David Christen

Bone Structure at the Distal Radius During Adolescent Growth

The incidence of distal forearm fractures peaks during the adolescent growth spurt, but the structural basis for this is unclear. Thus, we studied healthy 6‐ to 21‐yr‐old girls (n = 66) and boys (n = 61) using high‐resolution pQCT (voxel size, 82 μm) at the distal radius. Subjects were classified into five groups by bone‐age: group I (prepuberty, 6–8 yr), group II (early puberty, 9–11 yr), group III (midpuberty, 12–14 yr), group IV (late puberty, 15–17 yr), and group V (postpuberty, 18–21 yr). Compared with group I, trabecular parameters (bone volume fraction, trabecular number, and thickness) did not change in girls but increased in boys from late puberty onward. Cortical thickness and density decreased from pre‐ to midpuberty in girls but were unchanged in boys, before rising to higher levels at the end of puberty in both sexes. Total bone strength, assessed using microfinite element models, increased linearly across bone age groups in both sexes, with boys showing greater bone strength than girls after midpuberty. The proportion of load borne by cortical bone, and the ratio of cortical to trabecular bone volume, decreased transiently during mid‐ to late puberty in both sexes, with apparent cortical porosity peaking during this time. This mirrors the incidence of distal forearm fractures in prior studies. We conclude that regional deficits in cortical bone may underlie the adolescent peak in forearm fractures. Whether these deficits are more severe in children who sustain forearm fractures or persist into later life warrants further study.

Assessing forearm fracture risk in postmenopausal women

SummaryA diverse array of bone density, structure, and strength parameters were significantly associated with distal forearm fractures in postmenopausal women, but most of them were also correlated with femoral neck areal bone mineral density (aBMD), which provides an adequate measure of bone fragility at the wrist for routine clinical purposes.IntroductionThis study seeks to test the clinical utility of approaches for assessing forearm fracture risk.MethodsAmong 100 postmenopausal women with a distal forearm fracture (cases) and 105 with no osteoporotic fracture (controls), we measured aBMD and assessed radius volumetric bone mineral density, geometry, and microstructure; ultradistal radius failure load was evaluated in microfinite element (μFE) models.ResultsFracture cases had inferior bone density, geometry, microstructure, and strength. The most significant determinant of fracture in five categories were bone density (femoral neck aBMD; odds ratio (OR) per standard deviation (SD), 2.0; 95% confidence interval (CI), 1.4–2.8), geometry (cortical thickness; OR, 1.5; 95% CI, 1.1–2.1), microstructure (structure model index (SMI); OR, 0.5; 95% CI, 0.4–0.7), and strength (µFE failure load; OR, 1.8; 95% CI, 1.3–2.5); the factor-of-risk (applied load in a forward fall ÷ μFE failure load) was 15% worse in cases (OR, 1.9; 95% CI, 1.4–2.6). Areas under receiver operating characteristic curves (AUC) ranged from 0.62 to 0.68. The predictors of forearm fracture risk that entered a multivariable model were femoral neck aBMD and SMI (combined AUC, 0.71).ConclusionsDetailed bone structure and strength measurements provide insight into forearm fracture pathogenesis, but femoral neck aBMD performs adequately for routine clinical risk assessment.

Local Mechanical Stimuli Regulate Bone Formation and Resorption in Mice at the Tissue Level

Bone is able to react to changing mechanical demands by adapting its internal microstructure through bone forming and resorbing cells. This process is called bone modeling and remodeling. It is evident that changes in mechanical demands at the organ level must be interpreted at the tissue level where bone (re)modeling takes place. Although assumed for a long time, the relationship between the locations of bone formation and resorption and the local mechanical environment is still under debate. The lack of suitable imaging modalities for measuring bone formation and resorption in vivo has made it difficult to assess the mechanoregulation of bone three-dimensionally by experiment. Using in vivo micro-computed tomography and high resolution finite element analysis in living mice, we show that bone formation most likely occurs at sites of high local mechanical strain (p<0.0001) and resorption at sites of low local mechanical strain (p<0.0001). Furthermore, the probability of bone resorption decreases exponentially with increasing mechanical stimulus (R2 = 0.99) whereas the probability of bone formation follows an exponential growth function to a maximum value (R2 = 0.99). Moreover, resorption is more strictly controlled than formation in loaded animals, and ovariectomy increases the amount of non-targeted resorption. Our experimental assessment of mechanoregulation at the tissue level does not show any evidence of a lazy zone and suggests that around 80% of all (re)modeling can be linked to the mechanical micro-environment. These findings disclose how mechanical stimuli at the tissue level contribute to the regulation of bone adaptation at the organ level.

Computational finite element bone mechanics accurately predicts mechanical competence in the human radius of an elderly population

High-resolution peripheral quantitative computed tomography (HR-pQCT) is clinically available today and provides a non-invasive measure of 3D bone geometry and micro-architecture with unprecedented detail. In combination with microarchitectural finite element (μFE) models it can be used to determine bone strength using a strain-based failure criterion. Yet, images from only a relatively small part of the radius are acquired and it is not known whether the region recommended for clinical measurements does predict forearm fracture load best. Furthermore, it is questionable whether the currently used failure criterion is optimal because of improvements in image resolution, changes in the clinically measured volume of interest, and because the failure criterion depends on the amount of bone present. Hence, we hypothesized that bone strength estimates would improve by measuring a region closer to the subchondral plate, and by defining a failure criterion that would be independent of the measured volume of interest. To answer our hypotheses, 20% of the distal forearm length from 100 cadaveric but intact human forearms was measured using HR-pQCT. μFE bone strength was analyzed for different subvolumes, as well as for the entire 20% of the distal radius length. Specifically, failure criteria were developed that provided accurate estimates of bone strength as assessed experimentally. It was shown that distal volumes were better in predicting bone strength than more proximal ones. Clinically speaking, this would argue to move the volume of interest for the HR-pQCT measurements even more distally than currently recommended by the manufacturer. Furthermore, new parameter settings using the strain-based failure criterion are presented providing better accuracy for bone strength estimates.

Multiscale modelling and nonlinear finite element analysis as clinical tools for the assessment of fracture risk

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 models 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 individuals risk of fracture in a clinical setting.

Deformable image registration and 3d strain mapping for the quantitative assessment of cortical bone microdamage

The resistance to forming microcracks is a key factor for bone to withstand critical loads without fracturing. In this study, we investigated the initiation and propagation of microcracks in murine cortical bone by combining three-dimensional images from synchrotron radiation-based computed tomography and time-lapsed biomechanical testing to observe microdamage accumulation over time. Furthermore, a novel deformable image registration procedure utilizing digital volume correlation and demons image registration was introduced to compute 3D strain maps allowing characterization of the mechanical environment of the microcracks. The displacement and strain maps were validated in a priori tests. At an image resolution of 740 nm the spatial resolution of the strain maps was 10 μm (MTF), while the errors of the displacements and strains were 130 nm and 0.013, respectively. The strain maps revealed a complex interaction of the propagating microcracks with the bone microstructure. In particular, we could show that osteocyte lacunae play a dual role as stress concentrating features reducing bone strength, while at the same time contributing to the bone toughness by blunting the crack tip. We conclude that time-lapsed biomechanical imaging in combination with three-dimensional strain mapping is suitable for the investigation of crack initiation and propagation in many porous materials under various loading scenarios.

Improved fracture risk assessment based on nonlinear micro-finite element simulations from HRpQCT images at the distal radius

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.

Towards validation of computational analyses of peri-implant displacements by means of experimentally obtained displacement maps

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 (R2) 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 R2 between 0.81 and 0.84. The lowest R2 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.

Inverse Finite Element Modeling for Characterization of Local Elastic Properties in Image-Guided Failure Assessment of Human Trabecular Bone

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,intra trabecular heterogeneity of the material properties has been shown by experimental studies. We proposed an inverse μFE algorithm that iteratively changes the tissue level Youngs 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(SRlCT). 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.

Reproducibility for linear and nonlinear micro-finite element simulations with density derived material properties of the human radius

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.