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.     

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.     

Evaluation of cement stresses in finite element analyses of cemented orthopaedic implants.

Stress analysis of the cement fixation of orthopaedic implants to bone is frequently carried out using finite element analysis. However the stress distribution in the cement layer is usually intricate, and it is difficult to report it in a way that facilitates comparison of implants for pre-clinical testing. To study this problem, and make recommendations for stress reporting, a finite element analysis of a hip prosthesis implanted into a synthetic composite femur is developed. Three cases are analyzed: a fully bonded implant, a debonded implant, and a debonded implant where the cement is removed distal to the stem tip. In addition to peak stresses, and contour and vector plots, a stressed volume and probability-of-failure analysis is reported. It is predicted that the peak stress is highest for the debonded stem, and that removal of the distal cement more than halves this peak stress. This would suggest that omission of the distal cement is good for polished prostheses (as practiced for the Exeter design). However, if the percentage of cement stressed above a certain threshold (say 3 MPa) is considered, then the removal of distal cement is shown to be disadvantageous because a higher volume of cement is stressed to above the threshold. Vector plots clearly demonstrate the different load transfer for bonded and debonded prostheses: A bonded stem generates maximum tensile stresses in the longitudinal direction, whereas a debonded stem generates most tensile stresses in the hoop direction, except near the tip where tensile longitudinal stresses occur due to subsidence of the stem. Removal of the cement distal to the tip allows greater subsidence but alleviates these large stresses at the tip, albeit at the expense of increased hoop stresses throughout the mantle. It is concluded that a thorough analysis of cemented implants should not report peak stress, which can be misleading, but rather stressed volume, and that vector plots should be reported if a precise analysis of the load transfer mechanism is required.     

中国西北地区松科和柏科气孔器形态

现代针叶树气孔器的研究为鉴定化石气孔器奠定了基础,对第四纪植被变化和古气候的研究起着很重要的作用,是第四纪孢粉学的一个重要补充。本文运用常规的标准的孢粉分析方法,对中国西北地区常见的松科3属8种和柏科3属4种植物气孔器进行了观察分析。结果表明凭气孔器大小可以区分松科与柏科。利用气孔器大小、T型结构的形状?上部木质片与气孔器茎之间的夹角进行属的鉴别,再结合茎的长度、宽度、中间木质部的宽、T型外角度和上部木质片外缘形状等可以进行种的鉴别,并编制了一个初步的检索表。     

Sensitivity analysis of a cemented hip stem to implant position and cement mantle thickness

Patient-specific finite element models of the implanted proximal femur can be built from pre-operative computed tomography scans and post-operative X-rays. However, estimating three-dimensional positioning from two-dimensional radiographs introduces uncertainty in the implant position. Further, accurately measuring the thin cement mantle and the degree of cement–bone interdigitation from imaging data is challenging. To quantify the effect of these uncertainties in stem position and cement thickness, a sensitivity study was performed. A design-of-experiment study was implemented, simulating both gait and stair ascent. Cement mantle stresses and bone–implant interface strains were monitored. The results show that small variations in alignment affect the implant biomechanics, especially around the most proximal and most distal ends of the stem. The results suggest that implant position is more influential than cement thickness. Rotation around the medial–lateral axis is the dominant factor in the proximal zones and stem translations are the dominant factors around the distal tip.     

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.     

新疆18种木灵藓属(Orthotrichum Hedw.) 植物解剖结构研究

采用徒手切片法对新疆木灵藓属（Orthotrichum Hedw.）18种植物孢蒴上的气孔、茎和叶进行了比较解剖学观察。研究结果表明,木灵藓属植物茎横切结构形状稳定,由表皮和皮层组成,无中轴细胞分化;除半裸木灵藓（Orthotrichum hallii Sull.et Lesq.）外,其它种叶上部均为单层细胞;叶中部边缘外卷,叶细胞具有高度不同的分叉疣或单疣。在确定气孔显、隐型的基础上,茎和叶横切面的颜色、茎表皮和皮层细胞组成及细胞壁加厚程度、叶细胞疣的高度、叶中肋横切面的形状、中肋的宽度、细胞组成以及芽孢形态等特征可作为该属种间分类的依据。还根据18种木灵藓属植物孢蒴上的气孔显、隐型,及茎、叶的比较解剖学特征,编制了新疆木灵藓属植物的分种检索表。     

新疆18种木灵藓属(Orthotrichum Hedw.)植物解剖结构研究

采用徒手切片法对新疆木灵藓属(Orthotrichum Hedw.)18种植物孢蒴上的气孔、茎和叶进行了比较解剖学观察。研究结果表明,木灵藓属植物茎横切结构形状稳定,由表皮和皮层组成,无中轴细胞分化;除半裸木灵藓(Orthotrichum hallii Sull.et Lesq.)外,其它种叶上部均为单层细胞;叶中部边缘外卷,叶细胞具有高度不同的分叉疣或单疣。在确定气孔显、隐型的基础上,茎和叶横切面的颜色、茎表皮和皮层细胞组成及细胞壁加厚程度、叶细胞疣的高度、叶中肋横切面的形状、中肋的宽度、细胞组成以及芽孢形态等特征可作为该属种间分类的依据。还根据18种木灵藓属植物孢蒴上的气孔显、隐型,及茎、叶的比较解剖学特征,编制了新疆木灵藓属植物的分种检索表。     

In vitro interface and cement mantle analysis of different femur stem designs

The aim of this study is to define stem design related factors causing both gaps in the metal-bone cement interface and cracks within the cement mantle. Six different stem designs (Exeter; Lubinus SP II; Ceraver Osteal; Mueller-straight stem; Centega; Spectron EF) (n=15 of each design) were cemented into artificial femur bones. Ten stems of each design were loaded, while five stems served as an unloaded control. Physiologically adapted cyclical loading (DIN ISO 7206-4) was performed with a hip simulator. After loading both interfaces and the bone cement itself were analysed regarding gaps and cracks in the cement mantle. Significant differences between the stem designs concerning gaps in the metal-bone cement interface and cracks in the cement mantle became apparent. Additionally, a high correlation between gaps in the metal-bone cement interface and cracks within the cement mantle could be proven. Gaps in the metal-bone cement interface but no cracks within the cement mantle were seen in the unloaded specimens. Differences between the unloaded control groups and the cyclical loaded stems regarding the longitudinal extension and width of gaps in the metal-bone cement interface were obvious. The designs of cemented femoral stems have an influence on both the quality of the metal-bone cement contact and the failure rate of the cement mantle. Less interface gaps and less cement defects were found with anatomically formed, collared, well-rounded stem designs without undercuttings.     

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.     

Role of stem design and material on stress distributions in cemented total hip replacement

The risk of fatigue fractures of the femoral stem in a cemented total hip arthroplasty can be minimized by either increasing the stem cross-section and/or using a very high strength alloy. The object of this study was to compare important mechanical characteristics of five selected stem designs, differing in configuration and material (stainless steel, cast chrome cobalt alloy, nickel based alloy and titanium alloy). The strain pattern on the stem was analysed in a 3-point-bending jig and also after cementing it into cadaver femurs. Regardless of stem type or test method, the typical tensile stress distribution on the lateral stem was a bell shaped curve. For the cobalt-chrome and stainless steel stems, the larger the stem the lower were the stem stresses and the stress gradient, and the higher was the factor of safety. However, the factor of safety was increased even further by the use of super alloys such as MP35N and Ti₆Al₄V. In addition, Ti₆Al₄V alloy allowed the use of larger and stronger stems without the extra penalty of rigidity, which was enforced by either the steel or cobalt based alloy.     

Prevention of mesh-dependent damage growth in finite element simulations of crack formation in acrylic bone cement

Peak stress levels predicted in finite element analysis (FEA) usually depend on mesh density, due to singular points in the model. In an earlier study, an FEA algorithm was developed to simulate the damage accumulation process in the cement mantle around total hip replacement (THR) implants. It allows cement crack formation to be predicted, as a function of the local cement stress levels. As the simulation is driven by mesh-dependent peak stresses, predicted crack formation rates are also likely to be mesh dependent. The aim of this study was to evaluate the mesh dependence of the predicted crack formation process, and to present a method to reduce the mesh dependence. Crack-propagation experiments were simulated. Experimental specimens, representing transverse slices of cemented THR reconstructions, were subjected to cyclic torsional loading. Crack development around the corners of the stem was monitored. The experiments were simulated using three meshes with increasing levels of mesh refinement. Crack locations and orientations were accurately predicted, and were virtually independent of the level of mesh refinement. However, the experimental crack propagation rates were overestimated considerably, increasing with mesh refinement. To eliminate the effect of stress singularities around the corners of the stem, a stress averaging algorithm was applied in the simulation. This algorithm redistributed the stresses by weighted spatial averaging. When damage accumulation was computed based on averaged stresses, the crack propagation rates predicted were independent of the level of mesh refinement. The critical distance, a parameter governing the effect of the averaging algorithm, was optimized such that the predicted crack propagation rates accurately corresponded to the experimental ones. These results are important for the validity and standardization of pre-clinical testing methods for orthopaedic implants.     

The design of a model for a three dimensional stress analysis of the cement layer beneath the medial plateau of a knee prosthesis

Factors which have influenced the design of a large scale model for an analysis of the strain in three dimensions of the cement layer beneath the medial plateau of a knee prosthesis are discussed. Materials were selected to model the medial tibial plateau, underlying cement and bone for a typical prosthesis and a two dimensional finite element analysis was used to indicate where the strain gauges should be embedded in the model.     

A finite element analysis of hollow stemmed hip prostheses as a means of reducing stress shielding of the femur.

Stress shielding of the femur is known to be a principal factor in aseptic loosening of hip replacements. This paper considers the use of a hollow stemmed hip implant for reducing the effects of stress shielding, while maintaining acceptably low levels of stress in the cement. Using finite element modelling, the stresses in the proximal femur using different shapes of hollow stem were compared with those produced using comparable sizes of solid stem with different values of elastic modulus. A reduction in stress shielding could be achieved with a hollow stem. A cylindrical hollow stem design was then optimised in order to control the maximum allowable stress in the cement, the minimum allowable stresses in the bone, and a combination of the two. The resulting stems achieved an increase in proximal bone stress of about 15% for the first case and 32% for a model using high strength cement, compared with solid stems of the same nominal outside diameter. The gains of these theoretically optimised designs dropped off rapidly further down the stem. Linearly tapered hollow stems reached a 22% gain, which could be a good compromise between acceptable cement stresses and ease of manufacture.     

Residual stress due to curing can initiate damage in porous bone cement: experimental and theoretical evidence

Residual stress due to shrinkage of polymethylmethacrylate bone cement after polymerisation is possibly one factor capable of initiating cracks in the mantle of cemented hip replacements. No relationship between residual stress and observed cracking of cement has yet been demonstrated. To investigate if any relationship exists, a physical model has been developed which allows direct observation of damage in the cement layer on the femoral side of total hip replacement. The model contains medial and lateral cement layers between a bony surface and a metal stem; the tubular nature of the cement mantle is ignored. Five specimens were prepared and examined for cracking using manual tracing of stained cracks, observed by transmission microscopy; cracks were located and measured using image analysis. A mathematical approach for the prediction of residual stress due to shrinkage was developed which uses the thermal history of the material to predict when stress-locking occurs, and estimates subsequent thermal stress. The residual stress distribution of the cement layer in the physical model was then calculated using finite element analysis. Results show maximum tensile stresses normal to the observed crack directions, suggesting a link between residual stress and pre-load cracking. The residual stress predicted depends strongly on the definition of the reference temperature for stress-locking. The highest residual stresses (4-7 MPa) are predicted for shrinkage from maximum temperature; in this case, magnitudes are sufficiently high to initiate cracks when the influence of stress raisers such as pores or interdigitation at the bone/cement interface are taken into account (up to 24 MPa when calculating stress around a pore according to the method of Harrigan and Harris (J. Biomech. 24(11) (1991) 1047-1058). We conclude that the damage accumulation failure scenario begins before weight-bearing due to cracking induced by residual stress around pores or stress raisers.     

Influence of the change in stem length on the load transfer and bone remodelling for a cemented resurfaced femur

The effect of a short-stem femoral resurfacing component on load transfer and potential failure mechanisms has rarely been studied. The stem length has been reduced by approximately 50% as compared to the current long-stem design. Using 3-D FE models of natural and resurfaced femurs, the study is aimed at investigating the influence of a short-stem resurfacing component on load transfer and bone remodelling. Applied loading conditions include normal walking and stair climbing. The mechanical role of the stem along with implant–cement and stem–bone contact conditions was observed to be crucial. Shortening the stem length to half of the current length (long-stem) led to several favourable effects, even though the stress distributions in the implant and the cement were similar in both the cases. The short-stem implant led not only to a more physiological stress distribution but also to bone apposition (increase of 20–70% bone density) in the superior resurfaced head, when the stem–bone contact prevailed. This also led to a reduction in strain concentration in the cancellous bone around the femoral neck–component junction. The normalised peak strain in this region was lower for the short-stem design as compared to that of the long-stem one, thereby reducing the initial risk of neck fracture. The effect of strain shielding (50–75% reduction) was restricted to a small bone volume underlying the cement, which was approximately half of that of the long-stem design. Consequently, bone resorption was considerably less for the short-stem design. The short-stem design offers better prospects than the long-stem resurfacing component.     

Failure prediction of the total hip prosthesis system

The mechanical failure of the prosthesis-cement-femur system is analyzed by using a two-dimensional finite element model. The strain energy density (SED) criterion is applied to locate potential failure sites in the PMMA and prosthesis stem for five different prosthesis positions.

Medial and lateral failure sites in the proximal regions of the cement are found to be the most sensitive to prosthesis position. According to the SED criterion, these are the weakest regions of the cement. Additional bilateral failure sites are also located at the distal end of the prosthesis, but are less likely to fail. The overall structural integrity of the total hip system is found to be adequate for the ideal case considered herein. In practice, the combination of energy concentration coupled with imperfections such as voids and cracks in the cement are potential sites of failure initiation.

On the basis of clinical evidence on cement and prosthesis stem fracture, local reductions in the cement elastic modulus were introduced into the finite element model in order to model cement defects. The bilateral reduction of modulus by 40% in the cement adjacent to the distal portion of the prosthesis stem can lead to an increase of the strain energy density by 19%.     

Stress analysis and failure prediction in the proximal femur before and after total hip replacement

An investigation was performed to determine the effects of the presence of two lengths of proximal Müller prosthesis on predicted failure loads, as compared to those for an intact femur. Three-dimensional stresses in a bone/cement/prosthesis system were determined using finite element methods, with both isotropic and transversely isotropic material properties used for the diaphyseal cortex. Significant increases in prosthesis stem stresses were found when the transversely isotropic material properties were employed in the diaphyseal cortex. This leads to the conclusion that accurate anisotropic material properties for bone are essential for precise stress determination and optimum design in prosthetic implants. Failure loads were also predicted for vertical compression and axial torque, similar to available experimental conditions, and were within the range of the experimental failure data found in the literature. The technique developed herein can be used to systematically assess existing as well as future implant designs, taking into account the complex three-dimensional interaction effects of the overall bone/cement/prosthesis system.     

Application of circular statistics in the study of crack distribution around cemented femoral components

Cemented stem constructs were loaded in cyclic fatigue using stair climbing loading and the resulting fatigue damage to the cement mantle was determined in terms of angular position of crack and crack length. Techniques from circular statistics were used to determine if the distribution of micro-cracks was uniform. With a designated orientation of 0 degrees -90 degrees -180 degrees -270 degrees indicating lateral-anterior-medial-posterior anatomic directions, the overall distribution of cracks was not uniform (p<0.05) with a mean crack direction in the postero-medial (249 degrees) quadrant of the mantle. The crack angular distribution for proximal (postero-medial; 251 degrees) and distal (antero-medial; 112 degrees) regions of the cement mantle was also different (p<0.025). These findings suggest that the location of cement damage depends on anatomic position and appears to correspond with the tensile stress field in the cement mantle.     

Plant fiber intrusive growth characterized by NMR method

Intrusively growing plant cells insert themselves between surrounding cells, thus increasing the number of membranes on the tissue cross-section. This parameter can be assessed by spin echo NMR method with a magnetic field pulse gradient. Diffusion echo decay was measured for stem regions of long-fiber flax (Linum usitatissimum L.) differing in the stages of primary fiber development, which elongate thousand-fold during intrusive growth. Additionally, the number of fibers on stem cross-sections was counted under microscope. An increase in the slow component of the echo diffusion decay was correlated with an increase in the number of fibers on the stem cross-section in the zone of intrusive growth, while other stem-structure characteristics remained unchanged. Thus, NMR method can be used for characterization of intrusive fiber growth in situ.