Stochastic simulations of remodeling applied to a two-dimensional trabecular bone structure

In silico biology of bone modelling and remodelling: adaptation

Modelling and remodelling are the processes by which bone adapts its shape and internal structure to external influences. However, the cellular mechanisms triggering osteoclastic resorption and osteoblastic formation are still unknown. In order to investigate current biological theories, in silico models can be applied. In the past, most of these models were based on the continuum assumption, but some questions related to bone adaptation can be addressed better by models incorporating the trabecular microstructure. In this paper, existing simulation models are reviewed and one of the microstructural models is extended to test the hypothesis that bone adaptation can be simulated without particular knowledge of the local strain distribution in the bone. Validation using an experimental murine loading model showed that this is possible. Furthermore, the experimental model revealed that bone formation cannot be attributed only to an increase in trabecular thickness but also to structural reorganization including the growth of new trabeculae. How these new trabeculae arise is still an unresolved issue and might be better addressed by incorporating other levels of hierarchy, especially the cellular level. The cellular level sheds light on the activity and interplay between the different cell types, leading to the effective change in the whole bone. For this reason, hierarchical multi-scale simulations might help in the future to better understand the biomathematical laws behind bone adaptation.

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.

Bone microarchitecture in males with corticosteroid-induced osteoporosis

SUMMARY

Microarchitectural changes in trabecular bone were analyzed by microcomputed tomography (microCT) and histomorphometry in 24 patients with corticosteroid-induced osteoporosis. The microCT images revealed a reduction in trabecular thickness only on frequency distribution curves, with no increase in trabecular separation. Trabecular plate thinning and perforations were easily identified.

INTRODUCTION

Corticosteroid-induced osteoporosis (CSIOP) is mediated by direct actions of the drug on bone cells. The result is a decrease in trabecular bone mass and a reduction in trabecular thickness, but connectivity is believed to remain rather well preserved.

METHODS

Twenty-four transiliac bone biopsies from patients with CSIOP were studied conjointly by histomorphometry [with two-dimensional (2D) architectural descriptors] and microCT (with 3D analysis of trabecular characteristics, including trabecular thickness and separation). The frequency distribution of thickness and separation were compared with data obtained in nine control subjects.

RESULTS

2D histomorphometry revealed a decrease in bone volume and trabecular thickness in the bone biopsies of the CSIOP patients when compared to those of the controls. MicroCT appeared to be able to identify the reduction in thickness only when the frequency distribution of trabecular thickness was computed. No difference for the curves of the frequency distribution of trabecular separation was evidenced between patients and controls. MicroCT and 2D histomorphometric results were correlated, but 2D analysis appeared to be more sensitive. However, microCT identified a very specific thinning of the trabecular plates in their center that corresponds to the earlier stages of perforations.

CONCLUSION

Trabecular plate thinning can be observed and perforations occur on very thin plates in CSIOP patients.

Spatial and temporal regulation of cancellous bone structure: characterization of a rate equation of trabecular surface remodeling

A computer simulation of trabecular surface remodeling was carried out to investigate the spatial and temporal regulation of the cancellous bone structure caused by bone cellular activities responding to a local mechanical environment. In the remodeling simulation, the rate of trabecular surface movement was directly related to stress at the trabecular level. Two model parameters, the threshold value of the lazy zone and the sensing distance of the mechanical environment, were introduced into the remodeling rate equation to express the sensitivity of bone cells to mechanical stimuli. A rectangular cancellous bone model under simple and nonuniform compressive loads was constructed using pixel finite elements. A simulation result revealed that the trabecular structure underwent a temporal and spatial change depending on the loading condition. It was found that the threshold value of the lazy zone regulates the rate of structural changes in time, and that sensing distance regulates the spatial distribution of the trabecular structure. The results demonstrate the possibility that the spatial and temporal regulation of the trabecular structure is determined by the sensitivities of bone cells to mechanical stimuli.

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.

Simulated aging--a novel method for estimating the risk of fracture of trabecular bone

In the study we show how the methods of percolation theory could be used in the description of age-related changes of mechanical competence of trabecular bone. A previously introduced stochastic model of remodeling of trabecular bone is applied to the simulated aging of pairs of 2D sections of trabecular bone matched for apparent density, structural anisotropy, and the age of the donors. The critical density of the structures--defined here as the density below which percolating bone cluster disappears, i.e., the structure is fractured--is estimated for each structure. It is shown that structures belonging to pairs matched for density (clinically used as the principal determinant of fracture risk) lose mechanical competence at a different rate, depending on the value of critical density. Thus it is hypothesized that the risk of fracture must depend not only on the density of the structure but also on its critical density.