Morphometric analysis of trabecular bone thickness using different algorithms (original) (raw)

2007, Canadian journal of electrical and computer engineering

Abstract

Investigations have been carried out with the goal of assessing the trabecular bone thickness of biological samples using images obtained by micro-computed tomography and magnetic resonance imaging. There is no conventional definition of trabecular bone thickness, and many methods may be involved in determining it. However, the results of the available algorithms or software packages differ considerably from each other. This paper determines trabecular bone thickness on the basis of several algorithms. A deep understanding of the performance of different methods is achieved by studying pseudo-three-dimensional images of both geometrical models of well-defined thickness and real bone samples with different bone densities. The models facilitate comparisons between the algorithms or software packages. Comparison of the results obtained from these commercial software packages and other state-of-the-art algorithms shows that the thickness, spatial distribution, and shape of an object affect each result differently, but in a significant manner. This is primarily due to variations in the thresholding algorithms used to distinguish object area elements (pixels/voxels) from the background, or non-object, region. Additionally, the results show that the average difference in thickness measurements can vary by up to 102.34% for models and 46.49% for real bone samples. This data shows that the differences in measurements of the trabecular bone thickness due simply to the algorithm involved are remarkable. Therefore, biomedical engineers and scientists should be careful to select the algorithm that is most compatible with their specific application. Cetteétude aété menée avec l'intention d'évaluer l'épaisseur d'os trabéculaireà partir d'échantillons acquis par micro tomographie et résonance magnétique. Il n'existe pas de définition conventionnelle de l'épaisseur de l'os trabéculaire. Aussi, plusieurs approches ontété envisagées en vue de caractériser cette dernière. Cependant il est apparu que les résultats obtenus différaient considérablement suivant les algorithmes ou logiciels commerciaux utilisés. Uneétude plus approfondie a doncété menée afin de déterminer les performances de chacune des méthodes, ceci au moyen d'étude faisant intervenir des modèles tridimensionnels numériques auxépaisseurs connues et d'os de différentes densités osseuses. Le recoursà l'utilisation de modèles a facilité la comparaison des différents algorithmes et logiciels. Cette comparaison a révélé que l'épaisseur, la répartition spatiale et la forme d'un objet affectaient de manière significative les résultats obtenus. Ceci fut principalement dûà la capacité des différentes approchesà discriminer l'objet a analyser (pixel/voxel) de l'information non pertinente, c'est-à-dire le fond de l'image. En outre, les résultats ont montré que les mesures d'épaisseur avaient une erreur moyenne maximale de 102.34% pour les modèles numériques et de 46.49% pour les spécimens d'os. Ces données ont indiqué que les différences de mesure d'épaisseur en raison des algorithmes utilisés sont significatives. Aussi, les ingénieurs bio-médicaux et les scientifiques en biomécanique devraientêtre très prudent quantà la sélection d'algorithmes morphométriques afin que ceux-ci soient les plus compatibles possibles avec leurs applications.

Figures (6)

Figure 2: A modified binary image of the trabecular bone object in Fig. 1. Figure 1: A magnified image of a trabecular bone object after thresholding.

Figure 2: A modified binary image of the trabecular bone object in Fig. 1. Figure 1: A magnified image of a trabecular bone object after thresholding.

Figure 3: (a) A model containing rectangular objects with widths from 3 to 20 elements. (b) Histogram counts of the model of rectangular objects. (c) A model of a triangular objec (d) A 3D representation of the rectangular model. (e) A 3D representation of the triangular model.

Figure 3: (a) A model containing rectangular objects with widths from 3 to 20 elements. (b) Histogram counts of the model of rectangular objects. (c) A model of a triangular objec (d) A 3D representation of the rectangular model. (e) A 3D representation of the triangular model.

Figure 4: (a) 3D representation of bone sample. (b) s-CT image of high-density trabecular bone. (c) ,1-CT image of low-density trabecular bone. (d) Histogram counts of bone sampl

Figure 4: (a) 3D representation of bone sample. (b) s-CT image of high-density trabecular bone. (c) ,1-CT image of low-density trabecular bone. (d) Histogram counts of bone sampl

If the average thickness values of the DT algorithm for modified images are compared with those of the FDT algorithm, we observe larger values for the FDT algorithm. This result can be explained by the fuzzy and binary thresholding methods used for the FDT and DT algorithms respectively. Both CTan and ANT overestimate the bone thicknesses (compared to the average thickness based on the complete skeleton of the object), especially in the case of the CTan results for non-modified images. One reason for this overestimation is that the algorithm used by both CTan and ANT neglects thin objects: see Fig. 6(d), in which CTan could not find objects with thicknesses under 72 4m. Another expla- nation, in the case of non-modified images, is the error produced by CTan’s difficulty in handling arbitrary numbers of cross-sectional pix-

If the average thickness values of the DT algorithm for modified images are compared with those of the FDT algorithm, we observe larger values for the FDT algorithm. This result can be explained by the fuzzy and binary thresholding methods used for the FDT and DT algorithms respectively. Both CTan and ANT overestimate the bone thicknesses (compared to the average thickness based on the complete skeleton of the object), especially in the case of the CTan results for non-modified images. One reason for this overestimation is that the algorithm used by both CTan and ANT neglects thin objects: see Fig. 6(d), in which CTan could not find objects with thicknesses under 72 4m. Another expla- nation, in the case of non-modified images, is the error produced by CTan’s difficulty in handling arbitrary numbers of cross-sectional pix-

Figure 6: Histogram counts and average thicknesses of high- and low-density bone sam- ples using different pieces of software, as follows: (a) FDT, (b) DT for original image, (c) DT for modified image, (d) CTan for original image, (e) CTan for modified image, (f) ANT.

Figure 6: Histogram counts and average thicknesses of high- and low-density bone sam- ples using different pieces of software, as follows: (a) FDT, (b) DT for original image, (c) DT for modified image, (d) CTan for original image, (e) CTan for modified image, (f) ANT.

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References (21)

  1. Z.P. Luo et al., "Effects of mechanical stress/strain and estrogen on cancellous bone structure predicted by fuzzy decision," IEEE Trans. Bio-Med. Eng., vol. 47, no. 3, Mar. 2000, pp. 344-351.
  2. J.A. Kanis, D. Black, and C. Cooper, "A new approach to the development of assess- ment guidelines for osteoporosis," Osteoporosis Int., vol. 13, no. 7, 2002, pp. 527- 536.
  3. S. Kolta, A. Le Bras, and D. Mitton, "Three-dimensional X-ray absorptiometry (3D- XA): A method for reconstruction of human bones using a dual X-ray absorptio- metry device," Osteoporosis Int., vol. 16, no. 8, 2005, pp. 969-976.
  4. D.C. Newitt, et al., "In vivo assessment of architecture and micro-finite element analysis derived indices of mechanical properties of trabecular bone in the radius," Osteoporosis Int., vol. 13, no. 1, Jan. 2002, pp. 6-17.
  5. D.C. Newitt, B. Van Rietbergen, and S. Majumdar, "Processing and analysis of in vivo high-resolution MR images of trabecular bone for longitudinal studies: Repro- ducibility of structural measures and micro-finite element analysis derived mechan- ical properties," Osteoporosis Int., vol. 13, no. 4, 2002, pp. 278-287.
  6. R. Müller, "Bone microarchitecture assessment: Current and future trends," Osteo- porosis Int., vol. 14, Sept. 2003, suppl. 5, pp. 89-99.
  7. P.K. Saha and F.W. Wehrli, "Measurement of trabecular bone thickness in the lim- ited resolution regime of in vivo MRI by fuzzy distance transform," IEEE Trans. Med. Imag., vol. 23, no. 1, Jan. 2004, pp. 53-64.
  8. F.W. Wehrli et al., "Noninvasive assessment of bone architecture by magnetic reso- nance micro-imaging-based virtual bone biopsy," Proc. IEEE, vol. 91, no. 10, Oct. 2003, pp. 1520-1542.
  9. E. Mittra, C. Rubin, and Y.X. Qin, "Interrelationship of trabecular mechanical and microstructural properties in sheep trabecular bone," J. Biomech., vol. 38, no. 6, June 2005, pp. 1229-1237.
  10. B. Van Rietbergen et al., "Tissue stresses and strain in trabeculae of a canine prox- imal femur can be quantified from computer reconstructions," J. Biomech., vol. 32, no. 2, Feb. 1999, pp. 443-451.
  11. L. Pothuaud et al., "In vivo application of 3D-line skeleton graph analysis (LSGA) technique with high-resolution magnetic resonance imaging of trabecular bone structure," Osteoporosis Int., vol. 15, no. 5, May 2004, pp. 411-419.
  12. J.S. Gregory et al., "Analysis of trabecular bone structure using Fourier transforms and neural networks," IEEE Trans. Inform. Technol. Biomed., vol. 3, no. 4, Dec. 1999, pp. 289-294.
  13. B.R. Gomberg et al., "Topological analysis of trabecular bone MR images," IEEE Trans. Med. Imag., vol. 19, no. 3, Mar. 2000, pp. 166-174.
  14. A. Accardo et al., "Ex vivo assessment of trabecular bone structure from three- dimensional projection reconstruction MR micro-images," IEEE Trans. Bio-Med. Eng., vol. 50, no. 8, Aug. 2003, pp. 967-977.
  15. T. Hildebrand and P. Rüegsegger, "A new method for the model-independent as- sessment of thickness in three-dimensional images," J. Microscopy, vol. 185, no. 1, Jan. 1997, pp. 67-75.
  16. G. Borgefors and S. Svensson, "Fuzzy border distance transforms and their use in 2D skeletonization," in Proc. 16th IEEE Int. Conf. Pattern Recognition, vol. 1, 2002, pp. 180-183.
  17. F.Y. Shih and Y.-T. Wu, "Fast Euclidean distance transformation in two scans using a 3 × 3 neighborhood," Computer Vision and Image Understanding, vol. 93, no. 2, Feb. 2004, pp. 195-205.
  18. P.K. Saha, F.W. Wehrli, and B.R. Gomberg, "Fuzzy distance transform: Theory, algorithms, and applications," Computer Vision and Image Understanding, vol. 86, no. 3, June 2002, pp. 171-190.
  19. A. Darabi and G. Baroud, "A new fuzzy distance transform method applied to tra- becular bone thickness assessment," submitted to Computer Vision and Image Un- derstanding, 2007.
  20. O. Cuisenaire and B. Macq, "Fast Euclidean distance transformations by propaga- tion using multiple neighbourhoods," Computer Vision and Image Understanding, vol. 76, no. 2, Nov. 1999, pp. 163-172.
  21. Akbar Darabi received the B.Sc. degree in electrical en- gineering in 1987 from K.N. Toosi Technology University, Tehran, Iran, and the M.Sc. and Ph.D. degrees, both in elec- trical engineering, from Université Laval, Quebec, Quebec, Canada, in 1995 and 2000 respectively. He joined the Elec- trical and Computer Engineering Department of Shahid Be- heshti University, Tehran, Iran, as assistant professor, in 2000. He is currently working as a researcher in the Biome- chanics Laboratory at the Université de Sherbrooke, Sher- brooke, Quebec, Canada. He has developed a new fuzzy dis- tance transform algorithm in both two and three dimensions for low-resolution images such as those obtained by micro- computed tomography and magnetic resonance imaging. His main research interests include biomedical image process- ing, artificial intelligence, and nondestructive testing methods. Florent Chandelier, born in France in 1980, received the master's degree in signal treatment and electrical engineer- ing from the engineering school ESME SUDRIA, Paris, France, in 2004. Meanwhile, he joined and received the master's degree in "medical imagery: computational, phys- iological, and physical aspects" from the Medical Univer- sity of Paris, Paris, France, in 2004. To combine both the medical and the engineering aspects of his background, Flo- rent joined the team of Gamal Baroud as a Ph.D. student in the Biomechanics Laboratory at the Université de Sher- brooke, Sherbrooke, Quebec, Canada, in October 2004. His main research interest is the development of technologically new fuzzy approaches to three-dimensional morphological assessments and modelling. Gamal Baroud is a junior Canada Research Chair in Skele- tal Reconstruction and Biomedical Engineering. G. Baroud received his Ph.D. in 1997 in Germany. Since complet- ing a postdoctoral fellowship at the University of Calgary, Calgary, Alberta, Canada, and a research professorship at McGill University, Montreal, Quebec, Canada, he has been director of the Biomechanics Laboratory and an assistant professor at the Université de Sherbrooke, Sherbrooke, Que- bec, Canada, since September 2003. His research focus is the biomechanics and micro-instrumentation of minimally inva- sive stabilization of osteoporotic bone using medical bone cement.