Prediction of apparent trabecular bone stiffness through fourth-order fabric tensors

Predicting the trabecular bone apparent stiffness tensor with spherical convolutional neural networks

The apparent stiffness tensor is relevant for characterizing trabecular bone quality. Previous studies have used morphology-stiffness relationships for estimating the apparent stiffness tensor. In this paper, we propose to train spherical convolutional neural networks (SphCNNs) to estimate this tensor. Information of the edges, trabecular thickness, and spacing are summarized in functions on the unitary sphere used as inputs for the SphCNNs. The concomitant dimensionality reduction makes it possible to train neural networks on relatively small datasets. The predicted tensors were compared to the stiffness tensors computed by using the micro-finite element method (μFE), which was considered as the gold standard, and models based on fourth-order fabric tensors. Combining edges and trabecular thickness yields significant improvements in the accuracy compared to the methods based on fourth-order fabric tensors. From the results, SphCNNs are promising for replacing the more expensive μFE stiffness estimations.

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Characteristic stiffness tensors are derived from trabecular bone micro-CT samples.

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Previous approximation methods fall short on heterogeneous data-sets.

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The gradient, trabecular thickness and spacing are mapped to a spherical domain.

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Spherical convolutional neural networks are used for the prediction.

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The prediction error is significantly reduced compared to the state-of-the-art.

Can DXA image-based deep learning model predict the anisotropic elastic behavior of trabecular bone?

3D image-based finite element (FE) and bone volume fraction (BV/TV)/fabric tensor modeling techniques are currently used to determine the apparent stiffness tensor of trabecular bone for assessing its anisotropic elastic behavior. Inspired by the recent success of deep learning (DL) techniques, we hypothesized that DL modeling techniques could be used to predict the apparent stiffness tensor of trabecular bone directly using dual-energy X-ray absorptiometry (DXA) images. To test the hypothesis, a convolutional neural network (CNN) model was trained and validated to predict the apparent stiffness tensor of trabecular bone cubes using their DXA images. Trabecular bone cubes obtained from human cadaver proximal femurs were used to obtain simulated DXA images as input, and the apparent stiffness tensor of the trabecular cubes determined by using micro-CT based FE simulations was used as output (ground truth) to train the DL model. The prediction accuracy of the DL model was evaluated by comparing it with the micro-CT based FE models, histomorphometric parameter based multiple linear regression models, and BV/TV/fabric tensor based multiple linear regression models. The results showed that DXA image-based DL model achieved high fidelity in predicting the apparent stiffness tensor of trabecular bone cubes (R² = 0.905-0.973), comparable to or better than the histomorphometric parameter based multiple linear regression and BV/TV/fabric tensor based multiple linear regression models, thus supporting the hypothesis of this study. The outcome of this study could be used to help develop DXA image-based DL techniques for clinical assessment of bone fracture risk.

Application of an enhanced homogenization technique to the structural multiscale analysis of a femur bone

Bone is a complex hierarchical material that can be characterized from the microscale to macroscale. This work demonstrates the application of an enhanced homogenization methodology to the multiscale structural analysis of a femoral bone. The use of this homogenization technique allows to remove subjectivity and reduce the computational cost associated with the iterative process of creating a heterogeneous mesh. Thus, it allows to create simpler homogenized meshes with its mechanical properties defined using information directly from the mesh source: the medical images. Therefore, this methodology is capable to accurately predict bone mechanical behavior in a fraction of the time required by classical approaches. The results show that using the homogenization technique, despite the differences between the used homogeneous and heterogeneous meshes, its mechanical behavior is similar. The proposed homogenization technique is useful for a multiscale modelling and it is computationally efficient.

Predicting Trabecular Bone Stiffness from Clinical Cone-Beam CT and HR-pQCT Data; an In Vitro Study Using Finite Element Analysis

Stiffness and shear moduli of human trabecular bone may be analyzed in vivo by finite element (FE) analysis from image data obtained by clinical imaging equipment such as high resolution peripheral quantitative computed tomography (HR-pQCT). In clinical practice today, this is done in the peripheral skeleton like the wrist and heel. In this cadaveric bone study, fourteen bone specimens from the wrist were imaged by two dental cone beam computed tomography (CBCT) devices and one HR-pQCT device as well as by dual energy X-ray absorptiometry (DXA). Histomorphometric measurements from micro-CT data were used as gold standard. The image processing was done with an in-house developed code based on the automated region growing (ARG) algorithm. Evaluation of how well stiffness (Young’s modulus E3) and minimum shear modulus from the 12, 13, or 23 could be predicted from the CBCT and HR-pQCT imaging data was studied and compared to FE analysis from the micro-CT imaging data. Strong correlations were found between the clinical machines and micro-CT regarding trabecular bone structure parameters, such as bone volume over total volume, trabecular thickness, trabecular number and trabecular nodes (varying from 0.79 to 0.96). The two CBCT devices as well as the HR-pQCT showed the ability to predict stiffness and shear, with adjusted R²-values between 0.78 and 0.92, based on data derived through our in-house developed code based on the ARG algorithm. These findings indicate that clinically used CBCT may be a feasible method for clinical studies of bone structure and mechanical properties in future osteoporosis research.