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Biomedical Engineering / Biomedizinische Technik, 58 (Supplement 1), ISSN:0013-5585, ISSN:1862-278X

Finite element (FE) simulations based on high-resolution peripheral quantitative computed-tomography (HRpQCT) measurements provide an elegant and direct way to estimate bone strength. Parallel solvers for nonlinear FE simulations allow the assessment not only of the initial linear elastic behavior of the bone but also materially and geometrically nonlinear effects. The reproducibility of HRpQCT measurements, as well as their analysis of microarchitecture using linear-elastic FE simulations with a homogeneous elastic modulus has been investigated before. However, it is not clear to which extent density-derived and nonlinear FE simulations are reproducible. In this study, we introduced new mechanical indices derived from nonlinear FE simulations that describe the onset of yielding and the behavior at maximal load. Using 14 embalmed forearms that were imaged three times, we found that in general the in vitro reproducibility of the nonlinear FE simulations is as good as the reproducibility of linear FE. For the nonlinear simulations precision errors (PEs) ranged between 0.4 and 3.2% and intraclass correlation coefficients were above 0.9. In conclusion, nonlinear FE simulations with density derived material properties contain important additional information that is independent from the results of the linear simulations.

More accurate techniques to estimate fracture risk could help reduce the burden of fractures in postmenopausal women. Although micro-finite element (µFE) simulations allow a direct assessment of bone mechanical performance, in this first clinical study we investigated whether the additional information obtained using geometrically and materially nonlinear µFE simulations allows a better discrimination between fracture cases and controls. We used patient data and high-resolution peripheral quantitative computed tomography (HRpQCT) measurements from our previous clinical study on fracture risk, which compared 100 postmenopausal women with a distal forearm fracture to 105 controls. Analyzing these data with the nonlinear µFE simulations, the odds ratio (OR) for the factor-of-risk (yield load divided by the expected fall load) was marginally higher (1.99; 95% confidence interval [CI], 1.41–2.77) than for the factor-of-risk computed from linear µFE (1.89; 95% CI, 1.37–2.69). The yield load and the energy absorbed up to the yield point as computed from nonlinear µFE were highly correlated with the initial stiffness (R2 = 0.97 and 0.94, respectively) and could therefore be derived from linear simulations with little loss in precision. However, yield deformation was not related to any other measurement performed and was itself a good predictor of fracture risk (OR, 1.89; 95% CI, 1.39–2.63). Moreover, a combined risk score integrating information on relative bone strength (yield load-based factor-of-risk), bone ductility (yield deformation), and the structural integrity of the bone under critical loads (cortical plastic volume) improved the separation of cases and controls by one-third (OR, 2.66; 95% CI, 1.84–4.02). We therefore conclude that nonlinear µFE simulations provide important additional information on the risk of distal forearm fractures not accessible from linear µFE nor from other techniques assessing bone microstructure, density, or mass. © 2013 American Society for Bone and Mineral Research.

Micro-finite element (μFE) analysis has recently been introduced for the detailed quantification of the mechanical interaction between bone and implant. The technique has been validated at an apparent level. The aim of this study was to address the accuracy of μFE analysis at the trabecular level. Experimental displacement fields were obtained by deformable image registration, also known as strain mapping (SM), of dynamic hip screws implanted in three human femoral heads. In addition, displacement fields were calculated using μFE analysis. On a voxel-by-voxel basis, the coefficients of determination (R(2)) between experimental and μFE-calculated displacements ranged from 0.67 to 0.92. Linear regression of the mean displacements over nine volumes of interest yielded R(2) between 0.81 and 0.84. The lowest R(2) values were found in regions of very small displacements. In conclusion, we found that peri-implant bone displacements calculated with μFE analysis correlated well with displacements obtained from experimental SM.

The local interpretation of microfinite element (μFE) simulations plays a pivotal role for studying bone structure–function relationships such as failure processes and bone remodeling. In the past μFE simulations have been successfully validated on the apparent level, however, at the tissue level validations are sparse and less promising. Furthermore, intratrabecular heterogeneity of the material properties has been shown by experimental studies. We proposed an inverse μFE algorithm that iteratively changes the tissue level Young’s moduli such that the μFE simulation matches the experimental strain measurements. The algorithm is setup as a feedback loop where the modulus is iteratively adapted until the simulated strain matches the experimental strain. The experimental strain of human trabecular bone specimens was calculated from time-lapsed images that were gained by combining mechanical testing and synchrotron radiation microcomputed tomography (SRμCT). The inverse μFE algorithm was able to iterate the heterogeneous distribution of moduli such that the resulting μFE simulations matched artificially generated and experimentally measured strains.

The risk of osteoporotic fractures is currently estimated based on an assessment of bone mass as measured by dual-energy X-ray absorptiometry. However, patient-specific finite element (FE) simulations that include information from multiple scales have the potential to allow more accurate prognosis. In the past, FE models of bone were limited either in resolution or to the linearization of the mechanical behaviour. Now, nonlinear, high-resolution simulations including the bone microstructure have been made possible by recent advances in simulation methods, computer infrastructure and imaging, allowing the implementation of multiscale modelling schemes. For example, the mechanical loads generated in the musculoskeletal system define the boundary conditions for organ-level, continuum-based FE models, whose nonlinear material properties are derived from microstructural information. Similarly microstructure models include tissue-level information such as the dynamic behaviour of collagen by modifying the model's constitutive law. This multiscale approach to modelling the mechanics of bone allows a more accurate characterization of bone fracture behaviour. Furthermore, such models could also include the effects of ageing, osteoporosis and drug treatment. Here we present the current state of the art for multiscale modelling and assess its potential to better predict an individual's risk of fracture in a clinical setting.