Stochastic simulation of vertebral trabecular bone remodeling

Bone remodeling changes bone mass, architecture, and thereby bone strength, during normal aging. These changes seem to be accelerated during the menopause. Several therapeutic agents have been used in order to delay the onset of the menopause-related changes. The effects of these agents on the remodeling process have been determined histomorphometrically in several short-term clinical studies, but data from long-term clinical studies are difficult to achieve, as are data on the influence on bone strength.

The aim of this study was to develop a computer simulation model that could assist in predicting the long-term effects of changes in the remodeling process on bone mass, trabecular thickness, and perforations. The paper presents such a stochastic model of the remodeling process in human vertebral trabecular bone. The computer model is based on histomorphometric and structural data from human studies. It is presented in terms of flow charts, and simulations performed with the model are discussed in relation to measurements on human vertebral bone samples.

The results show that a menopause-related doubling of the activation frequency causes a transient, mainly reversible bone loss. If the menopause is accompanied by an increase in both activation frequency and resorption depth, then the resulting bone loss will be more pronounced and with a larger part being irreversible bone loss (perforations). The two antiresorptive agents Etidronate and estrogen both cause a slight increase in bone mass (reducing remodeling space), and Etidronate also seems capable of preventing perforations. During fluoride therapy, an initial increase in remodeling space followed by a reduction is seen. Very few perforations are found to take place during fluoride therapy.

The present model has been validated by assessing the effects of the menopause and treatment with antiresorptive or anabolic agents. It was found that the results mirrored very closely the results (bone mass measurements) from short-term clinical studies. It is therefore concluded that the model provides a tool for evaluating existing and new therapeutic regimens.     

Relationships between trabecular bone remodeling and bone vascularization: a quantitative study

Beside its well-known role in bone development, vascularization plays a major role in bone cell migration for bone remodeling and metastatic tumor invasion. However, the various techniques used to identify vessels in bone have never been tested for trabecular bone vessel quantification, whereas bone remodeling quantitative parameters are commonly assessed. In this context, we developed and compared various histological techniques used to visualize blood vessels in rat bone in order to quantify them. First, several products were tested by intracardiac infusion to opacify the bone vascular network. The best results were obtained using either an India ink-1% agarose solution or an India ink-saturated barium sulfate solution followed by X-ray microradiography. Second, to identify the types of vessels, we also performed histoenzymology and immunohistochemistry stainings. Neither alkaline phosphatase (for endothelial cells) nor adenosine triphosphatase (ATPase) stainings (for smooth muscle cells) provided a low enough background to allow for vessel identification and quantification. For immunohistochemistry, various specific vessel constituents were analyzed: laminin, smooth muscle cell alpha-actin, factor VIII, and lectin Griffonia simplifolia. Anti-laminin and anti-smooth muscle cell alpha-actin antibodies gave the best results for quantification. Third, after optimization of these techniques, we performed quantitative bone and vessel histomorphometry on two groups of 12 rats each, for which bone remodeling and vessel number and area parameters were measured. No statistical differences were observed between the two groups, confirming the reproducibility of our measurements. A significant relationship was found between vessel number and histodynamic parameters; that is, bone formation rate correlated positively with India ink-positive vessel area (p < 0.009, r2 = 0.54) and alpha-actin-positive vessel number (p < 0.05, r2 = 0.66). Furthermore, we report reproducible techniques for visualization and quantification of vessels in bone that also allowed for simultaneous conventional bone histomorphometry. This methodology should help researchers to better understand the functional and anatomical relationship between trabecular bone and its vascularization during normal or pathological processes.     

Ovariectomy and trabecular bone remodeling in the dog

Summary The early effects of ovariectomy (OX) on serum biochemistry and trabecular bone remodeling in the dog were investigated. Adult beagle dams were ovariectomized (n=8) or sham-ovariectomized (n=6) and followed for 6 months. All dogs received an iliac crest biopsy at the time of surgery to establish baseline remodeling data. A second contralateral biopsy was obtained at sacrifice. Serum osteocalcin became significantly elevated approximately 8 weeks following OX and remained elevated for the duration of the study. Histomorphometric analysis of serial transilial specimens showed that, at 6 months, OX had significantly increased the rate of bone remodeling in the ilium. Six months following OX in the dog, changes in serum biochemistry and trabecular bone remodeling in the ilium are consistent with those seen in postmenopausal women suffering from “high remodeling osteoporosis”.     

Evaluation of a microcomputed tomography system to study trabecular bone structure

A new microcomputed tomography (micro-CT) system and thresholding procedure was evaluated as a tool for nondestructive analysis of trabecular bone. Images of 6-mm trabecular bone cubes acquired from the micro-CT system were compared with optical images of corresponding histologic sections to determine the accuracy of representation. The stereologic measures of bone volume fraction (PP) and trabecular plate density (PL) were used to quantify the comparisons. The results showed that the micro-CT measures of PP were not significantly different from those measured from histologic sections and therefore were very accurate. Measures of PL were different by approximately 14%, which translated into discrepancies in trabecular plate thicknesses of about 19 microns. This difference was significantly correlated to the microstructural characteristics of the specific specimen scanned. The precision of both measurements was excellent.     

卵巢切除后大鼠骨小梁重建过程的电镜观察

目的：建立大鼠卵巢切除后骨质疏松模型，观察在卵巢切除诱发骨质疏松条件下骨小梁重建的电镜变化，分析骨小梁节点数减少而游离末端数增加的原因。方法：3月龄雌性Wistar大鼠36只，分4、8、12周组，每组分OVX(卵巢切除组)和SHAM(假手术组)两小组。用扫描电镜、透射电镜对胫骨近干骺端骨小梁的微结构进行观察。结果：①骨小梁骨重建活动分布于骨小梁微构筑各个部位，但以St、Nd-St区最显著；②OVX后骨小梁穿孔、断裂多见于水平骨小梁，骨小梁网状结构4周时完整，第8周和第12周后逐渐被破坏，12周最严重；OVX后骨小梁表面的胶原纤维逐渐变得杂乱、稀薄。结论：OVX后St、Nd-St区骨重建最活跃，这可能是骨质疏松时骨小梁节点数减少而游离末端数增加的原因。     

Subchondral and trabecular bone remodeling in canine experimental osteoarthritis

Introduction: We wanted to test the hypothesis that quality changes occur in early-stage arthritic subchondral cancellous bone after acute subchondral damage. So far, not much attention has been paid to changes of the subchondral bone after traumatic subchondral lesions. Materials and methods: With an established animal model, we produced pure subchondral damage without initial affection of the articular cartilage in 12 Beagle dogs under MRI and histological control. We utilized bone histomorphometry to evaluate bone turnover, its structure and the articular cartilage 6 months after the initial damage. Results: On follow-up, bone remodelling was indicated, e.g. by a significant increase in the trabecular bone volume and thickness, osteoblast number and osteoid surface and a decrease in the trabecular number in all 12 samples. Several other parameters showed a tendency, e.g. osteoblast surface and osteoclast number. Cartilage analysis showed degenerative changes in ten of 12 samples that had not shown any evidence of damage during the initial examination. Discussion: Our investigation indicates a significant deterioration in the architecture of the cancellous bone with degenerative changes of the overlying articular cartilage after subchondral lesions, which change the mechanical properties.     

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.     

Effect of calcitonin administration on young pig trabecular bone remodeling

Ten-week-old pigs were treated with 4 different treatment schedules of porcine calcitonin for 2 months. Groups C1 and C4 received continuous treatment: C1 had daily IM injections (4 IU/kg/BW (body weight) each injection), and C4 was infused with a minipump implanted subcutaneously delivering 4 IU/kg/BW/day. Groups C2 and C3 received intermittent calcitonin treatment (each injection 4 IU/kg/BW): C2 was given 1 out of every four days, C3 was injected 5 consecutive days out of 20 days. The total dosage received in C1 versus C4 and C2 versus C3 were the same. Results were evaluated by histomorphometry after double tetracycline labeling on iliac trabecular bone. Resorption surfaces were decreased in groups C2, C3 and C4, but bone volume, osteoclast surfaces, and interstitial bone thickness were not modified in any group receiving calcitonin. Osteoblast and mineralizing surfaces were increased in group C2, C3 and C4. Plasma 1,25-dihydroxyvitamin D concentration and bone formation rate were increased in groups C2 and C4. Plasma immunoreactive parathyroid hormone levels and parathyroid weights were not increased in any treated groups. In conclusion, 2-month calcitonin treatment did not decrease the amount of bone resorbed in growing pigs. Continuous calcitonin infusion and intermittent calcitonin administration induced an increase in the extent of active bone formation which might be in part dependent on an increased production of 1,25 dihydroxyvitamin D.     

Anisotropy changes in post-menopausal osteoporosis: characterization by a new index applied to trabecular bone radiographic images

Bone intrinsic strength is conditioned by several factors, including material property and trabecular micro-architecture. Bone mineral density (BMD) is a good surrogate for material property. Architectural anisotropy is of special interest in mechanics-architecture relations and characterizes the degree of directional organization of a material. We have developed anisotropy indices from the Fast Fourier Transform (FFT) on bone radiographs. We have validated these indices in a cross-sectional uni-center case-control study including 39 postmenopausal women with vertebral fracture and 70 age-matched control cases. BMD was measured at the lumbar spine and femoral neck. A fractal analysis of texture was performed on calcaneus radiographs at three regions of interest (ROIs), and the result was expressed as the H parameter (fractal dimension =H-2). The anisotropy evaluation was based on the FFT spectrum of these three ROIs extracted on calcaneus radiographs. On the FFT spectrum, we have measured the spreading angle of the longitudinal trabeculae called the dispersion longitudinal index (DLI) and the spreading angle of the transversal trabeculae called the dispersion transversal index (DTI). From the measured parameters, an anisotropy index was derived, and the degree of anisotropy (DA) calculated with DLI and DTI. We have compared the results from the vertebral fracture cases and control cases. The best distinction was obtained for the largest ROI located in the great tuberosity of the calcaneus for all parameters ( P <10^-4). The DA parameter showed a higher value in vertebral fracture cases (1.746±0.169) than in control cases (1.548±0.136); P <10^-4, and the difference persisted after removal of the subjects with hormonal replacement therapy. The analysis of the receiver operating characteristics (ROC) has shown the best results with DA and Hmean: areas under curves (AUCs) respectively of 0.765 and 0.683, while AUCs associated to LS-BMD and FN-BMD were 0.614 and 0.591 lower, respectively. We determined the odds ratios (OR) by uni- and multivariate analysis. Crude ORs were respectively 3.91 (95% CI: 2.22–6.87) and 3.08 (95% CI: 1.72–5.52) for DA and Hmean. Crude ORs were respectively 1.71 (95% CI: 1.15–2.56) and 1.56 (95% CI: 1.05–2.31) for LS-BMD and FN-BMD. All ORs were statistically significant, and those associated to Hmean and anisotropy indices were higher than those of BMD measurements. From a multivariate analysis including anisotropy indices, Hmean, age and FN-BMD, the remaining significant ORs were respectively 6.33 (95% CI: 2.80–14.30) and 3.08 (95% CI: 1.48–6.37) for DA and Hmean. These data have shown that anisotropy indices on calcaneus radiographs can distinguish vertebral fracture cases from control cases. This analysis provides complementary information concerning the BMD and fractal parameter. These data suggest that we can improve the fracture risk evaluation by adding information related to the directional organization of trabecular bone derived from the FFT spectrum on conventional radiographic images.     

Computer simulations of stress-related bone remodeling around noncemented acetabular components

The authors have used computer modeling techniques to examine stress-related bone changes in the acetabular region. Using a previously developed theory for bone development and adaptation, the authors simulated the distribution of bone density in the natural pelvis as well as changes in bone density following total hip arthroplasty. The geometry of the finite element model was based on a two-dimensional slice through the pelvis. Starting from a solid, homogeneous structure, the computer simulations predicted the distribution of bone density throughout the natural pelvis. The predicted bone density distribution in this first simulation agreed well with the actual bone density distribution only when loads representing multiple activities were incorporated. Using the predicted density distribution as a starting point the authors modified the finite element models to study two designs of noncemented, metal-backed acetabular cups. The simulations with fully fixed bone-implant interfaces predicted extensive loss of bone density medial and inferior to the prosthetic components. The simulations with loose interfaces led to more moderate losses of bone density, indicating a load transfer more similar to that which occurs in the natural joint. The differences in simulated bone remodeling between the two component designs were quite minimal. These results indicate that acetabular components with full bony ingrowth may induce significant stress-related bone remodeling due to a nonphysiologic transfer of load.     

The 3D structure of the collagen fibril network in human trabecular bone: Relation to trabecular organization

Trabecular bone is morphologically and functionally different from compact bone at the tissue level, but both are composed of lamellae at the micrometer-scale level. We present a three-dimensional study of the collagenous network of human trabecular lamellar bone from the proximal femur using the FIB-SEM serial surface view method. The results are compared to human compact lamellar bone of the femoral shaft, studied by the same method. Both demineralized trabecular and compact lamellar bone display the same overall structural organization, namely the presence of ordered and disordered materials and the confinement of the canalicular network to the disordered material. However, in trabecular bone lamellae a significant proportion of the ordered collagen fibril arrays is aligned with the long axis of the trabecula and, unlike in compact bone, is not related to the anatomical axis of the whole femur. The remaining ordered collagen fibrils are offset from the axis of a trabecula either by about 30° or 70°. Interestingly, at the tissue scale of millimeters, the most abundant angles between any two connected trabeculae — the inter-trabecular angles - center around 30° and 70°. This implies that within a framework of interconnected trabeculae the same lamellar structure will always have a significant component of the fibrils aligned with the long axes of connected trabeculae. This structural complementarity at different hierarchical levels presumably reflects an adaptation of trabecular bone to function.     

Comparison of trabecular bone microarchitecture and remodeling in glucocorticoid-induced and postmenopausal osteoporosis.

Long-term treatment with glucocorticoids (GCs) leads to a rapid bone loss and to a greater risk of fractures. To evaluate the specific effects of this treatment on cancellous bone remodeling, structure, and microarchitecture, we compared 22 transiliac biopsy specimens taken in postmenopausal women (65 +/- 6 years) receiving GCs (> or = 7.5 mg/day, for at least 6 months) and 22 biopsy specimens taken in age-matched women with postmenopausal osteoporosis (PMOP), all untreated and having either at least one vertebral fracture or a T score < -2.5 SD. On these biopsy specimens, we measured static and dynamic parameters reflecting trabecular bone formation and resorption. Also, we performed the strut analysis and evaluated the trabecular bone pattern factor (TBPf), Euler number/tissue volume (E/TV), interconnectivity index (ICI), and marrow star volume (MaSV). Glucocorticoid-induced osteoporosis (GIOP), when compared with PMOP, was characterized by lower bone volume (BV/TV), trabecular thickness (Tb.Th), wall thickness (W.Th), osteoid thickness (O.Th), bone formation rate/bone surface (BFR/BS), adjusted mineral apposition rate/bone surface (Aj.AR/BS), and higher ICI and resorption parameters. After adjustment for BV/TV, the W.Th remained significantly lower in GIOP (p < 0.0001). The active formation period [FP(a+)] was not different. Patients with GIOP were divided into two groups: high cumulative dose GCs (HGCs; 23.7 +/- 9.7 g) and low cumulative dose GCs (LGCs; 2.7 +/- 1.2 g). HGC when compared with LGC was characterized by lower W.Th (p < 0.05), BV/TV (p < 0.001), Tb.Th (p < 0.05), trabecular number (Tb.N; p < 0.05), FP(a+)(p < 0.05), and nodes (p < 0.05), and higher E/TV (p < 0.05), ICI (p < 0.005), and TBPf (p < 0.05). When HGC was compared with PMOP, the results were similar except for the MaSV, which was significantly higher (p < 0.005). In summary, GIOP was characterized by lower formation and higher resorption than in PMOP, already present after LGC. With HGCs, these changes were associated with a more dramatic bone loss caused by a major loss of trabecular connectivity.     

On the importance of geometric nonlinearity in finite-element simulations of trabecular bone failure

The finite element method, which has been successfully applied to studies of the elastic properties of trabecular bone, is now being used to simulate its failure. These simulations have used a geometrically linear (linear kinematic) approximation to the total stiffness matrix; nonlinear terms in the total stiffness matrix have been excluded from the computation in order to achieve efficiency. Because trabecular bone appears to be a slender (i.e., geometrically nonlinear) structure, we studied the validity of the linear kinematic approximation for simulating its failure. Two cases, designed to bracket the extremes of stability behavior, were explored: a single representative spicule of trabecular bone (case 1) and a volume of trabecular bone consisting of relatively low aspect ratio members (case 2). For case 1, geometrically linear (GL) and nonlinear (GNL) analyses were performed with two different materials models: a plastic damage model and a brittle damage model. When GNL terms were included in the total stiffness matrix, we found that load-path bifurcation preceded tissue failure regardless of the form of the damage model. This bifurcation was the result of a complex coupling between material yield and structural instability. The nature of this coupling was highly sensitive to the form of the damage model. None of these behaviors was observed in the linear analyses, where failure was insensitive to the form of the damage model and where structural instabilities were prevented from occurring. For case 2, compressive loading of a volume of trabecular bone, geometric nonlinear effects were pronounced. There was a bifurcation in load response that resulted in large apparent strain to failure. The GL simulations, on the other hand, precluded this bifurcation. We hypothesize that trabecular bone is a geometric nonlinear structure; nonlinear terms must be included in the total stiffness matrix to accurately simulate its failure.     

Primary hyperparathyroidism: iliac crest trabecular bone volume, structure, remodeling, and balance evaluated by histomorphometric methods.

Iliac bone biopsies from 69 patients (48 females, 21 males; median age 58 years; range 17-79 years) with primary hyperparathyroidism (PHP) were examined, and static histomorphometric parameters compared to 30 age- and sex-matched normal controls. The control group for the dynamic parameters constituted 20 sex-matched younger normal controls. Fractional volume of trabecular bone was normal, but the trabeculae were thinner (p less than 0.05) in PHP. The structural parameters marrow space star volume, intertrabecular distance, and mean trabecular plate density were not significantly different in PHP patients compared to normal controls, but the age-related increase, for females, in marrow space star volume and decrease, for both sexes, in mean plate density observed in the controls were not noticed in the PHP group. Trabecular bone remodeling was found significantly increased in the PHP patients reflected by increased extension of eroded (p less than 0.001), osteoid (p less than 0.001), and labeled surfaces (p less than 0.05). The activation frequency was increased by approximately 50% (p less than 0.001). Neither PHP patients nor controls showed age-related decrease in trabecular thickness, and accordingly in both groups the bone balance per remodeling cycle was very close to and not significantly different from zero. Normal postmenopausal women (age greater than or equal to 50 yr) had lower trabecular bone volume (p less than 0.001) and higher intertrabecular distance than normal pre-menopausal women (age less than 50 yr).(ABSTRACT TRUNCATED AT 250 WORDS)     

Model structure and control of bone remodeling: a theoretical study

It is generally accepted that RANKL is highly expressed in osteoblast precursor cells while OPG is highly expressed in mature osteoblasts, but to date no functional utility to the BMU has been proposed for this particular ligand-decoy-receptor expression profile. As discovered in the mid 90s, the RANK-RANKL-OPG signaling cascade is a major signaling pathway regulating bone remodeling. In this paper we study theoretically the functional implications of particular RANKL/OPG expression profiles on bone volume. For this purpose we formulate an extended bone-cell dynamics model describing functional behaviour of basic multicellular units (BMUs) responsible for bone resorption and formation. This model incorporates the RANK-RANKL-OPG signaling together with the regulating action of TGF-beta on bone cells. The bone-cell population model employed here builds on the work of Lemaire et al. (2004) [1], but incorporates the following significant modifications: (i) addition of a rate equation describing changes in bone volume with time as the key 'output function' tracking functional behaviour of BMUs, (ii) a rate equation describing release of TGF-beta from the bone matrix, (iii) expression of OPG and RANKL on both osteoblastic cell lines, and (iv) modified activator/repressor functions. Using bone volume as a functional selection criterion, we find that there is a preferred arrangement for ligand expression on particular cell types, and further, that this arrangement coincides with biological observations. We then investigate the model parameter space combinatorially, searching for preferred 'groupings' of changes in differentiation rates of various cell types. Again, a criterion of bone volume change is employed to identify possible ways of optimally controlling BMU responses. While some combinations of changes in differentiation rates are clearly unrealistic, other combinations of changes in differentiation rates are potentially functionally significant. Most importantly, the combination of parameter changes representing the signaling pathway for TGF-beta gives a unique result that appears to have a clear biological rationale. The methodological approach for the investigation of model structure described here offers a theoretical explanation as to why TGF-beta has its particular suite of biological effects on bone-cell differentiation rates.     

The relationship of radiologic bone structure image to mineral content and morphometric parameters of trabecular bone]

Radiographic, mineralogic and histomorphometric investigations of the distal radial metaphyses were performed in a group of 57 men who sustained sudden death. The radiographic image of bone structure was assessed by nude eye and with computerized analyses of the microdensitometric curves. Mineral in bone specimens content was estimated by Dulce method. Trabecular mineralized bone area (Vmin), osteoid area (Vos) and trabecular width (dt) were measured on undecalcified sections. Decrease of bone mineral content and Vmin were noted with the age of those investigated. This process affected the radiographic image of bone structure. The radiographic picture of bone structure depends mostly on the mineral content and to a smaller extent on histomorphometric parameters. Microdensitometric measurements make objective assessment of bone structure on the radiograph possible.     

Estimation of the three-dimensional wall thickness of completed remodeling sites in iliac trabecular bone

The wall thickness of completed remodeling sites in trabecular bone was estimated in 25 normal individuals and 5 patients with arthrosis of the knee, using 7 μm sections of undecalcified iliac crest bone. A systematic sampling procedure which gives a surface referent estimate of the thickness was applied. The efficiency of the sampling design was optimized by means of a cost-variance analysis. The proposed method of sampling which eliminates a common bias in bone histomorphometry is recommended for determinations of wall thickness, osteoid thickness, lamellar thickness, and distance between fluorochrome markers in trabecular bone.The intraindividual distributions of three-dimensional wall thickness were reconstructed from the measurements of apparent width by an unfolding procedure based on the geometric probability density function pertaining to randomly sectioned plates. Distributions of true wall thickness for the young normal individuals were unimodal and resembled normal distributions. The three-dimensional mean wall thickness was 61.4 ± 4.4 μm (± SID). It was demonstrated that the conventionally applied stereological transformation, which calculates the three-dimensional mean wall thickness from the mean apparent width by multiplying the latter by π/4, underestimates the three-dimensional mean wall thickness. An improved transformation is illustrated and is recommended for estimating three-dimensional mean thickness of plates from two-dimensional measurements in trabecular bone.