M.T. Bah

Mesh morphing for finite element analysis of implant positioning in cementless total hip replacements

Finite element (FE) analysis of the effect of implant positioning on the performance of cementless total hip replacements (THRs) requires the generation of multiple meshes to account for positioning variability. This process can be labour intensive and time consuming as CAD operations are needed each time a specific orientation is to be analysed. In the present work, a mesh morphing technique is developed to automate the model generation process. The volume mesh of a baseline femur with the implant in a nominal position is deformed as the prosthesis location is varied. A virtual deformation field, obtained by solving a linear elasticity problem with appropriate boundary conditions, is applied. The effectiveness of the technique is evaluated using two metrics: the percentages of morphed elements exceeding an aspect ratio of 20 and an angle of 165 degrees between the adjacent edges of each tetrahedron. Results show that for 100 different implant positions, the first and second metrics never exceed 3% and 3.5%, respectively. To further validate the proposed technique, FE contact analyses are conducted using three selected morphed models to predict the strain distribution in the bone and the implant micromotion under joint and muscle loading. The entire bone strain distribution is well captured and both percentages of bone volume with strain exceeding 0.7% and bone average strains are accurately computed. The results generated from the morphed mesh models correlate well with those for models generated from scratch, increasing confidence in the methodology. This morphing technique forms an accurate and efficient basis for FE based implant orientation and stability analysis of cementless hip replacements.

Efficient computational method for assessing the effects of implant positioning in cementless total hip replacements

The present work describes a statistical investigation into the effects of implant positioning on the initial stability of a cementless total hip replacement (THR). Mesh morphing was combined with design of computer experiments to automatically construct Finite Element (FE) meshes for a range of pre-defined femur-implant configurations and to predict implant micromotions under joint contact and muscle loading. Computed micromotions, in turn, are postprocessed using a Bayesian approach to: (a) compute the main effects of implant orientation angles, (b) predict the sensitivities of the considered implant performance metrics with respect to implant ante-retroversion, varus-valgus and antero-posterior orientation angles and (c) identify implant positions that maximise and minimise each metric. It is found that the percentage of implant area with micromotion greater than 50 μm, average and maximum micromotions are all more sensitive to antero-posterior orientation than ante-retroversion and varus-valgus orientation. Sensitivities, combined with the main effect results, suggest that bone is less likely to grow if the implant is increasingly moved from the neutral position towards the anterior part of the femur, where the highest micromotions occur. The computed implant best position leads to a percentage of implant area with micromotion greater than 50 μm of 1.14 when using this metric compared to 14.6 and 5.95 in the worst and neutrally positioned implant cases. In contrast, when the implant average/maximum micromotion is used to assess the THR performance, the implant best position corresponds to average/maximum micromotion of 9 μm/59 μm, compared to 20 μm/114 μm and 13 μm/71 μm in the worst and neutral positions, respectively. The proposed computational framework can be extended further to study the effects of uncertainty and variability in anatomy, bone mechanical properties, loading or bone-implant interface contact conditions.

Effect of geometrical uncertainty on cemented hip implant structural integrity

A large number of parameters such as material properties, geometry, and structural strength are involved in the design and analysis of cemented hip implants. Uncertainties in these parameters have a potential to compromise the structural performance and lifetime of implants. Statistical analyses are well suited to investigating this type of problem as they can estimate the influence of these uncertainties on the incidence of failure. Recent investigations have focused on the effect of uncertainty in cement properties and loading condition on the integrity of the construct. The present study hypothesizes that geometrical uncertainties will play a role in cement mantle failure. Finite element input parameters were simulated as random variables and different modes of failure were investigated using a response surface method (RSM). The magnitude of random von Mises stresses varied up to 8 MPa, compared with a maximum nominal value of 2.38 MPa. Results obtained using RSM are shown to match well with a benchmark direct Monte Carlo simulation method. The resulting probability that the maximum cement stress will exceed the nominal stress is 62%. The load and the bone and prosthesis geometries were found to be the parameters most likely to influence the magnitude of the cement stresses and therefore to contribute most to the probability of failure.

Forced response statistics of mistuned bladed disks: a stochastic reduced basis approach

This paper presents a stochastic reduced basis approach for predicting the forced response statistics of mistuned bladed-disk assemblies. In this approach, the system response in the frequency domain is represented using a linear combination of complex stochastic basis vectors with undermined coefficients. The terms of the preconditioned stochastic Krylov subspace are used here as basis vectors. Two variants of the stochastic Bubnov–Galerkin scheme are employed for computing the undetermined terms in the reduced basis representation, which arise from how the condition for orthogonality between two random vectors is interpreted. Explicit expressions for the response quantities can then be derived in terms of the random system parameters, which allow for the possibility of efficiently computing the response statistics in the post-processing stage. Numerical studies are presented for mistuned cyclic assemblies of mono-coupled single-mode components. It is demonstrated that the accuracy of the response statistical moments computed using stochastic reduced basis methods can be orders of magnitude better than classical perturbation methods.

Inter-subject variability effects on the primary stability of a short cementless femoral stem

This paper is concerned with the primary stability of the Furlong Evolution(®) cementless short stem across a spectrum of patient morphology. A computational tool is developed that automatically selects and positions the most suitable stem from an implant system made of a total of 48 collarless stems to best match a 3D model based on a library of CT femur scans (75 males and 34 females). Finite Element contact models of reconstructed hips, subjected to physiologically-based boundary constraints and peak loads of walking mode, were simulated using a coefficient of friction of 0.4 and an interference-fit of 50 μm. Maximum and average implant micromotions across the subpopulation were predicted to be 100±7 μm and 7±5 μm with ranges [15 μm, 350 μm] and [1 μm, 25 μm], respectively. The computed percentage of implant area with micromotions greater than reported critical values of 50 μm, 100 μm and 150 μm never exceeded 14%, 8% and 7%, respectively. To explore the possible correlations between anatomy and implant performance, response surface models for micromotion metrics were constructed. Detailed morphological analyses were conducted and a clear nonlinear decreasing trend was observed between implant average micromotion and both the metaphyseal canal flare indices and average densities in Gruen zones. The present study demonstrates that the primary stability and tolerance of the short stem to variability in patient anatomy were high, reducing the need for patient stratification. In addition, the developed tool could be utilised to support implant design and planning of femoral reconstructive surgery.

Statistical analysis of the forced response of mistuned bladed disks using stochastic reduced basis methods

This paper is concerned with the forced response statistics of mistuned bladed disk assemblies subjected to a deterministic sinusoidal excitation. A stochastic reduced basis method (SRBM) is used to compute the statistics of the system component amplitudes. In this approach, the system response in the frequency domain is represented using a linear combination of stochastic basis vectors with undermined coefficients. The three terms of the second-order perturbation approximation (which span the stochastic Krylov subspace) are used as basis vectors and the undetermined coefficients are evaluated using stochastic variants of the Bubnov- Galerkin Scheme. This results in explicit expressions for the response quantities in terms of the random system parameters. The statistics of the system response can hence be efficiently computed in the post-processing stage. Numerical results are presented for a model problem to demonstrate that the stochastic reduced basis formulation gives highly accurate results for the response statistical moments.

Femur Bone Segmentation Using a Pressure Analogy

It has been recently shown that preclinical analysis of computed tomography 3D image volumes can provide essential information to find the optimal position of an implant in hip replacement procedures. In order to extract such data, proper segmentation is crucial. Many of the currently-available methods depend on manually segmented data as the first step. Inherent difficulties concern the similar density of adjacent structures, and that physically-separated structures appear to touch in scanned imagery. In this study, we describe a new technique based on pressure analogy that depends on the local features of the image to accurately and automatically segment and visualize the femur bone and separate it from the acetabulum. The Dice coefficient was employed to study the similarity between the surface area of the segmentations compared with the manually segmented data, and a high value has been achieved. The same method also showed promising results in segmenting other limbs such as the pelvis, tibia and fibula bones.

Stochastic component mode synthesis

In this paper, a stochastic component mode synthesis method is developed for the dynamic analysis of large-scale structures with parameter uncertainties. The main idea is to represent each component displacement using a subspace spanned by a set of stochastic basis vectors in the same fashion as in stochastic reduced basis methods [1, 2]. These vectors represent however stochastic modes in contrast to the deterministic modes used in conventional substructuring methods [3]. The Craig-Bampton reduction procedure is used for illustration. A truncated set of stochastic fixed-free modes and a complete set of stochastic constraint modes are used to generate reduced matrices for each component. These are then coupled together through necessary compatibility constraints to form the global system matrices. The advantage of using stochastic component modes is that the Bubnov-Galerkin scheme can be applied for the computation of undetermined coefficients in the reduced approximation. Explicit expressions can be obtained for the responses in terms of the random parameters. Therefore the statistical moments of responses can be efficiently computed. The method is applied to a test case problem. Results obtained are compared with the traditional Craig-Bampton method, the first-order Taylor series and Monte Carlo Simulation benchmark results. We will refer to the proposed method as ROBUST or Reduced Order By Using Stochastic Techniques.

Effects of implant positioning in cementless total hip replacements

Cementless Total Hip Replacements (THRs) are required to approximate as closely as possible the natural joint function for the full postoperative life span. Unfortunately, implant positioning is not always perfect due to the curved shape of the thigh bone and the stem is often straight [1]. Surgeons need to decide on three orientation angles that directly influence the success of a cementless THR: the antero/retro version of the femur neck orientation, implant varus/valgus placement and anterior/posterior orientation. Ideally, to account for positioning variability, all possible implant orientations should be analysed and simulated. Unfortunately, this would be an intractable task if it was attempted experimentally, and computational simulations are often applied to reduce this burden. However, even in computational pre-clinical assessments of implant primary stability, this is a huge task, as it involves generating a new mesh for each new position and solving the corresponding Finite Element (FE) problem [2]. In the current work, this problem is addressed using a mesh morphing-based framework that can efficiently assess the effects of implant positioning.

Microembossing of ultrafine grained Al: microstructural analysis and finite element modelling

Ultra-fine-grained (UFG) Al-1050 processed by equal channel angular pressing and UFG Al–Mg–Cu–Mn processed by high-pressure torsion (HPT) were embossed at both room temperature and 300 ?C, with the aim of producing micro-channels. The behaviour of Al alloys during the embossing process was analysed using finite element modelling. The cold embossing of both Al alloys is characterized by a partial pattern transfer, a large embossing force, channels with oblique sidewalls and a large failure rate of the mould. The hot embossing is characterized by straight channel sidewalls, fully transferred patterns and reduced loads which decrease the failure rate of the mould. Hot embossing of UFG Al–Mg–Cu–Mn produced by HPT shows a potential of fabrication of microelectromechanical system components with micro channels.