Periosteal and endosteal control of bone remodeling under torsional loading.

The shape changes that occur in the mid-diaphysis of a long bone due to adaptive remodeling induced by increasing or decreasing the axial and/or torsional loading of the bone are investigated using a simple model. In this model the mid-diaphysis of a long bone is represented as a hollow thick-walled right-circular cylinder, and different optimal strategies for bone remodeling are considered. It is shown that if such a thick-walled right-circular cylinder capable of surface remodeling is subjected to an axial compressive load and a twisting torque, then the remodeling patterns depend on whether the periosteal surface or the endosteal surface controls the limits of the remodeling process. It is shown that the effect of increasing the torque is always opposite to the effect of increasing the compressive load. Thus, similar remodeling patterns are obtained by increasing one type of loading and decreasing the other. Aside from the restriction of idealized cylindrical geometry, the only assumptions made are that the bone tissue is linearly elastic and that there exists a finite range of remodeling equilibrium stresses. Only those loading situations which maintain the bone in remodeling equilibrium are considered in this work. It follows that the results presented are independent of the specific type of rule governing the temporal evolution of the bone shape, since any such rule applies only in situations where there is active remodeling and, hence, no remodeling equilibrium.     

Phenomenological model of bone remodeling cycle containing osteocyte regulation loop

Biological parameters, such as bone resorption and formation constants, are important variables to achieve optimised hard tissue scaffolds design. To help to understand the modelling process that occurs when a scaffold is implanted it is vital to understand the rather complex bone remodeling process prevalent in native bone. One approach to developing a mathematical model that predicts osteoactivity both in scaffolds, as well as in bone in vivo, is based on a bio-cybernetic vision of basic multicellular unit (BMU) action -. In the case of the model presented in this paper, an additional loop of regulation based on osteocyte activity has been added. This approach has resulted in a four-dimensional system, which shows steady-quasi-cyclic behaviour using a particular range of constants with real biological meaning. The initial findings suggesting that the basic steady-state appears as a torus in multidimensional phase space have been discussed. The existence of this surface in the osteoclasts-osteoblasts-osteocytes-bone subspace indicates that there is a first integral for this dynamic system. Biological and physical interpretation of this integral as a conservative value has been proposed. It is possible to draw an analogy between this conservative value, as a kind of substrate-energy regenerative potential of the bone remodeling system with a molecular nature, to the classical physical value (energy). There are clear indications that there is recovering potential within the BMU that results in a steady operating genetically predominated bone remodeling process. This recovering potential is directed against both mechanical and biomechanical damage to the bone. The current model has credibility when compared to the normal bone remodeling process. However, additional work is required to study a wider range of constants.     

An electron-microscopic study of the bone-remodeling sequence in the rat

Summary A detailed chronological electron-microscopic study of the bone remodeling sequence has been performed in the rat based on a previously described model (Tran Van et al. 1982) in which the remodeling activity is synchronized. This allowed the observation of the cellular and extracellular events during the bone remodeling process, including the activation of the sequential process and the reversal phase, intermediate between osteoclastic resorption and osteoblastic formation. Most important is the fact that throughout the whole process cells with the morphological characteristics of mononuclear phagocytes have been observed in proximity or in contact with the bone surface and/or the various bone cells. Coated pits (receptor-mediated endocytosis) are frequently observed in close apposition to bone spicules and gap junctions are frequent between the cells. These observations suggest that, besides being likely candidates as osteoclast precursors, mononuclear phagocytes may play an important role in 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.     

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.     

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.     

Bone remodeling: A review of the bone microenvironment perspective for fragility fracture (osteoporosis) of the hip

Bone remodeling is an active process throughout the skeleton. The concept of bone turnover surface has been developed and reported in the peer reviewed literature as the quotient of formation surface/resorption surface and is significantly lower in hip fracture. It is necessary to identify the molecular drivers of these changes in bone turnover. Factors that have been strongly implicated in bone metabolism are therefore divided into three categories, "Vascular", "Anabolic" and "Catabolic". Further data is required from the bone tissue-level microenvironment, of fragility fracture patients, on the variation in molecular signals, and the associated changes in bone structure and remodeling.     

Rib remodeling dynamics in a skeletal population from Kulubnarti, Nubia

Bone remodeling variables in the rib were analyzed for a skeletal population of medieval antiquity (ca. A.D. 550-1450) from Kulubnarti, in Sudanese Nubia. The skeletal remains are naturally mummified and in an excellent state of preservation. The study sample consists of thin sections from the ribs of 80 individuals, ranging in age from 15-50+ years. Ribs were examined using a standard microscope and image analysis software. Numbers of intact osteons, fragmentary osteons, forming osteons, and resorption spaces were counted, osteon and Haversian canal areas were measured, and several variables were calculated to assess morphometric and remodeling status in the rib. Variables calculated included mean annual activation frequency, mean bone formation rate, and net osteonal remodeling. Results indicate that age changes are consistent with those observed for other archaeological and modern samples. High numbers of resorption spaces in young males may reflect slower skeletal development in boys compared to girls. Comparisons of rib data with results of a previous study on patterns of femoral bone remodeling in the same population indicate that ribs have more osteons and higher bone formation rates compared to the femur. Also, sexual differences in osteon size observed in the femur were not observed in the rib. Activation frequency and bone formation rate are low in the Kulubnarti population compared to previously published data for a modern sample, a finding consistent with reported results from other archaeological samples. Genetic factors influencing the minimum effective strain setpoint and duration of skeletal maturation, in addition to repetitive high strains at Kulubnarti, may contribute to observed differences.     

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.     

Analysis of Bone Remodeling Under Piezoelectricity Effects Using Boundary Elements

Piezoelectric materials exhibit a response to mechanical-electrical coupling,which represents an important contribution to the electrical-mechanical interaction in bone remodeling process.Therefore,the study of the piezoelectric effect on bone remodeling has high interest in applied biomechanics.The effects of mechano-regulation and electrical stimulation on bone healing are explained.The Boundary Element Method (BEM) is used to simulate piezoelectric effects on bones when sheafing forces are applied to collagen fibers to make them slip past each other.The piezoelectric fundamental solutions are obtained by using the Radon transform.The Dual Reciprocity Method (DRM) is used to simulate the particular solutions in time-dependent problems.BEM analysis showed the strong influence of electrical stimulation on bone remodeling.The examples discussed in this work showed that,as expected,the electrically loaded bone surfaces improved the bone deposition.BEM results confirmed previous findings obtained by using the Finite Element Method (FEM).This work opens very promising doors in biomechanics research,showing that mechanical loads can be replaced,in part,by electrical charges that stimulate strengthening bone density.The obtained results herein are in good agreement with those found in literature from experimental testing and/or other simulation approaches.     

Interpretation of scanning electron microscopic images of abraded forming bone surfaces

The experimental abrasion of forming bone surfaces was conducted so that such surfaces could be characterized. This is particularly important to bone remodeling studies utilizing scanning electron microscope (SEM) imaging of archeological material. Forming surfaces derived from subadult macaque cranial bone were treated by particle abrasion, water abrasion, sliding abrasion, brushing, manual rubbing, weight, exfoliation, chipping and replication. Acetic acid treatments were also performed. The effects of abrasive agents are specific but generally fall into rough (particle and water abrasion) and smooth (sliding abrasion, brushing, rubbing and weight) categories. Protohistoric human and Plio-Pleistocene hominid subadult craniofacial remains were observed with the SEM for comparison with experimental data. The more recent material appeared smooth, probably as a result of specimen preparation procedures using brushes. Surfaces were still interpretable as forming, however, using a more abrasion-resistant feature called intervascular ridging (IVR) described in this study. The IVR pattern is also recognized on the hominid sample, confirming the possibility of performing remodeling studies on abraded fossil material. The abrasion characteristics are somewhat more difficult to classify, however. Abrasion is defined and discussed relative to remodeling studies and taphonomy. The usefulness of the experimental data reported here, however, in paleoenvironmental reconstruction, has yet to be fully realized. Acid and mechanical preparation techniques are briefly addressed. It is concluded that it is possible to characterize a forming surface as abraded according to the findings of this study and that acid, if handled with care, will more likely preserve microanatomical surface detail. It would also be in everyone's interest to employ a less abrasive cleaning regime on archeological specimens.     

The effect of surface roughness on the stress adaptation of trabecular architecture around a cylindrical implant

The effect of implant-bone bonding and the effect of implant surface roughness on bone remodeling near the bone-implant interface were studied by using a surface remodeling theory and the boundary element method. The study has shown that implant attachment plays an important role in bone remodeling near the implant. It has been observed in animal experiments and in clinical situations that the remodeled trabecular bone architecture around a cylindrical implant could vary, on one hand, from a hub surrounding the implant with a set of external spokes to, on the other hand, a hubless situation in which a set of spokes attach directly to the implant. It is shown here that the difference in these structures may be attributed to differences in implant attachment. The results show that the bone with perfect bonding or roller boundary condition without a gap remodeled to a hubless spoke trabecular bone architecture. On the other hand, the roller boundary condition with a specified gap yielded a spoke trabecular architecture with a hub or ring surrounding the implant. These quantitative results mirror the experimental and clinical observations. It is concluded that the hub is a consequence of the gap and not a consequence of the lack of friction between the implant and the bone.     

Analysis of microstructural and mechanical alterations of trabecular bone in a simulated three-dimensional remodeling process

Bone remodeling is a complex dynamic process, which modulates both bone mass and bone microstructure. In addition to bone mass, bone microstructure is an important contributor to bone quality in osteoporosis and fragility fractures. However, the quantitative knowledge of evolution of three-dimensional (3D) trabecular microstructure in adaptation to the external forces is currently limited. In this study, a new 3D simulation method of remodeling of human trabecular bone was developed to quantitatively study the dynamic evolution of bone mass and trabecular microstructure in response to different external loading conditions. The morphological features of trabecular plate and rod, such as thickness and number density in different orientations were monitored during the remodeling process using a novel imaging analysis technique, namely Individual Trabecula Segmentation (ITS). We showed that the volume fraction and microstructures of trabecular bone including, trabecular type and orientation, were determined by the applied mechanical load. Particularly, the morphological parameters of trabecular plates were more sensitive to the applied load, indicating that they played the major role in the mechanical properties of the trabecular bone. Reducing the applied load caused severe microstructural deteriorations of trabecular bone, such as trabecular plate perforation, rod breakage, and a conversion from plates to rods.     

Remodeling of cortical bone allografts mediated by adherent rAAV-RANKL and VEGF gene therapy

Structural allograft healing is limited because of a lack of vascularization and remodeling. To study this we developed a mouse model that recapitulates the clinical aspects of live autograft and processed allograft healing. Gene expression analyses showed that there is a substantial decrease in the genes encoding RANKL and VEGF during allograft healing. Loss-of-function studies showed that both factors are required for autograft healing. To determine whether addition of these signals could stimulate allograft vascularization and remodeling, we developed a new approach in which rAAV can be freeze-dried onto the cortical surface without losing infectivity. We show that combination rAAV-RANKL- and rAAV-VEGF-coated allografts show marked remodeling and vascularization, which leads to a new bone collar around the graft. In conclusion, we find that RANKL and VEGF are necessary and sufficient for efficient autograft remodeling and can be transferred using rAAV to revitalize structural allografts.     

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.     

Bone remodeling theory applied to the study of n unit-elements model.

The aim of this paper is to illustrate the application of mathematical tools for the analysis of non-linear dynamical systems to the study of global stability of one kind of bone remodeling scheme applied to n unit-elements model. The particular aspects analyzed here are the stationary states related to this theory and a condition of their stability. The non-linear equations governing the remodeling process are solved by finite-difference method and the well-known results on the heterogeneous spatial organizations have been retrieved and confirm the analytical study. This kind of remodeling theory is useful for investigating the effects of physiological parameters on the development, maintenance, and adaptation of bone under mechanical loading.