Predicting trabecular bone elastic properties from measures of bone volume fraction and fabric on the basis of micromagnetic resonance images

Studying trabecular bone samples demonstrates a power law relation between deteriorated structure and mechanical properties - a study combining 3D printing with the finite element method

Introduction

The bone volume fraction (BV/TV) significantly contributes to the mechanical properties of trabecular bone. However, when studies compare normal trabeculae against osteoporotic trabeculae (in terms of BV/TV decrease), only an "average" mechanical result has been determined because of the limitation that no two trabecular structures are the same and that each unique trabecular structure can be mechanically tested only once. The mathematic relation between individual structural deterioration and mechanical properties during aging or the osteoporosis process has yet to be further clarified. Three-dimensional (3D) printing and micro-CT-based finite element method (μFEM) can assist in overcoming this issue.

Methods

In this study, we 3D printed structural-identical but BV/TV value-attenuated trabecular bones (scaled up ×20) from the distal femur of healthy and ovariectomized rats and performed compression mechanical tests. Corresponding μFEM models were also established for simulations. The tissue modulus and strength of 3D printed trabecular bones as well as the effective tissue modulus (denoted as Ez) derived from μFEM models were finally corrected by the side-artifact correction factor.

Results

The results showed that the tissue modulus _corrected, strength _corrected and Ez _corrected exhibited a significant power law function of BV/TV in structural-identical but BV/TV value-attenuated trabecular samples.

Discussion

Using 3D printed bones, this study confirms the long-known relationship measured in trabecular tissue with varying volume fractions. In the future, 3D printing may help us attain better bone strength evaluations and even personal fracture risk assessments for patients who suffer from osteoporosis.

Biomechanical properties and clinical significance of cancellous bone in proximal femur: A review

Trabecular bone plays an important role in the load-bearing capacity of the femur. Understanding the structural characteristics, biomechanics, and mechanical conduction of the trabecular bone is of great value in studying the mechanism of fractures and formulating surgical plans. The past decade has witnessed unprecedented progress in imaging, biomechanics and finite element analysis techniques, translating into a better understanding of trabecular bone. This article reviews the research progress achieved over the years regarding femoral trabecular bone, especially on factors influencing the strength of the proximal femoral cancellous bone and cancellous bone microfractures and provides a comprehensive overview of the latest findings on proximal femoral trabecular bone and their clinical significance.

Micro-Finite Element Analysis of the Proximal Femur on the Basis of High-Resolution Magnetic Resonance Images

PURPOSE OF REVIEW

Hip fractures have catastrophic consequences. The purpose of this article is to review recent developments in high-resolution magnetic resonance imaging (MRI)-guided finite element analysis (FEA) of the hip as a means to determine subject-specific bone strength.

RECENT FINDINGS

Despite the ability of DXA to predict hip fracture, the majority of fractures occur in patients who do not have BMD T scores less than - 2.5. Therefore, without other detection methods, these individuals go undetected and untreated. Of methods available to image the hip, MRI is currently the only one capable of depicting bone microstructure in vivo. Availability of microstructural MRI allows generation of patient-specific micro-finite element models that can be used to simulate real-life loading conditions and determine bone strength. MRI-based FEA enables radiation-free approach to assess hip fracture strength. With further validation, this technique could become a potential clinical tool in managing hip fracture risk.

Accuracy of MRI-based finite element assessment of distal tibia compared to mechanical testing

High-resolution MRI-derived finite element analysis (FEA) has been used in translational research to estimate the mechanical competence of human bone. However, this method has yet to be validated adequately under in vivo imaging spatial resolution or signal-to-noise conditions. We therefore compared MRI-based metrics of bone strength to those obtained from direct, mechanical testing. The study was conducted on tibiae from 17 human donors (12 males and five females, aged 33 to 88years) with no medical history of conditions affecting bone mineral homeostasis. A 25mm segment from each distal tibia underwent MR imaging in a clinical 3-Tesla scanner using a fast large-angle spin-echo (FLASE) sequence at 0.137mm×0.137mm×0.410mm voxel size, in accordance with in vivo scanning protocol. The resulting high-resolution MR images were processed and used to generate bone volume fraction maps, which served as input for the micro-level FEA model. Simulated compression was applied to compute stiffness, yield strength, ultimate strength, modulus of resilience, and toughness, which were then compared to metrics obtained from mechanical testing. Moderate to strong positive correlations were found between computationally and experimentally derived values of stiffness (R²=0.77, p<0.0001), yield strength (R²=0.38, p=0.0082), ultimate strength (R²=0.40, p=0.0067), and resilience (R²=0.46, p=0.0026), but only a weak, albeit significant, correlation was found for toughness (R²=0.26, p=0.036). Furthermore, experimentally derived yield strength and ultimate strength were moderately correlated with MRI-derived stiffness (R²=0.48, p=0.0022 and R²=0.58, p=0.0004, respectively). These results suggest that high-resolution MRI-based finite element (FE) models are effective in assessing mechanical parameters of distal skeletal extremities.

Principal trabecular structural orientation predicted by quantitative ultrasound is strongly correlated with μFEA determined anisotropic apparent stiffness

The microarchitecture and alignment of trabecular bone adapts to the particular mechanical milieu applied to it. Due to this anisotropic mechanical property, measurement orientation has to be taken into consideration when assessing trabecular bone quality and fracture risk prediction. Quantitative ultrasound (QUS) has demonstrated the ability in predicting the principal structural orientation (PSO) of trabecular bone. Although the QUS prediction for PSO is very close to that of μCT, certain angle differences still exist. It remains unknown whether this angle difference can induce significant differences in mechanical properties or not. The objective of this study was to evaluate the mechanical properties in different PSOs predicted using different methods, QUS and μCT, thus to investigate the ability of QUS as a means to predict the PSO of trabecular bone noninvasively. By validating the ability of QUS to predict the PSO of trabecular bone, it is beneficial for future QUS applications because QUS measurements in the PSO can provide information more correlated with the mechanical properties than with other orientations. In this study, seven trabecular bone balls from distal bovine femurs were used to generate finite element models based on the 3-dimensional μCT images. Uniaxial compressive loading was performed on the bone ball models in the finite element analysis (FEA) in six different orientations (three anatomical orientations, two PSOs predicted by QUS and the longest vector of mean intercept length (MIL) tensor calculated by μCT). The stiffness was calculated based on the reaction force of the bone balls under loading, and the von Mises stress results showed that both the mechanical properties in the PSOs predicted by QUS are significantly higher than the anatomical orientations and comparatively close to the longest vector of MIL tensor. The stiffness in the PSOs predicted by QUS is also highly correlated with the stiffness in the MIL tensor orientation (ATTmax vs. MIL, R(2) = 0.98, p < 001; UVmax vs. MIL, R(2) = 0.92, p < 001). These results were validated by in vitro mechanical testing on the bone ball samples. This study demonstrates that the PSO of trabecular bone predicted by QUS has an equally strong apparent stiffness with the orientation predicted by μCT.

Magnetic resonance of calcified tissues

MRI of the human body is largely made possible by the favorable relaxation properties of protons of water and triacyl glycerides prevalent in soft tissues. Hard tissues--key among them bone--are generally less amenable to measurement with in vivo MR imaging techniques, not so much as a result of the lower proton density but rather due to the extremely short life-times of the proton signal in water bound to solid-like entities, typically collagen, or being trapped in micro-pores. Either mechanism can enhance T2 relaxation by up to three orders of magnitude relative to their soft-tissue counterparts. Detection of these protons requires solid-state techniques that have emerged in recent years and that promise to add a new dimension to the study of hard tissues. Alternative approaches to probe calcified tissues exploit their characteristic magnetic properties. Bone, teeth and extra-osseous calcium-containing biomaterials are unique in that they are more diamagnetic than all other tissues and thus yield information indirectly by virtue of the induced magnetic fields present in their vicinity. Progress has also been made in methods allowing very high-resolution structural imaging of trabecular and cortical bone relying on detection of the surrounding soft-tissues. This brief review, much of it drawn from work conducted in the author's laboratory, seeks to highlight opportunities with focus on early-stage developments for image-based assessment of structure, function, physiology and mechanics of calcified tissues in humans via liquid and solid-state approaches, including proton, deuteron and phosphorus NMR and MRI.