## Abstract

In the present paper, a three-dimensional finite element model of the Charnley implant has been developed to analyze the stress–strain distribution and deformation over the stem prosthesis. Patient-specific dynamic forces have been considered for the analytical evaluation using commercial finite element code. The impact of each dynamic activity has been analyzed separately using six different biocompatible alloy materials made of titanium and cobalt-chromium. Mechanical parameters have been evaluated to envisage the longevity and functionality of the implant. The performance of different materials for each suitable gait pattern is analyzed using finite element code. Consequently, Cobalt chromium alloys (CoCrMo alloy) demonstrate better results, i.e., maximum stress, minimum deformation, and strain as compared with other materials. Every dynamic motion, viz., walking, standing up, sitting down, going upstairs, and going downstairs are found in good agreement with the safety factor for every biomaterial. Additionally, going downstairs and sitting down gait motion exhibits the maximum and minimum stress–strain level, respectively. Based on the outcome of the presurgical study, it is recommended that CoCrMo alloys should be preferred over other materials.

## Introduction

The knowledge of the torsional and lateral bending forces for the analysis of prosthesis is essential to develop a suitable implant for dynamic loadings. Total hip arthroplasty (HA) has been an extensively used method for patient treatment to reduce pain and maintain the functionality of the joints. More than two million total hip replacements (THRs) are performed annually worldwide. The number of surgeries has increased rapidly in recent times due to an increase in the aged population [1]. As per Canadian Joint Replacement Surgery report (2018–2019), the numbers of THR have increased by 20.1% in the last five years [2].

Moreover, several studies revealed that there is a sharp enhancement in the number of younger patients undergoing hip surgery. Enhancing implant life to at least 30 years is the need of the hour [3]. Postoperative stability of THR plays a vital role in relieving pain and restore mobility of the patients. Dislocations are serious complications after the surgery and often lead to revision of surgery. The dislocations lead to the majority of revision surgeries. For instance, in the last 10 years, 26% and 22% revision surgeries have been reported in Sweden [4] and US [5], respectively.

It has been observed in the past [68] that the long-term stability of hip arthroplasty is primarily affected by aseptic loosening of implant and material biocompatibility. Titanium and cobalt chromium alloys are the foremost and widely used materials for the replacement and revision surgeries. In addition, mechanical/chemical properties and biomedical stability are some considerable factors that affect the longevity of HA [9,10]. Custom made designs of hip prosthesis prepared from computer software reduces the time and cost of prosthesis stem [11]. To predict the success rate of an implant, residual heat generation due to friction between femoral head and acetabular cup [12], biomedical constraints, anatomic loadings, and presurgical mechanical tests have also been advocated [13]. Before implantation, it is critical to investigate the loading after postoperative condition to minimize implant-related complications like over-sliding and sub trochanteric fractures. These complications do not occur due to leg instances but may occur due to postoperative dynamic movements [14]. Jiang [15] compared the mechanical characteristics of four different models of artificial joint under static and dynamic condition. It was observed that the metallic femur head model covered with an artificial cartilage outperformed the other models with close resemblance to the natural human joint. In addition, a long implant produces a large tensile load due to the significant bending moment [10].

The musculoskeletal simulation model gives valuable clinical data, which helps in assessing the pathological condition to understand the human moment. Heller et al. [16] revealed that hip joint loading and muscle forces substantially vary due to modification of the stem ante torsion. Simulation of the actual human movement has significantly impacted the treatment of osteoarthritis and THR [1719]. Hurwitz et al. [20] reported an increase in hip contact force up to 0.2 times of the body weight (BW) with 10% increase in antagonistic muscle force.

Finite element analysis provides the valuable estimation of stress and strain distribution over any specified structure which is quite challenging to measure in vivo [21]. However, the majority of previous studies [2224] have reported single load under static conditions, where force is being applied in a single or multiple direction. The commonly used load value for static analysis is several times higher than actual body weight, which is clinically unrealistic in many instances. Thus, dynamic analysis under patient-specific loading conditions is to be performed for getting realistic results.

In the present work, a three-dimensional model of Charnley's implant has been simulated as per clinically obtained gait cycle data. The patient activities like walking, sitting, standing, etc. are investigated which influence dynamic loading over the implant to improvise implant design. The implant has been analyzed dynamically for different loading cycles using multiple materials. Finite element analysis has been carried out to investigate the influence of loading pattern on mechanical parameters like stress, strain, and deformation to access the longevity of an implant. To validate the model, same implant model under a static analysis of 2.3 kN load has been analyzed and verified with Chethan et al. [24].

## Material and Method

### Geometric Modeling.

An implant model named Charnley has been developed using computer aided design (CAD) software SolidWorks for investigating the mechanical performance under dynamic loading. Figure 1 demonstrates a 3D model of an implant with the key geometrical parameters extracted from the implant catalogue for the present model [25]. Stem shapes with cutting edge influences the performance of prosthesis. Smooth-surfaced stem shapes reduces the stress concentration and lead to higher fatigue life prosthesis. However, nonsmooth or sharp shape provides better interface bonding capability and prevents interface sliding [26].

Fig. 1
Fig. 1
Close modal

### Finite Element Modeling

#### Meshing.

The mesh of the developed CAD model has been carried out using Ansys Workbench. The structural element of ten nodes tetrahedral shape has been used for generating the mesh (see Fig. 2). This element has three degrees of freedom at each node, i.e., translation into x, y, and z directions and shows quadratic displacement behavior, appropriately suited to model highly complex geometries. As the number of nodes and elements increases, the solid modeling of the body appears closer and accurate to the actual one. However, the longer computational time is required to solve the highly discretize complex problems. Therefore, a mesh independent test was carried out to have a compromise between an optimum grid size and the computational time.

Fig. 2
Fig. 2
Close modal

The mesh-independency test has been carried out using 188 k, 222 k, 315 k, 381 k, 449 k, 584 k, 618 k, and 640 k tetrahedral elements, where “k” represents the elements in thousands. It is found that beyond 381 k elements, the resulting stresses became almost consistent (can be seen in Fig. 3). Hence, the mesh geometry containing 449 k elements was finalized for the present study. Figure 3 illustrates the mesh independence test for the current implant. The 0.71 mm mesh size was adopted for analyzing the present model. Present implant model demonstrates orthogonal quality, skewness, and aspect ratio.

Fig. 3
Fig. 3
Close modal

### Material Property and Boundary Condition.

Six biocompatible alloys of titanium and cobalt-chromium have been considered for finite element analysis. Every material demonstrates an excellent biocompatibility, corrosive resistivity, and high fracture toughness and are linear isotopic and homogeneous in nature. The mechanical properties like density, modulus of elasticity, density, Poisson's ratio, yield, and ultimate strength are available in literature as summarized in Table 1.

Table 1

Material properties of implant materials [23,27,28]

Material (s)Density (kg/m3)Modulus (GPa)Poisson's ratioUltimate strength (MPa)Yield strength (MPa)
Co-Cr-Mo83002300.29970612
Ti–6Al–4V45001100.32900800
Ti-6Al-7Nb45101200.331050950
Ti-35Nb-5Ta-7Zr-0.4O5600660.341010976
Ti-29Nb-13Ta-4.6Zr5000800.3911864
Ti-15Mo-5Zr5060780.33960920
Material (s)Density (kg/m3)Modulus (GPa)Poisson's ratioUltimate strength (MPa)Yield strength (MPa)
Co-Cr-Mo83002300.29970612
Ti–6Al–4V45001100.32900800
Ti-6Al-7Nb45101200.331050950
Ti-35Nb-5Ta-7Zr-0.4O5600660.341010976
Ti-29Nb-13Ta-4.6Zr5000800.3911864
Ti-15Mo-5Zr5060780.33960920

Dynamic analysis has been carried out to ensure the design safety under actual musculoskeletal dynamic gait movement. A dynamic time-independent analysis of human gait is being extracted from Ref. [29] and used for the present simulation. Boundary conditions have been applied as per American Society for Testing and Materials (ASTM) standards (see Fig. 4). The distal end of the implant remains fixed and does not allow to move or rotate horizontally and vertically.

Fig. 4
Fig. 4
Close modal

### Validation.

No other prior studies had examined mechanical implant characteristics under different dynamic loadings with such a wide range of materials. A prior study [24] examined the femoral stem under 2.3 kN loading. The obtained simulated results using Charnley's model was validated against the available literature data, as illustrated in Table 2.

Table 2

Validation of present work with Ref. [24]

Material (s)Present workChethan et al.Percentage error
Ti-6Al-4VVon Mises stress (MPa)709.64662.457.12%
Deformation (mm)0.456390.4511.19%
Strain (mm/mm)0.00692970.005819.47%
CoCr AlloyVon Mises stress (MPa)722.7667.358.29%
Deformation (mm)0.256840.2570.0622%
Strain (mm/mm)0.00397070.003320.32%
Material (s)Present workChethan et al.Percentage error
Ti-6Al-4VVon Mises stress (MPa)709.64662.457.12%
Deformation (mm)0.456390.4511.19%
Strain (mm/mm)0.00692970.005819.47%
CoCr AlloyVon Mises stress (MPa)722.7667.358.29%
Deformation (mm)0.256840.2570.0622%
Strain (mm/mm)0.00397070.003320.32%

It has been analyzed that the present model gives satisfactory outcomes when validated against the published data. The stress, deformation, and strains for Ti-6Al-4V and CoCr alloys came within the error limit of (7.12%, 8.29%), (1.19%, 0.062%), and (19.47%, 20.32%), respectively. Table 2 demonstrates the mechanical performance of implants under patient-specific loadings. Therefore, the findings of the current model simulation are precise and accurate with the available literature.

## Results

The preliminary study was carried out for standard Charnley's implant next to dynamic walking motion using six biocompatible cobalt-chromium and titanium alloys to investigate their mechanical characteristics under patient-specific loadings. Average peak load under a dynamic motion for gait movement are reported from 250 to 310% of BW. Parameters like stress, deformation, and strain under dynamic motion are depicted in Figs. 510, respectively.

Fig. 5
Fig. 5
Close modal
Fig. 6
Fig. 6
Close modal
Fig. 7
Fig. 7
Close modal
Fig. 8
Fig. 8
Close modal
Fig. 9
Fig. 9
Close modal
Fig. 10
Fig. 10
Close modal

### Von Mises Stress.

Stress (σ) is expressed in terms of ratio of force (P) per unit area (A), explained through Eq. (1)
$σ=PA$
(1)

Since the current model reflects dynamic motion, the values obtained at different instances are also dynamic in nature. Stress contours for walking gait with Ti-6Al-4V alloy at five possible instances, i.e., 20, 40, 60, 80, and 100% over a gait cycle has been demonstrated in Fig. 5. It can be observed from the Fig. 5 that the stress level falls gradually with the instance of the gait cycle. For instance, the peak concentration of stress occurs at the midpoint-lateral side of the implant. Stresses are maximum at the 20, 40, and 60% of the gait cycle contours due to peak load (stance phase) and start reducing at 80 and 100% contours due to swinging phase of human leg movement.

Figure 6 presents the von Mises stress for six different biocompatible alloys under different conditions such as walking, sitting down, standing up, downstairs motion, and upstairs motion. When the heel touches the plain ground, i.e., heel strike, the significant number of forces starts developing over the prosthesis and reaches the maximum level at foot flat condition. In addition, it can be seen that the stresses start reducing toward the midstance phase then reaches the maximum level at the heel-off phase. This happens due to the preparation for the next step of human gait. Afterward, stresses start falling toward the toe-off condition and reach to the lowest due to the swinging phase of gait movement. From Fig. 6, it can be observed that CoCrMo and Ti-35Nb-5Ta-7Zr-0.4O alloys displayed the maximum and minimum stress under every dynamic motion. There is no significant difference in von Mises stress between six alloys. However, when it is closely monitored, it was found that the peak stress occurs in CoCrMo alloys (can be seen in the Fig. 6).

### Deformation.

Deformation (δ) is largely correlated to stress (σ), can be explained by the following formula:
$δ=PLAE=σLE$
(2)
where σ is the applied stress, L is the length, and E is the modulus of material.

Figure 7 depicts that the maximum deformation for walking occurs at the proximal end and continuously reduces toward the distal end up to the center of the implant. It can be attributed to the application of the forces at the proximal end while the distal end was fixed (not allowed to move or rotate). In addition, the maximum deformation was found to occur at 20–60% of gait instance during foot flat-midstance-heel-off motion due to high loading. Thereafter, it falls at the 80% of stance, i.e., swinging phase, and starts developing at 100% due to the preparation for the next step of the gait cycle.

Figure 8 demonstrates the maximum deformation under different dynamic activities. Deformation for walking, sitting down, standing up, downstairs, and upstairs are shown in Figs. 8(a)8(e), respectively. Implant alloy Ti-35Nb-5Ta-7Zr-0.4O and CoCrMo displayed the maximum and minimum deformation compared with others for every gait activity. Furthermore, it can be observed that the implant of alloy Ti-15Mo-5Zr and Ti-29Nv-13Ta-4.6Zr demonstrated almost similar deformation characteristics.

### Strain.

Strain (ɛ) can be explained as follows:
$ε=L−L0L0=ΔLL0$
(3)
where ΔL is termed as change in length and L0 is the actual length before deformation.

Strain is maximum where stress is maximum, both stress and strain have a corroborated relation with each other. That's how strain closely relates to stress, and thus, similar to stress contours, the maximum strain occurs at 20–60% of the walking instance, i.e., for foot flat-midstance-heel off (see Fig. 9). In the similar manner to stress, the minimum strain can be seen at 80% gait, i.e., toe-off and it starts increasing at 100% for the preparation of the next step.

Strain variations are further correlated with deformation, and it can be observed that the deformation varies almost similar to strain (see Fig. 10). Strain variation for six alloys under walking, sitting down, standing up, down stairs, and upstairs gait cycle are described in Figs. 10(a)10(e), respectively. The minimum strain was found for the implant of alloy CoCrMo followed by Ti-6Al-7Nb, Ti-6Al-4V, Ti-29Nb-13Ta-4.6Zr, and Ti-15Mo-5Zr, while the maximum strain was shown by Ti-35Nb-5Ta-7Zr-0.4O for every gait cycle. Implant alloy Ti-15Mo-5Zr and Ti-29Nb-13Ta-4.6Zr have similar mechanical properties and confirm approximately similar strain characteristics.

## Discussions

### General Findings.

Present analysis demonstrated a time-dependent change in the values of stress, strain, and deformation for each dynamic activity. The majority of the previous research were limited to the linear static load applied at the proximal end [30,31]. It is a considerable fact that neither a single point load nor the joint angle represents the actual outcome of the analysis. It is essential to have a dynamic test result for a successful implant. Therefore, in order to attain that Charnley's implant with six biocompatible materials is tested under actual dynamic loading conditions to choose the most suitable material that can survive under an actual biological loading environment. The outcomes of the current study revealed that CoCrMo material experiences the moderate stress and minimum deformation compared with other alloys. In addition, the alloys Ti-6Al-7Nb and Ti-6Al-4V also showed promising results compared with CoCrMo alloy and can be preferred due to lower modulus. High stiff materials lead to modulus mismatching in between implant and bone [32].

The current study is first of its kind, which simulate such a large variety of materials for daily dynamic activities such as walking, standing up, sitting down, walking up, and downstairs. von Mises stress for different gait activities are illustrated in Fig. 11. It is noticed that the maximum stress for walking, standing up, sitting down, downstairs, and upstairs activities occur in between (12–44%), (37–52%), (32–50%), (55–92%), and (15–50%) of gait instance, respectively.

Fig. 11
Fig. 11
Close modal

### Clinical Implantation.

The most common materials utilized for manufacturing implants are cobalt chromium and titanium alloys [33]. Selection of suitable design and material combination for prosthesis is very stringent to avoid revision caused by aseptic loosening [34]. The outcomes of the present simulation revealed that cobalt-chromium experiences the lowest deformation (Fig. 7), while stresses (Fig. 5) seem consistent for every material. Implant with low modulus like Ti-15Mo-5Zr, Ti-29Nb-13Ta-4.6Zr, and Ti-35Nb-5Ta-7Zr-0.4O (compared with commonly used implant model Ti-6Al-4V and CoCrMo) transfers more load to the femur bones, which consequently increases the service life and reduces the problem of loosening.

The present Charnley's implant is a most extensively used implant by proving its biocompatibility for more than 40 years. All the materials are within the safety limit under every dynamic activity. Chalernpon et al. [34] showcased that the maximum stress value was lesser than its yield strength for Ti-6Al-4V, while considering implant with femur bone.

### Novel Contributions.

It is quite difficult to analyze the implant under appropriate anatomical constraints while considering the all-significant forces of the musculoskeletal system. The quantifying changes into the loads during different dynamic activities are essential for consideration to check implant suitability before implanted in vivo. Dynamic analysis is an effective method to assess the postoperative risk of implant-related complications and provides a strong base for the future studies.

There are numerous novel contributions of this investigations, this is the only study, which compares different number of materials under a wide range of dynamic loading conditions to evaluate the essential parameters like stress, strain, and deformation. The range of selection of these materials is quite important. Some new materials with lower modulus have also been evaluated for dynamic loadings. The most suitable materials are those, which show minor modulus mismatch between bone and implant. Bergmann et al. [29] simulated the musculoskeletal model for average and peak loading for dynamic activities under 1000 N of loading. Present loading data have been taken from vivo analysis of four patients under different dynamic activities. Prior studies utilized only one or two dynamic activities with a limited number of alloys, and some significant data have been taken from literature to construct the finite element model [15,26,35]. Therefore, a new study is proposed with well validated implant model (for static analysis) to compare the mechanical parameters using materials in order to find the suitable one.

### Limitations.

Every analysis has some limitations, which surely be minimized as much as possible. First and the foremost limitation is that the present simulation is bounded to dynamic loading only, the moment or rotational force are not considered. For complete analysis, it is essential to consider the realistic loadings. However, as mentioned earlier, this is the first of its kind of study that investigated the performance of different material prosthesis under dynamic loading. Therefore, it is the first step toward the realistic loading condition.

Second, since only the implant model is considered for the current analysis, that is why muscle forces have been excluded from the present analysis. Application of muscle force over stem has considerable effect on the stress and deformation patterns. Anatomical constraints validate significant results to the actual ones over ISO and ASTM constraints.

Third, the implant is not clinically/experimentally implanted during the FE analysis. In order to check the implant performance, a large time period of approximately 15–20 years will be required. Bone and cement supports are some of the considerable factors which influence implant characteristics. Clinically, the absence of these supports is not permitted, except for some severe conditions like bone pathology and revision surgery.

Fourth, implant geometry largely varies for every patient therefore it is quite challenging to validate model with available literature. However, for the present analysis, the stress-induced over the implant for 2.3 kN load is being validated with Chethan et al. [24].

Fifth, the implant model was only be simulated for loading constraints, which means the implant has not been evaluated under the synovial fluids and inferior to surrounding tissue reactions.

The present model should be experimented clinically and/or experimentally in future work to simulate accurately under the clinical scenario. The present study is preliminary and focused on obtaining only some of the mechanical parameters, i.e., stress, strain, deformation rather than fatigue life, the effect of bone support, cement mental support, and clinical insertion depth. Future work could be extended including such consideration.

### Future Scope.

In material prospective, heterogeneous object modeling facilitates local control over multi-material distribution, even in the same part [3638]. In hip implant design, implant loosening is coming out as a major challenge that needs to be addressed with help of recent advancements in heterogeneous object modeling and functionally graded material distributions which may result in better mechanical and lubrication properties and longer product life. Some of the predominant work have been carried in the fields of additive manufacturing to make next generation implant model [39,40].

## Conclusion

The present study compares the mechanical behavior of various biocompatible implant materials under patient's specific human gait pattern. The main concluded point obtained from the present investigation is summarized as follows:

• CoCrMo alloy is found to have maximum stress, whereas Ti-35Nb-5Ta-7Zr-0.4O have the minimum stress. However, alloys like Ti-29Nb-13Ta-4.6Zr and Ti-15Mo-5Zr showcased approximately similar stresses.

• Ti-35Nb-5Ta-7Zr-0.4O alloy is observed to have maximum deformation followed by Ti-29Nb-13Ta-4.6Zr, Ti-15Mo-5Zr, Ti-6Al-4V, Ti-6Al-7Nb, and minimum for CoCrMo alloy. Strain also shows similar results as deformation.

• Going downstairs movement showcases the highest stress, strain, and deformation as compared with other dynamic activities.

• It is found that stress and deformation occur maximum at the foot flat stage followed by heel off.

• Mechanical parameters for walking, standing up, sitting down, downstairs, and upstairs movements are maximum at (12–44%), (37–52%), (32–50%), (55–92%), and (15–50%) of gait instances, respectively.

The present presurgical study under various dynamic motions suggests that CoCr alloy is preferable over other alloys. Although, CoCr alloys modulus are approximately 20 times than bone. Therefore, Ti alloys having modulus 5–8 times of femur bone with moderate deformation and strain are preferred. It is recommended that CoCr alloys are preferred due to lower deformation and strain as compared with others.

## Conflict of Interest

There are no conflicts of interest. This article does not include research in which human participants were involved. Informed consent not applicable. This article does not include any research in which animal participants were involved.

## Data Availability Statement

The authors attest that all data for this study are included in the paper.

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