The effect of three-dimensional shape optimization on the probabilistic response of a cemented femoral hip prosthesis

Probabilistic analyses allow the effect of uncertainty in system parameters on predicted model performance measures to be determined. Furthermore, using performance functions to describe a failure event, the probability of failure can be quantified. The effect of three-dimensional prosthesis shape optimization on the probabilistic response and failure probability of a cemented hip prosthesis system is investigated. Random variables include joint and muscle loading, cortical and cancellous bone and PMMA bone cement elastic properties, and strength parameters describing failure of the bone cement and the prosthesis-bone cement interface. Several performance functions describing the bone cement and prosthesis-cement interface are used to compute the probability of failure. When evaluated deterministically, most performance functions indicated a safe design, with the exception of interface tensile failure. However, when evaluated probabilistically, finite probabilities of failure were computed, some significant. The most likely mode of failure before shape optimization was prosthesis-bone cement interface tensile failure with a predicted probability of failure of 97.9%. Deterministic prosthesis shape optimization reduced the probability of failure for all performance functions and reduced prosthesis-bone cement interface tensile failure by 31.7%. Probability sensitivity factors indicate that the uncertainty in the joint loading, cement strength, and implant-cement interface strength have the greatest effect on the computed probability of failure. Implant shape optimization results in a more robust implant design that is less sensitive to uncertainties in joint loading, which cannot be easily controlled, and more sensitive to cement and interface properties, which are easier to modify.     

Development of a statistical shape-function model of the implanted knee for real-time prediction of joint mechanics

Outcomes of total knee arthroplasty (TKA) are dependent on surgical technique, patient variability, and implant design. Non-optimal design or alignment choices may result in undesirable contact mechanics and joint kinematics, including poor joint alignment, instability, and reduced range of motion. Implant design and surgical alignment are modifiable factors with potential to improve patient outcomes, and there is a need for robust implant designs that can accommodate patient variability. Our objective was to develop a statistical shape-function model (SFM) of a posterior stabilized implanted knee to instantaneously predict joint mechanics in an efficient manner. Finite element methods were combined with Latin hypercube sampling and regression analyses to produce modeling equations relating nine implant design and six surgical alignment parameters to tibiofemoral (TF) joint mechanics outcomes during a deep knee bend. A SFM was developed and TF contact mechanics, kinematics, and soft tissue loads were instantaneously predicted from the model. Average normalized root-mean-square error predictions were between 2.79% and 9.42%, depending on the number of parameters included in the model. The statistical shape-function model generated instantaneous joint mechanics predictions using a maximum of 130 training simulations, making it ideally suited for integration into a patient-specific design and alignment optimization pipeline. Such a tool may be used to optimize kinematic function to achieve more natural motion or minimize implant wear, and may aid the engineering and clinical communities in improving patient satisfaction and surgical outcomes.     

Shape optimization of a cementless hip stem for a minimum of interface stress and displacement

The primary stem stability is an essential factor for success of cementless hip stems. A correct choice of the stem geometry can improve the stem stability and, consequently, increase the life time of a hip implant. In this work, it is proposed a computational model for shape optimization of cementless hip stems. The optimization problem is formulated by the minimization of relative displacement and stress on bone/stem interface using a multi-criteria objective function. Also multiple loads are considered to incorporate several daily life activities. Design variables are parameters that characterize the geometry of selected cross sections, which are subject to geometric constraints to ensure a clinically admissible shape. The stem/bone set is considered a structure in equilibrium with contact conditions on interface. The contact formulation allows us to analyze different lengths of porous coating. The optimization problem is solved numerically by a steepest descent method. The interface stress and relative displacement are obtained solving the contact problem by the finite element method. Numerical examples are presented for a two-dimensional model of a hip stem, however, the formulation is general and can be applied to the three-dimensional case. The model gives indications about the relation between shape, porous coating and prosthesis stability.     

Shape Optimization of a Cementless Hip Stem for a Minimum of Interface Stress and Displacement

The primary stem stability is an essential factor for success of cementless hip stems. A correct choice of the stem geometry can improve the stem stability and, consequently, increase the life time of a hip implant. In this work, it is proposed a computational model for shape optimization of cementless hip stems. The optimization problem is formulated by the minimization of relative displacement and stress on bone/stem interface using a multi-criteria objective function. Also multiple loads are considered to incorporate several daily life activities. Design variables are parameters that characterize the geometry of selected cross sections, which are subject to geometric constraints to ensure a clinically admissible shape. The stem/bone set is considered a structure in equilibrium with contact conditions on interface. The contact formulation allows us to analyze different lengths of porous coating. The optimization problem is solved numerically by a steepest descent method. The interface stress and relative displacement are obtained solving the contact problem by the finite element method. Numerical examples are presented for a two-dimensional model of a hip stem, however, the formulation is general and can be applied to the three-dimensional case. The model gives indications about the relation between shape, porous coating and prosthesis stability.     

Design optimization of a total knee replacement for improved constraint and flexion kinematics

Total knee replacement (TKR) constraint and flexion range of motion can be limiting factors in terms of kinematics performance and cause for revision. These characteristics are closely related to the shape of the implant components. No previous studies have used a rigorous and systematic design optimization method to determine the optimal shape of TKR components. Previous studies have failed to define a quantifiable objective function for optimization, have not used any optimization algorithms, and have only considered a limited design space (4 or less design variables). This study addresses these limitations and determines the optimum shape of the femoral component and ultra high molecular weight polyethylene (UHMWPE) insert in terms of kinematics. The constraint characteristics with respect to those of the natural knee, the importance of the posterior cruciate ligament, and the flexion range of motion were all considered. The kinematics optimized design featured small femoral radii of curvature in the frontal and sagittal planes, but asymmetric with slightly larger radii of curvature for the lateral condyle. This condyle was also less conforming than the medial side. Compared to a commercially available TKR design, the kinematics performance (based on constraint and flexion range of motion) was improved by 81%, with constraint characteristics generally closer to those of the natural knee and a 12.6% increase in the flexion range of motion (up to 143°). The results yielded a new TKR design while demonstrating the feasibility of design optimization in TKR design.     

On the optimal shape of hip implants

The success of a total hip arthroplasty is strongly related to the initial stability of the femoral component and to the stress shielding effect. In fact, for cementless stems, initial stability is essential to promote bone ingrowth into the stem coating. An inefficient primary stability is also a cause of thigh pain. In addition, the bone adaptation after the surgery can lead to an excessive bone loss and, consequently, can compromise the success of the implant. These factors depend on prosthesis design, namely on material, interface conditions and shape. Although, surgeons use stems with very different geometries, new computational tools using structural optimization methods have been used to achieve a better design in order to improve initial stability and therefore, the implant durability. In this work, a multi-criteria shape optimization process is developed to study the relationship between implants performance and geometry. The multi-criteria objective function takes into account the initial stability of the femoral stem and the effect of stress shielding on bone adaptation after the surgery. Then, the optimized stems are tested using a concurrent model for bone remodeling and osseointegration to evaluate long-term performance. Additionally, the sensitivity to misalignments is analyzed, since femoral stems are often placed in varus or valgus position. Results show that the different criteria are contradictory resulting in different characteristics for the hip stem. However, the multi-criteria formulation leads to compromise solutions, with a combination of the geometric characteristics obtained for each criterion separately.     

Hexahedral modular bioreactor for solid state bioprocesses

The design of a modular bioreactor for solid state fermentation is a promising development because it keeps the homogeneity of the bed at optimal levels. This study determines the optimum geometry of elementary modules of hexahedral bioreactors subjected to constant volume. The bioreactors have a square section and do not need an external cooling system, because the optimization limits the temperature of the bed to 35°C. The geometric optimization followed the Constructal principle of minimum heat resistance. The numerical simulations take into account the following parameters: inlet air temperature and velocity, and module volume. Once the elementary module has been selected, the total volume of the bioreactor can be calculated.     

Three-dimensional computer-aided design based design sensitivity analysis and shape optimization of the stem using adaptive p-method

The number of stem designs for total hip arthroplasty is increasing, and occasionally design changes have yielded unexpected clinical results. At present, we are not able to clearly identify which parameter of the stem is most important, and the optimum value of many parameters. The goals of this study were to identify which parameter is most important, to understand the effect of design change, and to find the optimum stem shape. For this purpose, we used adaptive p-method together with three-dimensional computer-aided design software program for the design sensitivity analysis (DSA) and shape optimization of the stem. The results suggested that increasing the lateral and medial width of the distal cross-section together with decreasing the medial-lateral width and the medial radius of the distal cross-section from the default value would lead to a decrease in the largest maximum principal stress of the distal cement. The medial width of middle cross-section, however, was not so simple. The result of DSA suggested that decreasing this parameter from the default value decreased the stress in the distal cement, but the optimum shape was obtained by increasing this parameter. The method used in this study will assist our engineers and surgeons in the process of modifying and optimizing the stem design.     

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.     

Combined probabilistic and principal component analysis approach for multivariate sensitivity evaluation and application to implanted patellofemoral mechanics

Many aspects of biomechanics are variable in nature, including patient geometry, joint mechanics, implant alignment and clinical outcomes. Probabilistic methods have been applied in computational models to predict distributions of performance given uncertain or variable parameters. Sensitivity analysis is commonly used in conjunction with probabilistic methods to identify the parameters that most significantly affect the performance outcome; however, it does not consider coupled relationships for multiple output measures. Principal component analysis (PCA) has been applied to characterize common modes of variation in shape and kinematics. In this study, a novel, combined probabilistic and PCA approach was developed to characterize relationships between multiple input parameters and output measures. To demonstrate the benefits of the approach, it was applied to implanted patellofemoral (PF) mechanics to characterize relationships between femoral and patellar component alignment and loading and the resulting joint mechanics. Prior studies assessing PF sensitivity have performed individual perturbation of alignment parameters. However, the probabilistic and PCA approach enabled a more holistic evaluation of sensitivity, including identification of combinations of alignment parameters that most significantly contributed to kinematic and contact mechanics outcomes throughout the flexion cycle, and the predictive capability to estimate joint mechanics based on alignment conditions without requiring additional analysis. The approach showed comparable results for Monte Carlo sampling with 500 trials and the more efficient Latin Hypercube sampling with 50 trials. The probabilistic and PCA approach has broad applicability to biomechanical analysis and can provide insight into the interdependencies between implant design, alignment and the resulting mechanics.     

Method for the evaluation of factors influencing the dislocation stability of total hip endoprotheses]

Dislocation of the artificial joint is a serious complication of total hip replacement. Various factors with an influence on dislocation stability were determined clinically. Our goal was to develop a method for evaluating experimentally the parameters implant design, position and the load situation for their influence on joint stability. With the newly developed testing device the range of motion to impingement and to dislocation can be determined at different implant positions. In addition, the rotational moments on subluxation, i.e. the "levering out" of the femoral head, can be determined. By way of example several hip implants were examined during movements associated with dislocation, e.g. (internal-)rotation in 90 degrees flexion and 0 degrees adduction as well as with (external-)rotation in combination with 10 degrees extension and 15 degrees adduction. Irrespective of implant design and position, the following movement phases can be differentiated: undisturbed motion, impingement, subluxation and, finally, complete dislocation of the head. On the basis of the range of motion of the specific phases, the moments occurring and the direction of dislocation, different implant systems can be compared. In this study the influence of the head diameter on the dislocation stability of the hip endoprosthesis is shown. With the aid of the model presented herein, a data set showing the most favourable and/or most dislocation stable implant position can be acquired for different combinations of the implant components. Additionally, useful information for implant design can be deduced and applied to new developments and/or modifications of existing implant components.     

Shape optimization in steady blood flow: a numerical study of non-Newtonian effects

We investigate the influence of the fluid constitutive model on the outcome of shape optimization tasks, motivated by optimal design problems in biomedical engineering. Our computations are based on the Navier-Stokes equations generalized to non-Newtonian fluid, with the modified Cross model employed to account for the shear-thinning behavior of blood. The generalized Newtonian treatment exhibits striking differences in the velocity field for smaller shear rates. We apply sensitivity-based optimization procedure to a flow through an idealized arterial graft. For this problem we study the influence of the inflow velocity, and thus the shear rate. Furthermore, we introduce an additional factor in the form of a geometric parameter, and study its effect on the optimal shape obtained.     

Quantifying the competing relationship between durability and kinematics of total knee replacements using multiobjective design optimization and validated computational models

Durability and kinematics are two critical factors which must be considered during total knee replacement (TKR) implant design. It is hypothesized, however, that there exists a competing relationship between these two performance measures, such that improvement of one requires sacrifice with respect to the other. No previous studies have used rigorous and systematic methods to quantify this relationship. During this study, multiobjective design optimization (MOO) using the adaptive weighted sum (AWS) method is used to determine a set of Pareto-optimal implant designs considering durability and kinematics simultaneously. Previously validated numerical simulations and a parametric modeller are used in conjunction with the AWS method in order to generate a durability-versus-kinematics Pareto curve. In terms of kinematics, a design optimized for kinematics alone outperformed a design optimized for durability by 61.8%. In terms of durability, the design optimized for durability outperformed the kinematics-optimized design by 70.6%. Considering the entire Pareto curve, a balanced (1:1) trade-off could be obtained when equal weighting was placed on both performance measures; however improvement of one performance measure required greater sacrifices with respect to the other when the weighting was extremized. For the first time, the competing relationship between durability and kinematics was confirmed and quantified using optimization methods. This information can aid future developments in TKR design and can be expanded to other total joint replacement designs.     

Three-dimensional design optimisation of patient-specific femoral plates as a means of bone remodelling reduction

Previous investigations into the optimisation of internal plates have mostly focused on the material properties of the implant. In this work, we optimise the shape, size and placement of the plate for successfully minimising bone remodelling around the implant. A design optimisation algorithm based on strain energy density criterion, combined with the finite element analysis, has been used in this study. The main optimisation goal was to reduce this change and keep it close to the conditions of an intact femur. The results suggest that the anterolateral side of the bone would be the optimum location for the plate, as for the geometry, the optimum moves towards having a thick, wide and short plate. These important results could be directly applicable to orthopaedic surgeons treating a femur fracture with internal plates. Since the optimisation algorithm remains the same for any patient, this advancement provides the surgeon with a tool to minimise the post surgery remodelling by trying to maintain the natural structure of the bone.     

Finite element analysis of a cemented ceramic femoral component for the assembly situation in total knee arthroplasty]

The femoral components of the total knee replacements are generally made of metal. In contrast, ceramic femoral components promise improved tribological and allergological properties. However, ceramic components present a risk of failure as a result of stress peaks. Stress peaks can be minimised through adequate implant design, proper material composition and optimum force transmission between bone and implant. Thus, the quality of the implant fixation is a crucial factor. The objective of the present study was to analyse the influence of the cement layer thickness on stress states in the ceramic femoral component and in the femur. Two- and three- dimensional finite element analyses of an artificial knee joint with cement layers of different thickness and with an unbalanced cement layer thickness between the ceramic femoral component and the femur were performed. Higher stress regions occurred in the area of force transmission and in the median plane. The maximum calculated stresses were below the accepted tensile strength. Stresses were found to be lower for cement layer thickness of <2.0 mm.     

Periprosthetic bone remodelling of a collum femoris preserving cementless titanium femoral hip replacement

Total hip arthroplasty represents a major surgical achievement for pain relief and restoration of lifestyle quality due to the joint disease of osteoarthritis. Total hip replacement has evolved over the past 30 years utilising a variety of biocompatible materials, geometric shapes and fixation techniques. The main objective of this study is to investigate the long-term effects of strain adaptive bone remodelling due to the influence of a novel titanium cementless femoral hip replacement. The period of on-growth has been taken into account and the simulation has been run to predict the remodelling behaviour for a 36-month period. The main conclusion from this analysis is that the implant does shield the calcar to a similar degree as other cementless femoral hip designs. It does, however, tend to cause bone to be laid down along its length. This may, in part, be due to the novel geometry of the implant interlocking with and loading the bone.     

Forward dynamic optimization of handle path and muscle activity for handle based isokinetic wheelchair propulsion: A simulation study

Push-rim wheelchair propulsion is biomechanically inefficient and physiologically stressful to the musculoskeletal structure of human body. This study focuses to obtain a new, optimized propulsion shape for wheelchair users, which is within the ergonomic ranges of joint motion, thus reducing the probability of injuries. To identify the propulsion movement, forward dynamic optimization was performed on a 3D human musculoskeletal model linked to a handle based propulsion mechanism, having shape and muscle excitations as optimization variables. The optimization resulted in a handle path shape with a circularity ratio of 0.95, and produced a net propulsion power of 34.7 watts for an isokinetic propulsion cycle at 50?rpm. Compared to push-rim propulsion, the compact design of the new propulsion mechanism along with the ergonomically optimized propulsion shape may help to reduce the risk of injuries and thus improve the quality of life for wheelchair users.     

Periprosthetic bone remodelling of a collum femoris preserving cementless titanium femoral hip replacement

Total hip arthroplasty represents a major surgical achievement for pain relief and restoration of lifestyle quality due to the joint disease of osteoarthritis. Total hip replacement has evolved over the past 30 years utilising a variety of biocompatible materials, geometric shapes and fixation techniques. The main objective of this study is to investigate the long-term effects of strain adaptive bone remodelling due to the influence of a novel titanium cementless femoral hip replacement. The period of on-growth has been taken into account and the simulation has been run to predict the remodelling behaviour for a 36-month period. The main conclusion from this analysis is that the implant does shield the calcar to a similar degree as other cementless femoral hip designs. It does, however, tend to cause bone to be laid down along its length. This may, in part, be due to the novel geometry of the implant interlocking with and loading the bone.     

Modelling external bone adaptation using evolutionary structural optimisation

External remodelling is significant in the bone healing process, and it is essential to predict the bone external shape in the design of artificial bone grafts. This paper demonstrates the effectiveness of the evolutionary structural optimisation (ESO) method for the simulation of bone morphology. A two-dimensional ESO strategy is developed which is capable of finding the modified bone topology beginning with any geometry under any loading conditions. The morphology of bone structure is described by the quantitative bone adaptation theory, which is integrated with the finite element method. The evolutionary topology optimisation process is introduced to find the bone shape. A rectangle, which occupies a larger space than the external shape of the bone structure, is specified as a design domain; the evolutionary process iteratively eliminates and redistributes material throughout the domain to obtain an optimum arrangement of bone materials. The technique has been tested on a wide range of examples. In this paper, the formation of trabecular bone architecture around an implant is studied; as another example, the growth of the coronal section of a vertebral body is predicted. The examples support the assertion that the external shape of bone structure can be successfully predicted by the proposed ESO procedure.     

High-tech hip implant for wireless temperature measurements in vivo

When walking long distances, hip prostheses heat up due to friction. The influence of articulating materials and lubricating properties of synovia on the final temperatures, as well as any potential biological consequences, are unknown. Such knowledge is essential for optimizing implant materials, identifying patients who are possibly at risk of implant loosening, and proving the concepts of current joint simulators. An instrumented hip implant with telemetric data transfer was developed to measure the implant temperatures in vivo. A clinical study with 100 patients is planned to measure the implant temperatures for different combinations of head and cup materials during walking. This study will answer the question of whether patients with synovia with poor lubricating properties may be at risk for thermally induced bone necrosis and subsequent implant failure. The study will also deliver the different friction properties of various implant materials and prove the significance of wear simulator tests. A clinically successful titanium hip endoprosthesis was modified to house the electronics inside its hollow neck. The electronics are powered by an external induction coil fixed around the joint. A temperature sensor inside the implant triggers a timer circuit, which produces an inductive pulse train with temperature-dependent intervals. This signal is detected by a giant magnetoresistive sensor fixed near the external energy coil. The implant temperature is measured with an accuracy of 0.1°C in a range between 20°C and 58°C and at a sampling rate of 2-10 Hz. This rate could be considerably increased for measuring other data, such as implant strain or vibration. The employed technique of transmitting data from inside of a closed titanium implant by low frequency magnetic pulses eliminates the need to use an electrical feedthrough and an antenna outside of the implant. It enables the design of mechanically safe and simple instrumented implants.