Bone remodeling, energy metabolism, and the molecular clock

The adult skeleton is constantly renewed through bone remodeling. Four recent papers (Baldock et al., 2007; Lee et al., 2007; Lundberg et al., 2007; Sato et al., 2007) provide new insights into central and peripheral control of this remodeling sequence. Two of the studies add to our knowledge of the complex hypothalamic modulation of bone turnover mediated by NMU and NPY via the sympathetic nervous system, while the other two focus on the peripheral neural target, the osteoblast, and its regulation by neuropeptides and osteocalcin. These findings support a new paradigm concerning the regulation of bone remodeling and provide a foundation for novel approaches to preventing osteoporosis.     

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.     

应用三维有限元分析髋臼骨结核软骨下骨塌陷的风险

目的建立人体髋臼骨结核三维有限元模型,探讨不同部位髋臼骨结核软骨下骨塌陷的风险。方法通过正常髋关节CT数据,利用Mimics软件和ANSYS有限元软件,建立正常髋关节三维有限元模型（模型A）、髋臼顶部骨结核（模型B）、髋臼中心部骨结核（模型C）、髋臼前部骨结核（模型D）、髋臼后部骨结核（模型E）三维有限元模型,模拟人体单脚站立进行加载,分析髋臼软骨下骨峰值Von Mises应力和初始微动值。结果建立了正常髋关节和不同部位髋臼骨结核三维有限元模型,各模型含节点269284,三维四面体单元184786个。通过加载分析结果显示：与正常髋关节相比,峰值Von Mises应力,依次增加84%、3%、21%、67%;髋臼软骨下骨初始微动值依次增加66%、11%、17%、29%。结论髋臼顶部结核软骨下骨峰值Von Mises应力和初始微动值最大,塌陷的风险最大。     

Capturing microscopic features of bone remodeling into a macroscopic model based on biological rationales of bone adaptation

To understand Wolff’s law, bone adaptation by remodeling at the cellular and tissue levels has been discussed extensively through experimental and simulation studies. For the clinical application of a bone remodeling simulation, it is significant to establish a macroscopic model that incorporates clarified microscopic mechanisms. In this study, we proposed novel macroscopic models based on the microscopic mechanism of osteocytic mechanosensing, in which the flow of fluid in the lacuno-canalicular porosity generated by fluid pressure gradients plays an important role, and theoretically evaluated the proposed models, taking biological rationales of bone adaptation into account. The proposed models were categorized into two groups according to whether the remodeling equilibrium state was defined globally or locally, i.e., the global or local uniformity models. Each remodeling stimulus in the proposed models was quantitatively evaluated through image-based finite element analyses of a swine cancellous bone, according to two introduced criteria associated with the trabecular volume and orientation at remodeling equilibrium based on biological rationales. The evaluation suggested that nonuniformity of the mean stress gradient in the local uniformity model, one of the proposed stimuli, has high validity. Furthermore, the adaptive potential of each stimulus was discussed based on spatial distribution of a remodeling stimulus on the trabecular surface. The theoretical consideration of a remodeling stimulus based on biological rationales of bone adaptation would contribute to the establishment of a clinically applicable and reliable simulation model of bone remodeling.     

Changes in the Fabric and Compliance Tensors of Cancellous Bone due to Trabecular Surface Remodeling,Predicted by a Digital Image-based Model

Fabric and compliance tensors of a cube of cancellous bone with a complicated three-dimensional trabecular structure were obtained for trabecular surface remodeling by using a digital image-based model combined with a large-scale finite element method. Using mean intercept length and a homogenization method, the fabric and compliance tensors were determined for the trabecular structure obtained in the computer remodeling simulation. The tensorial quantities obtained indicated that anisotropic structural changes occur in cancellous bone adapting to the compressive loading condition. There were good correlations between the fabric tensor, bone volume fraction, and compliance tensor in the remodeling process. The result demonstrates that changes in the structural and mechanical properties of cancellous bone are essentially anisotropic and should be expressed by tensorial quantities.     

Changes in the fabric and compliance tensors of cancellous bone due to trabecular surface remodeling, predicted by a digital image-based model

Fabric and compliance tensors of a cube of cancellous bone with a complicated three-dimensional trabecular structure were obtained for trabecular surface remodeling by using a digital image-based model combined with a large-scale finite element method. Using mean intercept length and a homogenization method, the fabric and compliance tensors were determined for the trabecular structure obtained in the computer remodeling simulation. The tensorial quantities obtained indicated that anisotropic structural changes occur in cancellous bone adapting to the compressive loading condition. There were good correlations between the fabric tensor, bone volume fraction, and compliance tensor in the remodeling process. The result demonstrates that changes in the structural and mechanical properties of cancellous bone are essentially anisotropic and should be expressed by tensorial quantities.     

A mechanistic model for internal bone remodeling exhibits different dynamic responses in disuse and overload

Bone is a dynamic tissue which, through the process of bone remodeling in the mature skeleton, renews itself during normal function and adapts to mechanical loads. It is, therefore, important to understand the effect of remodeling on the mechanical function of bone, as well as the effect of the inherent time lag in the remodeling process. In this study, we develop a constitutive model for bone remodeling which includes a number of relevant mechanical and biological processes and use this model to address differences in the remodeling behavior as a volume element of bone is placed in disuse or overload. The remodeling parameters exhibited damped oscillatory behavior as the element was placed in disuse, with the amplitude of the oscillations increasing as the severity of disuse increased. In overload situations, the remodeling parameters exhibited critically sensitive behavior for loads beyond a threshold value. These results bear some correspondence to experimental findings, suggesting that the model may be useful when examining the importance of transient responses for bone in disuse, and for investigating the role fatigue damage removal plays in preventing or causing stress fractures. In addition, the constitutive algorithm is currently being employed in finite element simulations of bone adaptation to predict important features of the internal structure of the normal femur, as well as to study bone diseases and their treatment.     

Modeling of bone adaptative behavior based on cells activities

Bone remodeling occurs in an adult’s skeleton to adapt its architecture to external loadings. This involves bone resorption by osteoclasts cells followed by formation of new bone by osteoblasts cells. During bone remodeling, osteoclasts and osteoblasts interact with each other by expressing autocrine and paracrine factors that regulate cells’ population. Therefore, changes in bone density depend on the amount of each acting cell population. The aim of this paper is to propose a model for the bone remodeling process, which takes into account the opposite activity of both types of cells. For this purpose, a system of differential equations, proposed by Komarova et al. (Bone 33:206–215, 2003), is introduced to describe bone cell interactions using parameters which characterize the autocrine and paracrine factors. Such equations allow us to determine how the autocrine and paracrine factors vary in response to an external stimulus. It is assumed that an equilibrium state can be obtained for values of stimulus near to some reference quantity. Far from this value, unbalanced activity of osteoblasts and osteoclasts is observed, which leads to bone apposition or resorption. The proposed model has been implemented into the finite element software ABAQUS to analyze the qualitative response of a bone structure when subjected to certain mechanical loadings. Obtained results are satisfactory and in accordance with the expected bone remodeling behavior.     

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.     

The application of topology optimization on the quantitative description of the external shape of bone structure

The aim of this paper was to introduce the idea of topology optimization in engineering to the simulation of bone morphology. The external shape of bone structure was predicted with the quantitative bone functional adaptation theory. The high-order nonlinear equation of bone remodeling proposed by Zhu et al. (J. Biomech. 35(7)(2002)951) combining with the finite element method was adopted to a rectangular design domain, which occupies a larger space than the external shape of bone structure. It was at this point we imported the idea of topology optimization in engineering. The proximal femur was used here as an example, whose external shape and internal density distribution were simultaneously simulated quantitatively to validate that the external shape of bone structure could be successfully predicted in this way. Then the growth of vertebral body from young to old was simulated numerically in its coronal section to discuss the significance of the prediction of external shape. The study in this paper provides computational basis for further studies on osteophyte formation, osteoporosis, osteoarthritis, bone growth and even bone evolution, etc.     

Application of neural networks and finite element computation for multiscale simulation of bone remodeling

In this paper, a novel multiscale hierarchical model based on finite element analysis and neural network computation was developed to link mesoscopic and macroscopic scales to simulate the bone remodeling process. The finite element calculation is performed at the macroscopic level, and trained neural networks are employed as numerical devices for substituting the finite element computation needed for the mesoscale prediction. Based on a set of mesoscale simulations of representative volume elements of bones taken from different bone sites, a neural network is trained to approximate the responses at the meso level and transferred at the macro level.     

Functional adaptation of cancellous bone in human proximal femur predicted by trabecular surface remodeling simulation toward uniform stress state

Two-dimensional simulation of trabecular surface remodeling was conducted for a human proximal femur to investigate the structural change of cancellous bone toward a uniform stress state. Considering that a local mechanical stimulus plays an important role in cellular activities in bone remodeling, local stress nonuniformity was assumed to drive trabecular structural change to seek a uniform stress state. A large-scale pixel-based finite element model was used to simulate structural changes of individual trabeculae over the entire bone. As a result, the initial structure of trabeculae changed from isotropic to anisotropic due to trabecular microstructural changes caused by surface remodeling according to the mechanical environment in the proximal femur. Under a single-loading condition, it was shown that the apparent structural property evaluated by fabric ellipses corresponded to the apparent stress state in cancellous bone. As is observed in the actual bone, a distributed trabecular structure was obtained under a multiple-loading condition. Through these studies, it was concluded that trabecular surface remodeling toward a local uniform stress state at the trabecular level could naturally bring about functional adaptation phenomenon at the apparent tissue level. The proposed simulation model would be capable of providing insight into the hierarchical mechanism of trabecular surface remodeling at the microstructural level up to the apparent tissue level.     

Computer simulation of trabecular remodeling in human proximal femur using large-scale voxel FE models: Approach to understanding Wolff's law

Ever since Julius Wolff proposed the law of bone transformation in the 19th century, it has been widely known that the trabecular structure of cancellous bone adapts functionally to the loading environment. To understand the mechanism of Wolff's law, a three-dimensional (3D) computer simulation of trabecular structural changes due to surface remodeling was performed for a human proximal femur. A large-scale voxel finite element model was constructed to simulate the structural changes of individual trabeculae over the entire cancellous region. As a simple remodeling model that considers bone cellular activities regulated by the local mechanical environment, nonuniformity of local stress was assumed to drive the trabecular surface remodeling to seek a uniform stress state. Simulation results demonstrated that cell-scale (～10 μm) remodeling in response to mechanical stimulation created complex 3D trabecular structures of the entire bone-scale (～10 cm), as illustrated in the reference of Wolff. The bone remodeling reproduced the characteristic anisotropic structure in the coronal cross section and the isotropic structures in other cross sections. The principal values and axes of a structure characterized by fabric ellipsoids corresponded to those of the apparent stress of the structure. The proposed large-scale computer simulation indicates that in a complex mechanical environment of a hierarchical bone structure of over 10⁴ length scale (from ～10 μm to ～10 cm), a simple remodeling at the cellular/trabecular levels creates a highly complex and functional trabecular structure, as characterized by bone density and orientation.     

A Femur-Implant Model for the Prediction of Bone Remodeling Behavior Induced by Cementless Stem

Bone remodeling simulation is an effective tool for the prediction of long-term effect of implant on the bone tissue, as well as the selection of an appropriate implant in terms of architecture and material. In this paper, a finite element model of proximal femur was developed to simulate the structures of internal trabecular and cortical bones by incorporating quantitative bone functional adaptation theory with finite element analysis. Cementless stems made of titanium, two types of Functionally Graded Material (FGM) and flexible ‘iso-elastic’ material as comparison were implanted in the structure of proximal femur respectively to simulate the bone remodeling behaviors of host bone. The distributions of bone density, von Mises stress, and interface shear stress were obtained. All the prosthetic stems had effects on the bone remodeling behaviors of proximal femur, but the degrees of stress shielding were different. The amount of bone loss caused by titanium implant was in agreement with the clinical observation. The FGM stems caused less bone loss than that of the titanium stem, in which FGM I stem (titanium richer at the top to more HAP/Col towards the bottom) could relieve stress shielding effectively, and the interface shear stresses were more evenly distributed in the model with FGM I stem in comparison with those in the models with FGM II (titanium and bioglass) and titanium stems. The numerical simulations in the present study provided theoretical basis for FGM as an appropriate material of femoral implant from a biomechanical point of view. The next steps are to fabricate FGM stem and to conduct animal experiments to investigate the effects of FGM stem on the remodeling behaviors using animal model.     

Stress-shielding induced bone remodeling in cementless shoulder resurfacing arthroplasty: a finite element analysis and in vivo results

Cementless surface replacement arthroplasty (CSRA) of the shoulder was designed to preserve the individual anatomy and humeral bone stock. A matter of concern in resurfacing implants remains the stress shielding and bone remodeling processes. The bone remodeling processes of two different CSRA fixation designs, conical-crown (Epoca RH) and central-stem (Copeland), were studied by three-dimensional (3-D) finite element analysis (FEA) as well as evaluation of contact radiographs from human CSRA retrievals. FEA included one native humerus model with a normal and one with a reduced bone stock quality. Compressive strains were evaluated before and after virtual CSRA implantation and the results were then compared to the bone remodeling and stress-shielding pattern of eight human CSRA retrievals (Epoca RH n=4 and Copeland n=4). FEA revealed for both bone stock models increased compressive strains at the stem and outer implant rim for both CSRA designs indicating an increased bone formation at those locations. Unloading of the bone was seen for both designs under the central implant shell (conical-crown 50–85%, central-stem 31–93%) indicating high bone resorption. Those effects appeared more pronounced for the reduced than for the normal bone stock model. The assumptions of the FEA were confirmed in the CSRA retrieval analysis which showed bone apposition at the outer implant rim and stems with highly reduced bone stock below the central implant shell. Overall, clear signs of stress shielding were observed for both CSRAs designs in the in vitro FEA and human retrieval analysis. Especially in the central part of both implant designs the bone stock was highly resorbed. The impact of these bone remodeling processes on the clinical outcome as well as long-term stability requires further evaluation.     

Simulation of multi-stage nonlinear bone remodeling induced by fixed partial dentures of different configurations: a comparative clinical and numerical study

This paper aimed to develop a clinically validated bone remodeling algorithm by integrating bone’s dynamic properties in a multi-stage fashion based on a four-year clinical follow-up of implant treatment. The configurational effects of fixed partial dentures (FPDs) were explored using a multi-stage remodeling rule. Three-dimensional real-time occlusal loads during maximum voluntary clenching were measured with a piezoelectric force transducer and were incorporated into a computerized tomography-based finite element mandibular model. Virtual X-ray images were generated based on simulation and statistically correlated with clinical data using linear regressions. The strain energy density-driven remodeling parameters were regulated over the time frame considered. A linear single-stage bone remodeling algorithm, with a single set of constant remodeling parameters, was found to poorly fit with clinical data through linear regression (low \(R^{2}\) and R), whereas a time-dependent multi-stage algorithm better simulated the remodeling process (high \(R^{2}\) and R) against the clinical results. The three-implant-supported and distally cantilevered FPDs presented noticeable and continuous bone apposition, mainly adjacent to the cervical and apical regions. The bridged and mesially cantilevered FPDs showed bone resorption or no visible bone formation in some areas. Time-dependent variation of bone remodeling parameters is recommended to better correlate remodeling simulation with clinical follow-up. The position of FPD pontics plays a critical role in mechanobiological functionality and bone remodeling. Caution should be exercised when selecting the cantilever FPD due to the risk of overloading bone resorption.     

Design of partial pelvic replacement with calculation of stresses on the pelvic bone using the finite element method

Although tumors of the pelvic region are relatively rare, with regard to the provision of an individual prosthesis, they make great demands both on the engineer and on the surgeon. In the case of partial pelvic replacement, the main problem is that of fixation. The direction of the preload by the screw and counternut in the anchorage should make possible the introduction of forces into the bone that closely mimic the natural pre-operative situation, in order to keep bone remodeling and stressing to a minimum. A three-dimensional finite element (FE) analysis of the stresses at work in the pelvic bone was performed using an FE model of the pelvis constructed on the basis of computed tomographic data, since with the FE method it is possible to obtain information about deformations, internal stresses and local forces acting on the bone. The results show that the main stressing of the bony pelvis occurs in the region of the acetabulum and the iliosacral joints, and that further points of loading are located in the lower region of the ischium-and this while standing on one leg, on the side of the supporting leg.     

An Analysis and Comparison of Convergence and Uniqueness of Time-Independent Bone Adaptation Models

Several stimuli are proposed in the bone remodeling theory. It is not clear, if a unique solution exists and if the result is convergent using a certain stimulus. In this study, the strain stimulus, strain energy stimulus and the von Mises stress stimulus for bone remodeling are compared and applied to a square plate model using the finite element method. In the plane stress state, the remodeling equilibrium equations are transformed into functions of only the principal strains and the graphs of these functions are drawn in a diagram using the principal strains as the variables of two coordinate axes. The equation of the sum of principal strain squared equal to a constant is a circle in the diagram. The remodeling equilibrium equation of the strain stimulus is a quadrangle fitting into the circle, the remodeling equilibrium equation of the strain energy stimulus is an ellipse and the remodeling equilibrium equation of the von Mises stress stimulus is also an ellipse close to the principal strains circle when we take the same constants in the above equations. Using the finite element method, two models are performed with the uniform initial elastic properties and with the semi-random initial distribution of the elastic properties. The principal strains as the final finite element results converge within 2% of the objective constant for all the different stimuli. The obtained Young's moduli of two models as the adaptation object are different but in equilibrium, i.e. the equilibrium solution of adaptation model is not unique. The principal strains can not be used to examine the uniqueness of solution, since two different solutions can have the same results of principal strains. Using a certain stimulus, certain initial properties and a certain iterative equation, the solution is unique in equilibrium. The results using the model in this study show also that the same results can be obtained using any of the three stimuli when a proper constant in each remodeling equilibrium equation is chosen.     

Assessment of mechanobiological models for the numerical simulation of tissue differentiation around immediately loaded implants

Nowadays, there is a growing consensus on the impact of mechanical loading on bone biology. A bone chamber provides a mechanically isolated in vivo environment in which the influence of different parameters on the tissue response around loaded implants can be investigated. This also provides data to assess the feasibility of different mechanobiological models that mathematically describe the mechanoregulation of tissue differentiation. Before comparing numerical results to animal experimental results, it is necessary to investigate the influence of the different model parameters on the outcome of the simulations. A 2D finite element model of the tissue inside the bone chamber was created. The differentiation models developed by Prendergast, et al. ["Biophysical stimuli on cells during tissue differentiation at implant interfaces", Journal of Biomechanics, 30(6), (1997), 539-548], Huiskes et al. ["A biomechanical regulatory model for periprosthetic fibrous-tissue differentiation", Journal of Material Science: Materials in Medicine, 8 (1997) 785-788] and by Claes and Heigele ["Magnitudes of local stress and strain along bony surfaces predict the course and type of fracture healing", Journal of Biomechanics, 32(3), (1999) 255-266] were implemented and integrated in the finite element code. The fluid component in the first model has an important effect on the predicted differentiation patterns. It has a direct effect on the predicted degree of maturation of bone and a substantial indirect effect on the simulated deformations and hence the predicted phenotypes of the tissue in the chamber. Finally, the presence of fluid also causes time-dependent behavior. Both models lead to qualitative and quantitative differences in predicted differentiation patterns. Because of the different nature of the tissue phenotypes used to describe the differentiation processes, it is however hard to compare both models in terms of their validity.     

Bone ingrowth into a porous coated implant predicted by a mechano-regulatory tissue differentiation algorithm

Bone ingrowth into a porous surface is one of the primary methods for fixation of orthopaedic implants. Improved understanding of bone formation and fixation of these devices should improve their performance and longevity. In this study predictions of bone ingrowth into an implant porous coating were investigated using mechano-reculatory models. The mechano-regulatory tissue differentiation algorithm proposed by Lacroix et al., and a modified version that enforces a tissue differentiation pathway by transitioning from differentiation to bone adaptation were investigated. The modified algorithm resulted in nearly the same behavior as the original algorithm when applied to a fracture-healing model. The algorithms were further compared using micromechanical finite element model of a beaded porous scaffold. Predictions of bone and fibrous tissue formation were compared between the two algorithms and to clinically observed phenomena. Under loading conditions corresponding to a press-fit hip stem, the modified algorithm predicted bone ingrowth into approximately 25% of the pore space, which is similar to that reported in experimental studies, while the original algorithm was unstable. When micromotion at the bone-implant interface was simulated, 20 mum of transverse displacement resulted in soft tissue formation at the bone-implant interface and minimal bone ingrowth. In contrast, 10 and 5 mum of micromotion resulted in bone filling 40% of the pore space and a stable interface, again consistent with clinical and experimental observations.