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.

     

The effect of muscle loading on the simulation of bone remodelling in the proximal femur

A large number of finite element analyses of the proximal femur rely on a simplified set of muscle and joint contact loads to represent the boundary conditions of the model. In the context of bone remodelling analysis around hip implants, muscle loading affects directly the spatial distribution of the remodelling signal. In the present study we performed a sensitivity analysis on the effect of different muscle loading configurations on the outcome of the bone remodelling simulation. An anatomical model of the femur with the implanted stem in place was constructed using the CT data of the Visible Human Project dataset of the National Institute of Health. The model was loaded with three muscle force configurations with increasing level of complexity. A strain adaptive remodelling rule was employed to simulate the post-operative bone changes around the implant stem and the results of the simulation were assessed quantitatively in terms of the bone mineral content changes in 18 periprosthetic regions of interest. The results showed considerable differences in the amount of bone loss predicted between the three cases. The simplified models generally predicted more pronounced bone loss. Although the overall remodelling patterns observed were similar, the bone conserving effect of additional muscle forces in the vicinity of their areas of attachment was clear. The results of this study suggest that the loading configuration of the FE model does play an important role in the outcome of the remodelling simulation.     

Adaptive glenoid bone remodeling simulation

Glenoid prosthesis loosening is the most common cause for revision total shoulder arthroplasty. Stress-induced bone remodeling may compromise long-term prosthesis fixation and significantly contribute to loosening. Realistic, robust analysis of bone-prosthesis constructs need to look beyond initial post-implantation mechanics provided by static finite element (FE) simulation. Adaptive bone remodeling simulations based on Wolff's law are needed for evaluating long-term glenoid prostheses fixation. The purpose of this study was to take a first step towards this goal and create and validate two-dimensional FE simulations, using the intact glenoid, for computing subject-specific adaptive glenoid remodeling. Two-dimensional glenoid FE models were created from scapulae computed tomography images. Two distinct processes, “element” and “node” simulations, used the forward-Euler method to compute bone remodeling. Initial bone density was homogeneous. Center and offset load combinations were iteratively applied. To validate the simulations we performed location-specific statistical comparisons between predicted and actual bone density, load combinations, and “element” and “node” processes. Visually and quantitatively “element” simulations produced better results (p>0.22), and correlation coefficients ranged 0.51–0.69 (p<0.001). Having met this initial work's goals, we expect subject-specific FE glenoid bone remodeling simulations together with static FE stress analyses to be effective tools for designing and evaluating glenoid prostheses.     

Subject-specific bone remodelling of the scapula

Finite element analyses, with increasing levels of detail and complexity, are becoming effective tools to evaluate the performance of joint replacement prostheses and to predict the behaviour of bone. As a first step towards the study of the complications of shoulder arthroplasty, the aim of this work was the development and validation of a 3D finite element model of an intact scapula for the prediction of the bone remodelling process based on a previously published model that attempts to follow Wolff's law. The boundary conditions applied include full muscle and joint loads taken from a multibody system of the upper limb based on the same subject whose scapula was here analysed. To validate the bone remodelling simulations, qualitative and quantitative comparisons between the predicted and the specimen's bone density distribution were performed. The results showed that the bone remodelling model was able to successfully reproduce the actual bone density distribution of the analysed scapula.     

Influence of mastication and edentulism on mandibular bone density

The aim of this study was to demonstrate that external loading due to daily activities, including mastication, speech and involuntary open–close cycles of the jaw contributes to the internal architecture of the mandible. A bone remodelling algorithm that regulates the bone density as a function of stress and loading cycles is incorporated into finite element analysis. A three-dimensional computational model is constructed on the basis of computerised tomography (CT) images of a human mandible. Masticatory muscle activation involved during clenching is modelled by static analysis using linear optimisation. Other loading conditions are approximated by imposing mandibular flexure. The simulations predict that mandibular bone density distribution results in a tubular structure similar to what is observed in the CT images. Such bone architecture is known to provide the bone optimum strength to resist bending and torsion during mastication while reducing the bone mass. The remodelling algorithm is used to simulate the influence of edentulism on mandibular bone loss. It is shown that depending on the location and number of missing teeth, up to one-third of the mandibular bone mass can be lost due to lack of adequate mechanical stimulation.     

A microstructural finite element simulation of mechanically induced bone formation.

A finite element method to simulate the formation of an interconnected trabectular bone microstructure oriented with respect to applied in vivo mechanical forces is introduced and quantitatively compared to experimental data from a hydraulic bone chamber implant model. Randomly located 45 microm mineralized nodules were used as the initial condition for the model simulations to represent an early stage of intramembranous bone formation. Boundary conditions were applied consistent with the mechanical environment provided by the in vivo bone chamber model. A two-dimensional repair simulation algorithim that incorporated strain energy density (SED), SED gradient, principal strain, or principal strain gradient as the local objective criterion was utilized to simulate the formation of an oriented trabecular bone microstructure. The simulation solutions were convergent, unique, and relatively insensitive to the assumed initial distribution of mineralized nodules. Model predictions of trabecular bone morphology and anisotropy were quantitatively compared to experimental results. All simulations produced structures that qualitatively resembled oriented trabecular bone. However only simulations utilizing a gradient objective criterion yielded results quantitatively similar to in vivo observations. This simulation approach coupled with an experimental model that delivers controlled in vivo mechanical stimuli can be utilized to study the relationship between physical factors and microstructural adaptation during bone repair.     

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.     

Orthotropic bone remodelling around uncemented femoral implant: a comparison with isotropic formulation

Biomechanics and Modeling in Mechanobiology - Peri-prosthetic bone adaptation has usually been predicted using subject-specific finite element analysis in combination with remodelling algorithms...     

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.     

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.     

Effects of thresholding techniques on microCT-based finite element models of trabecular bone

Microimaging based finite element analysis is widely used to predict the mechanical properties of trabecular bone. The choice of thresholding technique, a necessary step in converting grayscale images to finite element models, can significantly influence the predicted bone volume fraction and mechanical properties. Therefore, we investigated the effects of thresholding techniques on microcomputed tomography (micro-CT) based finite element models of trabecular bone. Three types of thresholding techniques were applied to 16-bit micro-CT images of trabecular bone to create three different models per specimen. Bone volume fractions and apparent moduli were predicted and compared to experimental results. In addition, trabecular tissue mechanical parameters and morphological parameters were compared among different models. Our findings suggest that predictions of apparent mechanical properties and structural properties agree well with experimental measurements regardless of the choice of thresholding methods or the format of micro-CT images.     

Automated three-dimensional finite element modelling of bone: a new method

Three-dimensional finite element stress analysis of bone is a key to understanding bone remodelling, assessing fracture risk, and designing prostheses; however, the cost and complexity of predicting the stress field in bone with accuracy has precluded the routine use of this method. A new, automated method of generating patient-specific three-dimensional finite element models of bone is presented — it uses digital computed tomographic (CT) scan data to derive the geometry of the bone and to estimate its inhomogeneous material properties. Cubic elements of a user-specified size are automatically defined and then individually assigned the CT scan-derived material properties. The method is demonstrated by predicting the stress, strain, and strain energy in a human proximal femur in vivo. Three-dimensional loading conditions corresponding to the stance phase of gait were taken from the literature and applied to the model. Maximum principal compressive stresses of 8–23 MPa were computed for the medial femoral neck. Automated generation of additional finite element models with larger numbers of elements was used to verify convergence in strain energy.     

Implant–bone interface healing and adaptation in resurfacing hip replacement

Hip resurfacing demonstrates good survivorship as a treatment for young patients with osteoarthritis, but occasional implant loosening failures occur. On the femoral side there is radiographic evidence suggesting that the implant stem bears load, which is thought to lead to proximal stress shielding and adaptive bone remodelling. Previous attempts aimed at reproducing clinically observed bone adaptations in response to the implant have not recreated the full set of common radiographic changes, so a modified bone adaptation algorithm was developed in an attempt to replicate more closely the effects of the prosthesis on the host bone. The algorithm features combined implant–bone interface healing and continuum bone remodelling. It was observed that remodelling simulations that accounted for progressive gap filling at the implant–bone interface predicted the closest periprosthetic bone density changes to clinical X-rays and DEXA data. This model may contribute to improved understanding of clinical failure mechanisms with traditional hip resurfacing designs and enable more detailed pre-clinical analysis of new designs.     

Implant-bone interface healing and adaptation in resurfacing hip replacement

Hip resurfacing demonstrates good survivorship as a treatment for young patients with osteoarthritis, but occasional implant loosening failures occur. On the femoral side there is radiographic evidence suggesting that the implant stem bears load, which is thought to lead to proximal stress shielding and adaptive bone remodelling. Previous attempts aimed at reproducing clinically observed bone adaptations in response to the implant have not recreated the full set of common radiographic changes, so a modified bone adaptation algorithm was developed in an attempt to replicate more closely the effects of the prosthesis on the host bone. The algorithm features combined implant-bone interface healing and continuum bone remodelling. It was observed that remodelling simulations that accounted for progressive gap filling at the implant-bone interface predicted the closest periprosthetic bone density changes to clinical X-rays and DEXA data. This model may contribute to improved understanding of clinical failure mechanisms with traditional hip resurfacing designs and enable more detailed pre-clinical analysis of new designs.     

Simulation of bone adaptive remodeling using a stochastic process as loading history

In this simulation study for bone adaptive remodeling, loading conditions are described as stochastic processes to catch the unpredictable characteristics of daily physical activities, which are observed to be closely related with bone adaptive remodeling. This will not only eliminate the necessity of arbitrary choices for loading conditions, but also generate greater flexibility for simulations of bone adaptive remodeling. The sensitivity of simulation outcomes to the parameters in the simulation algorithm was examined by applying stochastic loading conditions on finite element models of simplified spine structures. In this way, the limitations induced by simplifying loading conditions into constant or cyclic loads can be avoided and, potentially, more clinical observations could be accommodated when more comprehensive finite element models are available.     

Comparison of HR-pQCT- and microCT-based finite element models for the estimation of the mechanical properties of the calcaneus trabecular bone

The calcaneus bone is formed of extensive trabecular bone and is therefore well suited to be used as an example of loaded bone to establish the ability of combining microfinite element (microFE) technique with high-resolution peripheral quantitative computed tomography (HR-pQCT) in determining its mechanical properties. HR-pQCT is increasingly used as a tool for in vivo bone clinical research, but its use has been limited to the distal radius and tibia. The goal of this study was to determine the applicability of HR-pQCT-derived microFE models of the calcaneus trabecular bone with 82 μm voxel size with reference to higher-resolution microCT-based models taken as gold standard. By comparing the outputs of microFE models generated from both HR-pQCT and microCT images of the trabecular bone of five calcaneus cadaveric specimens, it was found that the HR-pQCT-based models predicted mechanical properties for fracture load, total reaction force and von Mises stress are considerably different from microCT-based counterparts by 33, 64 and 70%, respectively. Also, the morphological analysis showed a comprehensive geometrical difference between HR-pQCT-based microFE models and their microCT-based equivalents. The results of the HR-pQCT-based models were found to have strong dependency on the threshold value chosen to binarise the images prior to finite element modelling. In addition, it was found that the voxel size has a strong impact on accuracy of imaged-based microFE models compared to other factors such as the presence of soft tissue and image scanning integration time. Therefore, although HR-pQCT has shown to be useful to predict overall structural and biomechanical changes, it is limited in providing local accurate biomechanical properties of trabecular bone and therefore should be used with caution when assessing bone remodelling through local changes of trabecular bone apposition and resorption in disease treatment monitoring.     

A generic 3-dimensional system to mimic trabecular bone surface adaptation

The paper presents the structure optimizing system based on surface remodelling. The grounds for algorithm formulation are given by the bone remodelling phenomenon leading to optimization of trabecular network in the bone. The assumptions, algorithms and limitations of the own mesh generator Cosmoprojector are described. Unlike other approaches, the system is able to mimic real bone evolution including tissue consolidation and separation. The article presents a closed system consisting of finite element mesh generation, decision criteria for structure adaptation and finite element analysis in parallel environment. It also provides some computation results obtained by using specially designed software.     

A generic 3-dimensional system to mimic trabecular bone surface adaptation

The paper presents the structure optimizing system based on surface remodelling. The grounds for algorithm formulation are given by the bone remodelling phenomenon leading to optimization of trabecular network in the bone. The assumptions, algorithms and limitations of the own mesh generator Cosmoprojector are described. Unlike other approaches, the system is able to mimic real bone evolution including tissue consolidation and separation. The article presents a closed system consisting of finite element mesh generation, decision criteria for structure adaptation and finite element analysis in parallel environment. It also provides some computation results obtained by using specially designed software.     

Numerical simulation of the remodelling process of trabecular architecture around dental implants

Dental implants may alter the mechanical environment in the jawbone, thereby causing remodelling and adaptation of the surrounding trabecular bone tissues. To improve the efficacy of dental implant systems, it is necessary to consider the effect of bone remodelling on the performance of the prosthetic systems. In this study, finite element simulations were implemented to predict the evolution of microarchitecture around four implant systems using a previously developed model that combines both adaptive and microdamage-based mechano-sensory mechanisms in bone remodelling process. Changes in the trabecular architecture around dental implants were mainly focused. The simulation results indicate that the orientational and ladder-like architecture around the implants predicted herein is in good agreement with those observed in animal experiments and clinical observations. The proposed algorithms were shown to be effective in simulating the remodelling process of trabecular architecture around dental implant systems. In addition, the architectural features around four typical dental implant systems in alveolar bone were evaluated comparatively.     

Generic rules of mechano-regulation combined with subject specific loading conditions can explain bone adaptation after THA

Bone adaptation after total hip arthroplasty is associated with the change in internal load environment, and can result in compromised bone stock, which presents a considerable challenge should a revision procedure be required. Under the assumption of a generic mechano-regulatory algorithm for governing bone adaptation, the aim of this study was to understand the contribution of subject specific loading conditions towards explaining the local periprosthetic remodelling variations in patients. CT scans of 3 consecutive THA patients were obtained and used for the construction of subject specific finite element models using verified musculoskeletal loading and physiological boundary conditions. Using either strain energy density or equivalent strain as mechano-transduction signals, predictions of bone adaptation were compared to DEXA derived BMD changes from 7 days to 12 months post-implantation. Individual changes in BMD of up to 33.6% were observed within the 12 month follow-up period, together with considerable inter-patient variability of up to 26%. Estimates of bone adaptation using equivalent strain and balanced loading conditions led to the best agreement with in vivo measured BMD, with RMS errors of only 3.9%, 7.3% and 7.3% for the individual subjects, compared to errors of over 10% when the loading conditions were simplified.This study provides evidence that subject specific loading conditions and physiological boundary constraints are essential for explaining inter-patient variations in bone adaptation patterns. This improved knowledge of the rules governing the adaptation of bone following THA helps towards understanding the interplay between mechanics and biology for better identifying patients at risk of excessive or problematic periprosthetic bone atrophy.