Total deformation Alumina.

Figure 46. Total deformation Zirconium.

One of the most meaningful magnitudes to calculate in this project is the equivalent VonMises strength in order to see if permanents deformations appear in the stem. As seen in Table 2, the ultimate tensile strength is 950 MPa. Figures 47 and 48 show that the values of the equivalent strength of the Von-Mises coefficient are 314.05 MPa and 312.48 43

MPa in the stem for alumina and zirconium oxide respectively. To find out if those results are within the optimum values they should be compared with the elastic limit of the material of the stem, Ti6Al4V titanium alloy. This material is very commonly used in implants, as has been discussed, so the equivalent strength of the Von-Mises coefficient shows that the material is still below the limit of elastic behavior, 950 MPa, and this proves that the stem will not suffer permanent deformation.

Figure 47. Stem TiAl4V. Head with alumina.

Figure 48. Stem TiAl4V. Head with zirconium.

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It is shown that the prosthesis neck size and femoral stress of the head of the femoral has more strength distribution. This result shows that hip prosthesis with less stress in the neck area must be the best option, which leads to the conclusion that the strains in the implants should match with the bone and this analysis helps to find better materials for implants.

Strain  Energy.  Proving  that  the  meshing  is  correct.      

The final model was conducted in order to test the mesh reliability. To do this, the prosthetic head model with the ceramic zirconium oxide ZrO2 was chosen as an example. The mesh used for experiments with Alumina was exactly the same. The maximum value of the equivalent stress of the Von-Mises coefficient in the prosthesis was screened according to the number of the nodes until it reached a steady state of convergence. Graphic 1 shows this convergence state in the mesh. The value of meshing begins to be stabilized after the third value that was tested in the mesh. In the modeling for both types of simulations the fourth mesh was selected. This mesh was chosen over a mesh with even more nodes because it requires less computational time than a finer mesh without any remarkable changes in the final solutions. To summarize, the meshing for the experiments was the meshing that had been discussed in detail in the Section 3.1.3 with 113706 nodes and 62809 elements.

45

Graphic 1. Convergence reliability of the mesh.

In terms of the equivalent stress of the Von-Mises coefficient, the low energy released by each partition of the selected mesh, as seen in Figure 49, had a maximum value of 0.24739 mJ in the problematic area of the neck and the head. This is yet another way to show that the mesh selected for this experiment was completely satisfactory.

Figure 49. Model in 3D with the correct meshing.

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Comparison   with   different   angles   in   the   prosthesis   between   the   head   and   the   polymer   with   the   cup.   Head   with   Zirconium   Oxide,   fixing   the   bone   and   applying   the   same   force.   Safety   factor,   Equivalent   Elastic   Strain   of   Von   Misses   and   Total   Deformation.    

Knowing Zirconium Oxide had better results than the Alumina, the final test was to subject the prosthesis to the maximum force in this study, 2300N, after fixing the stem to the piece which simulated the bone. Also the positional angle of the socket was changed by 50 degrees and the maximum force was applied in the Z axis. Figure 50 shows the safety factor in the prosthetic in the stem below the 12-14cm Morse taper. The picture on the left depicts a higher safety factor than the picture on the right. It is caused because of the variation of the socket angle.

Figure 50. Safety factor. 0 degrees and 50 degrees with ZO2.

This test indicates that a poorly positioned implants, a poor balance of soft tissue, or a bad relationship between the head and the acetabulum can create repeated microtraumas on the head prosthetic by subluxation or collisions between the two pieces. If this were to happen it would increase the pressure on certain points of the ceramic head that could cause cracks and 47

wear in the particles and eventually cause it to rupture [21]. Furthermore, it is shown that bone fragments, and even the wearing down of polyethylene, metal or ceramic particles itself can cause localized increases of pressure and irregularities in the surface of the ceramic head, which could contribute to the break as well. Figures 51 and 52 show the equivalent Von-Mises coefficients in both cases, with 0 degree and with 50 degree angles in the acetabulum, with both of them producing acceptable results.

Figure 51. Equivalent Von-Mises stress. 494.45 MPa. 0 degrees.

Figure 52. Equivalent Von-Mises stress. 498.68 MPa. 50 degrees.

It is logical that the equivalent Von-Mises coefficient increased with more force and a larger angle. 48

6.  Conclusions    

An essential component of any hip prosthesis is minimal stress in the neck area. Therefore, the new design of hip prosthesis must take these conditions into consideration for good clinical results and the decrease in implant damage. Maximum Equivalent Von-Mises stresses developed in the neck of the hip prosthesis and maximum total deformation in the implant for static condition were analyzed. The design of the implants should have stress distribution similar to the bone of the patient. After the study of hip prosthesis one can conclude that in the near future and thanks to modern engineering it is possible to simplify the problem and to solve the issue of bone fractures. Nowadays, thanks to technology, there are new prosthesis with a minimally-invasive design and with not only an aesthetic improvement, but also with a decrease in risk. Thanks to the software CAD models and simulation of the specific prosthesis for a patient were developed to find the best prosthesis for a patient. It was difficult to find a material with a Young's modulus very similar to the bone. It is expected that the risk of breakage of the head kernel is minimized with the use of new generation ceramics that are more homogeneous, have smaller granules and good surface polishing. In addition, using a larger diameter head and improving the design of the head-neck junction also reduces the chance of fracture. The ball radius and neck angle must be as low as possible to decrease fatigue stresses. The most dominate parameter to increase the safety factor is the radius of neck.

Finally, Zirconium Oxide was proven to be more adequate than Alumina in improving the safety factor and the wear of the polymer. Yttrium oxide (Y2O3) is usually added to improve the material properties of Zirconium as well. A new strategy is the use of so called "Zirconium

49

toughened Alumina." The combination of the two materials results in a composite with high strength and thermal stability Zirconium Alumina. Zirconium ceramics have overcome the limitations of alumina ceramics in regards to tenacity and flexural strength. Thus to reduce wear of the polyethylene is to improve the wear characteristics of the femoral head.  

7.  Bibliography  

[1] D Heinegård and A Oldberg.Structure and biology of cartilage and bone matrix non collagenous macromolecules. The FASEB Journal. July 1989 vol. 3 no. 9. 2042-2051. [2] Comín, Mario.Prat, Jaime.Dejoz, Ricardo. Biomecánica articular y sustituciones protésicas. Instituto de Biomecánica de Valencia (IBV), 1998. [3] Bone Curriculum, ASBMR. Educational resource materials by the American Society for Bone and Mineral Research. [4] Henry Gray. Anatomy of the Human Body. Philadelphia: LEA & FEBIGER, 1918. [5] R.K. Nalla. J.J. Kruzic. J.H. Kinney. M. Balooch. J.W. Ager III. R.O. Ritchie. Role of microstructure in the aging-related deterioration of the toughness of human cortical bone. Elsevier. [6] R.O. Ritchie. J.H. Kinney. J.J Kruzic. R.K. Nalla. A fracture mechanics and mechanistic approach to the failure of cortical bone. Elsevier. [7] ((M. Long and H.J. Rack, Titanium Alloys10 / Handbook of Materials for Medical Devices in Total Joint Replacement—A Materials Science Perspective, Biomaterials, Vol 19, 1998, p 1621–1636. [8] Apg-Ban. Medical discoveries. [9] J.R. Davis. Handbook of Materials for Medical Devices. 2003 ASM International. 50

[10] J. Katz, Developments in Medical Polymers for Biomaterials Applications. Med. Device Diagnostic Ind. p 122. [11] Tim Taylor,Anatomy and Physiology Instructor. Inner Body. Hip joint. [12] R.H. Doremus, Bioceramics. J. Mater. Sci. Vol 27. 1992. p 22-30. [13] S.H.Y. Catalog. Hip prosthesis. [14] Targos Groups Catalog. [15] SYNERGY Catalog. [16] Smith and Nephew Synergy Stem Catalog. [17] Lima corpotate orthopaedic motion femoral stems Catalog. National joint registry. [18] Dorre E, Ritcher HG, Willman G. Fracture load of ceramic ball heads of hip prostheses. Biomed Tech 1991; 36:305-9. [19] Winter M, Griss P, Scheller G, Moser T. Ten to 14 years results of a ceramic hip prosthesis. Clin Orthop 1992;282:73-80. [20] Mangione P, Pascarel X, Vinciguerra B, Honton JL. Fracture des tetes en ceramique dans les prostheses totales de hanche. Int Orthop 1994; 18:359-62. [21] Characteristics of Metal and Ceramic Total Hip Bearing Surfaces and Their Effect on Long-Term Ultra High Molecular Weight Polyethylene Wear. Davidson, James A. Ph.D.

     

 

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Annex  I.  Planes  of  the  prosthesis    

 

52

   

53

 

54

 

55

     

56

                         

57