Computational simulation of internal bone remodelling around dental implants: a sensitivity analysis

This study aimed to predict the distribution of bone trabeculae, as a density change per unit time, around a dental implant based on applying a selected mathematical remodelling model. The apparent bone density change as a function of the mechanical stimulus was the base of the applied remodelling model that describes disuse and overload bone resorption. The simulation was tested in a finite element model of a screw-shaped dental implant in an idealised bone segment. The sensitivity of the simulation to different mechanical parameters was investigated; these included element edge length, boundary conditions, as well as direction and magnitude of the implant loads. The alteration in the mechanical parameters had a significant influence on density distribution and model stability, in particular at the cortical bone region. The remodelling model could succeed to achieve trabeculae-like structure around osseointegrated dental implants. The validation of this model to a real clinical case is required.     

Computational simulation of internal bone remodelling around dental implants: a sensitivity analysis

This study aimed to predict the distribution of bone trabeculae, as a density change per unit time, around a dental implant based on applying a selected mathematical remodelling model. The apparent bone density change as a function of the mechanical stimulus was the base of the applied remodelling model that describes disuse and overload bone resorption. The simulation was tested in a finite element model of a screw-shaped dental implant in an idealised bone segment. The sensitivity of the simulation to different mechanical parameters was investigated; these included element edge length, boundary conditions, as well as direction and magnitude of the implant loads. The alteration in the mechanical parameters had a significant influence on density distribution and model stability, in particular at the cortical bone region. The remodelling model could succeed to achieve trabeculae-like structure around osseointegrated dental implants. The validation of this model to a real clinical case is required.     

Stress analysis of compression plate fixation and its effects on long bone remodeling

A three-dimensional finite element model is generated for an intact plexiglass tube with an attached six-hole stainless steel compression plate. The results for a wide range of loads, including cyclic external loads and static tensile preloads in the plate and screws, are examined as specifically related to plate-induced osteopenia. The model demonstrates that disuse osteopenia, resulting from a reduction in magnitude of cyclic axial stress, should be limited to the central region between the inner screws. Also, the addition of a static preload negates any reduced axial stress levels in this region, thus raising questions on the relative importance of static and cyclic stresses for the internal remodeling of bone.     

Trabecular architecture can remain intact for both disuse and overload enhanced resorption characteristics

The paradigm that bone metabolic processes are controlled by osteocyte signals have been the subject of investigation in many recent studies. One hypothesis is that osteoblast formation is enhanced by these signals, and that osteoclast resorption is enhanced by the lack of them. Reduced, or absent, osteocyte signaling can be an effect of reduced mechanical loading (disuse) or of defects in the canalicular network, due to microcracks. This would mean that bone is resorbed precisely there where it is mostly needed. In our study, we addressed this apparent contradiction. The purpose was to investigate how alternative strain-based local stimuli for osteoclasts to resorb bone would affect remodeling and adaptation of the trabecular architecture. For this purpose, a computer-simulation model was used, which couples morphological and mechanical effects of local bone metabolism to changes in trabecular architecture and density at large. Six resorption characteristics were studied in the model: (I) resorption occurs spatially random, (II) resorption is enhanced or (III) strongly enhanced where there is disuse, (IV) resorption is enhanced or (V) strongly enhanced where there are high strains, i.e. overload, and (VI) resorption is enhanced where there is disuse and where there are high strains. Results showed that the rates of structural adaptation to alternative loading were higher for disuse-controlled resorption than for overload-controlled resorption. Architecture and mass remained stable for all cases except (V) in which the structure deteriorated as in osteoporotic bone. We conclude that, given the potential of osteoblasts to form bone in highly strained areas, based on signals from osteocytes, osteoclast resorption can normally be compensated for.     

Brief communication: The effects of disuse on the mechanical properties of bone: What unloading tells us about the adaptive nature of skeletal tissue

The intricate link between load environment and skeletal health is exemplified by the severe osteopenia that accompanies prolonged periods of immobilization, frequently referred to as disuse osteoporosis. Investigating the effects disuse has on the structural properties of bone provides a unique opportunity to better understand how mechanical loads influence the adaptation and maintenance of skeletal tissue. Here, we report results from an examination of multiple indicators of bone metabolism (e.g., mean osteon density, mean osteon size, bone mass, and bone area distribution) within the major long bones of individuals with distinct activity level differences. Results are based on a sample comprising two subjects that suffered from long‐term quadriplegia and 28 individuals of comparable age that had full limb mobility. Although limited in sample size, our findings suggest bones associated with long‐term disuse have lower osteon densities and larger osteon areas compared to individuals of normal mobility, reflecting dramatically lower remodeling rates potentially related to reduced strain levels. Moreover, immobilized skeletal elements demonstrate a reduced percentage of cortical area present resulting from endosteal resorption. Differences between mobility groups in the percentage of cortical area present and bone distribution of all skeletal elements, suggests bone modeling activity is negligible in the unloaded adult skeleton. Additional histomorphometric comparisons reveal potential intraskeletal differences in bone turnover rates suggesting remodeling rates are highest within the humeri and femora. Addition of more immobilized individuals in the future will allow for quantitative statistical analyses and greater consideration of human variation within and between individuals. Am J Phys Anthropol 2012. © 2012 Wiley Periodicals, Inc.     

Constitutive relationship of tissue behavior with damage accumulation of human cortical bone

Microdamage accumulation has been identified as a major conduit for bone tissues to absorb fracture energy. Due to the poor understanding of its underlying mechanism, however, an adequate constitutive relationship between damage accumulation and the mechanical behavior of bone has not yet been established. In this study, the constitutive relationship between the damage accumulation induced by overload and the evolution of mechanical properties of bone with incremental deformation was established based on the experimental results obtained from a novel progressive loading protocol developed in our laboratory. First, a decayed exponential model was proposed to capture the damage accumulation (modulus loss) with increase in applied strain. Next, a power law function was proposed to represent the progression of plastic deformation with damage accumulation. Finally, a linear combination of the Kohlrausch–Williams–Watts (KWW) and the Debye functions was used to depict the viscoelastic behavior of bone associated with damage accumulation. The results of this study may help in developing a constitutive model for predicting the mechanical behavior of cortical bone tissues.     

Adaptive changes in micromechanical environments of cancellous and cortical bone in response to in vivo loading and disuse

The skeleton accommodates changes in mechanical environments by increasing bone mass under increased loads and decreasing bone mass under disuse. However, little is known about the adaptive changes in micromechanical behavior of cancellous and cortical tissues resulting from loading or disuse. To address this issue, in vivo tibial loading and hindlimb unloading experiments were conducted on 16-week-old female C57BL/6J mice. Changes in bone mass and tissue-level strains in the metaphyseal cancellous and midshaft cortical bone of the tibiae, resulting from loading or unloading, were determined using microCT and finite element (FE) analysis, respectively. We found that loading- and unloading-induced changes in bone mass were more pronounced in the cancellous than cortical bone. Simulated FE-loading showed that a greater proportion of elements experienced relatively lower longitudinal strains following load-induced bone adaptation, while the opposite was true in the disuse model. While the magnitudes of maximum or minimum principal strains in the metaphyseal cancellous and midshaft cortical bone were not affected by loading, strains oriented with the long axis were reduced in the load-adapted tibia suggesting that loading-induced micromechanical benefits were aligned primarily in the loading direction. Regression analyses demonstrated that bone mass was a good predictor of bone tissue strains for the cortical bone but not for the cancellous bone, which has complex microarchitecture and spatially-variant strain environments. In summary, loading-induced micromechanical benefits for cancellous and cortical tissues are received primarily in the direction of force application and cancellous bone mass may not be related to the micromechanics of cancellous bone.     

A Computational Model for Cortical Endosteal Surface Remodeling Induced by Mechanical Disuse

In mechanical disuse conditions associated with immobilization and microgravity in spaceflight, cortical endosteal surface moved outward with periosteal surface moving slightly or unchanged, resulting in reduction of cortical thickness. Reduced thickness of the shaft cortex of long bone can be considered as an independent predictor of fractures. Accordingly, it is important to study the remodeling process at cortical endosteal surface. This paper presents a computer simulation of cortical endosteal remodeling induced by mechanical disuse at the Basic Multicellular Units level with cortical thickness as controlling variables. The remodeling analysis was performed on a representative rectangular slice of the cross section of cortical bone volume. The pQCT data showing the relationship between the duration of paralysis and bone structure of spinal cord injured patients by Eser et al. (2004) were used as an example of mechanical disuse to validate the model. Cortical thickness, BMU activation frequency, mechanical load and principal compressive strain for tibia and femur cortical models were simulated. The effects of varying the mechanical load and maximum BMU activation frequency were also investigated. The cortical thicknesses of femur and tibia models were both consistent with the clinical data. Varying the decreasing coefficient in mechanical load equation had little effect on the steady state values of cortical thickness and BMU activation frequency. However, it had much effect on the time to reach steady state. The maximum BMU activation frequency had effects on both the steady state value and the time to reach steady state for cortical thickness and BMU activation frequency. The computational model for cortical endosteal surface remodeling developed in this paper can be further used to quantify and predict the effects of mechanical factors and biological factors on cortical thickness and help us to better understand the relationship between bone morphology and mechanical as well as biological environment.     

Numerical simulation of streaming potentials due to deformation-induced hierarchical flows in cortical bone

Bone is a very dynamic tissue capable of modiA,fing its composition, microstructure, and overall geometry in response to the changing biomechanical needs. Streaming potential has been hypothesized as a mechanotransduction mechanism that may allow osteocytes to sense their biomechanical environment. A correct understanding of the mechanism for streaming potential will illuminate our understanding of bone remodeling, such as the remodeling associated with exercise hypertrophy, disuse atrophy, and the bone remodeling arounid implants. In the current research, a numerical model based on the finite element discretization is proposed to simulate the fluid flows through the complicated hierarchical flow system and to calculate the concomitant stress generated potential (SGP) as a result of applied mechanical loading. The lacunae-canaliculi and the matrix microporosity are modeled together as discrete one-dimensional flow channels superposed in a biphasic poroelastic matrix. The cusplike electric potential distribution surrounding the Haversian canal that was experimentallv observed and reported in the literature earlier was successfully reproduced by the current numerical calculation.     

An adaptation model for trabecular bone at different mechanical levels

Background  

Bone has the ability to adapt to mechanical usage or other biophysical stimuli in terms of its mass and architecture, indicating that a certain mechanism exists for monitoring mechanical usage and controlling the bone's adaptation behaviors. There are four zones describing different bone adaptation behaviors: the disuse, adaptation, overload, and pathologic overload zones. In different zones, the changes of bone mass, as calculated by the difference between the amount of bone formed and what is resorbed, should be different.     

Osteocyte-viability-based simulations of trabecular bone loss and recovery in disuse and reloading

Osteocyte apoptosis is known to trigger targeted bone resorption. In the present study, we developed an osteocyte-viability-based trabecular bone remodeling (OVBR) model. This novel remodeling model, combined with recent advanced simulation methods and analysis techniques, such as the element-by-element 3D finite element method and the ITS technique, was used to quantitatively study the dynamic evolution of bone mass and trabecular microstructure in response to various loading and unloading conditions. Different levels of unloading simulated the disuse condition of bed rest or microgravity in space. The amount of bone loss and microstructural deterioration correlated with the magnitude of unloading. The restoration of bone mass upon the reloading condition was achieved by thickening the remaining trabecular architecture, while the lost trabecular plates and rods could not be recovered by reloading. Compared to previous models, the predictions of bone resorption of the OVBR model are more consistent with physiological values reported from previous experiments. Whereas osteocytes suffer a lack of loading during disuse, they may suffer overloading during the reloading phase, which hampers recovery. The OVBR model is promising for quantitative studies of trabecular bone loss and microstructural deterioration of patients or astronauts during long-term bed rest or space flight and thereafter bone recovery.     

Toward an identification of mechanical parameters initiating periosteal remodeling: a combined experimental and analytic approach

The ability of bone to adapt to its mechanical environment is well recognized, although the specific mechanical parameters initiating or maintaining the adaptive responses have yet to be identified. Recently introduced mathematical models offer the potential to aid in the identification of such parameters, although these models have not been well validated experimentally or clinically. We formulated a complementary experimental/analytic approach, using an animal model with a well-controlled mechanical environment combined with finite element modeling (FEM). We selected the functionally isolated turkey ulna, since the loading could be completely characterized and the periosteal adaptive responses subsequently monitored and quantified after four and eight weeks of loading. Known loads input into a three-dimensional, linearly elastic FEM of the ulna then permitted full-field mechanical characterization of the ulna. The FEM was validated against a normal strain-gaged turkey ulna, loaded in vivo in an identical fashion to the experimental ulnae. Twenty-four candidate mechanical parameters were then compared to the quantified adaptive responses, using statistical techniques. The data supported strain energy density, longitudinal shear stress, and tensile principal stress/strain as the mechanical parameters most likely related to the initiation of the remodeling response. Model predictions can now suggest new experiments, against which the predictions can be supported or falsified.     

Interstitial fluid flow in canaliculi as a mechanical stimulus for cancellous bone remodeling: in silico validation

Cancellous bone has a dynamic 3-dimensional architecture of trabeculae, the arrangement of which is continually reorganized via bone remodeling to adapt to the mechanical environment. Osteocytes are currently believed to be the major mechanosensory cells and to regulate osteoclastic bone resorption and osteoblastic bone formation in response to mechanical stimuli. We previously developed a mathematical model of trabecular bone remodeling incorporating the possible mechanisms of cellular mechanosensing and intercellular communication in which we assumed that interstitial fluid flow activates the osteocytes to regulate bone remodeling. While the proposed model has been validated by the simulation of remodeling of a single trabecula, it remains unclear whether it can successfully represent in silico the functional adaptation of cancellous bone with its multiple trabeculae. In the present study, we demonstrated the response of cancellous bone morphology to uniaxial or bending loads using a combination of our remodeling model with the voxel finite element method. In this simulation, cancellous bone with randomly arranged trabeculae remodeled to form a well-organized architecture oriented parallel to the direction of loading, in agreement with the previous simulation results and experimental findings. These results suggested that our mathematical model for trabecular bone remodeling enables us to predict the reorganization of cancellous bone architecture from cellular activities. Furthermore, our remodeling model can represent the phenomenological law of bone transformation toward a locally uniform state of stress or strain at the trabecular level.     

Bending properties, porosity, and ash fraction of black bear (Ursus americanus) cortical bone are not compromised with aging despite annual periods of disuse

In many species, including humans, disuse causes an imbalance in bone remodeling that leads to increased bone porosity as a result of increased bone resorption and decreased bone formation. However, black bears (Ursus americanus) may not develop disuse osteopenia, to the extent that other animals do, during long periods of disuse (i.e. hibernation) because they maintain osteoblastic bone formation during hibernation, even though bone resorption is increased during hibernation. Black bears may also have a mechanism to rapidly and completely recover the bone lost (by increased resorption during hibernation) during their remobilization period. Our findings suggest that cortical bone bending strength (211-328 MPa), bending modulus (16.0-29.5 MPa), fracture energy (0.0118-0.0205 J mm(-2)), porosity (2.3-7.1%), and ash fraction (0.638-0.672) are not compromised with age in black bears, despite annual periods of disuse. In fact, the ultimate strength (p=0.01), modulus (p=0.04), and ash fraction (p=0.03) of cortical bone were shown to significantly increase with age (2-14 yrs). Female bears give birth and nurse during hibernation; however, we found no significant (p>0.16) differences between male and female bone properties. Other animals require remobilization periods 2-3 times longer than the immobilization period to recover the bone lost during disuse. Our findings support the idea that black bears, which hibernate 5-7 months annually, have evolved a biological mechanism to mitigate the adverse effects of disuse on bone porosity and mechanical behavior.     

Microdamage propagation in trabecular bone due to changes in loading mode

Microdamage induced by falls or other abnormal loads that cause shear stress in trabecular bone could impair the mechanical properties of the proximal femur or spine. Existing microdamage may also increase the initiation and propagation of further microdamage during subsequent normal, on-axis, loading conditions, resulting in atraumatic or "spontaneous" fractures. Microdamage formation due to shear and compressive strains was studied in 14 on-axis cylindrical bovine tibial trabecular bone specimens. Microdamage was induced by a torsional overload followed by an on-axis compressive overload and quantified microscopically. Fluorescent agents were used to label microdamage and differentiate damage due to the two loading modes. Both the microcrack density and diffuse damage area caused by the torsional overload increased with increasing shear strain from the center to the edge of the specimen. However, the mean microcrack length was uniform across the specimen, suggesting that microcrack length is limited by microstructural features. The mean density of microcracks caused by compressive overloading was slightly higher near the center of the specimen, and the diffuse damage area was uniform across the specimen. Over 20% of the microcracks formed in the initial torsional overloading propagated during compression. Moreover the propagating microcracks were, on average, longer than microcracks formed by a single overload. As such, changes in loading mode can cause propagation of microcracks beyond the microstructural barriers that normally limit the length. Damage induced by in vivo off-axis loads such as falls may similarly propagate during subsequent normal loading, which could affect both remodeling activity and fracture susceptibility.     

Nanoindentation testing and finite element simulations of cortical bone allowing for anisotropic elastic and inelastic mechanical response

Anisotropy is one of the most peculiar aspects of cortical bone mechanical behaviour, and the numerical approach can be successfully used to investigate aspects of bone tissue mechanics that analytical methods solve in approximate way or do not cover. In this work, nanoindentation experimental tests and finite element simulations were employed to investigate the elastic-inelastic anisotropic mechanical properties of cortical bone. The model allows for anisotropic elastic and post-yield behaviour of the tissue. A tension-compression mismatch and direction-dependent yield stresses are allowed for. Indentation experiments along the axial and transverse directions were simulated with the purpose to predict the indentation moduli and hardnesses along multiple orientations. Results showed that the experimental transverse-to-axial ratio of indentation moduli, equal to 0.74, is predicted with a ～3% discrepancy regardless the post-yield material behaviour; whereas, the transverse-to-axial hardness ratio, equal to 0.86, can be correctly simulated (discrepancy ～6% w.r.t. the experimental results) only employing an anisotropic post-elastic constitutive model. Further, direct comparison between the experimental and simulated indentation tests evidenced a good agreement in the loading branch of the indentation curves and in the peak loads for a transverse-to-axial yield stress ratio comparable to the experimentally obtained transverse-to-axial hardness ratio. In perspective, the present work results strongly support the coupling between indentation experiments and FEM simulations to get a deeper knowledge of bone tissue mechanical behaviour at the microstructural level. The present model could be used to assess the effect of variations of constitutive parameters due to age, injury, and/or disease on bone mechanical performance in the context of indentation testing.     

Modeling microdamage behavior of cortical bone

Bone is a complex material which exhibits several hierarchical levels of structural organization. At the submicron-scale, the local tissue porosity gives rise to discontinuities in the bone matrix which have been shown to influence damage behavior. Computational tools to model the damage behavior of bone at different length scales are mostly based on finite element (FE) analysis, with a range of algorithms developed for this purpose. Although the local mechanical behavior of bone tissue is influenced by microstructural features such as bone canals and osteocyte lacunae, they are often not considered in FE damage models due to the high computational cost required to simulate across several length scales, i.e., from the loads applied at the organ level down to the stresses and strains around bone canals and osteocyte lacunae. Hence, the aim of the current study was twofold: First, a multilevel FE framework was developed to compute, starting from the loads applied at the whole bone scale, the local mechanical forces acting at the micrometer and submicrometer level. Second, three simple microdamage simulation procedures based on element removal were developed and applied to bone samples at the submicrometer-scale, where cortical microporosity is included. The present microdamage algorithm produced a qualitatively analogous behavior to previous experimental tests based on stepwise mechanical compression combined with in situ synchrotron radiation computed tomography. Our results demonstrate the feasibility of simulating microdamage at a physiologically relevant scale using an image-based meshing technique and multilevel FE analysis; this allows relating microdamage behavior to intracortical bone microstructure.     

Missense Mutations in LRP5 Associated with High Bone Mass Protect the Mouse Skeleton from Disuse- and Ovariectomy-Induced Osteopenia

The low density lipoprotein receptor-related protein-5 (LRP5), a co-receptor in the Wnt signaling pathway, modulates bone mass in humans and in mice. Lrp5 knock-out mice have severely impaired responsiveness to mechanical stimulation whereas Lrp5 gain-of-function knock-in and transgenic mice have enhanced responsiveness to mechanical stimulation. Those observations highlight the importance of Lrp5 protein in bone cell mechanotransduction. It is unclear if and how high bone mass-causing (HBM) point mutations in Lrp5 alter the bone-wasting effects of mechanical disuse. To address this issue we explored the skeletal effects of mechanical disuse using two models, tail suspension and Botulinum toxin-induced muscle paralysis, in two different Lrp5 HBM knock-in mouse models. A separate experiment employing estrogen withdrawal-induced bone loss by ovariectomy was also conducted as a control. Both disuse stimuli induced significant bone loss in WT mice, but Lrp5 A214V and G171V were partially or fully protected from the bone loss that normally results from disuse. Trabecular bone parameters among HBM mice were significantly affected by disuse in both models, but these data are consistent with DEXA data showing a failure to continue growing in HBM mice, rather than a loss of pre-existing bone. Ovariectomy in Lrp5 HBM mice resulted in similar protection from catabolism as was observed for the disuse experiments. In conclusion, the Lrp5 HBM alleles offer significant protection from the resorptive effects of disuse and from estrogen withdrawal, and consequently, present a potential mechanism to mimic with pharmaceutical intervention to protect against various bone-wasting stimuli.