A contact model with ingrowth control for bone remodelling around cementless stems.

This work presents a computational model for bone remodelling around cementless stems. The problem is formulated as a material optimisation problem considering the bone and stem surfaces to be in contact. To emphasise the behaviour of the bone/stem interface, the computer model detects the existence of bone ingrowth during the remodelling; consequently, the contact conditions are changed for a better interface simulation. The trabecular bone is modelled as a strictly orthotropic material with equivalent properties computed by homogenisation. The distribution of bone relative density is obtained by the minimisation of a function that considers both the bone structural stiffness and the biological cost associated with metabolic maintenance of bone tissue. The situation of multiple load conditions is considered. The remodelling law, obtained from the necessary conditions for an optimum, is derived analytically from the optimisation problem and solved numerically using a suitable finite element mesh. The formulation is applied to an implanted femur. Results of bone density and ingrowth distribution are obtained for different coating conditions. Bone ingrowth does not occur over the entire coated surfaces. Indeed, we observed regions where separation or high relative displacement occurs that preclude bone ingrowth attachment. This prediction of the model is consistent with clinical observations of bone ingrowth. Thus, this model, which detect bone ingrowth and allow modification of the interface conditions, are useful for analysis of existing stems as well as design optimisation of coating extent and location on such stems.     

Numerical modeling of bone tissue adaptation—A hierarchical approach for bone apparent density and trabecular structure

In this work, a three-dimensional model for bone remodeling is presented, taking into account the hierarchical structure of bone. The process of bone tissue adaptation is mathematically described with respect to functional demands, both mechanical and biological, to obtain the bone apparent density distribution (at the macroscale) and the trabecular structure (at the microscale). At global scale bone is assumed as a continuum material characterized by equivalent (homogenized) mechanical properties. At local scale a periodic cellular material model approaches bone trabecular anisotropy as well as bone surface area density. For each scale there is a material distribution problem governed by density-based design variables which at the global level can be identified with bone relative density. In order to show the potential of the model, a three-dimensional example of the proximal femur illustrates the distribution of bone apparent density as well as microstructural designs characterizing both anisotropy and bone surface area density. The bone apparent density numerical results show a good agreement with Dual-energy X-ray Absorptiometry (DXA) exams. The material symmetry distributions obtained are comparable to real bone microstructures depending on the local stress field. Furthermore, the compact bone porosity is modeled giving a transversal isotropic behavior close to the experimental data. Since, some computed microstructures have no permeability one concludes that bone tissue arrangement is not a simple stiffness maximization issue but biological factors also play an important role.     

A topology optimization based model of bone adaptation

A novel topology optimization model based on homogenization methods was developed for predicting bone density distribution and anisotropy, assuming the bone structure to be a self-optimizing biological material which maximizes its own structural stiffness. The feasibility and efficiency of this method were tested on a 2D model for a proximal femur under single and multiple loading conditions. The main aim was to compute homogenized optimal designs using an optimal laminated microstructure. The computational results showed that high bone density levels are distributed along the diaphysis and form arching struts within the femoral head. The pattern of bone density distribution and the anisotropic bone behavior predicted by the model in the multiple load case were both in good agreement with the structural architecture and bone density distribution occurring in natural femora. This approach provides a novel means of understanding the remodeling processes involved in fracture repair and the treatment of bone diseases.     

A topology optimization based model of bone adaptation

A novel topology optimization model based on homogenization methods was developed for predicting bone density distribution and anisotropy, assuming the bone structure to be a self-optimizing biological material which maximizes its own structural stiffness. The feasibility and efficiency of this method were tested on a 2D model for a proximal femur under single and multiple loading conditions. The main aim was to compute homogenized optimal designs using an optimal laminated microstructure. The computational results showed that high bone density levels are distributed along the diaphysis and form arching struts within the femoral head. The pattern of bone density distribution and the anisotropic bone behavior predicted by the model in the multiple load case were both in good agreement with the structural architecture and bone density distribution occurring in natural femora. This approach provides a novel means of understanding the remodeling processes involved in fracture repair and the treatment of bone diseases.     

A meshless microscale bone tissue trabecular remodelling analysis considering a new anisotropic bone tissue material law

In this work, a novel anisotropic material law for the mechanical behaviour of the bone tissue is proposed. This new law, based on experimental data, permits to correlate the bone apparent density with the obtained level of stress. Combined with the proposed material law, a biomechanical model for predicting bone density distribution was developed, based on the assumption that the bone structure is a gradually self-optimising anisotropic biological material that maximises its own structural stiffness. The strain and the stress field required in the iterative remodelling process are obtained by means of an accurate meshless method, the Natural Neighbour Radial Point Interpolation Method (NNRPIM). Comparing with other numerical approaches, the inclusion of the NNRPIM presents numerous advantages such as the high accuracy and the smoother stress and strain field distribution. The natural neighbour concept permits to impose organically the nodal connectivity and facilitates the analysis of convex boundaries and extremely irregular meshes. The viability and efficiency of the model were tested on several trabecular benchmark patch examples. The results show that the pattern of the local bone apparent density distribution and the anisotropic bone behaviour predicted by the model for the microscale analysis are in good agreement with the expected structural architecture and bone apparent density distribution.     

Computational simulation of simultaneous cortical and trabecular bone change in human proximal femur during bone remodeling

In this study, we developed a numerical framework that computationally determines simultaneous and interactive structural changes of cortical and trabecular bone types during bone remodeling, and we investigated the structural correlation between the two bone types in human proximal femur. We implemented a surface remodeling technique that performs bone remodeling in the exterior layer of the cortical bone while keeping its interior area unchanged. A micro-finite element (μFE) model was constructed that represents the entire cortical bone and full trabecular architecture in human proximal femur. This study simulated and compared the bone adaptation processes of two different structures: (1) femoral bone that has normal cortical bone shape and (2) perturbed femoral bone that has an artificial bone lump in the inferomedial cortex. Using the proposed numerical method in conjunction with design space optimization, we successfully obtained numerical results that resemble actual human proximal femur. The results revealed that actual cortical bone, as well as the trabecular bone, in human proximal femur has structurally optimal shapes, and it was also shown that a bone abnormality that has little contribution to bone structural integrity tends to disappear. This study also quantitatively determined the structural contribution of each bone: when the trabecular adaptation was complete, the trabecular bone supported 54% of the total load in the human proximal femur while the cortical bone carried 46%.     

The impact of the parameters of the constitutive model on the distribution of strain in the femoral head

The rapid spread of the finite element method has caused that it has become, among other methods, the standard tool for pre-clinical estimates of bone properties. This paper presents an application of this method for the calculation and prediction of strain and stress fields in the femoral head. The aim of the work is to study the influence of the considered anisotropy and heterogeneity of the modeled bone on the mechanical fields during a typical gait cycle. Three material models were tested with different properties of porous bone carried out in literature: a homogeneous isotropic model, a heterogeneous isotropic model, and a heterogeneous anisotropic model. In three cases studied, the elastic properties of the bone were determined basing on the Zysset-Curnier approach. The tensor of elastic constants defining the local properties of porous bone is correlated with a local porosity and a second order fabric tensor describing the bone microstructure. In the calculations, a model of the femoral head generated from high-resolution tomographic scans was used. Experimental data were drawn from publicly available database “Osteoporotic Virtual Physiological Human Project.” To realistically reflect the load on the femoral head, main muscles were considered, and their contraction forces were determined based on inverse kinematics. For this purpose, the results from OpenSim packet were used. The simulations demonstrated that differences between the results predicted by these material models are significant. Only the anisotropic model allowed for the plausible distribution of stresses along the main trabecular groups. The outcomes also showed that the precise evaluation of the mechanical fields is critical in the context of bone tissue remodeling under mechanical stimulations.

     

Consideration of multiple load cases is critical in modelling orthotropic bone adaptation in the femur

Functional adaptation of the femur has been investigated in several studies by embedding bone remodelling algorithms in finite element (FE) models, with simplifications often made to the representation of bone’s material symmetry and mechanical environment. An orthotropic strain-driven adaptation algorithm is proposed in order to predict the femur’s volumetric material property distribution and directionality of its internal structures within a continuum. The algorithm was applied to a FE model of the femur, with muscles, ligaments and joints included explicitly. Multiple load cases representing distinct frames of two activities of daily living (walking and stair climbing) were considered. It is hypothesised that low shear moduli occur in areas of bone that are simply loaded and high shear moduli in areas subjected to complex loading conditions. In addition, it is investigated whether material properties of different femoral regions are stimulated by different activities. The loading and boundary conditions were considered to provide a physiological mechanical environment. The resulting volumetric material property distribution and directionalities agreed with ex vivo imaging data for the whole femur. Regions where non-orthogonal trabecular crossing has been documented coincided with higher values of predicted shear moduli. The topological influence of the different activities modelled was analysed. The influence of stair climbing on the properties of the femoral neck region is highlighted. It is recommended that multiple load cases should be considered when modelling bone adaptation. The orthotropic model of the complete femur is released with this study.     

A model of bone adaptation as an optimization process

The internal bone adaptation of the proximal femur is considered. A three-dimensional finite element model of the proximal femur is used. The bone remodeling in this work is numerically described by an evolutionary remodeling scheme with anisotropic material parameters and time-dependent loading. The memory of past loading is included in the model to account for the delay in the bone response from the load changes. The remodeling rate equation is derived from the structural optimization task of maximizing the stiffness in each time step. Additional information can be extracted from the optimization process; the remodeling equilibrium parameter where no apposition or resorption takes place, is defined as the element optimality conditions and the optimal design is used as an initial design for the onset of the remodeling simulation. Two examples of bone adaptation resulting from load changes are given, and the irreversible nature of the model is illustrated.     

Material changes in osteoporotic human cancellous bone following infiltration with acrylic bone cement for a vertebral cement augmentation

Bone cement infiltration can be effective at mechanically augmenting osteoporotic vertebrae. While most published literature describes the gain in mechanical strength of augmented vertebrae, we report the first measurements of viscoelastic material changes of cancellous bone due to cement infiltration. We infiltrated cancellous core specimen harvested from osteoporotic cadaveric spines with acrylic bone cement. Bone specimen before and after cement infiltration were subjected to identical quasi-static and relaxation loading in confined and free compression. Testing data were fitted to a linear viscoelastic model of compressible material and the model parameters for cement, native cancellous bone, and cancellous bone infiltrated (composite) with cement were identified. The fitting demonstrated that the linear viscoelastic model presented in this paper accurately describes the mechanical behaviour of cement and bone, before and after infiltration. Although the composite specimen did not completely adopt the properties of bulk bone cement, the stiffening of cancellous bone due to cement infiltration is considerable. The composite was, for example, 8.5 times stiffer than native bone. The local stiffening of cancellous bone in patients may alter the load transfer of the augmented motion segment and may be the cause of subsequent fractures in the vertebrae adjacent to the ones infiltrated with cement. The material model and parameters in this paper, together with an adequate finite-element model, can be helpful to investigate the load shift, the mechanism for subsequent fractures, and filling patterns for ideal cement infiltration.     

Analysis of bone architecture sensitivity for changes in mechanical loading, cellular activity, mechanotransduction, and tissue properties

Bone has an architecture which is optimized for its mechanical environment. In various conditions, this architecture is altered, and the underlying cause for this change is not always known. In the present paper, we investigated the sensitivity of the bone microarchitecture for four factors: changes in bone cellular activity, changes in mechanical loading, changes in mechanotransduction, and changes in mechanical tissue properties. The goal was to evaluate whether these factors can be the cause of typical bone structural changes seen in various pathologies. For this purpose, we used an established computational model for the simulation of bone adaptation. We performed two sensitivity analyses to evaluate the effect of the four factors on the trabecular structure, in both developing and adult bone. According to our simulations, alterations in mechanical load, bone cellular activities, mechanotransduction, and mechanical tissue properties may all result in bone structural changes similar to those observed in various pathologies. For example, our simulations confirmed that decreases in loading and increases in osteoclast number and activity may lead to osteoporotic changes. In addition, they showed that both increased loading and decreased bone matrix stiffness may lead to bone structural changes similar to those seen in osteoarthritis. Finally, we found that the model may help in gaining a better understanding of the contribution of individual disturbances to a complicated multi-factorial disease process, such as osteogenesis imperfecta.     

Trabecular bone adaptation with an orthotropic material model.

Most bone adaptation algorithms, that attempt to explain the connection between bone morphology and loads, assume that bone is effectively isotropic. An isotropic material model can explain the bone density distribution, but not the structure and pattern of trabecular bone, which clearly has a mechanical significance. In this paper, an orthotropic material model is utilized to predict the proximal femur trabecular structure. Two hypotheses are combined to determine the local orientation and material properties of each element in the model. First, it is suggested that trabecular directions, which correspond to the orthotropic material axes, are determined locally by the maximal principal stress directions due to the multiple load cases (MLC) the femur is subject to. The second hypothesis is that material properties in each material direction can be determined using directional stimuli, thus extending existing adaptation algorithms to include directionality. An algorithm is utilized, where each iteration comprises of two stages. First, material axes are rotated to the direction of the largest principal stress that occurs from a multiple load scheme applied to the proximal femur. Next, material properties are modified in each material direction, according to a directional stimulus. Results show that local material directions correspond with known trabecular patterns, reproducing all main groups of trabeculae very well. The local directional stiffnesses, degree of anisotropy and density distribution are shown to conform to real femur morphology.     

Material Changes in Osteoporotic Human Cancellous Bone Following Infiltration with Acrylic Bone Cement for a Vertebral Cement Augmentation

Bone cement infiltration can be effective at mechanically augmenting osteoporotic vertebrae. While most published literature describes the gain in mechanical strength of augmented vertebrae, we report the first measurements of viscoelastic material changes of cancellous bone due to cement infiltration. We infiltrated cancellous core specimen harvested from osteoporotic cadaveric spines with acrylic bone cement. Bone specimen before and after cement infiltration were subjected to identical quasi-static and relaxation loading in confined and free compression. Testing data were fitted to a linear viscoelastic model of compressible material and the model parameters for cement, native cancellous bone, and cancellous bone infiltrated (composite) with cement were identified. The fitting demonstrated that the linear viscoelastic model presented in this paper accurately describes the mechanical behaviour of cement and bone, before and after infiltration. Although the composite specimen did not completely adopt the properties of bulk bone cement, the stiffening of cancellous bone due to cement infiltration is considerable. The composite was, for example, 8.5 times stiffer than native bone. The local stiffening of cancellous bone in patients may alter the load transfer of the augmented motion segment and may be the cause of subsequent fractures in the vertebrae adjacent to the ones infiltrated with cement. The material model and parameters in this paper, together with an adequate finite-element model, can be helpful to investigate the load shift, the mechanism for subsequent fractures, and filling patterns for ideal cement infiltration.     

The effects of simulated weightlessness on bone biomechanical and biochemical properties in the maturing rat

Histomorphometric and biomechanical changes in bone resulting from hypogravity (simulated weightlessness) were examined in this study. Using a head-down hindlimb suspension model, three groups of six male rats underwent simulated weightlessness for periods of one, two and three weeks while a fourth recovery group was suspended for two weeks followed by two weeks of normal activity. Biomechanical data were collected during static and dynamic bending and torsion tests on intact femora. Histomorphometric values were determined from midshaft bone cross sections and material properties were obtained using ash and calcium assays. The experimental groups exhibited significantly lower geometric and material properties than the controls, resulting in structural hypotrophy; geometric and material changes contributed equally to the structural changes. Recovery following a return to normal activity was indicated, although full recovery may take longer than the weightlessness period. In the rat, altered maturation and reduced bone strength were the sequelae of weightlessness.     

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.     

An improved method to assess torsional properties of rodent long bones

Torsion is an important testing modality commonly used to calculate structural properties of long bones. However, the effects of size and geometry must be excluded from the overall structural response in order to compare material properties of bones of different size, age and species. We have developed a new method to analyze torsional properties of bones using actual cross-sectional information and length-wise geometrical variations obtained by micro-computed topographic (μCT) imaging. The proposed method was first validated by manufacturing three rat femurs through rapid prototyping using a plastic with known material properties. The observed variations in calculated torsional shear modulus of the hollow elliptical model of mid-shaft cross-section (Ekeland et al.), multi-prismatic model of five true cross-sections (Levenston et al.) and multi-slice model presented in this study were 96%, ?7% and 6% from the actual properties of the plastic, respectively. Subsequently, we used this method to derive relationships expressing torsional properties of rat cortical bone as a function of μCT-based bone volume fraction or apparent density over a range of normal and pathologic bone densities. Results indicate that a regression model of shear modulus or shear strength and bone volume fraction or apparent density described at least 81% of the variation in torsional properties of normal and pathologic bones. Coupled with the structural rigidity analysis technique introduced by the authors, the relationships reported here can provide a non-invasive tool to assess fracture risk in bones affected by pathologies and/or treatment options.     

Analysis of arch‐like bones: The rodent mandible as a case study

Bone strength is determined by the mechanical properties of bone material, and the size and shape of the whole bone, i.e., its architecture. The mandible of vertebrates has been traditionally regarded as a beam oriented in relation to main masticatory loads, i.e., the longer dimension of its cross‐section being parallel to the load. Rodents follow this pattern but, in addition, their mandible possesses an intriguing arch‐like shape that is apparent when seen in the lateral view. Little attention was given to the structural capacity of this trait. The advantage of an arch is that it can withstand a greater load than a horizontal beam. The objective of this study was to model the rodent mandible like an arch to evaluate its structural strength. The bending moment in an arch‐like mandible was 15–25% lower with respect to a beam‐like mandible. Further, bending varies with mandible “slenderness” and incisor procumbency, a functionally relevant rodent trait. In the rodent Ctenomys talarum (Caviomorpha; Ctenomyidae), bone stress was substantially reduced when the mandible was modeled as an arch‐like structure as compared with a beam‐like structure, and safety factors were 15–34% higher. The shape of rodents' mandible might confer a functional advantage to high and repeatedly applied loads resulting from a unique feeding mode: gnawing. J. Morphol. 277:879–887, 2016. © 2016 Wiley Periodicals, Inc.     

Comparison of two systems for tibial external fixation in rabbits

BACKGROUND AND PURPOSE: Use of rabbits in orthopedic investigations is common. In this study, focus is on factors that influence bone healing and on distraction osteogenesis. Biomechanical characteristics of two external fixator systems (Orthofix device and Hoffmann device) for long bones were tested. METHODS: Twelve freshly dissected tibiae were obtained from six skeletally mature New Zealand White rabbits, and four-point bending stiffness in two planes (90 and 180 degrees to the fixator pins) and torsional stiffness and strength of the bone-fixator complex were evaluated by use of a material testing machine. RESULTS: In four-point bending, Orthofix device had higher stiffness and strength, compared with Hoffmann device. When the load was applied 180 degrees to the pins, both devices had higher stiffness, compared with that at 90 degrees. In torsional testing, Orthofix device had significantly higher stiffness and strength. CONCLUSIONS: Significant differences in structural properties between the two systems were evident. Loading direction and gap conditions were important factors in determining properties of the systems. Therefore, type of external fixation system and fixation technique should be considered when designing experiments, using the rabbit long bone model.     

Fracture prediction for the proximal femur using finite element models: Part II--Nonlinear analysis.

In Part I we reported the results of linear finite element models of the proximal femur generated using geometric and constitutive data collected with quantitative computed tomography. These models demonstrated excellent agreement with in vitro studies when used to predict ultimate failure loads. In Part II, we report our extension of those finite element models to include nonlinear behavior of the trabecular and cortical bone. A highly nonlinear material law, originally designed for representing concrete, was used for trabecular bone, while a bilinear material law was used for cortical bone. We found excellent agreement between the model predictions and in vitro fracture data for both the onset of bone yielding and bone fracture. For bone yielding, the model predictions were within 2 percent for a load which simulated one-legged stance and 1 percent for a load which simulated a fall. For bone fracture, the model predictions were within 1 percent and 17 percent, respectively. The models also demonstrated different fracture mechanisms for the two different loading configurations. For one-legged stance, failure within the primary compressive trabeculae at the subcapital region occurred first, leading to load transfer and, ultimately, failure of the surrounding cortical shell. However, for a fall, failure of the cortical and trabecular bone occurred simultaneously within the intertrochanteric region. These results support our previous findings that the strength of the subcapital region is primarily due to trabecular bone whereas the strength of the intertrochanteric region is primarily due to cortical bone.     

Numerical studies of the influence of various geometrical features of a multispiked connecting scaffold prototype on mechanical stresses in peri-implant bone

Abstract

The multispiked connecting scaffold (MSC-scaffold) prototype is an essential innovation in the fixation of components of resurfacing arthroplasty (RA) endoprostheses, providing their entirely non-cemented and bone-tissue-preserving fixation in peri-articular bone. An FE study is proposed to evaluate the influence of geometrical features of the MSC-scaffold on the transfer of mechanical load in peri-implant bone. For this study, an FE model of Ti-Alloy MSC-scaffold prototype embedded in a bilinear elastic, transversely isotropic bone material was built. For the compressive load on the MSC-scaffold, maps of Huber-Mises-Hencky (HMH) stress in peri-implant bone were determined. The influence of the distance between the bases of neighbouring spikes, the apex angle of spikes, and the height of the spherical cup of spikes of the MSC-scaffold were analysed. It was found that the changes in the distance between the bases of neighbouring spikes from 0.2 to 0.5?mm cause the HMH stress to increase in bone material by 32%. The changes of the apex angle of spikes from 2° to 4° decrease the HMH stress in bone material by 39%. The changes of height of the spherical cup of spikes from 0 to 0.12?mm increase the HMH stress in bone material by 24%. In conclusion, the spikes’ apex angle and the distance between the bases of spikes of the MSC-scaffold are the key geometrical features determining the appropriate MSC-scaffold prototype design. The built FE model was found to be useful in bioengineering design of the novel fixation system for RA endoprostheses by means of the MSC-scaffold.