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.     

Mechanisms of reduced implant stability in osteoporotic bone

The determining factors for the fixation of uncemented screws in bone are the bone-implant interface and the peri-implant bone. The goal of this work was to explore the role of the peri-implant bone architecture on the mechanics of the bone-implant system. In particular, the specific aims of the study were to investigate: (i) the impact of the different architectural parameters, (ii) the effects of disorder, and (iii) the deformations in the peri-implant region. A three-dimensional beam lattice model to describe trabecular bone was developed. Various microstructural features of the lattice were varied in a systematic way. Implant pull-out tests were simulated, and the stiffness and strength of the bone-implant system were computed. The results indicated that the strongest decrease in pull-out strength was obtained by trabecular thinning, whereas pull-out stiffness was mostly affected by trabecular removal. These findings could be explained by investigating the peri-implant deformation field. For small implant displacements, a large amount of trabeculae in the peri-implant region were involved in the load transfer from implant to bone. Therefore, trabecular removal in this region had a strong negative effect on pull-out stiffness. Conversely, at higher displacements, deformations mainly localized in the trabeculae in contact with the implant; hence, thinning those trabeculae produced the strongest decrease in the strength of the system. Although idealized, the current approach is helpful for a mechanical understanding of the role played by peri-implant bone.     

Stress-concentrating effect of resorption lacunae in trabecular bone

Analyses of the distributions of stress and strain within individual bone trabeculae have not yet been reported. In this study, four trabeculae were imaged and finite elements models were generated in an attempt to quantify the variability of stress/strain in real trabeculae. In three of these trabeculae, cavities were identified with depths comparable to values reported for resorption lacunae ( approximately 50 microm)-although we cannot be certain, it is most probable that they are indeed resorption lacunae. A tensile load was applied to each trabeculum to simulate physiological loading and to ensure that bending was minimized. The force carried by each trabecula was calculated from this value using the average cross sectional area of each trabecula. The analyses predict that very high stresses (>100 MPa) existed within bone trabecular tissue. Stress and strain distributions were highly heterogeneous in all cases, more so in trabeculae with the presumptive resorption lacunae where at least 30% of the tissue had a strain greater than 4000 micoepsilon in all cases. Stresses were elevated at the pit of the lacunae, and peak stress concentrations were located in the longitudinal direction ahead of the lacunae. Given these high strains, we suggest that microdamage is inevitable around resorption lacunae in trabecular bone, and may cause the bone multicellular unit to proceed to resorb a packet of bone in the trabeculum rather than just resorb whatever localized area was initially targeted.     

Perforation of cancellous bone trabeculae by damage-stimulated remodelling at resorption pits: a computational analysis

Loss of trabeculae in cancellous bone is often attributed to a general decline in the bone mass leading to fracture of the thin trabeculae. It has never been investigated whether trabecular perforation may have any other biomechanical mechanism. In this paper, an alternative hypothesis is proposed and tested using a computational model. Taking it as given that osteoclastic resorption is targeted to microdamage, it is hypothesised that the creation of a resorption cavity during normal bone remodelling could cause a stress-concentration in the bone tissue. If the resorption cavities were excessively deep, as is seen during osteoporosis, then this stress concentration may be sufficient to generate more microdamage so that osteoclasts "chase" newly formed damage leading to perforation. If this were true then we should find that, for a given trabecular thickness, there is a critical depth of resorption cavity such that smaller cavities refill whereas deeper cavities cause microdamage accumulation, continued osteoclast activity, and eventual trabecular perforation. Computer simulation is used to test this hypothesis. Using a remodelling stimulus calculated from both strain and damage and a simplified finite element model of a trabeculum with cavities of different sizes, it is predicted that such a critical depth of resorption cavity does indeed exist. Therefore we suggest that an increase in resorption depth relative to the thickness of trabeculae may be responsible for trabecular perforation during osteoporosis, rather than simply trabecular fracture due to insufficient strength.     

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.     

Bone turnover and trabecular plate survival after artificial menopause.

Considerable bone loss often occurs after menopause, particularly if menopause is induced by surgery. For perhaps two years bone formation fails to keep pace with the rapid acceleration of bone resorption that occurs after sex hormone withdrawal. The threat that this poses to the integrity of the skeleton is not clear. Because ethical constraints limit histological studies in normal women existing normal data and statistical modelling techniques were used to explore the dynamics of iliac trabecular bone after menopause. Trabeculae are breached during remodelling when the osteoclasts resorb to a depth equal to the trabecular thickness. Since holes in trabecular plates cannot normally be bridged such defects are probably permanent. Men lose 7% of their vertebral trabecular bone every 10 years; deeper than average resorption of trabeculae at the thin end of the normal range would account for it. The dramatic losses of trabecular bone that are seen in some postmenopausal women, however, require a period of imbalance between bone formation and bone resorption since this leads rapidly to generalised thinning. The statistical model suggested that an imbalance lasting only two years may account for eventual losses of up to half of the iliac trabecular bone. Further understanding is needed of what determines the amount of bone lost in the immediate postmenopause, which varies considerably among women. A simple mean is needed of identifying women who will lose bone most rapidly at the menopause. This must be suitable for use in general practice because these women should probably be offered long term hormone replacement treatment within a few months of the last menstruation.     

Analysis of crack growth in a 3D Voronoi structure: a model for fatigue in low density trabecular bone

Both creep and crack growth contribute to the reduction in modulus associated with fatigue loading in bone. Here we simulate crack growth and subsequent strut failure in fatigue in an open-cell, three-dimensional Voronoi structure which is similar to that of low density, osteoporotic bone. The model indicates that sequential failure of struts leads to a precipitous drop in modulus: the failure of 1% of the struts leads to about a 10% decrease in modulus. A parametric study is performed to assess the influence of normalized stress range, relative density, initial crack size, crack shape and cell geometry on the fatigue life. The fatigue life is most sensitive to the relative density and the initial crack length. The results lead to a quantitative expression for the fatigue life associated with crack growth. Data for the fatigue life of trabecular bone are compared with the crack growth model described in this paper as well as with a previous model for creep of a three-dimensional Voronoi structure. In our models, creep dominates the fatigue behavior in low cycle fatigue while crack growth dominates in high cycle fatigue, consistent with previous observations on cortical bone. The large scatter in the trabecular bone fatigue data make it impossible to identify a transition between creep dominated fatigue and crack growth dominated fatigue. The parametric study of the crack growth model indicates that variations in relative density among specimens, initial crack size within trabeculae and crack shape could easily produce such variability in the test results.     

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.     

Clues potentially distinguishing lytic lesions of multiple myeloma from those of metastatic carcinoma

This study was conducted to determine whether individual bony lesions are specific for recognizing multiple myeloma and thereby distinguish it from metastatic cancer and leukemia. The lytic skeletal lesions of multiple myeloma are characterized by sharply defined, spheroid lesions. They have smooth borders and effaced/erased trabeculae. Unique spheroid myeloma lesions appear to be responsible for the “punched out” appearance of affected bone. The total absence of remodeling in myeloma forms a contrast to irregular preservation of trabeculae and buttressing, isolated “fronts of” cortical bone “resorption” coalescing to confluence, and the “golf-ball surface” phenomenon observed in metastatic cancer. The uniform effacement of both cortical and trabecular bone in multiple myeloma also contrasts with some cortical preservation in metastatic cancer. Leukemic lesions are more numerous than those of myeloma, but they lack the latter's “space-occupied” appearance. The relatively small holes and “fronts of resorption” of leukemia are quite different from the “space-occupied” lesions of multiple myeloma. Uniform size is a characteristic traditionally attributed to the bone lesions of multiple myeloma. The occurrence of isolated examples of uniform size lesions in metastatic cancer and of variable size lesions in some individuals with multiple myeloma precludes unequivocal use of size in differential diagnosis. Fortunately, the newly recognized macroscopic characteristics appear to separate multiple myeloma from metastatic cancer, and also distinguish myeloma from leukemia. Am J Phys Anthropol 105:241–250, 1998. © 1998 Wiley-Liss, Inc.     

Trabecular bone structure and strength - remodelling and repair

The strength of the spinal trabecular bone declines by a factor of 4-5 from the age of 20 to 80 years. At the same time, the volumetric (apparent) density declines by a factor of only 2. This discrepancy can be explained by the known power relationship between density and strength; this power relationship is based on the fact that trabecular bone is a porous material. To date, it has not been possible to determine or quantify the influence other factors may have in determining the strength of a loadbearing trabecular network. However, it is known that with age: 1) There is a loss of connectivity through osteoclastic perforations of horizontal struts. 2) There is an increase in anisotropy - again due to loss of horizontal struts, and perhaps also due to micro-modelling drift or to thickening of some vertical trabeculae. 3) The changes in the network can lead to the slenderness ratio between vertical and horizontal struts reaching a certain magnitude and thereby inducing buckling under compression. 4) Microdamage and microfractures will occur - mainly in these very loaded vertical struts. The microfractures will be repaired by microcallus formation, and these calluses will later be removed by the remodelling process. 5) Bone material quality will slightly change, leading to a decrease in collagen content and a relative increase in the degree of mineralisation. But, it is not known how these factors will influence the power relationship between density and strength. Nor is it known how different treatment regimens will affect the 'natural' power relationship: will the same curve be followed, but in the opposite direction? Or will the curve be less or more steep? Will the gain in bone strength be larger if treatment is started early - on the steep part of the curve? Furthermore, as trabecular bone can never be isolated in vivo, other factors need to be investigated: The interplay between the cortical shell and the trabecular network; transmission of load; the interplay between soft tissues (cartilage, connective tissue, muscle) and bone; the shock absorbing capacity of the discs; and the hydraulic effect of the bone marrow. In order to answer these questions, more in vitro and in vivo studies on human bone in relation to aging, to immobilisation, to exercise and in relation to different treatment regimens are needed.     

Adaptive diffuse domain approach for calculating mechanically induced deformation of trabecular bone

Remodelling of trabecular bone is essentially affected by the mechanical load of the trabeculae. Mathematical modelling and simulation of the remodelling process have to include time-consuming calculations of the displacement field within the complex trabecular structure under loading. We present an adaptive diffuse domain approach for calculating the elastic bone deformation based on micro computer tomogram data of real trabecular bone structures and compared it with a conventional voxel-based finite element method. In addition to allowing for higher computational efficiency, the adaptive approach is characterised by a very smooth representation of the bone surface, which suggests that this approach would be suitable as a basis for future simulations of bone resorption and formation processes within the trabecular structure.     

A comparative study of the trabecular bony architecture of the talus in humans, non-human primates, and Australopithecus

This study tested the hypothesis that talar trabecular microarchitecture reflects the loading patterns in the primate ankle joint, to determine whether talar trabecular morphology might be useful for inferring locomotor behavior in fossil hominins. Trabecular microarchitecture was quantified in the anteromedial, anterolateral, posteromedial, and posterolateral quadrants of the talar body in humans and non-human primates using micro-computed tomography. Trabecular bone parameters, including bone volume fraction, trabecular number and thickness, and degree of anisotropy differed between primates, but not in a manner entirely consistent with hypotheses derived from locomotor kinematics. Humans have highly organized trabecular struts across the entirety of the talus, consistent with the compressive loads incurred during bipedal walking. Chimpanzees possess a high bone volume fraction, consisting of plate-like trabecular struts. Orangutan tali are filled with a high number of thin, connected trabeculae, particularly in the anterior portion of the talus. Gorillas and baboons have strikingly similar internal architecture of the talus. Intraspecific analyses revealed no regional differences in trabecular architecture unique to bipedal humans. Of the 22 statistically significant regional differences in the human talus, all can also be found in other primates. Trabecular thickness, number, spacing, and connectivity density had the same regional relationship in the talus of humans, chimpanzees, gorillas, and baboons, suggesting a deeply conserved architecture in the primate talus. Australopithecus tali are human-like in most respects, differing most notably in having more oriented struts in the posteromedial quadrant of the body compared with the posterolateral quadrant. Though this result could mean that australopiths loaded their ankles in a unique manner during bipedal gait, the regional variation in degree of anisotropy was similar in humans, chimpanzees, and gorillas. These results collectively suggest that the microarchitecture of the talus does not simply reflect the loading environment, limiting its utility in reconstructing locomotion in fossil primates.     

A morphological model of vertebral trabecular bone

In their micro-structures, typical natural cellular materials such as vertebral trabecular bone have a network of doubly tapered struts, thickening near the strut joints. However, past analytical models for vertebral trabecular bone do not take account of the effect of strut taper on the mechanical properties.This paper presents an analytical cell model comprised of doubly tapered struts to predict the global mechanical properties of vertebral trabecular bone. The predicted results for male, female, and both sexes fit the experimental data well. By considering several strut taper geometries, it is shown that the horizontal Young's modulus and the horizontal uniaxial collapse stress are, in some cases, approximately 1.8- and 2.2-fold higher, respectively, than those of the uniform strut model. This finding illustrates the importance of increased trabecular thickening near the strut joints (i) for improving the accuracy of calculating the mechanical properties and (ii) for the effective treatment of aged bone using drug therapy. It also highlights the need to combine trabecular architecture measurements with information about the morphology near the strut joints.     

Micro-CT analysis of cancellous bone fragments from the distal radius fracture zone in osteoporosis]

The incidence and prevalence of osteoporosis must be considered to continue to increase significantly due to the expected demographic development and environmental changes. In the diagnosis and staging of osteoporosis the three-dimensional bone structure should be as important as the bone mass or the mineral content of the bone. In this study, microfragments were taken from distal radius fracture zones and investigated in Micro-CT scans. Patients in which osteodensitometry of the lumbal spine had revealed osteoporosis in were found to have significantly reduced bone mass, bone density and trabecular thickness. Trabecular fractures which were found in non-osteoporotic patients even in robust trabeculae were detected by the two-dimensional analysis in thin locations and arborizations. Despite some trabeculae turned out to be very small the differences in the histomorphometry and the quality of trabecular fractures in osteoporotic as well as non-osteoporotic patients could be visualized very good in the Micro-CT analysis.     

Fluid–structure interactions in micro-interlocked regions of the cement–bone interface

Experimental tests and computational modelling were used to explore the fluid dynamics at the trabeculae–cement interlock regions found in the tibial component of total knee replacements. A cement–bone construct of the proximal tibia was created to simulate the immediate post-operative condition. Gap distributions along nine trabeculae–cement regions ranged from 0 to 50.4 μm (mean = 12 μm). Micro-motions ranged from 0.56 to 4.7 μm with a 1 MPa compressive load to the cement. Fluid–structure analysis between the trabeculae and the cement used idealised models with parametric evaluation of loading direction, gap closing fraction (GCF), gap thickness, loading frequency and fluid viscosity. The highest fluid shear stresses (926 Pa) along the trabecular surface were found for conditions with very thin and large GCFs, much larger than reported physiological levels (～1–5 Pa). A second fluid–structure model was created with a provision for bone resorption using a constitutive model with resorption velocity proportional to fluid shear rate. A lower cut-off was used, below which bone resorption would not occur (50 s^? 1). Results showed that there was initially high shear rates (>1000 s^? 1) that diminished after initial trabecular resorption. Resorption continued in high shear rate regions, resulting in a final shape with bone left deep in the cement layer, and is consistent with morphology found in post-mortem retrievals. Small gaps between the trabecular surface and the cement in the immediate post-operative state produce fluid flow conditions that appear to be supra-physiologic; these may cause fluid-induced lysis of trabeculae in the micro-interlock regions.     

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.     

Multiaxial strength characteristics of trabecular bone

Bovine trabecular bone specimens were tested in multiaxial stress, including pure shear, in a special test device. Shear strength was proportional to apparent density to the exponent 1.65, in approximate agreement with theoretical and experimental studies on the shear strengths of porous foams. The mean shear strength was 6.60 +/- 1.66 MPa, after normalizing for apparent density. This compares well with normalized shear strengths from Saha and Gorman's (1981) study on human femora. A scanning electron microscope study indicated random trabecular architecture and a complex fracture mechanism at the level of the individual trabecular struts. Hoffmann's (1967) 3-D isotropic failure criterion was applied to the multiaxial test data, along with data from uniaxial compression tests, indicating a compressive strength approximately three times the tensile strength.     

Spatial distribution of trabeculae in iliac bone from 145 osteoporotic females

145 women showing clinical and radiological signs of involutional osteoporosis of the spine were biopsed at the ilium for histomorphometric analysis of bone mass including trabecular bone volume and parameters reflecting the spatial distribution of bony elements (mean trabecular plate thickness, density and separation). Results were compared with an age-matched population of 22 healthy females. Postmenopausal osteoporotics (i.e. younger than 75 years) were characterized by a significant reduction in trabecular bone volume, plate density and thickness, while senile osteoporotics (i.e. older than 75 years) did not exhibit any difference with controls. 51% of the osteoporotic patients had a trabecular bone volume higher than the spontaneous vertebral crush threshold defined by Meunier. Osteoporotic patients with trabecular bone volume under the vertebral crush threshold had a significant decrease in all trabecular parameters. On the opposite, patients with trabecular bone volume above the vertebral crush threshold had only a significant decrease in the number of trabeculae. A negative correlation was found between age and plate density in both osteoporotic patients and controls. A linear correlation was found between trabecular bone volume and plate density, but thickness and density of trabecular plates were not correlated. This study confirms that involutional osteoporosis is not only a decreased bone mass disorder. A modified spatial distribution of trabeculae or a mechanically less resistant bone matrix could be additional factors.     

Trabecular involution in femoral heads of a prehistoric (X-group) population from Sudanese Nubia

An analysis of trabecular bone in the head of the femur of 33 males and 40 females from a prehistoric X-Group population from Sudanese Nubia indicates that as age increases from 17 to 50+ years loss of trabecular bone in males (16.01%) is greater than loss in females (13.47%). These results differ from previous studies of cortical bone and ash density of femoral head trabeculae which demonstrate a greater loss in females. An analysis of the differential reaction in the two trabecular systems reveals that principal tensile group trabeculae decrease in thickness with age while principal compressive group trabeculae show an increase with age.     

Biomechanical properties across trabeculae from the proximal femur of normal and ovariectomised sheep

The elastic behaviour of trabecular bone is a function not only of bone volume and architecture, but also of tissue material properties. Variation in tissue modulus can have a substantial effect on the biomechanical properties of trabecular bone. However, the nature of tissue property variation within a single trabecula is poorly understood. This study uses nanoindentation to determine the mechanical properties of bone tissue in individual trabeculae. Using an ovariectomised ovine model, the modulus and hardness distribution across trabeculae were measured. In both normal and ovariectomised bone, the modulus and hardness were found to increase towards the core of the trabeculae. Across the width of the trabeculae, the modulus was significantly less in the ovariectomised bone than in the control bone. However, in contrast to this hardness was found not to differ significantly between the two groups. This study provides valuable information on the variation of mechanical material properties in healthy and diseased trabecular bone tissue. The results of the current study will be useful in finite element modelling where more accurate values of trabecular bone modulus will enable the prediction of the macroscale behaviour of trabecular bone.