Abstract
Measurement of anisotropy of trabecular bone has clinical relevance in osteoporosis. In this study, anisotropy measurements of 15 trabecular bone biopsies from the radius estimated by different fabric tensors on images acquired through cone beam computed tomography (CBCT) and micro computed tomography (micro-CT) were compared. The results show that the generalized mean intercept length (MIL) tensor performs better than the global gray-scale structure tensor, especially when the von Mises-Fisher kernel is applied. Also, the generalized MIL tensor yields consistent results between the two scanners. These results suggest that this tensor is appropriate for estimating anisotropy in images acquired in vivo through CBCT.
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References
Burghardt A, Link T, Majumdar S (2011) High-resolution computed tomography for clinical imaging of bone microarchitecture. Clin Orthop Relat Res 469(8):2179–2193
Cowin S (1985) The relationship between the elasticity tensor and the fabric tensor. Mech Mater 4(2):137–147
Driscoll JR, Healy DM (1994) Computing Fourier transforms and convolutions on the 2-sphere. Adv Appl Math 15(2):202–250
Förstner W (1986) A feature based correspondence algorithm for image matching. Int Arch Photogramm Remote Sens 26:150–166
Geusens P, Chapurlat R, Schett G, Ghasem-Zadeh A, Seeman E, de Jong J, van den Bergh J (2014) High-resolution in vivo imaging of bone and joints: a window to microarchitecture. Nat Rev Rheumatol 10(5):304–313
Gomberg B, Wehrli F, Vasilić B, Weening R, Saha P, Song H, Wright A (2004) Reproducibility and error sources of μ-MRI-based trabecular bone structural parameters of the distal radius and tibia. Bone 35(1):266–276
Granlund GH, Knutsson H (1995) Signal processing for computer vision. Kluwer Academic, Dordrecht
Griffith J, Genant H (2012) New advances in imaging osteoporosis and its complications. Endocr 42:39–51
Groemer H (1996) Geometric applications of Fourier series and spherical harmonics. Cambridge University Press
Gross T, Pahr D, Zysset P (2013) Morphology-elasticity relationships using decreasing fabric information of human trabecular bone from three major anatomical locations. Biomech Model Mechanobiol 12(4):793–800
Hipp J, Jansujwicz A, Simmons C, Snyder B (1996) Trabecular bone morphology from micro-magnetic resonance imaging. J Bone Miner Res 11(2):286–297
Horn BKP (1984) Extended Gaussian images. Proc IEEE 72(12):1671–1686
Huiskes R (2000) If bone is the answer, then what is the question? J Anat 197:145–156
Jupp PE, Mardia KV (1989) A unified view of the theory of directional statistics, 1975–1988. Int Stat Rev 57(3):261–294
Köthe U, Felsberg M (2005) Riesz-transforms versus derivatives: on the relationship between the boundary tensor and the energy tensor. In: Scale Space and PDE Methods in Computer Vision, Hofgeismar Germany. LNCS 3459:179–191
Monje A, Monje F, Gonzalez-Garcia R, Galindo-Moreno P, Rodriguez-Salvanes F, Wang H (2014) Comparison between microcomputed tomography and cone-beam computed tomography radiologic bone to assess atrophic posterior maxilla density and microarchitecture. Cli Oral Implants Res 25(6):723–728
Moreno R, Smedby Ö (2014) Volume-based fabric tensors through lattice-Boltzmann simulations. In: Proceedings International Conference on Pattern Recognition (ICPR), Stockholm Sweden, pp 3179–3184
Moreno R, Borga M, Smedby Ö (2012) Generalizing the mean intercept length tensor for gray-level images. Med Phys 39(7):4599–4612
Moreno R, Pizarro L, Burgeth B, Weickert J, Garcia MA, Puig D (2012) Adaptation of tensor voting to image structure estimation. In: Laidlaw D, Vilanovaeds A (eds) New developments in the visualization and processing of tensor fields. Springer. pp 29–50
Moreno R, Borga M, Smedby Ö (2013) Correlations between fabric tensors computed on cone beam and micro computed tomography images. In: Tavares J, Natal-Jorge R (eds) Computational vision and medical image processing (VIPIMAGE). CRC Press (2013), pp 393–398
Moreno R, Borga M, Smedby Ö (2014) Techniques for computing fabric tensors: a review. In: Burgeth B, Vilanova A, Westin CF (eds) Visualization and processing of tensors and higher order descriptors for multi-valued data. Springer, pp 271–292
Mulder L, van Rietbergen B, Noordhoek NJ, Ito K (2012) Determination of vertebral and femoral trabecular morphology and stiffness using a flat-panel C-arm-based CT approach. Bone 50(1):200–208
Odgaard A, Kabel J, van Rietbergen B, Dalstra M, Huiskes R (1997) Fabric and elastic principal directions of cancellous bone are closely related. J Biomech 30(5):487–495
Tabor Z (2005) Novel algorithm detecting trabecular termini in μCT and MRI images. Bone 37(3):395–403
Tabor Z, Rokita E (2007) Quantifying anisotropy of trabecular bone from gray-level images. Bone 40(4):966–972
Tabor Z, Petryniak R, Latała Z, Konopka T (2013) The potential of multi-slice computed tomography based quantification of the structural anisotropy of vertebral trabecular bone. Med Eng Phys 35(1):7–15
Zysset PK (2003) A review of morphology-elasticity relationships in human trabecular bone: theories and experiments. J Biomech 36(10):1469–1485
Zysset PK, Goulet RW, Hollister SJ (1998) A global relationship between trabecular bone morphology and homogenized elastic properties. J Biomech Eng 120(5):640–646
Acknowledgements
We thank Andres Laib from SCANCO Medical AG for providing the micro-CT data of the specimens. The authors declare no conflict of interest.
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Moreno, R., Borga, M., Klintström, E., Brismar, T., Smedby, Ö. (2015). Anisotropy Estimation of Trabecular Bone in Gray-Scale: Comparison Between Cone Beam and Micro Computed Tomography Data. In: Tavares, J., Natal Jorge, R. (eds) Developments in Medical Image Processing and Computational Vision. Lecture Notes in Computational Vision and Biomechanics, vol 19. Springer, Cham. https://doi.org/10.1007/978-3-319-13407-9_13
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