Fractals in dentistry

Journal of Dentistry

Volumn 39, Issue 4, 2011, Pages 273-292

  Sánchez, Iván ^a   Uzcátegui, Gladys ^b  

^a INSTITUTO VENEZOLANO DE INVESTIGACIONES CIENTÍFICAS   (Venezuela)

^b UNIVERSIDAD CENTRAL DE VENEZUELA   (Venezuela)

Author keywords

Cancer; Dental materials; Diagnosis; Fractal dimension; Osteoporosis; Self similar

Indexed keywords

BIOMEDICAL AND DENTAL MATERIALS;

DENTAL CARIES; DENTIN; DENTISTRY; EPITHELIAL MESENCHYMAL TRANSITION; FRACTAL ANALYSIS; HISTOLOGY; HUMAN; JAW; MOUTH TUMOR; OSTEOPOROSIS; PATHOLOGY; REVIEW; SJOEGREN SYNDROME; TOOTH RADIOGRAPHY;

ALVEOLAR PROCESS; DENTAL CARIES; DENTAL MATERIALS; DENTIN; DENTISTRY; EPITHELIAL-MESENCHYMAL TRANSITION; FRACTALS; HUMANS; MOUTH NEOPLASMS; OSTEOPOROSIS; RADIOGRAPHY, DENTAL; SJOGREN'S SYNDROME;

EID: 79952987614     PISSN: 03005712     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jdent.2011.01.010     Document Type: Review

References (184)

1. S. Cross Fractals in pathology Journal of Pathology 182 1997 1 8 (Pubitemid 27240443)
2. A.L. Goldberger, and B.J. West Fractals in physiology and medicine The Yale Journal of Biology and Medicine 60 1987 421 435
3. A.L. Goldberger, D.R. Rigney, and B.J. West Chaos and fractals in human physiology Scientific American 262 1990 42 49 (Pubitemid 20033153)
4. S. Havlin, S.V. Buldyrev, A.L. Goldberger, R.N. Mantegna, S.M. Ossadnik, and C.K. Peng Fractals in biology and medicine Chaos, Solitons and Fractals 6 1995 171 201
5. O. Heymans, J. Fissette, P. Vico, S. Blacher, D. Masset, and F. Brouers Is fractal geometry useful in medicine and biomedical sciences? Medical Hypotheses 54 2000 360 366 (Pubitemid 30204319)
6. M. Hahn, M. Vogel, M. Pompesius-Kempa, and G. Delling Trabecular bone pattern factor - a new parameter for simple quantification of bone microarchitecture Bone 13 1992 327 330
7. B.B. Mandelbrot How long is the coast of Britain? - Statistical self-similarity and fractional dimension Science 156 1967 636 638
8. T.G. Smith, G.D. Lange, and W.B. Marks Fractal methods and results in cellular morphology - dimensions, lacunarity and multifractals Journal of Neuroscience Methods 69 1996 123 136 (Pubitemid 26377770)
9. W.G Geraets, and P.F. van der Stelt Fractal properties of bone Dentomaxillofacial Radiology 29 2000 144 153
10. R. Lopes, and N. Betrouni Fractal and multifractal analysis: a review Medical Image Analysis 13 2009 634 649
11. H.M. Eriksen, and V. Dimitrov Ecology of oral health: a complexity perspective European Journal of Oral Sciences 111 2003 285 290 (Pubitemid 37465495)
12. S.C. White, and D.J. Rudolph Alterations of the trabecular pattern of the jaws in patients with osteoporosis Oral Surgery, Oral Medicine, Oral Pathology, Oral Radiology & Endodontics 88 1999 628 635
13. R. Wilding, J. Slabbert, H. Kathree, C. Owen, K. Crombie, and P. Delport The use of fractal analysis to reveal remodelling in human alveolar bone following the placement of dental implants Archives of Oral Biology 40 1995 61 72
14. A. Wojtowicz, S. Chaberek, L. Kryst, E. Urbanowska, K. Ciechowicz, and K. Ostrowski Fourier and fractal analysis of maxillary alveolar ridge repair using platelet rich plasma (PRP) and inorganic bovine bone International Journal of Oral and Maxillofacial Surgery 32 2003 84 86 (Pubitemid 36284860)
15. J. Millard, P. Augat, T.M. Link, M. Kothari, D.C. Newitt, and H.K. Genant Power spectral analysis of vertebral trabecular bone structure from radiographs: orientation dependence and correlation with bone mineral density and mechanical properties Calcified Tissue International 63 1998 482 489 (Pubitemid 28531797)
16. Y.H. Jung Evaluation of peri-implant bone using fractal analysis Korean Journal of Oral and Maxillofacial Surgery 35 2005 121 125
17. M. Veltri, P. Balleri, and M. Ferrari Damping factor for monitoring the bone interface at dental implants Clinical Oral Implants Research 18 2007 738 742
18. D.H. Lee, Y. Ku, I.C. Rhyu, J.U. Hong, C.W. Lee, and M.S. Heo A clinical study of alveolar bone quality using the fractal dimension and the implant stability quotient Journal of Periodontal and Implant Science 40 2010 19 24
19. T. Traini, A.B. Novaes, A. Piattelli, V. Papalexiou, and V. Muglia The relationship between interimplant distances and vascularization of the interimplant bone Clinical Oral Implants Research 21 2010 822 829
20. Y. Oshida, A. Hashem, T. Nishihara, and M.V. Yapchulay Fractal dimension analysis of mandibular bones: toward a morphological compatibility of implants Bio-Medical Materials and Engineering 4 1994 397 407
21. D.M. Dohan Ehrenfest, P.G. Coelho, B.S. Kang, Y.T. Sul, and T. Albrektsson Classification of osseointegrated implant surfaces: materials, chemistry and topography Trends in Biotechnology 28 2010 198 206
22. F. Grizon, E. Aguado, G. Hure, M.F. Basle, and D. Chappard Enhanced bone integration of implants with increased surface roughness: a long term study in the sheep Journal of Dentistry 30 2002 195 203 (Pubitemid 40433430)
23. S. Longoni, and M. Sartori Fractal geometry of nature (bone) may inspire medical devices shape Nature Precedings 2010 Available from http://hdl.handle. net/10101/npre.2010.4512.1
24. W.J. Yi, M.S. Heo, S.S. Lee, S.C. Choi, K.H. Huh, and S.P. Lee Direct measurement of trabecular bone anisotropy using directional fractal dimension and principal axes of inertia Oral Surgery, Oral Medicine, Oral Pathology, Oral Radiology, and Endodontology 104 2007 110 116
25. W.J. Yi, M.S. Heo, S.S. Lee, S.C. Choi, and K.H. Huh Comparison of trabecular bone anisotropies based on fractal dimensions and mean intercept length determined by principal axes of inertia Medical and Biological Engineering and Computing 45 2007 357 364
26. S. Chen, T. Oviir, C. Lin, L. Leu, B. Cho, and L. Hollender Digital imaging analysis with mathematical morphology and fractal dimension for evaluation of periapical lesions following endodontic treatment Oral Surgery, Oral Medicine, Oral Pathology, Oral Radiology and Endodontology 100 2005 467 472 (Pubitemid 41331037)
27. J. Lee, H. Park, H. Jeong, K. Kim, and C. Park Bony change of apical lesion healing process using fractal analysis Korean Journal of Oral and Maxillofacial Radiology 35 2005 91 96
28. Y. Yu, H. Chen, C. Lin, C. Chen, T. Oviir, and S. Chen Fractal dimension analysis of periapical reactive bone in response to root canal treatment Oral Surgery, Oral Medicine, Oral Pathology, Oral Radiology, and Endodontology 107 2009 283 288
29. F. Grizzi, G. Taverna, and P.C. Muzzio On the morphological complexity of bone texture Oral Surgery, Oral Medicine, Oral Pathology, Oral Radiology and Endodontology 108 2009 311 312
30. M. Heo, K. Park, S. Lee, S. Choi, J. Koak, and S. Heo Fractal analysis of mandibular bony healing after orthognathic surgery Oral Surgery, Oral Medicine, Oral Pathology, Oral Radiology and Endodontology 94 2002 763 767 (Pubitemid 41124715)
31. K. Park, M. Heo, S. Lee, C. Choi, T. Park, and I. Jeon Radiologic assessment of bone healing after orthognathic surgery using fractal analysis Korean Journal of Oral and Maxillofacial Radiology 32 2002 201 206
32. H. Park, Y. Jung, and B. Cho Bone changes after bilateral sagittal split osteotomy for mandibular prognathism Korean Journal of Oral and Maxillofacial Radiology 36 2006 183 188
33. H. Koca, S. Ergün, P. Güeri, and H. Boyacioglu Evaluation of trabecular bone healing by fractal analysis and digital subtraction radiography on digitized panoramic radiographs: a preliminary study Oral Radiology 26 2010 1 8
34. G.E. Drgnescu, C. Sinescu, and D. Dodenciu Quantitative measurement of speech sound distortions due to inadequate dental mounting Computer Methods in Biomechanics and Biomedical Engineering 9 2006 25 34
35. W.H. Steeb The nonlinear workbook 3rd ed. 2005 World Scientific Singapore
36. J. Ichikawa, T. Hara, Y. Tamatsu, and Y. Ide Morphological changes in the internal structure of the articular eminence of the temporal bone during growth from deciduous to early mixed dentition Journal of Biomechanics 40 2007 3541 3547 (Pubitemid 350122497)
37. L.L. Otis, J.S.H. Hong, and O.C. Tuncay Bone structure effect on root resorption Orthodontics & Craniofacial Research 7 2004 165 177
38. N. Lane, G.C. Armitage, P. Loomer, S. Hsieh, S. Majumdar, and H.Y. Wang Bisphosphonate therapy improves the outcome of conventional periodontal treatment: results of a 12-month, randomized, placebo-controlled study Journal of Periodontology 76 2005 1113 1122 (Pubitemid 41065401)
39. F. Yasar, E. Yesilova, and F. Akgünlü Alveolar bone changes under overhanging restorations Clinical Oral Investigations 13 2009 1 7
40. ErgünS, A. Saraoglu, P. Güneri, and B. Özpinar Application of fractal analysis in hyperparathyroidism Dentomaxillofacial Radiology 38 2009 281 289
41. Y. Oshida, C.A. Munoz, M.M. Winkler, A. Hashem, and M. Itoh Fractal dimension analysis of aluminum oxide particle for sandblasting dental use Bio-Medical Materials and Engineering 3 1993 117 126
42. A. Eftekhari Fractal study of Ni-Cr-Mo alloy for dental applications: effect of beryllium Applied Surface Science 220 2003 343 348
43. Y. Takuma, T. Shiraishi, T. Fujita, and K. Hisatsune Tarnish resistance evaluation of experimental Pd-free Ag-Au-Pt-Cu dental alloys Dental Materials Journal 29 2010 330 335
44. C. Mangano, M. Raspanti, T. Traini, A. Piattelli, and R. Sammons Stereo imaging and cytocompatibility of a model dental implant surface formed by direct laser fabrication Journal of Biomedical Materials Research Part A 88A 2009 823 831
45. B.D. Venkatesh, D.L. Chen, and S.D. Bhole Effect of heat treatment on mechanical properties of Ti-6Al-4V ELI alloy Materials Science and Engineering A 506 2009 117 124
46. J. Löberg, I. Mattisson, S. Hansson, and E. Ahlberg Characterisation of titanium dental implants. I: Critical assessment of surface roughness parameters The Open Biomaterials Journal 2 2010 18 35
47. P.F. Chauvy, C. Madore, and D. Landolt Variable length scale analysis of surface topography: characterization of titanium surfaces for biomedical applications Surface and Coatings Technology 110 1998 48 56
48. C.A. Brown, W.A. Johnsen, and R.M. Butland Scale-sensitive fractal analysis of turned surfaces Annals of the CIRP 45 1996 515 518 (Pubitemid 126601500)
49. J.J. Mecholsky Fractal analysis and fractography: what can we learn that's new? Key Engineering Materials 409 2010 145 153
50. J.J. Mecholsky Estimating theoretical strength of brittle materials using fractal geometry Materials Letters 60 2006 2485 2488
51. A. Della Bona Characterizing ceramics and the interfacial adhesion to resin: I - The relationship of microstructure, composition, properties and fractography Journal of Applied Oral Science 13 2005 1 9
52. A. Della Bona, T.J. Hill, and J.J. Mecholsky The effect of contour angle on fractal dimension measurements for brittle materials Journal of Materials Science 36 2001 2645 2650 (Pubitemid 32610931)
53. T.J. Hill, A. Della Bona, and J.J. Mecholsky Establishing a protocol for measurements of fractal dimensions in brittle materials Journal of Materials Science 36 2001 2651 2657 (Pubitemid 32610932)
54. J.J. Mecholsky Fractography: determining the sites of fracture initiation Dental Materials 11 1995 113 116
55. J.L. Drummond, M. Thompson, and B.J. Super Fracture surface examination of dental ceramics using fractal analysis Dental Materials 21 2005 586 589 (Pubitemid 40655134)
56. B.B. Mandelbrot The fractal geometry of nature 1983 WH Freeman and Company New York
57. H.O. Peitgen, D. Saupe, The science of fractal images 1988 Springer-Verlag New York
58. 2 glass-ceramics Journal of the American Ceramic Society 83 2000 545 552 (Pubitemid 30563930)
59. J.L. Drummond Fractals, surface roughness, and fracture toughness of dental composite and unfilled resin fracture surfaces Cells and Materials 7 1997 95 102 (Pubitemid 28337452)
60. P. Bulpakdi, B. Taskonak, J. Yan, and J.J. Mecholsky Failure analysis of clinically failed all-ceramic fixed partial dentures using fractal geometry Dental Materials 25 2009 634 640
61. K.S. Wilson, A.J. Allen, N.R. Washburn, and J.M. Antonucci Interphase effects in dental nanocomposites investigated by small-angle neutron scattering Journal of Biomedical Materials Research Part A 81A 2006 113 123 (Pubitemid 46435459)
62. P.W. Schmidt Small-angle scattering studies of disordered, porous, and fractal systems Journal of Applied Crystallography 24 1991 414 435
63. J.E Martin, A.J. Hurd, Scattering from, and Fractals Journal of Applied Crystallography 20 1987 61 78
64. R.J. Roe Methods of X-ray and neutron scattering in polymer science 2000 Oxford University Press Oxford
65. J.E. Discacciati, and R.L. Oréfice Structural analysis on photopolymerized dental resins containing nanocomponents Journal of Material Science 42 2007 3883 3893 (Pubitemid 46855293)
66. A. Pefferkorn, E. Pefferkorn, and Y. Haïkel Influence of the colloidal crystal-like arrangement of polymethylmethacrylate bonded aerosol particles on the polymerization shrinkage of composite resins Dental Materials 22 2006 661 670 (Pubitemid 43849943)
67. A. Levstik, J. Leskovec, C. Filipič, Z. Kutnjak, B. Žekš, and M. Kord The deposition of AgCl into tubules of the human tooth dentine Journal of Physics D: Applied Physics 34 2001 852 856 (Pubitemid 32296978)
68. J. Leskovec, C. Filipič, and A. Levstik Dielectric response of the human tooth dentine Physica B 364 2005 111 116 (Pubitemid 40786432)
69. V.M. Zolotarev, D.V. Tulin, A.B. Oreshkov, G.I. Turner, B.Z. Volchek, and N.M. Drichko Interference of light in composite systems of ordered anisotropic fibers. Part 2. Optical study of how the structural organization of dentine tubules affects the structure and shape of the crown of the tooth Journal of Optical Technology 69 2002 15 20
70. A.A. Zinchik, A. Sharikova, and S.C. Stafeev Laser-based equipment for investigating fractal structure of dental tissue Proceedings of SPIE 3091 1997 147 151 (Pubitemid 34981937)
71. A. Wojtowicz, S. Chaberek, M. Hulisz-Secomska, M. Yamauchi, and K. Ostrowski Disturbed pattern of collagen fibers in dentinal dysplasia type I Dental and Medical Problems 39 2002 169 175
72. J. Reyes-Gasga, R. García, and L. Vargas-Ulloa In-situ observation of fractal structures and electrical conductivity in human tooth enamel Philosophical Magazine A 75 1997 1023 1040
73. F. Banhart Fractal carbon filaments grown on insulators under irradiation in an electron microscope Philosophical Magazine Letters 69 1994 45 51
74. H.Z. Wang, Q. Wu, H.G. Zhu, D. Li, X.H. Liu, and X. Wang Fractal carbon trees on polymer and metal substrates in TEM observation Journal of Materials Science Letters 19 2000 2225 2226 (Pubitemid 32873962)
75. E.Y. Vedmedenko, and M.V. Kurik Influence of an electric field on the structure of saliva crystals Technical Physics 42 1997 1440 1441 (Pubitemid 128011772)
76. S. Umemori, K. Tonami, H. Nitta, S. Mataki, and K. Araki The possibility of digital imaging in the diagnosis of occlusal caries International Journal of Dentistry 2010 2010 860515
77. K. Tonami, M. Konuma, H. Nitta, K. Araki, S. Mataki, and N. Kurosaki Basic study on digital image analysis of molar pit-and-fissure discoloration for caries diagnosis Japanese Journal of Conservative Dentistry 49 2006 725 730
78. P. Gutiérrez, C. Piña, V.H. Lara, and P. Bosch Characterization of enamel with variable caries risk Archives of Oral Biology 50 2005 843 848 (Pubitemid 41219330)
79. A. Eftekhari Electrochemical technique for the determination of fractal dimension of dental surfaces Colloids and Surfaces B 32 2003 375 381 (Pubitemid 37315916)
80. J.M. Gonzalez-Gonzalez Fractals in restorative treatment of teeth Journal of Oral Rehabilitation 24 1997 52 56 (Pubitemid 127732061)
81. J.M. Gonzalez-Gonzalez Fractal structure of caries Caries Research 31 1997 186 188 (Pubitemid 127520153)
82. G. Landini The fractal structure of caries? Caries Research 31 1997 401
83. C. Restrepo, A. Peláez, E. Álvarez, C. Paucar, and P. Abad Digital imaging of patterns of dental wear to diagnose bruxism in children International Journal of Paediatric Dentistry 16 2006 278 285 (Pubitemid 43825110)
84. L. Bjørndal, O. Carlsen, G. Thuesen, T. Darvann, and S. Kreiborg External and internal macromorphology in 3D-reconstructed maxillary molars using computerized X-ray microtomography International Endodontic Journal 32 1999 3 9
85. H.M. Eriksen, V. Dimitrov, M. Rohlin, K. Petersson, and G. Svensäter The oral ecosystem: implications for education European Journal of Dental Education 10 2006 192 196
86. M.D. Doyle, H. Rabin, and J.S. Suri Fractal analysis as a means for the quantification of intramandibular trabecular bone loss from dental radiographs Proceedings of SPIE 1380 1991 227 235
87. U.E. Ruttimann, R.L. Webber, and J.B. Hazelrig Fractal dimension from radiographs of peridental alveolar bone: a possible diagnostic indicator of osteoporosis Oral Surgery, Oral Medicine, Oral Pathology 74 1992 98 110
88. W.S. Kuklinski, K. Chandra, U.E. Ruttimann, and R.L. Webber Application of fractal texture analysis to segmentation of dental radiographs SPIE Proceeding on Medical Imaging III 1092 1989 111 117
89. A.N. Law, A.M. Bollen, and S.K. Chen Detecting osteoporosis using dental radiographs: a comparison of four methods Journal of the American Dental Association 127 1996 1734 1742 (Pubitemid 126432978)
90. T.E. Southard, K.A. Southard, J.R. Jakobsen, S.L. Hillis, and C.A. Najim Fractal dimension in radiographic analysis of alveolar process bone Oral Surgery, Oral Medicine, Oral Pathology, Oral Radiology, and Endodontology 82 1996 576 596
91. T.E. Southard, and K.A. Southard Detection of simulated osteoporosis in maxillae using radiographic texture analysis IEEE Transactions on Biomedical Engineering 43 1996 123 132 (Pubitemid 26055571)
92. T.E. Southard, K.A. Southard, K.E. Krizan, S.L. Hillis, J.W. Haller, and J. Keller Mandibular bone density and fractal dimension in rabbits with induced osteoporosis Oral Surgery, Oral Medicine, Oral Pathology, Oral Radiology & Endodontic 89 2000 244 249
93. T.E. Southard, K.A. Southard, and A. Lee Alveolar process fractal dimension and postcranial bone density Oral Surgery, Oral Medicine, Oral Pathology, Oral Radiology & Endodontics 91 2001 486 491 (Pubitemid 33601655)
94. K.A. Southard, T.E. Southard, J.A. Schlechte, and P.A. Meis The relationship between the density of the alveolar processes and postcranial bone Journal of Dental Research 79 2000 964 969 (Pubitemid 32501308)
95. S.K. Chen, and C.M. Chen The effects of projection geometry and trabecular texture on estimated fractal dimensions in two alveolar bone models Dentomaxillofacial Radiology 27 1998 270 274
96. A.M. Bollen, A. Taguchi, P.P. Hujoel, and L.G. Hollender Fractal dimension on dental radiographs Dentomaxillofacial Radiology 30 2001 270 275 (Pubitemid 33695417)
97. T.G. Smith, W.B. Marks, G.D. Lange, W.H. Sheriff, and E.A. Neale A fractal analysis of cell images Journal of Neuroscience Methods 27 1989 173 180 (Pubitemid 19067245)
98. G.M. Park, Y.H. Jung, and K.S. Nah Prediction of osteoporosis using fractal analysis on periapical radiographs Korean Journal of Oral and Maxillofacial Radiology 35 2005 41 46
99. J.Y. Kim, and K.S. Nah Prediction of osteoporosis using fractal analysis et cetera on panoramic radiographs Korean Journal of Oral and Maxillofacial Radiology 37 2007 79 82
100. J.Y. Kim, Y.H. Jung, and K.S. Nah Prediction of osteoporosis using fractal analysis on periapical and panoramic radiographs Korean Journal of Oral and Maxillofacial Radiology 38 2008 147 151
101. G.M. Tosoni, A.G. Lurie, A.E. Cowan, and J.A. Burleson Pixel intensity and fractal analyses: detecting osteoporosis in perimenopausal and postmenopausal women by using digital panoramic images Oral Surgery, Oral Medicine, Oral Pathology, Oral Radiology & Endodontics 102 2006 235 241 (Pubitemid 44094156)
102. W.G.M. Geraets, J.G.C. Verheij, P.F. van der Stelt, K. Horner, C. Lindh, and K. Nicopoulou-Karayianni Prediction of bone mineral density with dental radiographs Bone 40 2007 1217 1221 (Pubitemid 46566430)
103. W.G.M. Geraets, J.G.C. Verheij, P.F. van der Stelt, K. Horner, C. Lindh, and K. Nicopoulou-Karayianni Selecting regions of interest on intraoral radiographs for the prediction of bone mineral density Dentomaxillofacial Radiology 37 2008 375 379
104. J.G.C. Verheij, W.G.M. Geraets, P.F. van der Stelt, K. Horner, C. Lindh, and K. Nicopoulou-Karayianni Prediction of osteoporosis with dental radiographs and age Dentomaxillofacial Radiology 38 2009 431 437
105. F. Yasar, and F. Akgünlü The differences in panoramic mandibular indices and fractal dimension between patients with and without spinal osteoporosis Dentomaxillofacial Radiology 35 2006 1 9 (Pubitemid 43235459)
106. F. Yasar, and F. Akgünlü Evaluating mandibular cortical index quantitatively European Journal of Dentistry 2 2008 283 290
107. E. Klemetti, S. Kolmakov, and H. Kröger Pantomography in assessment of the osteoporosis risk group Scandinavian Journal of Dental Research 102 1994 68 72
108. F. Yasar, and F. Akgünlü Fractal dimension and lacunarity analysis of dental radiographs Dentomaxillofacial Radiology 34 2005 261 267 (Pubitemid 41329353)
109. M.K. Shrout, B. Roberson, B.J. Potter, J.M. Mailhot, and C.F. Hildebolt A comparison of 2 patient populations using fractal analysis Journal of Periodontology 69 1998 9 13 (Pubitemid 128526483)
110. S.X. Updike, and H. Nowzari Fractal analysis of dental radiographs to detect periodontitis-induced trabecular changes Journal of Periodontal Research 43 2008 658 664
111. C. Sang-Yun, H. Won-Jeong, and K. Eun-Kyung Usefulness of fractal analysis for the diagnosis of periodontitis Korean Journal of Oral Maxillofacial Radiology 31 2001 35 42
112. F. Caserta, W.D. Eldred, E. Fernandez, R.E. Hausman, L.R. Stanford, and S.V. Bulderev Determination of fractal dimension of physiologically characterized neurons in two and three dimensions Journal of Neuroscience Methods 56 1995 133 144
113. G. Landini A fractal model for periodontal breakdown in periodontal disease Journal of Periodontal Research 26 1991 176 179
114. G. Landini Is periodontal breakdown a fractal process? Simulations using the Weierstrass-Mandelbrot function Journal of Periodontal Research 32 1997 300 307 (Pubitemid 127521763)
115. L.E. Rothe, A. Bollen, R.M. Little, S.W. Herring, J.B. Chaison, and C.S. Chen Trabecular and cortical bone as risk factors for orthodontic relapse American Journal of Orthodontics and Dentofacial Orthopedics 130 2006 476 484 (Pubitemid 44512087)
116. N. Wagle, N. Do, J. Yu, and J.L. Borke Fractal analysis of the PDL-bone interface and implications for orthodontic tooth movement American Journal of Orthodontics and Dentofacial Orthopedics 127 2005 655 661 (Pubitemid 40799135)
117. M.S. Madan, Z.J. Liu, G.M. Gu, and G.J. King Effects of human relaxin on orthodontic tooth movement and periodontal ligaments in rats American Journal of Orthodontics and Dentofacial Orthopedics 131 2007 e1-8, e10
118. L. Goutzanis, N. Papadogeorgakis, P.M. Pavlopoulus, K. Katti, V. Petsinis, and I. Plochoras Nuclear fractal dimension as a prognostic factor in oral squamous cell carcinoma Oral Oncology 44 2008 345 353 (Pubitemid 351380979)
119. G. Landini, and J.W. Rippin Fractal dimensions of the epithelial-connective tissue interfaces in premalignant and malignant epithelial lesions of the floor of the mouth Analytical and Quantitative Cytology and Histology 15 1993 144 149 (Pubitemid 23158938)
120. G. Landini, and J.W. Rippin How important is tumour shape? Quantification of the epithelial-connective tissue interface in oral lesions using local connected fractal dimension analysis Journal of Pathology 179 1996 210 217
121. R. Abu-Eid, and G. Landini Quantification of the global and local complexity of the epithelial-connective tissue interface of normal, dysplastic, and neoplastic oral mucosae using digital imaging Pathology Research And Practice 199 2003 475 482 (Pubitemid 37098805)
122. G. Landini, and J.G. Geake Discrimination of complex histopathological tumor profiles by experienced and inexperienced observers Journal of Oral Pathology and Medicine 26 1997 477 479 (Pubitemid 27515385)
123. J.G. Geake, and G. Landini Individual differences in the perception of fractal curves Fractals 5 1997 1 15
124. R. Abu-Eid, and G. Landini Morphometry of pseudoepitheliomatous hyperplasia: objective comparison to normal and dysplastic oral mucosae Analytical and Quantitative Cytology and Histology 27 2005 232 240 (Pubitemid 41233500)
125. R. Abu-Eid, and G. Landini Tissue architecture and cell morphology of squamous cell carcinomas compared to granular cell tumours' pseudo- epitheliomatous hyperplasia and to normal oral mucosae Fractals in biology and medicine, mathematics and biosciences in interaction 2005 Birkhäuser Basel
126. R. Abu-Eid, and G. Landini Morphometrical differences between pseudo-epitheliomatous hyperplasia in granular cell tumours and squamous cell carcinomas Histopathology 48 2006 407 416
127. R. Abu-Eid, F. Sawair, T. Saku, and G. Landini Architectural changes associated with ageing of the normal oral buccal mucosa Fifth international symposium, fractals in biology and medicine - abstracts Locarno, March 2008 Rivista di Biologia-Biology Forum 101 2008 131 158
128. R. Abu-Eid, and G. Landini The complexity of the oral mucosa: a review of the use of fractal geometry Control Engineering and Applied Informatics 12 2010 10 14
129. P. Vico, D. Dequanter, N. De-Saint-Aubin-Somerhausen, G. Andry, and L. Cartilier Fractal dimension of the deep margin of tongue carcinoma: a prognostic tool? Microscopy and Analysis 90 2002 21 22
130. M. Muthu Rama Krishnan, P. Shah, M. Pal, C. Chakraborty, R.R. Paul, and J. Chatterjee Structural markers for normal oral mucosa and oral sub-mucous fibrosis Micron 41 2010 312 320
131. L.P. Goutzanis, N. Papadogeorgakis, P.M. Pavlopoulos, V. Petsinis, I. Plochoras, and E. Eleftheriadis Vascular fractal dimension and total vascular area in the study of oral cancer Head and Neck 31 2009 298 307
132. C. Margaritescu, M. Raica, D. Pirici, C. Simionescu, L. Mogoanta, and A.C. Stinga Podoplanin expression in tumor-free resection margins of oral squamous cell carcinomas: an immunohistochemical and fractal analysis study Histology and Histopathology 25 2010 701 711
133. C. De Felice, G. Latini, G. Bianciardi, S. Parrini, G.M. Fadda, and M. Marini Abnormal vascular network complexity: a new phenotypic marker in hereditary non-polyposis colorectal cancer syndrome Gut 52 2003 1764 1767 (Pubitemid 37510400)
134. H.J. Herrmann, and H.E. Stanley The fractal dimension of the minimum path in two- and three-dimensional percolation Journal of Physics A: Mathematical and General 21 1988 L829 L833
135. H.K. Roy, and H.T. Lynch Diagnosing Lynch syndrome: is the answer in the mouth? Gut 52 2003 1665 1667 (Pubitemid 37510382)
136. T. Chikui, K. Tokumori, K. Yoshiura, K. Oobu, S. Nakamura, and K. Nakamura Sonographic texture characterization of salivary gland tumors by fractal analyses Ultrasound in medicine and Biology 31 2005 1297 1304 (Pubitemid 41434045)
137. E. Honda, M. Domon, T. Sasaki, N. Obayashi, and M. Ida Fractal dimensions of ductal patterns in the parotid glands of normal subjects and patients with Sjogren syndrome Investigative Radiology 27 1992 790 795
138. E. Honda, M. Domon, and T. Sasaki A method for determination of fractal dimensions of sialographic images Investigative Radiologhy 26 1991 894 901
139. P. Rubin, and J.F. Holt Secretory sialography in diseases of the major salivary glands American Journal of Roentgenology 77 1957 575 598
140. Y. Takagi, Y. Kimura, H. Nakamura, M. Sasaki, K. Eguchi, and T. Nakamura Salivary gland ultrasonography: can it be an alternative to sialography as an imaging modality for Sjögren's syndrome? Annals of the Rheumatic Disease 69 2010 1321 1324
141. T. Chikui, K. Okamura, K. Tokumori, S. Nakamura, M. Shimizu, and M. Koga Quantitative analyses of sonographic images of the parotid gland in patients with Sjögren's syndrome Ultrasound in Medicine and Biology 32 2006 617 622
142. T. Chikui, M. Shimizu, T. Kawazu, K. Okamura, T. Shiraishi, and Y. Yoshiura A quantitative analysis of sonographic images of the salivary gland: a comparison between sonographic and sialographic findings Ultrasound in Medicine and Biology 35 2009 1257 1264
143. T. Morinushi, H. Kawasaki, Y. Masumoto, K. Shigeta, T. Ogura, and M. Takigawa Examination of the diagnostic value and estimation of the chaos phenomenon in masticatory movement using fractal dimension in patients with temporomandibular dysfunction syndrome Journal of Oral Rehabilitation 25 1998 386 394 (Pubitemid 128704901)
144. F. Chiappelli, J. Alwan, P. Prolo, R. Christensen, M. Fiala, and O.S. Cajulis Neuro-immunity in stress-related oral ulcerations: a fractal analysis Frontiers in Bioscience 10 2005 3034 3041 (Pubitemid 40910542)
145. H. Takada, S. Abe, Y. Tamatsu, S. Mitarashi, H. Saka, and Y. Ide Three-dimensional bone microstructures of the mandibular angle using micro-CT and finite element analysis: relationship between partially impacted mandibular third molars and angle fractures Dental Traumatology 22 2006 18 24 (Pubitemid 43415212)
146. A.K. Demirba, S. Ergün, P. Güneri, B.O. Aktener, and H. Boyaciolu Mandibular bone changes in sickle cell anemia: fractal analysis Oral Surgery, Oral Medicine, Oral Pathology, Oral Radiology, and Endodontology 106 2008 e41 e48
147. M. Créton, W. Geraets, J.W. Verhoeven, P.F. van der Stelt, H. Verhey, and M. Cune Radiographic features of mandibular trabecular bone structure in hypodontia Clinical Implant Dentistry and Related Research 2009 10.1111/j.1708-8208.2009.00246.x
148. R. Arisaka, A. Matsuo, H. Chiba, H. Takahashi, S. Takeuchi, and M. Watanabe Preliminary clinical study to evaluate the relationship between systemic bone turnover and the microstructure of the alveolar bone Oral Science International 6 2009 27 35
149. S. Majumdar, R.S. Weinstein, and R.R. Prasad Application of fractal geometry techniques to the study of trabecular bone Medical Physics 20 1993 1611 1619
150. N.L. Fazzalari, and I.H. Parkinson Fractal dimension and architecture of trabecular bone Journal of Pathology 178 1996 100 105 (Pubitemid 26052088)
151. C. De Felice, G. Bianciardi, L. DiLeo, G. Latini, and S. Parrini Abnormal oral vascular network geometric complexity in Ehlers-Danlos syndrome Oral Surgery, Oral Medicine, Oral Pathology, Oral Radiology & Endodontics 98 2004 429 434 (Pubitemid 39345625)
152. C. De Felice, G. Bianciardi, S. Parrini, R.N. Laurini, and G. Latini Congenital oral mucosal abnormalities in true umbilical cord knots Biology of the Neonate 86 2004 34 38 (Pubitemid 39077608)
153. S. Parrini, G. Bianciardi, G. Latini, G. Di Maggio, and C. De Felice Oral microvascular network geometry abnormalities in infantile hypertrophic pyloric stenosis Fractals 12 2004 311 318
154. C. De Felice, G. Latini, S. Parrini, G. Bianciardi, P. Toti, and R.J. Kopotic Oral mucosal microvascular abnormalities: an early marker of bronchopulmonary dysplasia Pediatric Research 56 2004 927 931 (Pubitemid 39552775)
155. C. De Felice, S. Parrini, A. Barducci, G. Chitano, G. Tonni, and G. Latini Abnormal oral mucosal light reflectance in bronchopulmonary dysplasia Early Human Development 82 2006 273 278
156. C. De Felice, S. Parrini, G. Di Maggio, N.R. Laurini, K. Shirriff, and G. Bianciardi Oral mucosal microvascular network abnormalities in de novo mutation achondroplasia Fractals 13 2005 73 82 (Pubitemid 40494243)
157. G. Latini, G. Bianciardi, S. Parrini, N.R. Laurini, and C. De Felice Abnormal oral vascular network pattern geometry: a new clinical sign of down syndrome The Journal of Pediatrics 148 2006 132 137 (Pubitemid 43098971)
158. D. Mancardi, G. Varetto, E. Bucci, F. Maniero, and C. Guiot Fractal parameters and vascular networks: facts & artifacts Theoretical Biology and Medical Modelling 5 2008 12
159. L. Pothuaud, C.L. Benhamou, P. Porion, E. Lespessailles, R. Harba, and P. Levitz Fractal dimension of trabecular bone projection texture is related to three-dimensional microarchitecture Journal of Bone and Mineral Research 15 2000 691 699 (Pubitemid 30174023)
160. E. Lespessailles, J.P. Roux, C.L. Benhamou, M.E. Arlot, E. Eynard, and R. Harba Fractal analysis of bone texture on oscalcis radiographs compared with trabecular microarchitecture analyzed by histomorphometry Calcified Tissue
161. J. Samarabandu, R. Acharya, E. Hausmann, and K. Allen Analysis of bone X-rays using morphological fractals IEEE Transactions on Medical Imaging 12 1993 466 470
162. K.H. Huh, W.J. Yi, I.S. Jeon, M.S. Heo, S.S. Lee, and S.C. Choi Relationship between two-dimensional and three-dimensional bone architecture in predicting the mechanical strength of the pig mandible Oral Surgery, Oral Medicine, Oral Pathology, Oral Radiology, and Endodontology 101 2006 363 373
163. S. Jett, M.K. Shrout, J.M. Mailhot, B.J. Potter, and J.L. Borke An evaluation of the origin of trabecular bone patterns using visual and digital image analysis Oral Surgery, Oral Medicine, Oral Pathology, Oral Radiology, and Endodontology 98 2004 598 604 (Pubitemid 39505031)
164. M. Shrout, S. Jett, J.M. Mailhot, B.J. Potter, J.L. Borke, and C.F. Hildebolt Digital image analysis of cadaver mandibular trabecular bone patterns Journal of Periodontology 74 2003 1342 1347 (Pubitemid 37345090)
165. M.K. Shrout, B.J. Potter, and C.F. Hildebolt The effect of image variations on fractal dimension calculations Oral Surgery, Oral Medicine, Oral Pathology, Oral Radiology & Endodontics 84 1997 96 100 (Pubitemid 127670940)
166. M.K. Shrout, B.J. Potter, and C.F. Hildebolt The effect of varying the ROI on calculations of the fractal index Dentomaxillofacial Radiology 26 1997 295 298 (Pubitemid 127495021)
167. E. Oczeretko, M. Borowska, I. Szarmach, A. Kitlas, J. Szarmach, and A. Radwański Fractal analysis of dental radiographic images in the irregular regions of interest Information Technologies in Biomedicine AISC 69 2010 191 199
168. E. Oczeretko, M. Borowska, A. Kitlas, A. Borusiewicz, and M. Sobolewska-Siemieniuk Fractal analysis of medical images in the irregular regions of interest 8th IEEE international conference on bioinformatics and bioengineering 2008
169. C.C. Chen, J.S. Daponte, and M.D. Fox Fractal feature analysis and classification in medical imaging IEEE Transactions on Medical Imaging 8 1989 133 142
170. L. Jolley, S. Majumdar, and S. Kapila Technical factors in fractal analysis of periapical radiographs Dentomaxillofacial Radiology 35 2006 393 397 (Pubitemid 44904794)
171. K.H. Lee, S.B. Lee, C.H. An, M.S. Heo, W.J. Yi, and K.H. Huh The influence of X ray beam angulation on the fractal analysis of trabecular architecture in human dry mandible using standardized tile counting method Korean Journal of Oral Maxillofacial Radiology 34 2004 179 183
172. K.I. Lee, S.C. Choi, T.W. Park, and D.S. You Fractal dimension calculated from two types of region of interest Dentomaxillofacial Radiology 28 1999 284 289
173. B.M. An, M.S. Heo, S.P. Lee, S.S. Lee, S.C. Choi, and T.W. Park Effect of exposure time and image resolution on fractal dimension Korean Journal of Oral Maxillofacial Radiology 32 2002 75 79
174. Y.H. Jung, K.S. Nah, and B.H. Cho Change of the fractal dimension according to the decalcification degree and the exposure time in the bovine rib Korean Journal of Oral Maxillofacial Radiology 36 2006 69 72
175. J.D. Kim, J.S. Kim, and C.Y. Lee A fractal analysis of bone phantoms from digital images Korean Journal of Oral Maxillofacial Radiology 35 2005 33 40
176. J.S. Baik, S.S. Lee, K.S. Park, K.H. Huh, W.J. Yi, and M.S. Heo The effects of voltage of X-ray tube on fractal dimension and anisotropy of diagnostic images Korean Journal of Oral Maxillofacial Radiology 37 2007 211 215
177. W.G.M. Geraets, J.G.C. Verheij, P.F. van der Stelt, K. Horner, C. Lindh, and K. Nicopoulou-Karayianni Osteoporosis and the general dental practitioner: reliability of some digital dental radiological measures Community Dentistry and Oral Epidemiology 35 2007 465 471
178. L.J. Cronbach Coefficient alpha and the internal structure of tests Psychometrika 16 1951 297 334
179. M.J. Allen, and W.M. Yen Introduction to measurement theory 2002 Waveland Press Long Grove
180. S.C. White Oral radiographic predictors of osteoporosis Dentomaxillofacial Radiology 31 2002 84 92 (Pubitemid 38993333)
181. E. Dervis Oral implications of osteoporosis Oral Surgery, Oral Medicine, Oral Pathology, Oral Radiology, and Endodontology 100 2005 349 356 (Pubitemid 41191349)
182. S. Silverman Jr. Demographics and occurrence of oral and pharyngeal cancers: the outcomes, the trends, the challenge Journal of the American Dental Association 132 2001 7S 11S
183. W.G. Shafer, M.K. Hine, and B.M. Levy A textbook of oral pathology 1974 W.B. Saunders Company Philadelphia
184. D.K. Benn Limitations of the digital image subtraction technique in assessing alveolar bone crest changes due to misalignment errors during image capture Dentomaxillofacial Radiology 19 1990 97 104