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

Regional, age and gender differences in architectural measures of bone quality and their correlation to bone mechanical competence in the human radius of an elderly population

An accurate prediction of bone strength in the human radius is of major interest because distal radius fractures are amongst the most common in humans. The objective of this study was to determine gender and age-related changes in bone morphometry at the radius and how these relate to bone strength. Specifically, our aims were to (i) analyze gender differences to get an insight into different bone quantities and qualities between women and men, (ii) to determine which microarchitectural bone parameters would best correlate with strength, (iii) to find the region of interest for the best assessment of bone strength, and (iv) to determine how loss of bone quality depends on age. Intact right forearms of 164 formalin-fixed cadavers from a high-risk elderly population were imaged with a new generation high-resolution pQCT scanner (HR-pQCT). Morphometric indices were derived for six different regions and were related to failure load as assessed by experimental uniaxial compression testing. Significant gender differences in bone quantity and quality were found that correlated well with measured failure load. The most relevant region to determine failure load based on morphometric indices assessed in this study was located just below the proximal end of the subchondral plate; this region differed from the one measured clinically today. Trends in bone changes with increasing age were found, even though for all morphometric indices the variation between subjects was large in comparison to the observed age-related changes. We conclude that HR-pQCT systems can determine how gender and age-related changes in morphometric parameters relate to bone strength, and that HR-pQCT is a promising tool for the assessment of bone quality in patient populations.

Bone micro-architecture and determinants of strength in the radius and tibia: age-related changes in a population-based study of normal adults measured with high-resolution pQCT

SUMMARY

We recruited a population-based sample of 58 males and 74 females aged 20-79 from a primary care medical practice to provide normative and descriptive data for high-resolution peripheral quantitative computed tomography (pQCT) parameters. Important effects of ageing and contrasts in the effects of sex on the micro-architecture and strength of upper and lower limb bones were revealed.

INTRODUCTION

The advent of high-resolution pQCT scanners has permitted non-invasive assessment of structural data on cortical and trabecular bone.

METHODS

We investigated age-related changes in pQCT and finite element (FE) modelling parameters at the distal radius and distal tibia in a population-based cross-sectional study of 58 males and 74 females aged 20-79 years. Linear regression models including quadratic terms for age were used for inference.

RESULTS

Age-related changes and sex differences were generally similar for pQCT parameters at the radius and tibia. At each site, mean values for bone density, cortical thickness and trabecular micro-architecture (number, separation and thickness) were lower (trabecular separation higher) in women than men. Changes with age were most apparent for bone density and cortical thickness, which declined with age, in contrast to trabecular micro-architecture parameters which were not significantly associated with age (p > 0.05) in either sex. Cortical bone density and thickness declined faster in women than men after age 50 and trabecular bone density was consistently lower in women. FE-analysis predicted failure load decreased with age and percentage of load carried by trabecular bone increased (p < 0.05).

CONCLUSIONS

These data show contrasts in the effects of sex on the micro-architecture and strength of upper and lower limb bones with ageing. The faster decline in cortical bone thickness and density in women than men after age 50 and consistently lower trabecular bone density in women have implications for the excess risks of wrist and hip fractures in women.

Development and validation of a predictive bone fracture risk model for astronauts

There are still many unknowns in the physiological response of human beings to space, but compelling evidence indicates that accelerated bone loss will be a consequence of long-duration spaceflight. Lacking phenomenological data on fracture risk in space, we have developed a predictive tool based on biomechanical and bone loading models at any gravitational level of interest. The tool is a statistical model that forecasts fracture risk, bounds the associated uncertainties, and performs sensitivity analysis. In this paper, we focused on events that represent severe consequences for an exploration mission, specifically that of spinal fracture resulting from a routine task (lifting a heavy object up to 60 kg), or a spinal, femoral or wrist fracture due to an accidental fall or an intentional jump from 1 to 2 m. We validated the biomechanical and bone fracture models against terrestrial studies of ground reaction forces, skeletal loading, fracture risk, and fracture incidence. Finally, we predicted fracture risk associated with reference missions to the moon and Mars that represented crew activities on the surface. Fracture was much more likely on Mars due to compromised bone integrity. No statistically significant gender-dependent differences emerged. Wrist fracture was the most likely type of fracture, followed by spinal and hip fracture.

Trabecular bone mechanical properties in patients with fragility fractures

Fragility fractures are generally associated with substantial loss in trabecular bone mass and alterations in structural anisotropy. Despite the high correlations between measures of trabecular mass and mechanical properties, significant overlap in density measures exists between individuals with osteoporosis and those who do not fracture. The purpose of this paper is to provide an analysis of trabecular properties associated with fragility fractures. While accurate measures of bone mass and 3-D orientation have been demonstrated to explain 80% to 90% of the variance in mechanical behavior, clinical and experimental experience suggests the unexplained proportion of variance may be a key determinant in separating high- and low-risk patients. Using a hierarchical perspective, we demonstrate the potential contributions of structural and tissue morphology, material properties, and chemical composition to the apparent mechanical properties of trabecular bone. The results suggest that the propensity for an individual to remodel or adapt to habitual damaging or nondamaging loads may distinguish them in terms of risk for failure.

DXA-based hip structural analysis of once-weekly bisphosphonate-treated postmenopausal women with low bone mass

SUMMARY

DXA-based hip structural analysis from 947 individuals completing two large osteoporosis clinical trials was pooled and analyzed. Treatment with once-weekly (OW) ALN or OW RIS resulted in significant improvements from baseline in geometric parameters at all three HSA ROIs. Improvements were generally greater with OW ALN than OW RIS.

INTRODUCTION

BMD can be altered by changes in distribution and quantity of bone and changes in mineralization. These effects cannot be distinguished with conventional measurements of BMD. Currently, tissue composition is evaluated only by invasive means. Structural geometry of the proximal femur, however, can be measured in vivo by several methods, including dual energy X-ray absorptiometry (DXA) using specialized hip structure analysis (HSA) software.

METHODS

DXA-based HSA was obtained and analyzed in a subset of 947 subjects participating in the Fosamax Actonel Comparison Trials. Data were pooled to evaluate treatment effects on the structural geometry of the proximal femur by once-weekly alendronate (ALN) 70 mg and risedronate (RIS) 35 mg in postmenopausal women with low bone mass.

RESULTS

Both ALN and RIS treatment over 2 years resulted in improvements in HSA-derived geometry at all three HSA regions of interest (ROI). The largest treatment effects were seen at the intertrochanteric ROI. Consistently greater treatment effects were seen with ALN compared with RIS at all three HSA-ROIs.

CONCLUSIONS

HSA offers insight into the potential mechanisms of fracture risk reduction from pharmacologic intervention. In the current study, treatment with once-weekly bisphosphonates resulted in significant improvements in hip geometric parameters.

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 microm) 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.

Numerical modelling of the shoulder for clinical applications

Research activity involving numerical models of the shoulder is dramatically increasing, driven by growing rates of injury and the need to better understand shoulder joint pathologies to develop therapeutic strategies. Based on the type of clinical question they can address, existing models can be broadly categorized into three groups: (i) rigid body models that can simulate kinematics, collisions between entities or wrapping of the muscles over the bones, and which have been used to investigate joint kinematics and ergonomics, and are often coupled with (ii) muscle force estimation techniques, consisting mainly of optimization methods and electromyography-driven models, to simulate muscular action and joint reaction forces to address issues in joint stability, muscular rehabilitation or muscle transfer, and (iii) deformable models that account for stress-strain distributions in the component structures to study articular degeneration, implant failure or muscle/tendon/bone integrity. The state of the art in numerical modelling of the shoulder is reviewed, and the advantages, limitations and potential clinical applications of these modelling approaches are critically discussed. This review concentrates primarily on muscle force estimation modelling, with emphasis on a novel muscle recruitment paradigm, compared with traditionally applied optimization methods. Finally, the necessary benchmarks for validating shoulder models, the emerging technologies that will enable further advances and the future challenges in the field are described.

Validation of an anatomy specific finite element model of Colles' fracture

Osteoporotic fractures are harmful injuries and their number is on the rise. Distal radius fractures are precursors of other osteoporotic fractures. The wrist's bony geometry and trabecular architecture can be assessed in vivo using the recently introduced HR-pQCT. The goal of this study was the validation of a newly developed HR-pQCT based anatomy specific FE technique including separation of cortical and trabecular bone regions using an experimental model for producing Colles' fractures. Mechanical compression tests of 21 embalmed human radii were conducted. Continuum level FE models were built using HR-pQCT images of the bones and nonlinear analyses were performed using boundary conditions highly similar to the mechanical tests. Density and fabric based material properties were taken from previous tests on biopsies and no adjustments were made. Numerical results provided good prediction of the experimental stiffness (R(2)=0.793) and even better for strength (R(2)=0.874). High damage zones of the FE models coincided with the actual failure patterns of the specimens. These encouraging results allow to conclude that the developed method represents an attractive and efficient tool for simulation of Colles' fracture.

Trabecular bone strength predictions using finite element analysis of micro-scale images at limited spatial resolution

Advances in micro-scanning technology have led to renewed clinical interest in the ability to predict bone strength using finite element (FE) analysis based on images with resolutions in the range of 80 microm. Using such images, we sought to determine whether predictions of yield stress provided by nonlinear FE models could improve correlations with bone strength as compared to the use of predictions of elastic modulus from linear FE models, and if this effect depended on voxel size or bone volume fraction. Linear and nonlinear FE analyses were conducted for 46 trabecular cores from three human anatomic sites using element sizes ranging from 20 to 120 microm to obtain measures of apparent yield stress and elastic modulus, and these measures were correlated against the predicted yield stress from the 20 microm models (assumed to be the gold standard strength for this study). Results indicated that when considering all samples and any resolution, yield stress and elastic modulus were both excellent predictors of strength (R2>0.99). When only low-density samples (BV/TV<0.15) were considered, yield stress was better correlated with 20 microm-strength than was elastic modulus (R2 increased from 0.93 to 0.99 at 40 microm and from 0.90 to 0.95 at 80 microm). However, at a voxel size of 120 microm, the predictive ability of yield stress was slightly less than that of stiffness, likely due to the large convergence-related errors that could develop with larger element sizes. As expected, a limit was observed in the ability of elastic modulus to predict strength--the predictive ability of elastic modulus measured at 20 microm was comparable to that of yield strength at 80 microm. We also found that strength predictions from FE models at clinical-type resolutions had nearly the same power to detect bone quality effects via variations in strength-density relationships as did high-resolution models. We conclude that nonlinear FE models can account for additional variations in strength relative to linear models when using images at resolutions of approximately 80 microm and less, and such models offer a promising method for examining microarchitecture-related bone quality effects associated with aging, disease, and treatment.

Non-invasive bone competence analysis by high-resolution pQCT: an in vitro reproducibility study on structural and mechanical properties at the human radius

Osteoporosis is defined as a skeletal disorder characterized by compromised bone strength. Bone strength depends, among others, on bone density, bone geometry and its internal architecture. With the recent introduction of a new generation high-resolution 3D peripheral quantitative computed tomography (HR-pQCT) system, direct quantification of structural bone parameters has become feasible. Furthermore, it has recently been demonstrated that bone mechanical competence can be derived from HR-pQCT based micro-finite element modeling (microFE). However, reproducibility data for HR-pQCT-derived mechanical indices is not well-known. Therefore, the aim of this study was to quantify reproducibility of HR-pQCT-derived indices. We measured 14 distal formalin-fixed cadaveric forearms three times and analyzed three different regions for each measurement. For each region cortical and trabecular parameters were determined. Reproducibility was assessed with respect to precision error (PE) and intraclass correlation coefficient (ICC). Reproducibility values were found to be best in all three regions for the full bone compartment with an average PE of 0.79%, followed by the cortical compartment (PE=1.19%) and the trabecular compartment with an average PE of 2.31%. The mechanical parameters showed similar reproducibility (PE=0.48%-2.93% for bone strength and stiffness, respectively). ICC showed a very high reproducibility of subject-specific measurements, ranging from 0.982 to 1.000, allowing secure identification of individual donors ranging from healthy to severely osteoporotic subjects. From these in vitro results we conclude that HR-pQCT derived morphometric and mechanical parameters are highly reproducible such that differences in bone structure and strength can be detected with a reproducibility error smaller than 3%; hence, the technique has a high potential to become a tool for detecting bone quality and bone competence of individual subjects.

Virtual trabecular bone models and their mechanical response

The study of the mechanical behaviour of trabecular bone has extensively employed micro-level finite element (μFE) models generated from images of real bone samples. It is now recognized that the key determinants of the mechanical behaviour of bone are related to its micro-architecture. The key indices of micro-architecture, in turn, depend on factors such as age, anatomical site, sex, and degree of osteoporosis. In practice, it is difficult to acquire sufficient samples that encompass these variations. In this preliminary study, a method of generating virtual finite element (FE) samples of trabecular bone is considered. Virtual samples, calibrated to satisfy some of the key micro-architectural characteristics, are generated computationally. The apparent level elastic and post-elastic mechanical behaviour of the generated samples is examined: the elastic mechanical response of these samples is found to compare well with natural trabecular bone studies conducted by previous investigators; the post-elastic response of virtual samples shows that material non-linearities have a much greater effect in comparison with geometrical non-linearity for the bone densities considered. Similar behaviour has been reported by previous studies conducted on real trabecular bone. It is concluded that virtual modelling presents a potentially valuable tool in the study of the mechanical behaviour of trabecular bone and the role of its micro-architecture.

Prediction of Colles' fracture load in human radius using cohesive finite element modeling

Osteoporotic and age-related fractures are a significant public health problem. One of the most common osteoporotic fracture sites in the aging population is distal radius. There is evidence in the literature that distal radius fractures (Colles' fracture) are an indicative of increased risk of future spine and hip fractures. In this study, a nonlinear fracture mechanics-based finite element method is applied to human radius to assess its fracture load as a function of cortical bone geometry and material properties. Seven three-dimensional finite element models of radius were created and the fracture loads were determined by using cohesive finite element modeling which explicitly represents the crack and the fracture process zone behavior. The fracture loads found in the simulations (731-6793 N) were in the range of experimental values reported in the literature. The fracture loads predicted by the simulations decreased by 4-5% per decade based only on material level changes and by 6-20% per decade when geometrical changes were also included. Cortical polar moment of inertia at 15% distal radius showed the highest correlation to fracture load (r(2)=0.97). These findings demonstrate the strength of fracture mechanics-based finite element modeling and show that combining geometrical and material properties provides a better assessment of fracture risk in human radius.

Measurement of trabecular bone microstructure does not improve prediction of mechanical failure loads at the distal radius compared with bone mass alone

Bone mass predicts a high proportion of variability in bone failure strength but is known to overlap among subjects with and without fractures. Here, we tested the hypothesis that trabecular bone microstructure, determined with micro-computed tomography (microCT), can improve the prediction of experimental failure loads in the distal forearm compared with bone mass alone. The right forearm and left distal radius of 130 human specimens were examined. Bone mineral density (BMD) was measured with peripheral dual energy X-ray absorptiometry (DXA). The specimens were mechanically tested to failure in a fall configuration, with the hand, elbow, ligaments, and tendons intact. Cylindrical bone samples from the metaphysis of the contralateral distal radius were obtained adjacent to the subchondral bone plate and scanned with microCT. When analyzing the total sample, BMD of the distal radius displayed a correlation of r = 0.82 with mechanical failure loads. After excluding 21 specimens with no obvious radiological sign of fracture after the test, the correlation increased to r = 0.85. When only including 79 specimens with loco typico fractures, the correlation was r = 0.82. The microstructural parameters showed correlation coefficients with the failure loads of < or =0.55 and did not add significant information to DXA in predicting failure loads in multiple regression models. These findings suggest that, under experimental conditions of mechanically testing entire bones, measurement of bone microstructure does not improve the prediction of distal radius bone strength. Determination of bone microstructure may thus be less promising in improving the prediction of fractures than commonly assumed.

In vivo microMRI-based finite element and morphological analyses of tibial trabecular bone in eugonadal and hypogonadal men before and after testosterone treatment

Osteoporosis is a major public health problem in men. Hypogonadal men have decreased BMD and deteriorated trabecular bone architecture compared with eugonadal men. Testosterone treatment improves their BMD and trabecular structure. We tested the hypothesis that testosterone replacement in hypogonadal men would also improve their bone's mechanical properties. Ten untreated severely hypogonadal and 10 eugonadal men were selected. The hypogonadal men were treated with a testosterone gel for 24 mo to maintain their serum testosterone concentrations within the normal range. Each subject was assessed before and after 6, 12, and 24 mo of testosterone treatment by microMRI of the distal tibia. A subvolume of each microMR image was converted to a microfinite element (microFE) model, and six analyses were performed, representing three compression and three shear tests. The anisotropic stiffness tensor was calculated, from which the orthotropic elastic material constants were derived. Changes in microarchitecture were also quantified using newly developed individual trabeculae segmentation (ITS)-based and standard morphological analyses. The accuracy of these techniques was examined with simulated microMR images. Significant differences in four estimated anisotropic elastic material constants and most morphological parameters were detected between the eugonadal and hypogonadal men. No significant change in estimated elastic moduli and morphological parameters was detected in the eugonadal group over 24 mo. After 24 mo of treatment, significant increases in estimated elastic moduli E(22) (9.0%), E(33) (5.1%), G(23) (7.2%), and G(12) (9.4%) of hypogonadal men were detected. These increases were accompanied by significant increases in trabecular plate thickness. These results suggest that 24 mo of testosterone treatment of hypogonadal men improves estimated elastic moduli of tibial trabecular bone by increased trabecular plate thickness.

Quantification of bone structural parameters and mechanical competence at the distal radius

For the clinician, predicting the fracture risk for individual patients is mainly restricted to the quantitative analysis of bone density. Several studies have shown that bone strength, an indicator for bone fracture risk, is only predicted moderately by bone density, indicating that there are other factors influencing bone competence. However, the relative importance of "bone quantity" and "bone quality" remains poorly understood. The objectives of this article are to describe some of the techniques used to measure the microarchitectural aspects of bone quality, how they can be quantified, and how these quantitative endpoints can be used in the assessment of bone competence. Special focus will be on the distal radius, a site with a high fracture incidence. With the introduction of high-resolution in vivo bone imaging systems, a new generation of imaging instruments has entered the arena allowing the reconstruction of the 3-dimensional microarchitecture of the bones at the wrist, thereby giving researchers and clinicians a powerful tool for the quantitative assessment of bone microstructure. In combination with large-scale finite element modeling, these methodologies have reached a level that it is now becoming possible to assess bone stiffness and strength in humans in a clinical setting. The procedure can help improve predictions of fracture risk, clarify the pathophysiology of skeletal diseases, and monitor the response to therapy.

Whole bone geometry and bone quality in distal forearm fracture

Fracture of the distal radius is a sentinel for future increased risk of other "osteoporotic" fractures, in which the peak age for incidence of distal radius fracture is 5 to 10 years before that for spine and hip fractures. Mean bone mineral density (BMD) of the distal radius was lower in patients with osteoporosis compared with age- and sex-matched normal subjects. However, it has been shown that to predict the strength of the distal radius at the site where fractures occur requires more than measurement of bone mineral content (BMC) or BMD. Only moderate correlations have been found between forearm sites, which may be a result of differences in bone composition between sites. Different forearm sites may be used interchangeably for diagnostic purposes, but the prognostic value is not known. Using the distal radius as a screening tool for identifying individuals at risk of "osteoporotic" fracture shows that forearm site selection and accuracy of measurement can be important confounders in group studies.Improving resolution of computed tomography (CT) scanners has enabled quantitation of cortical bone density and cortical thickness. These measurements have enabled the mechanism of bone loss in the distal radius to be elucidated and show that, after menopause, bone loss is primarily through thinning of the cortex. CT imaging allows the precise localization of bone changes in individuals and should be of value in the assessment of the severity of osteoporosis. It also shows that this technology has the potential to determine the efficacy of therapeutic interventions. A concerted effort has been made to elucidate the interrelationships between the amount of bone and the geometry and that clinical imaging of BMC and/or cross-sectional area in the radius would provide improved prediction of an individual's risk of fracture.The technological tools are available, in the clinic, to accurately measure the 3-dimensional (3D) geometry of the distal radius and the amount of bone. In addition, the cortical and cancellous bone compartments can be analyzed separately. This capability, along with the easy accessibility of the distal radius to clinical imaging modalities, provides an excellent framework for longitudinal prospective studies to determine morphologic risk factors for osteoporotic fractures of the distal radius.

Multiscale modelling of the skeleton for the prediction of the risk of fracture

BACKGROUND

The development of a multiscale model of the human musculoskeletal system able to accurately predict the risk of bone fracture is still a grand challenge. The aim of this paper is to present the Living Human Project, to describe the final system and to review the achievements obtained so far. The Living Human musculoskeletal supermodel is conceived as the interconnection of five interdependent sub-models: the continuum, the boundary condition, the constitutive equation, the remodelling history and the failure criterion sub-models.

METHODS

Methods are available to develop accurate subject-specific finite element models of bones that can incorporate the subject's tissue-density distribution and empirically derived constitutive laws. Anatomo-functional musculoskeletal models can be registered with gait analysis data to predict muscle and joint forces acting on the patient's skeleton during gait. These are the boundary conditions for the continuum models that showed an average error of 12% in the prediction of the failure load. Still, the entire supermodel is defined as a collection of procedural macros to predict the risk of fracture and should be improved.

FINDINGS

Even with these limitations, the organ-level model already found some clinically relevant applications, especially in the analysis of joint prostheses. Also, the body-organ level multiscale model finds some clinical applications in paediatric skeletal oncology. The tissue- and the cell-level models are not yet fully validated. Thus, they cannot be safely used in clinical applications.

INTERPRETATION

The continuum sub-model is the most mature model available. More powerful methods are needed for the generation of anatomo-functional musculoskeletal models. Muscle force prediction should be improved, investigating new probabilistic approaches to identify the neuro-motor strategy. The changes of the tissue properties in the various regions of the skeleton and predictive remodelling models should be included. An adequate information technology infrastructure should be developed to support collaborative work and integration of different sub-models.

Bone strength at the distal radius can be estimated from high-resolution peripheral quantitative computed tomography and the finite element method

Bone strength is a fundamental contributor to fracture risk, and with the recent development of in vivo 3D bone micro-architecture measurements by high-resolution peripheral quantitative computed tomography, the finite element (FE) analysis may provide a means to assess patient bone strength in the distal radius. The purpose of this study was to determine an appropriate FE procedure to estimate bone strength by comparison with experimental data. Models based on a homogeneous tissue modulus or a modulus scaled according to computed tomography attenuation were assessed, and these were solved by linear and non-linear FE analyses to estimate strength. The distal radius from fresh, human cadaver forearms (5 male/5 female, ages 55 to 93) was dissected free and four 9.1 mm sections were cut beginning at the subchondral plate to provide 40 test specimens. The sections were scanned using an in vivo protocol providing 3D image data with an 82 microm voxel size. All specimens were mechanically tested in uniaxial compression, and elastic and yield properties were determined. Linear FE analyses were performed on all specimens (N=40), and non-linear analyses using an asymmetric, bilinear yield strain criteria were performed on a sub-sample (N=10) corresponding to the normal clinical measurement site. Experimentally determined apparent elastic properties correlated highly with ultimate stress (R2=0.977, p<0.05, N=31) for the 31 specimens tested to failure. Subsequently, a linear FE analysis estimating apparent elastic properties also correlated highly with failure, and the correlation was higher when moduli were determined from scaled CT-attenuation values than a homogeneous modulus (R2=0.983 vs. R2=0.972, p<0.05, N=31). A non-linear analysis based on tensile and compressive yield strains of 0.0295 and 0.0493 for homogeneous models, and 0.0127 and 0.0212 for scaled models directly estimated ultimate stress, and correlated highly (R2=0.951 vs. R2=0.937, p<0.05, N=5). The linear relation between stiffness and strength may be unique to radius compressive loading. It supports the use of a linear FE analysis to determine bone strength by regression equations established here. Scaled tissue modulus models performed better than homogeneous modulus models, and the advantage of a scaled model is its potential to account for mineralization changes. The combined numerical-experimental procedure for FE model validation on the patient micro-CT technology demonstrated that bone strength can be estimated non-invasively, and this may provide important insight into fracture risk in patient populations.

Technology insight: noninvasive assessment of bone strength in osteoporosis

Fractures that result from osteoporosis are an enormous and growing concern for public health systems; as the population ages, the number of fractures worldwide will double or triple in the next 50 years. The ability of a bone to resist fracture depends not only on the amount of bone present, but also on the spatial distribution of the bone mass, the cortical and trabecular microarchitecture, and the intrinsic properties of the materials that comprise the bone. Although low bone mineral density is one of the strongest risk factors for fracture, a number of clinical studies have demonstrated the limitations of using measurements of areal bone mineral density by dual-energy X-ray absorptiometry to assess fracture risk and to monitor responses to therapy. As a result, new, noninvasive imaging techniques that are capable of assessing various components of bone strength are being developed. These techniques include three-dimensional assessments of bone density, geometry and microarchitecture, as well as integrated measurements of bone strength by engineering analyses. Although they show strong potential, further development and validation of these techniques is needed to define their role in the clinical management of individuals with osteoporosis.

Smooth surface micro finite element modelling of a cancellous bone analogue material

Tetrahedral finite element meshes with smooth surfaces can be created from computed tomography scans of cancellous bone in order to evaluate its mechanical properties. Image processing before creation of the mesh can affect the accuracy of determined mechanical properties. For a cancellous bone analogue, threshold, mesh density and surface smoothing parameters used in mesh generation were varied and the mechanical properties predicted by the resulting meshes were compared to experimental results. This study has shown that threshold selection is vital for accurate determination of volume fraction and resulting mechanical properties.

Does thoracic or lumbar spine bone architecture predict vertebral failure strength more accurately than density?

Trabecular bone microstructure was studied in 6 mm bone biopsies taken from the 10th thoracic and 2nd lumbar vertebra of 165 human donors and shown to not differ significantly between these sites. Microstructural parameters at the locations examined provided only marginal additional information to quantitative computed tomography in predicting experimental failure strength.

INTRODUCTION

It is unknown whether trabecular microstructure differs between thoracic and lumbar vertebrae and whether it adds significant information in predicting the mechanical strength of vertebrae in combination with QCT-based bone density.

METHODS

Six mm cylindrical biopsies taken at mid-vertebral level, anterior to the center of the thoracic vertebra (T) 10 and the lumbar vertebra (L) 2 were studied with micro-computed tomography (microCT) in 165 donors (age 52 to 99 years). The segment T11-L1 was examined with QCT and tested to failure using a testing machine.

RESULTS

The correlation of microstructural properties was moderate between T10 and L2 (r <or= 0.5). No significant differences were observed in the microstructural properties between the thoracic and lumbar spine, nor were sex differences at T10 or L2 observed. Cortical/subcortical density of T12 (r(2)=48%) was more strongly correlated with vertebral failure stress than trabecular density (r(2)=32%). BV/TV (of T10) improved the prediction by 52% (adjusted r(2)) in a multiple regression model.

CONCLUSION

Microstructural properties of trabecular bone biopsies displayed a high degree of heterogeneity between vertebrae but did not differ significantly between the thoracic and lumbar spine. At the locations examined, bone microstructure only marginally improved the prediction of structural vertebral strength beyond QCT-based bone density.

Improved reproducibility of high-resolution peripheral quantitative computed tomography for measurement of bone quality

A human high-resolution peripheral quantitative computed tomography scanner (HR-pQCT) (XtremeCT, Scanco Medical, Switzerland) capable of measuring three important indicators of bone quality (micro-architectural morphology, mineralization and mechanical stiffness) has been developed. The goal of this study was to evaluate the reproducibility of male and female HR-pQCT in vivo measurements, and elucidate the causes of error in these measurements through a comparison with in vitro measurements. The best possible short-term reproducibility was found using a set of 10 in vitro measurements without repositioning, and a set of 10 with repositioning. Subsequently, in vivo measurements were performed on 15 male and 15 female subjects at baseline and follow-ups of 1 week and 4 months to determine the short- and long-term reproducibility of the system. In addition to the 2D area matching method used in the standard evaluation protocol, a custom developed 3D registration method was used to find the common region between repeated scans. The best possible reproducibility without movement artifacts and repositioning error was less than 0.5%, while the reproducibility with repositioning error was less than 1.5%. The in vivo reproducibility of density (<1%), morphological (<4.5%) and stiffness (<3.5) measurements was consistently poorer than the reproducibility of cadaver measurements, presumably due to small movement artifacts and repositioning errors. Using 3D image registration, repositioning error was reduced on average by 23% and 8% for measurements of the radius and tibia sites, respectively. This study has provided bounds for the reproducibility of HR-pQCT to monitor bone quality longitudinally, and a basis for clinical study design to determine detectable changes.

Finite element analysis based on in vivo HR-pQCT images of the distal radius is associated with wrist fracture in postmenopausal women

BMD, bone microarchitecture, and bone mechanical properties assessed in vivo by finite element analysis were associated with wrist fracture in postmenopausal women.

INTRODUCTION

Many fractures occur in individuals with normal BMD. Assessment of bone mechanical properties by finite element analysis (FEA) may improve identification of those at high risk for fracture.

MATERIALS AND METHODS

We used HR-pQCT to assess volumetric bone density, microarchitecture, and microFE-derived bone mechanical properties at the radius in 33 postmenopausal women with a prior history of fragility wrist fracture and 33 age-matched controls from the OFELY cohort. Radius areal BMD (aBMD) was also measured by DXA. Associations between density, microarchitecture, mechanical parameters and fracture status were evaluated by univariate logistic regression analysis and expressed as ORs (with 95% CIs) per SD change. We also conducted a principal components (PCs) analysis (PCA) to reduce the number of parameters and study their association (OR) with wrist fracture.

RESULTS

Areal and volumetric densities, cortical thickness, trabecular number, and mechanical parameters such as estimated failure load, stiffness, and the proportion of load carried by the trabecular bone at the distal and proximal sites were associated with wrist fracture (p < 0.05). The PCA revealed five independent components that jointly explained 86.2% of the total variability of bone characteristics. The first PC included FE-estimated failure load, areal and volumetric BMD, and cortical thickness, explaining 51% of the variance with an OR for wrist fracture = 2.49 (95% CI, 1.32-4.72). Remaining PCs did not include any density parameters. The second PC included trabecular architecture, explaining 12% of the variance, with an OR = 1.82 (95% CI, 0.94-3.52). The third PC included the proportion of the load carried by cortical versus trabecular bone, assessed by FEA, explaining 9% of the variance, and had an OR = 1.61 (95% CI, 0.94-2.77). Thus, the proportion of load carried by cortical versus trabecular bone seems to be associated with wrist fracture independently of BMD and microarchitecture (included in the first and second PC, respectively).

CONCLUSIONS

These results suggest that bone mechanical properties assessed by microFE may provide information about skeletal fragility and fracture risk not assessed by BMD or architecture measurements alone and are therefore likely to enhance the prediction of wrist fracture risk.

Advanced imaging of bone macrostructure and microstructure in bone fragility and fracture repair

Research into the molecular and cellular pathways focusing on bone fragility and fracture-healing has led to new potential treatments to aid in fracture-healing. This research has focused on physical as well as biological modes of treatment. As new products and methods are derived, it is essential to develop effective and sensitive noninvasive means by which early changes in the fracture repair process can be detected. Specialized noninvasive and/or nondestructive techniques can provide structural information about local and systemic skeletal health, the propensity to fracture, and the pathophysiology of bone fragility. The methods available to quantitatively assess macrostructure include computed tomography and, particularly, volumetric quantitative computed tomography. Methods for assessing microstructure of trabecular bone include high-resolution computed tomography, microquantitative computed tomography, high-resolution magnetic resonance imaging, and micromagnetic resonance imaging. These new techniques help to illustrate the process of fracture-healing by defining the skeletal response to innovative therapies and assessing biomechanical relationships. This review presents perspectives on the advanced imaging modalities that are currently available and on recent developments that may improve the detection and understanding of bone fragility and fracture-healing.

Load distribution in the healthy and osteoporotic human proximal femur during a fall to the side

Due to remodeling of bone architecture, an optimal structure is created that minimizes bone mass and maximizes strength. In the case of osteoporotic vertebral bodies, however, this process can create over-adaptation, making them vulnerable for non-habitual loads. In a recent study, micro-finite element models of a healthy and an osteoporotic human proximal femur were analyzed for the stance phase of gait. In the present study, tissue stresses and strains were calculated with the same proximal femur micro-finite element models for a simulated fall to the side onto the greater trochanter. Our specific objectives were to determine the contribution of trabecular bone to the strength of the proximal femurs for this non-habitual load. Further, we tested the hypothesis that the trabecular structure of osteoporotic bone is over-adapted to habitual loads. For that purpose, we calculated the load distributions and estimated the apparent yield and ultimate loads from linear analyses. Two different methods were used for this purpose, which resulted in very similar values, all in a realistic range. Distributions of maximal principal strain and effective strain in the entire model suggest that the contributions to bone strength of the trabecular and cortical structures are similar. However, a thick cortical shell is preferred over a dense trabecular core in the femoral neck. When the load applied to the osteoporotic femur was reduced to approximately 61% of the original value, strain distributions were created similar in value to those obtained for the healthy femur. Since a comparable reduction factor was found for habitual load cases, it was concluded that the osteoporotic femur was not 'over-adapted'.

Effects of intracortical porosity on fracture toughness in aging human bone: a microCT-based cohesive finite element study

The extent to which increased intracortical porosity affects the fracture properties of aging and osteoporotic bone is unknown. Here, we report the development and application of a microcomputed tomography based finite element approach that allows determining the effects of intracortical porosity on bone fracture by blocking all other age-related changes in bone. Previously tested compact tension specimens from human tibiae were scanned using microcomputed tomography and converted to finite element meshes containing three-dimensional cohesive finite elements in the direction of the crack growth. Simulations were run incorporating age-related increase in intracortical porosity but keeping cohesive parameters representing other age-related effects constant. Additional simulations were performed with reduced cohesive parameters. The results showed a 6% decrease in initiation toughness and a 62% decrease in propagation toughness with a 4% increase in porosity. The reduction in toughnesses became even more pronounced when other age-related effects in addition to porosity were introduced. The initiation and propagation toughness decreased by 51% and 83%, respectively, with the combined effect of 4% increase in porosity and decrease in the cohesive properties reflecting other age-related changes in bone. These results show that intracortical porosity is a significant contributor to the fracture toughness of the cortical bone and that the combination of computational modeling with advanced imaging improves the prediction of the fracture properties of the aged and the osteoporotic cortical bone.

Noninvasive assessments of bone strength

PURPOSE OF REVIEW

Description of new noninvasive technologies or modifications of existing technologies with which individual components of bone strength and bone strength as a whole can be quantified.

RECENT FINDINGS

Although bone mineral density has served as an able surrogate for bone strength, it is clear that aspects of bone strength are either not captured or are not discernible within the measurement of bone density. New, noninvasive technologies have been developed to quantify aspects of bone strength such as biomechanical parameters based on geometry and scale and topological parameters of microarchitecture. Finite element modeling utilizes sophisticated mathematical approaches to predict the strength of the whole bone. At present, most of these technologies remain beyond the reach of clinicians, with the exception of hip structural or strength analysis.

SUMMARY

Hip strength or structural analysis is widely available because of its incorporation with dual energy X-ray absorptiometry and has been extensively used in clinical research. None of these new approaches has been shown to be superior to the measurement of bone density in the prediction of fracture risk. This fact does not diminish their potential to enhance the understanding of the pathophysiology of fracture and the mechanisms of therapeutic efficacy.

The effects of geometric and threshold definitions on cortical bone metrics assessed by in vivo high-resolution peripheral quantitative computed tomography

This study evaluates in vivo methods for calculating cortical thickness (Ct.Th) with respect to sensitivity to tissue-level changes in mineralization and the ability to predict whole-bone mechanical properties. Distal radial and tibial images obtained from normal volunteers using high-resolution peripheral quantitative computed tomography (HR-pQCT) were segmented using three thresholds including the manufacturer default and +/-5% in terms of equivalent mineral density. Ct.Th was determined in two ways: using a direct three-dimensional (3D) method and using an annular method, where cortical bone volume is divided by periosteal surface area. D(comp) (mg HA/cm(3)) was calculated based on the mean density-calibrated linear attenuation values of the cortical compartment. Finite element analysis was performed to evaluate the predictive ability of the annular and direct Ct.Th methods. Using the direct 3D method, a +/-5% change in threshold resulted in a 2% mean difference in Ct.Th for both the radius and tibia. An average difference of 5% was found using the annular method. The change in threshold produced changes in D(comp) ranging 0.50-1.56% for both the tibia and radius. Annular Ct.Th correlated more strongly with whole-bone apparent modulus (R(2)=0.64 vs. R(2)=0.41). Both thickness calculation methods and threshold selection have a direct impact on cortical parameters derived from HR-pQCT images. Indirectly, these results suggest that moderate changes in tissue-level mineralization can affect cortical measures. Furthermore, while the direct 3D Ct.Th method is less sensitive to threshold effects, both methods are moderate predictors of mechanical strength, with the annular method being the stronger correlate.

Contribution of in vivo structural measurements and load/strength ratios to the determination of forearm fracture risk in postmenopausal women

Bone structure, strength and load-strength ratios contribute to forearm fracture risk independently of areal BMD.

INTRODUCTION

Technological and conceptual advances provide new opportunities for evaluating the contribution of bone density, structure, and strength to the pathogenesis of distal forearm fractures.

MATERIALS AND METHODS

From an age-sratified random sample of Rochester, MN, women, we compared 18 with a distal forearm fracture (cases) to 18 age-matched women with no osteoporotic fracture (controls). High-resolution pQCT was used to assess volumetric BMD (vBMD), geometry, and microstructure at the ultradistal radius, the site of Colles' fractures. Failure loads in the radius were estimated from microfinite element (microFE) models derived from pQCT. Differences between case and control women were assessed, and the risk of fracture associated with each variable was estimated by logistic regression analysis.

RESULTS

Given similar heights, estimated loading in a fall on the outstretched arm was the same in cases and control. However, women with forearm fractures had inferior vBMD, geometry, microstructure, and estimated bone strength. Relative risks for the strongest determinant of fracture in each of the five main variable categories were as follows: BMD (total vBMD: OR per SD change, 4.2; 95% CI, 1.4-12), geometry (cortical thickness: OR, 4.0; 95% CI, 1.4-11), microstructure (trabecular number: OR, 2.3; 95% CI, 1.02-5.1), and strength (axial rigidity: OR, 3.8; 95% CI, 1.4-10); the factor-of-risk (fall load/microFE failure load) was 24 % greater (worse) in cases (OR, 3.0; 95% CI, 1.2-7.5). Areas under ROC curves ranged from 0.72 to 0.82 for these parameters.

CONCLUSIONS

Bone geometry, microstructure, and strength contribute to forearm fractures, as does BMD, and these additional determinants of risk promise greater insights into fracture pathogenesis.

Load distribution and the predictive power of morphological indices in the distal radius and tibia by high resolution peripheral quantitative computed tomography

A 3D high resolution peripheral quantitative computed tomography scanner (HR-pQCT) (XtremeCT, Scanco Medical, voxel size 82 microm) has been recently developed that can perform in vivo human measurements on peripheral sites, including the wrist and tibia. The goals of this study were to use HR-pQCT measurements to determine the ability of morphological and density measurements to predict bone apparent stiffness and apparent Young's modulus in the distal radius and tibia, to determine the relative importance of cortical and trabecular bone in carrying load in the human distal radius and tibia. Furthermore, the ability of a sub-volume of trabecular bone apparent Young's modulus to predict the Young's modulus of a whole radius and tibia section was determined. A total of 25 measurements of the radius and 12 measurements of the tibia were used for morphological and finite element analyses of sections, and sub-volume cubes of trabecular bone from the distal radius and tibia. The subjects were chosen to obtain a large variation in age ranges and bone architecture and density. By combining multiple measurements, a strong ability to predict bone apparent stiffness and apparent Young's modulus was found for morphological and density measurements in the radius and tibia (R(2)>0.80). The relative importance of the trabecular and cortical bone in carrying load was also found to vary consistently with location in the sample for both the radius and the tibia. This indicates that measurements of the cortical and trabecular bone are required for assessing fracture risk. A cubic section of trabecular bone was found to be insufficient to accurately represent the apparent bone Young's modulus of a radius or tibia section. Morphological and density measurements of the distal radius and tibia have been shown in this study to predict bone apparent Young's modulus and apparent stiffness, and may indicate when a more time consuming finite element analysis is warranted. It should be noted that these results may be an overestimation of the predictive ability of structural parameters, as the influence of bone density is removed from the finite element analyses, and the results were only influenced by bone structure. A measurement of bone apparent Young's modulus is independent of subject size (as opposed to reaction force), and may provide the ability to distinguish between two patients that have similar mean morphological and density measurements; but different overall structures, and therefore, different fracture risk.

The influence of wire positioning upon the initial stability of scaphoid fractures fixed using Kirschner wires

A finite element model of the carpal scaphoid and its joints was developed to study how wire positioning affects the initial stability of the fixation of scaphoid waist fractures using Kirschner wires. A transverse fracture of the scaphoid waist was simulated along with its fixation using five different two-wire configurations. The resulting models were subjected to a load simulating a 200N force passing through the wrist. Friction between bony fragments was taken into account; as the friction coefficient of cancellous bone is unknown, three different values were analysed. For each of these friction coefficient values, the smallest transverse interfragmentary displacements, and consequently maximum initial stability, were obtained for the model that simulated the maximum gap between wires in the plane of fracture. Results also show that for a similar gap in the plane of fracture, more stable fixation can be achieved when wires cross each other not only in the frontal plane of the hand, but also perpendicularly to it.

A local adaptive threshold strategy for high resolution peripheral quantitative computed tomography of trabecular bone

High resolution peripheral quantitative computed tomography (HR-pQCT) is a promising method for detailed in vivo 3D characterization of the densitometric, geometric, and microstructural features of human bone. Currently, a hybrid densitometric, direct, and plate model-based calculation is used to quantify trabecular microstructure. In the present study, this legacy methodology is compared to direct methods derived from a new local thresholding scheme independent of densitometric and model assumptions. Human femoral trabecular bone samples were acquired from patients undergoing hip replacement surgery. HR-pQCT (82 microm isotropic voxels) and micro-tomography (16 microm isotropic voxels) images were acquired. HR-pQCT images were segmented and analyzed in three ways: (1) using the hybrid method provided by the manufacturer based on a fixed global threshold, (2) using direct 3D methods based on the fixed global threshold segmentation, and (3) using direct 3D methods based on a novel local threshold scheme. The results were compared against standard direct 3D indices from microCT analysis. Standard trabecular parameters determined by HR-pQCT correlated strongly to microCT. BV/TV and Tb.Th were significantly underestimated by the hybrid method and significantly overestimated by direct methods based on the global threshold segmentation while the local method yielded optimal intermediate results. The direct-local method also performed favorably for Tb.N (R(2) = 0.85 vs. R(2) = 0.70 for direct-global method) and Tb.Sp (R(2) = 0.93 vs. R(2) = 0.85 for the hybrid method and R(2) = 0.87 for the direct-global method). These results indicate that direct methods, with the aid of advanced segmentation techniques, may yield equivalent or improved accuracy for quantification of trabecular bone microstructure without relying on densitometric or model assumptions.

The Influence of Mineralization on Intratrabecular Stress and Strain Distribution in Developing Trabecular Bone

The load-transfer pathway in trabecular bone is largely determined by its architecture. However, the influence of variations in mineralization is not known. The goal of this study was to examine the influence of inhomogeneously distributed degrees of mineralization (DMB) on intratrabecular stresses and strains. Cubic mandibular condylar bone specimens from fetal and newborn pigs were used. Finite element models were constructed, in which the element tissue moduli were scaled to the local DMB. Disregarding the observed distribution of mineralization was associated with an overestimation of average equivalent strain and underestimation of von Mises equivalent stress. From the surface of trabecular elements towards their core the strain decreased irrespective of tissue stiffness distribution. This indicates that the trabecular elements were bent during the compression experiment. Inhomogeneously distributed tissue stiffness resulted in a low stress at the surface that increased towards the core. In contrast, disregarding this tissue stiffness distribution resulted in high stress at the surface which decreased towards the core. It was concluded that the increased DMB, together with concurring alterations in architecture, during development leads to a structure which is able to resist increasing loads without an increase in average deformation, which may lead to damage.

Establishment of an architecture-specific experimental validation approach for finite element modeling of bone by rapid prototyping and high resolution computed tomography

A new experimental validation method for assessing the accuracy of large-scale finite element (FE) models of bone micro-structure at the apparent and tissue level was developed. Augmented scaled bone replicas were built using rapid prototype machines based on micro-computed tomography (micro-CT) data. The geometric accuracy of the model was evaluated by comparing experimental tests with the replicas to the FE solution based on the same micro-CT data. A new version of the large-scale FE solver was developed to incorporate orthotropic material properties, hence the experimentally determined properties of the rapid prototype material were input into the FE models. The modified FE solver predicted the experimental apparent level stiffness within less than 1%, and the difference between experimental strain gauge measurements and FE-calculated surface stresses was 7% and 49% on a flat and curved surface region, respectively. While absolute error estimates of surface stresses were limited due to strain gauge errors, the relatively larger difference on the curved surface is indicative of the limitations of a hexahedron FE model for representing such geometries. Although the validation approach is applied here for hexahedron based meshes, the method is flexible for varying bone architectures and will be important for validation of future large-scale FE modeling developments that utilize techniques such as mesh smoothing and tetrahedron elements.

Off-axis loads cause failure of the distal radius at lower magnitudes than axial loads: a finite element analysis

Distal radius (Colles') fractures are a common fall-related injury in older adults and frequently result in long-term pain and reduced ability to perform activities of daily living. Because the occurrence of a fracture during a fall depends on both the strength of the bone and upon the kinematics and kinetics of the impact itself, we sought to understand how changes in bone mineral density (BMD) and loading direction affect the fracture strength and fracture initiation location in the distal radius. A three-dimensional finite element model of the radius, scaphoid, and lunate was used to examine changes of +/-2% and +/-4% BMD, and both axial and physiologically relevant off-axis loads on the radius. Changes in BMD resulted in similar percent changes in fracture strength. However, modifying the applied load to include dorsal and lateral components (assuming a dorsal view of the wrist, rather than an anatomic view) resulted in a 47% decrease in fracture strength (axial failure load: 2752N, off-axis: 1448N). Loading direction also influenced the fracture initiation site. Axially loaded radii failed on the medial surface immediately proximal to the styloid process. In contrast, off-axis loads, containing dorsal and lateral components, caused failure on the dorsal-lateral surface. Because the radius appears to be very sensitive to loading direction, the results suggest that much of the variability in fracture strength seen in cadaver studies may be attributed to varying boundary conditions. The results further suggest that interventions focused on reducing the incidence of Colles' fractures when falls onto the upper extremities are unavoidable may benefit from increasing the extent to which the radius is loaded along its axis.

Accuracy of high-resolution peripheral quantitative computed tomography for measurement of bone quality

The introduction of three-dimensional high-resolution peripheral in vivo quantitative computed tomography (HR-pQCT) (XtremeCT, Scanco Medical, Switzerland; voxel size 82 microm) provides a new approach to monitor micro-architectural bone changes longitudinally. The accuracy of HR-pQCT for three important determinants of bone quality, including bone mineral density (BMD), architectural measurements and bone mechanics, was determined through a comparison with micro-computed tomography (microCT) and dual energy X-ray absorptiometry (DXA). Forty measurements from 10 cadaver radii with low bone mass were scanned using the three modalities, and image registration was used for 3D data to ensure identical regions were analyzed. The areal BMD of DXA correlated well with volumetric BMD by HR-pQCT despite differences in dimensionality (R(2) = 0.69), and the correlation improved when non-dimensional bone mineral content was assessed (R(2) = 0.80). Morphological parameters measured by HR-pQCT in a standard patient analysis, including bone volume ratio, trabecular number, derived trabecular thickness, derived trabecular separation, and cortical thickness correlated well with muCT measures (R(2) = 0.59-0.96). Additionally, some non-metric parameters such as connectivity density (R(2) = 0.90) performed well. The mechanical stiffness assessed by finite element analysis of HR-pQCT images was generally higher than for microCT data due to resolution differences, and correlated well at the continuum level (R(2) = 0.73). The validation here of HR-pQCT against gold-standards microCT and DXA provides insight into the accuracy of the system, and suggests that in addition to the standard patient protocol, additional indices of bone quality including connectivity density and mechanical stiffness may be appropriate to include as part of a standard patient analysis for clinical monitoring of bone quality.

Intrinsic mechanical properties of trabecular calcaneus determined by finite-element models using 3D synchrotron microtomography

To determine intrinsic mechanical properties (elastic and failure) of trabecular calcaneus bone, chosen as a good predictor of hip fracture, we looked for the influence of image's size on a numerical simulation. One cubic sample of cancellous bone (9 x 9 x 9 mm(3)) was removed from the body of the calcaneus (6 females, 6 males, 79+/-9 yr). These samples were tested under compressive loading. Before compressive testing, these samples were imaged at 10.13 microm resolution using a 3D microcomputed tomography (muCT) (ESRF, France). The muCT images were converted to finite-element models. Depending on the bone density values (BV/TV), we compared two different finite element models: a linear hexahedral and a linear beam finite element models. Apparent experimental Young's modulus (E(app)(exp)) and maximum apparent experimental compressive stress (sigma(max)(exp)) were significantly correlated with bone density obtained by Archimedes's test (E(app)(exp)=236+/-231 MPa [19-742 MPa], sigma(max)(exp)=2.61+/-1.97 MPa [0.28-5.81 MPa], r>0.80, p<0.001). Under threshold at 40 microm, the size of the numerical samples (5.18(3) and 6.68(3)mm(3)) seems to be an important parameter on the accuracy of the results. The numerical trabecular Young's modulus was widely higher (E(trabecular)(num)=34,182+/-22,830 MPa [9700-87,211 MPa]) for the larger numerical samples and high BV/TV than those found classically by other techniques (4700-15,000 MPa). For rod-like bone samples (BV/TV<12%, n=7), Young's modulus, using linear beam element (E(trabecular)(num-skeleton): 10,305+/-5500 MPa), were closer to the Young's modulus found by other techniques. Those results show the limitation of hexahedral finite elements at 40 microm, mostly used, for thin trabecular structures.

Variations in mineralization affect the stress and strain distributions in cortical and trabecular bone

The mechanical properties of bone depend largely on its degree and distribution of mineralization. The present study analyzes the effect of an inhomogeneous distribution of mineralization on the stress and strain distributions in the human mandibular condyle during static clenching. A condyle was scanned with a micro-CT scanner to create a finite element model. For every voxel the degree of mineralization (DMB) was determined from the micro-CT scan. The Young's moduli of the elements were calculated from the DMB using constant, linear, and cubic relations, respectively. Stresses, strains, and displacements in cortical and trabecular bone, as well as the condylar deformation (extension along the antero-posterion axis) and compliance were compared. Over 90% of the bone mineral was located in the cortical bone. The DMB showed large variations in both cortical bone (mean: 884, SD: 111 mg/cm(3)) and trabecular bone (mean: 738, SD: 101 mg/cm(3)). Variations of the stresses and the strains were small in cortical bone, but large in trabecular bone. In the cortical bone an inhomogeneous mineral distribution increased the stresses and the strains. In the trabecular bone, however, it decreased the stresses and increased the strains. Furthermore, the condylar compliance remained relatively constant, but the condylar deformation doubled. It was concluded that neglect of the inhomogeneity of the mineral distribution results in a large underestimation of the stresses and strains of possibly more than 50%. The stiffness of trabecular bone strongly influences the condylar deformation. Vice versa, the condylar deformation largely determines the magnitude of the strains in the trabecular bone.

Severity of vertebral fracture reflects deterioration of bone microarchitecture

INTRODUCTION

Bone microarchitecture, a component of bone strength, is generally measured on transiliac bone biopsy samples. The objective of this study was to determine whether assessment of four grades of vertebral fracture severity could serve as a noninvasive surrogate marker for trabecular bone volume and microarchitecture.

METHODS

Baseline vertebral fracture severity was determined by semiquantitative assessment of spine radiographs from 190 postmenopausal women with osteoporosis. Bone-structure indices were obtained by 2D histomorphometry and 3D microcomputed tomography (CT) analyses. Significance of differences was determined after adjusting for age, height, and lumbar spine bone mineral density.

RESULTS

There were significant (P < 0.05) trends in decreasing bone volume, trabecular number, and connectivity, and increasing trabecular separation with greater vertebral fracture severity. Histomorphometric bone volume was 25 and 36% lower (P < 0.05) in women with moderate and severe fractures than in women with no fractures, respectively. Compared with women without fractures, women with mild, moderate, and severe fractures had lower (P < 0.05) microCT bone volume (23, 30, and 51%, respectively).

CONCLUSIONS

Microarchitectural deterioration was progressively worse in women with increasing severity of vertebral fractures. We conclude that assessment of vertebral fracture severity is an important clinical tool to evaluate the severity of postmenopausal osteoporosis.

Specimen-specific beam models for fast and accurate prediction of human trabecular bone mechanical properties

Direct assessment of bone competence in vivo is not possible, hence, it is inevitable to predict it using appropriate simulation techniques. Although accurate estimates of bone competence can be obtained from micro-finite element models (muFE), it is at the expense of large computer efforts. In this study, we investigated the application of structural idealizations to represent individual trabeculae by single elements. The objective was to implement and validate this technique. We scanned 42 human vertebral bone samples (10 mm height, 8 mm diameter) with micro-computed tomography using a 20 microm resolution. After scanning, direct mechanical testing was performed. Topological classification and dilation-based algorithms were used to identify individual rods and plates. Two FE models were created for each specimen. In the first one, each rod-like trabecula was modeled with one thickness-matched beam; each plate-like trabecula was modeled with several beams. From a simulated compression test, assuming one isotropic tissue modulus for all elements, the apparent stiffness was calculated. After reducing the voxel size to 40 microm, a second FE model was created using a standard voxel conversion technique. Again, one tissue modulus was assumed for all elements in all models, and a compression test was simulated. Bone volume fraction ranged from 3.7% to 19.5%; Young's moduli from 43 MPa to 649 MPa. Both models predicted measured apparent moduli equally well (R2 = 0.85), and were in excellent agreement with each other (R2 = 0.97). Tissue modulus was estimated at 9.0 GPa and 10.7 GPa for the beam FE and voxel FE models, respectively. On average, the beam models were solved in 219 s, reducing CPU usage up to 1150-fold as compared to 40 microm voxel FE models. Relative to 20 microm voxel models 10,000-fold reductions can be expected. The presented beam FE model is an abstraction of the intricate real trabecular structure using simple cylindrical beam elements. Nevertheless, it enabled an accurate prediction of global mechanical properties of microstructural bone. The strong reduction in CPU time provides the means to increase throughput, to analyze multiple loading configuration and to increase sample size, without increasing computational costs. With upcoming in vivo high-resolution imaging systems, this model has the potential to become a standard for mechanical characterization of bone.

Effect of specimen conditioning on the microarchitectural parameters of trabecular bone assessed by micro-computed tomography

The best way to preserve the mechanical properties of bone specimens is hydration in NaCl, whereas the reference process in microCT analysis is defatting. However, for finite element modelling (FEM) it is necessary to use the same bone specimens for biomechanical testing and 3D imaging. This study aimed to evaluate the effect of sample conditioning on trabecular bone microarchitectural parameters. Trabecular bones were analysed by microCT under three successive conditions: first, the fatted samples were analysed immersed in NaCl (process N); second, they were hydrated for 24 h then imaged without immersion (process H); third, the samples were defatted before analysis (process D). The microarchitectural parameters bone volume/tissue volume (BV/TV), trabecular spacing (Tb.Sp), number (Tb.N) and thickness (Tb.Th) were calculated. Except for BV/TV, there was no significant difference between the processes N and D. In process H, BV/TV, Tb.Th and Tb.N were higher and BS/BV and Tb.Sp were lower than in process D. Results showed that the process D may be replaced by the process N. The process H induced significant differences in microarchitectural parameters when compared to process D. Nevertheless, this sample conditioning should be used to develop FEM when microCT images are to be acquired during compressive testing.

Advanced Imaging Assessment of Bone Quality

Noninvasive and/or nondestructive techniques can provide structural information about bone, beyond simple bone densitometry. While the latter provides important information about osteoporotic fracture risk, many studies indicate that bone mineral density (BMD) only partly explains bone strength. Quantitative assessment of macrostructural characteristics, such as geometry, and microstructural features, such as relative trabecular volume, trabecular spacing, and connectivity, may improve our ability to estimate bone strength. Methods for quantitatively assessing macrostructure include (besides conventional radiographs) dual X ray absorptiometry (DXA) and computed tomography (CT), particularly volumetric quantitative computed tomography (vQCT). Methods for assessing microstructure of trabecular bone noninvasively and/or nondestructively include high-resolution computed tomography (hrCT), microcomputed tomography (micro-CT), high-resolution magnetic resonance (hrMR), and micromagnetic resonance (micro-MR). vQCT, hrCT, and hrMR are generally applicable in vivo; micro-CT and micro-MR are principally applicable in vitro. Despite progress, problems remain. The important balances between spatial resolution and sampling size, or between signal-to-noise and radiation dose or acquisition time, need further consideration, as do the complexity and expense of the methods versus their availability and accessibility. Clinically, the challenges for bone imaging include balancing the advantages of simple bone densitometry versus the more complex architectural features of bone, or the deeper research requirements versus the broader clinical needs. The biological differences between the peripheral appendicular skeleton and the central axial skeleton must be further addressed. Finally, the relative merits of these sophisticated imaging techniques must be weighed with respect to their applications as diagnostic procedures, requiring high accuracy or reliability, versus their monitoring applications, requiring high precision or reproducibility.

Population-based analysis of the relationship of whole bone strength indices and fall-related loads to age- and sex-specific patterns of hip and wrist fractures

In an age- and sex-stratified population sample (n = 700), we estimated fall-related loads and bone strength indices at the UDR and FN. These load/strength ratios more closely simulated patterns of wrist and hip fractures occurring in the same population than did measurement of vBMD.

INTRODUCTION

Areal BMD measurements, although associated with fracture risk, incompletely explain patterns of fragility fractures. Moreover, population-based assessments relating applied loads and whole bone strength to fracture patterns have not been made.

MATERIALS AND METHODS

Using QCT, we assessed volumetric BMD (vBMD), cross-sectional geometry, and axial (EA) and flexural (EI) rigidities (indices of bone's resistance to compressive and bending loads, respectively) at the ultradistal radius (UDR) and femoral neck (FN) and estimated the loads applied to the wrist and hip during a fall. We used fall load (FL)/bone strength ratios to estimate fracture risk.

RESULTS

vBMD in young adults was similar between sexes. Decreases in vBMD over life were also similar (30% and 28%) at UDR but were somewhat greater (46% and 34%) at FN in women versus men, respectively. In young adults, FL/strength ratios at UDR were 32-51% lower (better) in men than in women and increased (worsened) over life less in men (+4% to +22%) than in women (+20% to +33%). In young adults, FL/strength ratios at FN were only marginally better in men than in women but worsened less over life in men (+22% to +36%) than in women (+40% to +62%).

CONCLUSIONS

The 6:1 female preponderance and the virtual immunity of men for age-related increases in wrist fractures are largely explained by the more favorable FL/strength ratios at UDR in young adult men (because of larger bone size and more favorable geometry) versus women and to maintaining this advantage over life. The 2-fold lower incidence of hip fractures in men versus women is largely explained by age-related increases (worsening) of FL/bone strength ratios that are only one-half of the increases in women. The moderate increases in these ratios with aging are insufficient to explain the >4-fold increase in hip fracture incidence after age 75 in both sexes, suggesting contributions of other factors, especially the well-documented increased frequency of injurious falls among the elderly.

Smooth surface meshing for automated finite element model generation from 3D image data

Finite element (FE) modelling based on data from three-dimensional high-resolution computed tomography (CT) imaging systems provides a non-invasive method to assess structural mechanics. Automated mesh generation from these voxel based image data can be achieved by direct conversion to hexahedron elements, however these model representations have jagged edges. This paper proposes an automated method to generate smoothed FE meshes from voxel-based image data. Mesh fairing processes are utilized that allow constraints that control the smoothing process, and are computationally efficient. Surfaces of the mesh on the exterior, as well as interfaces between two tissues, can be smoothed by varying fairing parameters and constraint criteria. The method was tested on a variety of real and simulated three-dimensional data sets, resulting in both hexahedron and tetrahedron meshes. It was shown that the fairing process is linearly related to the number of smoothing iterations, and that peak stresses are reduced in FE simulations of the smoothed models. Although developed for micro-CT data sets, this fast and reliable mesh smoothing method could be applied to any three-dimensional image data where node and element connectivity have been defined.

Comparison of micro-level and continuum-level voxel models of the proximal femur

Continuum-level finite element (FE) models became standard computational tools for the evaluation of bone mechanical behavior from in vivo computed tomography scans. Such scans do not account for the anisotropy of the bone. Instead, local mechanical properties in the continuum-level FE models are assumed isotropic and are derived from bone density, using statistical relationships. Micro-FE models, on the other hand, incorporate the anisotropic structure in detail. This study aimed to quantify the effects of assumed isotropy, by comparing continuum-level voxel models of a healthy and a severely osteoporotic proximal femur with recently analyzed micro-FE models of the same bones. The micro-model element size was coarsened to generate continuum FE models with two different element sizes (0.64 and 3.04 mm) and two different density-modulus relationships found in the literature for wet and ash density. All FE models were subjected to the same boundary conditions that simulated a fall to the side, and the stress and strain distributions, model stiffness and yield load were compared. The results indicated that the stress and strain distributions could be reproduced well with the continuum models. The smallest differences between the continuum-level model and micro-level model predictions of the stiffness and yield load were obtained with the coarsest element size. Better results were obtained for both continuum-element sizes when isotropic moduli were based on ash density rather than wet density.

Computational biomechanical modelling of the lumbar spine using marching-cubes surface smoothened finite element voxel meshing

There is a need for the development of finite element (FE) models based on medical datasets, such as magnetic resonance imaging and computerized tomography in computation biomechanics. Direct conversion of graphic voxels to FE elements is a commonly used method for the generation of FE models. However, conventional voxel-based methods tend to produce models with jagged surfaces. This is a consequence of the inherent characteristics of voxel elements; such a model is unable to capture the geometries of anatomical structures satisfactorily. We have developed a robust technique for the automatic generation of voxel-based patient-specific FE models. Our approach features a novel tetrahedronization scheme that incorporates marching-cubes surface smoothing together with a smooth-distortion factor (SDF). The models conform to the actual geometries of anatomical structures of a lumbar spine segment (L3). The resultant finite element analysis (FEA) at the surfaces is more accurate compared to the use of conventional voxel-based generated FE models. In general, models produced by our method were superior compared to that obtained using the commercial software ScanFE.