Equivalence of mean intercept length and gradient fabric tensors - 3D study.

In this study the relationship between the mean intercept length (MIL) method - the current standard histomorphometric method of assessing structural anisotropy and an alternative method of the gray-level structure tensor (GST) is investigated. Both methods are applied to a set of 25 three-dimensional binary μCT images of trabecular bone. It is shown that there is a very strong correlation between the logarithms of the principal values of the MIL and the GST fabric tensors (Pearson's coefficient of correlation higher than 0.98) and between the logarithms of the invariants of the MIL and the GST fabric tensors (Pearson's coefficient of correlation higher than 0.999). There is also a good correlation between the degree of anisotropy calculated from the MIL and from the GST tensors (Pearson's coefficient of correlation equal to 0.90). The principal anisotropy directions of the MIL and the GST fabric tensors coincide at the 5% significance level. Additionally, the performance of both methods is tested, based on a set of artificial structures with prescribed orientations.

[1]  C Illueca,et al.  Fourier analysis methodology of trabecular orientation measurement in the human tibial epiphysis , 2001, Journal of anatomy.

[2]  S A Goldstein,et al.  The relationship between the structural and orthogonal compressive properties of trabecular bone. , 1994, Journal of biomechanics.

[3]  Zbisław Tabor,et al.  On the equivalence of two methods of determining fabric tensor. , 2009, Medical engineering & physics.

[4]  Jack Bresenham,et al.  Algorithm for computer control of a digital plotter , 1965, IBM Syst. J..

[5]  Hisham M. Haddad,et al.  Proceedings of the 2003 ACM Symposium on Applied Computing (SAC), March 9-12, 2003, Melbourne, FL, USA , 2003, SAC.

[6]  Theodore Raphan,et al.  Quantification of trabecular bone mass and orientation using Gabor wavelets , 2003, SAC '03.

[7]  H. Imhof,et al.  Autocorrelation analysis of bone structure , 2001, Journal of magnetic resonance imaging : JMRI.

[8]  Ernest L. Hall,et al.  Computer Image Processing and Recognition , 1980, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[9]  Zbisław Tabor,et al.  A novel method of estimating structure model index from gray-level images. , 2011, Medical engineering & physics.

[10]  Péter Varga,et al.  Sampling sphere orientation distribution: An efficient method to quantify trabecular bone fabric on grayscale images , 2009, Medical Image Anal..

[11]  Philippe K Zysset,et al.  A review of morphology-elasticity relationships in human trabecular bone: theories and experiments. , 2003, Journal of biomechanics.

[12]  Sandra J Shefelbine,et al.  BoneJ: Free and extensible bone image analysis in ImageJ. , 2010, Bone.

[13]  Punam K. Saha,et al.  A robust method for measuring trabecular bone orientation anisotropy at in vivo resolution using tensor scale , 2004, Pattern Recognit..

[14]  Punam K Saha,et al.  Spatial autocorrelation and mean intercept length analysis of trabecular bone anisotropy applied to in vivo magnetic resonance imaging. , 2007, Medical physics.

[15]  W. J. Whitehouse.  The quantitative morphology of anisotropic trabecular bone , 1974, Journal of microscopy.

[16]  R. Huiskes,et al.  Constitutive relationships of fabric, density, and elastic properties in cancellous bone architecture. , 1999, Bone.

[17]  Maarten Moesen,et al.  A symmetry invariant formulation of the relationship between the elasticity tensor and the fabric tensor. , 1985, Mechanics of materials : an international journal.

[18]  Donald Ervin Knuth,et al.  The Art of Computer Programming , 1968 .

[19]  Nicholas I. Fisher,et al.  Statistical Analysis of Spherical Data. , 1987 .

[20]  Punam K. Saha,et al.  Measurement of trabecular bone thickness in the limited resolution regime of in vivo MRI by fuzzy distance transform , 2004, IEEE Transactions on Medical Imaging.

[21]  Z. Tabor,et al.  Quantifying anisotropy of trabecular bone from gray-level images. , 2007, Bone.

[22]  K. Engelke,et al.  High resolution computed tomography of the vertebrae yields accurate information on trabecular distances if processed by 3D fuzzy segmentation approaches. , 2009, Bone.

[23]  P. Zysset,et al.  Assessment of volume fraction and fabric in the distal radius using HR-pQCT. , 2009, Bone.

[24]  Rik Huiskes,et al.  The dependence of the elastic properties of osteoporotic cancellous bone on volume fraction and fabric. , 2003, Journal of biomechanics.

[25]  Uwe Wolfram,et al.  Vertebral trabecular main direction can be determined from clinical CT datasets using the gradient structure tensor and not the inertia tensor--a case study. , 2009, Journal of biomechanics.

[26]  Patrik Rogalla,et al.  Assessment of trabecular bone structure of the calcaneus using multi-detector CT: correlation with microCT and biomechanical testing. , 2009, Bone.

[27]  Milton Abramowitz,et al.  Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables , 1964 .

[28]  S. Majumdar,et al.  Direct measures of trabecular bone architecture from MR images. , 2001, Advances in experimental medicine and biology.