Patient-specific modelling of bone and bone-implant systems: the challenges

Biomechanical design of a new proximal humerus fracture plate using alternative materials

Comminuted proximal humerus fractures are often repaired by metal plates, but potentially still experience bone refracture, bone "stress shielding," screw perforation, delayed healing, and so forth. This "proof of principle" investigation is the initial step towards the design of a new plate using alternative materials to address some of these problems. Finite element modeling was used to create design graphs for bone stress, plate stress, screw stress, and interfragmentary motion via three different fixations (no, 1, or 2 "kickstand" [KS] screws across the fracture) using a wide range of plate elastic moduli (EP = 5-200 GPa). Well-known design optimization criteria were used that could minimize bone, plate, and screw failure (i.e., peak stress < ultimate tensile strength), reduce bone "stress shielding" (i.e., bone stress under the new plate ≥ bone stress for an intact humerus, titanium plate, and/or steel plate "control"), and encourage callus growth leading to early healing (i.e., 0.2 mm ≤ axial interfragmentary motion ≤ 1 mm; shear/axial interfragmentary motion ratio <1.6). The findings suggest that a potentially optimal configuration involves the new plate being manufactured from a material with an EP of 5-41.5 GPa with 1 KS screw; but, using no KS screws would cause immediate bone fracture and 2 KS screws would almost certainly lead to delayed healing. A prototype plate might be fabricated using alternative materials suggested for orthopedics and other industries, like fiber-metal laminates, fiber-reinforced polymers, metal foams, pure polymers, shape memory alloys, or 3D-printed porous metals.

Clinical management and innovation in fracture non-union

INTRODUCTION

With the introduction and continuous improvement in operative fracture fixation, even the most severe bone fractures can be treated with a high rate of successful healing. However, healing complications can occur and when healing fails over prolonged time, the outcome is termed a fracture non-union. Non-union is generally believed to develop due to inadequate fixation, underlying host-related factors, or infection. Despite the advancements in fracture fixation and infection management, there is still a clear need for earlier diagnosis, improved prediction of healing outcomes and innovation in the treatment of non-union.

AREAS COVERED

This review provides a detailed description of non-union from a clinical perspective, including the state of the art in diagnosis, treatment, and currently available biomaterials and orthobiologics.Subsequently, recent translational development from the biological, mechanical, and infection research fields are presented, including the latest in smart implants, osteoinductive materials, and in silico modeling.

EXPERT OPINION

The first challenge for future innovations is to refine and to identify new clinical factors for the proper definition, diagnosis, and treatment of non-union. However, integration of in vitro, in vivo, and in silico research will enable a comprehensive understanding of non-union causes and correlations, leading to the development of more effective treatments.

Longitudinal CT-based finite element analyses provide objective fracture healing measures in an ovine tibia model

Measuring the healing status of a bone fracture is important to determine the clinical care a patient receives. Implantable devices can directly and continuously assess the healing status of fracture fixation constructs, while subject-specific virtual biomechanical tests can noninvasively determine callus structural integrity at single time points. Despite their potential for objectification, both methods are not yet integrated into clinical practice with further evidence of their benefits required. This study correlated continuous data from an implantable sensor assessing healing status through implant load monitoring with computer tomography (CT) based longitudinal finite element (FE) simulations in a large animal model. Eight sheep were part of a previous preclinical study utilizing a tibial osteotomy model and equipped with such a sensor. Sensor signal was collected over several months, and CT scans were acquired at six interim time points. For each scan, two FE analyses were performed: a virtual torsional rigidity test of the bone and a model of the bone-implant construct with the sensor. The longitudinal simulation results were compared to the sensor data at corresponding time points and a cohort-specific empirical healing rule was employed. Healing status predicted by both in silico simulations correlated significantly with the sensor data at corresponding time points and correctly identified a delayed and a nonunion in the cohort. The methodology is readily translatable with the potential to be applied to further preclinical or clinical cohorts to find generalizable healing criteria. Virtual mechanical tests can objectively measure fracture healing progressing using longitudinal CT scans.

Quantification of long-term nonlinear stress relaxation of bovine trabecular bone

The reliability of computational models in orthopedic biomechanics depends often on the accuracy of the bone material properties. It is widely recognized that the mechanical response of trabecular bone is time-dependent, yet it is often ignored for the sake of simplicity. Previous investigations into the viscoelastic properties of trabecular bone have not explored the relationship between nonlinear stress relaxation and bone mineral density. The inclusion of this behavior could enhance the accuracy of simulations of orthopedic interventions, such as of primary fixation of implants. Although methods to quantify the viscoelastic behavior are known, the time period during which the viscoelastic properties should be investigated to obtain reliable predictions is currently unclear. Therefore, this study aimed to: 1) Investigate the duration of stress relaxation in bovine trabecular bone; 2) construct a material model that describes the nonlinear viscoelastic behavior of uniaxial stress relaxation experiments on trabecular bone; and 3) implement bone density into this model. Uniaxial compressive stress relaxation experiments were performed with cylindrical bovine femoral trabecular bone samples (n = 16) with constant strain held for 24 h. Additionally, multiple stress relaxation experiments with four ascending strain levels with a holding time of 30 min, based on the results of the 24-h experiment, were executed on 18 bovine bone cores. The bone specimens used in this study had a mean diameter of 12.80 mm and a mean height of 28.70 mm. A Schapery and a Superposition model were used to capture the nonlinear stress relaxation behavior in terms of applied strain level and bone mineral density. While most stress relaxation happened in the first 10 min (up to 53 %) after initial compression, the stress relaxation continued even after 24 h. Up to 69 % of stress relaxation was observed at 24 h. Extrapolating the results of 30 min of experimental data to 24 h provided a good fit for accuracy with much improved experimental efficiency. The Schapery and Superposition model were both capable of fitting the repeated stress relaxation in a sample-by-sample approach. However, since bone mineral density did not influence the time-dependent behavior, only the Superposition model could be used for a group-based model fit. Although the sample-by-sample approach was more accurate for an individual specimen, the group based approach is considered a useful model for general application.

Biomechanical effects of different loads and constraints on finite element modeling of the humerus

Currently, there is no established finite element (FE) method to apply physiologically realistic loads and constraints to the humerus. This FE study showed that 2 'simple' methods involving direct head loads, no head constraints, and rigid elbow or mid-length constraints created excessive stresses and bending. However, 2 'intermediate' methods involving direct head loads, but flexible head and elbow constraints, produced lower stresses and bending. Also, 2 'complex' methods involving muscles to generate head loads, plus flexible head and elbow constraints, generated the lowest stresses and moderate bending. This has implications for FE modeling research on intact and implanted humeri.

Mapping the use of computational modelling and simulation in clinics: A survey

In silico medicine describes the application of computational modelling and simulation (CM&S) to the study, diagnosis, treatment or prevention of a disease. Tremendous research advances have been achieved to facilitate the use of CM&S in clinical applications. Nevertheless, the uptake of CM&S in clinical practice is not always timely and accurately reflected in the literature. A clear view on the current awareness, actual usage and opinions from the clinicians is needed to identify barriers and opportunities for the future of in silico medicine. The aim of this study was capturing the state of CM&S in clinics by means of a survey toward the clinical community. Responses were collected online using the Virtual Physiological Human institute communication channels, engagement with clinical societies, hospitals and individual contacts, between 2020 and 2021. Statistical analyses were done with R. Participants (n = 163) responded from all over the world. Clinicians were mostly aged between 35 and 64 years-old, with heterogeneous levels of experience and areas of expertise (i.e., 48% cardiology, 13% musculoskeletal, 8% general surgery, 5% paediatrics). The CM&S terms "Personalised medicine" and "Patient-specific modelling" were the most well-known within the respondents. "In silico clinical trials" and "Digital Twin" were the least known. The familiarity with different methods depended on the medical specialty. CM&S was used in clinics mostly to plan interventions. To date, the usage frequency is still scarce. A well-recognized benefit associated to CM&S is the increased trust in planning procedures. Overall, the recorded level of trust for CM&S is high and not proportional to awareness level. The main barriers appear to be access to computing resources, perception that CM&S is slow. Importantly, clinicians see a role for CM&S expertise in their team in the future. This survey offers a snapshot of the current situation of CM&S in clinics. Although the sample size and representativity could be increased, the results provide the community with actionable data to build a responsible strategy for accelerating a positive uptake of in silico medicine. New iterations and follow-up activities will track the evolution of responses over time and contribute to strengthen the engagement with the medical community.

Hip joint load prediction using inverse bone remodeling with homogenized FE models: Comparison to micro-FE and influence of material modeling strategy

BACKGROUND AND OBJECTIVE

Measuring physiological loading conditions in vivo can be challenging, as methods are invasive or pose a high modeling effort. However, the physiological loading of bones is also imprinted in the bone microstructure due to bone (re)modeling. This information can be retrieved by inverse bone remodeling (IBR). Recently, an IBR method based on micro-finite-element (µFE) modeling was translated to homogenized-FE (hFE) to decrease computational effort and tested on the distal radius. However, this bone has a relatively simple geometry and homogeneous microstructure. Therefore, the objective of this study was to assess the agreement of hFE-based IBR with µFE-based IBR to predict hip joint loading from the head of the femur; a bone with more complex loading as well as more heterogeneous microstructure.

METHODS

hFE-based IBR was applied to a set of 19 femoral heads using four different material mapping laws. One model with a single homogeneous material for both trabecular and cortical volume and three models with a separated cortex and either homogeneous, density-dependent inhomogeneous, or density and fabric-dependent orthotropic material. Three different evaluation regions (full bone, trabecular bone only, head region only) were defined, in which IBR was applied. µFE models were created for the same bones, and the agreement of the predicted hip joint loading history obtained from hFE and µFE models was evaluated. The loading history was discretized using four unit load cases.

RESULTS

The computational time for FE solving was decreased on average from 500 h to under 1 min (CPU time) when using hFE models instead of µFE models. Using more information in the material model in the hFE models led to a better prediction of hip joint loading history. Inhomogeneous and inhomogeneous orthotropic models gave the best agreement to µFE-based IBR (RMSE% <14%). The evaluation region only played a minor role.

CONCLUSIONS

hFE-based IBR was able to reconstruct the dominant joint loading of the femoral head in agreement with µFE-based IBR and required considerably lower computational effort. Results indicate that cortical and trabecular bone should be modeled separately and at least density-dependent inhomogeneous material properties should be used with hFE models of the femoral head to predict joint loading.

A Density-Dependent Target Stimulus for Inverse Bone (Re)modeling with Homogenized Finite Element Models

Inverse bone (re)modeling (IBR) can infer physiological loading conditions from the bone microstructure. IBR scales unit loads, imposed on finite element (FE) models of a bone, such that the trabecular microstructure is homogeneously loaded and the difference to a target stimulus is minimized. Micro-FE (µFE) analyses are typically used to model the microstructure, but computationally more efficient, homogenized FE (hFE) models, where the microstructure is replaced by an equivalent continuum, could be used instead. However, also the target stimulus has to be translated from the tissue to the continuum level. In this study, a new continuum-level target stimulus relating relative bone density and strain energy density is proposed. It was applied using different types of hFE models to predict the physiological loading of 21 distal radii sections, which was subsequently compared to µFE-based IBR. The hFE models were able to correctly identify the dominant load direction and showed a high correlation of the predicted forces, but mean magnitude errors ranged from − 14.7 to 26.6% even for the best models. While µFE-based IBR can still be regarded as a gold standard, hFE-based IBR enables faster predictions, the usage of more sophisticated boundary conditions, and the usage of clinical images.

Toward an artificial intelligence-assisted framework for reconstructing the digital twin of vertebra and predicting its fracture response

This article presents an effort toward building an artificial intelligence (AI) assisted framework, coined ReconGAN, for creating a realistic digital twin of the human vertebra and predicting the risk of vertebral fracture (VF). ReconGAN consists of a deep convolutional generative adversarial network (DCGAN), image-processing steps, and finite element (FE) based shape optimization to reconstruct the vertebra model. This DCGAN model is trained using a set of quantitative micro-computed tomography (micro-QCT) images of the trabecular bone obtained from cadaveric samples. The quality of synthetic trabecular models generated using DCGAN are verified by comparing a set of its statistical microstructural descriptors with those of the imaging data. The synthesized trabecular microstructure is then infused into the vertebra cortical shell extracted from the patient's diagnostic CT scans using an FE-based shape optimization approach to achieve a smooth transition between trabecular to cortical regions. The final geometrical model of the vertebra is converted into a high-fidelity FE model to simulate the VF response using a continuum damage model under compression and flexion loading conditions. A feasibility study is presented to demonstrate the applicability of digital twins generated using this AI-assisted framework to predict the risk of VF in a cancer patient with spinal metastasis.

Finite Element Analysis of Fracture Fixation

PURPOSE OF REVIEW

Fracture fixation aims to provide stability and promote healing, but remains challenging in unstable and osteoporotic fractures with increased risk of construct failure and nonunion. The first part of this article reviews the clinical motivation behind finite element analysis of fracture fixation, its strengths and weaknesses, how models are developed and validated, and how outputs are typically interpreted. The second part reviews recent modeling studies of the femur and proximal humerus, areas with particular relevance to fragility fractures.

RECENT FINDINGS

There is some consensus in the literature around how certain modeling aspects are pragmatically formulated, including bone and implant geometries, meshing, material properties, interactions, and loads and boundary conditions. Studies most often focus on predicted implant stress, bone strain surrounding screws, or interfragmentary displacements. However, most models are not rigorously validated. With refined modeling methods, improved validation efforts, and large-scale systematic analyses, finite element analysis is poised to advance the understanding of fracture fixation failure, enable optimization of implant designs, and improve surgical guidance.

Effect of geometrical structure variations on the viscoelastic and anisotropic behaviour of cortical bone using multi-scale finite element modelling

Multi-scale finite element analysis is performed to ascertain the effect of geometrical changes at multiple structural scales on the mechanical properties of cortical bone. Finite element models are developed, with reference to experimental data from existing literature, to account for bone's viscoelastic behaviour and anisotropic structure from the most fundamental level of bone consisting of mineralised collagen fibrils, up to the macroscopic level consisting of osteons and the Haversian canals. A statistical approach is incorporated to perform sensitivity analyses on the effects of different geometrical parameters on the effective material properties of cortical bone at each length scale. Numerical results indicate that there is an exponential correlation between the mineral volume fraction and the effective stiffness constants at each length scale. This contributes to the exponential behaviour of the instantaneous moduli describing cortical bone's two-phase stress relaxation process: a fast and slow response relaxation behaviour. Results indicate that the fast response relaxation time is independent of bone's structural anisotropy, whilst being dependent on variations in the global mineral volume fraction between length scales. However, the slow response relaxation time is independent of the changes in mineral volume fraction. It is also observed that the slow response relaxation time varies with bone's anisotropic structure, and therefore, contributes to the anisotropic properties of bone.

A finite element analysis of tibial tritanium cones without stems in varying bone defects

BACKGROUND

In the UK around 10% of hip and knee arthroplasties are revision operations. At revision total knee arthroplasty (rTKA), bone loss management is critical to achieving a stable bone-implant construct. Though tritanium cones have been used to manage bone defects in rTKA, their biomechanical performance with varying defects remains unknown.

METHODS

Uncontained tibial bone defects at four anatomic locations, with varying depths and widths (Type T2A and T2B) were investigated computationally in a composite tibia which was subjected to four loading scenarios. The ability of the tritanium cone to replace the tibial bone defect was examined using the outcome measures of bone strain distribution and interface micromotions.

RESULTS

It was found that anterior and lateral defects do not significantly alter the strain distribution compared with intact bone. For medial defects, strain distribution is sensitive to defect width; while strain distributions for posterior defects are associated with defect width and depth. In general, micromotions at the bone-implant interface are small and are primarily influenced by defect depth.

CONCLUSIONS

Our models show that the cone is an acceptable choice for bone defect management in rTKA. Since all observed micromotions were small, successful osteointegration would be expected in all types of uncontained defects considered in this study. Tritanium cones safely accommodate uncontained tibial defects up to 10 mm deep and extending up to 9 mm from the centre of the cone. Medial and posteriorly based defects managed with symmetric cones display the greatest bone strains and asymmetric cones may be useful in this context.

Metaphyseal cones in revision total knee arthroplasty: The role of stems

Aims

Metaphyseal tritanium cones can be used to manage the tibial bone loss commonly encountered at revision total knee arthroplasty (rTKA). Tibial stems provide additional fixation and are generally used in combination with cones. The aim of this study was to examine the role of the stems in the overall stability of tibial implants when metaphyseal cones are used for rTKA.

Methods

This computational study investigates whether stems are required to augment metaphyseal cones at rTKA. Three cemented stem scenarios (no stem, 50 mm stem, and 100 mm stem) were investigated with 10 mm-deep uncontained posterior and medial tibial defects using four loading scenarios designed to mimic activities of daily living.

Results

Small micromotions (mean < 12 µm) were found to occur at the bone-implant interface for all loading cases with or without a stem. Stem inclusion was associated with lower micromotion, however these reductions were too small to have any clinical significance. Peak interface micromotion, even when the cone is used without a stem, was too small to effect osseointegration. The maximum difference occurred with stair descent loading. Stress concentrations in the bone occurred around the inferior aspect of each implant, with the largest occurring at the end of the long stem; these may lead to end-of-stem pain. Stem use is also found to result in stress shielding in the bone along the stem.

Conclusion

When a metaphyseal cone is used at rTKA to manage uncontained posterior or medial defects of up to 10 mm depth, stem use may not be necessary.

Cite this article:Bone Joint Res. 2020;9(4):162–172.

Multiscale design of artificial bones with biomimetic elastic microstructures

Cancellous bone is a highly porous, heterogeneous, and anisotropic material which can be found at the epiphyses of long bones and in the vertebral bodies. The hierarchical architecture makes cancellous bone a prime example of a lightweight natural material that combines strength with toughness. Better understanding the mechanics of cancellous bone is of interest for the diagnosis of bone diseases, the evaluation of the risk of fracture, and for the design of artificial bones and bone scaffolds for tissue engineering. A multiscale optimization method to maximize the stiffness of artificial bones using biomimetic cellular microstructures described by a finite set of geometrical micro-parameters is presented here. The most outstanding characteristics of its implementation are the use of: an interior point optimization algorithm, a precalculated response surface methodology for the evaluation of the elastic tensor of the microstructure as an analytical function of the micro-parameters, and the adjoint method for the computation of the sensitivity of the macroscopic mechanical response to the variation of the micro-parameters. The performance and effectiveness of the tool are evaluated by solving a problem that consists in finding the optimal distribution of the microstructures for a proximal end of a femur subjected to physiological loads. Two strategies for the specification of the solid volume fraction constraints are assessed. The results are compared with data of a computed tomography study of an actual human bone. The model successfully predicts the main features of the spatial arrangement of the trabecular and cortical microstructures of the natural bone.

The risk of loosening of extramedullary fracture fixation devices

Extramedullary devices that use screws, pins or wires are used extensively to treat fractures in normal and diseased bone. A common failure mode is implant loosening at the bone-screw/pin/wire interface before fracture healing occurs. This review first considers the fundamental mechanics of the bone-fixator construct with focus on interfacial strains that result in loosening. It then evaluates the time-independent and time-dependent material models of bone that have been used to simulate and predict loosening. It is shown that the recently developed time-dependent models are capable of predicting loosening due to cyclic loads in bone of varying quality.

Time-dependent behaviour of bone accentuates loosening in the fixation of fractures using bone-screw systems

Aims

Loosening is a well-known complication in the fixation of fractures using devices such as locking plates or unilateral fixators. It is believed that high strains in the bone at the bone-screw interface can initiate loosening, which can result in infection, and further loosening. Here, we present a new theory of loosening of implants. The time-dependent response of bone subjected to loads results in interfacial deformations in the bone which accumulate with cyclical loading and thus accentuates loosening.

Methods

We used an 'ideal' bone-screw system, in which the screw is subjected to cyclical lateral loads and trabecular bone is modelled as non-linear viscoelastic and non-linear viscoelastic-viscoplastic material, based on recent experiments, which we conducted.

Results

We found that the interfacial deformation in the bone increases with the number of cycles, and the use of a non-linear viscoelastic-viscoplastic model results in larger deformations, some of which are irrecoverable. There is an apparent trend in which interfacial deformations increase with increasing porosity of bone.

Conclusion

The developed time-dependent model of the mechanical behaviour of bone permits prediction of loosening due to cyclical loads, which has not been possible previously. Application of this model shows that implant loosening will be accentuated by cyclical loading due to physiological activities, and the risks of loosening are greater in osteoporotic patients.Cite this article: S. Xie, K. Manda, P. Pankaj. Time-dependent behaviour of bone accentuates loosening in the fixation of fractures using bone-screw systems. Bone Joint Res 2018;7:580-586. DOI: 10.1302/2046-3758.710.BJR-2018-0085.R1.

How can a short stem hip implant preserve the natural, pre-surgery force flow? A finite element analysis on a collar cortex compression concept (CO4)

The present work proposes a simple, novel fixation concept for short stem hip endoprostheses, which preserves the pre-surgery force flow through femoral bone to an unprecedented extent. It is demonstrated by finite element analyses that a standard implant model endowed with minor geometrical changes can overcome bone loading reduction and can achieve almost physiological conditions. The numerical results underpin that the key aspect of the novel, so-called "collar cortex compression concept CO4" is the direct, almost full load transmission from the implant collar to the resected femur cortex, which implies that the implant stem must be smooth and therefore interacts mainly by normal contact with the surrounding bone. For a stem endowed with surface porosity at already small areas, it is mainly the stem which transmits axial forces by shear, whereas the collar shows considerable unloading, which is the standard metaphyseal fixation. Only in the latter case the implant-bone stiffness contrast induces stress shielding, whereas for CO4 stress shielding is avoided almost completely, although the implant is made of a stiff Ti-alloy. CO4 is bionics-inspired in that it mimics force transmission at implant-bone interfaces following the natural conditions and it thereby preserves pre-surgery bone architecture as an optimized solution of nature.

Using Non-linear Homogenization to Improve the Performance of Macroscopic Damage Models of Trabecular Bone

Realistic macro-level finite element simulations of the mechanical behavior of trabecular bone, a cellular anisotropic material, require a suitable constitutive model; a model that incorporates the mechanical response of bone for complex loading scenarios and includes post-elastic phenomena, such as plasticity (permanent deformations) and damage (permanent stiffness reduction), which bone is likely to experience. Some such models have been developed by conducting homogenization-based multiscale finite element simulations on bone micro-structure. While homogenization has been fairly successful in the elastic regime and, to some extent, in modeling the macroscopic plastic response, it has remained a challenge with respect to modeling damage. This study uses a homogenization scheme to upscale the damage behavior from the tissue level (microscale) to the organ level (macroscale) and assesses the suitability of different damage constitutive laws. Ten cubic specimens were each subjected to 21 strain-controlled load cases for a small range of macroscopic post-elastic strains. Isotropic and anisotropic criteria were considered, density and fabric relationships were used in the formulation of the damage law, and a combined isotropic/anisotropic law with tension/compression asymmetry was formulated, based on the homogenized results, as a possible alternative to the currently used single scalar damage criterion. This computational study enhances the current knowledge on the macroscopic damage behavior of trabecular bone. By developing relationships of damage progression with bone's micro-architectural indices (density and fabric) the study also provides an aid for the creation of more precise macroscale continuum models, which are likely to improve clinical predictions.

Application of quality by design for 3D printed bone prostheses and scaffolds

3D printing is an emergent manufacturing technology recently being applied in the medical field for the development of custom bone prostheses and scaffolds. However, successful industry transformation to this new design and manufacturing approach requires technology integration, concurrent multi-disciplinary collaboration, and a robust quality management framework. This latter change enabler is the focus of this study. While a number of comprehensive quality frameworks have been developed in recent decades to ensure that the manufacturing of medical devices produces reliable products, they are centred on the traditional context of standardised manufacturing techniques. The advent of 3D printing technologies and the prospects for mass customisation provides significant market opportunities, but also presents a serious challenge to regulatory bodies tasked with managing and assuring product quality and safety. Before 3D printing bone prostheses and scaffolds can gain traction, industry stakeholders, such as regulators, clients, medical practitioners, insurers, lawyers, and manufacturers, would all require a high degree of confidence that customised manufacturing can achieve the same quality outcomes as standardised manufacturing. A Quality by Design (QbD) approach to custom 3D printed prostheses can help to ensure that products are designed and manufactured correctly from the beginning without errors. This paper reports on the adaptation of the QbD approach for the development process of 3D printed custom bone prosthesis and scaffolds. This was achieved through the identification of the Critical Quality Attributes of such products, and an extensive review of different design and fabrication methods for 3D printed bone prostheses. Research outcomes include the development of a comprehensive design and fabrication process flow diagram, and categorised risks associated with the design and fabrication processes of such products. An extensive systematic literature review and post-hoc evaluation survey with experts was completed to evaluate the likely effectiveness of the herein suggested QbD framework.

Effect of including damage at the tissue level in the nonlinear homogenisation of trabecular bone

Being able to predict bone fracture or implant stability needs a proper constitutive model of trabecular bone at the macroscale in multiaxial, non-monotonic loading modes. Its macroscopic damage behaviour has been investigated experimentally in the past, mostly with the restriction of uniaxial cyclic loading experiments for different samples, which does not allow for the investigation of several load cases in the same sample as damage in one direction may affect the behaviour in other directions. Homogenised finite element models of whole bones have the potential to assess complicated scenarios and thus improve clinical predictions. The aim of this study is to use a homogenisation-based multiscale procedure to upscale the damage behaviour of bone from an assumed solid phase constitutive law and investigate its multiaxial behaviour for the first time. Twelve cubic specimens were each submitted to nine proportional strain histories by using a parallel code developed in-house. Evolution of post-elastic properties for trabecular bone was assessed for a small range of macroscopic plastic strains in these nine load cases. Damage evolution was found to be non-isotropic, and both damage and hardening were found to depend on the loading mode (tensile, compression or shear); both were characterised by linear laws with relatively high coefficients of determination. It is expected that the knowledge of the macroscopic behaviour of trabecular bone gained in this study will help in creating more precise continuum FE models of whole bones that improve clinical predictions.

Time Dependent Behaviour of Trabecular Bone at Multiple Load Levels

The deformation of bone when subjected to loads is not instantaneous but varies with time. To investigate this time-dependent behaviour sixteen bovine trabecular bone specimens were subjected to compressive loading, creep, unloading and recovery at multiple load levels corresponding to apparent strains of 2000-25,000 με. We found that: the time-dependent response of trabecular bone comprises of both recoverable and irrecoverable strains; the strain response is nonlinearly related to applied load levels; and the response is linked to bone volume fraction. Although majority of strain is recovered after the load-creep-unload-recovery cycle some residual strain always exists. The analysis of results indicates that trabecular bone becomes stiffer initially and then experiences stiffness degradation with the increasing load levels. Steady state creep rate was found to be dependent on applied stress level and bone volume fraction with a power law relationship.

Nonlinear homogenisation of trabecular bone: Effect of solid phase constitutive model

Micro-finite element models have been extensively employed to evaluate the elastic properties of trabecular bone and, to a limited extent, its yield behaviour. The macroscopic stiffness tensor and yield surface are of special interest since they are essential in the prediction of bone strength and stability of implants at the whole bone level. While macroscopic elastic properties are now well understood, yield and post-yield properties are not. The aim of this study is to shed some light on what the effect of the solid phase yield criterion is on the macroscopic yield of trabecular bone for samples with different microstructure. Three samples with very different density were subjected to a large set of apparent load cases (which is important since physiological loading is complex and can have multiple components in stress or strain space) with two different solid phase yield criteria: Drucker-Prager and eccentric-ellipsoid. The study found that these two criteria led to small differences in the macroscopic yield strains for most load cases except for those that were compression-dominated; in these load cases, the yield strains for the Drucker-Prager criterion were significantly higher. Higher density samples resulted in higher differences between the two criteria. This work provides a comprehensive assessment of the effect of two different solid phase yield criteria on the macroscopic yield strains of trabecular bone, for a wide range of load cases, and for samples with different morphology.

The effects of musculoskeletal loading regimes on numerical evaluations of acetabular component

The importance of clinical studies notwithstanding, the failure assessment of implant–bone structure has alternatively been carried out using finite element analysis. However, the accuracy of the finite element predicted results is dependent on the applied loading and boundary conditions. Nevertheless, most finite element–based evaluations on acetabular component used a few selective load cases instead of the eight load cases representing the entire gait cycle. These in silico evaluations often suffer from limitations regarding the use of simplified musculoskeletal loading regimes. This study attempts to analyse the influence of three different loading regimes representing a gait cycle, on numerical evaluations of acetabular component. Patient-specific computer tomography scan-based models of intact and resurfaced pelvises were used. One such loading regime consisted of the second load case that corresponded to peak hip joint reaction force. Whereas the other loading regime consisted of the second and fifth load cases, which corresponded to peak hip joint reaction force and peak muscle forces, respectively. The third loading regime included all the eight load cases. Considerable deviations in peri-acetabular strains, standard error ranging between 115 and 400 µε, were observed for different loading regimes. The predicted bone strains were lower when selective loading regimes were used. Despite minor quantitative variations in bone density changes (less than 0.15 g cm−3), the final bone density pattern after bone remodelling was found to be similar for all the loading regimes. Underestimations in implant–bone micromotions (40–50 µm) were observed for selective loading regimes after bone remodelling. However, at immediate post-operative condition, such underestimations were found to be less (less than 5 µm). The predicted results highlight the importance of inclusion of eight load cases representing the gait cycle for in silico evaluations of resurfaced pelvis.

Linear viscoelasticity - bone volume fraction relationships of bovine trabecular bone

Trabecular bone has been previously recognized as time-dependent (viscoelastic) material, but the relationships of its viscoelastic behaviour with bone volume fraction (BV/TV) have not been investigated so far. Therefore, the aim of the present study was to quantify the time-dependent viscoelastic behaviour of trabecular bone and relate it to BV/TV. Uniaxial compressive creep experiments were performed on cylindrical bovine trabecular bone samples (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\textit{n}\,{=}\,13$$\end{document}n=13) at loads corresponding to physiological strain level of 2000 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\upmu }{\upvarepsilon }$$\end{document}με. We assumed that the bone behaves in a linear viscoelastic manner at this low strain level and the corresponding linear viscoelastic parameters were estimated by fitting a generalized Kelvin–Voigt rheological model to the experimental creep strain response. Strong and significant power law relationships (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$r^2\,{=}\,0.73,\ p\,{<}\,0.001$$\end{document}r2=0.73,p<0.001) were found between time-dependent creep compliance function and BV/TV of the bone. These BV/TV-based material properties can be used in finite element models involving trabecular bone to predict time-dependent response. For users’ convenience, the creep compliance functions were also converted to relaxation functions by using numerical interconversion methods and similar power law relationships were reported between time-dependent relaxation modulus function and BV/TV.

Comparison of proximal femur and vertebral body strength improvements in the FREEDOM trial using an alternative finite element methodology

Denosumab reduced the incidence of new fractures in postmenopausal women with osteoporosis by 68% at the spine and 40% at the hip over 36 months compared with placebo in the FREEDOM study. This efficacy was supported by improvements from baseline in vertebral (18.2%) strength in axial compression and femoral (8.6%) strength in sideways fall configuration at 36 months, estimated in Newtons by an established voxel-based finite element (FE) methodology. Since FE analyses rely on the choice of meshes, material properties, and boundary conditions, the aim of this study was to independently confirm and compare the effects of denosumab on vertebral and femoral strength during the FREEDOM trial using an alternative smooth FE methodology. Unlike the previous FE study, effects on femoral strength in physiological stance configuration were also examined. QCT data for the proximal femur and two lumbar vertebrae were analyzed by smooth FE methodology at baseline, 12, 24, and 36 months for 51 treated (denosumab) and 47 control (placebo) subjects. QCT images were segmented and converted into smooth FE models to compute bone strength. L1 and L2 vertebral bodies were virtually loaded in axial compression and the proximal femora in both fall and stance configurations. Denosumab increased vertebral body strength by 10.8%, 14.0%, and 17.4% from baseline at 12, 24, and 36 months, respectively (p<0.0001). Denosumab also increased femoral strength in the fall configuration by 4.3%, 5.1%, and 7.2% from baseline at 12, 24, and 36 months, respectively (p<0.0001). Similar improvements were observed in the stance configuration with increases of 4.2%, 5.2%, and 5.2% from baseline (p≤0.0007). Differences between the increasing strengths with denosumab and the decreasing strengths with placebo were significant starting at 12 months (vertebral and femoral fall) or 24 months (femoral stance). Using an alternative smooth FE methodology, we confirmed the significant improvements in vertebral body and proximal femur strength previously observed with denosumab. Estimated increases in strength with denosumab and decreases with placebo were highly consistent between both FE techniques.

Patient-specific geometrical modeling of orthopedic structures with high efficiency and accuracy for finite element modeling and 3D printing

We improved the geometrical modeling procedure for fast and accurate reconstruction of orthopedic structures. This procedure consists of medical image segmentation, three-dimensional geometrical reconstruction, and assignment of material properties. The patient-specific orthopedic structures reconstructed by this improved procedure can be used in the virtual surgical planning, 3D printing of real orthopedic structures and finite element analysis. A conventional modeling consists of: image segmentation, geometrical reconstruction, mesh generation, and assignment of material properties. The present study modified the conventional method to enhance software operating procedures. Patient's CT images of different bones were acquired and subsequently reconstructed to give models. The reconstruction procedures were three-dimensional image segmentation, modification of the edge length and quantity of meshes, and the assignment of material properties according to the intensity of gravy value. We compared the performance of our procedures to the conventional procedures modeling in terms of software operating time, success rate and mesh quality. Our proposed framework has the following improvements in the geometrical modeling: (1) processing time: (femur: 87.16 ± 5.90 %; pelvis: 80.16 ± 7.67 %; thoracic vertebra: 17.81 ± 4.36 %; P < 0.05); (2) least volume reduction (femur: 0.26 ± 0.06 %; pelvis: 0.70 ± 0.47, thoracic vertebra: 3.70 ± 1.75 %; P < 0.01) and (3) mesh quality in terms of aspect ratio (femur: 8.00 ± 7.38 %; pelvis: 17.70 ± 9.82 %; thoracic vertebra: 13.93 ± 9.79 %; P < 0.05) and maximum angle (femur: 4.90 ± 5.28 %; pelvis: 17.20 ± 19.29 %; thoracic vertebra: 3.86 ± 3.82 %; P < 0.05). Our proposed patient-specific geometrical modeling requires less operating time and workload, but the orthopedic structures were generated at a higher rate of success as compared with the conventional method. It is expected to benefit the surgical planning of orthopedic structures with less operating time and high accuracy of modeling.

A Hertzian Integrated Contact Model of the Total Knee Replacement Implant for the Estimation of Joint Contact Forces

The prediction of lower limb muscle and contact forces may provide useful knowledge to assist the clinicians in the diagnosis as well as in the development of appropriate treatment for musculoskeletal disorders. Research studies have commonly estimated joint contact forces using model-based muscle force estimation due to the lack of a reliable contact model and material properties. The objective of this present study was to develop a Hertzian integrated contact model. Then, in vivo elastic properties of the Total Knee Replacement (TKR) implant were identified using in vivo contact forces leading to providing reliable material properties for modeling purposes. First, a patient specific rigid musculoskeletal model was built. Second, a STL-based implant model was designed to compute the contact area evolutions during gait motions. Finally, a Hertzian integrated contact model was defined for the in vivo identification of elastic properties (Young’s modulus and Poisson coefficient) of the instrumented TKR implant. Our study showed a potential use of a new approach to predict the contact forces without knowledge of muscle forces. Thus, the outcomes may lead to accurate and reliable prediction of human joint contact forces for new case study.

Initial Stability of Subtrochanteric Oblique Osteotomy in Uncemented Total Hip Arthroplasty: A Preliminary Finite Element Study

BACKGROUND

Subtrochanteric oblique osteotomy (SOO) has been widely used to reconstruct highly dislocated hips in uncemented total hip arthroplasty. The occurrence of complications can be attributed to the instability of the osteotomy region. The aim of this study was to evaluate the initial stability of SOO in uncemented total hip arthroplasty.

MATERIAL AND METHODS

A 3-dimensional finite element femur-stem model was created, and a virtual SOO was performed at 4 oblique angles: 30°, 45°, 60°, and 90°. The von Mises stress distribution in the femur-stem complex and the displacement under different oblique angles were evaluated in the SOO models, in comparison with that of the intact model.

RESULTS

The study demonstrated that the distal fragment of the femur bore more stresses than the proximal fragment, and the maximum stress was concentrated in the femoral neck and the cortical bone, which contacted with the distal end of the stem. SOO increased the stress of both the femur and the stem, and fractures may occur in the stress concentration sites. Additionally, comparing the displacement at different oblique angles, the lateral region was larger than that of the medial region on the subtrochanteric osteotomy plane. The minimum micromotion on the osteotomy plane was obtained when the oblique angle was 45°.

CONCLUSIONS

The fit and fill of the distal fragment of the femur and the stem is essential for the stability of the subtrochanteric osteotomy region. The optimal oblique angle for SOO appears to be 45°.

Muscle optimization techniques impact the magnitude of calculated hip joint contact forces

In musculoskeletal modelling, several optimization techniques are used to calculate muscle forces, which strongly influence resultant hip contact forces (HCF). The goal of this study was to calculate muscle forces using four different optimization techniques, i.e., two different static optimization techniques, computed muscle control (CMC) and the physiological inverse approach (PIA). We investigated their subsequent effects on HCFs during gait and sit to stand and found that at the first peak in gait at 15-20% of the gait cycle, CMC calculated the highest HCFs (median 3.9 times peak GRF (pGRF)). When comparing calculated HCFs to experimental HCFs reported in literature, the former were up to 238% larger. Both static optimization techniques produced lower HCFs (median 3.0 and 3.1 pGRF), while PIA included muscle dynamics without an excessive increase in HCF (median 3.2 pGRF). The increased HCFs in CMC were potentially caused by higher muscle forces resulting from co-contraction of agonists and antagonists around the hip. Alternatively, these higher HCFs may be caused by the slightly poorer tracking of the net joint moment by the muscle moments calculated by CMC. We conclude that the use of different optimization techniques affects calculated HCFs, and static optimization approached experimental values best.

Four decades of finite element analysis of orthopaedic devices: where are we now and what are the opportunities?

Finite element has been used for more than four decades to study and evaluate the mechanical behaviour total joint replacements. In Huiskes seminal paper "Failed innovation in total hip replacement: diagnosis and proposals for a cure", finite element modelling was one of the potential cures to avoid poorly performing designs reaching the market place. The size and sophistication of models has increased significantly since that paper and a range of techniques are available from predicting the initial mechanical environment through to advanced adaptive simulations including bone adaptation, tissue differentiation, damage accumulation and wear. However, are we any closer to FE becoming an effective screening tool for new devices? This review contains a critical analysis of currently available finite element modelling techniques including (i) development of the basic model, the application of appropriate material properties, loading and boundary conditions, (ii) describing the initial mechanical environment of the bone-implant system, (iii) capturing the time dependent behaviour in adaptive simulations, (iv) the design and implementation of computer based experiments and (v) determining suitable performance metrics. The development of the underlying tools and techniques appears to have plateaued and further advances appear to be limited either by a lack of data to populate the models or the need to better understand the fundamentals of the mechanical and biological processes. There has been progress in the design of computer based experiments. Historically, FE has been used in a similar way to in vitro tests, by running only a limited set of analyses, typically of a single bone segment or joint under idealised conditions. The power of finite element is the ability to run multiple simulations and explore the performance of a device under a variety of conditions. There has been increasing usage of design of experiments, probabilistic techniques and more recently population based modelling to account for patient and surgical variability. In order to have effective screening methods, we need to continue to develop these approaches to examine the behaviour and performance of total joint replacements and benchmark them for devices with known clinical performance. Finite element will increasingly be used in the design, development and pre-clinical testing of total joint replacements. However, simulations must include holistic, closely corroborated, multi-domain analyses which account for real world variability.

Reasons why dynamic compression plates are inferior to locking plates in osteoporotic bone: a finite element explanation

While locking plate fixation is becoming increasingly popular for complex and osteoporotic fractures, for many indications compression plating remains the standard choice. This study compares the mechanical behaviour of the more recent locking compression plate (LCP) device, with the traditional dynamic compression plates (DCPs) in bone of varying quality using finite element modelling. The bone properties considered include orthotropy, inhomogeneity, cortical thinning and periosteal apposition associated with osteoporosis. The effect of preloads induced by compression plating was included in the models. Two different fracture scenarios were modelled: one with complete reduction and one with a fracture gap. The results show that the preload arising in DCPs results in large principal strains in the bone all around the perimeter of the screw hole, whereas for LCPs large principal strains occur primarily on the side of the screw proximal to the load. The strains within the bone produced by the two screw types are similar in healthy bone with a reduced fracture gap; however, the DCP produces much larger strains in osteoporotic bone. In the presence of a fracture gap, the DCP results in a considerably larger region with high tensile strains and a slightly smaller region with high compressive strains. These findings provide a biomechanical basis for the reported improved performance of locking plates in poorer bone quality.