Prediction of Apparent Trabecular Bone Stiffness through Fourth-Order Fabric Tensors

• The apparent stiffness tensor is an important mechanical parameter for characterizing trabecular bone. Previous studies have modeled this parameter as a function of mechanical properties of the tissue, bone density and a second-order fabric tensor, which encodes both anisotropy and orientation of trabecular bone. Although these models yield strong correlations between observed and predicted stiffness tensors, there is still space for reducing accuracy errors.In this paper we propose a model that uses fourth-order instead of second-order fabric tensors. First, the totally symmetric part of the stiffness tensor is assumed proportional to the fourth-order fabric tensor in the logarithmic scale. Second, the asymmetric part of the stiffness tensor is derived from relationships among components of the harmonic tensor decomposition of the stiffness tensor. The mean intercept length (MIL), generalized MIL (GMIL) and global structure tensor fourth-order were computed from images acquired through micro computed tomography of 264 specimens of the femur. The predicted tensors were compared to the stiffness tensors computed by using the micro finite element method (micro-FE), which was considered as the gold standard, yielding strong correlations (R^2 above 0.962). The GMIL tensor yielded the best results among the tested fabric tensors. The Frobenius error, geodesic error and the error of the norm were reduced by applying the proposed model by 3.75%, 0.07% and 3.16%, respectively compared to the model by Zysset and Curnier (1995) with the second-order MIL tensor. From the results, fourth-order fabric tensors are a good alternative to the more expensive micro-FE stiffness predictions.

Ämnesord

TEKNIK OCH TEKNOLOGIER  -- Medicinteknik -- Medicinsk bildbehandling (hsv//swe)

ENGINEERING AND TECHNOLOGY  -- Medical Engineering -- Medical Image Processing (hsv//eng)

TEKNIK OCH TEKNOLOGIER  -- Maskinteknik -- Teknisk mekanik (hsv//swe)

ENGINEERING AND TECHNOLOGY  -- Mechanical Engineering -- Applied Mechanics (hsv//eng)

Nyckelord

Fabric tensors

stiffness tensor

mechanical properties

trabecular bone

mean intercept length

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