van B Bert Rietbergen

Estimation of distal radius failure load with micro-finite element analysis models based on three-dimensional peripheral quantitative computed tomography images

There is increasing evidence that, in addition to bone mass, bone microarchitecture and its mechanical load distribution are important factors for the determination of bone strength. Recently, it has been shown that new high-resolution imaging techniques in combination with new modeling algorithms based on the finite element (FE) method can account for these additional factors. Such models thus could provide more relevant information for the estimation of bone failure load. The purpose of the present study was to determine whether results of whole-bone micro-FE (microFE) analyses with models based on three-dimensional peripheral quantitative computer tomography (3D-pQCT) images (isotropic voxel resolution of 165 microm) could predict the failure load of the human radius more accurately than results with dual-energy X-ray absorptiometry (DXA) or bone morphology measurements. For this purpose, microFE models were created using 54 embalmed cadaver arms. It was assumed that bone failure would be initiated if a certain percentage of the bone tissue (varied from 1% to 7%) would be strained beyond the tissue yield strain. The external force that produced this tissue strain was calculated from the FE analyses. These predictions were correlated with results of real compression testing on the same cadaver arms. The results of these compression tests were also correlated with results of DXA and structural measurements of these arms. The compression tests produced Colles-type fractures in the distal 4 cm of the radius. The predicted failure loads calculated from the FE analysis agreed well with those measured in the experiments (R(2) = 0.75 p < 0.001). Lower correlations were found with bone mass (R(2) = 0.48, p < 0.001) and bone structural parameters (R(2) = 0.57 p < 0.001). We conclude that application of the techniques investigated here can lead to a better prediction of the bone failure load for bone in vivo than is possible from DXA measurements, structural parameters, or a combination thereof.

Processing and Analysis of In Vivo High-Resolution MR Images of Trabecular Bone for Longitudinal Studies: Reproducibility of Structural Measures and Micro-Finite Element Analysis Derived Mechanical Properties

Abstract: The authors have developed a system for the characterization of trabecular bone structure from high-resolution MR images. It features largely automated coil inhomogeneity correction, trabecular bone region segmentation, serial image registration, bone/marrow binarization, and structural calculation steps. The system addresses problems of efficiency and inter- and intra-operator variability inherent in previous analyses. The system is evaluated on repetitive scans of 8 volunteers for both two-dimensional (2D) apparent structure calculations and three-dimensional (3D) mechanical calculations using micro-finite element analysis. Coil correction methods based on a priori knowledge of the coil sensitivity and on low-pass filtering of the high-resolution mages are compared and found to perform similarly. Image alignment is found to cause small but significant changes in some structural parameters. Overall the automated system provides on the order of a 3-fold decrease in trained operator time over previous manual methods. Reproducibility is found to be dependent on image quality for most parameters. For 7 subjects with good image quality, reproducibility of 2–4% is found for 2D structural parameters, while 3D mechanical parameters vary by 4–9%, with percent standardized coefficients of variation in the ranges of 15–34% and 20–38% respectively.

In Vivo Assessment of Architecture and Micro-Finite Element Analysis Derived Indices of Mechanical Properties of Trabecular Bone in the Radius

Abstract: Measurement of microstructural parameters of trabecular bone noninvasively in vivo is possible with high-resolution magnetic resonance (MR) imaging. These measurements may prove useful in the determination of bone strength and fracture risk, but must be related to other measures of bone properties. In this study in vivo MR imaging was used to derive trabecular bone structure measures and combined with micro-finite element analysis (μFE) to determine the effects of trabecular bone microarchitecture on bone mechanical properties in the distal radius. The subjects were studied in two groups: (I) postmenopausal women with normal bone mineral density (BMD) (n= 22, mean age 58 ± 7 years) and (II) postmenopausal women with spine or femur BMD −1 SD to −2.5 SD below young normal (n= 37, mean age 62 ± 11 years). MR images of the distal radius were obtained at 1.5 T, and measures such as apparent trabecular bone volume fraction (App BV/TV), spacing, number and thickness (App TbSp, TbN, TbTh) were derived in regions of interest extending from the joint line to the radial shaft. The high-resolution images were also used in a micro-finite element model to derive the directional Young’s moduli (E1, E2 and E3), shear moduli (G12, G23 and G13) and anisotropy ratios such as E1/E3. BMD at the distal radius, lumbar spine and hip were assessed using dual-energy X-ray absorptiometry (DXA). Bone formation was assessed by serum osteocalcin and bone resorption by serum type I collagen C-terminal telopeptide breakdown products (serum CTX) and urinary CTX biochemical markers. The trabecular architecture displayed considerable anisotropy. Measures of BMD such as the ultradistal radial BMD were lower in the osteopenic group (p<0.01). Biochemical markers between the two groups were comparable in value and showed no significant difference between the two groups. App BV/TV, TbTh and TbN were higher, and App TbSp lower, in the normal group than the osteopenic group. All three directional measures of elastic and shear moduli were lower in the osteopenic group compared with the normal group. Anisotropy of trabecular bone microarchitecture, as measured by the ratios of the mean intercept length (MIL) values (MIL1/MIL3, etc.), and the anisotropy in elastic modulus (E1/E3, etc.), were greater in the osteopenic group compared with the normal group. The correlations between the measures of architecture and moduli are higher than those between elastic moduli and BMD. Stepwise multiple regression analysis showed that while App BV/TV is highly correlated with the mechanical properties, additional structural measures do contribute to the improved prediction of the mechanical measures. This study demonstrates the feasibility and potential of using MR imaging with μFE modeling in vivo in the study of osteoporosis.

High-resolution MRI and micro-FE for the evaluation of changes in bone mechanical properties during longitudinal clinical trials: application to calcaneal bone in postmenopausal women after one year of idoxifene treatment

OBJECTIVE To investigate whether recently developed in vivo high-resolution magnetic resonance-imaging and micro-finite element techniques can monitor changes in bone mechanical properties during long-term clinical trials aiming at evaluating the efficacy of new drugs for the treatment of osteoporosis. DESIGN Comparison of baseline and follow-up mechanical parameters calculated using micro-finite element analysis of the calcaneus for subjects participating in a study investigating the effect of idoxifene. BACKGROUND Contemporary measurements for the evaluation of bone mechanical properties, based on dual-energy X-ray absorptiometry measurements, are not very accurate and require large trial populations. METHODS A total of 56 postmenopausal subjects received either a placebo, 5 mg or 10 mg per day of idoxifene. Magnetic resonance-images of the calcaneus were made at baseline and after one year. Mechanical parameters of a trabecular volume of interest in the calcaneus were calculated using micro-finite element analysis. RESULTS Although there were no significant differences between the mean changes in the treated groups and the placebo group, there were significant changes from baseline within groups after one year of treatment. Significant changes, however, were found only for mechanical parameters and only in the treated groups. CONCLUSIONS The present study is the first demonstration that longitudinal changes in bone mechanical properties due to trabecular micro-architectural changes may be quantified in long-term clinical studies. Since significant changes in mechanical parameters were obtained for the treated groups whereas no significant change in bone mass was found we conclude that the application of these techniques may increase the clinical significance of these trials. RELEVANCE A precise diagnosis of in vivo bone mechanical properties that accounts for (changes in) trabecular bone architecture is of particular importance for longitudinal clinical trials aiming at evaluating the efficacy of new drugs since it can lead to clinically relevant results from shorter follow-up intervals and may enable a reduction of the number of patients involved in the trial.

Micro-FE analyses of bone: state of the art

Micro-finite element (µFE) analysis is a numerical technique to calculate mechanical properties of trabecular bone as they relate to its micro-structure. It is based on two recent developments. The first is a method for the three-dimensional graphics computer reconstruction of trabecular structure. With this method, high-resolution images of sequential cross-sections of a trabecular bone region are created. These images are digitized and stored in a computer. By stacking the cross-sectional images the original structure can be rebuild in the computer as a three-dimensional voxel (i.e. 3-D pixel) grid. Methods to create the high-resolution images can be destructive (e.g. serial sectioning and serial milling techniques1,2) or non-destructive (e.g. µCT and µMR imaging3,4.5,6) In both cases a resolution of 50 microns or better can usually be achieved for trabecular bone regions of approximately 1 cm3in size.

Fractures during Childhood and Adolescence in Healthy Boys: Relation with Bone Mass, Microstructure, and Strength

CONTEXT In healthy boys, fractures result from trauma of various severity, suggesting contribution of an intrinsic biomechanical fragility. OBJECTIVES Our objective was to characterize bone mineral mass, microstructure, and strength in boys with and without fractures. PARTICIPANTS AND DESIGN We followed 176 healthy boys from 7.4 ± 0.5 to 15.2 ± 0.5 (mean ± sd) yr of age. OUTCOMES Areal (a) bone mineral density (BMD) was measured by dual-energy x-ray absorptiometry at radius metaphysis and diaphysis, total hip, femoral neck and diaphysis, and L2-L4 vertebrae. Volumetric (v) BMD and microstructure were assessed by high-resolution peripheral computerized tomography at both distal tibia and radius. Bone strength was evaluated by micro-finite element analysis. RESULTS A total of 156 fractures were recorded in 87 of 176 boys with peak incidence between 10 and 13 yr. At 7.4 yr, subjects with fractures had lower aBMD in all sites and at 15.2 yr in femoral and spinal, but not in radius, sites. At that age, boys with fractures displayed lower trabecular (Tb) vBMD (P = 0.029) and number (P = 0.040), stiffness (P = 0.024), and failure load (P = 0.016) at distal tibia, but not distal radius. Odds ratios of fracture risk per 1 sd decrease were 1.80 (P = 0.006) for femoral neck aBMD and 1.46 (P = 0.038) for distal tibia Tb vBMD, 1.59 (P = 0.031) for Tb number, 1.53 (P = 0.072) for stiffness, and 1.60 (P = 0.056) for failure load. CONCLUSION In a homogeneous cohort of healthy boys, fractures recorded until 15.2 ± 05 yr of age were associated with lower femoral neck aBMD and with lower distal tibia trabecular vBMD and number, stiffness and failure load. These deficits in bone mineral mass, microstructure and strength could contribute to the occurrence of fractures during growth.

Predictive value of femoral head heterogeneity for fracture risk.

Osteoporosis (OP) is characterized by low bone mass and weak bone structure, which results in increased fracture risk. It has been suggested that osteoporotic bone is strongly adapted to the main loading direction and less adapted to the other directions. In this study, we hypothesized that osteoporotic femoral heads have 1) an increased anisotropy; 2) a more heterogenic distribution of bone volume fraction (BV/TV) throughout the femoral head; and, 3) a more heterogenic distribution of the trabecular thickness (Tb.Th.) throughout the femoral head, as compared to non-osteoporotic bone. To test these hypotheses, we used 7 osteoporotic femoral heads from patients who fractured their femoral neck and 7 non-fractured femoral heads from patients with osteoarthrosis (OA). Bone structural parameters from the entire trabecular region were analyzed using microCT. We found that the degree of anisotropy was higher in the fractured femoral heads, i.e. 1.72, compared to a value of 1.61 in the non-fractured femoral heads. The BV/TV and Tb.Th. and their variations throughout the femoral head, however, were all significantly lower in the fractured group. Hence, the first hypothesis was confirmed, whereas the other two were rejected. Interestingly, the variation of Tb.Th. throughout the femoral head provided a 100% discrimination between the OP and OA groups, i.e. for the same BV/TV, all fractured cases had a less heterogenic distribution. In conclusion, our results suggest that bone loss in OP takes place uniformly throughout the femoral head, leading to an overall decrease in bone mass and trabecular thickness. Furthermore, the variation of Tb.Th. in the femoral head could be an interesting parameter to improve the prediction of fracture risk in the proximal femur.

Decreased bone tissue mineralization can partly explain subchondral sclerosis observed in osteoarthritis

For many years, pharmaceutical therapies for osteoarthritis (OA) were focused on cartilage. However, it has been theorized that bone changes such as increased bone volume fraction and decreased bone matrix mineralization may play an important role in the initiation and pathogenesis of OA as well. The mechanisms behind the bone changes are subject of debate, and a better understanding may help in the development of bone-targeting OA therapies. In the literature, the increase in bone volume fraction has been hypothesized to result from mechanoregulated bone adaptation in response to decreased mineralization. Furthermore, both changes in bone volume fraction and mineralization have been reported to be highest close to the cartilage, and bone volume fraction has been reported to be correlated with cartilage degeneration. These data indicate that cartilage degeneration, bone volume fraction, and bone matrix mineralization may be related in OA. In the current study, we aimed to investigate the relationships between cartilage degeneration, bone matrix mineralization and bone volume fraction at a local level. With microCT, we determined bone matrix mineralization and bone volume fraction as a function of distance from the cartilage in osteochondral plugs from human OA tibia plateaus with varying degrees of cartilage degeneration. In addition, we evaluated whether mechanoregulated bone adaptation in response to decreased bone matrix mineralization may be responsible for the increase in bone volume fraction observed in OA. For this purpose, we used the experimentally obtained mineralization data as input for bone adaptation simulations. We simulated the effect of mechanoregulated bone adaptation in response to different degrees of mineralization, and compared the simulation results to the experimental data. We found that local changes in subchondral bone mineralization and bone volume fraction only occurred underneath severely degenerated cartilage, indicating that bone mineralization and volume fraction are related to cartilage degeneration at a local level. In addition, both the experimental data and the simulations indicated that a depth-dependent increase in bone volume fraction could be caused by decreased bone matrix mineralization. However, a quantitative comparison showed that decreased mineralization can only explain part of the subchondral sclerosis observed in OA.

The role of pressurized fluid in subchondral bone cyst growth

Pressurized fluid has been proposed to play an important role in subchondral bone cyst development. However, the exact mechanism remains speculative. We used an established computational mechanoregulated bone adaptation model to investigate two hypotheses: 1) pressurized fluid causes cyst growth through altered bone tissue loading conditions, 2) pressurized fluid causes cyst growth through osteocyte death. In a 2D finite element model of bone microarchitecture, a marrow cavity was filled with fluid to resemble a cyst. Subsequently, the fluid was pressurized, or osteocyte death was simulated, or both. Rather than increasing the load, which was the prevailing hypothesis, pressurized fluid decreased the load on the surrounding bone, thereby leading to net bone resorption and growth of the cavity. In this scenario an irregularly shaped cavity developed which became rounded and obtained a rim of sclerotic bone after removal of the pressurized fluid. This indicates that cyst development may occur in a step-wise manner. In the simulations of osteocyte death, cavity growth also occurred, and the cavity immediately obtained a rounded shape and a sclerotic rim. Combining both mechanisms increased the growth rate of the cavity. In conclusion, both stress-shielding by pressurized fluid, and osteocyte death may cause cyst growth. In vivo observations of pressurized cyst fluid, dead osteocytes, and different appearances of cysts similar to our simulation results support the idea that both mechanisms can simultaneously play a role in the development and growth of subchondral bone cysts.

Analysis of bone architecture sensitivity for changes in mechanical loading, cellular activity, mechanotransduction, and tissue properties

Bone has an architecture which is optimized for its mechanical environment. In various conditions, this architecture is altered, and the underlying cause for this change is not always known. In the present paper, we investigated the sensitivity of the bone microarchitecture for four factors: changes in bone cellular activity, changes in mechanical loading, changes in mechanotransduction, and changes in mechanical tissue properties. The goal was to evaluate whether these factors can be the cause of typical bone structural changes seen in various pathologies. For this purpose, we used an established computational model for the simulation of bone adaptation. We performed two sensitivity analyses to evaluate the effect of the four factors on the trabecular structure, in both developing and adult bone. According to our simulations, alterations in mechanical load, bone cellular activities, mechanotransduction, and mechanical tissue properties may all result in bone structural changes similar to those observed in various pathologies. For example, our simulations confirmed that decreases in loading and increases in osteoclast number and activity may lead to osteoporotic changes. In addition, they showed that both increased loading and decreased bone matrix stiffness may lead to bone structural changes similar to those seen in osteoarthritis. Finally, we found that the model may help in gaining a better understanding of the contribution of individual disturbances to a complicated multi-factorial disease process, such as osteogenesis imperfecta.