Numerical estimation of bone density and elastic constants distribution in a human mandible

In this paper, we try to predict the distribution of bone density and elastic constants in a human mandible, based on the stress level produced by mastication loads using a mathematical model of bone remodelling. These magnitudes are needed to build finite element models for the simulation of the mandible mechanical behavior. Such a model is intended for use in future studies of the stability of implant-supported dental prostheses. Various models of internal bone remodelling, both phenomenological and more recently mechanobiological, have been developed to determine the relation between bone density and the stress level that bone supports. Among the phenomenological models, there are only a few that are also able to reproduce the level of anisotropy. These latter have been successfully applied to long bones, primarily the femur. One of these models is here applied to the human mandible, whose corpus behaves as a long bone. The results of bone density distribution and level of anisotropy in different parts of the mandible have been compared with various clinical studies, with a reasonable level of agreement.     

Comparative analysis of bone remodelling models with respect to computerised tomography-based finite element models of bone

Subject-specific finite element models are an extensively used tool for the numerical analysis of the biomechanical behaviour of human bones. However, bone modelling is not an easy task due to the complex behaviour of bone tissue, involving non-homogeneous and anisotropic mechanical properties. Moreover, bone is a living tissue and therefore its microstructure and mechanical properties evolve with time in a known process called bone remodelling. This phenomenon has been widely studied, many being the numerical models that have been formulated to predict density distribution and its evolution in several bones. The aim of the present study is to assess the capability of a bone remodelling model to predict the bone density distribution of different types of human bone (femur, tibia and mandible) comparing the obtained results with the bone density estimated by means of computerised tomography. Good accuracy was observed for the bone remodelling predictions including the thickness of the cortical layer.     

Impact of low-dose prednisolone on bone synthesis and resorption in early rheumatoid arthritis: experiences from a two-year randomized study

Introduction  

Patients with rheumatoid arthritis (RA) have an increased frequency of osteoporosis, mainly because of increased bone resorption. Reduction of disease activity is suggested to reduce bone remodelling. It might also be possible that prednisolone treatment could cause this effect because prednisolone has been shown to arrest the development of joint destruction in early RA. Therefore, we examined the effects of low-dose prednisolone on serum concentrations of bone remodelling markers and insulin-like growth factor-1 (IGF-1) in RA patients in relation to bone mineral density.     

Finite element analysis of bone remodelling with piezoelectric effects using an open-source framework

Bone tissue exhibits piezoelectric properties and thus is capable of transforming mechanical stress into electrical potential. Piezoelectricity has been shown to play a vital role in bone adaptation and remodelling processes. Therefore, to better understand the interplay between mechanical and electrical stimulation during these processes, strain-adaptive bone remodelling models without and with considering the piezoelectric effect were simulated using the Python-based open-source software framework. To discretise numerical attributes, the finite element method (FEM) was used for the spatial variables and an explicit Euler scheme for the temporal derivatives. The predicted bone apparent density distributions were qualitatively and quantitatively evaluated against the radiographic scan of a human proximal femur and the bone apparent density calculated using a bone mineral density (BMD) calibration phantom, respectively. Additionally, the effect of the initial bone density on the resulting predicted density distribution was investigated globally and locally. The simulation results showed that the electrically stimulated bone surface enhanced bone deposition and these are in good agreement with previous findings from the literature. Moreover, mechanical stimuli due to daily physical activities could be supported by therapeutic electrical stimulation to reduce bone loss in case of physical impairment or osteoporosis. The bone remodelling algorithm implemented using an open-source software framework facilitates easy accessibility and reproducibility of finite element analysis made.

     

Bone histological correlates of high-frequency flapping flight and body mass in the furculae of birds: a phylogenetic approach

A parsimony optimization of the presence of high-frequency flapping flight onto a phylogeny of 29 species of birds shows that this is a derived character state that has been acquired at least four independent times: by the last common ancestor of Alcidae, that of Podicipedidae, that of Anatidae, and that of Rallidae. Cineradiographic analysis has shown that the furculae of birds underwent extraordinary deformations during the wingbeat cycle. Cyclical deformations are known to produce microfractures in the bone tissue, which may be a stimulus for Haversian remodelling, a mechanism of resorption and reconstruction of bone tissue that may repair bone microdamage. In the present study, we performed a comparative analysis in a phylogenetic context to test the effect of the frequency of cyclical deformations and body mass on the rate of Haversian remodelling in the furculae of birds. A variation partitioning analysis showed that the type of flight (high-frequency flapping flight vs. other kinds of flight of lower wing beat frequency) and body mass explained a significant portion of Haversian bone density (the outcome of Haversian remodelling) and that the phylogeny also explained a significant part of this variation. This phylogenetic signal on Haversian bone density variation may be the outcome of phylogenetic signal on the proximate causes producing Haversian remodelling.  © 2007 The Linnean Society of London, Biological Journal of the Linnean Society , 2007, 91 , 729–738.     

Prediction of bone adaptation in the ulnar-osteotomized sheep's forelimb using an anatomical finite element model

A method for the prediction of the time-course of bone adaptation based on an alternative hypothesis of strength optimization has been previously investigated and developed by Prendergast and Taylor¹. This paper extends our work in the study of the effectiveness of this bone adaptation model in predicting similar bone remodelling to that observed in animal experiments. In particular the experimental work which has been modelled is that of Lanyon, Goodship, Pye and McFie². An anatomical finite element model of the sheep's forelimb has been generated for this purpose and is used to estimate stresses in the bone structure for the normal and osteotomized condition. The propensity for remodelling of the altered bone structure is predicted using the proposed remodelling law for the new stress field in the bone structure. The preliminary results indicate an initial bone adaptation pattern similar to that observed experimentally without the necessity to use arbitrarily different constants for the endosteal and periosteal surfaces. We therefore suggest that the remodelling law based on damage and repair gives a better predictive model of bone adaptation than previous models.     

Computational simulation of internal bone remodelling around dental implants: a sensitivity analysis

This study aimed to predict the distribution of bone trabeculae, as a density change per unit time, around a dental implant based on applying a selected mathematical remodelling model. The apparent bone density change as a function of the mechanical stimulus was the base of the applied remodelling model that describes disuse and overload bone resorption. The simulation was tested in a finite element model of a screw-shaped dental implant in an idealised bone segment. The sensitivity of the simulation to different mechanical parameters was investigated; these included element edge length, boundary conditions, as well as direction and magnitude of the implant loads. The alteration in the mechanical parameters had a significant influence on density distribution and model stability, in particular at the cortical bone region. The remodelling model could succeed to achieve trabeculae-like structure around osseointegrated dental implants. The validation of this model to a real clinical case is required.     

Computational simulation of internal bone remodelling around dental implants: a sensitivity analysis

This study aimed to predict the distribution of bone trabeculae, as a density change per unit time, around a dental implant based on applying a selected mathematical remodelling model. The apparent bone density change as a function of the mechanical stimulus was the base of the applied remodelling model that describes disuse and overload bone resorption. The simulation was tested in a finite element model of a screw-shaped dental implant in an idealised bone segment. The sensitivity of the simulation to different mechanical parameters was investigated; these included element edge length, boundary conditions, as well as direction and magnitude of the implant loads. The alteration in the mechanical parameters had a significant influence on density distribution and model stability, in particular at the cortical bone region. The remodelling model could succeed to achieve trabeculae-like structure around osseointegrated dental implants. The validation of this model to a real clinical case is required.     

Fluid-induced osteolysis: modelling and experiments

A model to calculate bone resorption driven by fluid flow at the bone–soft tissue interface is developed and used as a basis for computer calculations, which are compared to experiments where bone is subjected to fluid flow in a rat model. Previous models for bone remodelling calculations have been based on the state of stress, strain or energy density of the bone tissue as the stimulus for remodelling. We believe that there is experimental support for an additional pathway where an increase in the amount of the cells directly involved in bone removal, the osteoclasts, is caused by fluid pressure, flow velocity or other parameters related to fluid flow at the bone–soft tissue interface, resulting in bone resorption.     

Fluid-induced osteolysis: modelling and experiments

A model to calculate bone resorption driven by fluid flow at the bone-soft tissue interface is developed and used as a basis for computer calculations, which are compared to experiments where bone is subjected to fluid flow in a rat model. Previous models for bone remodelling calculations have been based on the state of stress, strain or energy density of the bone tissue as the stimulus for remodelling. We believe that there is experimental support for an additional pathway where an increase in the amount of the cells directly involved in bone removal, the osteoclasts, is caused by fluid pressure, flow velocity or other parameters related to fluid flow at the bone-soft tissue interface, resulting in bone resorption.     

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.     

Volume to density relation in adult human bone tissue

Uniformity of tissue mineralisation is a strongly debated issue, due to its relation with bone mechanical behaviour. Bone mineral density (BMD) is measured in the clinical practice and is applied in computational application to derive material proprieties of bone tissue. However, BMD cannot identify if the variation in bone density is related to a modification of tissue mineral density (TMD), a change in bone volume or a combination of the two. This study was aimed to investigate whether TMD can be assumed as a constant in adult human bone (trabecular and cortical).A total number of 115 cylindrical bone specimens were collected. An inter-site analysis (96 specimens, 2 donors) was performed on cortical and trabecular specimens extracted from different anatomical sites. An intra-site study (19 specimens, 19 donors) was performed on specimens extracted from femoral heads. Bone volume fraction (BV/TV) was computed by means of a micro-computed tomography. Furthermore, ash density (ρ_ash) was measured. TMD was computed as the ratio between ρ_ash and BV/TV.It was found that the TMD of trabecular (1.24±0.16 g/cm³) and cortical (1.19±0.06 g/cm³) bone were not statistically different (p=0.31). Furthermore, the linear regression between ρ_ash and BV/TV was statistically significant (r²=0.99, p<0.001). Intra- and inter-site analyses demonstrated that the mineral distribution was independent of the extraction site.The present study suggests that TMD can be assumed reasonably constant in non-pathological adult bone tissue. Consequently, it is suggested that TMD can be managed as a constant in computational models, varying only BV in relation to clinical densitometric analysis.     

The ontogeny of bone growth in two species of dormice: Reconstructing life history traits

Though bone histology has become a powerful tool to reconstruct life history strategies and physiology in living and extinct reptiles and amphibians, it is of limited use in mammals. Dormice (Myoxidae) are good candidates for assessing the relation between bone microstructure and life history due to their long life span, marked physiological cycles and negligible bone remodelling. We carried out the most comprehensive study so far analyzing 16 wild individuals of unknown age belonging to two different species of dormice, Glis glis and Eliomys quercinus. Our study shows a high degree of consistency in the number of resting lines present in bones of the same individual, with femora providing the most accurate age estimations. Moreover, the presence of a single LAG in some juveniles allows discerning between offspring from different reproductive events (early or late litters).     

Bone remodelling around the tibia due to total ankle replacement: effects of implant material and implant–bone interfacial conditions

Abstract

One of the major causes of implant loosening is due to excessive bone resorption surrounding the implant due to bone remodelling. The objective of the study is to investigate the effects of implant material and implant–bone interface conditions on bone remodelling around tibia bone due to total ankle replacement. Finite element models of intact and implanted ankles were developed using CT scan data sets. Bone remodelling algorithm was used in combination with FE analysis to predict the bone density changes around the ankle joint. Dorsiflexion, neutral, and plantar flexion positions were considered, along with muscle force and ligaments. Implant–bone interfacial conditions were assumed as debonded and bonded to represent non-osseointegration and fully osseointegration at the porous coated surface of the implant. To investigate the effect of implant material, three finite element models having different material combinations of the implant were developed. For model 1, tibial and talar components were made of Co–Cr–Mo, and meniscal bearing was made of UHMWPE. For model 2, tibial and talar components were made of ceramic and meniscal bearing was made of UHMWPE. For model 3, tibial and talar components were made of ceramic and meniscal bearing was made of CFR-PEEK. Changes in implant material showed no significant changes in bone density due to bone remodelling. Therefore, ceramic appears to be a viable alternative to metal and CFR-PEEK can be used in place of UHMWPE. This study also indicates that proper bonding between implant and bone is essential for long-term survival of the prosthetic components.     

Bone surface structure in osteopetrotic grey lethal (gl/gl) and microphthalmic (mi/mi) mutant mice as revealed by scanning electron microscopy

The surface structure of bone from two genetically distinct osteopetrotic strains of mice, grey lethal (gl) and microphthalmic (mi) has been examined by scanning electron microscopy. Although both conditions produce a classical osteopetrolic phenotype the means by which this is achieved is quite different. gl mice appear to retain woven bone and show no evidence of resorption: mi mice show evidence of imperfect remodelling. These results are in accordance with what is already known of osteoclast structure and function in these mutations.     

Sensitivity Analysis and Optimal Shape Design for Bone-Prosthesis Interfaces in a Femoral Head Surface Replacement

Abstract

A numerical optimization procedure has been applied for the shape optimal design of a femoral head surface replacement. The failure modes of the prosthesis that were considered in the formulation of the objective functions concerned the interface stress magnitude and the bone remodelling activity beneath the implant. In order to find a compromising solution between different requirements demanded by the two objective functions, a two step optimization procedure has been developed. Through step I the minimization of interface stress was achieved, through step 2 the minimization of bone remodelling was achieved with constraints on interface stresses.

The results obtained provided an optimal design that generates limited bone remodelling activity with controlled interface stress distribution.

The computational procedure was based on the application of the finite element method, linked to a mathematical programming package and a design sensitivity analysis package.     

A coupled mechano-biochemical model for bone adaptation

Bone remodelling is a fundamental biological process that controls bone microrepair, adaptation to environmental loads and calcium regulation among other important processes. It is not surprising that bone remodelling has been subject of intensive both experimental and theoretical research. In particular, many mathematical models have been developed in the last decades focusing in particular aspects of this complicated phenomenon where mechanics, biochemistry and cell processes strongly interact. In this paper, we present a new model that combines most of these essential aspects in bone remodelling with especial focus on the effect of the mechanical environment into the biochemical control of bone adaptation mainly associated to the well known RANKL-RANK-OPG pathway. The predicted results show a good correspondence with experimental and clinical findings. For example, our results indicate that trabecular bone is more severely affected both in disuse and disease than cortical bone what has been observed in osteoporotic bones. In future, the methodology proposed would help to new therapeutic strategies following the evolution of bone tissue distribution in osteoporotic patients.     

Simulating localised cellular inflammation and substrate properties in a strain energy density based bone remodelling algorithm for use in modelling trauma

Bone responds to mechanical stimulus and a range of pre-existing finite element models have been suggested to reproduce the internal physiological structure of bone. Inflammation effects are not included in these models, yet inflammation is a key component of bone repair in trauma. Therefore, a model is proposed and tested here that extends these methods to include parameters that could be considered to represent the behaviour of bone remodelling when influenced by inflammation. The proposed model regulates remodelling based on findings from recent studies into the nature of heterotopic ossification, the formation of heterotopic bone, which have revealed information about the nature of bone after high levels of trauma. These parameters include consideration of the distance from the zone of trauma, the density of mesenchymal stem cells, and substrate stiffness as a trigger for cells becoming osteogenic. The method is tested on a two-dimensional plate model and shows that the new extended algorithm can produce a range of structures depending on inputs that could be used in the future to replicate physiological scenarios.