Finite Element Analysis of Tibial Implants — Effect of Fixation Design and Friction Model

Abstract

A three dimensional nonlinear finite element model was developed to investigate tibial fixation designs and friction models (Coulomb's vs nonlinear) in total knee arthroplasty in the immediate postoperative period with no biological attachment. Bi-directional measurement-based nonlinear friction constitutive equations were used for the bone-porous coated implant interface. Friction properties between the polyethylene and femoral components were measured for this study. Linear elastic isotropic but heterogeneous mechanical properties taken from literature were considered for the bone. The Tensile behaviour of polyethylene was measured and subsequently modeled by an elasto-plastic model. Based on the earlier finite element and experimental pull-out studies, pegs and screws were also realistically modeled. The geometry of every component was obtained through measurement. The PCA tibial baseplate with three different configurations was considered; one with three screws, one with one screw and two short inclined porous-coated pegs, and a third one with no fixation for the sake of comparison. The axial load of 2000N was applied through the femoral component on the medial plateau of articular insert. It was found that Coulomb's friction significantly underestimates the relative micromotion at the bone-implant interface. The lowest micromotion and lift-off were found for the design with screws. Relative micromotion and stress transfer at the bone-implant interface depended significantly on the friction model and on the baseplate anchorage configuration. Cortical and cancellous bones carried, respectively, 10–13% and 65–86% of the axial load depending on the fixation configuration used. The remaining portion was transmitted as shear force by screws and pegs. Normal and Mises stresses as well as contact area in the polyethylene insert were nearly independent of the baseplate fixation design. The Maximum Mises stress in the polyethylene exceeded yield and was found 1–2 mm below the contact surface for all designs.     

Quantifying the competing relationship between adduction range of motion and baseplate micromotion with lateralization of reverse total shoulder arthroplasty

Lateralizing the center of rotation (COR) of reverse total shoulder arthroplasty (rTSA) could improve functional outcomes and mitigate scapular notching, a commonly occurring complication of the procedure. However, resulting increases in torque at the bone-implant interface may negatively affect initial fixation of the glenoid-side component, especially if only two fixation screws can be placed. Shoulder-specific finite element (FE) models of four fresh-frozen cadaveric shoulders were constructed. Scapular geometry and material property distributions were derived from CT data. Generic baseplates with two and four fixation screws were virtually implanted, after which superiorly-oriented shear loads, accompanied by a compressive load, were applied incrementally further from the glenoid surface to simulate lateralization of the COR. Relationships between lateralization, adduction range of motion (ROM), the number of fixation screws and micromotion of the baseplate (initial implant fixation) were characterized. Lateralization significantly increases micromotion (p=0.015) and adduction ROM (p=0.001). Using two, versus four, baseplate fixation screws significantly increases micromotion (p=0.008). The effect of lateralization and the number of screws on adduction ROM and baseplate fixation is variable on a shoulder-specific basis. Trade-offs exist between functional outcomes, namely adduction ROM, and initial implant fixation and the negative effect of lateralization on implant fixation is amplified when only two fixation screws are used. The possibility of lateralizing the COR in order to improve functional outcomes of the procedure should be considered on a patient-specific basis accounting for factors such as availability and quality of bone stock.     

Analysis of bone–prosthesis interface micromotion for cementless tibial prosthesis fixation and the influence of loading conditions

A lack of initial stability of the fixation is associated with aseptic loosening of the tibial components of cementless knee prostheses. With sufficient stability after surgery, minimal relative motion between the prosthesis and bone interfaces allows osseointegation to occur thereby providing a strong prosthesis-to-bone biological attachment. Finite element modelling was used to investigate the bone–prosthesis interface micromotion and the relative risk of aseptic loosening. It was anticipated that by prescribing different joint loads representing gait and other activities, and the consideration of varying tibial–femoral contact points during knee flexion, it would influence the computational prediction of the interface micromotion. In this study, three-dimensional finite element models were set up with applied loads representing walking and stair climbing, and the relative micromotions were predicted. These results were correlated to in-vitro measurements and to the results of prior retrieval studies. Two load conditions, (i) a generic vertical joint load of 3×body weight with 70%/30% M/L load share and antero-posterior/medial-lateral shear forces, acted at the centres of the medial and lateral compartments of the tibial tray, and (ii) a peak vertical joint load at 25% of the stair climbing cycle with corresponding antero-posterior shear force applied at the tibial–femoral contact points of the specific knee flexion angle, were found to generate interface micromotion responses which corresponded to in-vivo observations. The study also found that different loads altered the interface micromotion predicted, so caution is needed when comparing the fixation performance of various reported cementless tibial prosthetic designs if each design was evaluated with a different loading condition.     

Experimental and finite element comparison of various fixation designs in combined loads

The short- and long-term successes of tibial cementless implants depend on the initial fixation stability often provided by posts and screws. In this work, a metallic plate was fixed to a polyurethane block with either two bone screws, two smooth-surfaced posts, or two novel smooth-surfaced posts with adjustable inclinations. For this last case, inclinations of 0, 1.5, and 3 deg were considered following insertion. A load of 1031 N was eccentrically applied on the plate at an angle of approximately 14 deg, which resulted in a 1000 N axial compressive force and a 250 N shear force. The response was measured under static and repetitive loading up to 4000 cycles at 1 Hz. The measured results demonstrate subsidence under load, lift-off on the unloaded side, and horizontal translation of the plate specially at the loaded side. Fatigue loading increased the displacements, primarily during the first 100 cycles. Comparison of various fixation systems indicated that the plate with screw fixation was the stiffest with the least subsidence and liftoff. The increase in post inclination from 0 to 3 deg stiffened the plate by diminishing the liftoff. All fixation systems demonstrated deterioration under repetitive loads. In general, the finite element predictions of the experimental fixation systems were in agreement with measurements. The finite element analyses showed that porous coated posts (modeled with nonlinear interface friction with and without coupling) generated slightly less resistance to liftoff than smooth-surfaced posts. In the presence of porous coated posts, Coulomb friction greatly overestimated the rigidity by reducing the liftoff and subsidence to levels even smaller than those predicted for the design with screw fixation. The sequence of combined load application also influenced the predicted response. Finally, the finite element model incorporating measured interface friction and pull-out responses can be used for the analysis of cementless total joint replacement systems during the post-operation period.     

Material and surface factors influencing backside fretting wear in total knee replacement tibial components

Retrieval studies have shown that the interface between the ultra-high molecular weight polyethylene insert and metal tibial tray of fixed-bearing total knee replacement components can be a source of substantial amounts of wear debris due to fretting micromotion. We assessed fretting wear of polyethylene against metal as a function of metal surface finish, alloy, and micromotion amplitude, using a three-station pin-on-disc fretting wear simulator. Overall, the greatest reduction in polyethylene wear was achieved by highly polishing the metal surface. For example, highly polished titanium alloy surfaces produced nearly 20 times less polyethylene wear compared with blasted titanium alloy, whereas, decreasing the micromotion amplitude from 200 to 50 μm produced approximately four times less polyethylene wear for the same blasted titanium alloy surface. Although the effect of the metal alloy was much smaller than the effect of metal surface roughness or the micromotion amplitude, CoCr discs produced slightly greater polyethylene fretting wear than titanium alloy discs under each condition. The results are essential in design and manufacturing decisions related to fixed-bearing total knee replacements.     

Limited rotation of the mobile-bearing in a rotating platform total knee prosthesis

The hypothesis of this study was that the polyethylene bearing in a rotating platform total knee prosthesis shows axial rotation during a step-up motion, thereby facilitating the theoretical advantages of mobile-bearing knee prostheses. We examined 10 patients with rheumatoid arthritis who had a rotating platform total knee arthroplasty (NexGen LPS mobile, Zimmer Inc. Warsaw, USA). Fluoroscopic data was collected during a step-up motion six months postoperatively. A 3D-2D model fitting technique was used to reconstruct the in vivo 3D kinematics. The femoral component showed more axial rotation than the polyethylene mobile-bearing insert compared to the tibia during extension. In eight knees, the femoral component rotated internally with respect to the tibia during extension. In the other two knees the femoral component rotated externally with respect to the tibia. In all 10 patients, the femur showed more axial rotation than the mobile-bearing insert indicating the femoral component was sliding on the polyethylene of the rotating platform during the step-up motion. Possible explanations are a too limited conformity between femoral component and insert, the anterior located pivot location of the investigated rotating platform design, polyethylene on metal impingement and fibrous tissue formation between the mobile-bearing insert and the tibial plateau.     

The conflicting requirements of laxity and conformity in total knee replacement

Bearing surfaces of total condylar knees which are designed with a high degree of conformity to produce low stresses in the polyethylene tibial insert may be overconstrained. This study determines femoral and tibial bearing surface geometries which will induce the least destructive fatigue mechanisms in the polyethylene whilst conserving the laxity of the natural knee. Sixteen knee designs were generated by varying four parameters systematically to cover the range of contemporary knee designs. The parameters were the femoral frontal radius (30 or 70 mm), the difference between the femoral and tibial frontal radii (2 or 10 mm), the tibial sagittal radius (56 or 80 mm) and the posterior-distal transition angle (-8 or -20 degrees), which is the angle at which the small posterior arc of the sagittal profile transfers to the larger distal arc. Rigid body analyses determined the anterior-posterior and rotational motions as well as the contact points during the stance phase of gait for the different designs. In addition, a damage function which accumulated the fluctuating maximum shear stresses was used to predict the susceptibility to delamination wear of the polyethylene (damage score). This study predicted that of the 16 designs, the knee with a frontal radius of 70 mm, a difference in femoral and tibial frontal radii of 2 mm, a tibial sagittal radius of 80 mm and a posterior distal transition angle of -20 degrees would satisfy the conflicting needs of both resistance to delamination wear and natural kinematics.     

Epiphyseal-based designs for tibial plateau components--I. Stress analysis in the frontal plane

Two-dimensional, finite element studies were conducted of the proximal tibia before and after joint arthroplasty. Equivalent-thickness models projected onto the mid-frontal plane were created for the natural, proximal tibia and for the proximal tibia with four different types of tibial plateau components. All components simulated bony ingrowth fixation, i.e. no cement layer existed between component and bone. In addition, the interface between component and bone was assumed to be intimately connected, representing complete bony ingrowth and a rigid state of fixation. Loads consisted of bi-condylar and uni-condylar forces. Results indicated that conventional plateau designs with central posts or multiple pegs led to higher stress magnitudes in the trabecular bone near the distal ends of the post/pegs and stress shielding at more proximal locations. A design without posts or pegs whose interface geometry mimics the epiphyseal plate minimizes bone stress shielding. An implant consisting of separate components covering each condyle was found effective in limiting component tilting and the consequent tensile stresses caused by non-symmetrical, uni-condylar loading.     

Finite Element Analysis of Minimal Invasive Transforaminal Lumbar Interbody Fusion

The purpose of our study is to develop and validate three-dimensional finite element models of transforaminal lumbar interbody fusion, and explore the most appropriate method of fixation and fusion by comparing biomechanical characteristics of different fixation method. We developed four fusion models: bilateral pedicle screws fixation with a single cage insertion model (A), bilateral pedicle screws fixation with two cages insertion model (B), unilateral pedicle screws fixation with a single cage insertion model (C), and unilateral pedicle screws fixation with two cages insertion model (D); the models were subjected to different forces including anterior bending, posterior extension, left bending, right bending, rotation, and axial compressive. The von Mises stress of the fusion segments on the pedicle screw and cages was recorded. Angular variation and stress of pedicle screw and cage were compared. There were differences of Von Mises peak stress among four models, but were within the range of maximum force. The angular variation in A, B, C, and D decreased significantly compared with normal. There was no significant difference of angular variation between A and B, and C and D. Bilateral pedicle screws fixation had more superior biomechanics than unilateral pedicle screws fixation. In conclusion, the lumbar interbody fusion models were established using varying fixation methods, and the results verified that unilateral pedicle screws fixation with a single cage could meet the stability demand in minimal invasive transforaminal interbody fusion.     

A finite element model for evaluation of tibial prosthesis-bone interface in total knee replacement

A numerical model based on the finite element method was developed for the load transfer analysis at the tibial bone-implant interfaces in total knee replacement. A transverse isotropic material model, based on a quadratic elastic potential and on Hill's quadratic yield criterion, was next developed for bone constitutive laws. The bone-cement and bone-prosthesis interfaces were both assumed to be discontinuous. A dry friction model based on Coulomb's criterion was adopted for the interfaces friction. The model was shown to be able to give compressive and shear stresses distributions and distractive and relative shear micromotions at these interfaces. A preliminary application was conducted for cemented metal tray total condylar (MTTC) and for cemented and uncemented porous coated anatomic (PCA) tibial plateaus. The PCA plateaus were found to be more deformable and had greater global displacements than the MTTC one. Debonding of the bone-peg interface was observed for the uncemented PCA. Correspondingly, the stress peaks at the interface beneath the tray were lower for the PCA than for the MTTC. Shear micromotions appeared under the tray for both the two prostheses. We observed that bone anisotropy and interface discontinuity affected the results sensibly.     

Finite element modelling of primary hip stem stability: the effect of interference fit

The most commonly reported complications related to cementless hip stems are loosening and thigh pain; both of these have been attributed to high levels of relative micromotion at the bone-implant interface due to insufficient primary fixation. Primary fixation is believed by many to rely on achieving a sufficient interference fit between the implant and the bone. However, attempting to achieve a high interference fit not infrequently leads to femoral canal fracture either intra-operatively or soon after. The appropriate range of diametrical interference fit that ensures primary stability without risking femoral fracture is not well understood. In this study, a finite element model was constructed to predict micromotion and, therefore, instability of femoral stems. The model was correlated with an in vitro micromotion experiment carried out on four cadaver femurs. It was confirmed that interference fit has a very significant effect on micromotion and ignoring this parameter in an analysis of primary stability is likely to underestimate the stability of the stem. Furthermore, it was predicted that the optimal level of interference fit is around 50 microm as this is sufficient to achieve good primary fixation while having a safety factor of 2 against femoral canal fracture. This result is of clinical relevance as it indicates a recommendation for the surgeon to err on the side of a low interference fit rather than risking femoral fracture.     

Biomechanical comparison of locking plate and crossing metallic and absorbable screws fixations for intra-articular calcaneal fractures

The locking plate and percutaneous crossing metallic screws and crossing absorbable screws have been used clinically to treat intra-articular calcaneal fractures, but little is known about the biomechanical differences between them. This study compared the biomechanical stability of calcaneal fractures fixed using a locking plate and crossing screws. Three-dimensional finite-element models of intact and fractured calcanei were developed based on the CT images of a cadaveric sample. Surgeries were simulated on models of Sanders type III calcaneal fractures to produce accurate postoperative models fixed by the three implants. A vertical force was applied to the superior surface of the subtalar joint to simulate the stance phase of a walking gait. This model was validated by an in vitro experiment using the same calcaneal sample. The intact calcaneus showed greater stiffness than the fixation models. Of the three fixations, the locking plate produced the greatest stiffness and the highest von Mises stress peak. The micromotion of the fracture fixated with the locking plate was similar to that of the fracture fixated with the metallic screws but smaller than that fixated with the absorbable screws. Fixation with both plate and crossing screws can be used to treat intra-articular calcaneal fractures. In general, fixation with crossing metallic screws is preferable because it provides sufficient stability with less stress shielding.     

Evaluation of Functional and Biomechanical Properties of Bone Regenerates

Functional tests with incrementing axial load on the affected limb were performed in patients with humerus, tibia and fibula fractures, or undergoing tibial bone lengthening using the Ilizarov apparatus (n = 75). It was found that oossification was associated with a decrease in the blood flow velocity in the arteries of the bone regenerate. In the humerus, the exercise tolerance was two to three times lower, while the micromotion rate of bone fragments and the blood flow velocity were higher. The micromotion rate and the blood flow velocity decreased by the end of the fixation period, since they were no longer affected by the incrementing load.     

A Biomechanical Comparison of Expansive Pedicle Screws for Severe Osteoporosis: The Effects of Screw Design and Cement Augmentation

Expansive pedicle screws significantly improve fixation strength in osteoporotic spines. However, the previous literature does not adequately address the effects of the number of lengthwise slits and the extent of screw expansion on the strength of the bone/screw interface when expansive screws are used with or without cement augmentation. Herein, four designs for expansive pedicle screws with different numbers of lengthwise slits and different screw expansion levels were evaluated. Synthetic bones simulating severe osteoporosis were used to provide a comparative platform for each screw design. The prepared specimens were then tested for axial pullout failure. Regardless of screw design, screws with cement augmentation demonstrated significantly higher pullout strength than pedicle screws without cement augmentation (p < 0.001). For screws without cement augmentation, solid screws exhibited the lowest pullout strength compared to the four expansive groups (p < 0.01). No significant differences in pullout strength were observed between the expansive screws with different designs (p > 0.05). Taken together, our results show that pedicle screws combined with cement augmentation may greatly increase screw fixation regardless of screws with or without expansion. An increase in both the number of slits and the extent of screw expansion had little impact on the screw-anchoring strength. Cement augmentation is the most influential factor for improving screw pullout strength.     

Influence of the stiffness of bone defect implants on the mechanical conditions at the interface--a finite element analysis with contact

The study focused on the influence of the implant material stiffness on stress distribution and micromotion at the interface of bone defect implants. We hypothesized that a low-stiffness implant with a modulus closer to that of the surrounding trabecular bone would yield a more homogeneous stress distribution and less micromotion at the interface with the bony bed. To prove this hypothesis we generated a three-dimensional, non-linear, anisotropic finite element (FE) model. The FE model corresponded to a previously developed animal model in sheep. A prismatic implant filled a standardized defect in the load-bearing area of the trabecular bone beneath the tibial plateau. The interface was described by face-to-face contact elements, which allow press fits, friction, sliding, and gapping. We assumed a physiological load condition and calculated contact pressures, shear stresses, and shear movements at the interface for two implants of different stiffness (titanium: E=110GPa; composite: E=2.2GPa). The FE model showed that the stress distribution was more homogeneous for the low-stiffness implant. The maximum pressure for the composite implant (2.1 MPa) was lower than for the titanium implant (5.6 MPa). Contrary to our hypothesis, we found more micromotion for the composite (up to 6 microm) than for the titanium implant (up to 4.5 microm). However, for both implants peak stresses and micromotion were in a range that predicts adequate conditions for the osseointegration. This was confirmed by the histological results from the animal studies.     

Study of micromotion in modular acetabular components during gait and subluxation: a finite element investigation

Polyethylene wear after total hip arthroplasty may occur as a result of normal gait and as a result of subluxation and relocation with impact. Relocation of a subluxed hip may impart a moment to the cup creating sliding as well as compression at the cup liner interface. The purpose of the current study is to quantify, by a validated finite element model, the forces generated in a hip arthroplasty as a result of subluxation relocation and compare them to the forces generated during normal gait. The micromotion between the liner and acetabular shell was quantified by computing the sliding track and the deformation at several points of the interface. A finite element analysis of polyethylene liner stress and liner/cup micromotion in total hip arthroplasty was performed under two dynamic profiles. The first profile was a gait loading profile simulating the force vectors developed in the hip arthroplasty during normal gait. The second profile is generated during subluxation and subsequent relocation of the femoral head. The forces generated by subluxation relocation of a total hip arthroplasty can exceed those forces generated during normal gait. The induced micromotion at the cup polyethylene interface as a result of subluxation can exceed micromotion as a result of the normal gait cycle. This may play a significant role in the generation of backsided wear. Minimizing joint subluxation by restoring balance to the hip joint after arthroplasty should be explored as a strategy to minimize backsided wear.     

Application of Novel Design Bone Grafting for Treatment of Segmental Acetabular Rim Defects During Revision Total Hip Arthroplasty

The study aimed to develop efficient techniques with different novel graft structures to enhance the treatment of acetabular bone deficiency.The inhomogeneous material properties Finite Element Analysis(FEA)model was reconstructed according to computed tomography images based on a healthy patient without any peri-acetabular bony defect according to the Ameri-can Academy of Orthopedic Surgeons(AAOS).The FEA model of acetabular bone deficiency was performed to simulate and evaluate the mechanical performances of the grafts in different geometric structures,with the use of fixation implants(screws),along with the stress distribution and the relative micromotion of graft models.The stress distribution mainly con-centrated on the region of contact of the screws and superolateral bone.Among the different structures,the mortise-tenone structure provided better relative micromotion,with suitable biomechanical property even without the use of screws.The novel grafting structures could provide sufficient biomechanical stability and bone remodeling,and the mortise-tenone structure is the optimal treatment option for acetabulum reconstruction.     

Can markers injected into a single-loop anterior cruciate ligament graft define the axes of the tibial and femoral tunnels? A cadaveric study using roentgen stereophotogrammetric analysis

Lengthening of a soft-tissue anterior cruciate ligament (ACL) graft construct over time, which leads to an increase in anterior laxity following ACL reconstruction, can result from relative motions between the graft and fixation devices and between the fixation devices and bone. To determine these relative motions using Roentgen stereophotogrammetry (RSA), it is first necessary to identify the axes of the tibial and femoral tunnels. The purpose of this in vitro study was to determine the error in using markers injected into the portions of a soft-tissue tendon graft enclosed within the tibial and femoral tunnels to define the axes of these tunnels. Markers were injected into the tibia, femur, and graft in six cadaveric legs the knees of which were reconstructed with single-loop tibialis grafts. The axes of the tunnels were defined by marker pairs that were injected into the bones on lines parallel to the walls of the tibial and femoral tunnels (i.e., standard). By using marker pairs injected into the portions of the graft enclosed within the tibial and femoral tunnels and the marker pairs aligned with the tunnel axes, the directions of vectors were determined by using RSA, while a 150 N anterior force was transmitted at the knee. The average and standard deviations of the angle between the two vectors were 5.5+/-3.3 deg. This angle translates into an average error and standard deviation of the error in lengthening quantities (i.e., relative motions along the tunnel axes) at the sites of fixation of (0.6+/-0.8)%. Identifying the axes of the tunnels by using marker pairs in the graft rather than marker pairs in the walls of the tunnels will shorten the surgical procedure by eliminating the specialized tools and time required to insert marker pairs in the tunnel walls and will simplify the data analysis in in vivo studies.     

Cortical bone viscoelasticity and fixation strength of press-fit femoral stems: finite element model

Many cementless implant designs rely upon a diaphyseal press-fit in conjunction with a porous coated implant surface to achieve primary or short term fixation, thereby constraining interface micromotion to such a level that bone ingrowth and consequent secondary or long-term fixation, i.e., osseointegration, can occur. Bone viscoelasticity, however, has been found to affect stem primary stability by reducing push-out load. In this investigation, an axisymmetric finite element model of a cylindrical stem and diaphyseal cortical bone section was created in order to parametrically evaluate the effect of bone viscoelasticity on stem push-out while controlling coefficient of friction (mu = 0.15, 0.40, and 1.00) and stem-bone diametral interference (delta = 0.01, 0.05, 0.10, and 0.50 mm). Based on results from a previous study, it was hypothesized that stem-bone interference (i.e., press-fit) would elicit a bone viscoelastic response which would reduce the initial fixation of the stem as measured by push-out load. Results indicate that for all examined combinations of mu and delta, bone viscoelastic behavior reduced the push-out load by a range of 2.6-82.6% due to stress relaxation of the bone. It was found that the push-out load increased with mu for each value of delta, but minimal increases in the push-out load (2.9-4.9%) were observed as delta was increased beyond 0.10 mm. Within the range of variables reported for this study, it was concluded that bone viscoelastic behavior, namely stress relaxation, has an asymptotic affect on stem contact pressure, which reduces stem push-out load. It was also found that higher levels of coefficient of friction are beneficial to primary fixation, and that an interference "threshold" exists beyond which no additional gains in push-out load are achieved.     

Development and Physical Validation of a Finite Element Model of Total Hip Dislocation

Component-on-component impingement, followed by levering of the femoral head, is a common mode of dislocation in total hip arthroplasty. While there have been many registry-based studies of dislocation incidence, confounding factors and sources of variability in the clinical domain make it difficult to identify specific parameter influences. A three dimensional nonlinear finite element model has been developed for the purpose of studying the dislocation event, to allow determination of how individual factors such as component design and clinical implantation position affect the propensity for dislocation. Also, a laboratory testing apparatus was constructed to provide physical validation of the computational model. The finite element model correctly predicted the range of motion observed in the physical apparatus to within 1%, and predicted the peak resisting moment to within 2.5%. Under even a light joint load of 200 N, the von Mises stresses developed in the polyethylene insert reached 13 MPa, and the contact stresses rose to as high as 30 MPa. These deleterious elevations occurred not only at the site of neck impingement, but also at the site of head egress from the liner.