Mechanical loading characteristics of total hip prosthetics subjected to dynamic loading cycles

Abstract

The selection of best material pair in the hip prosthetics design for improved performance and life relies on the estimation of hip joint contact stresses and contact pressure distribution during various dynamic loading cycles: Climbing Upstairs, Climbing downstairs and Knee bending. The maximum Von Mises stress, contact pressure and deformation are considered factors in selecting the material pair in this current study. This is done by analysis of a three-dimensional finite element model of the acetabular component during the different dynamics cycles using ANSYS^®. The different material combination of bearing couples considered for this analysis are metal in contact with plastic, metal on metal, metal on ceramic, ceramic on plastic, ceramic on metal and ceramic on ceramic. The numerical results were validated by comparing them with the FEA results of Hai-Bo Jiang et al. for the existing material combinations and a high correlation of 92% was observed. We found that the Alumina femoral head paired with ultra-high molecular weight polyethylene (UHMWPE) cup reduces the maximum Von Mises stress and maximum contact pressure developed at the interface amongst other material pairs.

Keywords

Hip prosthesis materials finite element method dynamic loading cycle bearing couples

1. Introduction

The acetabulo femoral joint (commonly called the hip joint) is one of the most crucial joint of a human body, serving as the structural link between the axial skeleton and the lower parts of the body. They transmit forces from the ground to the upper extremities and vice versa [1]. The joint is synovial in nature with ability to undergo combinational motion in multiple planes and take up both normal axial and torsional loads. It is thus exposed to greater risk of local loading, degeneration of the cartilage and shock. It consists of a joint cavity filled with synovial fluid (which helps in lubrication), enclosing the articulating coxal bone and the femur (thigh bone) which enables free movement. Anatomically, the hip joint is a classic ball-and-socket joint connecting the femoral head with the cup-shaped acetabulam of the coxal bone [2] as shown in Fig. 1. The actual articular surface is the concave acetabulam - shaped by unnamed bone with contributions from the ilum, ischium and the pubis–which appears lunate when looked into it [3]. The femoral head is a typical ball measuring about 1–2 inches in diameter connected through the neck of the femur. The biomechanics of this joint is essential for the understanding of the gait cycle and various pathologic conditions, as it plays a vital role in weight-bearing and movement of the human body [4].

Fig. 1.

Frontal section of the hip joint [2].

The total hip arthroplasty (THA) is one of the most performed surgical orthopaedic procedures in the United States [5]. It involves the replacement of the coxal joint with an artificial prosthetic by the excision of femoral head, proximal neck and the acetabular cartilage. The preparation of the joint is done by sawing the femur head and then creating a hemispherical cavity through reaming of the coxal bone. The fixation of the implant in the pelvic girdle and the femur is done by either polymethyl methacrylate cement or by bony ingrowths into porous coatings, which depends on the surgeon and the procedure that was followed [6]. The complete procedure is complicated as it depends on the accuracy of various joint parameters such as joint center, neck angle, offset, lever arm and the motion range until impingement. The positioning of the implant is crucial as it affects the local loading of the prosthetics [7]. This is important in design of the implant because the material deformation should be limited to ensure correct positioning and prevent the removal of the head. Hip dislocation occurs when it is flexed and the femur is made to drive posteriorly, which leads to tearing of the acetabular labrum, fibrous cap and the ligaments. It can also be traumatic when associated with femoral head fracture. Depending on the severity of the injury, the treatment maybe surgical restoration or prosthetic replacement [8]. The degeneration of the joint due to diseases like common osteoarthritis, the risk of which increases with the age and wear of the cartilage also warrants an implant as it can become highly painful.

During unstable motions like stumbling and jumping, the load acting on the joint rises upto 8 times the body weight, which increases the risk of fracture [9]. The human hip is subjected to cyclic loading which can place loads three to five times that of the body weight on prosthetic components even during normal ambulation. The gait cycle which is the continuous cyclic pattern of movement, like walking or running, is usually split into two phases – Stance and Swing, both of which takes place in a single gait cycle. The hip joint reaction forces are frequently approximated with a 2-dimensional analysis. Under static loading, i.e. standing pose, the center of gravity lies between the hips and the reactive forces are distributed equally by the two femur bones. When the body becomes dynamically loaded, the center of gravity is moved distally to the non-supporting legs, which are accounted along with the body mass. This induces turning moment around the femoral head component and this combined effect of the abductors result in multiplication of the body weight [10]. This emphasises the importance of the dynamic loading effects on the design and material selection of the prosthetics in addition to the static analysis.

The location of peak stress occurs was found to occur at a distance of 80.9 mm to 95.6 mm from the head center [11]. The effect of the shape of the implant on the stresses have been reported by few authors. The parallel and tapered hollow stems produce an increase in both proximal bone and cement stresses when compared to the solid stem [12]. The conventional prosthesis with the trapezoidal cross-section was experimentally confirmed to carry less stress than those with other cross-sections [13]. Also, all the new stem shapes were found to have higher safety factor values according to all fatigue criteria than the original Charnley shape [14]. Kayabasi et al. notes that the shape optimization of the implants results in the reduction of Von Mises stress on the system [15]. Even though the minimum stress values were lower for trapezoidal and oval cross-section of the stem, they do not distribute them evenly as circle and ellipse sections do [16], which effects the micromotion and the stress shielding of the implants. The study on the effect of interface gaps on the primary stability of a particular anatomical cement less stem during stair climbing by Viceconti et al. predicts that 2% of the patients will have acute problems after the surgery [17]. The reversible micro motion rather than subsidence contributes more to overall relative motion between the bone and the implant [18]. Analysis involving the titanium case was found to have the maximum amount of displacement, which is an important contributor of hip dislocation [19]. Between the fatigue life of bone cement implanted Ti-6Al-4V and CoCr alloy, it was seen that the Ti-6Al-4V was more durable for cemented designs [20].

The mechanical behaviour of the skeletal parts subjected to various physiological loads [21] was studied by Brekelmans et al. by means of failure analysis. The stairway usages require different muscle, force and movement patterns from that of level walking, and the current staircase designs require extra dexterity to avoid the danger of injury [22]. The musculoskeletal loading during dynamics cycles such as running, show higher loading forces than level walking at the same speed and it was seen that the muscle reactions are also an important contributor [23]. The static analysis of the hip prosthetics [24,25] and the dynamic contact analysis between the femoral head and the acetabular cup, specifically for walking cycle [26] was also conducted in our previous work. The results of the contact analysis of the implant interface for the stumbling cycle favours UHMWPE and Alumina material combination over common pair of materials [27]. The UHMWPE cup failure is mostly due to overheating owing to the lack of lubrication [28]. The complexity of the bio-tribology and the fundamental role it plays in improving hip implant design [29] is brought out by Di Puccio et al. The nominal wear depth of 0.138 mm/year for CoCrMo-UHMWPE combination subjected to the walking cycle while neglecting the wear of bone cement has been estimated [30]. The revision rates for the Metal on Metal (MoM) hip implants have been increasing due to adverse effects of metal debris causing inflammation [31]. Under starved conditions in Ceramic on Ceramic (CoC), the lubrication thickness level decreases and this condition is equally important in selecting the implant materials [32]. The peak contact stress and peak fluid pressures are found to occur in the superior dome or lateral roof of the acetabulum [33]. It is observed that the increased femoral head radius [34] and cup radius [35] reduces the magnitude of the maximum von Mises stress. A large diameter head also closely relates to the anatomy of the healthy hip joint, which serves to increase the stability of the joints. But, the problem of friction and wears prevents the use of large head sizes. The stick-slip effect characterized by squeaking was numerically calculated [36] by using a 3-dimensional spherical contact model. The stripe wear occurs due to granulation of ceramic particles in hard-on-hard implants due to friction which can give rise to noise. But, this phenomenon is not observed in hard-on-soft bearings as it cannot reach such high coefficient of friction values [7]. Finite element analysis and fuzzy matter-element method was used to optimize the femoral head and stem material selection according to patient’s requirement [37]. The relevance of finite element models than the axisymmetric models in providing realistic results was investigated by Cilingir et al. [38].

The impact loads as encountered when it is subjected to a dynamic loading like stairs climbing or jumping, causes the artificial hip joints to fail. New material combinations are required as the existing combinations are still not satisfactory in terms of life and tribological properties. As the search for such superior material combinations ensues, several researchers have utilized the Finite element method to analyse the effect of different combinations. The life and performance of such prosthetics depends on the geometrical parameters and the material selection. The hip implant has been commonly designed using materials such as Cobalt chrome alloy (CoCrMo), Stainless Steel (SS) and Titanium alloys (Ti-6Al-4V). Additionally, the other materials frequently used, including Cobalt-Chrome (Co-Cr), Alumina (Al₂O₃) and Zirconia (ZrO₂) are utilized for analysis in this paper. The authors made a research attempt on human hip joints considering static loading for the same combinations of materials [24,25]. Mainly previous studies are conducted by assuming the peak loads during the normal gait at a particular time (static loads), but mostly the hip is exposed to dynamic loads, like climbing the stairs, stumbling, Knee bending and jumping. These loads are impact loads which causes the artificial hip joints to fail. The present work focuses to compile the effect of mechanical loading of various bearing couples on the basis of contact stress for the dynamic loading cycles, i.e. Climbing upstairs (CU), Climbing downstairs (CD) and Knee bending (KB), by the assessment of contact stresses and deformation in the lines of our previous static model.

2. Material selection and properties

The material combination and the geometrical parameters play the most important role in the load bearing characteristics of the human hip joint. The geometrical parameters that influence the most are the femoral head radius (R1 = 16 mm) and thickness (d = 9.423 mm) of the acetabular cup (Fig. 2). This optimized radius of the femoral head and the thickness of acetabular cup are obtained from our previous static analysis of the total hip prosthetics [25].

Fig. 2.

Geometrical parameter of prosthetic joint.

Table 1

Material properties used in the finite element model [25,26]

Materials/Alloy	Young’s modulus (N/mm²)	Poisson’s ratio	Yield strength (N/mm²)	Density (Ton/mm²)
Co-Cr	230E3	0.3	720	0.83E-9
UHMWPE	2200	0.33	21	0.97E-9
Co-Cr-Mo	230E3	0.3	517	8.387E-9
Alumina	375E3	0.3	580	0.961E-9
Stainless steel	200E3	0.31	650	8.190E-9
Zirconia	210E3	0.3	1000	5.680E-9
Titanium	110E3	0.32	800	4.507E-9

The materials are selected based on the three factors – Biocompatibility, corrosion resistance and similarity between the mechanical properties as that of the bone. This is because of the hostile environment the prosthetics would be exposed in the human body for a prolonged period. The different combination of bearing couplings considered for the analysis are metal (femoral head) in contact with plastic (acetabular cup) (MoP), metal on metal (MoM), metal on ceramic (MoC), ceramic on plastic (CoP), ceramic on metal (CoM) and ceramic on ceramic (CoC) combinations. The pairs utilized in the above order are CoCr on UHMWPE, Alumina on UHMWPE, Titanium on CoCrMo, 316L on Alumina, Zirconia on CoCrMo and Zirconia on Alumina, whose properties have been tabulated in Table 1 [25,26].

3. Development of 3-dimensional FEA model

The three-dimensional model of the acetabular cup and the femoral head was generated using ANSYS^®. The material properties are modelled as homogenous, isotropic and non-linear [25,26]. The hip joint interface consisting of the acetabular cup and the femoral head is discretized using 8-noded hexahedral element. The boundary is assumed to be a suitable surface-to-surface contact model to simulate the force transmission and its effects. To enable faster computation, symmetric boundary conditions are assumed to restrict calculation to one half of the model. In static case, the materials are assumed to be linear elastic; but, for dynamic cases it is non-linear. Convergence test have been performed to find the optimal mesh size. The finite element model consists of 81388 numbers of nodes 103322 numbers of elements with an element size of 0.5 mm. The mesh size of the FEA model used is 0.5 mm. The mesh size was solved for 1 mm 0.9 mm, 0.8 mm, 0.7 mm, 0.6 mm and then the convergence occurred at 0.5 mm. For finite element analysis, the materials are modelled as bilinear isotropic elastic-plastic which also includes it’s yield strength for analysis and the algorithm used in the analysis is Explicit algorithm. To obtain the mechanical characteristics and the best combination of the bearing couples, the maximum contact pressure, maximum von Mises stress and the maximum deformation for the dynamic cycles - CU, CD and KB are investigated by solving this structural non-linear contact problem.

4. Boundary conditions for loading

The boundary conditions for static and dynamic loading differ considerably. In the static analysis, the human body is assumed to be standing in which the hip joint bear’s one-third of the body weight. The load on the hip joint is simulated as 200 N, considering an average human weight of 60 Kg [39]. This loading condition may fail under the dynamic loading cycles like walking, jumping, stumbling, climbing upstairs, climbing downstairs, etc. Thus, the dynamic analysis of prosthetic implants is vital to design of such implants to predict the life better. The acetabular cup is taken as a cement fixation to fully constraint the bottom surface, which enables symmetrical boundary conditions.

The loading parameters – Fx, Fy, Fz are applied on the center of the femoral head to fulfill the symmetry of the boundary conditions. The loading cycle obtained from the work of El’Sheikh et al. [40] is shown in Fig. 3, which represents the loading cycle for Climbing upstairs. It represents only the muscle force. The symmetrical boundary conditions shown in Fig. 4 are utilized to reduce the computational time for solving the model. The loading parameter Fx refers to lateral/medical load, Fy to anterior/posterior load and Fz to proximal/distal component – all of which acts on the center of the femur. The authors at the present study have not included about the coefficient of friction, lubrication mechanisms and joint moments occurring in the joints. In general for dynamic analysis joint moments are not considered since for predicting the wear analysis of hip joints using FEM only maximum peak values are considered [42].

Fig. 3.

The force response of the load applied on the hip prosthetics during Climbing upstairs.

Fig. 4.

The boundary conditions for the loading of the hip prosthetics.

Fig. 5.

Stress variation in acetabulum for different material combinations - Normal walking cycle.

5. Validation for FEA results

The FEA methodology followed in this paper is corroborated with Hai-Bo Jiang’s model results [39] for the case of the normal walking cycle. Figure 6 shows the comparison of the results of the maximum von Mises stress of Hai-Bo Jiang’s model and the current FEA results for the metallic heads (CoCr, Ti, and SS) against UHMWPE cup. To make the comparison with the existing literature more pertinent, the maximum load acting on the femur head, i.e. the time between 2s to 3.5s during the mid-stand condition, is taken. It is found that maximum von Mises stress values occurring at the head and cup interfacial region as shown in Fig. 5 for different material combinations are in close correlation with comparison with Hai-Bo Jiang’s result. The correlation was made for the maximum load that occurs between 2 secs to 3.5 secs. A smaller range of deviation is observed between the other load data that is from 0 secs to 5 secs.

Fig. 6.

Validation of FEA results with those of Hai-Bo Jiang [39].

In the case of dynamic analysis there is no experimental data available in the literature that examines gait analysis in particular. Therefore, the authors validated the results from the FEA model.

The comparison shows a high correlation of about 92% match between the present FEA results and the existing results for 316L on UHMWPE case. This provides the confidence to extend the same methodology in this paper for the entire time duration for all possible material combinations for three dynamic cycles considered

6. Results and discussions

6.1. Variation of maximum stress for different material combinations

The peak stress, contact pressure and deformation of the acetabular cup by dynamic loading cycles are complicated than the static conditions. The peak contact pressure is developed on the localized plastic deformation of the prosthetics [26]. Both tensile and compressive stresses are developed on the acetabular cup due to the applied load. Figure 7 depicts the maximum von Mises stress developed in the different bearing couples for the three loading cycles: (a) Climbing upstairs, (b) Climbing downstairs and (c) Knee bending.

In the Climbing upstairs dynamic model (Fig. 7(a)), the maximum load acts at 0.25 s when the upward force by the knee results in flexion movement of the thigh so as to climb the stairs. The maximum load acting on the femur head is about 2.51 times the body weight (BW = 60 Kg) at 17% of the gait cycle [41]. In the available material combination, the MoM (Titanium on CoCrMo) experiences the peak stress value of 269 MPa at the interface between the femur head and the acetabular cup. On the other end, Alumina on UHMWPE (CoP) yields the best results throughout the gait cycle with a low stress magnitude of 171 MPa with a relative percentage decrease of 46.18%. While climbing down (Fig. 7(b)), the maximum load occurs at 0.24 seconds, which again involves flexion of the thigh to raise the knee a little to take the step downwards. The maximum load acting on the interface is about 2.60 times the body weight at 8.5% of the gait cycle [41]. Again, Titanium on CoCrMo (MoM) generates the maximum stress value of 150 MPa. The CoP (Alumina on UHMWPE) suffers the least amount of peak stress with a magnitude of 54 MPa in the entire gait cycle, reducing the contact pressure by 36.11%. At 2.25 seconds of the Knee bending cycle (Fig. 7(c)), i.e. 50% of the gait cycle, the maximum von Mises stress occurs at the maximum contraction position of the knee. The maximum load that acts at the interface is about 1.43 of times the body weight [41]. The MoM (Titanium on CoCrMo) pair causes a relatively high magnitude of stress of 524 MPa magnitudes, while the CoP (Alumina on UHMWPE) generates only a peak stress of 170 MPa magnitudes. This reduces the peak stress intensity by 32.41%. It is evident that Alumina with UHMWPE pair incurs lower contact stress than the other pairs. Also, the average of the stress produced by CoP pair in all loading cycles is lower than their counterparts. This is because of the reduction in stiffness value with load and thus resulting in lower contact stress at the interface [25,26].

Fig. 7.

(a) Stress variation for different material combinations - Climbing upstairs. (b) Stress variation for different material combinations - Climbing downstairs. (c) Stress variation for different material combinations - Knee bending.

6.2. Induction of maximum contact pressure under different dynamic loading conditions

The prosthetic surface wear that occurs during its usage depends on the contact pressure developed at the interface. The maximum contact pressure develops at different part of the gait cycle depending on the type of dynamic loading condition. For climbing upstairs and Climbing downstairs cycle, the peak load occurs at the beginning of the thigh flexion and thus the maximum contact pressure between the femur head and the acetabular cup is evaluated at that time. The effective center of gravity moves distally towards the unsupported leg, which is assumed to be a part of the body because the weight of that is also balanced by the supporting leg along with rest of the body mass.

Figure 8 shows the variation of the contact pressure for the entire gait cycle for (a) Climbing upstairs, (b) Climbing downstairs and (c) Knee bending. As expected for CU and CD cycles, the maximum contact pressure occurs at 0.25 s and 0.24 s respectively. For KB cycle, this occurs at 2.25 s. This peak contact pressure is due to the action of maximum contact force at that time on the acetabulum. Throughout the gait cycle, it can be seen that peak contact pressure distribution for CoP (Alumina on UHMWPE) is minimum for CU, CD and KB cycles with a peak magnitude of 5.4 MPa, 2.6 MPa and 8.4 MPa respectively. The peak contact pressure occurs in a relatively larger magnitude for MoM (Titanium on CoCrMo) when compared with the rest of the material combinations with contact pressure distribution intensity of 15.7 MPa, 9.6 MPa and 23 MPa respectively for CU, CD and KB. The maximum contact pressure at the interface region of Alumina on UHMWPE has been reduced by 34.2%, 26.6% and 36.1% respectively for the three loading conditions. This reduction in contact stress in the plastic acetabular cup is due to its low Young’s modulus and hardness value. This leads to enlarging of the contact area of the cup with application of force, hence decreasing the contact pressure. Lesser the contact area, the higher is the contact pressure. This occurs in higher hardness material like CoCrMo alloy, where the hardness value is higher and thus, the resistance to loading increases, i.e. the contact pressure increases. From the obtained results, the Alumina in contact with plastic cup (UHMWPE) concurs to lowest contact pressure.

Fig. 8.

(a) The variation of contact pressure for different material combinations - Climbing upstairs. (b) The variation of contact pressure for different material combinations - Climbing downstairs. (c) The variation of contact pressure for different material combinations - Knee bending.

6.3. Deformation of the femoral head under dynamics loading cycle

The displacement of the implant is an important factor in the design of the prosthetics as the displacement of the head should be limited to avoid dislocation of the ball joint. The hardness value of the material is essential for determining the level of deformation. Figures 9, 10 and 11 show the comparison of the deformation levels for (a) hard-on-hard and (b) hard-on-soft materials for the three dynamic loading conditions. This is done by unselecting the femoral head in the model and finding the deformation for each loading of the bearing couple.

In Figs 9(a), 10(a) and 11(a), among the hard-on-hard materials, Titanium head with CoCrMo encumbers the maximum deformation in all three cases (CU, CD and KB) with a magnitude of 0.0183 mm, 0.00048 mm and 0.00265 mm respectively. But in Figs 9(b), 10(b) and 11(b), for the case of hard-on-soft materials, the minimum deformation is exhibited by Alumina on UHMWPE with peak deformation values of 0.0499 mm, 0.0111 mm and 0.0795 mm respectively for CU, CD and KB cycles. The lower values of the former results are due to hardness of the metals compared to the plastic (UHMWPE). Thus, the deformation values for the hard-on-hard materials are lower. In the latter case, Alumina has higher elastic modulus than the CoCr material. This results in minimum deformation compared to CoCr even though both share the same Poisson’s ratio. As the Brinell hardness of the Alumina is 1440 which is higher than the other materials, the maximum deformation occurs for this pair at the peak load. The ceramic material also shows characteristics like better wear resistance, better corrosive resistance, high scratch resistance, no ion dissolution along with a better surface finish. It can be seen that the deformation, contact pressure and the stresses induced are significantly higher for the dynamic cases considered than the static loading conditions.

Fig. 9.

Deformation pattern for Climbing upstairs (CU) cycle. From left: (a) Hard-on-hard implants, (b) Hard-on-soft implants.

Fig. 10.

Deformation pattern for Climbing downstairs (CD) cycle. From left: (a) Hard-on-hard implants, (b) Hard-on-soft implants.

Fig. 11.

Deformation pattern for Knee bending (KB) cycle. From left: (a) Hard-on-hard implants, (b) Hard-on-soft implants.

7. Conclusion

The dynamic loading effects on the total hip prosthetics (THA) has been analysed for various material combinations for three different dynamic cycles: Climbing upstairs, Climbing downstairs and Knee bending. This is done by comparing the peak values of von Mises stress, contact pressure and the deformation for the different bearing couples. Overall, it can be seen that the ceramic in contact with plastic, i.e. Alumina on UHMWPE, provides the best results among the material combinations considered. Amidst the considered material pairs, this combination reduces the maximum stress value by 46.18%, 36.11% and 32.41%, and the maximum contact pressure by 35.2%, 26.6% and 36.1% for CU, CD and KB cycles respectively. However in the static analysis conducted by the authors previously, the results found that metal (CoCr) on plastic (UHMWPE) bearings couple yields the better results. However static loading may fail under dynamic repetitive loadings. Further the hard-on-hard pair, though it has better tribological characteristics, relies on fluid film lubrication which is highly sensitive to positioning effects. The stress and contact pressure developed are higher than the other combinations which makes it vulnerable to fracture and prosthetic wear. These problems are overcome by ceramic on plastic implant, as the plastic cup cannot reach the higher co-efficient of friction values necessary for stripe wear to occur. This increases the life and reliability of such implants. The alumina on UHMWPE pair is also preferred for its ease in manufacturing and surgical parameters. The study concentrates on the variation of the mechanical effects on different material pairs under the dynamic loading conditions by simplification of the femur head and acetabular cup interface, which will vary for different radial clearance and boundary conditions. This present paper will be useful to compare the effect of different material combinations, which can act as the starting point for the design of THA for longer life and better performance.

Conflict of interest

None to report.

References

Campbell

J.D.

Higgs

Wright

and Leaver-Dunn (eds)

, Pelvis, hip and thigh injuries, in: Athletic Training and Sports Medicine, Academy of Orthopaedic Surgeons, 2001.

Tate

, Seeley’s Principles of Anatomy & Physiology, McGraw-Hill, 2009.

Schünke

Ross

L.M.

Schulte

Lamperti

E.D.

and Schumacher

, Thieme Atlas of Anatomy: General Anatomy and Musculoskeletal System, Thieme, 2006.

Byrne

D.P.

Mulhall

K.J.

and J.F.

Baker

, Anatomy & biomechanics of the hip, The Open Sports Medicine Journal 4(1) (2010).

Rivero

and DeCoster

, Total hip arthroplasty–a cure?, Western Journal of Medicine 162(3) (1995), 274.

Siopack

J.S.

and Jergesen

H.E.

, Total hip arthroplasty, Western Journal of Medicine 162(3) (1995), 243.

Morlock

M.M.

Bishop

and Huber

, Biomechanics of hip arthroplasty, in: Tribology in Total Hip Arthroplasty, Springer, 2011, pp. 11–24.

Henderson

Johnston

Mockford

and Craig

, Posterior hip dislocation and ipsilateral isolated femoral neck fracture: A novel fixation method, Journal of Surgical Case Reports 2012(10) (2012), 14.

Villarraga

M.L.

and Ford

C.M.

, Applications of bone mechanics, in: Bone Mechanics Handbook, 2nd edn, CRC Press, 2001, p. 33.

10.

Johnston

Noble

Hurwitz

and Andriacchi

, Biomechanics of the hip, The Adult Hip 1 (2007), 81–90.

11.

Baleani

Viceconti

Muccini

and Ansaloni

, Endurance verification of custom-made hip prostheses, International Journal of Fatigue 22(10) (2000), 865–871.

12.

Gross

and Abel

, A finite element analysis of hollow stemmed hip prostheses as a means of reducing stress shielding of the femur, Journal of Biomechanics 34(8) (2001), 995–1003.

13.

Oshkour

A.A.

Osman

N.A.A.

Bayat

Afshar

and Berto

, Three-dimensional finite element analyses of functionally graded femoral prostheses with different geometrical configurations, Materials & Design (1980–2015) 56 (2014), 998–1008.

14.

Senalp

A.Z.

Kayabasi

and Kurtaran

, Static, dynamic and fatigue behavior of newly designed stem shapes for hip prosthesis using finite element analysis, Materials & Design 28(5) (2007), 1577–1583.

15.

Kayabasi

and Ekici

, Probabilistic design of a newly designed cemented hip prosthesis using finite element method, Materials & Design 29(5) (2008), 963–971.

16.

Sabatini

A.L.

and Goswami

, Hip implants VII: Finite element analysis and optimization of cross-sections, Materials & Design 29(7) (2008), 1438–1446.

17.

Viceconti

Brusi

Pancanti

and Cristofolini

, Primary stability of an anatomical cementless hip stem: A statistical analysis, Journal of Biomechanics 39(7) (2006), 1169–1179.

18.

Abdul-Kadir

M.R.

Hansen

Klabunde

Lucas

and Amis

, Finite element modelling of primary hip stem stability: The effect of interference fit, Journal of Biomechanics 41(3) (2008), 587–594.

19.

Bennett

and Goswami

, Finite element analysis of hip stem designs, Materials & Design 29(1) (2008), 45–60.

20.

Kayabasi

and Ekici

, The effects of static, dynamic and fatigue behavior on three-dimensional shape optimization of hip prosthesis by finite element method, Materials & Design 28(8) (2007), 2269–2277.

21.

Brekelmans

Poort

and Slooff

, A new method to analyse the mechanical behaviour of skeletal parts, Acta Orthopaedica Scandinavica 43(5) (1972), 301–317.

22.

Jacobs

J.V.

, A review of stairway falls and stair negotiation: Lessons learned and future needs to reduce injury, Gait \& Posture 49 (2016), 159–167.

23.

Giarmatzis

Jonkers

Wesseling

Van Rossom

and Verschueren

, Loading of hip measured by hip contact forces at different speeds of walking and running, Journal of Bone and Mineral Research: The Official Journal of the American Society for Bone and Mineral Research 30(8) (2015), 1431–1440.

24.

Kalayarasan

Prakash

and Shankar

, Material selection of acetabular component in human hip prosthesis using finite element concepts, International Journal of Experimental and Computational Biomechanics 2(2) (2013), 118–135.

25.

Shankar

Prakash

and Kalayarasan

, Finite element analysis of different contact bearing couples for human hip prosthesis, International Journal of Biomedical Engineering and Technology 11(1) (2013), 66–80.

26.

Shankar

Manikandan

and Kalayarasan

, Dynamic contact analysis of total hip prosthesis during normal active walking cycle, International Journal of Biomedical Engineering and Technology 15(2) (2014), 114–127.

27.

Shankar

and Manikandan

, Dynamic contact analysis of total hip prosthesis during stumbling cycle, Journal of Mechanics in Medicine and Biology 14(03) (2014), 1450041.

28.

Burger

N.D.L.

De Vaal

P.L.

and Meyer

J.P.

, Failure analysis on retrieved ultra high molecular weight polyethylene (UHMWPE) acetabular cups, Engineering Failure Analysis 14(7) (2007), 1329–1345.

29.

Di Puccio

and Mattei

, Biotribology of artificial hip joints, World Journal of Orthopedics 6(1) (2015), 77–94.

30.

Desai

Hirani

and Chawla

, Life estimation of hip joint prosthesis, Journal of the Institution of Engineers (India): Series C 96(3) (2014), 261–267.

31.

Drummond

Tran

and Fary

, Metal-on-metal hip arthroplasty: A review of adverse reactions and patient management, Journal of Functional Biomaterials 6(3) (2015), 486–499.

32.

Meng

Wang

Yang

Jin

and Fisher

, The lubrication performance of the ceramic-on-ceramic hip implant under starved conditions, Journal of the Mechanical Behavior of Biomedical Materials 50 (2015), 70–76.

33.

Pawaskar

S.S.

Ingham

Fisher

and Jin

, Fluid load support and contact mechanics of hemiarthroplasty in the natural hip joint, Medical Engineering & Physics 33(1) (2011), 96–105.

34.

Phillips

A.T.

Pankaj Usmani

A.S.

and Howie

C.R.

, The effect of acetabular cup size on the short-term stability of revision hip arthroplasty: A finite element investigation, Proceedings of the Institution of Mechanical Engineers, Part H: Journal of Engineering in Medicine 218(4) (2004), 239–249.

35.

Jin

Heng

and Auger

, An axisymmetric contact model of ultra high molecular weight polyethylene cups against metallic femoral heads for artificial hip joint replacements, Proceedings of the Institution of Mechanical Engineers, Part H: Journal of Engineering in Medicine 213(4) (1999), 317–327.

36.

Kang

, Finite element algorithm reproducing hip squeak measured in experiment, Journal of Sound and Vibration 393 (2017), 374–387.

37.

Wang

, Optimization of femoral prosthesis based on comprehensive evaluation of structure and material properties, Journal of Mechanics in Medicine and Biology 16(08) (2016), 1640013.

38.

Cilingir

A.C.

Ucar

and Ucar

, Comparison of finite element models of natural hip joint, Journal of Biomechanics 44 (2011), 5.

39.

Jiang

H.-b.

, Static and dynamic mechanics analysis on artificial hip joints with different interface designs by the finite element method, Journal of Bionic Engineering 4(2) (2007), 123–131.

40.

El’Sheikh

H.F.

MacDonald

B.J.

and Hashmi

M.S.J.

, Finite element simulation of the hip joint during stumbling: A comparison between static and dynamic loading, Journal of Materials Processing Technology 143-144 (2003), 249–255.

41.

Bergmann

Deuretzbacher

Heller

Graichen

Rohlmann

Strauss

, Hip contact forces and gait patterns from routine activities, Journal of Biomechanics 34(7) (2001), 859–871.

42.

Nithyaprakash

Shankar

and Uddin

M.S.

, Computational wear assessment of hard on hard hip implants subject to physically demanding tasks, Medical \& Biological Engineering \& Computing 56(5) (2018), 899–910.