Computational investigation of various stem designs with different radial clearances in total hip arthroplasty

Abstract Hip implants are available in various shapes and sizes. This study aims to select the better hip implant stem design and the optimal material that can be used for the implant. For all the material combinations, radial clearance of 0, 0.1, 0.2, and 0.3 had been given between each of the junctions. Analytical calculation using Hertz contact stress formulation to find the contact pressure has been employed for a load of 2300N, which goes hand in hand with the Finite element method (FEM). The results showed that the optimal combination consists of a CoCr alloy stem, femoral head, and cup material, paired with a UHMWPE liner, for the most effective performance. This study thoroughly evaluates various hip implant options and offers important insights into their effectiveness. The results of this research will assist in choosing the most appropriate hip implant design and material, leading to better patient outcomes and advancements in medical technology for the betterment of mankind.


Introduction
The human body at the time of birth has about 270 bones which eventually reduce to 206 during adulthood due to the fusing up of bones (Clarke, 2008).The femoral head size, as it increases yields an increase in the movement of the joint, but it depends on the person's anatomy (Bhawe et al.,

PUBLIC INTEREST STATEMENT
Total hip arthroplasty is a common procedure that can significantly improve the quality of life for countless patients.However, the success of this procedure heavily relies on the design and fit of the implant.This research explores various stem designs and their radial clearances, delving into the intricate details of how these factors impact patient outcomes.The findings from this study have the potential to revolutionize the field of orthopaedics.By understanding how different stem designs and radial clearances affect the performance and longevity of hip implants, surgeons and researchers can make more informed decisions.Ultimately, this research can lead to improved implant designs, better surgical techniques, and enhanced patient well-being.This work represents a significant step forward in the quest to provide more effective, longer-lasting solutions for those in need of hip arthroplasty, offering hope for a future with improved outcomes and increased mobility for countless individuals.

2022
).The femoral head usually ranges from 22 mm to 54 mm based on the individual's anatomy.The hip takes the total weight of a person's body, giving the stability needed for walking and other activities (Chethan et al., 2018).
In the event of an accident or due to age, an artificial hip implant is needed to replace the hip joint.This was successfully done in 1935, giving rise to an essential hip implant design (Dattani, 2007;Dowson, 2001).It was proposed by Sir Charnley, the pioneer in total hip arthroplasty (THA).In THA, the femoral head and the acetabulum are separated by a bearing.This helps reduce the pain developed in that area, and the joint's motion is achieved.The stability of the hip implant is mainly provided by the stem (Ulrich et al., 2008).Gender disparities are evident in hip surgeries with 58% of primary hip procedures involve women, highlighting a notable gender skew in this medical intervention (Moldovan et al., 2022).On top of the stem is present the femoral head, followed by the liner, and finally the acetabular cup.Various biomaterials have been used in THA and currently have a life span of 10 years.The bearing couple can be metal-on-polyethylene and ceramic-on-polyethylene, also known as hard-on-soft; metal-on-metal, ceramic-on-ceramic, and ceramic-on-metal, known as head-on-head bearings.The hard-on-soft bearing has a major problem as it produces debris-inducing Osteolysis (Evans et al., 2019;Furnes et al., 2001).Small polyethylene particles mix in the bloodstream giving rise to this condition.Although there are millions of designs available there is still the need for the long-lasting implant design since there is a demand among patients like athletes and sportspersons.There is a constant need to extend the life expectancy of the implant by improving the material combinations, design, and surgical procedure to help it last for more than 10 years (Sabatini & Goswami, 2008).Finite Element Analysis (FEM) is a powerful computational method used in various fields, including dental and other implant applications (Güvercin et al., 2022a(Güvercin et al., , 2022b)).In addition to this, FEA is also used in Various Treatment Options for ankle injuries (Bağ et al., n.d.).
Many studies have been done considering various loads and implant designs (Göktaş et al., 2022;Mihcin et al., 2023;Nur NİŞANCİ et al., 2020).Published literature has indicated the use of variousshaped stem profiles used instead of traditional ones (Charnley).Some researchers have suggested using lightweight implants for hip replacements.This approach offers valuable insights into the design, manufacturing, and fatigue analysis of these implants.By using advanced design techniques and materials, it is possible to reduce the weight of the implant, which could lead to improved outcomes for hip arthroplasty.Some of the research findings suggest that porous hip implants could be considered for hip replacement, maintaining mechanical integrity while offering a potential alternative for implant procedures (Delikanli & Kayacan, 2019).Previously published literature has shown that using Ti6Al-4 V-on-Ti6Al4V in Metal-on-Metal Total Hip Implants is more effective in reducing contact pressure than other materials (Terzi et al., 2021).Additionally, Ti6Al4V-on-Ti6Al4V demonstrates the most significant reduction in Tresca stress, with a 45.76% improvement compared to CoCrMo-on-CoCrMo and SS 316 L-on-SS 316 L configurations (Ammarullah et al., 2021).From a mechanical standpoint, utilizing polycrystalline diamond as a hard-on-hard bearing material is the most secure option when compared to the examined metal and ceramic hard-on-hard bearings (Ammarullah et al., 2023).Porous hip implants have the potential for use in hip replacement procedures while maintaining mechanical integrity (Salaha et al., 2023).Researchers are investigating the application of 3D modeling and printing technologies using medical images to examine femoral head fractures through Finite Element Analysis (Ciklacandir et al., 2022).
The need for novel hip implant stem designs arises from the quest to extend implant longevity beyond the typical 10-year span, especially for active individuals.Addressing wear-related issues, using advanced materials, and accommodating diverse patient needs underscore the urgency for innovative solutions, aligning with advancements in surgical techniques and technologies.Given the significance of implant longevity and the demand for improved performance in active individuals, there is a clear need for the development of novel stem designs that enhance stability and durability in hip joint replacements.The current work investigates the four novel stem designs that have been made, which will have a constant femoral head diameter of 34 mm, a liner thickness of 3 mm, and an acetabular cup thickness of 6 mm (Boese et al., 2016;Gao et al., 2021;Kayabasi & Ekici, 2008;Kladovasilakis et al., 2020).The stem design with the lowest yielding von Mises stress value will be selected for further analysis.This chosen design will be assessed with different clearances at three critical junctions: the stem-head (HS), headliner (HL), and the liner-acetabular cup (LA).Additionally, the study aims to investigate the contact pressures generated at various interfaces for different material combinations.The interfaces of interest include the stem-head (HS), head-liner (HL), and liner-acetabular cup (LA) junctions.By examining these contact pressures, the research seeks to gain insights into the mechanical behavior and performance of the hip implant under different material combinations at these crucial interfaces.

Hip Implant Stem Designs
There are several designs of hip implants available on the market.The cross-sectional area of the stem influences the values of stress and deflection produced in the implant.This is because the stem provides stability to the total implant.The stem designs can vary in their cross-section shape, and their surface design changes due to material reduction using various algorithms.To find which crosssection performs better, a study has been done taking into account four different stem cross-section designs, namely circular, elliptical trapezoidal, and oval, as shown in Figure 1.The best among the four designs is selected, and the radial clearance is varied from 0, 0.1 mm, 0.2 mm, and 0.3 mm between the stem and femoral head junction, the Liner and femoral head junction, and the backing cup and liner junction.All the designs were modeled using SOLIDWORKS 2021.Static structural analysis was done using ANSYS 19.1 software to determine the total deflection and von Mises stress.The materials used are Ti alloy, CoCr alloy, and ultrahigh molecular weight polyethylene (UHMWPE).These combinations were used in the analysis, and their properties are given in Table 1.
The stem length of all the designs is considered as 173 mm.The femoral head radius is taken as 17 mm, which is uniform for all the designs.The liner thickness is taken as 3 mm, and the backing cup thickness is taken as 6 mm (Sabatini & Goswami, 2008).For the second part of the analysis, radial clearance is given to all the implant interfaces.Table 1 shows the different properties used for the materials during analysis.

Meshing and Boundary Conditions
In accordance with ASTM F299-13, the boundary Conditions were applied, and ISO 7206-4:2010(E), the loading conditions were implemented.The ASTM F299-13 standard gives the guidelines for where the marking lines are to be made on the stem.At 80 mm from the stem tip, a marking line is made, and another at a distance of 90 mm from the stem tip.The bottom portion of the stem below the 90 mm marking line is fixed.A load of 2300N is applied to the cup, normal to the femoral head though gait cycle reflects the actual condition on the implant (Ammarullah et al., 2022;El Sallah Zagane et al., 2023;Guvercin et al., 2022;Jamari et al., 2022;Moulgada et al., 2023).
The contact between the interfaces is given as frictional contact and the friction coeffiecient plays a major role in induced localized stress (Danny et al., 2023;Lamura et al., 2023).The coefficient of friction between CoCr alloy and UHMWPE is considered 0.15, between CoCr alloy and CoCr alloy is considered 0.2, and between CoCr alloy and Ti alloy is considered 0.24 (Chethan et al., 2022;Gutmann et al., 2023).The loading and boundary conditions are in accordance with ASTM F299-13 as shown in Figure 2(a) and the discretized implant model in Figure 2(b).Mesh convergence is refining the mesh in a finite element analysis (FEA) model until the results no longer change significantly with further refinement.This is done to ensure that the results of the FEA analysis are accurate and not affected by the mesh size (Basri et al., 2019).The mesh sizes available range from 5 mm to 1 mm, with a 1 mm interval.In finalizing the mesh size, von Mises stresses were taken into consideration and it was discovered that there were insignificant changes in the von Mises stress when the mesh size was below 2 mm and the same was considered in this study.The mesh convergence is shown in Figure 3.The number of nodes used is 1,14,847 and the number of elements used is 33,081.

Influence of Stem Design in THA
The first part of the analysis is done with different stem designs on the press-fit model for the material combination 1.The stem design with the least von Mises stress is selected for the second part.
From Figure 4, we observe that the deflection, which is the minimum, is for the stem design with the circular cross-sectional area In Figure 5 we see that the von Mises stress is the least for the stem design with circular cross-sectional area.This can be because the stress is distributed along its boundaries and does not contain any edges.The stem design selected for the second part of this work is the circular cross-section, which yields the minimum von Mises stress value.

Influence Of Different Material Combinations
In this we would also be focusing on four different material combinations.We will consider the material combination as given in Table 2.  CoCr alloy and UHWMPE are considered as the liner material.CoCr alloy, which is a metal, would result in metal-on-metal abrasion taking place.This would result in higher contact pressure being produced in those junctions.The stem material is CoCr alloy and Ti alloy, both of which are very commonly used materials.

Influence of Radial Clearance in THA
Radial clearance is on parameter which plays a vital role in THA.The clearance provided between the various components of the implant is referred to as radial clearance, as shown in Figure 6.The clearance of 0 mm,0.1 mm,0.2 mm, and 0.3 mm are given between the three junctions, namely between stem and head (HS), between head and liner (HL), and between the liner and acetabular cup (AL).
Total deflection for all the material combination is shown in Figure 7.In Figure 7 we see that when we consider all the materials in a homogenous fashion i.e., all the components use CoCr alloy as their material, which is also the material combination 2, the deflection produced is the least among them.This may be because the deflection on metal bodies is less compared to polyethylene.We also see in that same image that the deflection is maximum for material combination 3, which comprises Ti alloy as the stem and UHMWPE as the linear material.
The von Mises stress induced in the complete circular stem implants is shown in Figure 8 for material combination 2. It can be inferred that the stress induced is minimum for press fit condition.However it is worth noting that with the increase in the radial clearance, there is no significant change in the stress induced.The contour plot depicting the stress distribution, deflection, and strain is shown in Figure 9 for the press-fit assembly for material combination 2 for full circular stem implant.

Analytical model (Hertz theory)
Hertz's contact theory is mostly used in calculating the contact pressure values, especially on spherical models.The formula which is used to find the contact pressure between the cup and the ball is considered (Tudor et al., 2013).The load (P) is applied on the femoral head (D 1 ) which is in contact with the acetabular cup (D 2 ) considering the material of the ball as CoCr alloy and the cup as UHMWPE.The various parameters such as the material-dependent parameter (Ce), load case dependent parameter (Kd), and the radius of the circular contact area(a) and the maximum contact pressure (P max ) (Shigley's Mechanical Engineering Design 8th Edition.Pdf -Google Drive, n.d.).
The clearance between the ball and cup is taken as 0.1 mm.
Where E1,E2 are the Young's moduli of femoral head and acetabular cup with values of 200 GPa each, µ1 µ2 are the Poisson's ratio of femoral head and acetabular cup with values of 0.3 each.
Where D 1 and D 2 are diameter of femoral head and acetabular cup with values of 34 mm and 52 mm respectively.The radius of the circular contact area is given in Equation 3Where Kd is the load case dependent parameter The maximum contact pressure is given in Equation 4Where, P is the applied load of 2300 N.
The contact pressure is the pressure developed due to the contact occurring between two bodies.The analytical equation was developed by Hertz and is famously known as Hertz contact theory.Figure 10 shows the contact pressure developed between the femoral head and the liner for 0.1 mm radial clearance assembly under material combination 1. Table 3 shows the deviation percentage which is around 9% which is within the acceptance limit Many studies have been done previously with the common hip implant material like cobaltchromium alloy, titanium alloy, and stainless steel.The majority of the previous studies have made design changes to the stem and the acetabular but it is difficult to come to the conclusion of which implant is the best design as various boundary conditions are applied not in accordance with the standards.Ultra-high molecular weight polyethylene (UHMWPE), CoCrMo alloy, 316 L stainless steel, and Ti-6Al-4 V alloy were used to create four distinct structural models.When the mechanical characteristics were examined, it was discovered that the implants made of Ti-6Al-4 V had a deflection of 0.1 mm (Jiang, 2007).The hip implant material with Ti alloy yielded stress of 256MPa when a load of 6000N was applied (Colic et al., 2016).
The contact pressures are analyzed for all the interfaces, for all the radial clearance models and for all the material combinations.Figure 11 shows the contour plot of the contact pressures for the press-fit assembly for the material combination 1. Table 4 shows the contact pressures for the various material combinations and the radial clearance between the junctions.The contact pressure developed between the femoral head and the stem (HS) is higher for all the material combinations.So there could be a possibility for the maximum wear to be produced at that junction.The contact pressure value is higher in the material combination 2 and material combination 4 between the Head and Liner (HL), Liner and Cup (LA).This can be because the liner material in these combinations is CoCr alloy, which has a higher Young's modulus and is a metal.So the contact pressure developed between metal-on-metal contacts is higher.The materials used in this work are considered as isotropic and linear but the UHMWPE material should be treated as nonlinearly plastic due to its plastic strain characteristics (Prado-Novoa et al., 2022).Additionally, it's important to highlight that hip joint implants are lubricated by synovial fluid, a naturally occurring lubricant within human joints (Farah et al., 2022).To achieve more realistic and accurate contact pressure outcomes for dual-mobility hip joint prostheses, it's essential to incorporate dynamic forces throughout the entire cycle (Reginald et al., 2023).Opting for a larger diameter femoral head and configuring the acetabular cup at a 45° inclination can help reduce the potential for implant failure caused by wear (Tauviqirrahman et al., 2023).
We see an increase in contact pressure when the radial clearance increases.This can be because the contact area is reduced as the radial clearance increases.The material combination that gives approximately equal pressure development in all interfaces is the press fit.The future scope would be to find the wear rate produced at the various junctions.The contact pressures in material combinations 1 and 3 have higher values at the HS interface.This can be because the liner material used in both the cases is UHMWPE, as its Young's modulus is lesser compared to metals.So the pressure developed in HL and LA interface is also less.In the place where metal is used as a liner, we see higher contact pressure being developed.

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Figure 2. (a) loading and boundary conditions (b) discretized model of the implant.

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Figure 3. Mesh convergence study for circular shaped hip implant.

Figure 4 .
Figure 4. Total deflection for the press-fit assembly for different stem cross-section.

Figure 5 .
Figure 5. von Mises stress for the press-fit assembly for different stem cross-sections.

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Figure 7.Total deflection for all circular stem assemblies for different material combinations.

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Figure 9. Contour plot of (a) total deflection (b) von Mises stress (c) strain in a press-fit assembly for material combination 2 for circular stem.

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Figure 10.Contact pressure between head and liner in 0.1mm assembly model.

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Figure 11.Contact pressure between (a) head and stem (b) head and liner (c) liner and cup.