Mathematical shape optimization of hip prosthesis design

The long-term success of artificial-joint replacement depends partly on the chances for acrylic cement failure and interface disruption. These chances can be diminished by an optimal load-transfer mechanism, whereby stress concentrations are avoided. The present paper introduces a method for numerical shape optimization, whereby the finite element method is used iteratively to determine optimal prosthetic designs, which minimize interface stresses. The method is first applied in a simplified one-dimensional model of a cemented femoral stem fixation, using acrylic cement. The results show that 30-70% cement and interface stress reductions can be obtained in principle with an optimized design. Although the actual optimal shape is susceptible to the characteristics of the joint load, the stem length, stem modulus, cement modulus and bone properties, its general geometrical characteristics are consistent, featuring proximal and distal tapers, and a belly-shaped middle region. These general characteristics are confirmed in a more realistic two-dimensional FEM model. It is concluded that this method of shape optimization can provide a meaningful basis for prosthetic design and analysis activities in general.     

Stem surface roughness alters creep induced subsidence and 'taper-lock' in a cemented femoral hip prosthesis

The clinical success of polished tapered stems has been widely reported in numerous long term studies. The mechanical environment that exists for polished tapered stems, however, is not fully understood. In this investigation, a collarless, tapered femoral total hip stem with an unsupported distal tip was evaluated using a 'physiological' three-dimensional (3D) finite element analysis. It was hypothesized that stem-cement interface friction, which alters the magnitude and orientation of the cement mantle stress, would subsequently influence stem 'taper-lock' and viscoelastic relaxation of bone cement stresses. The hypothesis that creep-induced subsidence would result in increases to stem-cement normal (radial) interface stresses was also examined. Utilizing a viscoelastic material model for the bone cement in the analysis, three different stem-cement interface conditions were considered: debonded stem with zero friction coefficient (mu=0) (frictionless), debonded stem with stem-cement interface friction (mu=0.22) ('smooth' or polished) and a completely bonded stem ('rough'). Stem roughness had a profound influence on cement mantle stress, stem subsidence and cement mantle stress relaxation over the 24-h test period. The frictionless and smooth tapered stems generated compressive normal stress at the stem-cement interface creating a mechanical environment indicative of 'taper-lock'. The normal stress increased with decreasing stem-cement interface friction but decreased proximally with time and stem subsidence. Stem subsidence also increased with decreasing stem-cement interface friction. We conclude that polished stems have a greater potential to develop 'taper-lock' fixation than do rough stems. However, subsidence is not an important determinant of the maintenance of 'taper-lock'. Rather subsidence is a function of stem-cement interface friction and bone cement creep.     

A three-dimensional non-linear finite element study of the effect of cement-prosthesis debonding in cemented femoral total hip components.

A three-dimensional non-linear finite element analysis of a cemented femoral component in which the component was partially debonded from the cement mantle was used to assess the effects of debonding on stresses in the cement. Three cases of partial cement-metal debonding were modelled with debonding of the proximal portion of the implant down to a horizontal plane which was 35, 62.5, or 82.5 mm below the prosthesis collar. Each situation was studied under loads simulating both gait and stairclimbing. Also, complete debonding between the implant and the surrounding cement mantle was modeled for loads simulating gait. Under stair climbing loads with partial cement-mental debonding, hoop stresses of 13-18 MPa were observed in the cement at the cement-metal interface at the proximal postero-medial corner of the implant. Similarly, in stair climbing, the maximum principal stresses in the cement were also adjacent to the proximal postero-medial region of the implant. These stresses were compressive and increased from 15 MPa with fully bonded interfaces to 48 MPa with debonding down to 82.5 mm below the prosthesis collar. Under gait loads, complete debonding caused high compressive stresses up to 34.9 MPa in the cement distal to the prosthesis tip. Thus, cement failure subsequent to prosthesis debonding is likely in the proximal region in a partially debonded implant due to stair climbing loads and is likely below the prosthesis tip in a fully debonded implant due to gait loading.     

Aseptic loosening of the femoral component in cemented total hip replacement

The purpose of this study was to identify factors which predispose to aseptic loosening of the femoral component in cemented total hip replacement. Its design was based on rigid selection critria, so that successful and loose replacements which employed the same surgical technique were compared. Measurements of patient anatomy and of the insertion of the femoral component were made, by an accurate computer technique, on initial post-operative radiographs. Loosening was associated with heavier patients with a wider medullary canal which was flared proximally. This difference in anatomy led to differing distributions of cement in the successful and loose replacements. Medial cement-bone demarcation, at the mid-stem level, was also associated with loosening. These findings indicate the importance of optimizing the size of the prosthesis with respect to the femoral morphology.     

Analysis of a femoral hip prosthesis designed to reduce stress shielding

The natural stress distribution in the femur is significantly altered after total hip arthroplasty (THA). When an implant is introduced, it will carry a portion of the load, causing a reduction of stress in some regions of the remaining bone. This phenomenon is commonly known as stress shielding. In response to the changed mechanical environment the shielded bone will remodel according to Wolff's law, resulting in a loss of bone mass through the biological process called resorption. Resorption can, in turn, cause or contribute to loosening of the prosthesis. The problem is particularly common among younger THA recipients. This study explores the hypothesis that through redesign, a total hip prosthesis can be developed to substantially reduce stress shielding. First, we describe the development of a new femoral hip prosthesis designed to alleviate this problem through a new geometry and system of proximal fixation. A numerical comparison with a conventional intramedullary prosthesis as well as another proximally fixed prosthesis, recently developed by Munting and Verhelpen (1995. Journal of Biomechanics 28(8), 949–961) is presented. The results show that the new design produces a more physiological stress state in the proximal femur.     

Bending vibrations of the femur and the oscillatory behavior of a cemented femoral hip endoprosthesis

The paper presents a novel method for recording amplitude and phase of 6D-vibrations of a spatial pendulum over a wide frequency range (10 Hz up to 20 kHz). The six degrees of freedom of the pendulum mass were monitored by three electrodynamic stereo pickups. At rest, the tips of the needles and the pendulum's center of mass defined the reference system with respect to which the oscillations of the mass were recorded in terms of their amplitudes and phases. Its small dimensions, constant transfer characteristics, linearity, high dynamics, and virtual lack of reaction onto the moving system over the entire frequency range provided the advantages of the measuring system. This method was used to analyze the spatial 6D-vibrations of the head of a cemented femoral hip endoprosthesis when the femur was stimulated to bending vibrations. The head of the prosthesis carried out axial rotational vibrations at every frequency used to stimulate the femur. The amplitudes of the axial rotations of the cortical bone were small in comparison to the ones of the prosthesis head, indicating that axial rotational vibrations following femur bending vibrations mainly stressed the spongiosa and the cement layer. This was observed over the entire frequency range, including at the low frequencies relevant for gait. Over the low-frequency range, as well as at some of the higher resonance frequencies, stationary instantaneous helical axes characterized the vibrations. The measurements suggest the mechanism that the interface "implant-bone" may already be stressed by axial torsional loads when the femur is loaded by bending impacts that are known to occur during walking.     

Bending and fracture of the femoral component in cemented total hip replacement

A computer method was used to make 41 measurements on the geometry of insertion of the femoral component in 200 Charnley total hip replacements. Surgery had been performed at least 12 years before, giving results which were classified as: success (90); fracture (56); or loose (54), according to rigid selection criteria. Fracture was associated with heavier patients in which there was poor proximal fixation of the femoral component but adequate distal fixation. Stems with a medial disposition proximally were more common in the fracture group than in the successful or loose groups. Sequential measurements of bending and subsequent fracture were made on the follow-up radiographs of 24 of the 200 cases (6 fracture and 18 successful). These measurements allowed bending to be detected at an earlier stage than by simple inspection of the radiographs.     

The biomechanical effect of the collar of a femoral stem on total hip arthroplasty

To investigate the biomechanical effect of collars, finite element analyses are carried out through two hip joints that are implanted using collared and collarless stems, respectively, and an intact hip joint model. For the analyses, the sacrum, coxal bone, and the cancellous and cortical bones of a femur are modelled using finite elements based on X-ray computed tomographic images taken from a 27-year-old woman. From the results, it is found that a collar with perfect calcar contact prevents stem subsidence and decreases the proximal–lateral gap and the lateral stem tilting. Therefore, it can impart reasonable biomechanical stability for total hip arthroplasty. However, its low load transmission ability and increased stem tilting effect due to the imperfect contact between the collar and the calcar are found to be serious problems that need to be solved. Results of clinical follow-up are presented for supporting the computational results.     

The biomechanical effect of the collar of a femoral stem on total hip arthroplasty

To investigate the biomechanical effect of collars, finite element analyses are carried out through two hip joints that are implanted using collared and collarless stems, respectively, and an intact hip joint model. For the analyses, the sacrum, coxal bone, and the cancellous and cortical bones of a femur are modelled using finite elements based on X-ray computed tomographic images taken from a 27-year-old woman. From the results, it is found that a collar with perfect calcar contact prevents stem subsidence and decreases the proximal-lateral gap and the lateral stem tilting. Therefore, it can impart reasonable biomechanical stability for total hip arthroplasty. However, its low load transmission ability and increased stem tilting effect due to the imperfect contact between the collar and the calcar are found to be serious problems that need to be solved. Results of clinical follow-up are presented for supporting the computational results.     

The effect of cross-sectional stem shape on the torsional stability of cemented implant components

Stability of a cemented implant, once the stem-cement interface has debonded, is reliant upon stem geometry and surface finish. There are relatively few studies addressing the effect of cross-sectional stem shape on cemented implant fixation. The purpose of this investigation was to compare the torsional stability of five different stem cross-sectional shapes-circular, oval, triangular, rectangular with rounded edges, and rectangular with sharp edges-under monotonically increasing and cyclic loading conditions. Seven samples of each stem geometry were tested. Stems were potted in bone cement and loaded to 5 deg of rotation. For monotonic loading, torque was applied at a constant rate of 2.5 deg/min. For cyclic loading, a sine wave torque pattern was applied, with a maximum magnitude that began at 4.5 Nm for 1500 cycles and then increased by 2.25 Nm every 1500 cycles until 5 deg of rotation. The rectangular stem with the sharp edges always provided the greatest resistance to torque, followed by the rectangular with rounded edges, triangular, oval, and circular. These results, including the effects of sharp corners, may differ for modes of loading other than torsion. These experimental results support the findings of earlier finite element models, indicating stem shape has a significant effect on resistance to torsional loading.     

Design optimization of a prosthesis stem reinforcing shell in total hip arthroplasty

The use of a perforated, titanium funicular shell to support the proximal femoral cortex in total hip arthroplasty was evaluated with the aid of both analytical and numerical techniques. The principal interactions between the femoral cortex, the metal shell, the implant stem and the acrylic bone cement were modeled using beam on elastic foundations theory and two-dimensional elasticity theory. Subsequent formulation of this model as a nonlinear design optimization problem enabled the determination of the dimensions of the implant and reinforcing shell which minimized an objective function based on a simplified material failure criterion. Two cases were examined, each with two cervico-diaphyseal angles: case A: with a rigid contact between a proximal prosthesis collar and the calcar femorale and case B: no collar contact (a collarless prosthesis or post-operative loosening). Case A achieved an optimal solution at a stem diameter 11-23 percent of the cortex inner diameter, a stem length to diameter ratio of 12-40, shell diameter 22-53 percent and thickness 0.2-7.2 percent of the cortex inner diameter and thickness, respectively. Case B achieved an optimal solution at a stem diameter 67-92 percent of the cortex inner diameter, length to diameter ratio of 4-6, and no shell. In case A the collar support makes the type of internal fixation unimportant, while in the more realistic case B, the shell is not recommended.     

Shape optimal design of the stem of a cemented hip prosthesis to minimize stress concentration in the cement layer

An optimal shape of the metal stem of a cemented total hip prosthesis minimizing stress concentration in the cement layer was searched for. A gradient projection method of numerical optimization and a finite element method of stress analysis were employed. A two-dimensional model of the femoral part of a total hip prosthesis was derived equivalent to a simplified three-dimensional axisymmetric model. The result of the stress analysis of the two-dimensional model compared favorably with that of the three-dimensional axisymmetric model. Using this two-dimensional model, an optimal shape of the stem, minimizing stress concentration in the cement layer, was obtained by a gradient projection method and the shape was checked again by the three-dimensional finite element analysis. The resulting optimal shape of the stem profile was in good agreement with conventional ones, except in the proximal region where a significant amount of stress reduction in the cement layer was achieved by tapering the stem to the limit that the stem still could withstand the increased stem stress.     

Pre-clinical validation of a new partially cemented femoral prosthesis by synergetic use of numerical and experimental methods

The present work reports the pre-clinical validation of an innovative partially cemented femoral prosthesis called cement-locked uncemented (CLU) prosthesis. The inventors of the device under investigation claimed that, when compared to a comparable fully cemented stem, the new stem would present various advantages. Two previous experimental studies confirmed that primary stability and stress shielding were comparable to those of cemented stems. Aim of the present study was to investigate if the remaining claims were confirmed as well. A complete finite element model of the bone-implant complex was created from CT data. The model was validated against in vitro measurements of bone surface strains as well as against primary stability measurements. The peak stresses predicted in the CLU cement mantle were not found significantly lower than those reported in other studies on fully cemented stems. However, once the cement inlet geometry is optimised and the associated stress risers are eliminated, the CLU cement mantle should be subjected to much lower stresses. The stress induced in the stems by both load cases was well below the fatigue limit of the Ti6Al4V alloy. Finite element models predicted for all load cases relative motion between cement and metal lower than 60 microm. This amplitude may be fully accommodated by elastic deformations of the cement micro-ridges. The experimental and numerical results showed the validity of the new fixation concept, although a further optimisation of the geometry of the cement pockets is needed in order to further reduce the stresses in the cement.     

Comparison of different hip prosthesis shapes considering micro-level bone remodeling and stress-shielding criteria using three-dimensional design space topology optimization

Since the late 1980s, computational analysis of total hip arthroplasty (THA) prosthesis components has been completed using macro-level bone remodeling algorithms. The utilization of macro-sized elements requires apparent bone densities to predict cancellous bone strength, thereby, preventing visualization and analysis of realistic trabecular architecture. In this study, we utilized a recently developed structural optimization algorithm, design space optimization (DSO), to perform a micro-level three-dimensional finite element bone remodeling simulation on the human proximal femur pre- and post-THA. The computational simulation facilitated direct performance comparison between two commercially available prosthetic implant stems from Zimmer Inc.: the Alloclassic and the Mayo conservative. The novel micro-level approach allowed the unique ability to visualize the trabecular bone adaption post-operation and to quantify the changes in bone mineral content by region. Stress-shielding and strain energy distribution were also quantified for the immediate post-operation and the stably fixated, post-remodeling conditions. Stress-shielding was highest in the proximal region and remained unchanged post-remodeling; conversely, the mid and distal portions show large increases in stress, suggesting a distal shift in the loadpath. The Mayo design conserves bone mass, while simultaneously reducing the incidence of stress-shielding compared to the Alloclassic, revealing a key benefit of the distinctive geometry. Several important factors for stable fixation, determined in clinical evaluations from the literature, were evident in both designs: high levels of proximal bone loss and distal bone densification. The results suggest this novel computational framework can be utilized for comparative hip prosthesis shape, uniquely considering the post-operation bone remodeling as a design criterion.     

The influence of cement mantle thickness and stem geometry on fatigue damage in two different cemented hip femoral prostheses

Experimental models can be used for pre-clinical testing of cemented and other type of hip replacements. Total hip replacement (THR) failure scenarios include, among others, cement damage accumulation and the assessment of accurate stress and strain magnitudes at the cement mantle interfaces (stem-cement and cement-bone) can be used to predict mechanical failure. The aseptic loosening scenario in cemented hip replacements is currently not fully understood, and methods of evaluating medical devices must be developed to improve clinical performance. Different results and conclusions concerning the cement micro-cracking mechanism have been reported.The aim of this study was to verify the in vitro behavior of two cemented femoral stems with respect to fatigue crack formation. Fatigue crack damage was assessed at the medial, lateral, anterior and posterior sides of the Lubinus SPII and Charnley stems. All stems were loaded and tested in stair climbing fatigue loading during one million cycles at 2 Hz. After the experiments each implanted synthetic femur was sectioned and analyzed. We observed more damage (cracks per area) for the Lubinus SPII stem, mainly on the proximal part of the cement mantle. The micro-cracking formation initiated in the stem–cement interface and grew towards the direction of cortical bone of the femur.Overall, the cement–bone interface seems to be crucial for the success of the hip replacement. The Charnley stem provoked more damage on the cement–bone interface. A failure index (maximum length of crack/maximum thickness of cement) considered was higher for the cement–stem interface of the Lubinus SPII stem. For a cement mantle thickness higher than 5 mm, cracking initiated at the cement–bone interface and depended on the opening canal process (reaming procedure and instrumentation). The analysis also showed that fatigue-induced damage on the cement mantle, increasing proximally, and depended on the axial position of the stem. The cement thickness is an important factor for the success of THR and this study evidenced that cement thickness higher than 2 mm apparently does not affect the mechanical behavior of the cement mantel and induce more crack formation on the cement–bone interface.     

A comparative study of the characteristics of femoral hip prosthesis heads--study and results ceramic-coated hip joint heads of titanium]

Today, only hard/soft cup and femoral head combinations are employed for hip joint prostheses. Highly polished ceramic is a material with very good tribological properties for femoral heads, being highly resistant to mechanical wear and tear, and highly resistant to chemical reactions in the biological environment. The advantage of metal heads, in contrast, undoubtedly lies in their resistance to breakage and the ease with which their geometry can be modified with respect, for example, to antirotation angle and neck length. The ideal material for femoral heads is a combination of the two materials. The new multi-layer combination of titanium-niobium oxide/nitride ceramic coating applied to a prehardened titanium head combines the positive material properties in an ideal manner. Femoral heads made of CoCrMo, oxide-hardened titanium, aluminium oxide or multilayer titanium-niobium ceramic were compared by means of friction an wear and tear tests. The TiNb-ceramic-metal heads showed similar abrasion at the surface as the ceramic heads. At the high loads of more than 400 kp, which may also be reached under physiological conditions, the specially coated titanium-ceramic heads proved to be superior in terms of resistance to fracture and tribological properties.     

Design optimization of cementless femoral hip prostheses using finite element analysis

Implant separation from bone tissue, resulting in the necessity for revision surgery, is a serious drawback of cementless total joint replacement. Unnatural stress distribution around the implant is considered the main reason for the failure. Optimization of the implant properties, especially its geometric parameters, is believed to be the right way to improve reliability of joint prosthetics. An efficient numerical model of thefemur-implant system is presented in the paper, including the finite element formulation featuring computation of sensitivity gradients, parametric mesh generator, and a gradient-based optimization scheme. Numerical examples show results of shape optimization of an implant for two sets of design parameters and for the initial stability criterion taken as the optimization goal. The optimum shape appears to be relatively long and proximally porous-coated on about half of its length. The method can be flexibly adjusted to various implant types, stress- and displacement-based optimum criteria, and geometric design parameters.     

The influence of proximal stem geometry and surface finish on the fixation of a double-tapered cemented femoral stem

In this study, the in vitro fixation of four otherwise identical double-tapered stem-types, varying only in surface finish (polished or matte) and proximal stem geometry (with or without flanges) were compared under two conditions. First, four specimens of each stem type were tested with initially bonded stem–cement interfaces, representing early post-operative conditions. Then, simulating conditions a few weeks to months later, stems were implanted in unused synthetic femurs, with a thin layer coating the stem to prevent stem–cement adhesion. Per-cycle motions were measured at both cement interfaces throughout loading. Overall, surface finish had the smallest relative effect on fixation compared to flanges. Flanges increased axial fixation by 22 μm per-cycle, regardless of surface finish (P=0.01). Further, all stems moved under dynamic load at the stem–cement interface during the first few cycles of loading, even without a thin film. The results indicate that flanges have a greater effect on fixation than surface finish, and therefore adverse findings about matte surfaces should not necessarily apply to all double-tapered stems. Specifically, dorsal flanges enhance the stability of a tapered cemented femoral stem, regardless of surface finish.