Long-term study of bone remodelling after femoral stem: a comparison between dexa and finite element simulation

A hip replacement with a cemented or cementless femoral stem produces an effect on the bone called adaptive remodelling, attributable to mechanical and biological factors. The objective of all of cementless prostheses designs has been to achieve a perfect transfer of loads in order to avoid stress-shielding, which produces an osteopenia. In order to quantify this, the long term and mass-produced study with dual energy X-ray absorptiometry (DEXA) is necessary. Finite element (FE) simulation makes possible the explanation of the biomechanical changes which are produced in the femur after stem implantation. The good correlation obtained between the results of the FE simulation and the densitometric study allow, on one hand, to explain from the point of view of biomechanical performance the changes observed in bone density in the long-term, where it is clear that these are due to a different transfer of load in the implanted model compared to the healthy femur; on the other hand, it validates the simulation model, in a way that it can be used in different conditions and at different time periods, to carry out a sufficiently precise prediction of the evolution of the bone density from the biomechanical behaviour in the interaction between the prosthesis and femur.     

Prediction of shape and internal structure of the proximal femur using a modified level set method for structural topology optimisation

A computational framework was developed to simulate the bone remodelling process as a structural topology optimisation problem. The mathematical formulation of the Level Set technique was extended and then implemented into a coronal plane model of the proximal femur to simulate the remodelling of internal structure and external geometry of bone into the optimal state. Results indicated that the proposed approach could reasonably mimic the major geometrical and material features of the natural bone. Simulation of the internal bone remodelling on the typical gross shape of the proximal femur, resulted in a density distribution pattern with good consistency with that of the natural bone. When both external and internal bone remodelling were simulated simultaneously, the initial rectangular design domain with a regularly distributed mass reduced gradually to an optimal state with external shape and internal structure similar to those of the natural proximal femur.     

Femoral neck bone adaptation to weight-bearing physical activity by computational analysis

Individual differences in bone mass distribution at the proximal femur may be determined by daily weight-bearing physical activity (PA) since bone self-adapts according to the mechanical loads that is submitted. The aim of this study was to analyse computationally the effect of different weight-bearing PA types in the adaptation of the femoral neck (FN) by analysing regional differences in bone mineral density (BMD) at the integral FN and its superior, inferior, anterior and posterior subregions. To achieve this, it was adopted a 3-D femoral finite element (FE) model coupled with a suitable bone remodeling model. Different PA types were determined based both on ordinary lifestyle and mechanically more demanding PA as low magnitude impacts (L–I), moderate-magnitude impacts from odd directions (O–I) and high-magnitude vertical impacts (H–I). It was observed that as time spent in weight-bearing PA increases, BMD augment around the integral FN, but with different bone mass gain rates between subregions depending on the magnitude and directions of the hip contact forces; H–I was the type of weight-bearing PA which structurally most favor the gain of bone mass superiorly at the FN while both the H–I and the O–I types of PA promoted the largest bone mass gain rates at the anterior and posterior subregions of the FN. Because these types of weight-bearing PA were associated with a more uniform bone mass spatial distribution at the FN, they should provide a potential basis for targeted PA-based intervention programs for improving hip strength.     

Subject-specific modeling of the scapula bone tissue adaptation

Adaptation of the scapula bone tissue to mechanical loading is simulated in the current study using a subject-specific three-dimensional finite element model of an intact cadaveric scapula. The loads experienced by the scapula during different types of movements are determined using a subject-specific large-scale musculoskeletal model of the shoulder joint. The obtained density distributions are compared with the CT-measured density distribution of the same scapula. Furthermore, it is assumed that the CT-measured density distribution can be estimated as a weighted linear combination of the density distributions calculated for different loads experienced during daily life. An optimization algorithm is used to determine the weighting factors of fourteen different loads such that the difference between the weighted linear combination of the calculated density distributions and the CT-measured density is minimal. It is shown that the weighted linear combination of the calculated densities matches the CT-measured density distribution better than every one of the density distributions calculated for individual movements. The weighting factors of nine out of fourteen loads were estimated to be zero or very close to zero. The five loads that had larger weighting factors were associated with either one of the following categories: (1) small-load small-angle abduction or flexion movements that occur frequently during our daily lives or (2) large-load large-angle abduction or flexion movements that occur infrequently during our daily lives.     

A novel approach to estimate trabecular bone anisotropy using a database approach

Continuum finite element (FE) models of bones have become a standard pre-clinical tool to estimate bone strength. These models are usually based on clinical CT scans and material properties assigned are chosen as isotropic based only on the density distribution. It has been shown, however, that trabecular bone elastic behavior is best described as orthotropic. Unfortunately, the use of orthotropic models in FE analysis derived from CT scans is hampered by the fact that the measurement of a trabecular orientation (fabric) is not possible from clinical CT images due to the low resolution of such images. In this study, we explore the concept of using a database (DB) of high-resolution bone models to derive the fabric information that is missing in clinical images. The goal of this study was to investigate if models with fabric derived from a relatively small database can already produce more accurate results than isotropic models.     

Relation between subject-specific hip joint loading, stress distribution in the proximal femur and bone mineral density changes after total hip replacement

In the prediction of bone remodelling processes after total hip replacement (THR), modelling of the subject-specific geometry is now state-of-the-art. In this study, we demonstrate that inclusion of subject-specific loading conditions drastically influences the calculated stress distribution, and hence influences the correlation between calculated stress distributions and changes in bone mineral density (BMD) after THR.For two patients who received cementless THR, personalized finite element (FE) models of the proximal femur were generated representing the pre- and post-operative geometry. FE analyses were performed by imposing subject-specific three-dimensional hip joint contact forces as well as muscle forces calculated based on gait analysis data. Average values of the von Mises stress were calculated for relevant zones of the proximal femur. Subsequently, the load cases were interchanged and the effect on the stress distribution was evaluated. Finally, the subject-specific stress distribution was correlated to the changes in BMD at 3 and 6 months after THR.We found subject-specific differences in the stress distribution induced by specific loading conditions, as interchanging of the loading also interchanged the patterns of the stress distribution. The correlation between the calculated stress distribution and the changes in BMD were affected by the two-dimensional nature of the BMD measurement.Our results confirm the hypothesis that inclusion of subject-specific hip contact forces and muscle forces drastically influences the stress distribution in the proximal femur. In addition to patient-specific geometry, inclusion of patient-specific loading is, therefore, essential to obtain accurate input for the analysis of stress distribution after THR.     

Direct mechanics assessment of elastic symmetries and properties of trabecular bone architecture

A method is presented to find orthotropic elastic symmetries and constants directly from the elastic coefficients in the overall stiffness matrix of trabecular bone test specimens. Contrary to earlier developed techniques, this method does not require pure orthotropic behavior or additional fabric measurements. The method uses high-resolution computer reconstructions of trabecular bone specimens as input for large-scale FE-analyses to determine all the 21 elastic coefficients in the overall stiffness matrix of the specimen, using a direct mechanics approach. An optimization procedure is then used to find the coordinate transformation that yields the best orthotropic representation of this matrix. The method is illustrated here relative to two trabecular bone specimens. The techniques developed here can be used to obtain a complete characterization of the mechanical properties of trabecular architecture. With the development of in vivo reconstruction techniques, even in vivo measurements will be possible.     

Bone ingrowth on the surface of endosseous implants. Part 1: Mathematical model

Osseointegration, understood as an intimate apposition and interdigitation of bone to a biomaterial, is usually regarded as a major condition for the long-term clinical success of bone implants. Clearly, the anchorage of an implant to bone tissue critically relies on the formation of new bone between the implant and the surface of the old peri-implant bone and depends on factors such as the surface microtopography, chemical composition and geometry of the implant, the properties of the surrounding bone and the mechanical loading process. The main contribution of this work is the proposal of a new mathematical framework based on a set of reaction-diffusion equations that try to model the main biological interactions occurring at the surface of implants and is able to reproduce most of the above mentioned biological features of the osseointegration phenomenon. This is a two-part paper. In this first part, a brief biological overview is initially given, followed by the presentation and discussion of the model. In addition, two-dimensional finite element simulations of the bone-ingrowth process around a dental implant with two different surface properties are included to assess the validity of the model. Numerical solutions show the ability of the model to reproduce features such as contact/distance osteogenesis depending upon the specific surface microtopography. In Part 2 [Moreo, P., García-Aznar, J.M., Doblaré, M., 2008. Bone ingrowth on the surface of endosseous implants. Part 2: influence of mechanical stimulation, type of bone and geometry. J. Theor. Biol., submitted for publication], two simplified versions of the whole model are proposed. An analytical study of the stability of fixed points as well as the existence of travelling wave-type solutions has been done with both simplified models, providing a significant insight into the behaviour of the model and giving clues to interpret the effectiveness of recently proposed clinical therapies. Furthermore, we also show that, although the mechanical state of the tissue is not directly taken into account in the model equations, it is possible to analyse in detail the effect that mechanical stimulation would have on the predictions of the model. Finally, numerical simulations are also included in the second part of the paper, with the aim of looking into the influence of implant geometry on the osseointegration process.     

Trabecular bone fracture healing simulation with finite element analysis and fuzzy logic

Trabecular bone fractures heal through intramembraneous ossification. This process differs from diaphyseal fracture healing in that the trabecular marrow provides a rich vascular supply to the healing bone, there is very little callus formation, woven bone forms directly without a cartilage intermediary, and the woven bone is remodelled to form trabecular bone. Previous studies have used numerical methods to simulate diaphyseal fracture healing or bone remodelling, however not trabecular fracture healing, which involves both tissue differentiation and trabecular formation. The objective of this study was to determine if intramembraneous bone formation and remodelling during trabecular bone fracture healing could be simulated using the same mechanobiological principles as those proposed for diaphyseal fracture healing. Using finite element analysis and the fuzzy logic for diaphyseal healing, the model simulated formation of woven bone in the fracture gap and subsequent remodelling of the bone to form trabecular bone. We also demonstrated that the trabecular structure is dependent on the applied loading conditions. A single model that can simulate bone healing and remodelling may prove to be a useful tool in predicting musculoskeletal tissue differentiation in different vascular and mechanical environments.     

The cellular transducer in damage-stimulated bone remodelling: a theoretical investigation using fracture mechanics

This paper reports on some theoretical work which used fracture mechanics concepts to draw conclusions about the nature of the so-called 'cellular transducer': the means by which bone cells detect the presence of damage and thus initiate remodelling and adaptation activities. Using analytical and numerical methods, we estimated the strains and displacements around cracks of the typical size, shape and orientation that normally occur in compact bone. We predicted that it is not possible for osteocytes or their processes to be fractured as a result of direct tensile strains, because the strains generated are much less than the expected failure strains of cellular material. We proposed a new failure mechanism by which osteocyte processes spanning the crack are cut by shearing motions between the crack faces. We predicted that failures of this type can occur. Failures begin to occur if crack lengths become greater than normal (100 microm), so this could act as a signal to initiate repair processes for individual cracks. Very large numbers of cell processes (greater than 1000) will fail if the crack length and/or applied stress reach dangerous levels (300 microm and 60 Mpa, respectively) at which point bone deposition may be required to prevent stress fractures. Similar results also occurred if we proposed a different mechanism of damage detection, involving cells' ability to detect the high levels of strain that occur near crack tips. This work, though based on theoretical mechanics considerations, suggests some biological experiments which might confirm our findings.     

Numerical simulation of load-induced bone structural remodelling using stress-limit criterion

A simple and efficient numerical method for predicting the remodelling of adaptive materials and structures under applied loading was presented and implemented within a finite element framework. The model uses the trajectorial architecture theory of optimisation to predict the remodelling of material microstructure and structural organisation under mechanical loading. We used the proposed model to calculate the density distribution of proximal femur in the frontal plane. The loading considered was the hip joint contact forces and muscular forces at the attachment sites of the muscles to the bone. These forces were estimated from a separate finite element calculation using a heterogeneous three-dimensional model of the proximal femur. The density distributions obtained by this procedure has a qualitative similarity with in vivo observations. Solutions displayed the characteristic high-density channels that are evident in the Dual X-ray Absorptiometry scan. There is also evidence of the intramedullary canal, as well as low-density regions in the femoral neck. Several parametric studies were carried out to highlight the advantages of the proposed method, which includes fast convergence and low-computational cost. The potential applications of the proposed method in predicting bone structural remodelling in cancer are also briefly discussed.     

Thermal analysis of bone cement polymerisation at the cement-bone interface

The two major problems that have been reported with the use of polymethylmethacrylate (PMMA) cement are thermal necrosis of surrounding bone due to the high heat generation during polymerisation and chemical necrosis due to unreacted monomer release. Computer models have been used to study the temperature and monomer distribution after cementation. In most of these models, however, polymerisation is modelled as temperature independent and cancellous bone is modelled as a continuum. Such models thus cannot account for the expected important role of the trabecular bone micro-structure. The aim of this study is to investigate the distribution of temperature and monomer leftover at the cancellous bone–cement interface during polymerisation for a realistic trabecular bone—cement micro-structure and realistic temperature-dependent polymerisation kinetics behaviour.

A 3-D computer model of a piece of bovine cancellous bone that underwent pressurization with bone–cement was generated using a micro-computed tomography scanner. This geometry was used as the basis for a finite element model and a temperature-dependent problem for bone cement polymerisation kinetics was solved to simulate the bone cement polymerisation process in the vicinity of the interface. The transient temperature field throughout the interface was calculated, along with the polymerisation fraction distribution in the cement domain.

The calculations revealed that the tips of the bone trabeculae that are embedded in the cement attain temperatures much higher than the average temperature of the bone volume. A small fraction of the bone (10%) is exposed to temperatures exceeding 70°C, but the exposure time to these high temperatures is limited to 50 s. In the region near the bone, the cement polymerisation fraction (about 84%) is less than that in the centre (where it is reaching values of over 96%). An important finding of this study thus is the fact that the bone tissue that is subjected to the highest temperatures is also subjected to high leftover monomer concentration. Furthermore the maximum bone temperature is reached relatively early, when monomer content in the neighbouring cement is still quite high.     

A bone remodelling model including the directional activity of BMUs

Bone is able to adapt itself to the mechanical and biological environment by changing its porosity and/or orientation of its internal microstructure in a process known as bone remodelling. As a consequence, a change of bone mechanical properties is produced leading to an optimum structure, able to bear the external loads with the minimum weight. This adaptation is carried out by a temporal association of cells known as BMUs (basic multicellular units) that resorb old bone and sometimes produce new organic extracellular matrix (osteoid) that is later mineralized. This involves changes in porosity, damage level (density of microcracks accumulated by cyclic loads) and mineral content. All of these features were taken into account in a previous model, but the whole process and therefore the resulting bone constitutive behaviour was considered isotropic. The model proposed herein, recognizing that bone is actually anisotropic, tries to explain how BMUs modify the anisotropy by changing their progressing direction. We check the potential of the model to predict the alignment of the bone microstructure with the external loads in different situations. Then, the model is also applied to obtain the anisotropy and mechanical properties of the human proximal femur under physiological loads with initial conditions corresponding to a heterogeneous, but otherwise isotropic bone.     

Influence of gait loads on implant integration in rat tibiae: Experimental and numerical analysis

Implanted rat bones play a key role in studies involving fracture healing, bone diseases or drugs delivery among other themes. In most of these studies the implants integration also depends on the animal daily activity and musculoskeletal loads, which affect the implants mechanical environment. However, the tissue adaption to the physiological loads is often filtered through control groups or not inspected. This work aims to investigate experimentally and numerically the effects of the daily activity on the integration of implants inserted in the rat tibia, and to establish a physiological loading condition to analyse the peri-implant bone stresses during gait. Two titanium implants, single and double cortex crossing, are inserted in the rat tibia. The animals are caged under standard conditions and divided in three groups undergoing progressive integration periods. The results highlight a time-dependent increase of bone samples with significant cortical bone loss. The phenomenon is analysed through specimen-specific Finite Element models involving purpose-built musculoskeletal loads. Different boundary conditions replicating the post-surgery bone–implant interaction are adopted. The effects of the gait loads on the implants integration are quantified and agree with the results of the experiments. The observed cortical bone loss can be considered as a transient state of integration due to bone disuse atrophy, initially triggered by a loss of bone–implant adhesion and subsequently by a cyclic opening of the interface.     

Determining the most important cellular characteristics for fracture healing using design of experiments methods

Computational models are employed as tools to investigate possible mechanoregulation pathways for tissue differentiation and bone healing. However, current models do not account for the uncertainty in input parameters, and often include assumptions about parameter values that are not yet established. The objective of this study was to determine the most important cellular characteristics of a mechanoregulatory model describing both cell phenotype-specific and mechanobiological processes that are active during bone healing using a statistical approach. The computational model included an adaptive two-dimensional finite element model of a fractured long bone. Three different outcome criteria were quantified: (1) ability to predict sequential healing events, (2) amount of bone formation at early, mid and late stages of healing and (3) the total time until complete healing. For the statistical analysis, first a resolution IV fractional factorial design (L₆₄) was used to identify the most significant factors. Thereafter, a three-level Taguchi orthogonal array (L₂₇) was employed to study the curvature (non-linearity) of the 10 identified most important parameters. The results show that the ability of the model to predict the sequences of normal fracture healing was predominantly influenced by the rate of matrix production of bone, followed by cartilage degradation (replacement). The amount of bone formation at early stages was solely dependent on matrix production of bone and the proliferation rate of osteoblasts. However, the amount of bone formation at mid and late phases had the rate of matrix production of cartilage as the most influential parameter. The time to complete healing was primarily dependent on the rate of cartilage degradation during endochondral ossification, followed by the rate of cartilage formation. The analyses of the curvature revealed a linear response for parameters related to bone, where higher rates of formation were more beneficial to healing. In contrast, parameters related to fibrous tissue and cartilage showed optimum levels. Some fibrous connective tissue- and cartilage formation was beneficial to bone healing, but too much of either tissue delayed bone formation. The identified significant parameters and processes are further confirmed by in vivo animal experiments in the literature. This study illustrates the potential of design of experiments methods for evaluating computational mechanobiological model parameters and suggests that further experiments should preferably focus at establishing values of parameters related to cartilage formation and degradation.     

Intravoxel bone micromechanics for microCT-based finite element simulations

While micro-FE simulations have become a standard tool in computational biomechanics, the choice of appropriate material properties is still a relevant topic, typically involving empirical grey value-to-elastic modulus relations. We here derive the voxel-specific volume fractions of mineral, collagen, and water, from tissue-independent bilinear relations between mineral and collagen content in extracellular bone tissue (J. Theor. Biol. 287: 115, 2011), and from the measured X-ray attenuation information quantified in terms of grey values. The aforementioned volume fractions enter a micromechanics representation of bone tissue, as to deliver voxel-specific stiffness tensors. In order to check the relevance of this strategy, we convert a micro Computer Tomograph of a mouse femur into a regular Finite Element mesh, apply forces related to the dead load of a standing mouse, and then compare simulation results based on voxel-specific heterogeneous elastic properties to results based on homogeneous elastic properties related to the spatial average over the solid bone matrix compartment, of the X-ray attenuation coefficients. The element-specific strain energy density illustrates that use of homogeneous elastic properties implies overestimation of the organ stiffness. Moreover, the simulation reveals large tensile normal stresses throughout the femur neck, which may explain the mouse femur neck's trabecular morphology being quite different from the human case, where the femur neck bears compressive forces and bending moments.