Shannon's entropy and fractal dimension provide an objective account of bone tissue organization during calvarial bone regeneration

Microscopy Research and Technique

Volumn 71, Issue 8, 2008, Pages 619-625

  Rocha, Lenaldo B ^a   Adam, Randall L ^b   Leite, Neucimar J ^b   Metze, Konradin ^b   Rossi, Marcos A ^a  

^a UNIVERSITY OF SÃO PAULO   (Brazil)

^b UNIVERSITY OF CAMPINAS   (Brazil)

Author keywords

Bioengineering; Biomaterials; Bone histomorphometry; Growth and development; Tissue remodeling

Indexed keywords

BIOMATERIALS; BONE; COLLAGEN; ENTROPY; FINITE DIFFERENCE METHOD; IMAGE TEXTURE; LAMELLAR STRUCTURES; TISSUE REGENERATION;

BIOENGINEERING; BONE HISTOMORPHOMETRY; BONE REGENERATION; BONE TISSUE; CALVARIAL BONES; COMPACT BONE; GROWTH AND DEVELOPMENT; SHANNON'S ENTROPY; STANDARD ERRORS; TISSUE REMODELING;

FRACTAL DIMENSION;

COLLAGEN; POLYANION;

ANIMAL EXPERIMENT; ANIMAL TISSUE; ARTICLE; BONE DEVELOPMENT; BONE GRAFT; BONE REGENERATION; BONE REMODELING; BONE TISSUE; CALVARIA; ENTROPY; FRACTAL ANALYSIS; IMAGE ANALYSIS; MALE; MORPHOMETRICS; NONHUMAN; OSSIFICATION; PRIORITY JOURNAL; RAT; SKULL DEFECT;

RATTUS;

EID: 49749103311     PISSN: 1059910X     EISSN: 10970029     Source Type: Journal    
DOI: 10.1002/jemt.20598     Document Type: Article

References (39)

1. Adam RL, Corsini TCG, Silva PV, Cintra ML, Leite NJ, Metze K. 2004. Fractal dimensions applied to thick contour detection and residues - Comparison of keloids and hypertrophic scars. Cytometry A 59:63-64.
2. Adam RL, Silva RC, Pereira FG, Leite NJ, Lorand-Metze I, Metze K. 2006. The fractal dimension of nuclear chromatin as a prognostic factor in acute precursor B lymphoblastic leukemia. Cell Oncol 28:55-59.
3. Bet MR, Goissis G, Lacerda CA. 2001. Characterization of polyanionic collagen prepared by selective hydrolysis of asparagine and glutamine carboxyamide side chains. Biomacromolecules 2:1074-1079.
4. Bet MR, Goissis G, Vargas S, Selistre-de-Araujo HS. 2003. Cell adhesion and cytotoxicity studies over polyanionic collagen surfaces with variable negative charge and wettability. Biomaterials 24: 131-137.
5. Bruhn J, Lehmann LE, Ropcke H, Bouillon TW, Hoeft A. 2001. Shannon entropy applied to the measurement of the electroencephalographic effects of desflurane. Anesthesiology 95:30-35.
6. Chappard D, Legrand E, Pascaretti C, Basle MF, Audran M. 1999. Comparison of eight histomorphometric methods for measuring trabecular bone architecture by image analysis on histological sections. Microsc Res Technol 45:303-312.
7. Chappard D, Legrand E, Haettich B, Chalès G, Auvinet B, Eschard JP, Hamelin JP, Baslé MF, Audran M. 2001. Fractal dimension of trabecular bone: Comparison of three histomorphometric computed techniques for measuring the architectural two-dimensional complexity. J Pathol 195:515-521.
8. Chung HW, Chu CC, Underweiser M, Wehrli FW. 1994. On the fractal nature of trabecular structure. Med Phys 21:1535-1540.
9. Cross SS. 1997. Fractals in pathology. J Pathol 182:1-8.
10. Fazzalari NL, Parkinson IH. 1996. Fractal dimension and architecture of trabecular bone. J Pathol 178:100-105.
11. Ferreira RC, de Matos PS, Adam RL, Leite NJ, Metze K. 2006. Application of the Minkowski-Bouligan fractal dimension for the differential diagnosis of thyroid follicular neoplasias. Cell Oncol 28:331-333.
12. Garcia Y, Breen A, Burugapalli K, Dockery P, Pandit A. 2007. Stereological methods to assess tissue response for tissue-engineered scaffolds. Biomaterials 28:175-186.
13. Geraets WG, van der Stelt PF. 2000. Fractal properties of bone. Dentomaxillofac Radiol 29:144-153.
14. Gerstenfeld LC, Wronski TJ, Hollinger JO, Einhorn TA. 2005. Application of histomorphometric methods to the study of bone repair. J Bone Miner Res 20:1715-1722.
15. Goissis G, Piccirili L, Goes JC, de Guzzi Plepis AM, Das-Gupta DK. 1998. Anionic collagen: Polymer composites with improved dielectric and rheological properties. Artif Organs 22:203-209.
16. Hastings GW. 2002. What process drives bone formation at bone-implant interfaces? Key Eng Mater 218:109-112.
17. Losa GA, Nonnenmacher TF. 1996. Self-similarity and fractal irregularity in pathologic tissues. Mod Pathol 9:174-182.
18. Majumdar S, Weinstein RS, Prasad RR. 1993. Application of fractal geometry techniques to the study of trabecular bone. Med Phys 20:1611-1619.
19. McLean IW, Nakane PK. 1974. Periodate-lysine-paraformaldehyde fixative - a new fixative for immunoelectron microscopy. J Histochem Cytochem 22:1077-1083.
20. Metze K, Lobo AM, Lorand-Metze I. 2000. Nucleolus organizer regions (AgNORs) and total tumor mass are independent prognostic parameters for treatment-free period in chronic lymphocytic leukemia. Int J Cancer 89:440-443.
21. Metze K, Adam RL, Leite NJ. 2002. Are higher order estimates of Shannon's entropy important for image analysis? Anal Cell Pathol 24:192.
22. Mori S, Sawai T, Teshima T, Kyogoku M. 1988. A new decalcifying technique for immunohistochemical studies of calcified tissue, especially applicable for cell surface marker demonstration. J Histochem Cytochem 36:111-114.
23. Nair MK, Seyedain A, Webber RL, Nair UP, Piesco NP, Agarwal S, Mooney MP, Gröndahl HG. 2001. Fractal analyses of osseus healing using tuned aperture computed tomography images. Eur Radiol 11:1510-1515.
24. Parfitt AM, Drezner MK, Glorieux FH, Kanis JA, Malluche H, Meunier PJ, Ott SM, Recker RR. 1987. Bone histomorphometry: Standardization of nomenclature, symbols, and units. Report of the ASBMR Histomorphometry Nomenclature Committee. J Bone Miner Res 2:595-610.
25. Parkinson IH, Fazzalari NL. 2000. Methodological principles for fractal analysis of trabecular bone. J Microsc 198(Part 2):134-142.
26. Pothuaud L, Benhamou CL, Porion P, Lespessailles E, Harba R, Levitz P. 2000. Fractal dimension of trabecular bone projection texture is related to three-dimensional microarchitecture. J Bone Miner Res 15:691-699.
27. Rho JY, Kuhn-Spearing L, Zioupos P. 1998. Mechanical properties and the hierarchical structure of bone. Med Eng Phys 20:92-102.
28. Rocha LB, Goissis G, Rossi MA. 2002. Biocompatibility of anionic collagen matrix as scaffold for bone healing. Biomaterials 23:449-456.
29. Rocha LB, Brochi MA, Bellucci AD, Rossi MA. 2004. Efficacy of polyanionic collagen matrices for bone defect healing. J Biomed Mater Res B: Appl Biomater 71:355-359.
30. Rocha LB, Adam RL, Leite NJ, Metze K, Rossi MA. 2006. Biomineralization of polyanionic collagen-elastin matrices during cavarial bone repair. J Biomed Mater Res A 79:237-245.
31. Rosa FP, Lia RC, de Souza KO, Goissis G, Marcantonio E, Jr. 2003. Tissue response to polyanionic collagen: Elastin matrices implanted in rat calvaria. Biomaterials 24:207-212.
32. Sarkar N, Chaudhuri BB. 1994. An efficient differential box-counting approach to compute fractal dimension of image. IEEE Trans Syst Man Cybern 24:115-120.
33. Schmitt AO, Herzel H. 1997. Estimating the entropy of DNA sequences. J Theor Biol 188:369-377.
34. Shannon CE. 1948. A mathematical theory of communication. Bell System Tech J 27:379-423.
35. von Wowern N. 1977. Variations in structure within the trabecular bone of the mandible. Scand J Dent Res 85:613-622.
36. Weibel ER. 1992. Stereology in perspective: A mature science evolve. Acta Stereol 11(Suppl I):1-13.
37. Weiner S, Traub W, Wagner D. 1999. Lamellar bone: Structure-function relations. J Struct Biol 126:241-255.
38. Weinkamer R, Hartmann MA, Brechet Y, Fratzl P. 2004. Stochastic lattice model for bone remodeling and aging. Phys Rev Lett 93:228102.
39. Yadollahi A, Moussavi ZM. 2006. A robust method for heart sounds localization using lung sounds entropy. IEEE Trans Biomed Eng 53:497-502.