Effect of glenoid prosthesis design on glenoid bone remodeling: Adaptive finite element based simulation

Glenoid prosthesis loosening is the most common cause for revision total shoulder arthroplasty. Improved glenoid prosthesis design requires looking beyond initial post-implantation static stress analyses. Adaptive bone remodeling simulations based on Wolff’s law are needed for predicting long-term glenoid prosthesis results. This study demonstrates the capability of predicting glenoid bone remodeling produced by changing prosthesis design features. Twelve glenoid prostheses were designed to fit each of six donor human glenoids, using combinations of three peg types and four backing-peg material combinations (polyethylene and or metal). The twelve FE prosthesis models were individually combined, simulating surgical implantation, with the glenoid models. Remodeling simulations, using a validated adaptive bone remodeling simulation, commenced with homogeneous glenoid bone density. To produce bone remodeling, center, posterior-offset, and anterior-offset physiologic loads were consecutively applied to the bone–prosthesis FE models for 300 iterations. Upon completion, region-specific mean predicted bone apparent densities were compared between bone–prosthesis and intact glenoid FE models. Metal fixations significantly increased proximal-center bone density. Polyethylene fixations resulted in bone density approximately equal to intact. Two angled polyethylene peg designs with longer-anterior and shorter-posterior pegs, reflecting natural glenoid shape, best maintained mid and distal glenoid bone density. While these initial results were not validated, they demonstrate the capability and potential of adaptive glenoid bone remodeling simulation. We expect FE glenoid bone remodeling simulations to become powerful and robust tools in the design and evaluation of glenoid prostheses.     

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

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

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.     

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

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

Continuum remodeling revisited

Recent research effort in bone remodeling has been directed toward describing interstitial fluid flow in the lacuno-canalicular system and its potential as a cellular stimulus. Regardless of the precise contents of the mechanotransduction “black box”, it seems clear that the fluid flow on which the remodeling is predicated cannot occur under static loading conditions. In an attempt to help continuum remodeling simulations catch up with cellular and subcellular research, this paper presents a simple, strain rate driven remodeling algorithm for density allocation and principal material direction rotations. An explicit finite element code was written and deployed on a supercomputer which discretizes the remodeling process and uses an objective hypoelastic constitutive law to simulate trabecular realignment. Results indicate that a target strain rate for this dynamic approach is |D _I ^*| = 1.7% per second which seems reasonable when compared to observed strain rates. Simulations indicate that a morpho-mechanically realistic three-dimensional bone can be synthesized by applying a few dynamic loads at the envelope of common daily physiological rates, even with no static loading component.     

Theoretical and numerical study of a bone remodeling model: The effect of osteocyte cells distribution

It is well argued that osteocytes are mechanosensory cells and are involved in the regulation of bone remodeling. In previous works, the predictions from a simulation model have suggested that both the influencing distance of osteocytes and the magnitude of the mechanical loads determine the thickness of trabeculae whereas the number of osteocytes primarily affects the rate of bone remodeling. The question that remains not completely answered is: for the same number of osteocytes, what is the effect of different distributions on the remodeling process? Based on a particular regulatory bone remodeling model, the question is addressed, in part, by performing a stability analysis in connection with numerical simulations. The results allow us to demonstrate that, on one hand, we cannot reach a conclusion about the stability of the model for a nonuniform osteocyte distribution. This implies that there is no relationship between the different parameters conveying the stability of the model. On the other hand, we show that the osteocyte cell distribution has a significant influence on the bone morphology, which seems to be confirmed by simulations with real data obtained from rat tibia.     

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.     

Age and gender effects on bone mass density variation: finite elements simulation

Bone remodeling is a physiological process by which bone constantly adapts its structure to changes in long-term loading manifested by interactions between osteoclasts and osteoblasts. This process can be influenced by many local factors, via effects on bone cells differentiation and proliferation, which are produced by bone cells and act in a paracrine or autocrine way. The aim of the current work is to provide mechanobiological finite elements modeling coupling both cellular activities and mechanical behavior in order to investigate age and gender effects on bone remodeling evolution. A series of computational simulations have been performed on a 2D and 3D human proximal femur. An age- and gender-related impacts on bulk density alteration of trabecular bone have been noticed, and the major actors responsible of this phenomenon have been then discussed.     

The behavior of adaptive bone-remodeling simulation models

The process of adaptive bone remodeling can be described mathematically and simulated in a computer model, integrated with the finite element method. In the model discussed here, cortical and trabecular bone are described as continuous materials with variable density. The remodeling rule applied to simulate the remodeling process in each element individually is, in fact, an objective function for an optimization process, relative to the external load. Its purpose is to obtain a constant, preset value for the strain energy per unit bone mass, by adapting the density. If an element in the structure cannot achieve that, it either turns to its maximal density (cortical bone) or resorbs completely.

It is found that the solution obtained in generally a discontinuous patchwork. For a two-dimensional proximal femur model this patchwork shows a good resemblance with the density distribution of a real proximal femur.

It is shown that the discontinuous end configuration is dictated by the nature of the differential equations describing the remodeling process. This process can be considered as a nonlinear dynamical system with many degrees of freedom, which behaves divergent relative to the objective, leading to many possible solutions. The precise solution is dependent on the parameters in the remodeling rule, the load and the initial conditions. The feedback mechanism in the process is self-enhancing; denser bone attracts more strain energy, whereby the bone becomes even more dense. It is suggested that this positive feedback of the attractor state (the strain energy field) creates order in the end configuration. In addition, the process ensures that the discontinuous end configuration is a structure with a relatively low mass, perhaps a minimal-mass structure, although this is no explicit objective in the optimization process.

It is hypothesized that trabecular bone is a chaotically ordered structure which can be considered as a fractal with characteristics of optimal mechanical resistance and minimal mass, of which the actual morphology depends on the local (internal) loading characteristics, the sensor-cell density and the degree of mineralization.     

A mixed boundary representation to simulate the displacement of a biofluid by a biomaterial in porous media

Characterization of the biomaterial flow through porous bone is crucial for the success of the bone augmentation process in vertebroplasty. The biofluid, biomaterial, and local morphological bone characteristics determine the final shape of the filling, which is important both for the post-treatment mechanical loading and the risk of intraoperative extraosseous leakage. We have developed a computational model that describes the flow of biomaterials in porous bone structures by considering the material porosity, the region-dependent intrinsic permeability of the porous structure, the rheological properties of the biomaterial, and the boundary conditions of the filling process. To simulate the process of the substitution of a biofluid (bone marrow) by a biomaterial (bone cement), we developed a hybrid formulation to describe the evolution of the fluid boundary and properties and coupled it to a modified version of Darcy's law. The apparent rheological properties are derived from a fluid-fluid interface tracking algorithm and a mixed boundary representation. The region- specific intrinsic permeability of the bone is governed by an empirical relationship resulting from a fitting process of experimental data. In a first step, we verified the model by studying the displacement process in spherical domains, where the spreading pattern is known in advance. The mixed boundary model demonstrated, as expected, that the determinants of the spreading pattern are the local intrinsic permeability of the porous matrix and the ratio of the viscosity of the fluids that are contributing to the displacement process. The simulations also illustrate the sensitivity of the mixed boundary representation to anisotropic permeability, which is related to the directional dependent microstructural properties of the porous medium. Furthermore, we compared the nonlinear finite element model to different published experimental studies and found a moderate to good agreement (R(2)=0.9895 for a one-dimensional bone core infiltration test and a 10.94-16.92% relative error for a three-dimensional spreading pattern study, respectively) between computational and experimental results.     

Optimal principle of bone structure

Bone modeling and remodeling is an optimization process where no agreement has been reached regarding a unified theory or model. We measured 384 pieces of bone in vivo by 64-slice CT and discovered that the bone's center of mass approximately superposes its centroid of shape. This phenomenon indicates that the optimization process of non-homogeneous materials such as bone follows the same law of superposition of center of mass and centroid of shape as that of homogeneous materials. Based upon this principle, an index revealing the relationship between the center of mass and centroid of shape of the compact bone is proposed. Another index revealing the relationship between tissue density and distribution radius is followed. Applying these indexes to evaluate the strength of bone, we have some new findings.     

Multiscale modeling of bone tissue with surface and permeability control

Natural biological materials usually present a hierarchical arrangement with various structural levels. The biomechanical behavior of the complex hierarchical structure of bone is investigated with models that address the various levels corresponding to different scales. Models that simulate the bone remodeling process concurrently at different scales are in development. We present a multiscale model for bone tissue adaptation that considers the two top levels, whole bone and trabecular architecture. The bone density distribution is calculated at the macroscale (whole bone) level, and the trabecular structure at the microscale level takes into account its mechanical properties as well as surface density and permeability. The bone remodeling process is thus formulated as a material distribution problem at both scales. At the local level, the biologically driven information of surface density and permeability characterizes the trabecular structure. The model is tested by a three-dimensional simulation of bone tissue adaptation for the human femur. The density distribution of the model shows good agreement with the actual bone density distribution. Permeability at the microstructural level assures interconnectivity of pores, which mimics the interconnectivity of trabecular bone essential for vascularization and transport of nutrients. The importance of this multiscale model relays on the flexibility to control the morphometric parameters that characterize the trabecular structure. Therefore, the presented model can be a valuable tool to define bone quality, to assist with diagnosis of osteoporosis, and to support the development of bone substitutes.     

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.     

On a new law of bone remodeling based on damage elasticity: a thermodynamic approach

Background

Bone tissue is the main element of the human skeleton and is a dynamic tissue that is continuously renewed by bone-resorbing osteoclasts and bone-forming osteoblasts.The bone is also capable of repairing itself and adapting its structure to changes in its load environment through the process of bone remodeling.Therefore, this phenomenon has been gaining increasing interest in the last years and many laws have been developed in order to simulate this process.

Results

In this paper, we develop a new law of bone remodeling in the context of damaged elastic by applying the thermodynamic approach in the case of small perturbations.The model is solved numerically by a finite difference method in the one-dimensional bone structure of a n-unit elements model.

Conclusion

In addition, several numerical simulations are presented that confirm the accuracy and effectiveness of the model.

     

Computational analysis of bone remodeling during an anterior cervical fusion

The anterior cervical fusion is an established surgical procedure for spine stabilization after the removal of an intervertebral disc. However, it is not yet clear which bone graft represents the best choice and whether surgical devices can be efficient and beneficial for fusion. The aim of this work is to study the influence of the spine instrumentation on bone remodeling after a cervical spine surgery and, consequently, on the fusion process. A finite element model of the cervical spine was developed, having computed tomography images as input. Bone was modeled as a porous material characterized by the relative density at each point and the bone remodeling law was derived assuming that bone self-adapts in order to achieve the stiffest structure for the supported loads, with the total bone mass regulated by the metabolic cost of maintaining bone tissue. Apart from the analysis of healthy cervical spine, different surgical scenarios were tested: bone graft with or without a cage and the use of a stabilization plate system. Results showed that the anterior and posterior regions of the disc space are more important to stress transmission and that spinal devices reduce bone growth within bone grafts, being plate systems the most interfering elements. The material of the interbody cages plays a major role in fusion and, therefore, it should be carefully chosen.     

Bone morphology allows estimation of loading history in a murine model of bone adaptation

Bone adapts its morphology (density/micro- architecture) in response to the local loading conditions in such a way that a uniform tissue loading is achieved (‘Wolff’s law’). This paradigm has been used as a basis for bone remodeling simulations to predict the formation and adaptation of trabecular bone. However, in order to predict bone architectural changes in patients, the physiological external loading conditions, to which the bone was adapted, need to be determined. In the present study, we developed a novel bone loading estimation method to predict such external loading conditions by calculating the loading history that produces the most uniform bone tissue loading. We applied this method to murine caudal vertebrae of two groups that were in vivo loaded by either 0 or 8 N, respectively. Plausible load cases were sequentially applied to micro-finite element models of the mice vertebrae, and scaling factors were calculated for each load case to derive the most uniform tissue strain-energy density when all scaled load cases are applied simultaneously. The bone loading estimation method was able to predict the difference in loading history of the two groups and the correct load magnitude for the loaded group. This result suggests that the bone loading history can be estimated from its morphology and that such a method could be useful for predicting the loading history for bone remodeling studies or at sites where measurements are difficult, as in bone in vivo or fossil bones.     

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.     

Effect of rehabilitation exercise durations on the dynamic bone repair process by coupling polymer scaffold degradation and bone formation

Implantation of biodegradable scaffold is considered as a promising method to treat bone disorders, but knowledge of the dynamic bone repair process is extremely limited. In this study, based on the representative volume cell of a periodic scaffold, the influence of rehabilitation exercise duration per day on the bone repair was investigated by a computational framework. The framework coupled scaffold degradation and bone remodeling. The scaffold degradation was described by a function of stochastic hydrolysis independent of mechanical stimulation, and the bone formation was remodeled by a function of the mechanical stimulation, i.e., strain energy density. Then, numerical simulations were performed to study the dynamic bone repair process. The results showed that the scaffold degradation and the bone formation in the process were competitive. An optimal exercise duration per day emerged. All exercise durations promoted the bone maturation with a final Young’s modulus of 1.9 ± 0.3 GPa. The present study connects clinical rehabilitation and fundamental research, and is helpful to understand the bone repair process and further design bone scaffold for bone tissue engineering.     

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.     

New Insights into BAR Domain-Induced Membrane Remodeling

Mesoscopic simulations and electron microscopy of N-BAR domain-induced liposome remodeling are used to characterize the process of liposome tubulation and vesiculation. The overall process of membrane remodeling is found to involve complex couplings among the N-BAR protein density, the degree of N-BAR oligomerization, and the membrane density. A comparison of complex remodeled liposome structures from mesoscopic simulations with those measured by electron microscopy experiments suggests that the process of membrane remodeling can be described via an appropriate mesoscopic free energy framework. Liposome remodeling more representative of F-BAR domains is also presented within the mesoscopic simulation framework.