Introduction

For several decades, areal bone mineral density (aBMD) has been the gold standard to assess fracture risk. Areal BMD as measured by dual X-ray absorptiometry (DXA) is the basis of the WHO operational definition of osteoporosis and is widely used to monitor age- and treatment-related changes. In vitro, there is a high correlation between aBMD [or vBMD as measured by quantitative computed tomography (QCT)] and bone strength as determined by mechanical testing with r 2 values between 0.6 and 0.8 [1–9]. However, the number of patients at risk needed to treat (NNT) to avoid one hip fracture is still about 30–70 [10, 11] with lower NNTs being reported for the spine [12–15]. Of course, there are many other risk factors in addition to BMD but eventually a bone fractures because it cannot sustain the external loads acting upon it. Therefore, a direct measurement of bone strength seems to be preferable to the measurement of densitometric parameters such as BMD.

So far, in vivo, a direct measurement of bone strength is not possible; however, strength can be estimated using the finite element (FE) method, which is routinely used in mechanical engineering to calculate strength of complex structures under the action of external forces. During recent years, in vivo finite element analysis (FEA) applied to computed tomography (CT) scans has developed into a mature application to estimate bone strength of the hip, spine and distal radius. This was acknowledged by 2015 consensus positions of the International Society of Clinical Densitometry (ISCD) [16], which state that bone strength as estimated by FEA can be used for fracture prediction in postmenopausal women and elderly men and that the FE technique can also be used for monitoring of age- or treatment-related strength changes in the elderly population. The ISCD positions apply to FEA of spine and hip CT scans taken from whole-body clinical CT scanners. For CT scans of the forearm, typically dedicated high-resolution peripheral CT devices are used. State of the art of this approach and its related FE techniques were recently summarized in a review on FEA of the forearm [17].

Despite the advances in FE technology, all recent reviews [16–20] showed that currently the improvement in fracture prediction using strength-related variables instead of BMD is modest at best with the largest advantage being demonstrated in the spine. From a clinical perspective the use of FEA may still be questioned. Thus, this review will primarily address the question: What are benefits and limitations for a more widespread use of FEA in clinical practice? The recent exhaustive literature reviews of FE techniques [16–20] will serve as references but will not be repeated here. Nevertheless, a basic understanding of the FE technique is necessary for an adequate interpretation of the clinical results. In particular, there are different flavors of FEA, which affect clinical outcome, and an appreciation of their respective strengths and limitations is key for an assessment of the clinical value of FEA.

FE Technology

Basics

The main idea of FEA is to reduce a complicated mechanical problem, in this case the calculation of strength of a complex structure such as bone, to a set of algebraic equations. Specifically, a bone is divided into a number of small finite elements of a simple geometry for which deformations, stresses or even failure can be calculated easily. For this purpose, material properties of each of the elements need to be known. Under the requirement of an equilibrium of forces and moments for every element and the definition of these material properties, the mechanical response of a whole bone subjected to external forces can be calculated.

An engineering analog for the trabecular architecture of the vertebra is an old-fashioned steel bridge. External forces applied to the bridge, for example by the weight of a truck, cause elastic, reversible deformations of the steel bars such as bending and small changes in length. An increase in external forces eventually causes irreversible deformations and cracks that ultimately cause the failure of the bridge or the fracture of the bone. The analogy between the bridge and the trabecular structure presumes that the spatial resolution of the imaging technique is high enough to separate the individual trabeculae, so that the mesh of the finite elements represents the trabecular structure.

In this case, we talk of µFE. Typical applications are the investigation of trabecular bone samples imaged with µCT with spatial resolutions below approximately 40 µm. As discussed further below, µFE analysis can be applied in vivo at the distal forearm or tibia. In contrast, in the spine and hip, the spatial resolution achievable with whole-body clinical CT scanners is only around 0.5 mm and the segmentation of individual trabeculae is no longer possible. Instead, the measured CT values are calibrated to BMD; in essence, quantitative CT (QCT) is the basis of FEA at the spine and hip. These are the so-called homogenized FE models. A mesh is applied to the entire vertebral body or hip resulting in individual elements with a size in the millimeter range containing mineralized bone as well as bone marrow. The term homogenization denotes the averaging process used in determining the apparent material properties of the bone–marrow mixture, which are essential input parameters for FE analysis.

The outcome parameters of FEA are the same structural properties as the ones retrieved in biomechanical tests using cadaveric bones. The application of an external load to the bone causes a displacement at that location, and the progressions of these two variables in time produce a load–displacement curve (Fig. 1). The slope of the initial linear part of this curve, i.e., of the range of the elastic deformation is termed stiffness. The ultimate or failure load is the maximal load attained before the bone breaks. The energy to failure is the area under the curve. This load–displacement curve can also be simulated with FEA. The linear part of the curve, i.e., stiffness, can be obtained with linear FEA, while simulation of the yielding of the curve, the maximal force and the energy to failure requires nonlinear FEA. For in vivo measurements, estimated failure load reported typically in kN is the most widely used parameter and is often reported as bone strength not to be confused with ultimate stress, which is a material variable (Table 1; Fig. 1).

Fig. 1
figure 1

Comparison of structural and material properties. Structural properties depend on size, while material properties normalize displacements by length into strains, forces by area into stresses and energy by volume into energy density. Structural properties are the principal outcome variables, while material properties are the necessary input variables for finite element analysis

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Table 1 Typical parameters used in FEA analysis; see also Fig. 1
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Structural properties such as stiffness, failure load and energy to failure depend on bone size. Normalizing displacement by length, failure load by area, and energy by volume results in material variables called strain, stress and energy density (Table 1; Fig. 1). Instead of a load–displacement curve, a stress–strain curve is obtained that is independent of sample shape and size. The slope of the linear portion of the stress–strain curve is Young’s modulus. The maximum stress at which the bone breaks is termed ultimate stress, and the energy density to failure is called toughness. Young’s modulus, ultimate stress and toughness are therefore (intrinsic) material properties, independent of shape and size. In fact, these variables are the material properties needed as input for FEA and are determined in ex vivo biomechanical tests of compact or trabecular bone samples with regular shapes.

The same normalization idea can also be applied to FEA output variables for bones with regular shapes such as radial or vertebral sections. The ultimate force can be divided by the average cross-sectional area providing an ultimate stress that may be more meaningful in terms of fracture risk because it takes the size of the bone into account. Unfortunately, this normalization cannot be applied to bones with irregular shapes such as the proximal femur.

Advanced Topics

Material Properties: Trabecular—Cortical Bone

Bone tissue is a quasi-brittle, heterogeneous and anisotropic material that deforms elastically under small strains and exhibits a microcracking mechanism resulting in the simultaneous accumulation of irreversible strains and the reduction of the original elastic modulus when deformed beyond yield strains of approximately 0.3–0.4 % [21, 22]. This material behavior holds for compact and trabecular bone, as both are constituted of lamellar bone tissue. In practice, bone is modeled as a linear elastic material (linear material law) that may lead to plasticity or damage beyond a given yield criterion (nonlinear material laws) [23]. Beyond yielding, the material behavior is modeled with some strain hardening or softening function that mimics the increasing or decreasing post-yield stresses observed in experiments. The various material models are then characterized by material constants such as Young’s modulus, yield stress or ultimate stress and linear hardening slope.

The actual material constants of compact bone are dominated by porosity and Haversian orientation [24], while the ones of trabecular bone are almost entirely controlled by bone volume fraction (BV/TV) and architectural anisotropy also called fabric [25]. X-ray attenuation exploited in computer tomography is well suited to quantify bone volume fraction and to a certain degree porosity, but Haversian orientation and trabecular fabric depend on image resolution and cannot be easily assessed in vivo.

In µCT-based FE or µFE (≤40 µm), bone tissue properties are generally assumed to be homogeneous and isotropic, which is justified by the fact that mineralization has a narrow range [26, 27] and that trabeculae are principally loaded along their length in compression, bending or torsion. In high-resolution peripheral CT of the distal radius or tibia (60–80 µm), the vascular and resorption space contributions to cortical porosity can be resolved and trabecular architecture can be estimated [28]. However, the actual bone volume fraction is often overestimated in µFE and homogenized FE is an attractive alternative for these spatial resolutions as well [29].

In whole-body QCT of the vertebral body or proximal femur (300–500 µm), Haversian orientation and fabric are hardly detectable, porosity and volume fraction can be estimated from local BMD, and homogenized FE is the only option. At these resolutions, compact and trabecular bone are often not distinguished and the material properties are assumed isotropic. In the vertebral body, principal trabecular orientation is sometimes assumed to run along the cranio-caudal direction [30], while in the femur, registration or machine learning tools are currently explored to retrieve the fabric information indirectly from a given anatomical database [31–33]. Material property mapping, the assignment of material properties to each element using the underlying CT image, is an important feature of homogenized FE models [34, 35]. FE outcome measures somewhat depend on whether the mapping is performed voxel by voxel, interpolated from a virtual grid or averaged over a specific volume [34].

Meshing Techniques

In computational engineering practice, mesh generation is a time-consuming task, which explains the attractiveness of voxel meshes that automatically convert voxels coarsened from a CT image into finite elements (Fig. 2). The main disadvantages of voxel meshes are the irregular boundaries and the lack of refinement at locations where failure occurs. Alternatively, marching tetrahedron meshing options have been developed that can mesh the models with tetrahedron elements and have smooth boundaries, but typically these meshes use only one element size and thus may contain many elements. More general hexahedral or tetrahedral meshes require more effort, can be only partly automated, offer smooth boundaries and can be refined where needed [36]. Moreover, these meshes offer the possibility to model distinctly the compact shell and the trabecular core of whole bones (Fig. 3).

Fig. 2
figure 2

µFE model resolving the trabecular microstructure. The mesh can be voxel-based or smooth. The bone tissue is usually assumed homogeneous

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Fig. 3
figure 3

Voxel and a smooth meshes of a vertebral body section for homogenized FE adapted from [78]. The color map designates bone volume fraction (BV/TV) (Color figure online)

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Linear Versus Nonlinear FEA

Linear FEA considers only the elastic behavior of the bone matrix and assumes that only small strains and rotations occur in the structure. Nonlinearity of the computational problem may be introduced from a geometrical or material point of view. Bending of a slender linear elastic beam results in a geometrical nonlinearity, while the microcracking mechanism of bone tissue represents a material nonlinearity. Nonlinear material properties are necessary to simulate loading beyond the yield point, reach an ultimate load and describe the permanent displacements and reduction in stiffness appearing after unloading.

Nonlinear FEA exploits linear iterative methods that convert the nonlinear numerical problem into a sequence of linear problems and requires therefore approximately an order of magnitude longer computing time for each load step. Unlike linear analyses, nonlinear analyses necessitate multiple load steps to ensure convergence of the iterative method, which results into even larger differences in computing time. Since computing time is also a power function of the number of elements, nonlinear analyses of large µFE models reach the limits of standard computational resources and require computing clusters or high-performance computer centers.

Definition of Failure Criteria

Failure criteria allow to estimate bone strength and to predict the anatomical locations where failure is initiated and progresses. They also play a central role in FE validation in biomechanical experiments.

In linear FE analysis, force–displacement curves are linear and do not reach a maximum to determine ultimate force. Consequently, failure criteria are generally computed from the strain distribution as stresses scale with material properties and no plastic or damage variables are calculated. A typical definition is the fraction of bone tissue that exceeds a given strain level [37]. For instance, in µFE analysis of the distal radius, the so-called Pistoia criterion defines the force where 2 % of the tissue exceeds an effective strain of 0.007 [38]. Such definitions depend on bone geometry, mesh, material properties and load case and must be interpreted carefully.

In nonlinear FEA, the actual maximum of force–displacement curves can be simulated and is therefore the preferred outcome [39]. However, the computed ultimate load depends on the yield criterion and the hardening properties selected at the material level [40]. With a few exceptions, most of the yield criteria used for bone have been borrowed from other engineering materials without further validation. The sensitivity of ultimate load to these criteria has been investigated with mixed results that reflect the limitations of the FE models and the related experiments [41]. Nevertheless, strain measures are currently favored, a distinct criterion in tension and compression is meaningful, and the compressibility of trabecular bone yielding was demonstrated in several studies [42, 43].

Validation

FE methods have been validated in numerous experimental studies using cadaveric bones. Correlations (r 2) between estimated and measured failure loads or ultimate strength ranged from 0.78 to 0.96 in the spine, from 0.85 to 0.9 in the hip (see [19] for a summary) and from 0.66 to 0.94 in the distal radius (Table 2). When directly comparing FE simulations with BMD or BMC as measured by DXA or QCT, at the radius, spine and hip FE parameters in general correlated higher with experimental measures than with aBMD. Differences between FE and QCT parameters were smaller, but FE correlations were still slightly higher. However, it is important to note that the structural variable of failure load should be compared with BMC or a size-adjusted vBMD measure, whereas the material variable ultimate strength should be compared with vBMD and not with BMC.

Table 2 Overview of validation studies for µFE using HR-pQCT
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In the hip, failure load estimated by FEA also correlated higher with the experimental measurement than aBMD or BMC. Thus, when just considering the external forces acting on bone, strength parameters are better predictors of fracture than surrogate QCT or DXA BMD or BMD measurements. The combination of BMD or BMC with geometrical parameters such as cortical thickness, which in the hip in vivo has shown improved fracture prediction over vBMD alone [44], has not been tested for failure load prediction in vitro. However, the combination of multiple parameters to predict fracture requires a multivariate analysis and is more difficult to interpret than a single parameter such as ultimate load.

A validation of forearm µFE results was performed in several studies using cadaver arms [45–48]. Most of these studies also included DXA scans of the distal forearm. µFE and experimental results were highly correlated, with a coefficient of determination r 2 > 0.66 (Table 2). The accuracy depended on the accuracy of the experimental test (intact forearm testing is not very accurate) and on the material properties chosen, which varied widely among studies. When using accurate tests and tuned tissue material properties, however, highly accurate results were obtained [45, 47]. Interestingly, in all these studies µFE better predicted bone strength than DXA, although in some of these studies the improvement was rather small.

Precision of FE Parameters

Reproducibility of the FEA outcome variables primarily depends on the reproducibility of the CT or other images on which the models are based. In vivo root-mean-square precision errors of advanced QCT or HR-pQCT analyses techniques are comparable to DXA: 1–2 % for integral BMD in the total vertebral bodies of the lumbar spine [49, 50], total hip [51–54] and distal forearm [55, 56]. For FEA a precision error of 1.9 % for total hip stiffness was reported [57]. Due to the use of local BMD values in bone segmentation and in the assignment of material properties, the original QCT precision will be degraded in a resolution-dependent manner along the FE model production and execution pipeline. A recent study suggests that femoral strength computed by linear FE in a fall configuration has a CV of 6.4 % compared to the one of a nonlinear FE in a stance configuration with a CV of 1.6 %.

The short-term reproducibility of the µFE results was reported in several studies [58–60], in which a group of subjects was scanned twice or thrice at different days or after repositioning. Typically, root mean square of the coefficient of variation was better than 4.4 % for stiffness and 3.7 % for strength, which are values comparable to the reproducibility of the microstructural parameters.

Clinical Use of FE Techniques

The application of FEA in the bone field is still a topic of ongoing research activities, and many studies were carried out with university-based experimental software. So far, for spine and hip FEA software is not available off the shelf although a number of companies offer services for data analysis. Among them ON-Diagnostics’ (Berkeley, CA) VirtuOst software and its predecessors have been used for the analysis of epidemiological studies and of many clinical studies to develop new pharmaceutical drugs to prevent fractures. VirtuOst has been recently approved by the FDA. Likewise, FEA of the forearm has been mostly performed by university-based software. An FEA analysis option for HR-pQCT scans of the distal radius and tibia has been integrated into the analysis software installed on the XtremeCT scanners (Scanco Medical, Brüttisellen, Switzerland). In the next two sections, state-of-the-art in vivo FEA at the forearm using HR-pQCT scanners and at the spine and hip using whole-body clinical CT scanners will be summarized.

FEA of Spine and Hip

Spine and hip are the most important fracture sites. One focus of FEA (Fig. 4) is the necessity to improve fracture prediction and to more accurately identify subjects at high risk in whom treatment is highly indicated. From a clinical perspective, the main questions are: Is FEA more accurate than DXA, what is the additional effort and will it benefit the patient? First, there are a number of logistical issues. As described above access to FE technology in particular for spine and hip is still limited. In addition, a QCT dataset is a prerequisite for FEA. While there are probably more clinical whole-body CT scanners than DXA scanners, historically physicians treating osteoporosis have easier access to DXA. Finally, there is the issue of radiation exposure that is considerably higher for CT than for DXA: about 1 mSv effective dose for QCT of two lumbar vertebrae and 2–3 mSv for a total hip scan compared to about 5 µSv each for DXA of the lumbar spine and total hip. On an absolute scale, radiation exposure for QCT is rather low, approximately equivalent to the annual background radiation and the benefit may largely outweigh the potential risks, in particular in elderly people, where osteoporosis is of major concern. However, if the benefits of a QCT or FE analysis do not outweigh those of DXA then there is no rationale to perform a CT scan. So how do the techniques compare with respect to fracture prediction?

Fig. 4
figure 4

Two examples of boundary value problems resolved with the FE method. Loading of the proximal femur in a side fall configuration and axial compression of a vertebral body section. Adapted from [79]. The color map designates bone volume fraction (BV/TV) (Color figure online)

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The most solid data to date were generated from two epidemiological studies: MrOs a US study in elderly men and Ages Reykjavik an Icelandic study in elderly females. In a subcohort of the MrOs study, standardized HRs were higher for failure load of L2 than for DXA aBMD of L1–L4 [61], and in a subcohort of the Ages Reykjavik study, ORs were higher for strength of L2 than for vBMD of L2 [20]. In comparison with aBMD of the spine, two other studies in women showed either larger AUC values or higher correlations of strength parameters for discrimination of vertebral fractures [62, 63]. With respect to the hip, standardized HRs in the MrOs study were higher for hip failure load than for DXA hip aBMD [64]. Several cross-sectional studies in women showed that the power of FEA-derived strength measures to discriminate hip fractures was comparable to aBMD or vBMD measures of the total femur [20, 65, 66].

Thus, in vivo ‘FEA of the spine was superior to DXA spine aBMD and superior or equivalent to QCT spine vBMD/BMC to predict failure load of the vertebral body. FEA of the hip was superior or equivalent to DXA hip aBMD and superior to QCT hip vBMD/BMC to predict failure load of the hip’ [1]. In particular, in the spine, in vivo and in vitro data show a consistent superiority of vertebral facture prediction or discrimination of FEA strength measures but also of QCT BMC or BMD compared to aBMD as measured by DXA. The main reason is the 3D imaging technique of QCT and FEA that allows for a separate analysis of the vertebral body, unaffected by the spinous and transversal processes, the pedicles and potential aortic calcifications that falsely contribute to vertebral aBMD as measured in the projectional DXA technique. In addition, degenerative changes frequently observed in the elderly can more easily be omitted from the QCT/FEA than from the DXA analysis. These limitations of DXA that typically falsely increase aBMD in the spine have been known for a long time, but appropriate 3D imaging techniques were only developed after the invention of spiral CT.

In the hip differences are smaller. Even in vitro, the difference in correlations between estimated and experimentally measured failure load and between aDXA and experimentally measured failure load was much smaller than in the spine [19]. This translates to the in vivo situation where ultimate load by FEA of the hip improved fracture prediction only marginally compared to aBMD [20, 64, 65, 67]. Further, reported confidence intervals for hazard or odds ratios from FEA calculations are usually considerably larger than those from DXA. Therefore, even larger reported numerical differences among techniques may not have achieved statistical significance. The hip differs from the spine because hip DXA is not affected by the same limitations as spine DXA. Hip DXA is affected by the rotation of the leg, and the acetabulum often overlaps the most proximal part of the femur. Thus, in DXA only part of the neck is included in the analysis, whereas in QCT/FEA often a smaller part of the intertrochanteric region is included in the total femur VOI. Nevertheless, the analyzed total hip VOI is very similar between QCT/FEA and DXA.

However, the most important reason that in vivo FEA and aBMD still give very similar results in the hip is the fact that hip fracture is almost exclusively caused by a fall and the risk of falling is captured by neither DXA, QCT nor FEA. Thus, in particular in the hip in vitro experiments do not fully reflect the in vivo situation, although the part related to bone strength can be better captured by FEA than by DXA. Nevertheless, when following the argumentation at the beginning of the section, in the hip the use of CT instead of DXA may be questioned potentially limiting the use of FEA. However, many CT scans are routinely taken for other diagnostic purposes than for osteoporosis. Examples are standard abdominal or pelvic CT scans. Their potential in the diagnosis of osteoporosis or for the identification of high-risk fracture groups is currently being explored. These approaches are summarized as opportunistic screening [68, 69].

In short, existing clinical CT scans even those with contrast applications are ‘externally’ calibrated to BMD, i.e., using phantom scans obtained separately from the patient scan or are calibrated internally using air and soft tissues such as fat. Some researchers even suggest using the CT values directly [70, 71]. Then with appropriate thresholds, obtained, for example, in a comparative DXA study, DXA T-score equivalent thresholds for the diagnosis or at least for a rough stratification in high, normal, low fracture risk can be made. Obviously, this is not a diagnosis of osteoporosis in accordance with the WHO criteria but an alternative attractive risk stratification. Whether patients identified as being at high fracture risk according to this scenario will then undergo an additional DXA scan or not is still under debate. Of course, QCT as well as FEA parameters can be obtained with such an approach using existing data. Failure load of hip and spine could be a secondary outcome to other CT-based diagnoses. While first very promising results have been published [68], many methods related questions in particular with respect to the standardization of the CT acquisition and calibration process have to be answered. Nevertheless, this is a very promising approach to make FEA widely available in clinical routine.

FEA of the Forearm

The forearm is the third major fracture site for osteoporotic patients. Typically, these fractures occur as the result of a fall from standing height in subjects that are still capable to stretch out their hand to soften the fall. Although it is a major osteoporotic fracture site, the forearm is not a common site for DXA measurement or strength assessment by FEA. For research studies, however, this has changed with the introduction of HR-pQCT imaging around a decade ago. This technique enabled the imaging of the distal radius in vivo at a resolution that is high enough to resolve the bone microstructure (isotropic voxel size of 82 µm), thus offering a unique opportunity for microstructural and µFE analyses in patient studies (Fig. 5).

Fig. 5
figure 5

Left a typical µFE model of the scanned section of the distal radius with the cortical bone tissue colored green and the cancellous bone tissue pink. Right the von Mises stress in the bone tissue for a 1 % compressive loading of the segment. The section is cut into two parts to reveal the stresses in the trabeculae (Color figure online)

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The radiation exposure for such measurements is around 3 µSv effective dose, which is comparable to a DXA scan and very low compared to a spine or hip CT scan. Since presently only one manufacturer is producing this type of equipment and only 2 models are available, the scanning procedure and microstructural and µFE analyses are highly standardized. The FE analysis can be performed in a fully automated manner, without any user intervention, making it highly suitable for clinical applications. For the µFE analyses, the images are usually first filtered and thresholded, after which each bone voxel is converted to a brick element. Then, a compression test is simulated on the scanned section, from which the stiffness of the section, the strength (estimated using the ‘Pistoia criterion’ mentioned earlier, or by performing a nonlinear analyses) and the distribution of the load between the cortical and cancellous compartment are calculated.

As discussed above, the validation studies showed that µFE analyses better predicted forearm bone strength than DXA, but it remains to be proven that it can better predict bone fracture risk [17]. In several retrospective studies, the association between prevalence of a distal radius fracture and µFE or DXA results was quantified by odds ratios per standard deviation change. In postmenopausal women, odds ratios for µFE results generally were about the same as those for forearm DXA [72–74]. Interestingly, some studies indicated that biomechanical properties of the distal radius and tibia, based on in vivo HR-pQCT images, were associated with all types of fractures, including spine and hip, and were partially independent from hip aBMD [75, 76]. This suggests that microstructural changes at the distal radius might be representative for other sites as well and might provide additional information about the strength at other sites.

Nevertheless, to date, µFE and DXA give very similar results with respect to forearm fracture discrimination. As with the hip, the most important reason for this is probably the fact that forearm fractures are almost exclusively caused by a fall. It should be noted, however, that all fracture risk studies were retrospective studies, in which the fracture could have occurred more than a decade before the HR-pQCT scan was made, and in which the patients had been pharmaceutically treated since the fracture. Thus, the bone microstructure used for the µFE analyses might not have been representative for that during the fracture. Clearly, prospective studies are needed to better evaluate whether µFE can improve upon fracture risk prediction of the distal radius or even other sites. It should also be noted that all studies mentioned above were performed using the first generation of HR-pQCT devices. A second-generation device that offers 61 µm isotropic voxel size has just become available and was shown to provide an improved assessment of bone microstructure [77]. Although no bone strength studies have been reported using this device yet, it is possible that the increase in image resolution will further improve the strength assessment.

Conclusion

Despite the limitations listed above, FE is currently the most accurate method to estimate bone strength when a QCT reconstruction is available. This makes it the tool of choice for the evaluation of treatments aiming at increasing bone strength.

Since bone strength is only part of the fracture risk equation, the clinically added value of the improved accuracy in terms of fracture risk and the related gradient remains to be determined more accurately for each anatomical site.

Exploitation of opportunistic CT scans seems to be an attractive approach to screen for high fracture risk in our aging populations with minimal costs and to disseminate FEA more widely in clinical routine.

Knowledge of the underlying bone matrix mechanics, of the CT imaging procedure and calibration, of segmentation and meshing tools and of numerical algorithms is constantly improving. Thus, the FE method has the potential to estimate bone strength with an even higher accuracy. By intelligent combination of FEA with other risk factors, this should further improve the clinical assessment of fracture risk.