Diş Hekimliğinde Fraktal Boyut Analizinin Kullanımı
Özet
Fraktal kavramı kırılmış ya da parçalanmış anlamına gelen Latince "fractus" sözcüğünden türetilmiş ve ilk olarak 1975'te matematikçi Benoit B. Mandelbrot tarafından öne sürülmüştür. Fraktal geometri, karmaşık kendine benzeyen şekilleri karakterize etmek için kullanılan nicel bir araç sunar. Fraktal boyut, karmaşıklığı ölçen nicel bir parametredir. Fraktal boyutun hesaplanması amacıyla birçok yöntem kullanılmıştır. Diş hekimliğinde en sık kullanılan yöntem White ve Rudolph’un 1999 yılındaki çalışmalarında yararlandığı “kutu sayma yöntemi”dir. Diş hekimliğinde fraktal boyut analizi kullanılarak dental materyal analizi, diş dokusu analizi, çürük tayini, temporomandibular eklem bozuklukları, oral kanserler, çeşitli sistemik hastalıklar, tedavi ve iyileşme izleme gibi pek çok konuda çalışma yapılmaktadır.
The term fractal is derived from the Latin word "fractus", which means fragmented or broken. It was first put forward by Polish mathematician Benoit B. Mandelbrot in 1975. Fractal geometry offers a quantitative tool to characterize complex self-similar shapes, and therein lies its applicability. The concept of fractal dimension arises as a quantitative parameter that measures complexity. Many methods have been used to calculate the fractal dimension. The most frequently used and popular method in dentistry is the "box counting method", which was used by White and Rudolph in their study in 1999. In dentistry, fractal dimension analysis is used to study many subjects such as dental material analysis, tooth analysis, caries detection, temporomandibular joint disorders, oral cancers, various systemic diseases, treatment and recovery monitoring.
Referanslar
Mandelbrot BB. Fractal geometry: what is it, and what does it do? Proceedings of the Royal Society of London A Mathematical and Physical Sciences. 1989;423(1864):3-16.
Sánchez I, Uzcátegui G. Fractals in dentistry. J Dent. 2011;39(4):273-292.
Demirbaş AK, Ergün S, Güneri P, Aktener BO, Boyacıoğlu H. Mandibular bone changes in sickle cell anemia: fractal analysis. Oral Surgery, Oral Medicine, Oral Pathology, Oral Radiology, and Endodontology. 2008;106(1):e41-e48.
Cross SS. Fractals in pathology. The Journal of Pathology: A Journal of the Pathological Society of Great Britain and Ireland. 1997;182(1):1-8.
Güleç M, Taşsöker M, Şener S. Tıpta ve Diş Hekimliğinde Fraktal Analiz. Ege Üniversitesi Diş Hekimliği Fakültesi Dergisi. 2019;40(1):17-31.
Flook A. The use of dilation logic on the quantimet to achieve fractal dimension characterisation of textured and structured profiles. Powder Technology. 1978;21(2):295-298.
Smith Jr T, Lange G, Marks WB. Fractal methods and results in cellular morphology—dimensions, lacunarity and multifractals. J Neurosci Methods. 1996;69(2):123-136.
Barnsley MF. Fractals everywhere. Academic press; 2014.
Lopes R, Betrouni N. Fractal and multifractal analysis: a review. Med Image Anal. Aug 2009;13(4):634-49. doi:10.1016/j.media.2009.05.003
Geraets WG, van der Stelt PF. Fractal properties of bone. Dentomaxillofac Radiol. May 2000;29(3):144-53. doi:10.1038/sj/dmfr/4600524
Russell DA, Hanson JD, Ott E. Dimension of strange attractors. Phys Rev Lett. 1980;45(14):1175.
Pehlİvan MZY, Boz AF. Görüntü işleme tabanlı kutu sayma yöntemi ile fraktal boyut hesabı için arayüz tasarımı.
White SC, Rudolph DJ. Alterations of the trabecular pattern of the jaws in patients with osteoporosis. Oral Surg Oral Med Oral Pathol Oral Radiol Endod. Nov 1999;88(5):628-35. doi:10.1016/s1079-2104(99)70097-1
Broe R, Rasmussen ML, Frydkjaer-Olsen U, et al. Retinal vascular fractals predict long-term microvascular complications in type 1 diabetes mellitus: the Danish Cohort of Pediatric Diabetes 1987 (DCPD1987). Diabetologia. Oct 2014;57(10):2215-21. doi:10.1007/s00125-014-3317-6
Bianchi FD, Bonetto RD. FERImage: an interactive program for fractal dimension, d(per) and d(min) calculation. Scanning. May-Jun 2001;23(3):193-7. doi:10.1002/sca.4950230305
Shrout MK, Potter BJ, Hildebolt CF. The effect of image variations on fractal dimension calculations. Oral Surg Oral Med Oral Pathol Oral Radiol Endod. Jul 1997;84(1):96-100. doi:10.1016/s1079-2104(97)90303-6
Camargo AJ, Cortes ARG, Aoki EM, Baladi MG, Arita ES, Watanabe PCA. Diagnostic performance of fractal dimension and radiomorphometric indices from digital panoramic radiographs for screening low bone mineral density. Brazilian Journal of Oral Sciences. 2016;15(2):131-136.
Shrout MK, Hildebolt CF, Potter BJ. The effect of varying the region of interest on calculations of fractal index. Dentomaxillofac Radiol. Sep 1997;26(5):295-8. doi:10.1038/sj.dmfr.4600260
Oliveira-Santos N, Michels M, Freitas DQ, Haiter-Neto F, Oliveira ML. Influence of phosphor plate-based radiographic image specifications on fractal analysis of alveolar bone. Oral Surgery Oral Medicine Oral Pathology Oral Radiology. Oct 2019;128(4):418-423. doi:10.1016/j.oooo.2019.06.011
Bollen AM, Taguchi A, Hujoel PP, Hollender LG. Fractal dimension on dental radiographs. Dentomaxillofac Radiol. Sep 2001;30(5):270-5. doi:10.1038/sj/dmfr/4600630
Magat G, Ozcan Sener S. Evaluation of trabecular pattern of mandible using fractal dimension, bone area fraction, and gray scale value: comparison of cone-beam computed tomography and panoramic radiography. Oral radiol. Jan 2019;35(1):35-42. doi:10.1007/s11282-018-0316-1
Chen S-K, Oviir T, Lin C-H, Leu L-J, Cho B-H, Hollender L. 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. 2005;100(4):467-472.
Jolley L, Majumdar S, Kapila S. Technical factors in fractal analysis of periapical radiographs. Dentomaxillofac Radiol. Nov 2006;35(6):393-7. doi:10.1259/dmfr/30969642
Baksi BG, Fidler A. Fractal analysis of periapical bone from lossy compressed radiographs: a comparison of two lossy compression methods. J Digit Imaging. 2011;24:993-998.
Eftekhari A. Fractal study of Ni-Cr-Mo alloy for dental applications: effect of beryllium. Applied Surface Science. Dec 30 2003;220(1-4):343-348. doi:10.1016/S0169-4332(03)00842-0
Takuma Y, Shiraishi T, Fujita T, Hisatsune K. Tarnish resistance evaluation of experimental Pd-free Ag-Au-Pt-Cu dental alloys. Dent Mater J. May 2010;29(3):330-5. doi:10.4012/dmj.2009-093
Venkatesh BD, Chen DL, Bhole SD. Effect of heat treatment on mechanical properties of Ti-6Al-4V ELI alloy. Materials Science and Engineering a-Structural Materials Properties Microstructure and Processing. Apr 25 2009;506(1-2):117-124. doi:10.1016/j.msea.2008.11.018
Wilson KS, Allen AJ, Washburn NR, Antonucci JM. Interphase effects in dental nanocomposites investigated by small‐angle neutron scattering. Journal of Biomedical Materials Research Part A. 2007;81(1):113-123.
Wojtowicz A CS, Hulisz-Secomska M, Yamauchi, M OK. Disturbed pattern of collagen fibres in dentinal dysplasia type I. Dent Med Probl. 2002;39(2):169-175.
Gutierrez P, Pina C, Lara VH, Bosch P. Characterization of enamel with variable caries risk. Arch Oral Biol. Oct 2005;50(10):843-8. doi:10.1016/j.archoralbio.2004.11.018
Shrout MK, Roberson B, Potter BJ, Mailhot JM, Hildebolt CF. A comparison of 2 patient populations using fractal analysis. J Periodontol. Jan 1998;69(1):9-13. doi:10.1902/jop.1998.69.1.9
Kayipmaz S, Akcay S, Sezgin OS, Candirli C. Trabecular structural changes in the mandibular condyle caused by degenerative osteoarthritis: a comparative study by cone-beam computed tomography imaging. Oral radiol. Jan 2019;35(1):51-58. doi:10.1007/s11282-018-0324-1
Arsan B, Köse TE, Çene E, Özcan İ. Assessment of the trabecular structure of mandibular condyles in patients with temporomandibular disorders using fractal analysis. Oral surgery, oral medicine, oral pathology and oral radiology. 2017;123(3):382-391.
Morinushi T, Kawasaki H, Masumoto Y, Shigeta K, Ogura T, Takigawa M. Examination of the diagnostic value and estimation of the chaos phenomenon in masticatory movement using fractal dimension in patients with temporomandibular dysfunction syndrome. J Oral Rehabil. May 1998;25(5):386-94. doi:10.1046/j.1365-2842.1998.00230.x
Margaritescu C, Raica M, Pirici D, et al. Podoplanin expression in tumor-free resection margins of oral squamous cell carcinomas: an immunohistochemical and fractal analysis study. Histol Histopathol. Jun 2010;25(6):701-11. doi:10.14670/HH-25.701
Chikui T, Tokumori K, Yoshiura K, Oobu K, Nakamura S, Nakamura K. Sonographic texture characterization of salivary gland tumors by fractal analyses. Ultrasound Med Biol. 2005;31(10):1297-1304.
Phulari RG, Rathore RS, Talegaon TP. Nuclear fractal dimension: A new objective approach for discriminating normal mucosa, dysplasia and carcinoma. J Oral Maxillofac Pathol. Sep-Dec 2016;20(3):400-404. doi:10.4103/0973-029X.190912
Yu YY, Chen H, Lin CH, et al. Fractal dimension analysis of periapical reactive bone in response to root canal treatment. Oral Surg Oral Med Oral Pathol Oral Radiol Endod. Feb 2009;107(2):283-8. doi:10.1016/j.tripleo.2008.05.047
Pârvu A, Ţălu Ş, Crăciun C, Alb S. Evaluation of scaling and root planing effect in generalized chronic periodontitis by fractal and multifractal analysis. J Periodontal Res. 2014;49(2):186-196.
Jung Y-H. Evaluation of peri-implant bone using fractal analysis. Imaging Science in Dentistry. 2005;35(3):121-125.
Abdulhameed EA, Al-Rawi NH, Uthman AT, Samsudin AR. Bone texture fractal dimension analysis of ultrasound-treated bone around implant site: a double-blind clinical trial. International journal of dentistry. 2018;2018
Park H-J, Jung Y-H, Cho B-H. Bone changes after bilateral sagittal split osteotomy for mandibular prognathism. Imaging Science in Dentistry. 2006;36(4):183-188.
Koca H, Ergün S, Güneri P, Boyacioglu H. Evaluation of trabecular bone healing by fractal analysis and digital subtraction radiography on digitized panoramic radiographs: a preliminary study. Oral radiol. Jun 2010;26(1):1-8. doi:10.1007/s11282-009-0029-6
Aydın ZU, Toptaş O, Bulut DG, Akay N, Kara T, Akbulut N. Effects of root-end filling on the fractal dimension of the periapical bone after periapical surgery: retrospective study. Clin Oral Investig. 2019;23(9):3645-3651.
Camargo AJ, Cortes ARG, Aoki EM, Baladi MG, Arita ES, Watanabe PCA. Diagnostic performance of fractal dimension and radiomorphometric indices from digital panoramic radiographs for screening low bone mineral density. Brazilian Journal of Oral Sciences. 2016:131-136.
Sindeaux R, Figueiredo PT, de Melo NS, et al. Fractal dimension and mandibular cortical width in normal and osteoporotic men and women. Maturitas. Feb 2014;77(2):142-8. doi:10.1016/j.maturitas.2013.10.011
Şener E, Baksı BG. Sağlıklı ve osteoporoz tanılı hastalarda fraktal boyut ve mandibular kortikal indeks değerlendirilmesi. Ege Üniversitesi Dişhekimliği Fakültesi Dergisi. 2016;37(3):159-167.
Bayrak S, Goller Bulut D, Orhan K, et al. Evaluation of osseous changes in dental panoramic radiography of thalassemia patients using mandibular indexes and fractal size analysis. Oral radiol. Jan 2020;36(1):18-24. doi:10.1007/s11282-019-00372-7
Chikui T, Shimizu M, Kawazu T, Okamura K, Shiraishi T, Yoshiura K. A quantitative analysis of sonographic images of the salivary gland: a comparison between sonographic and sialographic findings. Ultrasound Med Biol. 2009;35(8):1257-1264.
ErgüN S, Saraçoglu A, GüNeri P, Ozpınar B. Application of fractal analysis in hyperparathyroidism. Dentomaxillofacial Radiology. 2009;38(5):281-289.
GÜmÜŞsoy İ, Duman ŞB, MİloĞlu Ö. Hiperparatiroidili hastalarda panoramik indeksler ve fraktal analiz kullanılarak mandibular kemiğin incelenmesi. Selcuk Dental Journal. 6(4):299-303.
Neves FS, Barros AS, Cerqueira GA, et al. Assessment of fractal dimension and panoramic radiomorphometric indices in women with celiac disease. Oral radiol. Apr 2020;36(2):141-147. doi:10.1007/s11282-019-00388-z
Kurşun-Çakmak EŞ, Bayrak S. Comparison of fractal dimension analysis and panoramic-based radiomorphometric indices in the assessment of mandibular bone changes in patients with type 1 and type 2 diabetes mellitus. Oral surgery, oral medicine, oral pathology and oral radiology. 2018;126(2):184-191.
Apolinário AC, Sindeaux R, De Souza Figueiredo PT, et al. Dental panoramic indices and fractal dimension measurements in osteogenesis imperfecta children under pamidronate treatment. Dentomaxillofacial Radiology. 2016;45(4):20150400.
Coşgunarslan A, Çabuk DS, Aşantoğrol F, Canger EM. Kronik Böbrek Hastalarında Mandibular Kemik Kalitesinin Değerlendirilmesi. Turkiye Klinikleri Dishekimligi Bilimleri Dergisi. 2021;27(1)
Ersan N, Ozel B. Fractal dimension analysis of different mandibular regions in familial Mediterranean fever patients: A cross-sectional retrospective study. PLoS One. 2023;18(6):e0288170. doi:10.1371/journal.pone.0288170
Altunok Ünlü N, Coşgun A, Altan H. Evaluation of bone changes on dental panoramic radiography using mandibular indexes and fractal dimension analysis in children with familial Mediterranean fever. Oral radiol. 2023;39(2):312-320.
Temur KT, Magat G, Cosgunarslan A, Ozcan S. Evaluation of Jaw Bone Change in Children and Adolescents with Rheumatic Heart Disease by Fractal Analysis. Niger J Clin Pract. Feb 1 2024;27(2):260-267. doi:10.4103/njcp.njcp_346_23
Yasar F, Yesilova E, Akgunlu F. Alveolar bone changes under overhanging restorations. Clin Oral Investig. Oct 2010;14(5):543-9. doi:10.1007/s00784-009-0334-9
Lucchese A, Gentile E, Capone G, De Vico G, Serpico R, Landini G. Fractal analysis of mucosal microvascular patterns in oral lichen planus: a preliminary study. Oral Surg Oral Med Oral Pathol Oral Radiol. Nov 2015;120(5):609-15. doi:10.1016/j.oooo.2015.06.029
Créton M, Geraets W, Verhoeven JW, Van Der Stelt PF, Verhey H, Cune M. Radiographic features of mandibular trabecular bone structure in hypodontia. Clin Implant Dent Relat Res. 2012;14(2):241-249.
Köse E, Ay Ünüvar Y, Uzun M. Assessment of the relationship between fractal analysis of mandibular bone and orthodontic treatment duration: A retrospective study. Journal of Orofacial Orthopedics/Fortschritte der Kieferorthopädie. 2022;83(Suppl 1):102-110.
Eninanç İ, Büyükbayraktar ZÇ. Assessment of correlation between hand-wrist maturation and cervical vertebral maturation: a fractal analysis study. BMC Oral Health. 2023;23(1):798.
Gulec M, Tassoker M, Ozcan S, Orhan K. Evaluation of the mandibular trabecular bone in patients with bruxism using fractal analysis. Oral radiol. Jan 2021;37(1):36-45. doi:10.1007/s11282-020-00422-5
Yasar F, Akgunlu F. Fractal dimension and lacunarity analysis of dental radiographs. Dentomaxillofac Radiol. Sep 2005;34(5):261-7. doi:10.1259/dmfr/85149245
Kwak KH, Kim SS, Kim YI, Kim YD. Quantitative evaluation of midpalatal suture maturation via fractal analysis. Korean J Orthod. Sep 2016;46(5):323-30. doi:10.4041/kjod.2016.46.5.323
Coşgunarslan A, Canger EM, Çabuk DS, Kış HC. The evaluation of the mandibular bone structure changes related to lactation with fractal analysis. Oral radiol. 2020;36(3):238-247.
Referanslar
Mandelbrot BB. Fractal geometry: what is it, and what does it do? Proceedings of the Royal Society of London A Mathematical and Physical Sciences. 1989;423(1864):3-16.
Sánchez I, Uzcátegui G. Fractals in dentistry. J Dent. 2011;39(4):273-292.
Demirbaş AK, Ergün S, Güneri P, Aktener BO, Boyacıoğlu H. Mandibular bone changes in sickle cell anemia: fractal analysis. Oral Surgery, Oral Medicine, Oral Pathology, Oral Radiology, and Endodontology. 2008;106(1):e41-e48.
Cross SS. Fractals in pathology. The Journal of Pathology: A Journal of the Pathological Society of Great Britain and Ireland. 1997;182(1):1-8.
Güleç M, Taşsöker M, Şener S. Tıpta ve Diş Hekimliğinde Fraktal Analiz. Ege Üniversitesi Diş Hekimliği Fakültesi Dergisi. 2019;40(1):17-31.
Flook A. The use of dilation logic on the quantimet to achieve fractal dimension characterisation of textured and structured profiles. Powder Technology. 1978;21(2):295-298.
Smith Jr T, Lange G, Marks WB. Fractal methods and results in cellular morphology—dimensions, lacunarity and multifractals. J Neurosci Methods. 1996;69(2):123-136.
Barnsley MF. Fractals everywhere. Academic press; 2014.
Lopes R, Betrouni N. Fractal and multifractal analysis: a review. Med Image Anal. Aug 2009;13(4):634-49. doi:10.1016/j.media.2009.05.003
Geraets WG, van der Stelt PF. Fractal properties of bone. Dentomaxillofac Radiol. May 2000;29(3):144-53. doi:10.1038/sj/dmfr/4600524
Russell DA, Hanson JD, Ott E. Dimension of strange attractors. Phys Rev Lett. 1980;45(14):1175.
Pehlİvan MZY, Boz AF. Görüntü işleme tabanlı kutu sayma yöntemi ile fraktal boyut hesabı için arayüz tasarımı.
White SC, Rudolph DJ. Alterations of the trabecular pattern of the jaws in patients with osteoporosis. Oral Surg Oral Med Oral Pathol Oral Radiol Endod. Nov 1999;88(5):628-35. doi:10.1016/s1079-2104(99)70097-1
Broe R, Rasmussen ML, Frydkjaer-Olsen U, et al. Retinal vascular fractals predict long-term microvascular complications in type 1 diabetes mellitus: the Danish Cohort of Pediatric Diabetes 1987 (DCPD1987). Diabetologia. Oct 2014;57(10):2215-21. doi:10.1007/s00125-014-3317-6
Bianchi FD, Bonetto RD. FERImage: an interactive program for fractal dimension, d(per) and d(min) calculation. Scanning. May-Jun 2001;23(3):193-7. doi:10.1002/sca.4950230305
Shrout MK, Potter BJ, Hildebolt CF. The effect of image variations on fractal dimension calculations. Oral Surg Oral Med Oral Pathol Oral Radiol Endod. Jul 1997;84(1):96-100. doi:10.1016/s1079-2104(97)90303-6
Camargo AJ, Cortes ARG, Aoki EM, Baladi MG, Arita ES, Watanabe PCA. Diagnostic performance of fractal dimension and radiomorphometric indices from digital panoramic radiographs for screening low bone mineral density. Brazilian Journal of Oral Sciences. 2016;15(2):131-136.
Shrout MK, Hildebolt CF, Potter BJ. The effect of varying the region of interest on calculations of fractal index. Dentomaxillofac Radiol. Sep 1997;26(5):295-8. doi:10.1038/sj.dmfr.4600260
Oliveira-Santos N, Michels M, Freitas DQ, Haiter-Neto F, Oliveira ML. Influence of phosphor plate-based radiographic image specifications on fractal analysis of alveolar bone. Oral Surgery Oral Medicine Oral Pathology Oral Radiology. Oct 2019;128(4):418-423. doi:10.1016/j.oooo.2019.06.011
Bollen AM, Taguchi A, Hujoel PP, Hollender LG. Fractal dimension on dental radiographs. Dentomaxillofac Radiol. Sep 2001;30(5):270-5. doi:10.1038/sj/dmfr/4600630
Magat G, Ozcan Sener S. Evaluation of trabecular pattern of mandible using fractal dimension, bone area fraction, and gray scale value: comparison of cone-beam computed tomography and panoramic radiography. Oral radiol. Jan 2019;35(1):35-42. doi:10.1007/s11282-018-0316-1
Chen S-K, Oviir T, Lin C-H, Leu L-J, Cho B-H, Hollender L. 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. 2005;100(4):467-472.
Jolley L, Majumdar S, Kapila S. Technical factors in fractal analysis of periapical radiographs. Dentomaxillofac Radiol. Nov 2006;35(6):393-7. doi:10.1259/dmfr/30969642
Baksi BG, Fidler A. Fractal analysis of periapical bone from lossy compressed radiographs: a comparison of two lossy compression methods. J Digit Imaging. 2011;24:993-998.
Eftekhari A. Fractal study of Ni-Cr-Mo alloy for dental applications: effect of beryllium. Applied Surface Science. Dec 30 2003;220(1-4):343-348. doi:10.1016/S0169-4332(03)00842-0
Takuma Y, Shiraishi T, Fujita T, Hisatsune K. Tarnish resistance evaluation of experimental Pd-free Ag-Au-Pt-Cu dental alloys. Dent Mater J. May 2010;29(3):330-5. doi:10.4012/dmj.2009-093
Venkatesh BD, Chen DL, Bhole SD. Effect of heat treatment on mechanical properties of Ti-6Al-4V ELI alloy. Materials Science and Engineering a-Structural Materials Properties Microstructure and Processing. Apr 25 2009;506(1-2):117-124. doi:10.1016/j.msea.2008.11.018
Wilson KS, Allen AJ, Washburn NR, Antonucci JM. Interphase effects in dental nanocomposites investigated by small‐angle neutron scattering. Journal of Biomedical Materials Research Part A. 2007;81(1):113-123.
Wojtowicz A CS, Hulisz-Secomska M, Yamauchi, M OK. Disturbed pattern of collagen fibres in dentinal dysplasia type I. Dent Med Probl. 2002;39(2):169-175.
Gutierrez P, Pina C, Lara VH, Bosch P. Characterization of enamel with variable caries risk. Arch Oral Biol. Oct 2005;50(10):843-8. doi:10.1016/j.archoralbio.2004.11.018
Shrout MK, Roberson B, Potter BJ, Mailhot JM, Hildebolt CF. A comparison of 2 patient populations using fractal analysis. J Periodontol. Jan 1998;69(1):9-13. doi:10.1902/jop.1998.69.1.9
Kayipmaz S, Akcay S, Sezgin OS, Candirli C. Trabecular structural changes in the mandibular condyle caused by degenerative osteoarthritis: a comparative study by cone-beam computed tomography imaging. Oral radiol. Jan 2019;35(1):51-58. doi:10.1007/s11282-018-0324-1
Arsan B, Köse TE, Çene E, Özcan İ. Assessment of the trabecular structure of mandibular condyles in patients with temporomandibular disorders using fractal analysis. Oral surgery, oral medicine, oral pathology and oral radiology. 2017;123(3):382-391.
Morinushi T, Kawasaki H, Masumoto Y, Shigeta K, Ogura T, Takigawa M. Examination of the diagnostic value and estimation of the chaos phenomenon in masticatory movement using fractal dimension in patients with temporomandibular dysfunction syndrome. J Oral Rehabil. May 1998;25(5):386-94. doi:10.1046/j.1365-2842.1998.00230.x
Margaritescu C, Raica M, Pirici D, et al. Podoplanin expression in tumor-free resection margins of oral squamous cell carcinomas: an immunohistochemical and fractal analysis study. Histol Histopathol. Jun 2010;25(6):701-11. doi:10.14670/HH-25.701
Chikui T, Tokumori K, Yoshiura K, Oobu K, Nakamura S, Nakamura K. Sonographic texture characterization of salivary gland tumors by fractal analyses. Ultrasound Med Biol. 2005;31(10):1297-1304.
Phulari RG, Rathore RS, Talegaon TP. Nuclear fractal dimension: A new objective approach for discriminating normal mucosa, dysplasia and carcinoma. J Oral Maxillofac Pathol. Sep-Dec 2016;20(3):400-404. doi:10.4103/0973-029X.190912
Yu YY, Chen H, Lin CH, et al. Fractal dimension analysis of periapical reactive bone in response to root canal treatment. Oral Surg Oral Med Oral Pathol Oral Radiol Endod. Feb 2009;107(2):283-8. doi:10.1016/j.tripleo.2008.05.047
Pârvu A, Ţălu Ş, Crăciun C, Alb S. Evaluation of scaling and root planing effect in generalized chronic periodontitis by fractal and multifractal analysis. J Periodontal Res. 2014;49(2):186-196.
Jung Y-H. Evaluation of peri-implant bone using fractal analysis. Imaging Science in Dentistry. 2005;35(3):121-125.
Abdulhameed EA, Al-Rawi NH, Uthman AT, Samsudin AR. Bone texture fractal dimension analysis of ultrasound-treated bone around implant site: a double-blind clinical trial. International journal of dentistry. 2018;2018
Park H-J, Jung Y-H, Cho B-H. Bone changes after bilateral sagittal split osteotomy for mandibular prognathism. Imaging Science in Dentistry. 2006;36(4):183-188.
Koca H, Ergün S, Güneri P, Boyacioglu H. Evaluation of trabecular bone healing by fractal analysis and digital subtraction radiography on digitized panoramic radiographs: a preliminary study. Oral radiol. Jun 2010;26(1):1-8. doi:10.1007/s11282-009-0029-6
Aydın ZU, Toptaş O, Bulut DG, Akay N, Kara T, Akbulut N. Effects of root-end filling on the fractal dimension of the periapical bone after periapical surgery: retrospective study. Clin Oral Investig. 2019;23(9):3645-3651.
Camargo AJ, Cortes ARG, Aoki EM, Baladi MG, Arita ES, Watanabe PCA. Diagnostic performance of fractal dimension and radiomorphometric indices from digital panoramic radiographs for screening low bone mineral density. Brazilian Journal of Oral Sciences. 2016:131-136.
Sindeaux R, Figueiredo PT, de Melo NS, et al. Fractal dimension and mandibular cortical width in normal and osteoporotic men and women. Maturitas. Feb 2014;77(2):142-8. doi:10.1016/j.maturitas.2013.10.011
Şener E, Baksı BG. Sağlıklı ve osteoporoz tanılı hastalarda fraktal boyut ve mandibular kortikal indeks değerlendirilmesi. Ege Üniversitesi Dişhekimliği Fakültesi Dergisi. 2016;37(3):159-167.
Bayrak S, Goller Bulut D, Orhan K, et al. Evaluation of osseous changes in dental panoramic radiography of thalassemia patients using mandibular indexes and fractal size analysis. Oral radiol. Jan 2020;36(1):18-24. doi:10.1007/s11282-019-00372-7
Chikui T, Shimizu M, Kawazu T, Okamura K, Shiraishi T, Yoshiura K. A quantitative analysis of sonographic images of the salivary gland: a comparison between sonographic and sialographic findings. Ultrasound Med Biol. 2009;35(8):1257-1264.
ErgüN S, Saraçoglu A, GüNeri P, Ozpınar B. Application of fractal analysis in hyperparathyroidism. Dentomaxillofacial Radiology. 2009;38(5):281-289.
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