Effect of mechanical set point of bone cells on mechanical control of trabecular bone architecture

Load adaptation through bone remodeling: a mechanobiological model coupled with the finite element method

This work proposes a novel tissue-scale mechanobiological model of bone remodeling to study bone's adaptation to distinct loading conditions. The devised algorithm describes the mechanosensitivity of bone and its impact on bone cells' functioning through distinct signaling factors. In this study, remodeling is mechanically ruled by variations of the strain energy density (SED) of bone, which is determined by performing a linear elastostatic analysis combined with the finite element method. Depending on the SED levels and on a set of biological signaling factors ([Formula: see text] parameters), osteoclasts and osteoblasts can be mechanically triggered. To reproduce this phenomenon, this work proposes a new set of [Formula: see text] parameters. The combined response of osteoclasts and osteoblasts will then affect bone's apparent density, which is correlated with other mechanical properties of bone, through a phenomenological law. Thus, this novel model proposes a constant interplay between the mechanical and biological components of the process. The spatiotemporal simulation used to validate this new approach is a benchmark example composed by two distinct phases: (1) pre-orientation and (2) load adaptation. On both of them, bone is able to adapt its morphology according to the loading condition, achieving the required trabecular distribution to withstand the applied loads. Moreover, the equilibrium morphology reflects the orientation of the load. These preliminary results support the new approach proposed in this study.

Tissue-level remodeling simulations of cancellous bone capture effects of in vivo loading in a rabbit model

The adaptation of cancellous bone to mechanical stimuli occurs throughout normal skeletal growth and aging, as well as in response to surgery, disease and device implantation. Previously we developed an in vivo cancellous loading model in the distal lateral femur of the rabbit. In response to daily in vivo loading for four weeks, bone mass increased, trabeculae thickened and the apparent modulus of the underlying cancellous bone increased. Here, we simulated our prior in vivo rabbit loading experiment using a cell-based tissue remodeling algorithm (Mullender et al., 1994) and compared the results to the in vivo experimental data published previously. Cancellous bone tissue was added or removed from the surface of trabeculae in regions of high and low mechanical stimulus, respectively. To examine the effect of material properties on mechanically regulated adaptation, we implemented both a homogeneous material model and a model where the relative density of tissue was lower for new and surface bone tissue compared to interior tissue. The simulations captured the changes in histomorphometric parameters and mechanical properties measured in the in vivo experiment illustrating the ability of computational simulations to predict the effect of mechanically regulated adaptation on cancellous bone histomorphometry and apparent modulus.

Bone cell mechanosensitivity, estrogen deficiency, and osteoporosis

Adaptation of bone to mechanical stresses normally produces a bone architecture that combines a proper resistance against failure with a minimal use of material. This adaptive process is governed by mechanosensitive osteocytes that transduce the mechanical signals into chemical responses, i.e. the osteocytes release signaling molecules, which orchestrate the recruitment and activity of bone forming osteoblasts and/or bone resorbing osteoclasts. Computer models have shown that the maintenance of a mechanically-efficient bone architecture depends on the intensity and spatial distribution of the mechanical stimulus as well as on the osteocyte response. Osteoporosis is a condition characterized by a reduced bone mass and a compromized resistance of bone against mechanical loads, which has led us to hypothesize that mechanotransduction by osteocytes is altered in osteoporosis. One of the major causal factors for osteoporosis is the loss of estrogen, the major hormonal regulator of bone metabolism. Loss of estrogen may increase osteocyte-mediated activation of bone remodeling, resulting in impaired bone mass and architecture. In this review we highlight current insights on how osteocytes perceive mechanical stimuli placed on whole bones. Particular emphasis is placed on the role of estrogen in signaling pathway activation by mechanical stimuli, and on computer simulation in combination with cell biology to unravel biological processes contributing to bone strength.

Trabecular bone structure in lumbosacral transitional vertebrae: distribution and densities across sagittal vertebral body segments

BACKGROUND CONTEXT

Lumbosacral transitional vertebrae (LSTV) are associated with altered articular morphology at the L5-S1 junction. Studies related to lumbo-sacral trabecular architecture in LSTV are few. Altered lumbosacral load bearing at these anomalous junctions possibly results in changes in the number, density, and trajectory of the trabecular bone in transitional lumbosacral vertebral bodies.

PURPOSE

To investigate the pattern, distribution, and density of trabecular bone in the terminal lumbar vertebrae and the first sacral segments in LSTV-affected spines. Measurements were compared with those obtained from normal lumbosacral specimens.

STUDY DESIGN

Observational and descriptive human cadaveric study of vertebral trabecular architecture.

METHODS

Blocks of tissues were obtained from normal (n=20) and LSTV cadaveric specimens (n=16) by sectioning vertically through the fifth lumbar and the first sacral vertebra on either side of the midsagittal plane. Photographs of the cut surfaces were computationally enlarged and mapped for vertical and transverse trabecular numbers and surface areas using the software Image J. All parameters including the trabecular density were computed for anterior, middle, and posterior segments of each of the vertebral elements.

RESULTS

The anterior and the posterior segments showed greater number of trabeculae across all LSTV subtypes in both the terminal lumbar and first sacral vertebrae in comparison with the middle segment. L5 exhibited greater number of vertical trabeculae, whereas the first sacral segments demonstrated greater number and densities of transverse trabeculae. Transition-associated vertebrae showed overall reduced number of the lumbar trabeculae but relatively compact sacral posterior segments with greater number of horizontal trabeculae.

CONCLUSIONS

Findings suggest that some of these variations have overall reduced number of trabeculae across lumbo-sacral vertebrae in LSTV. Screw placements and subsequent pullouts in LSTV may be reviewed in light of different trabecular patterns as reported in this study.

Is bone loss the reversal of bone accrual? Evidence from a cross-sectional study in daughter-mother-grandmother trios

Bone adapts to mechanical loads applied on it. During aging, loads decrease to a greater extent at those skeletal sites where loads increase most in earlier life. Thus, the loss of bone may occur preferentially at sites where most bone has been deposited previously; ie, bone loss could be the directional reversal of accrual. To test this hypothesis, we compared the bone mass distribution at weight-bearing (tibia) and non-weight-bearing (radius) bones among 18-year-old girls, their premenopausal mothers, and their postmenopausal maternal grandmothers. Bone and muscle properties were measured by pQCT, and polar distribution of bone mass was obtained in 55 girl-mother-maternal grandmother trios. Site-matched differences in bone mass were compared among three generations. The differences between girls and mothers and between mothers and grandmothers were used to represent the patterns of bone mass accrual from early adulthood to middle age and bone loss from middle to old age, respectively. Compared to the mothers, 18-year old girls had less bone mass in the anterior and medial-posterior regions of the tibial shaft, while the grandmothers had less bone in the anterior and posterior regions. In contrast, the bone mass differences in the radial shaft between girls and mothers and mothers and grandmothers were relatively uniform. We conclude that both bone accrual and loss are direction-specific in weight-bearing bones but relatively uniform in non-weight-bearing bones. Bone loss in old age is largely, but not completely, a reversal of the preferential deposition of bone in the most highly loaded regions during early life.

The importance of cortical bone orthotropicity, maximum stiffness direction and thickness on the reliability of mandible numerical models

AIM

To identify mechanical and geometrical variables affecting the biofidelity of numerical models of human mandible. Computed results sensibility to cortical bone orthotropy and thicknesses is investigated.

METHODS

Two mandible numerical models of different bone complexities are setup. In the low-complexity model, cortical bone is coupled with isotropic materials properties; constant thickness for cortical bone is adopted along the mandible structure. In the higher complexity model, the cortical bone is considered as an orthotropic material according to an independent mechanical characterization performed on fresh human dentate mandibles. Cortical thickness distribution, the values of the principal elastic moduli and principal directions of orthotropy are considered as piecewise heterogeneous. Forces for masseter (10 N), medial pterigoid (6 N), anterior (4 N) and posterior (4 N) temporalis muscles are applied to the models. Computed strains fields are compared with those experimentally measured in an independent test performed on a real human mandible in the same loading conditions.

RESULTS

Under closure muscles forces both models shows similar strain distribution. On the contrary, strain fields values are significantly different between the presented models.

CONCLUSIONS

The mandible structure is sensible to compact bone orthotropy and thickness at the facial side of condylar neck, retro molar area and at the lingual side of middle portion of the corpus in molars area, anterior margin of the ramus. In these areas, it is advisable to use orthotropic properties for cortical bone to accurately describe the strain state.

Simulation of vertebral trabecular bone loss using voxel finite element analysis

Trabecular bone loss in human vertebral bone is characterised by thinning and eventual perforation of the horizontal trabeculae. Concurrently, vertical trabeculae are completely lost with no histological evidence of significant thinning. Such bone loss results in deterioration in apparent modulus and strength of the trabecular core. In this study, a voxel-based finite element program was used to model bone loss in three specimens of human vertebral trabecular bone. Three sets of analyses were completed. In Set 1, strain adaptive resorption was modelled, whereby elements which were subject to the lowest mechanical stimulus (principal strain) were removed. In Set 2, both strain adaptive and microdamage mechanisms of bone resorption were included. Perforation of vertical trabeculae occurred due to microdamage resorption of elements with strains that exceeded a damage threshold. This resulted in collapse of the trabecular network under compression loading for two of the specimens tested. In Set 3, the damage threshold strain was gradually increased as bone loss progressed, resulting in reduced levels of microdamage resorption. This mechanism resulted in trabecular architectures in which vertical trabeculae had been perforated and which exhibited similar apparent modulus properties compared to experimental values reported in the literature. Our results indicate that strain adaptive remodelling alone does not explain the deterioration in mechanical properties that have been observed experimentally. Our results also support the hypothesis that horizontal trabeculae are lost principally by strain adaptive resorption, while vertical trabeculae may be lost due to perforation from microdamage resorption followed by rapid strain adaptive resorption of the remaining unloaded trabeculae.

Biomechanical effect of mineral heterogeneity in trabecular bone

Due to daily loading, trabecular bone is subjected to deformations (i.e., strain), which lead to stress in the bone tissue. When stress and/or strain deviate from the normal range, the remodeling process leads to adaptation of the bone architecture and its degree of mineralization to effectively withstand the sustained altered loading. As the apparent mechanical properties of bone are assumed to depend on the degree and distribution of mineralization, the goal of the present study was examine the influences of mineral heterogeneity on the biomechanical properties of trabecular bone in the human mandibular condyle. For this purpose nine right condyles from human dentate mandibles were scanned and evaluated with a microCT system. Cubic regional volumes of interest were defined, and each was transformed into two different types of finite element (FE) models, one homogeneous and one heterogeneous. In the heterogeneous models the element tissue moduli were scaled to the local degree of mineralization, which was determined using microCT. Compression and shear tests were simulated to determine the apparent elastic moduli in both model types. The incorporation of mineralization variation decreased the apparent Young's and shear moduli by maximally 21% in comparison to the homogeneous models. The heterogeneous model apparent moduli correlated significantly with bone volume fraction and degree of mineralization. It was concluded that disregarding mineral heterogeneity may lead to considerable overestimation of apparent elastic moduli in FE models.

Dynamic simulation of three dimensional architectural and mechanical alterations in human trabecular bone during menopause

A three dimensional (3D) computational simulation of dynamic process of trabecular bone remodeling was developed with all the parameters derived from physiological and clinical data. Contributions of the microstructural bone formation deficits: trabecular plate perforations, trabecular rod breakages, and isolated bone fragments, to the rapid bone loss and disruption of trabecular microarchitecture during menopause were studied. Eighteen human trabecular bone samples from femoral neck (FN) and spine were scanned using a micro computed tomography (microCT) system. Bone resorption and formation were simulated as a computational cycle corresponding to 40-day resorption/160-day formation. Resorption cavities were randomly created over the bone surface according to the activation frequency, which was strictly based on clinical data. Every resorption cavity was refilled during formation unless it caused trabecular plate perforation, trabecular rod breakage or isolated fragments. A 20-year-period starting 5 years before and ending 15 years after menopause was simulated for each specimen. Elastic moduli, standard and individual trabeculae segmentation (ITS)-based morphological parameters were evaluated for each simulated 3D image. For both spine and FN groups, the time courses of predicted bone loss pattern by microstructural bone formation deficits were fairly consistent with the clinical measurements. The percentage of bone loss due to trabecular plate perforation, trabecular rod breakage, and isolated bone fragments were 73.2%, 18.9% and 7.9% at the simulated 15 years after menopause. The ITS-based plate fraction (pBV/BV), mean plate surface area (pTb.S), plate number density (pTb.N), and mean rod thickness (rTb.Th) decreased while rod fraction (rBV/BV) and rod number density (rTb.N) increased after the simulated menopause. The dynamic bone remodeling simulation based on microstructural bone formation deficits predicted the time course of menopausal bone loss pattern of spine and FN. Microstructural plate perforation could be the primary cause of menopausal trabecular bone loss. The combined effect of trabeculae perforation, breakage, and isolated fragments resulted in fewer and smaller trabecular plates and more but thinner trabecular rods.

Computational Determination of the Critical Microcrack Size That Causes a Remodeling Response in a Trabecula: A Feasibility Study

Bone is a living tissue, which undergoes continuous renewal to repair local defects. Two separate processes, adaptation and remodeling, are involved when a defect appears. The defect produces stress concentrations that provoke regional adaptation, and is gradually repaired, first by resorption and then by deposition of new bone. Using a mathematical formulation of the adaptation mechanism in trabeculae of cancellous bone, we hypothesize that in some cases, where a microcrack is small enough relative to the dimensions of the trabecula, the adaptation response of the whole trabecula may be sufficient to regain homeostatic mechanical conditions (with no need for a remodeling process). The simulation results showed that for trabeculae with nominal length of 900 µm and nominal thickness of 80–800 µm, a microcrack with minimal length of 48 µm and minimal depth of 13% of the trabecula’s thickness was required to initiate a remodeling process. A longer (100 µm) but shallower (depth of 7% of the trabecula’s thickness) crack also triggered remodeling. These computational results support our hypothesis that when a microcrack small enough relative to the dimensions of the trabecula occurs, adaptation of the whole trabecula may be sufficient to regain homeostatic mechanical conditions with no need for a local remodeling process.

Vertebral osteoporosis and trabecular bone quality

Vertebral fractures due to osteoporosis commonly occur under non-traumatic loading conditions. This problem affects more than 1 in 3 women and 1 in 10 men over a lifetime. Measurement of bone mineral density (BMD) has traditionally been used as a method for diagnosis of vertebral osteoporosis. However, this method does not fully account for the influence of changes in the trabecular bone quality, such as micro-architecture, tissue properties and levels of microdamage, on the strength of the vertebra. Studies have shown that deterioration of the vertebral trabecular architecture results in a more anisotropic structure which has a greater susceptibility to fracture. Transverse trabeculae are preferentially thinned and perforated while the remaining vertical trabeculae maintain their thickness. Such a structure is likely to be more susceptible to buckling under normal compression loads and has a decreased ability to withstand unusual or off-axis loads. Changes in tissue material mechanical properties and levels of microdamage due to osteoporosis may also compromise the fracture resistance of vertebral trabecular bone. New diagnostic techniques are required which will account for the influence of these changes in bone quality. This paper reviews the influence of the trabecular architecture, tissue properties and microdamage on fracture risk for vertebral osteoporosis. The morphological characteristics of normal and osteoporotic architectures are compared and their potential influence on the strength of the vertebra is examined. The limitations of current diagnostic methods for osteoporosis are identified and areas for future research are outlined.

Additional weight bearing during exercise and estrogen in the rat: the effect on bone mass, turnover, and structure

Mechanical loading and estrogen play important roles in bone homeostasis. The aim of this study was to evaluate the effects of mechanical loading on trabecular bone in the proximal femur of ovariectomized rats. We hypothesized that mechanical loading suppresses bone resorption and increases bone formation, which differs from the suppressive effects of estrogen on both resorption and formation. Furthermore, we expected to find changes in trabecular architecture elicited by the effects of mechanical loading and estrogen deficiency. Sixty female Wistar rats, 12 weeks old, were assigned to either the sedentary groups sham surgery (SED), ovariectomy (SED+OVX), and ovariectomy with estrogen replacement (SED+OVX+E2) or to the exercise groups EX, EX+OVX, EX+OVX+E2. Following ovariectomy, 5 microg 17beta-estradiol was given once weekly to the estrogen replacement groups. Exercise consisted of running with a backpack (load +/-20% of body weight) for 15 minutes/day, 5 days/week, for 19 weeks. Dual-energy X-ray absorptiometry (DXA) scans were performed before (T0), during (T6), and after (T19) the exercise period to obtain bone mineral content (BMC) and bone mineral density (BMD) data. After the exercise program, all rats were killed and right and left femora were dissected and prepared for micro-CT scanning and histomorphometric analysis of the proximal femoral metaphysis. After 19 weeks, increases in BMC (P = 0.010) and BMD (P = 0.031) were significant. At T19, mechanical loading had a significant effect on BMC (P = 0.025) and BMD (P = 0.010), and an interaction between mechanical loading and estrogen (P = 0.023) was observed. Bone volume and trabecular number decreased significantly after ovariectomy, while trabecular separation, mineralizing surface, bone formation rate, osteoclast surface, degree of anisotropy, and structure model index increased significantly after ovariectomy (P < 0.05). Trabecular bone turnover and structural parameters in the proximal femur were not affected by exercise. Estrogen deficiency resulted in a less dense and more oriented trabecular bone structure with increased marrow cavity and a decreased number of trabeculae. In conclusion, mechanical loading has beneficial effects on BMC and BMD of the ovariectomized rat. This indicates that the load in the backpack was high enough to elicit an osteogenic response sufficient to compensate for the ovariectomy-induced bone loss. The results confirm that estrogen suppresses both bone resorption and bone formation in the proximal metaphysis in the femoral head of our rat-with-backpack model. The effects of mechanical loading on the trabecular bone of the femoral head were not significant. This study suggests that the effect of mechanical loading in the rat-with-backpack model mainly occurs at cortical bone sites.

Bone response to different strength orthodontic forces in animals with periodontitis

BACKGROUND

Occlusal alterations resulting from tooth movements caused by periodontitis-related bone loss are often corrected with orthodontic treatments. Although the outcome is usually satisfactory, a quantitative histomorphometric study of bone response would contribute to improving treatment planning and optimizing results.

METHODS AND RESULTS

This study is a histomorphometric analysis of alveolar bone response to 51 and 75-g orthodontic forces applied to rat molars subjected to experimental periodontitis by placing a ligature around the neck of the molar during 48 h. The orthodontic device consisted of two bands with a tube welded to their palatine aspect, through which the arms of a helicoidal spring were threaded so as to exert force toward palatine. The device was placed immediately and 48 h after removing the ligatures. When applied 48 h post-removal of the ligature, both orthodontic forces caused an increase in bone volume in the periodontitis group.

CONCLUSIONS

Our study shows that application of orthodontic forces once periodontal infection has been controlled contributes to increasing alveolar bone volume, consequently improving bone quality.

Trabecular bone fracture healing simulation with finite element analysis and fuzzy logic

Trabecular bone fractures heal through intramembraneous ossification. This process differs from diaphyseal fracture healing in that the trabecular marrow provides a rich vascular supply to the healing bone, there is very little callus formation, woven bone forms directly without a cartilage intermediary, and the woven bone is remodelled to form trabecular bone. Previous studies have used numerical methods to simulate diaphyseal fracture healing or bone remodelling, however not trabecular fracture healing, which involves both tissue differentiation and trabecular formation. The objective of this study was to determine if intramembraneous bone formation and remodelling during trabecular bone fracture healing could be simulated using the same mechanobiological principles as those proposed for diaphyseal fracture healing. Using finite element analysis and the fuzzy logic for diaphyseal healing, the model simulated formation of woven bone in the fracture gap and subsequent remodelling of the bone to form trabecular bone. We also demonstrated that the trabecular structure is dependent on the applied loading conditions. A single model that can simulate bone healing and remodelling may prove to be a useful tool in predicting musculoskeletal tissue differentiation in different vascular and mechanical environments.

Contribution of muscular weakness to osteoporosis: computational and animal models

BACKGROUND

Chronic weakness of the femoral musculature with old age may result in prolonged exposure of bone to critical understressing and, thus, cause osteoporotic changes. This study aims at quantifying long-term changes in thickness and mechanical properties of trabecular bone at the proximal femur due to muscular weakness.

METHODS

We utilized computational models of typical planar trabecular lattices at the proximal femur for simulating long-term changes in morphological and mechanical properties of trabecular bone. Incorporating cellular communication network with osteocytes as mechanosensors, the models were able to mimic mechanotransduction and consequent thickening and/or thinning of individual trabeculae in response to altered gluteus muscle and hip joint loads. We also studied a rat model (n=14) in which we surgically detached the gluteus muscle, to approximately 50% or completely.

FINDINGS

The computational simulations showed that when the force of the gluteus decreased (with or without simultaneous decrease in hip joint load), the most dramatic degradation in bone density, strength and stiffness occurred at the greater trochanter. Animal studies also demonstrated significant thinning of femoral trabeculae after 19 weeks of adaptation. Specifically, Tukey-Kramer analysis showed that rats subjected to partial surgical detachment of the gluteus had femoral trabeculae that were 22% thinner than controls (P<0.05).

INTERPRETATION

The present study showed that in both the computer and animal models, manipulation of muscle loading produced a significant stimulus for bone to adapt, i.e., a stimulus that is beyond its irresponsive 'lazy zone'. Accordingly, the results obtained herein indicate that muscular weakness may be an important factor contributing to osteoporosis.

A theoretical framework for strain-related trabecular bone maintenance and adaptation

It is assumed that density and morphology of trabecular bone is partially controlled by mechanical forces. How these effects are expressed in the local metabolic functions of osteoclast resorption and osteoblast formation is not known. In order to investigate possible mechano-biological pathways for these mechanisms we have proposed a mathematical theory (Nature 405 (2000) 704). This theory is based on hypothetical osteocyte stimulation of osteoblast bone formation, as an effect of elevated strain in the bone matrix, and a role for microcracks and disuse in promoting osteoclast resorption. Applied in a 2-D Finite Element Analysis model, the theory explained the formation of trabecular patterns. In this article we present a 3-D FEA model based on the same theory and investigated its potential morphological predictability of metabolic reactions to mechanical loads. The computations simulated the development of trabecular morphological details during growth, relative to measurements in growing pigs, reasonably realistic. They confirmed that the proposed mechanisms also inherently lead to optimal stress transfer. Alternative loading directions produced new trabecular orientations. Reduction of load reduced trabecular thickness, connectivity and mass in the simulation, as is seen in disuse osteoporosis. Simulating the effects of estrogen deficiency through increased osteoclast resorption frequencies produced osteoporotic morphologies as well, as seen in post-menopausal osteoporosis. We conclude that the theory provides a suitable computational framework to investigate hypothetical relationships between bone loading and metabolic expressions.

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's mechanostat: a 2003 update

The still-evolving mechanostat hypothesis for bones inserts tissue-level realities into the former knowledge gap between bone's organ-level and cell-level realities. It concerns load-bearing bones in postnatal free-living bony vertebrates, physiologic bone loading, and how bones adapt their strength to the mechanical loads on them. Voluntary mechanical usage determines most of the postnatal strength of healthy bones in ways that minimize nontraumatic fractures and create a bone-strength safety factor. The mechanostat hypothesis predicts 32 things that occur, including the gross anatomical bone abnormalities in osteogenesis imperfecta; it distinguishes postnatal situations from baseline conditions at birth; it distinguishes bones that carry typical voluntary loads from bones that have other chief functions; and it distinguishes traumatic from nontraumatic fractures. It provides functional definitions of mechanical bone competence, bone quality, osteopenias, and osteoporoses. It includes permissive hormonal and other effects on bones, a marrow mediator mechanism, some limitations of clinical densitometry, a cause of bone "mass" plateaus during treatment, an "adaptational lag" in some children, and some vibration effects on bones. The mechanostat hypothesis may have analogs in nonosseous skeletal organs as well.

Effect of different masticatory functional and mechanical demands on the structural adaptation of the mandibular alveolar bone in young growing rats

The influence of masticatory functional and mechanical demands on the structural adaptation of the alveolar bone has not been investigated in both animals and humans. The effect of two experimental factors, the insertion of a bite-opening appliance and the alteration of food consistency, was investigated in young growing rats, with a particular emphasis on three-dimensional (3D) bone microstructure. Thirty-six male albino rats were divided into two equal groups, fed with either the standard hard diet or soft diet, at the age of 4 weeks. After 2 weeks, half of the animals in both groups had their upper molars fitted with an upper posterior bite block, an appliance similar to those used in clinical orthodontics. The remaining animals served as a control. After another 4 weeks, the animals were sacrificed, and their left hemimandibles were excised. Bone mineral density (BMD) and bone microstructure parameters of the alveolar process were subsequently measured, using dual-energy X-ray absorptiometry (DXA) and micro-computed tomography (micro-CT). The alveolar process width was also measured. Both experimental factors led to significant shape and structure modification of the mandibular alveolar bone in the growing rat. The bite block applied a continuous light force, which was associated with an inhibition of alveolar process vertical growth and a significant increase of cortical thickness. Soft diet and the consequent reduction of the intermittent forces applied to the alveolar bone during mastication resulted in a reduction of bone mineral density, accompanied by decreased trabecular bone volume and thickness. This rat model could prove to be a useful tool for the in vivo investigation of the role of muscular forces on the shape and structure adaptation of bone.

Altered tissue properties induce changes in cancellous bone architecture in aging and diseases

The mechanical properties of cancellous bone depend on its architecture and the tissue properties of the mineralized matrix. The architecture is continuously adapted to external loads. In this paper, it was assumed that changes in tissue properties leading to changes in tissue deformation can induce adaptation of the architecture. We asked whether changes in cancellous bone architecture with aging and in e.g. early osteoarthrosis can be explained from changes in tissue properties. This was investigated using computer models in which the cancellous architecture was adapted to external loads. Bone tissue with deformations below a certain threshold was resorbed, deformations above another threshold induced formation. Deformations between these two boundaries, in the 'lazy zone', did not induce bone adaptation. The effects of changes in bone tissue stiffness on bone mass, global stiffness and architecture were investigated. The bone gain (40-60%) resulting from a 50% decrease in tissue stiffness (simulating diseased tissue) was much larger than the bone loss (2-30%) resulting from a 50% increase in tissue stiffness (simulating highly mineralized, old tissue). The adaptation induced by a decrease in tissue stiffness resulted in an almost constant stiffness in the main load bearing direction, but the transversal stiffness decreased. An increased tissue stiffness resulted in a higher stiffness in the main direction and overcompensation in the transversal directions: the global stiffness could become even smaller than the stiffness of the original model. Concluding, we showed that changes in trabecular bone in aging and diseases can be partly explained from changes in tissue properties.

A simulation model at trabecular level to predict effects of antiresorptive treatment after menopause

Antiresorptive drugs are widely used to prevent osteoporotic fractures in men and women. Large clinical trials have shown vertebral fracture risk reductions up to 50%, resulting from relatively small increases of 3-8% in bone mineral density (BMD). We developed a computer model that mimics bone turnover in human vertebral cancellous bone during menopause and antiresorptive treatment. This model links cell activity in trabeculae to changes in bone volume and mechanical properties. We asked whether treatment started shortly after menopause is better than treatment started late after menopause. In order to answer this question we used the model to simulate menopause and 5 years of anti-resorptive treatment with two different agents: one incorporated in the tissue, one not incorporated. We found that late treatment can result in almost the same bone mass as early treatment, but early treatment is much better in conserving the strength and stiffness of the cancellous bone. The effect of the incorporation of drugs in the tissue (giving the drugs a long half-life) was small. After discontinuation of treatment, bone was lost slower, but after 20 years the difference between the incorporated and the not incorporated drug in stiffness and bone volume was below 3%. This kind of simulation model may be used to preclinically test new pharmaceuticals and treatment protocols and to predict long-term effects of treatment before patient data become available.

Mechanical significance of the trabecular microstructure of the human mandibular condyle

The human mandibular condyle has a parasagittal plate-like trabecular structure. We tested the hypothesis that this structure reflects the mechanical loading of the condyle. We developed a finite element model of the condyle to analyze the strains occurring during static compressive loading. The principal strains in the trabecular bone were primarily oriented in the sagittal plane. The first component was compressive and oriented supero-inferiorly. The second component was negligibly small and oriented medio-laterally. The third component was tensile, oriented antero-posteriorly, and almost equal to the compressive strain. This tensile strain was caused by antero-posterior bulging of the cortex. This means that the trabecular structure is also subjected to significant tensile forces. The orientation of the parasagittal strains followed the direction of the applied load. It was concluded that the trabecular structure of the mandibular condyle is optimal in resisting the compressive and tensile strains to which it is subjected.

Optimizing the assessment of age-related changes in trabecular bone

The goal of this study was to develop an optimal procedure to determine age-related changes in trabecular bone. The investigations were based on two-dimensional images of the human vertebral trabecular bone specimens. The following indices of trabecular structure were considered: bone volume/total volume, star volume of the marrow cavity, Euler number and the probability of disconnection (straightforwardly connected with the number of separated parts of the network). To follow precisely the changes in the trabecular structure with age, a computer simulation model was used. Up to 35 years of physiological remodelling were simulated. The validation of the model calculations was based on a quantitative comparison with the data measured for older individuals. The simulations confirmed that the description of the age-related changes in the trabecular bone by means of the architectural parameter (star volume) constitutes a promising tool for subjects older than approximately 50 years. For individuals younger than approximately 50 years bone mineral density (bone volume/total volume) seems to be the best suited descriptor. The results suggest that the optimal diagnostic procedure is age-dependent and should not be limited to the bone mineral density measurement. The clinical usefulness of the procedure has been validated by examination of the CT images.

Postmenopausal osteoporosis as a failure of bone's adaptation to functional loading: a hypothesis

There is substantial evidence that bones' ability to withstand functional loading without damage depends on the processes of bone modeling and remodeling, which are responsible for establishing and maintaining bone architecture, being influenced by a feedback mechanism related to the control of functional strains. It is probably useful to consider the diminished ability to maintain bone strength in postmenopausal osteoporosis as a failure of this mechanism. Acceptance of this approach would not only increase understanding of the etiology of postmenopausal osteoporosis but also significantly influence the ways in which it is investigated and treated. This would not mean that the many other factors affecting bone mass and bone cell activity will be ignored, but rather these factors will be put in perspective. Research to prevent or treat osteoporosis could be directed usefully to understanding how osteoblasts, lining cells, and osteocytes respond to mechanically derived information and how these responses are converted into stimuli controlling structurally appropriate modeling and remodeling. Evidence suggesting that early strain-related responses of bone cells in males and females involve the estrogen receptor (ER) could explain decreased effectiveness of this pathway when ER levels are low.

Trabecular surface remodeling simulation for cancellous bone using microstructural voxel finite element models

A computational simulation method for three-dimensional trabecular surface remodeling was proposed, using voxel finite element models of cancellous bone, and was applied to the experimental data. In the simulation, the trabecular microstructure was modeled based on digital images, and its morphological changes due to surface movement at the trabecular level were directly expressed by removing/adding the voxel elements from/to the trabecular surface. A remodeling simulation at the single trabecular level under uniaxial compressive loading demonstrated smooth morphological changes even though the trabeculae were modeled with discrete voxel elements. Moreover, the trabecular axis rotated toward the loading direction with increasing stiffness, simulating functional adaptation to the applied load. In the remodeling simulation at the trabecular structural level, a cancellous bone cube was modeled using a digital image obtained by microcomputed tomography (microCT), and was uniaxially compressed. As a result, the apparent stiffness against the applied load increased by remodeling, in which the trabeculae reoriented to the loading direction. In addition, changes in the structural indices of the trabecular architecture coincided qualitatively with previously published experimental observations. Through these studies, it was demonstrated that the newly proposed voxel simulation technique enables us to simulate the trabecular surface remodeling and to compare the results obtained using this technique with the in vivo experimental data in the investigation of the adaptive bone remodeling phenomenon.

A three-dimensional simulation of age-related remodeling in trabecular bone

After peak bone mass has been reached, the bone remodeling process results in a decrease in bone mass and strength. The formation deficit, the deficit of bone formation compared with previous resorption, results in bone loss. Moreover, trabeculae disconnected by resorption cavities probably are not repaired. The contributions of these mechanisms to the total bone loss are unclear. To investigate these contributions and the concomitant changes in trabecular architecture and mechanical properties, we made a computer simulation model of bone remodeling using microcomputed tomography (micro-CT) scans of human vertebral trabecular bone specimens. Up to 50 years of physiological remodeling were simulated. Resorption cavities were created and refilled 3 months later. These cavities were not refilled completely, to simulate the formation deficit. Disconnected trabeculae were not repaired; loose fragments generated during the simulation were removed. Resorption depth, formation deficit, and remodeling space were based on biological data. The rate of bone loss varied between 0.3% and 1.1% per year. Stiffness anisotropy increased, and morphological anisotropy (mean intercept length [MIL]) was almost unaffected. Connectivity density increased or decreased, depending on the remodeling parameters. The formation deficit accounted for 69-95%, disconnected trabeculae for 1-21%, and loose fragments for 1-17% of the bone loss. Increasing formation deficit from 1.8% to 5.4% tripled bone loss but only doubled the decrease in stiffness. Increasing resorption depth from 28 to 56 microm slightly increased bone loss but drastically decreased stiffness. Decreasing the formation deficit helps to prevent bone loss, but reducing resorption depth is more effective in preventing loss of mechanical stiffness.

Finite Element Analysis of Simulations of Cancellous Bone Resorption

A stochastic simulation of the resorption of cancellous bone has been developed and integrated with a finite element model to predict the resultant change in structural properties of bone as bone density decreases. The resorption represents the net imbalance of osteoclast and osteoblast activity that occurs in osteoporosis. A simple lattice structure of trabecular bone is considered, with an examination of the lattice geometry and discretization indicating that just five trabeculae need to be modelled. The results from the analysis show how the mechanical properties of the cancellous bone degrade with osteoporosis and demonstrate how the method can be used to predict the relationships between stiffness and density or porosity.

Cybernetic aspects of bone modeling and remodeling, with special reference to osteoporosis and whole-bone strength

Assume mythical physiologists were taught that renal physiology and its disorders depend on "kidney cells" and their regulation by nonmechanical factors, but were taught nothing about nephrons. For decades they "knew" that idea was correct, just as Ptolemy "knew" the universe centers on our planet. But then others began to describe nephrons, their roles in renal physiology and disorders, and problems they revealed in former views, so doubts and controversies began. Today real physiologists encounter a similar situation for bone health and its disorders. A 1960 paradigm attributed such things to bone's effector cells (osteoblasts and osteoclasts) and their regulation by nonmechanical factors, without "nephron-equivalent" or biomechanical input. But both mechanical and nonmechanical factors regulate bone's nephron equivalents. Adding features of those equivalents to the 1960 views led to the Utah paradigm, which suggests problems in former views and better explanations for "osteoporosis," whole-bone strength, and other bone disorders. Such things incited controversies among current skeletal physiologists. Cybernetics concerns the relationships, mechanisms, signals, and message traffic that help to control the behavior and other features of dynamic systems. A cybernetic analysis of the bone physiology in the Utah paradigm can add many features to the 1960 paradigm that help to understand osteoporoses, other bone disorders, and whole-bone strength (and bone mass). The added features also show new and pertinent targets for the related research.

Estimation of bone matrix apparent stiffness variation caused by osteocyte lacunar size and density

The role of osteocyte lacunar size and density on the apparent stiffness of bone matrix was predicted using a mechanical model from the literature. Lacunar size and lacunar density for different bones from different gender and age groups were used to predict the range of matrix apparent stiffness values for human cortical and cancellous tissue. The results suggest that bone matrix apparent stiffness depends on tissue type (cortical versus cancellous), age, and gender, the magnitudes of the effects being significant but small in all cases. Males had a higher predicted matrix apparent stiffness than females for vertebral cancellous bone (p< I0(-7)) and the difference increased with age (p =0.0007). In contrast, matrix apparent stiffness was not different between males and females forfemoral cortical bone and increased with age in both males (p < 0.0001) and females (p < 0.0364). Osteocyte lacunar density and size may cause significant gender and age-related variations in bone matrix apparent stiffness. The magnitude of variations in matrix apparent stiffness was small within the physiological range of lacunar size and density for healthy bone, whereas the variations can be profound in certain pathological cases. It was proposed that the mechanical effects of osteocyte density be uncoupled from their biological effects by controlling lacunar size in normal bone.

If bone is the answer, then what is the question?

In the 19th century, several scientists attempted to relate bone trabecular morphology to its mechanical, load-bearing function. It was suggested that bone architecture was an answer to requirements of optimal stress transfer, pairing maximal strength to minimal weight, according to particular mathematical design rules. Using contemporary methods of analysis, stress transfer in bones was studied and compared with anatomical specimens, from which it was hypothesised that trabecular architecture is associated with stress trajectories. Others focused on the biological processes by which trabecular architectures are formed and on the question of how bone could maintain the relationship between external load and architecture in a variable functional environment. Wilhelm Roux introduced the principle of functional adaptation as a self-organising process based in the tissues. Julius Wolff, anatomist and orthopaedic surgeon, entwined these 3 issues in his book The Law of Bone Remodeling (translation), which set the stage for biomechanical research goals in our day. 'Wolff's Law' is a question rather than a law, asking for the requirements of structural optimisation. In this article, based on finite element analysis (FEA) results of stress transfer in bones, it is argued that it was the wrong question, putting us on the wrong foot. The maximal strength/minimal weight principle does not provide a rationale for architectural formation or adaptation; the similarity between trabecular orientation and stress trajectories is circumstantial, not causal. Based on computer simulations of bone remodelling as a regulatory process, governed by mechanical usage and orchestrated by osteocyte mechanosensitivity, it is shown that Roux's paradigm, conversely, is a realistic proposition. Put in a quantitative regulatory context, it can predict both trabecular formation and adaptation. Hence, trabecular architecture is not an answer to Wolff's question, in the sense of this article's title. There are no mathematical optimisation rules for bone architecture; there is just a biological regulatory process, producing a structure adapted to mechanical demands by the nature of its characteristics, adequate for evolutionary endurance. It is predicted that computer simulation of this process can help us to unravel its secrets.

The three-dimensional cancellous bone architecture of the human mandibular condyle

In the present study, we tested the hypothesis that the cancellous bone of the mandibular condyle is inhomogeneous and anisotropic. For this purpose, 11 mandibular condyles from embalmed human cadavers were scanned in a micro-CT system. Within each condyle, 9 volumes of interest were selected from different mediolateral and supero-inferior regions. Several bone parameters were calculated to describe the morphology. It appeared that the cancellous bone of the condyle could be approximated by parallel plates. These plates were almost vertically oriented at an angle of 17 degrees relative to the sagittal plane, i.e., perpendicular to the condylar axis. In the superior regions of the condyle, the cancellous bone had the largest bone volume fraction (0.19), associated with the thickest trabeculae (0.11 mm), and the highest trabecular number (1.72 mm(-1)). The lowest bone volume fraction (0.15) was found more inferiorly. The degree of anisotropy increased from superior to inferior across the condyle. No mediolateral differences in bone morphology were found, but superiorly central regions contained more bone than peripheral regions. The plate-like trabeculae could indicate that the condyle is optimally adapted to sustain loads from all directions in a plane perpendicular to the condylar axis. The high bone mass and lower anisotropy in the superior regions could enable the condyle to sustain multiple load directions. Toward the collum, the trabeculae are more aligned. This could point to stresses acting predominantly in one direction.

Fractal dimension of trabecular bone projection texture is related to three-dimensional microarchitecture

The purpose of this work was to understand how fractal dimension of two-dimensional (2D) trabecular bone projection images could be related to three-dimensional (3D) trabecular bone properties such as porosity or connectivity. Two alteration processes were applied to trabecular bone images obtained by magnetic resonance imaging: a trabeculae dilation process and a trabeculae removal process. The trabeculae dilation process was applied from the 3D skeleton graph to the 3D initial structure with constant connectivity. The trabeculae removal process was applied from the initial structure to an altered structure having 99% of porosity, in which both porosity and connectivity were modified during this second process. Gray-level projection images of each of the altered structures were simply obtained by summation of voxels, and fractal dimension (Df) was calculated. Porosity (phi) and connectivity per unit volume (Cv) were calculated from the 3D structure. Significant relationships were found between Df, phi, and Cv. Df values increased when porosity increased (dilation and removal processes) and when connectivity decreased (only removal process). These variations were in accordance with all previous clinical studies, suggesting that fractal evaluation of trabecular bone projection has real meaning in terms of porosity and connectivity of the 3D architecture. Furthermore, there was a statistically significant linear dependence between Df and Cv when phi remained constant. Porosity is directly related to bone mineral density and fractal dimension can be easily evaluated in clinical routine. These two parameters could be associated to evaluate the connectivity of the structure.

Improving the local solution accuracy of large-scale digital image-based finite element analyses

Digital image-based finite element modeling (DIBFEM) has become a widely utilized approach for efficiently meshing complex biological structures such as trabecular bone. While DIBFEM can provide accurate predictions of apparent mechanical properties, its application to simulate local phenomena such as tissue failure or adaptation has been limited by high local solution errors at digital model boundaries. Furthermore, refinement of digital meshes does not necessarily reduce local maximum errors. The purpose of this study was to evaluate the potential to reduce local mean and maximum solution errors in digital meshes using a post-processing filtration method. The effectiveness of a three-dimensional, boundary-specific filtering algorithm was found to be mesh size dependent. Mean absolute and maximum errors were reduced for meshes with more than five elements through the diameter of a cantilever beam considered representative of a single trabecula. Furthermore, mesh refinement consistently decreased errors for filtered solutions but not necessarily for non-filtered solutions. Models with more than five elements through the beam diameter yielded absolute mean errors of less than 15% for both Von Mises stress and maximum principal strain. When applied to a high-resolution model of trabecular bone microstructure, boundary filtering produced a more continuous solution distribution and reduced the predicted maximum stress by 30%. Boundary-specific filtering provides a simple means of improving local solution accuracy while retaining the model generation and numerical storage efficiency of the DIBFEM technique.

On the trabecular "thickness"-number problem

The decrease in trabecular number with aging and in osteoporosis seems to be naturally irreversible. In one view the resulting loss of bone strength would be irreversible too, but in another view the remaining trabeculae could increase their strength, chiefly by thickening. Whether that can occur has become important for osteoporosis research and management as well as for some biomechanical issues. This article reviews evidence and ideas that concern that matter. It suggests why the second view could be correct although previous studies did not detect it. However, that view still needs the kind of proof the general skeletal science community could accept.