Change search
ReferencesLink to record
Permanent link

Direct link
Prediction of Apparent Trabecular Bone Stiffness through Fourth-Order Fabric Tensors
KTH, School of Technology and Health (STH), Medical Engineering, Medical Image Processing and Visualization.ORCID iD: 0000-0001-5765-2964
KTH, School of Technology and Health (STH), Medical Engineering, Medical Image Processing and Visualization.ORCID iD: 0000-0002-7750-1917
(Institute for Lightweight Design and Structural Biomechanics, Technical University of Vienna)
2015 (English)In: Biomechanics and Modeling in Mechanobiology, ISSN 1617-7959, E-ISSN 1617-7940Article in journal (Refereed) Published
Abstract [en]

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.

Place, publisher, year, edition, pages
Springer Berlin/Heidelberg, 2015.
Keyword [en]
Fabric tensors, stiffness tensor, mechanical properties, trabecular bone, mean intercept length
National Category
Medical Image Processing Applied Mechanics
URN: urn:nbn:se:kth:diva-173118DOI: 10.1007/s10237-015-0726-5ISI: 000380117900006ScopusID: 2-s2.0-84940880957OAI: diva2:851756
Swedish Research Council, 2012-3512Swedish Research Council, 2014-6153Swedish Heart Lung Foundation, 2011-0376

QC 20160115

Available from: 2015-09-07 Created: 2015-09-07 Last updated: 2016-09-30Bibliographically approved

Open Access in DiVA

fulltext(7970 kB)2 downloads
File information
File name FULLTEXT01.pdfFile size 7970 kBChecksum SHA-512
Type fulltextMimetype application/pdf

Other links

Publisher's full textScopusPublishers website

Search in DiVA

By author/editor
Moreno, RodrigoSmedby, Örjan
By organisation
Medical Image Processing and Visualization
In the same journal
Biomechanics and Modeling in Mechanobiology
Medical Image ProcessingApplied Mechanics

Search outside of DiVA

GoogleGoogle Scholar
Total: 2 downloads
The number of downloads is the sum of all downloads of full texts. It may include eg previous versions that are now no longer available

Altmetric score

Total: 33 hits
ReferencesLink to record
Permanent link

Direct link