Annals of Biomedical Engineering

, Volume 42, Issue 5, pp 950–959 | Cite as

Assessment of Transverse Isotropy in Clinical-Level CT Images of Trabecular Bone Using the Gradient Structure Tensor

  • David LarssonEmail author
  • Benoît Luisier
  • Mariana E. Kersh
  • Enrico Dall’Ara
  • Philippe K. Zysset
  • Marcus G. Pandy
  • Dieter H. PahrEmail author


The aim of this study was to develop a GST-based methodology for accurately measuring the degree of transverse isotropy in trabecular bone. Using femoral sub-regions scanned in high-resolution peripheral QCT (HR-pQCT) and clinical-level-resolution QCT, trabecular orientation was evaluated using the mean intercept length (MIL) and the gradient structure tensor (GST) on the HR-pQCT and QCT data, respectively. The influence of local degree of transverse isotropy (DTI) and bone mineral density (BMD) was incorporated into the investigation. In addition, a power based model was derived, rendering a 1:1 relationship between GST and MIL eigenvalues. A specific DTI threshold (DTI thres) was found for each investigated size of region of interest (ROI), above which the estimate of major trabecular direction of the GST deviated no more than 30° from the gold standard MIL in 95% of the remaining ROIs (mean error: 16°). An inverse relationship between ROI size and DTI thres was found for discrete ranges of BMD. A novel methodology has been developed, where transversal isotropic measures of trabecular bone can be obtained from clinical QCT images for a given ROI size, DTI thres and power coefficient. Including DTI may improve future clinical QCT finite-element predictions of bone strength and diagnoses of bone disease.


Human proximal femur Structural anisotropy Clinical-level quantitative computed tomography Fabric tensors Degree of transverse isotropy 



The authors wish to thank Ms. Linda Ringqvist for help with illustrations.

Conflict of interest

There is no financial or personal conflict of interest with other people or organizations that could inappropriately influence the manuscript material and the authors work.


  1. 1.
    Christen, P., K. Ito, R. Muller, M. R. Rubin, D. W. Dempster, J. P. Bilezikian, and B. van Rietbergen. Patient-specific bone modelling and remodelling simulation of hypoparathyroidism based on human iliac crest biopsies. J. Biomech. 45(14):2411–2416, 2012.PubMedCentralPubMedCrossRefGoogle Scholar
  2. 2.
    Cody, D. D., G. J. Gross, F. J. Hou, H. J. Spencer, S. A. Goldstein, and D. P. Fyhrie. Femoral strength is better predicted by finite element models than QCT and DXA. J. Biomech. 32(10):1013–1020, 1999.PubMedCrossRefGoogle Scholar
  3. 3.
    Consensus development conference. Prophylaxis and treatment of osteoporosis. Am. J. Med. 90(1):107–110, 1991.CrossRefGoogle Scholar
  4. 4.
    Cosmi, F. Morphology-based prediction of elastic properties of trabecular bone samples. Acta Bioeng. Biomech. 11(1):3–9, 2009.PubMedGoogle Scholar
  5. 5.
    Cowin, S. C. The relationship between the elasticity tensor and the fabric tensor. Mech. Mater. 4(2):137–147, 1985.CrossRefGoogle Scholar
  6. 6.
    Dall’Ara, E., B. Luisier, R. Schmidt, F. Kainberger, P. Zysset, and D. Pahr. A nonlinear QCT-based finite element model validation study for the human femur tested in two configurations in vitro. Bone 52(1):27–38, 2013.PubMedCrossRefGoogle Scholar
  7. 7.
    Dragomir-Daescu, D., J. Op Den Buijs, S. McEligot, Y. Dai, R. C. Entwistle, C. Salas, L. J. Melton, III, K. E. Bennet, S. Khosla, and S. Amin. Robust QCT/FEA models of proximal femur stiffness and fracture load during a sideways fall on the hip. Ann. Biomed. Eng. 39(2):742–755, 2011.Google Scholar
  8. 8.
    Fedorov, A., R. Beichel, J. Kalpathy-Cramer, J. Finet, J. C. Fillion-Robin, S. Pujol, C. Bauer, D. Jennings, F. Fennessy, M. Sonka, J. Buatti, S. Aylward, J. V. Miller, S. Pieper, and R. Kikinis. 3D Slicer as an image computing platform for the Quantitative Imaging Network. Magn. Reson. Imaging 30(9):1323–1341, 2012.PubMedCentralPubMedCrossRefGoogle Scholar
  9. 9.
    Geraets, W. G., L. J. van Ruijven, J. G. Verheij, P. F. van der Stelt, and T. M. van Eijden. Spatial orientation in bone samples and Young’s modulus. J. Biomech. 41(10):2206–2210, 2008.PubMedCrossRefGoogle Scholar
  10. 10.
    Harrigan, T. P., and R. W. Mann. Characterization of microstructural anisotropy in orthotropic materials using a second rank tensor. J. Mater. Sci. 19(3):761–767, 1984.CrossRefGoogle Scholar
  11. 11.
    Kang, Y., K. Engelke, and W. A. Kalender. A new accurate and precise 3-D segmentation method for skeletal structures in volumetric CT data. IEEE Trans. Med. Imaging 22(5):586–598, 2003.PubMedCrossRefGoogle Scholar
  12. 12.
    Kersh, M., P. Zysset, D. Pahr, U. Wolfram, D. Larsson, and M. Pandy. “Measurement of structural anisotropy in femoral trabecular bone using clinical-resolution CT images. J. Biomech. 46(15):2659–2666, 2013.PubMedCrossRefGoogle Scholar
  13. 13.
    Lenaerts, L., and G. H. van Lenthe. Multi-level patient-specific modelling of the proximal femur. A promising tool to quantify the effect of osteoporosis treatment. Philos. Trans. R. Soc. A. 367(1895):2079–2093, 2009.Google Scholar
  14. 14.
    Liu, Y., P. K. Saha, and Z. Xu. Quantitative characterization of trabecular bone micro-architecture using tensor scale and multi-detector CT imaging. Lect. Notes Comput. Sci. 15(1):124–131, 2012.Google Scholar
  15. 15.
    Matsuura, M., F. Eckstein, E. M. Lochmuller, and P. K. Zysset. The role of fabric in the quasi-static compressive mechanical properties of human trabecular bone from various anatomical locations. Biomech. Model Mechan. 19:19, 2007.Google Scholar
  16. 16.
    Ohman, C., M. Baleani, E. Perilli, E. Dall’Ara, S. Tassani, F. Baruffaldi, and M. Viceconti. Mechanical testing of cancellous bone from the femoral head: experimental errors due to off-axis measurements. J. Biomech. 40(11):2426–2433, 2007.PubMedCrossRefGoogle Scholar
  17. 17.
    Pahr, D., and P. Zysset. A comparison of enhanced continuum FE with micro FE models of human vertebral bodies. J. Biomech. 42(4):455–462, 2009.PubMedCrossRefGoogle Scholar
  18. 18.
    Pahr, D. H., and P. K. Zysset. From high-resolution CT data to finite element models: development of an integrated modular framework. Comput. Methods Biomech. 12(1):45–57, 2009.CrossRefGoogle Scholar
  19. 19.
    Pahr, D., J. Schwiedrzik, E. Dall’Ara, and P. Zysset. Clinical versus pre-clinical FE models for vertebral body strength predictions. J. Mech. Behav. Biomed. 12:S1751–S6161, 2012.Google Scholar
  20. 20.
    Pieper, S., M. Halle, and R. Kikinis. 3D SLICER. I S Biomed Imaging. Vol. 1, pp. 632–635, 2004.Google Scholar
  21. 21.
    Pieper, S., W. Lorensen, W. Schroeder, and R. Kikinis. The NA-MIC Kit: ITK, VTK, Pipelines, Grids and 3D Slicer as an Open Platform for the Medical Image Computing Community. I S Biomed Imaging, Vol. 1, pp. 698–701, 2006.Google Scholar
  22. 22.
    Ridler, T. W., and S. Calvard. Picture thresholding using an iterative selection method. IEEE Trans. Syst. Man Cybern. B 8(8):630–632, 1978.CrossRefGoogle Scholar
  23. 23.
    Rotter, M., A. Berg, H. Langenberger, S. Grampp, H. Imhof, and E. Moser. Autocorrelation analysis of bone structure. J. Magn. Reson. Imaging 14(1):87–93, 2001.PubMedCrossRefGoogle Scholar
  24. 24.
    San Antonio, T., M. Ciaccia, C. Müller-Karger, and E. Casanova. Orientation of orthotropic material properties in a femur FE model: a method based on the principal stresses directions. Med. Eng. Phys. 34(7):914–919, 2012.Google Scholar
  25. 25.
    Scherf, H., and R. Tilgner. A new high-resolution computed tomography (CT) segmentation method for trabecular bone architectural analysis. Am. J. Phys. Anthropol. 140(1):39–51, 2009.PubMedCrossRefGoogle Scholar
  26. 26.
    Schulte, F. A., A. Zwahlen, F. M. Lambers, G. Kuhn, D. Ruffoni, D. Betts, D. J. Webster, and R. Muller. Strain-adaptive in silico modeling of bone adaptation—a computer simulation validated by in vivo micro-computed tomography data. Bone 52(1):485–492, 2013.PubMedCrossRefGoogle Scholar
  27. 27.
    Siris, E. S., P. D. Miller, E. Barrett-Connor, K. G. Faulkner, L. E. Wehren, T. A. Abbott, M. L. Berger, A. C. Santora, and L. M. Sherwood. Identification and fracture outcomes of undiagnosed low bone mineral density in postmeno-pausal women. JAMA 286(22):2815–2822, 2001.PubMedCrossRefGoogle Scholar
  28. 28.
    Tabor, Z. On the equivalence of two methods of determining fabric tensor. Med. Eng. Phys. 31:1313–1322, 2009.PubMedCrossRefGoogle Scholar
  29. 29.
    Tabor, Z. Anisotropic resolution biases estimation of fabric from 3D gray-level images. Med. Eng. Phys. 32:39–48, 2010.PubMedCrossRefGoogle Scholar
  30. 30.
    Tabor, Z. Equivalence of mean intercept length and gradient fabric tensors—3D study. Med. Eng. Phys. 34(5):598–604, 2012.PubMedCrossRefGoogle Scholar
  31. 31.
    Tabor, Z., and E. Rokita. Quantifying anisotropy of trabecular bone from gray-level images. Bone 40(4):966–972, 2007.PubMedCrossRefGoogle Scholar
  32. 32.
    Trabelsi, N., and Z. Yosibash. Patient-specific finite-element analyses of the proximal femur with orthotropic material properties validated by experiments. J. Biomed. Eng. 133(6):061001, 2011.Google Scholar
  33. 33.
    Varga, P. Prediction of Distal Radius Fracture Load Using HR-pQCT-Based Finite Element Analysis. Vienna: Vienna University of Technology, 2009.Google Scholar
  34. 34.
    Varga, P., and P. K. Zysset. Sampling sphere orientation distribution: an efficient method to quantify trabecular bone fabric on grayscale images. Med. Image Anal. 13(3):530–541, 2009.PubMedCrossRefGoogle Scholar
  35. 35.
    Wald, M. J., B. Vasilic, P. K. Saha, and F. W. Wehrli. Spatial autocorrelation and mean intercept length analysis of trabecular bone anisotropy applied to in vivo magnetic resonance imaging. Med. Phys. 34(3):1110–1120, 2007.PubMedCrossRefGoogle Scholar
  36. 36.
    WHO. Assessment of Fracture Risk and Its Application to Screening for Postmenopausal Osteoporosis. Geneve: WHO, 1994.Google Scholar
  37. 37.
    Wolfram, U., B. Schmitz, F. Heuer, M. Reinehr, and H. J. Wilke. Vertebral trabecular main direction can be determined from clinical CT datasets using the gradient structure tensor and not the inertia tensor–a case study. J. Biomech. 42(10):1390–1396, 2009.PubMedCrossRefGoogle Scholar
  38. 38.
    Zysset, P. K., and A. Curnier. An alternative model for anisotropic elasticity based on fabric tensor. Mech. Mater. 21:243–250, 1995.CrossRefGoogle Scholar

Copyright information

© Biomedical Engineering Society 2014

Authors and Affiliations

  • David Larsson
    • 1
    Email author
  • Benoît Luisier
    • 1
  • Mariana E. Kersh
    • 2
  • Enrico Dall’Ara
    • 1
  • Philippe K. Zysset
    • 3
  • Marcus G. Pandy
    • 2
  • Dieter H. Pahr
    • 1
    Email author
  1. 1.Institute of Lightweight Design and Structural BiomechanicsVienna University of TechnologyViennaAustria
  2. 2.Department of Mechanical EngineeringUniversity of MelbourneParkvilleAustralia
  3. 3.Institute of Surgical Technology and BiomechanicsUniversity of BernBernSwitzerland

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