Quantifying trabecular bone material anisotropy and orientation using low resolution clinical CT images: A feasibility study

Activation of Focal Adhesion Kinase Restores Simulated Microgravity-Induced Inhibition of Osteoblast Differentiation via Wnt/Β-Catenin Pathway

Simulated microgravity (SMG) inhibits osteoblast differentiation (OBD) and induces bone loss via the inhibition of the Wnt/β-catenin pathway. However, the mechanism by which SMG alters the Wnt/β-catenin pathway is unknown. We previously demonstrated that SMG altered the focal adhesion kinase (FAK)-regulated mTORC1, AMPK and ERK1/2 pathways, leading to the inhibition of tumor cell proliferation/metastasis and promoting cell apoptosis. To examine whether FAK similarly mediates SMG-dependent changes to Wnt/β-catenin in osteoblasts, we characterized mouse MC3T3-E1 cells cultured under clinostat-modeled SMG (µg) conditions. Compared to cells cultured under ground (1 g) conditions, SMG reduces focal adhesions, alters cytoskeleton structures, and down-regulates FAK, Wnt/β-catenin and Wnt/β-catenin-regulated molecules. Consequently, protein-2 (BMP2), type-1 collagen (COL1), alkaline-phosphatase activity and matrix mineralization are all inhibited. In the mouse hindlimb unloading (HU) model, SMG-affected tibial trabecular bone loss is significantly reduced, according to histological and micro-computed tomography analyses. Interestingly, the FAK activator, cytotoxic necrotizing factor-1 (CNF1), significantly suppresses all of the SMG-induced alterations in MC3T3-E1 cells and the HU model. Therefore, our data demonstrate the critical role of FAK in the SMG-induced inhibition of OBD and bone loss via the Wnt/β-catenin pathway, offering FAK signaling as a new therapeutic target not only for astronauts at risk of OBD inhibition and bone loss, but also osteoporotic patients.

Effect of CT imaging on the accuracy of the finite element modelling in bone

The finite element (FE) analysis is a highly promising tool to simulate the behaviour of bone. Skeletal FE models in clinical routine rely on the information about the geometry and bone mineral density distribution from quantitative computed tomography (CT) imaging systems. Several parameters in CT imaging have been reported to affect the accuracy of FE models. FE models of bone are exclusively developed in vitro under scanning conditions deviating from the clinical setting, resulting in variability of FE results (< 10%). Slice thickness and field of view had little effect on FE predicted bone behaviour (≤ 4%), while the reconstruction kernels showed to have a larger effect (≤ 20%). Due to large interscanner variations (≤ 20%), the translation from an experimental model into clinical reality is a critical step. Those variations are assumed to be mostly caused by different “black box” reconstruction kernels and the varying frequency of higher density voxels, representing cortical bone. Considering the low number of studies together with the significant effect of CT imaging on the finite element model outcome leading to high variability in the predicted behaviour, we propose further systematic research and validation studies, ideally preceding multicentre and longitudinal studies.

Statistical analysis of the inter-individual variations of the bone shape, volume fraction and fabric and their correlations in the proximal femur

Including structural information of trabecular bone improves the prediction of bone strength and fracture risk. However, this information is available in clinical CT scans, only for peripheral bones. We hypothesized that a correlation exists between the shape of the bone, its volume fraction (BV/TV) and fabric, which could be characterized using statistical modeling. High-resolution peripheral computed tomography (HR-pQCT) images of 73 proximal femurs were used to build a combined statistical model of shape, BV/TV and fabric. The model was based on correspondence established by image registration and by morphing of a finite element mesh describing the spatial distribution of the bone properties. Results showed no correlation between the distribution of bone shape, BV/TV and fabric. Only the first mode of variation associated with density and orientation showed a strong relationship (R²>0.8). In addition, the model showed that the anisotropic information of the proximal femur does not vary significantly in a population of healthy, osteoporotic and osteopenic samples. In our dataset, the average anisotropy of the population was able to provide a close approximation of the patient-specific anisotropy. These results were confirmed by homogenized finite element (hFE) analyses, which showed that the biomechanical behavior of the proximal femur was not significantly different when the average anisotropic information of the population was used instead of patient-specific fabric extracted from HR-pQCT. Based on these findings, it can be assumed that the fabric information of the proximal femur follows a similar structure in an elderly population of healthy, osteopenic and osteoporotic proximal femurs.

Accounting for spatial variation of trabecular anisotropy with subject-specific finite element modeling moderately improves predictions of local subchondral bone stiffness at the proximal tibia

INTRODUCTION

Previously, a finite element (FE) model of the proximal tibia was developed and validated against experimentally measured local subchondral stiffness. This model indicated modest predictions of stiffness (R²=0.77, normalized root mean squared error (RMSE%)=16.6%). Trabecular bone though was modeled with isotropic material properties despite its orthotropic anisotropy. The objective of this study was to identify the anisotropic FE modeling approach which best predicted (with largest explained variance and least amount of error) local subchondral bone stiffness at the proximal tibia.

METHODS

Local stiffness was measured at the subchondral surface of 13 medial/lateral tibial compartments using in situ macro indentation testing. An FE model of each specimen was generated assuming uniform anisotropy with 14 different combinations of cortical- and tibial-specific density-modulus relationships taken from the literature. Two FE models of each specimen were also generated which accounted for the spatial variation of trabecular bone anisotropy directly from clinical CT images using grey-level structure tensor and Cowin's fabric-elasticity equations. Stiffness was calculated using FE and compared to measured stiffness in terms of R² and RMSE%.

RESULTS

The uniform anisotropic FE model explained 53-74% of the measured stiffness variance, with RMSE% ranging from 12.4 to 245.3%. The models which accounted for spatial variation of trabecular bone anisotropy predicted 76-79% of the variance in stiffness with RMSE% being 11.2-11.5%.

CONCLUSIONS

Of the 16 evaluated finite element models in this study, the combination of Synder and Schneider (for cortical bone) and Cowin's fabric-elasticity equations (for trabecular bone) best predicted local subchondral bone stiffness.

μCT-based trabecular anisotropy can be reproducibly computed from HR-pQCT scans using the triangulated bone surface

The trabecular structure can be assessed at the wrist or tibia via high-resolution peripheral quantitative computed tomography (HR-pQCT). Yet on this modality, the performance of the existing methods, evaluating trabecular anisotropy is usually overlooked, especially in terms of reproducibility. We thus proposed to compare the TRI routine used by SCANCO Medical AG (Brüttisellen, Switzerland), the classical mean intercept length (MIL), and the grey-level structure tensor (GST) to the mean surface length (MSL), a new method for evaluating a second-order fabric tensor based on the triangulation of the bone surface. The distal radius of 24 fresh-frozen human forearms was scanned three times via HR-pQCT protocols (61μm, 82μm nominal voxel size), dissected, and imaged via micro computed tomography (μCT) at 16μm nominal voxel size. After registering the scans, we compared for each resolution the fabric tensors, determined by the mentioned techniques for 182 trabecular regions of interest. We then evaluated the reproducibility of the fabric information measured by HR-pQCT via precision errors. On μCT, TRI and GST were respectively the best and worst surrogates for MIL_μCT (MIL computed on μCT) in terms of eigenvalues and main direction of anisotropy. On HR-pQCT, however, MSL provided the best approximation of MIL_μCT. Surprisingly, surface-based approaches (TRI, MSL) also proved to be more precise than both MIL and GST. Our findings confirm that MSL can reproducibly estimate MIL_μCT, the current gold standard. MSL thus enables the direct mapping of the fabric-dependent material properties required in homogenised HR-pQCT-based finite element models.

Optimizing finite element predictions of local subchondral bone structural stiffness using neural network-derived density-modulus relationships for proximal tibial subchondral cortical and trabecular bone

BACKGROUND

Quantitative computed tomography based subject-specific finite element modeling has potential to clarify the role of subchondral bone alterations in knee osteoarthritis initiation, progression, and pain. However, it is unclear what density-modulus equation(s) should be applied with subchondral cortical and subchondral trabecular bone when constructing finite element models of the tibia. Using a novel approach applying neural networks, optimization, and back-calculation against in situ experimental testing results, the objective of this study was to identify subchondral-specific equations that optimized finite element predictions of local structural stiffness at the proximal tibial subchondral surface.

METHODS

Thirteen proximal tibial compartments were imaged via quantitative computed tomography. Imaged bone mineral density was converted to elastic moduli using multiple density-modulus equations (93 total variations) then mapped to corresponding finite element models. For each variation, root mean squared error was calculated between finite element prediction and in situ measured stiffness at 47 indentation sites. Resulting errors were used to train an artificial neural network, which provided an unlimited number of model variations, with corresponding error, for predicting stiffness at the subchondral bone surface. Nelder-Mead optimization was used to identify optimum density-modulus equations for predicting stiffness.

FINDINGS

Finite element modeling predicted 81% of experimental stiffness variance (with 10.5% error) using optimized equations for subchondral cortical and trabecular bone differentiated with a 0.5g/cm³ density.

INTERPRETATION

In comparison with published density-modulus relationships, optimized equations offered improved predictions of local subchondral structural stiffness. Further research is needed with anisotropy inclusion, a smaller voxel size and de-blurring algorithms to improve predictions.