Assessment of changes in bone trabeculation after mandibular expansion treatment using fractal dimension analysis

Background: This study evaluated region-specific mandibular trabecular bone changes after expansion using fractal dimension analysis (FDA) on panoramic radiographs and their association with mandibular arch width. Methods: In this retrospective controlled longitudinal study, 50 patients (25 per group) aged 8–11 years (mean age: 9.50 ± 0.95) were included. The treatment group comprised patients treated with a mandibular Schwarz appliance, with panoramic radiographs and digital models obtained before (T0) and after expansion (T1). The control group included age- and sex-matched untreated subjects with two panoramic radiographs obtained over matched intervals. FDA was performed on five mandibular regions (condyles, angles, and symphysis), and mandibular arch widths were measured on digital models. Group comparisons were analyzed using t-tests, and correlations between arch width and FDA changes were assessed using Pearson’s coefficient. Results: In the treatment group, FDA significantly decreased in the symphysis (p < 0.001) and condylar regions (p < 0.05) and increased in the angular region (p < 0.05), whereas no significant changes were observed in controls (p > 0.05). Post-treatment, FDA values differed between groups in all regions (p < 0.05), with greater changes in the symphysis and angulus. Mandibular arch widths increased in the treatment group, with mean increases of 2.36 ± 0.31 mm (intercanine), 3.28± 0.48 mm (first interdeciduous molar/first interpremolar), 3.46 ± 0.37 mm (second interdeciduous molar), and 2.51 ± 0.64 mm (first intermolar). Intercanine and first interdeciduous molar/first interpremolar changes correlated positively with symphysis FDA changes (r = 0.202 and r = 0.254, p < 0.05), while intermolar changes correlated negatively with angulus FDA (r = −0.464, p < 0.05). Conclusions: Mandibular expansion is associated with region-specific alterations in mandibular trabecular bone microarchitecture. These findings indicate that its effects are not limited to dentoalveolar changes but also involve adaptive responses in the underlying bone.

Digital model analysis; Fractal dimension analysis; Mandibular expansion; Panoramic radiographs

[1] Zhou C, Duan P, He H, Song J, Hu M, Liu Y, et al. Expert consensus on pediatric orthodontic therapies of malocclusions in children. International Journal of Oral Science. 2024; 16: 32.

[2] Watted N, Lone IM, Midlej K, Zohud O, Awadi O, Masarwa S, et al. The complexity of skeletal transverse dimension: from diagnosis, management, and treatment strategies to the application of collaborative cross (CC) mouse model. Journal of Functional Morphology and Kinesiology. 2024; 9: 51.

[3] Elias KG, Sivamurthy G, Bearn DR. Extraction vs. nonextraction orthodontic treatment: a systematic review and meta-analysis. The Angle Orthodontist. 2024; 94: 83–106.

[4] Angle EH. Occlusion. In Angle EH (ed.) Treatment of malocclusion of the teeth and fractures of the maxillae: Angle’s system (pp. 5–15). 6th edn. S. S. White Dental Mfg. Co.: Philadelphia. 1907.

[5] García-Miralles E, Guinot-Barona C, Marqués-Martínez L, Aura-Tormos JI, Marco-Cambra V. Mandibular dentoalveolar expansion in early mixed dentition using the Clara expander: a case series. Children. 2025; 12: 951.

[6] Gandhi V, Malek F, Mehta S, Tadinada A, Goldman R, Yadav S. Skeletal and dentoalveolar changes with mandibular expansion in growing children. Cureus. 2023; 15: e47723.

[7] Shen T, Zhao B, Wang C, Xiao Y, Han Y, Zhao G, et al. Efficacy of different designs of mandibular expanders: a three-dimensional finite element study. American Journal of Orthodontics and Dentofacial Orthopedics. 2020; 157: 641–650.

[8] McNamara JA Jr. Early intervention in the transverse dimension: is it worth the effort? American Journal of Orthodontics and Dentofacial Orthopedics. 2002; 121: 572–574.

[9] Proffit WR, Fields HW, Larson BE, Sarver DM. Contemporary orthodontics. 6th edn. Elsevier: St. Louis. 2018.

[10] Graber LW, Vanarsdall RL, Vig KWL. Orthodontics: current principles and techniques. 2nd edn. Mosby: St. Louis. 1994.

[11] Frost HM. Bone’s mechanostat: a 2003 update. The Anatomical Record. Part A, Discoveries in Molecular, Cellular, and Evolutionary Biology. 2003; 275: 1081–1101.

[12] White SC, Rudolph DJ. Alterations of the trabecular pattern of the jaws in patients with osteoporosis. Oral Surgery, Oral Medicine, Oral Pathology, Oral Radiology, and Endodontology. 1999; 88: 628–635.

[13] Temur KT, Magat G, Cukurluoglu A, Sogukpınar Onsuren A, Ozcan S. Evaluation of mandibular trabecular bone by fractal analysis in pediatric patients with hypodontia of the mandibular second premolar tooth. BMC Oral Health. 2024; 24: 1005.

[14] Tasdemir T, Tassoker M. Fractal analysis of mandibular bone structure in children with amelogenesis imperfecta. Bone. 2025; 199: 117571.

[15] Kato CN, Barra SG, Tavares NP, Amaral TM, Brasileiro CB, Mesquita RA, et al. Use of fractal analysis in dental images: a systematic review. Dentomaxillofacial Radiology. 2020; 49: 20180457.

[16] Kolcakoglu K, Amuk M, Sirin Sarıbal G. Evaluation of mandibular trabecular bone by fractal analysis on panoramic radiograph in paediatric patients with sleep bruxism. International Journal of Paediatric Dentistry. 2022; 32: 776–784.

[17] Özkaymaz GS, Çiftçi Özkan E. Investigation of changes caused by rapid maxillary expansion in mandibular bone and temporomandibular joint trabecular structure using fractal analysis. BMC Oral Health. 2024; 24: 1436.

[18] Bolat Gümüş E, Yavuz E, Tufekci C. Effects of functional orthopedic treatment on mandibular trabecular bone in Class II patients using fractal analysis. Journal of Orofacial Orthopedics. 2023; 84: 155–164.

[19] Çiçek O, Yılmaz H, Melayim H. Evaluation of changes in alveolar bone remodeling after orthodontic treatment using fractal analysis: a retrospective study. International Dental Research. 2024; 14: 19–26.

[20] Kussaba II, Felipe BC, Poluha RL, Filho LI, da Silva MC, Vessoni Iwaki LC. Fractal analysis of the mandibular ramus in Class II and III patients undergoing orthognathic surgery: retrospective study through cone-beam computed tomography. Oral and Maxillofacial Surgery. 2025; 29: 135.

[21] Vandenbroucke JP, von Elm E, Altman DG, Gøtzsche PC, Mulrow CD, Pocock SJ, et al. Strengthening the reporting of observational studies in epidemiology (STROBE): explanation and elaboration. Epidemiology. 2007; 18: 805–835.

[22] Gulec M, Tassoker M, Ozcan S, Orhan K. Evaluation of the mandibular trabecular bone in patients with bruxism using fractal analysis. Oral Radiology. 2021; 37: 36–45.

[23] Salem FM, Messih MSA, Hadhoud RM. Analysis of mandibular and maxillary intercanine and intermolar widths and total arch length for sex and age differences in an adult Egyptian sample. Egyptian Journal of Forensic Sciences. 2025; 15: 16.

[24] Ali MJ, Reshma AG, Sam N, Prem D, Subhalakshmi V. Validity of maxillary intra-incisor–canine width as a novel indicator for sex determination. Journal of Indian Academy of Forensic Medicine. 2026; 48: 131–137.

[25] McNamara JA, Brudon WL, Kokich VG. Orthodontics and dentofacial orthopedics. 2nd edn. Needham Press: Ann Arbor (MI). 2001.

[26] Louly F, Nouer PRA, Janson G, Pinzan A. Dental arch dimensions in the mixed dentition: a study of Brazilian children from 9 to 12 years of age. Journal of Applied Oral Science. 2011; 19: 169–174.

[27] Franciotti R, Moharrami M, Quaranta A, Bizzoca ME, Piatelli A, Aprile G, et al. Use of fractal analysis in dental images for osteoporosis detection: a systematic review and meta-analysis. Osteoporosis International. 2021; 32: 1041–1052.

[28] Tassoker M, Balel Y, Erturk M, Sagtas K. Automated fractal analysis for mandibular bone evaluation in type 1 diabetes mellitus using a novel single-click approach. Scientific Reports. 2025; 15: 30266.

[29] Tai K, Park JH. Dental and skeletal changes in the upper and lower jaws after treatment with Schwarz appliances using cone-beam computed tomography. Journal of Clinical Pediatric Dentistry. 2010; 35: 111–120.

[30] Quinzi V, Mummolo S, Bertolazzi F, Campanella V, Marzo G, Marchetti E. Comparison of mandibular arch expansion by the Schwartz appliance using two activation protocols: a preliminary retrospective clinical study. Journal of Functional Morphology and Kinesiology. 2020; 5: 61.

[31] Jain RK, Vokes T. Dual-energy X-ray absorptiometry. Journal of Clinical Densitometry. 2017; 20: 291–303.

[32] Ngan DCS, Kharbanda OP, Geenty JP, Darendeliler MA. Comparison of radiation levels from computed tomography and conventional dental radiographs. Australian Orthodontic Journal. 2003; 19: 67–75.

[33] Grünheid T, Kolbeck Schieck JR, Pliska BT, Ahmad M, Larson BE. Dosimetry of a cone-beam computed tomography machine compared with a digital X-ray machine in orthodontic imaging. American Journal of Orthodontics and Dentofacial Orthopedics. 2012; 141: 436–443.

[34] Balel Y, Sağtaş K. Single-click automated fractal analysis for dental radiographs: a comparative evaluation with classic ImageJ method. BMC Oral Health. 2025; 25: 1360.

[35] Cesur E, Bayrak S, Kursun-Çakmak EŞ, Arslan C, Köklü A, Orhan K. Evaluating the effects of functional orthodontic treatment on mandibular osseous structure using fractal dimension analysis of dental panoramic radiographs. The Angle Orthodontist. 2020; 90: 783–793.

[36] Oenning AC, Jacobs R, Salmon B. ALADAIP, beyond ALARA and towards personalized optimization for paediatric cone-beam CT. International Journal of Paediatric Dentistry. 2021; 31: 676–678.

[37] Herring SW, Rafferty KL, Liu ZJ, Marshall CD. Jaw muscles and the skull in mammals: the biomechanics of mastication. Comparative Biochemistry and Physiology Part A: Molecular & Integrative Physiology. 2001; 131: 207–219.

[38] Kiliaridis S. The importance of masticatory muscle function in dentofacial growth. Seminars in Orthodontics. 2006; 12: 110–119.

[39] Turner CH. Three rules for bone adaptation to mechanical stimuli. Bone. 1998; 23: 399–407.

[40] Smotrova E, Li S, Silberschmidt VV. Mechanoregulated trabecular bone adaptation: progress report on in silico approaches. Biomaterials and Biosystems. 2022; 7: 100058.

[41] Borowska M, Bebas E, Hładuński M, Mojsak M, Oczeretko E. Fractal dimension analysis of PET-MRI liver images for various ROI sizes. Polish Conference on Biocybernetics and Biomedical Engineering. Zielona Góra, Poland, 25–27 September 2019. Springer: Cham. 2019.

[42] Önsüren AS, Temur KT. Evaluation of fractal and radiomorphometric measurements of mandibular bone structure in pediatric patients with molar incisor hypomineralization. International Journal of Paediatric Dentistry. 2025; 35: 945–953.

[43] Boztaş Demir G, Doğrugören R, Topsakal KG, Duran GS, Görgülü S. Assessment of mandibular trabecular bone structure in hypodivergent growth patterns using fractal analysis. Fractal and Fractional. 2025; 9: 517.

[44] Provatidis C, Georgiopoulos B, Kotinas A, McDonald JP. On the FEM modeling of craniofacial changes during rapid maxillary expansion. Medical Engineering and Physics. 2007; 29: 566–579.

[45] Staderini E, Guglielmi F, Bonetti AA, Cavalcanti I, Grande NM, Costagnola R, et al. Fractal analysis of trabecular bone before and after orthodontic and surgical extrusion: a retrospective case-control study. Fractal and Fractional. 2025; 9: 818.

[46] Pirttiniemi P, Peltomäki T, Müller L, Luder HU. Abnormal mandibular growth and the condylar cartilage. European Journal of Orthodontics. 2009; 31: 1–11.

[47] Gv V, Tripathi T. Fractal analysis of mandibular trabecular pattern following protraction facemask therapy: a pilot study. Journal of Orofacial Orthopedics. 2025; 86: 22–30.

[48] Geraets WG, Van der Stelt PF. Fractal properties of bone. Dentomaxillofacial Radiology. 2000; 29: 144–153.

[49] O’Grady PW, McNamara JA Jr, Baccetti T, Franchi L. A long-term evaluation of the mandibular Schwarz appliance and the acrylic splint expander in early mixed dentition patients. American Journal of Orthodontics and Dentofacial Orthopedics. 2006; 130: 202–213.

[50] Kojima Y, Fukui H. Numerical simulation of canine retraction by sliding mechanics. American Journal of Orthodontics and Dentofacial Orthopedics. 2005; 127: 542–551.

[51] Cattaneo PM, Dalstra M, Melsen B. The finite element method: a tool to study orthodontic tooth movement. Journal of Dental Research. 2005; 84: 428–433.

[52] Karslı N, Arslan C, Çakan DG, Altuğ AT, Dönmez ST, Yücesan AA. Comparison of the effects of fixed and removable functional orthodontic treatment on the mandibular trabecular bone in fractal analysis. Turkish Journal of Orthodontics. 2024; 37: 265–275.

[53] Murakami K, Kawakami M, Yamamoto K, Horita S. Finite element analysis of strain energy density and facial morphology. BMC Oral Health. 2025; 25: 859.

[54] Vas NV, Ramasamy N, Harikrishan S, Ramalingam K, Di Blasio M, Uzuncıbuk H, et al. Finite element method analysis of dentoskeletal changes on temporary anchorage device-assisted mandibular advancement. Turkish Journal of Orthodontics. 2025; 38: 97–106.

[55] Shi Q, Zhiyuan G, Lai D, Dai Q, Yu F. Three-dimensional evaluation of condylar morphology after orthodontic treatment in adult patients with Class II malocclusion by cone-beam computed tomography. BMC Oral Health. 2024; 24: 48.

[56] Rizk M, Niederau C, Florea A, Kiessling F, Morgenroth A, Mottaghy FM, et al. Periodontal ligament and alveolar bone remodeling during long orthodontic tooth movement analyzed by a novel user-independent 3D methodology. Scientific Reports. 2023; 13: 19919.