Primary stability of a cementless acetabular cup in a cohort of patient-specific finite element models

Virtual biomechanical assessment of porous tantalum and custom triflange components in the treatment of patients with acetabular defects and pelvic discontinuity

Aims

The aim of this study was to compare the biomechanical models of two frequently used techniques for reconstructing severe acetabular defects with pelvic discontinuity in revision total hip arthroplasty (THA) - the Trabecular Metal Acetabular Revision System (TMARS) and custom triflange acetabular components (CTACs) - using virtual modelling.

Methods

Pre- and postoperative CT scans from ten patients who underwent revision with the TMARS for a Paprosky IIIB acetabular defect with pelvic discontinuity were retrospectively collated. Computer models of a CTAC implant were designed from the preoperative CT scans of these patients. Computer models of the TMARS reconstruction were segmented from postoperative CT scans using a semi-automated method. The amount of bone removed, the implant-bone apposition that was achieved, and the restoration of the centre of rotation of the hip were compared between all the actual TMARS and the virtual CTAC implants.

Results

The median amount of bone removed for TMARS reconstructions was significantly greater than for CTAC implants (9.07 cm3 (interquartile range (IQR) 5.86 to 21.42) vs 1.16 cm3 (IQR 0.42 to 3.53) (p = 0.004). There was no significant difference between the median overall implant-bone apposition between TMARS reconstructions and CTAC implants (54.8 cm2 (IQR 28.2 to 82.3) vs 56.6 cm2 (IQR 40.6 to 69.7) (p = 0.683). However, there was significantly more implant-bone apposition within the residual acetabulum (45.2 cm2 (IQR 28.2 to 72.4) vs 25.5 cm2 (IQR 12.8 to 44.1) (p = 0.001) and conversely significantly less apposition with the outer cortex of the pelvis for TMARS implants compared with CTAC reconstructions (0 cm2 (IQR 0 to 13.1) vs 23.2 cm2 (IQR 16.4 to 30.6) (p = 0.009). The mean centre of rotation of the hip of TMARS reconstructions differed by a mean of 11.1 mm (3 to 28) compared with CTAC implants.

Conclusion

In using TMARS, more bone is removed, thus achieving more implant-bone apposition within the residual acetabular bone. In CTAC implants, the amount of bone removed is minimal, while the implant-bone apposition is more evenly distributed between the residual acetabulum and the outer cortex of the pelvis. The differences suggest that these implants used to treat pelvic discontinuity might achieve short- and long-term stability through different biomechanical mechanisms.

Corroboration of coupled musculoskeletal model and finite element predictions with in vivo RSA migration of an uncemented acetabular component

While finite element (FE) models have been used extensively in orthopedic studies, validation of their outcome metrics has been limited to comparison against ex vivo testing. The aim of this study was to validate FE model predictions of the initial cup mechanical environment against patient-matched in vivo measurements of acetabular cup migration using radiostereometric analysis (RSA). Tailored musculoskeletal and FE models were developed using a combination of three-dimensional (3D) motion capture data and clinical computerized tomography (CT) scans for a cohort of eight individuals who underwent primary total hip replacement and were prospectively enrolled in an RSA study. FE models were developed to calculate the mean modulus of cancellous bone, composite peak micromotion (CPM), composite peak strain (CPS) and percentage area of bone ingrowth. The RSA cup migration at 3 months was used to corroborate the FE output metrics. Qualitatively, all FE-predicted metrics followed a similar rank order as the in vivo RSA 3D migration data. The two cases with the lowest predicted CPM (<20 µm), lowest CPS (<0.0041), and high bone modulus (>917 MPa) were confirmed to have the lowest in vivo RSA 3D migration (<0.14 mm). The two cases with the largest predicted CPM (>80 µm), larger CPS (>0.0119) and lowest bone modulus (<472 MPa) were confirmed to have the largest in vivo RSA 3D migration (>0.78 mm). This study enabled the first corroboration between tailored musculoskeletal and FE model predictions with in vivo RSA cup migration. Investigation of additional patient-matched CT, gait, and RSA examinations may allow further development and validation of FE models.

Identifying the patient harms to include in an in silico clinical trial

BACKGROUND AND OBJECTIVE

Clinical trials represent a crucial step in the development and approval of medical devices. These trials involve evaluating the safety and efficacy of the device in a controlled setting with human subjects. However, traditional clinical trials can be expensive, time-consuming, and ethically challenging. Augmenting clinical trials with data from computer simulations, so called in silico clinical trials (ISCT), has the potential to address these challenges while satisfying regulatory requirements. However, determination of the patient harms in scope of an ISCT is necessary to ensure all harms are sufficiently addressed while maximizing the utility of the ISCT. This topic is currently lacking guidance. The objective of this work is to propose a general method to determine which patient harms should be included in an ISCT for a regulatory submission.

METHODS

The proposed method considers the risk associated with the harm, the impact of the device on the likelihood of occurrence of the harm and the technical feasibility of evaluating the harm via ISCT. Consideration of the risk associated with the harm provides maximum clinical impact of the ISCT, in terms of focusing on those failure modes which are most relevant to the patient population. Consideration of the impact of the device on a particular harm, and the technical feasibility of modeling a particular harm supports that the technical effort is devoted to a problem that (1) is relevant to the device in question, and (2) can be solved with contemporary modeling techniques.

RESULTS AND CONCLUSIONS

As a case study, the proposed method is applied to a total shoulder replacement humeral system. With this framework, it is hoped that a consistent approach to scoping an ISCT can be adopted, supporting investment in ISCT by the industry, enabling consistent review of the ISCT approach across device disciplines by regulators, and providing maximum impact of modeling technologies in support of devices to improve patient outcomes.

A finite element study on the interactive effect between the damage of the cup-bone interface and the bone strain of hip implants under various fixation conditions

Interfacial damage has a high impact on the loosening of the acetabular cup. However, monitoring this damage induced by the variations in loading conditions, such as the angle, amplitude, and frequency in vivo, is challenging. In this study, we evaluated the risk of loosening of the acetabular cup due to interfacial damages induced by the deviation in loading conditions and amplitudes. A three-dimensional model of the acetabular cup component was developed, and the interfacial crack growth between the cup and the bone was modeled using a fracture mechanics approach, which simulated the extent of interfacial damage and associated cup displacement. The interfacial delamination mechanism changed with the increasing inclination angle, wherein a fixation angle of 60° exhibited the largest area of contact loss. The compressive strain of embedding the simulated bone at the remaining bonding area accumulated as the lost contact area widened. Such interfacial damages, namely, the growth of the lost contact area and accumulated compressive strain in the simulated bone, promoted both embedding and rotational displacement of the acetabular cup. In the worst case of a fixation angle of 60°, the total displacement of the acetabular cup exceeded the limit of the modified safe zone, suggesting a quantitative risk of dislocation of the acetabular cup induced by the accumulated interfacial damage. Furthermore, nonlinear regression analyses between the degree of displacement of the acetabular cup and the extent of the two types of interfacial damage demonstrated that the interactive effect of the fixation angle with the loading amplitude showed a significant effect on increasing cup displacement. These findings suggest that proper control of the fixation angle during operation is useful in preventing the loosening of the hip joint.

Design of a functionally graded porous uncemented acetabular component: Influence of polar gradation

The functionally graded porous metal-backed (FGPMB) acetabular component has the potential to minimize strain-shielding induced bone resorption, caused by stiffness mismatch of implant and host bone. This study is aimed at a novel design of FGPMB acetabular component, which is based on numerical investigations of the mechanical behavior of acetabular components with regard to common failure scenarios, considering various daily activities and implant-bone interface conditions. Both radial and polar functional gradations were implemented, and the effects of the polar gradation exponent on the failure criteria were evaluated. The relationships between porosity and orthotropic mechanical properties of a tetrahedron-based unit cell were obtained using a numerical homogenization method. Strain-shielding in cancellous bone was relatively lesser for the FGPMB than solid metal-backing. Few nodes around the rim were susceptible to implant-bone interfacial debonding, irrespective of the polar gradation exponent. Although the most favorable bone remodeling predictions were obtained for a polar gradation exponent of 0.1, a sudden change in the porosity was observed near the rim of FGPMB. Bone remodeling patterns were similar for polar gradation exponent of 5.0 and solid metal-backing. Moreover, the volumetric wear was maximum and minimum for polar gradation exponents of 0.1 and 5, respectively. Furthermore, the micromotions of different polar gradation exponents were within a range (20-40 μm) that might facilitate bone ingrowth. Considering common failure mechanisms, the FGPMB having polar gradation exponents in the range of 0.1-0.5 appeared to be a viable alternative to the solid acetabular component, within which a gradation exponent of 0.25 seemed the most appropriate design parameter.

The role of muscle forces and gait cycle discretization when assessing acetabular cup primary stability: A finite element study

The aim of this study was to investigate the influence of the muscle force contribution and loading cycle discretization on the predicted micromotion and interfacial bone strains in the implanted acetabulum. To this end, a patient specific finite element model of the hemipelvis was developed, based on the CT-scan and gait analysis results, collected as part of the authors' previous work. Outcomes of this study suggests that the acetabular cup micromotion and interfacial bone strains can be predicted just using the joint contact force. This helps to reduce the complexity of the finite element models by ignoring the contribution of muscle forces and the associated challenges of mapping these forces to the pelvis. However, the gait cycle needs to be adequately discretised to capture the micromotion at the bone-implant interface.

BACKGROUND AND OBJECTIVE

The Dalstra load case, which includes muscle forces, has been widely adopted in the literature for studying the mechanical environment in the intact and implanted acetabulum. To simplify the modelling approach, some researchers ignore the contribution of muscle forces. The Dalstra load case is also divided into eight separate load steps (five in the stance phase and three in the swing phase), however, it is unclear whether this adequately captures the micromotions, for a cementless acetabular cup, during a simulated activity. The aim of this study was to investigate the influence of the muscle force contribution and loading cycle discretization on the predicted micromotion and interfacial bone strains.

METHODS

In this work, a patient specific finite element model of the hemipelvis was developed, based on the CT-scan and gait analysis results, collected as part of the authors' previous work. Finite element simulations were performed using the joint contact and muscle forces derived from two sources. The first approach was used the load case proposed by Dalstra et al. The second approach used joint contact and muscle forces predicted by a musculoskeletal model. Additionally, the musculoskeletal load case was discretised into 50 equal load steps and the results compared with the equivalent Dalstra load steps.

RESULTS

The results showed that the contribution of the muscle forces resulted in minor differences in both the magnitude and distribution of the predicted acetabular micromotion (up to 4.01% in the mean acetabular micromotion) and interfacial bone strains (up to 10.34% in the mean interfacial bone strains). The degree of gait cycle discretisation had a significant influence on the acetabular micromotion with a difference of 20.89% in the mean acetabular micromotion.

CONCLUSION

Outcomes of this study suggests that the acetabular cup micromotion and interfacial bone strains can be predicted just using the joint contact force. This helps to reduce the complexity of the finite element models by ignoring the contribution of muscle forces and the associated challenges of mapping these forces to the pelvis. However, the gait cycle needs to be adequately discretised to capture the micromotion at the bone-implant interface.

Finite element analysis of coronoid prostheses with different fixation methods in the treatment of comminuted coronoid process fracture

BACKGROUND

Comminuted fractures of the coronoid process significantly compromise the stability and function of the elbow joint. Reconstruction of the coronoid process with a prosthesis has been suggested as an alternative to restore the architecture. The purpose of this study was to investigate the strength and stability of various methods for the fixation of a coronoid prosthesis by finite element analysis.

MATERIALS AND METHODS

A coronoid prosthesis was designed based on the morphological information from computed tomography images acquired from 64 subjects in whom the top 40% of the coronoid process height was replaced. Four methods for the fixation of the prosthesis were suggested: (1) a double 2.0-mm fixation bolt, anterior to posterior; (2) a double 2.5-mm fixation bolt, anterior to posterior; (3) a single 4.0-mm fixation bolt, posterior to anterior; (4) a single 4.5-mm fixation bolt, posterior to anterior. The integrated prosthesis-bone constructs were analyzed via the finite element analysis of 10 simulated proximal ulna models with loading applied along the axis of the humerus and with three different elbow flexion angles (30°, 90°, and 130°). The maximum principal stress and the total deformation were quantified and compared.

RESULTS

A coronoid prosthesis was developed. The maximum principal stress of the fixation bolts occurred around the neck of the fixation bolt. For a comparison of the strengths of the four fixation methods, the maximum principal stress was the lowest for fixation using a single 4.5-mm fixation bolt. The value of the maximum principal stress significantly decreased with increased elbow flexion angle for all fixation methods. The maximum deformation of the fixation bolts occurred at the head of the fixation bolt. For a comparison of the maximum deformations in the four fixation methods, the maximum deformation was the lowest for fixation using a single 4.5-mm fixation bolt. The value of the maximum deformation significantly decreased with increased elbow flexion angle for all fixation methods.

CONCLUSIONS

The present study suggested that fixation of a coronoid prosthesis with a single 4.5-mm fixation bolt from posterior to anterior is an excellent option in terms of the strength and stability. Level of Evidence Experimental study.

Assigning trabecular bone material properties in finite element models simulating the pelvis before and after the development of peri-prosthetic osteolytic lesions

Estimating strain distribution in the acetabulum before and after the development of peri-prosthetic osteolytic lesions secondary to total hip arthroplasty may assist with understanding the pathogenesis of this condition. This could be achieved by performing patient-specific finite element analysis of (1) total hip arthroplasty recipients with developed acetabular osteolytic lesions, and (2) models simulating the patient's pelvis and implant immediately after primary surgery. State of the art patient-specific total hip arthroplasty finite element analysis simulations obtain trabecular bone material properties from Hounsfield units within computed tomography (CT) scans of patients. However, this is not feasible when an implant is already in situ due to metal artefact disruption and, in turn, incorrectly reproduced Hounsfield units. Therefore, alternative methods of assigning trabecular bone material properties within such models were tested and strain results compared. It was found that assigning set material properties throughout the trabecular bone geometry was sufficient for the desired application. Simulating the primary implant and pelvis requires geometric and material based assumptions. Therefore, comparisons were made between strain values obtained from simulated primary models, from state of the art methods using material properties obtained from intact bone within a CT scan, and from models with osteolytic lesions. Strain values found using the finite element models simulating the pelvis before osteolytic lesion developed were considerably closer to those found using state of the art methods than those found for the bone loss models. These models could be used to determine relationships between strain distribution and factors such as bone loss.

Primary stability of the Activ L® intervertebral disc prosthesis in cadaver bone and comparison of the keel and spike anchoring concept

Background

High primary stability is the key prerequisite for safe osseointegration of cementless intervertebral disc prostheses. The aim of our study was to determine the primary stability of intervertebral disc prostheses with two different anchoring concepts – keel and spike anchoring.

Methods

Ten ActivL intervertebral disc prostheses (5 x keel anchoring, 5 x spike anchoring) implanted in human cadaver lumbar spine specimens were tested in a spine movement simulator. Axial load flexion, extension, left and right bending and axial rotation motions were applied on the lumbar spine specimens through a defined three-dimensional movement program following ISO 2631 and ISO/CD 18192-1.3 standards. Tri-dimensional micromotions of the implants were measured for both anchor types and compared using Student’s T-test for significance after calculating 95 % confidence intervals.

Results

In the transverse axis, the keel anchoring concept showed statistically significant (p < 0.05) lower mean values of micromotions compared to the spike anchoring concept. The highest micromotion values for both types were observed in the longitudinal axis. In no case the threshold of 200 micrometers was exceeded.

Conclusions

Both fixation systems fulfill the required criteria of primary stability. Independent of the selected anchorage type an immediate postoperative active mobilization doesn’t compromise the stability of the prostheses.

Stress shielding at the bone-implant interface: Influence of surface roughness and of the bone-implant contact ratio

Short and long-term stabilities of cementless implants are strongly determined by the interfacial load transfer between implants and bone tissue. Stress-shielding effects arise from shear stresses due to the difference of material properties between bone and the implant. It remains difficult to measure the stress field in periprosthetic bone tissue. This study proposes to investigate the dependence of the stress field in periprosthetic bone tissue on (i) the implant surface roughness, (ii) the material properties of bone and of the implant, (iii) the bone-implant contact ratio. To do so, a microscale two-dimensional finite element model of an osseointegrated bone-implant interface was developed where the surface roughness was modeled by a sinusoidal surface. The results show that the isostatic pressure is not affected by the presence of the bone-implant interface while shear stresses arise due to the combined effects of a geometrical singularity (for low surface roughness) and of shear stresses at the bone-implant interface (for high surface roughness). Stress-shielding effects are likely to be more important when the bone-implant contact ratio value is low, which corresponds to a case of relatively low implant stability. Shear stress reach a maximum value at a distance from the interface comprised between 0 and 0.1 time roughness wavelength λ and tend to 0 at a distance from the implant surface higher than λ, independently from bone-implant contact ratio and waviness ratio. A comparison with an analytical model allows validating the numerical results. Future work should use the present approach to model osseointegration phenomena.

Risk assessment of resurfacing implant loosening and femur fracture under low-energy impacts taking into account degenerative changes in bone tissues. Computer simulation

BACKGROUND AND OBJECTIVE

Degenerative diseases of the musculoskeletal system significantly reduce the quality of human life. Hip resurfacing is used to treat degenerative diseases in the later stages. After surgery, there is a risk of endoprosthesis loosening and low-energy fracture during daily physical activity. Computer modeling is a promising way to predict the optimal low-energy loads that do not lead to bone destruction. This paper aims to study numerically the mechanical behavior of the proximal femur, amenable to degenerative changes and subjected to hip resurfacing under low-energy impact equivalent to physiological loads.

METHODS

A numerical model of the mechanical behavior of the femur after hip resurfacing arthroplasty under low-energy impacts equivalent to physiological loads is presented. The model is based on the movable cellular automaton method (discrete elements), where the mechanical behavior of bone tissue is described using the Biot poroelasticity accounting for the presence and transfer of interstitial biological fluid.

RESULTS

For the first time, it is shown that a poroelastic model allows predicting the service life of endoprostheses, taking into account the individual characteristics of the bone tissues amenable to various degenerative diseases. The obtained results indicate that the changes in the bone properties have a significant influence on the critical forces corresponding to the first appearance of microcracks and the fracture formation. At the same time, their effect on the type of fracture is negligible. A much more impact on the type of fracture has the kinematic and dynamic conditions of the exposure.

CONCLUSIONS

The obtained results show the promise of using the proposed model for predicting the operational resource of resurfacing endoprostheses, taking into account the physiological features of the structure of the patient's bone tissues.

Vitamin E-blended highly cross-linked polyethylene liners in total hip arthroplasty: a randomized, multicenter trial using virtual CAD-based wear analysis at 5-year follow-up

BACKGROUND

Progressive oxidation of highly cross-linked ultra-high molecular weight (UHMPWE-X) liners is considered to be a risk factor for material failure in THA. Antioxidants such as vitamin E (alpha-tocopherol) (UHMWPE-XE) were supplemented into the latest generation of polyethylene liners. To prevent inhomogenous vitamin E distribution within the polymer, blending was established as an alternative manufacturing process to diffusion. The purpose of the present study was to investigate the in vivo wear behavior of UHMWPE-XE in comparison with conventional UHMWPE-X liners using virtual CAD-based radiographs.

METHODS

Until now, 94 patients from a prospective, randomized, controlled, multicenter study were reviewed at 5-year follow-up. Of these, 51 (54%) received UHMWPE-XE and 43 (46%) UHMWPE-X liners. Anteroposterior pelvic radiographs were made immediately after surgery and at 1 and 5 years postoperatively. The radiographs were analyzed using the observer-independent analysis software RayMatch^® (Raylytic GmbH, Leipzig, Germany).

RESULTS

The mean wear rate was measured to be 23.6 μm/year (SD 13.7; range 0.7-71.8 μm). There were no significant differences between the two cohorts (UHMWPE-X: 23.2 μm/year vs. UHMWPE-XE: 24.0 μm/year, p = 0.73). Cup anteversion significantly changed within the 1st year after implantation independent from the type of polyethylene liner [UHMWPE-X: 18.2-23.9° (p = 0.0001); UHMWPE-XE: 21.0-25.5° (p = 0.002)]. No further significant changes of cup anteversion in both groups were found between year 1 and 5 after implantation [UHMWPE-X (p = 0.46); UHMWPE-XE (p = 0.56)].

CONCLUSION

The present study demonstrates that the addition of vitamin E does not adversely affect the midterm wear behavior of UHMWPE-X. The antioxidative benefit of vitamin E is expected to become evident in long-term follow-up. Cup anteversion increment by 5° within the 1st year is likely a result of the released hip flexion contracture resulting in an enhanced posterior pelvic tilt. Therefore, a reassessment of target values in acetabular cup placement might be considered.

Patient and surgical variability in the primary stability of cementless acetabular cups: A finite element study

Aseptic loosening is the most common indication for revision of cementless acetabular cups and often depends on the primary stability achieved following surgery. Cup designs must be capable of achieving primary stability for a wide variety of individuals and surgical conditions to be successful. Typically, preclinical finite element (FE) testing of cups involves assessing the performance in a single patient and under a limited set of idealized conditions. The aim of this study was to assess the effect of patient and surgical parameters on the primary stability of an acetabular cup design in a set of subject-specific FE models. Interference fit was varied in a representative set of 12 patient-specific models of the implanted hemipelvis. Linear mixed models showed a significant association with micromotion for interference fit (P < .0001), acetabular bone elastic modulus (P < .001), native acetabular diameter (P  = .03), and the interference fit-elastic modulus interaction (P = .01). There were no significant associations between the polar gap and any of the parameters considered. The significant interference fit-elastic modulus interaction suggests that increasing the interference fit in patients with low bone quality leads to a greater reduction in micromotion than in patients with higher bone quality. However, the significant association between percentage bone yielding and interference fit (P < .0001) suggests a higher periacetabular fracture risk at higher interference fits. This work supports the development of preclinical testing of cup designs for the broad range patients and surgical conditions a cup may face following surgery.

Incorporation of screwless press-fit acetabular cups and disappearance of polar gaps

BACKGROUND

Uncemented press-fit acetabular cups without screws rely on the elastic recoil of the bone for its primary stability and tend to leave polar gaps with its use. The clinical significance of these gaps and the functional outcome of the patients with polar gaps is evaluated in this study.

METHODS

This comparative analysis was done on 224 cementless primary THA using Deltamotion® Hip System from January 2010 to December 2017. Patients were divided into two groups based on the presence or absence of polar gaps on immediate post-operative radiographs. Patients were observed for their clinical, radiological and functional outcomes with regular follow ups. At each follow-up, patients' clinical outcome was evaluated using the Harris Hip Score (HHS) and Patient Reported Outcome Measures (PROMs).

RESULTS

14 of 224 patients(6.25%) demonstrated polar gaps in their immediate post-operative radiographs. No statistically significant difference was noted in the final mean HHS between the two groups. The polar gaps ranged from 0.5 to 1.8 mm (mean-1.09 mm). None of the patients showed progression of the polar gaps. All patients showed bony ingrowth into the gaps at a mean of 8.57 months.

CONCLUSION

The presence of polar gaps in the immediate post-operative radiographs are not of a major clinical significance provided a secure peripheral fit is achieved intra-operatively. The functional outcome and rehabilitation in such patients is at par with that seen in the patients without polar gaps. Disappearance of these polar gaps is a rule rather than an exception.

Micromechanical modeling of the contact stiffness of an osseointegrated bone-implant interface

Background

The surgical success of cementless implants is determined by the evolution of the biomechanical properties of the bone–implant interface (BII). One difficulty to model the biomechanical behavior of the BII comes from the implant surface roughness and from the partial contact between bone tissue and the implant. The determination of the constitutive law of the BII would be of interest in the context of implant finite element (FE) modeling to take into account the imperfect characteristics of the BII. The aim of the present study is to determine an effective contact stiffness \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\left( {K_{c}^{\text{FEM}} } \right)$$\end{document}KcFEM of an osseointegrated BII accounting for its micromechanical features such as surface roughness, bone–implant contact ratio (BIC) and periprosthetic bone properties. To do so, a 2D FE model of the BII under normal contact conditions was developed and was used to determine the behavior of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$K_{c}^{\text{FEM}}$$\end{document}KcFEM.

Results

The model is validated by comparison with three analytical schemes based on micromechanical homogenization including two Lekesiz’s models (considering interacting and non-interacting micro-cracks) and a Kachanov’s model. \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$K_{c}^{\text{FEM}}$$\end{document}KcFEM is found to be comprised between 10¹³ and 10¹⁵ N/m³ according to the properties of the BII. \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$K_{c}^{\text{FEM}}$$\end{document}KcFEM is shown to increase nonlinearly as a function of the BIC and to decrease as a function of the roughness amplitude for high BIC values (above around 20%). Moreover, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$K_{c}^{\text{FEM}}$$\end{document}KcFEM decreases as a function of the roughness wavelength and increases linearly as a function of the Young’s modulus of periprosthetic bone tissue.

Conclusions

These results open new paths in implant biomechanical modeling since this model may be used in future macroscopic finite element models modeling the bone–implant system to replace perfectly rigid BII conditions.

Sampling strategies for approximating patient variability in population-based finite element studies of total hip replacement

Total hip replacements must be robust to patient variability for long-term success in the population. The challenge during the design process is evaluating an implant in a diverse population but the computational cost of simulating a population of subject-specific finite element (FE) models is not practical. We examined five strategies to generate representative subsets of subjects from a cohort of 103 implanted hip joint FE models to approximate the variability in output metrics. Comparing with the median and distribution of the 95^th percentile composite peak micromotion (CPM) and polar gap in the full cohort (CPM median: 136 μm, interquartile range [IQR]: 74-230 μm) (Polar Gap median: 467 μm, IQR: 434-548 μm), the Anatomic Sampling strategy (12 subjects) achieved the best balance of computational cost and approximation of the output metrics (CPM median: 169 μm, IQR: 78-236 μm) (Polar Gap median: 469 μm, IQR: 448-537 μm). Convex hull sampling (41 subjects) more closely captured the output metrics (CPM median: 99 μm, IQR: 70-191 μm) (Polar Gap median: 456 μm, IQR: 418-533 μm) but required over three times the number of subjects. Volume reduction of the convex hull captured the extremes of variability with subsets of 5 to 20 subjects, while the largest minimum-distance strategy captured the variability toward the middle of the cohort. These strategies can estimate the level of variability in FE model output metrics with a low computational cost when evaluating implants during the design process.