Bone Remodeling Simulation Research Articles

Structural design and evaluation of bone remodeling effect of fracture internal fixation implants with time-varying stiffness

The stiffness of an ideal fracture internal fixation implant should have a time-varying performance, so that the fracture can generate reasonable mechanical stimulation at different healing stages, and biodegradable materials meet this performance. A topology optimization design method for composite structures of fracture internal fixation implants with time-varying stiffness is proposed, considering the time-dependent degradation process of materials. Using relative density and degradation residual rate to describe the distribution and degradation state of two materials with different degradation rates and elastic modulus, a coupled mathematical model of degradation simulation mechanical analysis was established. Biomaterial composite structures were designed based on variable density method to exhibit time-varying stiffness characteristics. Taking the bone plate used for the treatment of tibial fractures as an example, a composite structure bone plate with time-varying stiffness characteristics was designed using the proposed method. The optimization results showed that material 1 with high stiffness formed a columnar support structure, while material 2 with low stiffness was distributed at the degradation boundary and inside. Using a bone remodeling simulation model, the optimized bone plates were evaluated. After 11 months of remodeling, the average elastic modulus of callus using degradable time-varying stiffness plates, titanium alloy plates, and stainless steel plates were 8 634 MPa, 8 521 MPa, and 8 412 MPa, respectively, indicating that the use of degradable time-varying stiffness plates would result in better remodeling effects on the callus.

Phase diagrams of bone remodeling using a 3D stochastic cellular automaton.

We propose a 3D stochastic cellular automaton model, governed by evolutionary game theory, to simulate bone remodeling dynamics. The model includes four voxel states: Formation, Quiescence, Resorption, and Environment. We simulate the Resorption and Formation processes on separate time scales to explore the parameter space and derive a phase diagram that illustrates the sensitivity of these processes to parameter changes. Combining these results, we simulate a full bone remodeling cycle. Furthermore, we show the importance of modeling small neighborhoods for studying local bone microenvironment controls. This model can guide experimental design and, in combination with other models, it could assist to further explore external impacts on bone remodeling. Consequently, this model contributes to an improved understanding of complex dynamics in bone remodeling dynamics and exploring alterations due to disease or drug treatment.

A novel design of hip-stem with reduced strain-shielding.

The use of uncemented stems in hip arthroplasty has been increasing, even in osteoporotic patients. The major concerns of uncemented hip-stems, however, are peri-prosthetic fracture, thigh pain, and proximal femoral stress-/strain-shielding. In this study, a novel design of uncemented hip-stem is proposed that will reduce such concerns, improve osseointegration, and benefit both osteoporotic and arthritic patients. The stem has a central titanium alloy core surrounded by a set of radial buttresses that are partly porous titanium, as is the stem tip. The aim of the study was to investigate the mechanical behaviour of the proposed partly-porous design, examining load transfer in the short-term, and comparing its strain-shielding behaviour with a solid metal implant. The long-term effect of implant-induced bone remodelling was also simulated. Computed tomography based three-dimensional finite element models of an intact proximal femur, and the same femur implanted with the proposed design, were developed. Peak hip contact and major muscle forces corresponding to level-walking and stair climbing were applied. The proposed partly-porous design had approximately 50% lower strain-shielding than the solid-metal counterpart. Results of bone remodelling simulation indicated that only 16% of the total bone volume is subjected to reduction of bone density. Strain concentrations were observed in the bone around the stem-tip for both solid and porous implants; however, it was less prominent for the porous design. Lower strain-shielding and reduced bone resorption are advantageous for long-term fixation, and the reduced strain concentration around the stem-tip indicates a lower risk of peri-prosthetic fracture.

A gradient-enhanced bone remodelling approach to avoid the checkerboard phenomenon

Numerical simulation of bone remodelling enables the investigation of short- and long-term stability of bone implants and thus can be an essential tool for surgical planning. The first development of related mathematical models dates back to the early 90’s, and these models have been continuously refined since then. However, one issue which has been under discussion since those early days concerns a numerical instability known as checkerboarding. A literature review of recent approaches guided us to adopt a technique established in damage mechanics and topology optimisation, where similar mesh dependencies and instabilities occur. In our investigations, the so-called gradient enhancement is used to regularise the internal variable field, representing the evolution of the bone mass density. For this, a well-established mathematical model for load-adaptive bone remodelling is employed. A description of the constitutive model, the gradient enhancement extension and the implementation into an open-access Abaqus user element subroutine is provided. Parametric studies on the robustness of the approach are demonstrated using two benchmark examples. Finally, the presented approach is used to simulate a detailed femur model.

A fully implicit and thermodynamically consistent finite element framework for bone remodeling simulations

This work addresses the thermodynamically consistent formulation of bone remodeling as a fully implicit finite element material model. To this end, bone remodeling is described in the framework of thermodynamics for open systems resulting in a thermodynamically consistent constitutive law. In close analogy to elastoplastic material modeling, the constitutive equations are implicitly integrated in time and incorporated into a finite element weak form. A consistent linearization scheme is provided for the subsequent incremental non-linear boundary value problem, resulting in a computationally efficient description of bone remodeling. The presented model is suitable for implementation in any standard finite element framework with quadratic or higher-order element types. Two numerical examples in three dimensions are shown as proof of the efficiency of the proposed method.

Numerical Simulation of Mechanically Adaptive Bone Remodeling Around Teeth and Implants: A Comparison with Clinical Images

The results of numerical simulation of mechanically adaptive bone remodeling have been compared with clinical images. Cone beam computed tomography (CBCT) images of multiple human subjects were superimposed to obtain a continuous bone density spatial distribution map inside the mandible supporting the lateral incisor. Strain energy density in the bone under normal chewing and biting forces was computed using finite element analysis. A bone remodeling algorithm was implemented to compute the bone density distribution at equilibrium. Linear regression analysis was performed between the bone density computed by numerical simulation and that obtained from image analysis, for every trabecular bone element. The results exhibited close agreement with a coefficient of correlation of 0.8499. The bite forces were transmitted through tooth roots to the surrounding bone, thus stimulating high trabecular bone density near the roots. The bending and torsion moments on the sagittal section of the mandible resulted in lower bone density near the center than those towards the edge of the mandible. The results provide a new method to compare the results of adaptive bone remodeling simulation with experimental data, and also provide model parameters to predict the bone density distribution surrounding a dental implant that replaced the tooth.

Framework of sampling the subject-specific static loads from the gait cycle of interindividual variation

Background and ObjectiveNumerous techniques for bone remodeling simulation have been developed based on Wolff's law. However, most studies have been conducted with empirically determined static loads, which cannot reflect subject-specific characteristics. We recently proposed a new concept of representative static loads (RSLs) to efficiently consider the effect of cyclically repeated dynamic loads on bone remodeling simulation. Based on this concept, the goal of this study is to sample the subject-specific static loads (SSL) from a general gait cycle of interindividual variation. MethodsA total of 15 gait cycles (ten normal and five abnormal cycles) obtained from the public database were used in this study. Each gait cycle was applied to a femur FE model constructed from the clinical CT scan data to evaluate the strain energy distribution as a reference. Then, a natural coordinate was introduced to maintain the predefined locations of extreme points (i.e., two peaks and one valley) for both normal and abnormal gait cycles. To determine the RSLs in the natural coordinate, five out of ten normal gait cycles were used. Through an inverse transformation for each gait cycle, the RSLs in the natural coordinate were converted to the SSLs in the original coordinate. Topology optimization results with the proposed SSLs were compared with those with a single full gait cycle (reference). For comparison, topology optimization was also conducted with empirically determined loads (EDLs) which have been widely used in the literature. ResultsFor normal gait cycles, the proposed SSLs reduced the average computing cost by 95.86% while suppressing the errors of bone mass distribution and apparent stiffness below maximum 4.24% and 1.72%, respectively. Even for abnormal gait cycles, the errors of bone mass distribution and apparent stiffness were suppressed below maximum 9.49% and 2.12%, respectively. Conversely, the conventional EDLs (peak loads selected in this study) showed significantly larger errors of maximum 47.28% and 30.31% in bone mass distribution and apparent stiffness for normal gait cycles. ConclusionBy virtue of using the coordinate transformation for each gait cycle, the proposed SSLs achieved a higher accuracy in the bone mass distribution and apparent stiffness than the previous RSLs and EDLs. Furthermore, this approach can be used for abnormal gait cycles which have higher interindividual variation.

Influence of the angle between tibial and prosthesis mechanical axes on tibial bone remodeling in total knee arthroplasty.

Osteoarthritis of the knee is one of the most common diseases that affect the quality of life in the elderly population, and Total Knee Arthroplasty is considered the only real treatment for it, and as with any other surgery, a suboptimal technique may lead to an undesirable outcome. This paper aims to investigate the effects of the angle between mechanical axes of the tibia and the implant on the bone remodeling process. A 3D model was reconstructed using CT images, which was then used in an ABAQUS model with a USDFLD subroutine to simulate bone remodeling post TKA. The USDFLD subroutine compares the strain energy density from each increment to that of the previous increment to determine how the bone density will change. Simulation results suggest that when the prosthesis is inclined to one side, stress and density distribution increase, whereas stress and bone density decrease substantially on the opposite side. This decrease in bone density can be as much as 35% in the coronal plane. Sagittal malalignment results suggest that the effect would be relatively localized to the vicinity of the cutting plane. Results suggest uniform load distribution may be achieved when the two mechanical axes are kept parallel, which in turn can lead to decreased prosthesis loosening and bone fractures.

Simulation on bone remodeling with stochastic nature of adult and elderly using topology optimization algorithm

Reliable and accurate predictions of bone remodeling provide essential assistance for personalized implant design and orthopedic diagnosis. However, the bone remodeling simulations fail to accurately mimic the sophisticated architecture of trabecular bone so far, due to the neglection of the stochastic behaviors of bone remodeling. In this study, we coupled the Physiological Stochasticity in Bone Remodeling into the conventional Topology Optimization algorithm (named PSBR-TO method) to predict the cancellous structure of human femur. The sensitivity function of topology optimization was amended according to the bone remodeling rules from in vivo study (Razi et al., 2015) to reflect the stochastic process of bone remodeling in various physiological conditions. To demonstrate the algorithm, the bone structures of adults and the elderly were simulated by adopting the corresponding remodeling rules. The results showed that PSBR-TO gives rise to highly similar morphological features with the natural femur bone, in terms of the trabecular orientations and bone content distribution. The predicted femurs for adults and the elderly showed that the region-dependent variations in trabecular structural parameters during aging, including BV/TV, Tb.Th, and Tb.Sp, were consistent with the natural bone. Additionally, a loading collection of thirteen activities was employed in the algorithm and succeeded in driving the femur model to reproduce cancellous structure without extra constraint of structure perimeter or local density. By means of PSBR-TO, the trabecular structure in diverse physiological conditions can be accurately predicted, showing the valuable contribution on the clinical diagnosis and patient-specific design of bone implants.

Techniques for mitigating the checkerboard formation: application in bone remodeling simulations

The checkerboard phenomenon is a numerical problem that can occur in bone remodeling simulations. This phenomenon degrades the quality of the results and emphasizes a strong mesh dependency. The node-based approach is a well-used method for solving this problem. However, this method does not provide a stable solution, and long-time simulations do not reach steady-state. This paper aims to discuss techniques for mitigating the checkerboard formation and obtaining bone characterization. For this, we apply the simple nodal average technique on stress, density, or both simultaneously. Then, we compare the element-based and node-based approaches with and without smoothing. Also, we introduced a quantification parameter called standard density variation. This parameter measures the intensity of the checkerboard formation and analyzes the evolution of the bone tissue behavior. The application of the smoothing techniques mitigates the checkerboard formation. Also, the application allows obtaining a stable behavior for long-time simulations. The standard density variation allowed visualizing this stable behavior. In particular, the stress field smoothing technique provides the best results. Besides the stabilization and checkerboard control, the technique allows obtaining a physiological density distribution.

Parameter reduction, sensitivity studies, and correlation analyses applied to a mechanobiologically regulated bone cell population model of the bone metabolism.

When striving for reconstructing and predicting bone remodeling processes by means of mathematical models, cell population models have become a popular option. From a conceptual point of view, these models are able to take into account an arbitrary amount of regulatory mechanisms driving the development of bone cells and their activities. However, in most cases, the models include a large number of parameters; and most of those parameters cannot be measured, which certainly compromises the credibility of cell population models. Here, new insights are presented as to the potential improvement of this unsatisfactory situation. In particular, a previously published bone remodeling model was considered, and based on combination and merging of the original parameters, the total number of parameters could be reduced from 28 to 18, without impairing the model's versatility and significance. Furthermore, a comprehensive number of one- and two-variable sensitivity studies were performed, pointing out which parameters (alone and in combination with other parameters) influence the model predictions significantly - for that purpose, the mean squared relative error (MSRE) between simulations based on the original parameters and based on varied parameters was considered as failure measure. It has turned out that the model is significantly more sensitive to parameters which can be considered as phenomenological (such as differentiation, proliferation, and apoptosis rates) than to parameters which are directly related to specific processes (such as dissociation rate constants, and maximum concentrations of the involved factors). Using common correlation measures (such as Pearson, Spearman, and partial ranked correlation coefficients), correlation studies revealed that the correlations between most parameters and the MSRE are weak, while a few parameters exhibited moderate correlations. In conclusion, the results shown in this paper provide valuable insights concerning the design of new experiments allowing for measurement of the parameters which are most influential in the context of bone remodeling simulation.

Combined Effects of Exercise and Denosumab Treatment on Local Failure in Post-menopausal Osteoporosis-Insights from Bone Remodelling Simulations Accounting for Mineralisation and Damage.

Denosumab has been shown to increase bone mineral density (BMD) and reduce the fracture risk in patients with post-menopausal osteoporosis (PMO). Increase in BMD is linked with an increase in bone matrix mineralisation due to suppression of bone remodelling. However, denosumab anti-resorptive action also leads to an increase in fatigue microdamage, which may ultimately lead to an increased fracture risk. A novel mechanobiological model of bone remodelling was developed to investigate how these counter-acting mechanisms are affected both by exercise and long-term denosumab treatment. This model incorporates Frost's mechanostat feedback, a bone mineralisation algorithm and an evolution law for microdamage accumulation. Mechanical disuse and microdamage were assumed to stimulate RANKL production, which modulates activation frequency of basic multicellular units in bone remodelling. This mechanical feedback mechanism controls removal of excess bone mass and microdamage. Furthermore, a novel measure of bone local failure due to instantaneous overloading was developed. Numerical simulations indicate that trabecular bone volume fraction and bone matrix damage are determined by the respective bone turnover and homeostatic loading conditions. PMO patients treated with the currently WHO-approved dose of denosumab (60 mg administrated every 6 months) exhibit increased BMD, increased bone ash fraction and damage. In untreated patients, BMD will significantly decrease, as will ash fraction; while damage will increase. The model predicted that, depending on the time elapsed between the onset of PMO and the beginning of treatment, BMD slowly converges to the same steady-state value, while damage is low in patients treated soon after the onset of the disease and high in patients having PMO for a longer period. The simulations show that late treatment PMO patients have a significantly higher risk of local failure compared to patients that are treated soon after the onset of the disease. Furthermore, overloading resulted in an increase of BMD, but also in a faster increase of damage, which may consequently promote the risk of fracture, specially in late treatment scenarios. In case of mechanical disuse, the model predicted reduced BMD gains due to denosumab, while no significant change in damage occurred, thus leading to an increased risk of local failure compared to habitual loading.

Integration of mechanics and biology in computer simulation of bone remodeling

Bone remodeling is a complex physiological process that spans across multiple spatial and temporal scales and is regulated by both mechanical and hormonal cues. An imbalance between bone resorption and bone formation in the process of bone remodeling may lead to various bone pathologies. One powerful and non-invasive approach to gain new insights into mechano-adaptive bone remodeling is computer modeling and simulation. Recent findings in bone physiology and advances in computer modeling have provided a unique opportunity to study the integration of mechanics and biology in bone remodeling. Our objective in this review is to critically appraise recent advances and developments and discuss future research opportunities in computational bone remodeling approaches that enable integration of mechanics and cellular and molecular pathways. Based on the critical appraisal of the relevant recent published literature, we conclude that multiscale in silico integration of personalized bone mechanics and mechanobiology combined with data science and analytics techniques offer the potential to deepen our knowledge of bone remodeling and provide ample opportunities for future research.

Nonlinear Mathematical Modelling of Bone Damage and Remodelling Behaviour in Human Femur

Abstract The simulation of bone remodelling is highly complex due to the high nonlinear coupled relations between the damage and repair behaviours. In this paper, a new bone remodelling model based on the fatigue damage mechanism is proposed. Then the repair process of the human femur is simulated based on the finite element method. The results show that the new damage model can well simulate the bone damage evolution caused by overloadings. This indicates that the new mathematical model suggested in this paper can simulate the effect of external load on the cortical bone density and the related mechanical properties of the cortical bone.

Determination of the representative static loads for cyclically repeated dynamic loads: a case study of bone remodeling simulation with gait loads

Background and ObjectiveBone has the self-optimizing capability to adjust its structure in order to efficiently support external loads. Bone remodeling simulations have been developed to reflect the above characteristics in a more effective way. In most studies, however, only a set of static loads have been empirically determined although both static and dynamic loads affect bone remodeling phenomenon. The goal of this study is to determine the representative static loads (RSLs) to efficiently consider the statically equivalent effect of cyclically repeated dynamic loads on bone remodeling simulation. MethodsBased on the concept of two-scale approach, the RSLs for the gait cycles are determined from five subjects. First, the gait profiles at the hip joint are selected from the public database and then are preprocessed. The finite element model of the proximal femur is constructed from the clinical CT scan data to determine the strain energy distribution during the gait cycles. An optimization problem is formulated to determine the candidate static loads that minimize the errors of the spatial strain energy distribution for five gait profiles. Then, all candidate static loads from five gait profiles are partitioned into multiple clusters. The RSLs and the corresponding coefficients can be determined at the center of the densest cluster. For verification, topology optimization is separately conducted with the whole gait cycle (reference), empirically determined loads (conventional), and the RSLs (proposed). The strain energy density-based bone remodeling simulation is also conducted for another comparison. ResultsFor the gait loads, the use of the RSLs enables a 99% reduction of the function calls with negligible errors in the bone spatial distribution (6.75% for two representative static loads and 6.24% for three representative static loads) and apparent stiffness (4.84% for two representative static loads and 4.47% for three representative static loads), compared with the use of a whole gait cycle as reference. ConclusionThis study shows the feasibility of the RSLs and provides a theoretical foundation for investigating the relationship between static and dynamic loads in the aspect of bone remodeling simulation.

Denosumab 10-year simulation of bone remodeling in human biopsies

Denosumab 10-year simulation of bone remodeling in human biopsies

Simulation of bone remodeling around a femoral prosthesis using a model that accounts for biological and mechanical interactions

The present study focuses on a model for three-dimensional bone remodeling of the human femur that considers cellular dynamics to determine the volume fraction of new bone. The model considers the interaction among responsive osteoblasts, active osteoblasts, and osteoclasts, as well as signaling molecules and parathyroid hormone (PTH). The stimulus of the model has a systemic origin due to the PTH effect, and a local origin due to the action of cytokines, growth factors, and mechanical stimuli near the site of the bone cells. The present work considers that the mechanical stimulus that activates cellular activity is obtained from stresses acting on the bone tissue and the number of daily loading cycles. In addition to simulating the bone modeling process in an intact femur, the numerical model is used to simulate bone adaptation in relation to the stress shielding phenomenon after the implantation of a femoral prosthesis. The results showed that the simulations provide a distribution of bone density that is similar to a radiograph and, in addition, allows the visualization of osteoblast and osteoclast dynamics in bone adaptation response after prosthesis implantation.

HUMAN MANDIBULAR BONE DENSITY DISTRIBUTION: IMAGE ANALYSIS AND BONE REMODELING SIMULATION

<h3>Background</h3> Bone density distribution affects the short-term and long-term success of dental treatments. Currently, there is no quantitative method to analyze bone density distribution in alveolar bone. <h3>Objective</h3> In this study, the bone density distribution in human mandibles was obtained from quantitative analysis on medical images and was also modeled by using biomechanics simulations. <h3>Materials and Methods</h3> Cone beam computed tomography (CBCT) images from 33 patients were obtained from dental clinics. The CBCT scanner was calibrated by using our self-made phantoms to convert gray-scale to mineral density. The CBCT images of multiple human mandibles were analyzed. Finite element models were used to simulate the effects of normal chewing and bite force on bone density distribution. A strain energy density–based bone remodeling algorithm was used in the simulations. <h3>Results</h3> For the same materials in phantoms, there was no significant difference in gray scale in different locations inside the regions of interest, despite the known drawbacks of CBCT. At the chosen effective energy level, the gray scale in CBCT images had high linearity with attenuation coefficients for all materials in the phantoms. The averaged trend in mandibular bone density distribution was obtained. It was higher near the root of the tooth and lower away from the tooth, especially near the lingual arc of the jaw. The numerical simulation results showed a similar trend in bone density distribution under chewing force. <h3>Discussion</h3> The gray scale in CBCT images from the 1 CBCT scanner used in this study had linearity and spatial consistency inside certain regions of interest. The bone density distribution obtained from image analysis had good agreement with that obtained from bone remodeling simulations based on biomechanics analysis. The results may provide detailed information on dental anatomy and can also build the foundation for future improvements in dental treatments using image-based biomechanics analysis.

Evaluation of Mechanical Adaptation on Preoperative Planning for Total Hip Arthroplasty

Bone structure can change by remodeling to adapt to mechanical status. Such change can result in bone affecting the long-term stability of the stem. The objective of this study was to propose a method to evaluate mechanical adaptation for preoperative planning of total hip arthroplasty. Finite element models of preoperative planning were examined in two ways: bone remodeling simulation and initial mechanical status of femur. A mathematical model of remodeling for long-term changes of bone was developed assuming that bone resorption/formation could be distinguished by strain magnitude of bone. Also, initial compatibility between stem and bone was set with four strain levels based on mechanostat theory. The results of bone remodeling simulation were shown average equivalent stress change was mainly observed in Gruen zone 1 and zone 7 where stress shielding or bone resorption could occur. The proportion of this value was the smallest in the first choice of the stem by a specialist surgeon. Also, these are showed same tendency with evaluation of initial strain distribution results that Gruen zone 1 and 7. Initial strain distribution after total hip arthroplasty was correlated with the long-term change of bone structures after total hip arthroplasty. Bone structure changes around prostheses occur due to changes in the mechanical environment, and this is correlated with strain distribution of immediate post-operative model. Findings of this study suggest that biomechanical indices might be useful for exploring difference in long-term fitting among different surgical plans.

Effect of stress-shielding-induced bone resorption on glenoid loosening in reverse total shoulder arthroplasty.

Aseptic loosening of the glenoid component is one of the main reasons for the high revision rates of reverse total shoulder arthroplasty (RTSA). It has been reported that the bulky implant designs may lead to stress shielding. However, it is uncertain whether the shielding effect is severe enough to lead to bone resorption and glenoid loosening. The purpose of this study was to evaluate the level of stress-shielding and assess whether bone resorption plays a role in aseptic glenoid loosening following RTSA. A cadaveric in vitro test model was used to validate a finite element model (FEM) of the scapula. The FEM of the scapula, incorporating adaptive bone remodeling algorithms, was used to predict changes in postoperative bone density after RTSA. Changes in bone strength after implantation were also analyzed. The strain values predicted from the FEM of the scapula were in agreement with the in vitro measurements. Analysis of postoperative bone adaptation revealed that strain-induced bone resorption began at the peg of the implant and around the resected bone surface and then gradually expended to the peripheral regions. The bone strength also reduced postoperatively and appeared particularly around the implant peg. Strain-induced bone resorption is a likely source of the bone loss commonly observed in RTSA. The finite element glenoid bone remodeling simulation may be used as a tool to evaluate glenoid implant design.