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Article

Fractal Analysis of Trabecular Bone Before and After Orthodontic and Surgical Extrusion: A Retrospective Case–Control Study

by
Edoardo Staderini
1,2,
Federica Guglielmi
1,2,*,
Anna Alessandri Bonetti
1,2,
Irene Cavalcanti
1,*,
Nicola Maria Grande
1,
Raffaella Castagnola
1 and
Patrizia Gallenzi
1,2
1
School of Dentistry, Catholic University of the Sacred Heart, Largo Agostino Gemelli 1, 00168 Rome, Italy
2
Department of Orthodontic, IRCCS “A. Gemelli” University Polyclinic Foundation, Largo Agostino Gemelli 8, 00168 Rome, Italy
*
Authors to whom correspondence should be addressed.
Fractal Fract. 2025, 9(12), 818; https://doi.org/10.3390/fractalfract9120818 (registering DOI)
Submission received: 14 November 2025 / Revised: 2 December 2025 / Accepted: 11 December 2025 / Published: 15 December 2025
(This article belongs to the Special Issue Fractal Mechanics of Engineering Materials, 2nd Edition)
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Abstract

The present study explores bone healing patterns induced by orthodontic (OE) and surgical extrusion (SE) of structurally compromised teeth, where extrusion techniques are commonly used in rehabilitation. Changes in the trabecular bone were assessed by means of fractal analysis (FA) of consecutive periapical radiographs. (2) The present study is a retrospective case–control study. Pre- and post-treatment periapical radiographs from 44 adults undergoing orthodontic (OE) or surgical extrusion (SE) were retrieved. The radiographs were taken at T0 (pre-treatment), T1 (post-treatment), T2 (3-month follow-up), and T3 (6-month follow-up). Bone density (fractal dimension, FD) was analyzed in the apical and proximal bone regions (ROIs) of the extruded teeth, and both intra-group and inter-group differences were examined. (3) In all the regions of interest (ROIs), statistically significant intra-group differences in terms of bone density (FD) for both groups were found. In the OE group, the FD value increased, respectively, at T1, T2, and T3 in the apical ROI, compared to T0. For the proximal ROI, nearly the same trend was observed, respectively, at T1, T2, and T3 versus T0. As for the SE group, a statistically significant increase in the apical ROI was noted at T1, T2, and T3 when compared to T0. The same trend was registered in the proximal ROI compared to T0. However, no statistically significant inter-group differences in FD were detected between the two groups. (4) Orthodontic extrusion and surgical extrusion both resulted in an increased bone density (FD) despite the different healing patterns. Further prospective studies with a longer follow-up in this field are required.

1. Introduction

Dental extrusion is defined as tooth movement from the alveolar bone in a coronal direction; it is indicated for a coronal repositioning of the subgingival remaining tooth structure of “non-restorable” or “structurally compromised” teeth, experiencing partial loss of the clinical crown (corono-radicular fractures, very extensive carious lesions, and cervical root resorptions) [1].
Indeed, there are two fundamental requirements for the longevity of a prosthetic restoration: the “biological width” and the “ferrule effect” [2,3,4,5].
In periodontics, the “biological width” is defined as the natural distance between the base of the gingival sulcus and the supracrestal bone peak, which is filled by the junctional epithelium and the connective tissue attachment; the function of the biological width is to provide a protective barrier for the underlying periodontal ligament and alveolar bone [6,7]. Several meta-analyses suggest that the biological width is set approximately at 2.15–2.30 mm [8,9].
Since 2017, according to the World Workshop on the New Classification of Periodontal and Peri-implant Diseases, biological width is defined as “supracrestal tissue attachment” (STA) [10].
In prosthetics, the “ferrule effect” is the marginal seal of the prosthetic restoration on the parallel walls of the abutment, placed coronally to the margin of the preparation [11]. The presence of a circumferential tooth structure higher than 1.5 mm ensures an optimal marginal seal of the prosthetic restoration [12,13].
Dental extrusion can be achieved by means of orthodontic extrusion and surgical extrusion [14].
Orthodontic extrusion (OE), also known as “forced extrusion” or “forced eruption”, defines tooth movement caused by coronally directed orthodontic forces (Figure 1) [15].
Surgical extrusion (SE), also called “intra-alveolar transplantation”, is the procedure by which the remaining structure of a tooth element is intentionally repositioned in the coronal and/or supragingival direction, within the same dental socket (Figure 2) [16].
Orthodontic extrusion is a gradual, minimally invasive procedure that preserves bone but requires high patient compliance and extended treatment time [1].
On the other hand, surgical extrusion offers a more immediate solution, enabling tooth repositioning and retrograde endodontic treatment in a single session; still, it carries a greater risk of ankylosis and root resorption from surgical trauma [1].
As a result of orthodontic extrusion, the ongoing eruption of the teeth gradually induces bone apposition through traction from the fibers on the periosteum [15].
On the other hand, surgical extrusion exerts its effect through a rapid coronal repositioning of the tooth, leading to bone healing through the formation of a blood clot in the area between where the tooth is located and where it is repositioned [17].
While numerous studies have addressed the clinical implications of orthodontic and surgical extrusion, no investigation to date has characterized the bone-level changes induced by these procedures in the human model [1,14,16,18].
In fact, periapical and periradicular bone density can be assessed by fractal analysis (FA) of bi-dimensional radiographs; fractal analysis is a mathematical method used to measure irregularly shaped objects, including trabecular bone [19,20,21].
Fractal analysis employs an algorithm to quantify the interface between different surfaces and calculate the “fractal dimension” (FD): a higher FD value indicates a greater complexity and density of the examined structure [22,23,24].
It is possible to perform fractal analysis of 2D digital radiographic images (orthopantomographs, periapical, and bitewing radiograms) to assess the interface between cortical and medullary bone by calculating their FD value; the technique for processing radiographic images was initially described by White and Rudolph [25].
Fractal analysis of the trabecular bone has been widely employed in dentistry for different conditions and purposes [26,27]. In fact, several studies have documented the use of FA in various areas of dentistry, highlighting its versatility and diagnostic value.
As described by Sanchez and Uzcategui, FA is an effective tool for assessing the structural complexity of bone tissue and for detecting morphological changes that may be difficult to identify with conventional diagnostic methods [28].
In implant dentistry, multiple authors have demonstrated that FA can be used to evaluate the process of osseointegration over time, revealing bone remodeling dynamics and contributing to predictions regarding implant success [29,30].
The same technique has also proven particularly useful in the assessment of conditions that affect the mandibular trabecular architecture, such as bruxism: Gulec et al. showed that FA is capable of identifying trabecular alterations associated with parafunctional activity [31]. Likewise, in the field of periodontology, fractal analysis has shown promising results: Soltani and colleagues reported that FA enables the early detection of trabecular bone changes in patients with periodontitis, thereby enhancing the diagnostic value of routine periapical radiographs [32].
In orthodontics, Arslan et al. showed that FA can effectively evaluate alterations in the mandibular trabecular structure following functional orthodontic interventions such as reverse headgear therapy, highlighting the treatment-induced changes in bone density and architecture [33].
FA has also been employed to investigate the maturation of the mid-palatal suture, a key factor in determining the appropriate timing and modality of maxillary expansion [34].
Furthermore, FA has been utilized to analyze postoperative bone remodeling and healing patterns: Muftuoglu and Karasu reported that fractal dimension analysis allows for detailed evaluation of the mandibular condyle, angulus, and overall bony healing following orthognathic surgery, providing insights into patient-specific responses to surgical interventions [35].
Together, these studies underline the expanding role of fractal analysis in orthodontics, where it contributes to a deeper understanding of craniofacial growth, treatment effects, and skeletal adaptation [36,37,38].
So far, fractal analysis has not been employed in the evaluation of changes in the trabecular bone architecture after orthodontic and surgical extrusion yet.
The present investigation addresses an important clinical question by comparing bone healing patterns after OE and SE. This is an issue that has not been thoroughly investigated in the literature but is implicated in the biomechanics and long-term prognosis of structurally compromised teeth.
Therefore, the primary aim of this study was to use fractal analysis of consecutive periapical radiographs to assess and compare the intra-group changes occurring in the trabecular bone of patients after orthodontic and surgical extrusion. The null hypothesis for the primary aim was that there were no intra-group differences for T0 vs. T1, T0 vs. T2, and T0 vs. T3.
The secondary aim was to assess the inter-group differences between the two therapeutic approaches via fractal analysis. The null hypothesis for this aim was that there were no inter-group differences between the OE group and the SE group.
The present manuscript was reported in compliance with STROBE guidelines (Supplementary Materials Table S1) [39].

2. Materials and Methods

2.1. Study Design

The present study is a retrospective single-center case–control study. It was approved by the Ethical Committee of Agostino Gemelli Polyclinic Foundation (ID number: 6132; date of approval: 12 October 2023). The study is in accordance with the Declaration of Helsinki of 1975 and its amendments [40]. Written informed consent was obtained from all the study participants.

2.2. Sample Size Calculation

The sample size was determined based on a power analysis using JMP software (version 13), with an alpha of 0.05 and a power of 80%. The power analysis showed that a minimum of 34 patients should be included [32]. Therefore, 44 subjects, who had previously undergone an orthodontic or surgical extrusion treatment, were enrolled for the present study.

2.3. Participants

A total of 44 adults (≥18 years old), both males and females, from Agostino Gemelli Polyclinic Foundation, who had been consecutively treated with surgical or orthodontic extrusion by the same operator (N.M.G.) between January 2021 and May 2023, were enrolled for the present study: 22 patients underwent orthodontic extrusion (OE-case group) and the remaining 22 were subjected to surgical extrusion (SE-control group) (Table 1). Inclusion and exclusion criteria are listed in Table 2.
A total number of 44 teeth was analyzed, including 38 premolars and 6 molars.

2.4. Clinical Procedures

The decision to perform orthodontic or surgical extrusion was based on the following conditions:
  • Presence of adjacent teeth or anchorage elements for positioning the orthodontic appliance.
  • Presence of sufficient clinical crown for the placement of orthodontic brackets.
  • Orthodontic extrusion was, when possible, performed on single-rooted teeth, as higher forces are required for orthodontic movements of multi-rooted teeth [14].
  • Presence of periapical lesions and/or root resorptions, which are a contraindication for orthodontic movement unless the tooth undergoes endodontic treatment and apical Periodontal repair is achieved [41,42].
  • Patient’s possibility to undergo orthodontic treatment (e.g., attending follow-up visits).
  • Patient’s need for shorter treatment (surgical extrusion).
  • Patient’s inability to undergo surgical procedures (surgical extrusion) due to systemic conditions.
All extruded teeth presented the following characteristics:
  • Intrusion compared to the occlusal plane level (teeth that have suffered intrusive trauma or retained and/or included teeth).
  • Need for a prosthetic restoration, but with insufficient ferrule and/or restorations that violate the biological width.
  • Presence of a favorable crown/root ratio.
  • Presence of a coronal fracture.
  • Presence of subgingival carious lesions.
As for the OE group, the following clinical procedures were followed:
  • All teeth were subject to circumferential supracrestal fiberotomy performed at the beginning of the extrusive treatment, using a 15C micro-blade parallel to the root along the perimeter of the gingival sulcus.
  • All teeth were subjected to a vitality test prior to the beginning of the extrusive treatment, and endodontic treatment was performed on those that responded negatively.
  • The employed extrusive technique was the SW (Straight-Wire) Technique.
  • The patients followed a two-week follow-up recall, in order to check the amount of extrusion, reactivate the orthodontic appliance, and adjust the occlusion if necessary.
  • The extrusive treatment lasted until the desired quantity of extrusion was achieved, which was a sufficient ferrule for placing a prosthetic restoration.
  • Twenty-one orthodontically-extruded teeth were restored by placing an endocanalar fiberglass post and a lithium disilicate single crown; the remaining tooth helped with the development of the implant site.
As for the SE group, the following clinical procedures were followed:
  • All teeth were subjected to a vitality test prior to the beginning of the extrusive treatment, and endodontic treatment was performed before or during the extrusive procedures for those that responded negatively.
  • All teeth were atraumatically luxated using microsyndesmotomes and elevators and repositioned coronally to their original position, in order to achieve sufficient ferrule for placing a prosthetic restoration.
  • The extruded tooth was splinted to the adjacent tooth (or teeth), where composite resin and a passive stainless-steel wire were placed, and was kept in situ for 10 days; if necessary, the tooth was adjusted in its occlusion as well.
  • All surgically extruded teeth were restored by placing an endocanalar fiberglass post and a lithium disilicate prosthetic restoration (18 were single crowns, and the remaining 4 were part of a fixed dental prosthesis supported by natural teeth).

2.5. Protocol and Measurements

Patients were allocated into two groups, depending on whether they had undergone orthodontic (OE-case group) or surgical (SE-control group) extrusive treatment. Pre- and post-treatment periapical radiographs were retrieved from the database (DBSWIN 5.17, [43]) and then processed and analyzed using the open-source software ImageJ version 1.54b (National Institute of Health, Bethesda, MD, USA) [44].
All radiographs were obtained using an intraoral X-ray unit (Siemens Healthineers, Forcheim, Germany) with exposure settings of 70 kVp, 8 mA, and 0.16 s. All radiographs were also performed using the paralleling technique, and a silicone bite for each patient was applied to the positioning X-ray device, so that the follow-up radiographs could always be taken in the same position.
Three “regions of interest” (ROIs) were selected using the “Rectangle” tool on ImageJ, according to the protocol described by Soltani et al. [32] (Figure 3):
  • Apical ROI: extending horizontally between the mesial and distal root surfaces of the tooth and vertically between the root apex and the lower edge of the image.
  • Mesial proximal ROI: extending vertically from the mesial alveolar ridge to the tooth apex and horizontally between the root surfaces of the two adjacent teeth.
  • Distal proximal ROI: extending vertically from the distal alveolar ridge to the tooth apex and horizontally between the root surfaces of the two adjacent teeth.
Also, according to Soylu et al., during ROI selection, areas such as dental roots, lamina dura, and periodontal ligament were excluded [29].
ROI selection was carried out independently by two different experienced operators with high inter-examiner reliability (kappa = 0.85) and was repeated after 30 days [45].
The selected ROIs were cropped using the “Crop” tool, and the resulting images were duplicated.
The “Gaussian Blur” filter (sigma radius = 10) was applied to the duplicates, based on the protocol by Soltani et al. for periapical (PA) radiographs [32].
The resulting image was then subtracted from the original one (“Process → Image Calculator → Subtract”), resulting in a third image. The “Binary” filter was applied to the third image in order to obtain a black and white image.
The “fractal dimension” (FD) of the obtained image was calculated using the “BoneJ” Plugin present on Fiji (an open-source extension to ImageJ) [46].
Higher FD values indicated a greater complexity and density of the trabecular architecture [22,23,24]. Values obtained from pre- and post-measurements were then compared (Figure 4a–c).
Image analysis (FD calculation) was also performed independently by two different operators and repeated within 30 days.
The reproducibility of the method was measured with Cohen’s Kappa coefficient [45].

2.6. Study Timeline

The collected radiographs followed the timeline described by Choi et al. [47]:
  • T0: pre-treatment.
  • T1: post-treatment, which was set at the removal of the splint for SE and at the reaching of the desired amount of extrusion for OE.
  • T2: follow-up at 3 months.
  • T3: follow-up at 6 months.

2.7. Statistical Methods

As descriptive statistics, mean and Standard Deviation (SD) were used for quantitative variables, while frequency and percentages were used for qualitative variables.
Normal distribution of data was assessed using the Kolmogorov–Smirnov test (p > 0.05).
To assess the differences between pre-treatment (baseline, T0) and post-treatment (T1, T2, and T3) within each group, paired t-tests were employed.
To compare the baseline differences between the two groups (orthodontic extrusion vs. surgical extrusion), independent t-tests were used for quantitative variables, and Fisher’s exact test was used for dichotomous variables.
To compare the two groups in the outcome variable of the difference in apical FD (fractal dimension) between baseline and 3 months and between baseline and 6 months, analysis of covariance (ANCOVA) was employed using the baseline value as a covariate.
Given the different times required by OE and SE to achieve the desired amount of extrusion, analysis of covariance (ANCOVA) was not applied at T1 in order to avoid a methodological error [14,17,48].
Similarly, in order to assess the differences between the two groups, ANCOVA was used, setting the baseline value as a covariate. A similar model was used for the difference between baseline and 3 months and between baseline and 6 months.
The significance threshold was set at 0.05, with 95% confidence intervals (95% CIs). In order to reduce type I errors, a Bonferroni correction was also performed [49].
ROI selection and image analysis were performed independently by two different operators and repeated within 30 days.
The reproducibility of the method was measured with Cohen’s Kappa coefficient [45].
Statistical analysis was performed using JMP software (version 13.0).

3. Results

All measurements were carried out by two different operators and repeated within 30 days. Cohen’s Kappa coefficient showed a significant inter-examiner reliability (kappa > 0.8) [45].

3.1. Baseline (T0)

In total, 22 patients were treated with orthodontic extrusion, and 22 patients underwent surgical extrusion. In the present study, orthodontic and surgical extrusion allowed for the rehabilitation of 43 teeth by means of endocanal fiberglass posts and lithium disilicate restorations, as well as the development of the implant site for the remaining tooth.
Table 3 shows the baseline characteristics of the patients.
At baseline, variables such as gender, smoking habits, and tooth location (maxillary vs. mandibular) showed no statistical significance according to Fisher’s exact test (Table 3). Likewise, age and the number of multi-rooted teeth were not statistically significant according to Student’s t-test for independent data (Table 3).
FD measurements were carried out by two different operators and repeated within 30 days with high inter-examiner reliability (kappa = 0.8).

3.2. Post-Extrusion (T1)

The difference in FD between baseline and post-extrusion was significant in both groups for both apical and proximal FD. Apical FD increased by 0.044 (p = 0.001) in the orthodontic extrusion group and by 0.049 (p < 0.001) in the surgical extrusion group (Table 4).
Proximal FD increased by 0.046 (p < 0.001) in the orthodontic extrusion group and by 0.042 (p < 0.001) in the surgical extrusion group (Table 5).
FD measurements were carried out by two different operators and repeated within 30 days with high inter-examiner reliability (apical FD kappa = 0.81; proximal FD kappa = 0.8).

3.3. Three-Month Follow-Up (T2)

The difference in FD between baseline and the 3-month follow-up was significant in both groups for both apical and proximal FD. Apical FD increased by 0.039 (p = 0.008) and 0.058 (p <0.001) after orthodontic and surgical extrusion, respectively (Table 6).
Proximal FD increased by 0.050 (p < 0.001) in the orthodontic extrusion group and by 0.047 (p < 0.001) in the surgical extrusion group (Table 6). However, the analysis of covariance (ANCOVA) did not show significant differences between the two groups for the apical FD (p = 0.303) (Table 6) and for the proximal FD (p = 0.122) (Table 7).
FD measurements were carried out by two different operators and repeated within 30 days with high inter-examiner reliability (apical FD kappa = 0.83; proximal FD kappa = 0.81).

3.4. Six-Month Follow-Up (T3)

The difference in FD between baseline and the 6-month follow-up was significant in both groups for both apical and proximal FD. Apical FD increased by 0.034 (p = 0.036) and 0.051 (p < 0.001) after orthodontic and surgical extrusion, respectively (Table 8). Proximal FD increased by 0.060 (p < 0.001) in the orthodontic extrusion group and by 0.057 (p < 0.001) in the surgical extrusion group (Table 9). However, the analysis of covariance (ANCOVA) did not show significant differences between the two groups for apical FD (p = 0.113) (Table 8) and proximal FD (p = 0.228) (Table 9).
FD measurements were carried out by two different operators and repeated within 30 days with high inter-examiner reliability (apical FD kappa = 0.82; proximal FD kappa = 0.8).
As for the apical ROI, the group of patients treated with OE experienced a larger increase in the FD value at T1; FD then slightly decreased at T2 and stabilized at T3 (Figure 5). The patients treated with SE experienced a large FD increase at T1 as well, which further increased at T2 and then stabilized at T3 (Figure 5).
As for the proximal ROI, the highest increase was found at T1, both for OE and SE. The FD exponentially increased at T2 and at T3 for both groups (Figure 6).

4. Discussion

The present study aimed to assess the different healing patterns following orthodontic and surgical extrusion through fractal analysis (FA) of consecutive periapical radiographs.
Orthodontic extrusion is a slow but minimally invasive treatment, requiring higher patient compliance and longer timing [1].
Surgical extrusion is, on the other hand, a more immediate alternative; however, it involves a higher risk of ankylosis and root resorption due to surgical trauma [1].
The rationale for the use of fractal analysis was to compare the different healing patterns associated with OE and SE through radiographical changes in the surrounding bone in order to understand whether this kind of treatment allows for the long-term survival and restoration of structurally compromised teeth.
Fractal analysis of bone architecture was able to assess subtle bone changes following OE and SE, showing that an increase in bone density is expected, although through different biological mechanisms (Table 4, Table 5, Table 6, Table 7, Table 8 and Table 9).
This was shown by a statistically significant increase in FD values for both groups (apical and proximal regions) (Table 4, Table 5, Table 6, Table 7, Table 8 and Table 9), which is consistent with the underlying healing patterns and biological mechanisms of the two therapeutic approaches.
The findings in our study were consistent with a recent study on an animal model, according to which OE led to the formation of new trabecular bone around the extruded teeth [18].
As for surgical extrusion, there are no studies in the literature that specifically detail bone neo-formation following the extrusive procedure; however, a reduction in apical radiolucency and healing of the surgical wound through clot formation—resulting in new bone formation—were demonstrated, which is in line with the findings of the present study [16,17,50].

4.1. OE Group

The highest increase in the FD values for the OE group was detected between baseline (T0) and the 1-month follow-up (T1), both in the apical and proximal regions (Table 4 and Table 5).
This is most likely motivated by the effect of the extrusive forces on the alveolar bone: in fact, orthodontic extrusion exerts tension on the surrounding tissues, gradually stimulating marginal bone apposition through increasing osteoblastic activity [14,51].
Furthermore, OE can take anywhere from 3–6 weeks to 3–6 months to expose sufficient dental structure [14]; this allows time for the alveolar bone to acquire an organized structure and increase its density [48], leading to higher FD values for the OE group at T1 (Table 4 and Table 5).
As for the T2 and T3 FD values, the FD values slightly decreased from the T1, yet were higher for both ROIs when compared to T0 (Table 6, Table 7, Table 8 and Table 9).
This could be related to the light forces applied during the intermediate tooth stabilization (ITS) period following OE, with the aim of allowing for the reorganization of the supracrestal gingival fibers and the bone matrix [14].

4.2. SE Group

According to the surgical extrusion group (SE), a statistically significant increase was measured in FD values between baseline (T0) and post-extrusion (T1), both in the apical and proximal regions (Table 4 and Table 5). The highest increases in the FD values for the SE group in the apical ROI were detected at T2 vs. T0 (Table 4, Table 5, Table 6 and Table 7).
In fact, this aspect might be explained by the phenomenon of bony apposition originating from a blood clot and the subsequent re-mineralization of the surgical wound [17].
The FD values were greater at T2 than at T1 and further increased at T3 (Table 6, Table 7, Table 8 and Table 9), particularly concerning the apical ROI, where the blood clot is generally located (Table 6, Table 7, Table 8 and Table 9).
In fact, surgical extrusion leads to the organization of the blood clot, leading to bone marrow (BM) formation in approximately 60–180 days, followed by an increase in its mineralization and density [17].

4.3. Clinical Implications

Optimal bone density is essential for the long-term stability and maintenance of structurally compromised teeth, as well as for obtaining bone tissue suitable for implant placement [31].
In this regard, several studies have emphasized the importance of accurately assessing bone quality to predict treatment outcomes. Soylu et al. demonstrated that fractal analysis can serve as a reliable predictor of osseointegration, highlighting its potential value in evaluating the bone microarchitecture at prospective implant sites [29].
Beyond implant-related applications, maintaining adequate bone density is also crucial in orthodontic and restorative procedures aimed at preparing compromised areas for future rehabilitation. For example, Conserva and colleagues showed that orthodontic extrusion techniques can effectively regenerate and develop implant sites, further underscoring the relevance of evaluating initial bone conditions to ensure predictable results [51].
Moreover, Hayek et al. explored the relationship between radiographic fractal analysis and primary implant stability, demonstrating that higher fractal dimensions correlate with improved mechanical anchorage at the time of placement, thereby reinforcing the role of bone density as a determinant of implant success [52]. The importance of optimal bone conditions also emerges in clinical contexts involving rare systemic or genetic disorders.
Studies by Azzi and collaborators describe how conditions such as ADULT syndrome or selective IgA deficiency can exhibit oral manifestations that compromise bone and soft-tissue structures, indirectly influencing dental stability and the feasibility of implant therapy [53,54]. Altogether, these findings highlight that achieving and preserving suitable bone density is fundamental not only for implant integration but also for the overall management of compromised dentition.
The timing of the placement of a prosthetic restoration in structurally compromised tooth can be a key factor for the long-term success of this challenging treatment. In fact, according to Wolff’s law, repeated loading of bone tissue triggers adaptive changes, allowing the bone to better withstand those forces [30,55,56].
Fractal analysis can be considered a cost-effective and easily accessible method to assess the periodontal healing status of an extruded tooth through the assessment of the optimal bone density.
As such, it can be integrated with clinical examination for challenging therapeutic approaches, in order to evaluate both the prognosis of teeth undergoing orthodontic and surgical extrusion and to schedule the prosthetic rehabilitation of structurally compromised teeth.
Secondly, hopeless teeth can be slowly extruded completely out of the socket before their extraction to improve the bone and gum tissues around the tooth, making it easier to replace with an implant or other restorations later (the so-called “guided orthodontic regeneration” approach) [51,57].
Therefore, the FA method can be useful to assess the bone healing after the development of the implant site through a slow orthodontic extrusion of hopeless teeth, because it provides an immediate numerical quantification of bone turnover changes through a box-counting algorithm, without requesting additional sets of exams (e.g., CBCTs) [33,34,58].

4.4. Limitations and Strengths

The present study was the first one to assess bone changes after dental extrusion using fractal analysis.
Fractal analysis also represents a cost-effective and easily accessible method to assess changes in the trabecular bone; in fact, since periapical radiographs are routinely employed for treatment planning of structurally compromised teeth [47], FA can provide an added analysis to evaluate the prognosis of teeth undergoing orthodontic and surgical extrusion with respect to the “ALARA” (As Low As Reasonably Achievable) principles [59,60].
Indeed, when using FA, factors such as image quality and standardization are of crucial importance.
A recent paper revised the image processing method, comparing it to White and Rudolph’s traditional technique [25,61]; however, full standardization of image processing has not been achieved yet.
Still, periapical (PA) radiographs are reported to have higher resolution than other 2D radiographs [31]; in addition, the digital systems are able to prevent the loss of data resulting from the digitization process of periapical radiographs [62].
Moreover, variables such as patients’ ages, smoking habits, and any factors that might affect bone healing processes must be taken into consideration.
However, based on Fisher’s exact test conducted at baseline (Table 3), neither age nor smoking habit emerged as statistically significant variables in the present study.
Still, one potential limitation could be that both single- and multi-rooted teeth, from both upper and lower jaws, were taken into consideration in the present study.
Orthodontic extrusion was more frequently performed on single-rooted teeth, due to the fact that heavier forces are required to extrude multi-rooted teeth [14].
In fact, five of the six analyzed molars were extruded surgically.
However, neither tooth type nor location turned out to be statistically significant variables (Table 3); therefore, both single- and multi-rooted teeth were included to ensure adequate statistical representativeness.
Also, at baseline, a statistically significant difference between OE and SE patients was detected, with lower values in the SE group (Table 3).
The lower baseline apical FD values observed in the SE group may reflect greater pre-existing periodontal and periapical structural compromise, which is often the clinical reason for selecting surgical rather than orthodontic extrusion [1].
This initial difference in trabecular integrity may explain the baseline FD disparity between the two groups.
Another potential drawback is the retrospective nature of the present study and the relatively short follow-up; since dental extrusion is a niche procedure when compared to implant placement [63], the recruitment of eligible patients for a prospective study is often challenging.
Finally, although it would be valuable to examine potential statistical correlations between fractal dimension and the elapsed time after extrusion, this analysis could not be performed in the present study due to the lack of standardized radiographic time at T1 (post-extrusion).
In fact, in the OE group, the follow-up interval at T1 ranged between 15 days and 1 month, depending on how long it took to achieve the sufficient ferrule effect orthodontically; on the other hand, SE follow-up occurred approximately 10 days after the extrusive procedure, at the splint removal time.
Future prospective studies with homogeneous and predefined radiographic time intervals are required.

4.5. Implications for Future Research

Bone apposition and changes in mineral bone density are biologically distinct phenomena but are strictly connected.
In fact, according to the model proposed by Weinans et al., bone adapts to mechanical loading by increasing density in areas of elevated stress to achieve uniform strain. If this adaptation fails, the tissue either reaches cortical bone density or undergoes resorption [64].
Therefore, an increase in FD suggests enhanced trabecular complexity associated with osteogenesis and increased density, whereas a decrease indicates reduced bone density or resorptive activity [65].
However, although changes in fractal dimension may reflect biological processes such as neo-osteogenesis, which inherently implies increased mineral density, or bone resorption, which implies density loss, FA itself does not allow these two phenomena to be distinguished independently so far.
FD values should therefore be carefully interpreted as an indirect measure of overall trabecular remodeling, rather than as a selective indicator of either bone density or trabecular architecture alone.
Future studies should focus on attempting to distinguish the two phenomena through the FA of radiographic images.

5. Conclusions

The present study showed that both orthodontic and surgical extrusion lead to an increased density of the trabecular bone, both in the apical and proximal regions, allowing for the restoration and long-term maintenance of structurally compromised teeth. According to fractal analysis (FD), orthodontic and surgical extrusion showed different healing patterns: for OE, the highest FD increase was detected at T1 (post-extrusion); for SE, the highest increase was detected at T2 (3-month follow-up). After T2 and T3, the differences between the two groups leveled out.
On the other hand, the inter-group differences between orthodontic and surgical extrusion were not statistically significant.
Moreover, FA is a valuable technique to provide an added analysis for the evaluation of long-term maintenance of teeth undergoing orthodontic and surgical extrusion with respect to the “ALARA” (As Low As Reasonably Achievable) principles.
These findings also suggest relevant clinical implications for the timing of prosthetic rehabilitation of structurally compromised teeth. Since the peak FD increase occurred immediately after extrusion in OE and at 3 months in SE, prosthetic restoration may be scheduled earlier in OE and postponed in SE to allow sufficient trabecular recovery before loading.
However, further prospective and multi-centered studies in this field are required to further explore the potential of fractal analysis of radiographic images.

Supplementary Materials

The following supporting information can be downloaded at https://www.mdpi.com/article/10.3390/fractalfract9120818/s1: Table S1: STROBE guidelines.

Author Contributions

Conceptualization, E.S. and I.C.; methodology, E.S.; software, I.C.; validation, N.M.G. and P.G.; formal analysis, F.G. and R.C.; investigation, F.G. and A.A.B.; resources, N.M.G.; data curation, A.A.B., N.M.G., and R.C.; writing—original draft preparation, I.C.; writing—review and editing, E.S.; visualization, F.G. and P.G.; supervision, F.G. and A.A.B.; project administration, E.S. and I.C.; funding acquisition, P.G. All authors have read and agreed to the published version of the manuscript.

Funding

This research received no external funding.

Data Availability Statement

The authors agree to make data and materials supporting the results or analyses available upon reasonable request.

Acknowledgments

The authors would like to express sincere gratitude to Michele Nieri for the sincere commitment and support in terms of the statistical analysis and to Elisabetta Ada Cavalcanti for support with the software.

Conflicts of Interest

The authors declare no conflicts of interest.

References

  1. Cordaro, M.; Staderini, E.; Torsello, F.; Grande, N.M.; Turchi, M.; Cordaro, M. Orthodontic Extrusion vs. Surgical Extrusion to Rehabilitate Severely Damaged Teeth: A Literature Review. Int. J. Environ. Res. Public Health 2021, 18, 9530. [Google Scholar] [CrossRef] [PubMed]
  2. Carvalho, B.A.S.; Duarte, C.A.B.; Silva, J.F.; Batista, W.; Douglas-de-Oliveira, D.W.; de Oliveira, E.S.; Soares, L.G.; Galvao, E.L.; Rocha-Gomes, G.; Gloria, J.C.R.; et al. Clinical and radiographic evaluation of the Periodontium with biologic width invasion. BMC Oral Health 2020, 20, 116. [Google Scholar] [CrossRef] [PubMed]
  3. Rosenberg, E.S.; Cho, S.C.; Garber, D.A. Crown lengthening revisited. Compend. Contin. Educ. Dent. 1999, 20, 527–532, 534, 536–538 passim; quiz 542. [Google Scholar]
  4. Nugala, B.; Kumar, B.S.; Sahitya, S.; Krishna, P.M. Biologic width and its importance in periodontal and restorative dentistry. J. Conserv. Dent. 2012, 15, 12–17. [Google Scholar] [CrossRef]
  5. Savadi, A.; Rangarajan, V.; Savadi, R.C.; Satheesh, P. Biologic perspectives in restorative treatment. J. Indian Prosthodont. Soc. 2011, 11, 143–148. [Google Scholar] [CrossRef]
  6. Gargiulo, A.; Krajewski, J.; Gargiulo, M. Defining biologic width in crown lengthening. CDS Rev. 1995, 88, 20–23. [Google Scholar]
  7. Ingber, J.S.; Rose, L.F.; Coslet, J.G. The “biologic width”—A concept in periodontics and restorative dentistry. Alpha Omegan 1977, 70, 62–65. [Google Scholar] [PubMed]
  8. Schmidt, J.C.; Sahrmann, P.; Weiger, R.; Schmidlin, P.R.; Walter, C. Biologic width dimensions—A systematic review. J. Clin. Periodontol. 2013, 40, 493–504. [Google Scholar] [CrossRef]
  9. Padbury, A., Jr.; Eber, R.; Wang, H.L. Interactions between the gingiva and the margin of restorations. J. Clin. Periodontol. 2003, 30, 379–385. [Google Scholar] [CrossRef]
  10. Jepsen, S.; Caton, J.G.; Albandar, J.M.; Bissada, N.F.; Bouchard, P.; Cortellini, P.; Demirel, K.; de Sanctis, M.; Ercoli, C.; Fan, J.; et al. Periodontal manifestations of systemic diseases and developmental and acquired conditions: Consensus report of workgroup 3 of the 2017 World Workshop on the Classification of Periodontal and Peri-Implant Diseases and Conditions. J. Periodontol. 2018, 89, S237–S248. [Google Scholar] [CrossRef]
  11. Zicari, F.; Van Meerbeek, B.; Scotti, R.; Naert, I. Effect of ferrule and post placement on fracture resistance of endodontically treated teeth after fatigue loading. J. Dent. 2013, 41, 207–215. [Google Scholar] [CrossRef]
  12. Juloski, J.; Radovic, I.; Goracci, C.; Vulicevic, Z.R.; Ferrari, M. Ferrule effect: A literature review. J. Endod. 2012, 38, 11–19. [Google Scholar] [CrossRef]
  13. Stankiewicz, N.R.; Wilson, P.R. The ferrule effect: A literature review. Int. Endod. J. 2002, 35, 575–581. [Google Scholar] [CrossRef]
  14. Gonzalez-Martin, O.; Solano-Hernandez, B.; Torres Munoz, A.; Gonzalez-Martin, S.; Avila-Ortiz, G. Orthodontic Extrusion: Guidelines for Contemporary Clinical Practice. Int. J. Periodontics Restor. Dent. 2020, 40, 667–676. [Google Scholar] [CrossRef]
  15. Bach, N.; Baylard, J.F.; Voyer, R. Orthodontic extrusion: Periodontal considerations and applications. J. Can. Dent. Assoc. 2004, 70, 775–780. [Google Scholar] [PubMed]
  16. Plotino, G.; Abella Sans, F.; Duggal, M.S.; Grande, N.M.; Krastl, G.; Nagendrababu, V.; Gambarini, G. Clinical procedures and outcome of surgical extrusion, intentional replantation and tooth autotransplantation—A narrative review. Int. Endod. J. 2020, 53, 1636–1652. [Google Scholar] [CrossRef] [PubMed]
  17. Cardaropoli, G.; Araujo, M.; Lindhe, J. Dynamics of bone tissue formation in tooth extraction sites. An experimental study in dogs. J. Clin. Periodontol. 2003, 30, 809–818. [Google Scholar] [CrossRef]
  18. da Silva, V.C.; de Molon, R.S.; Martins, R.P.; Ribeiro, F.S.; Pontes, A.E.F.; Zandim-Barcelos, D.L.; Leite, F.R.M.; Benatti Neto, C.; Marcantonio, R.A.C.; Cirelli, J.A. Effects of orthodontic tooth extrusion produced by different techniques, on the periodontal tissues: A histological study in dogs. Arch. Oral Biol. 2020, 116, 104768. [Google Scholar] [CrossRef]
  19. Apolinario, A.C.; Sindeaux, R.; de Souza Figueiredo, P.T.; Guimaraes, A.T.; Acevedo, A.C.; Castro, L.C.; de Paula, A.P.; de Paula, L.M.; de Melo, N.S.; Leite, A.F. Dental panoramic indices and fractal dimension measurements in osteogenesis imperfecta children under pamidronate treatment. Dentomaxillofacial Radiol. 2016, 45, 20150400. [Google Scholar] [CrossRef] [PubMed]
  20. Goller Bulut, D.; Bayrak, S.; Uyeturk, U.; Ankarali, H. Mandibular indexes and fractal properties on the panoramic radiographs of the patients using aromatase inhibitors. Br. J. Radiol. 2018, 91, 20180442. [Google Scholar] [CrossRef]
  21. Bayrak, S.; Goller Bulut, D.; Orhan, K.; Sinanoglu, E.A.; Kursun Cakmak, E.S.; Misirli, M.; Ankarali, H. Evaluation of osseous changes in dental panoramic radiography of thalassemia patients using mandibular indexes and fractal size analysis. Oral Radiol. 2020, 36, 18–24. [Google Scholar] [CrossRef] [PubMed]
  22. Demiralp, K.O.; Kursun-Cakmak, E.S.; Bayrak, S.; Akbulut, N.; Atakan, C.; Orhan, K. Trabecular structure designation using fractal analysis technique on panoramic radiographs of patients with bisphosphonate intake: A preliminary study. Oral Radiol. 2019, 35, 23–28. [Google Scholar] [CrossRef] [PubMed]
  23. Kursun-Cakmak, E.S.; 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 Surg. Oral. Med. Oral Pathol. Oral Radiol. 2018, 126, 184–191. [Google Scholar] [CrossRef] [PubMed]
  24. Cesur, E.; Bayrak, S.; Kursun-Cakmak, E.S.; Arslan, C.; Koklu, A.; Orhan, K. Evaluating the effects of functional orthodontic treatment on mandibular osseous structure using fractal dimension analysis of dental panoramic radiographs. Angle Orthod. 2020, 90, 783–793. [Google Scholar] [CrossRef]
  25. White, S.C.; Rudolph, D.J. Alterations of the trabecular pattern of the jaws in patients with osteoporosis. Oral Surg. Oral Med. Oral Pathol. Oral Radiol. Endod. 1999, 88, 628–635. [Google Scholar] [CrossRef]
  26. Kato, C.N.; Barra, S.G.; Tavares, N.P.; Amaral, T.M.; Brasileiro, C.B.; Mesquita, R.A.; Abreu, L.G. Use of fractal analysis in dental images: A systematic review. Dentomaxillofac. Radiol. 2020, 49, 20180457. [Google Scholar] [CrossRef]
  27. Sanchez, I.; Uzcategui, G. Fractals in dentistry. J. Dent. 2011, 39, 273–292. [Google Scholar] [CrossRef]
  28. Soylu, E.; Cosgunarslan, A.; Celebi, S.; Soydan, D.; Demirbas, A.E.; Demir, O. Fractal analysis as a useful predictor for determining osseointegration of dental implant? A retrospective study. Int. J. Implant. Dent. 2021, 7, 14. [Google Scholar] [CrossRef]
  29. Gulec, M.; Tassoker, M.; Ozcan, S.; Orhan, K. Evaluation of the mandibular trabecular bone in patients with bruxism using fractal analysis. Oral Radiol. 2021, 37, 36–45. [Google Scholar] [CrossRef]
  30. Soltani, P.; Sami, S.; Yaghini, J.; Golkar, E.; Riccitiello, F.; Spagnuolo, G. Application of Fractal Analysis in Detecting Trabecular Bone Changes in Periapical Radiograph of Patients with Periodontitis. Int. J. Dent. 2021, 2021, 3221448. [Google Scholar] [CrossRef]
  31. Wilding, R.J.; Slabbert, J.C.; Kathree, H.; Owen, C.P.; Crombie, K.; Delport, P. The use of fractal analysis to reveal remodelling in human alveolar bone following the placement of dental implants. Arch. Oral Biol. 1995, 40, 61–72. [Google Scholar] [CrossRef] [PubMed]
  32. Ciavarella, D.; Lorusso, M.; Fanelli, C.; Ferrara, D.; Esposito, R.; Laurenziello, M.; Esperouz, F.; Lo Russo, L.; Tepedino, M. The Efficacy of the RME II System Compared with a Herbst Appliance in the Treatment of Class II Skeletal Malocclusion in Growing Patients: A Retrospective Study. Dent. J. 2024, 12, 254. [Google Scholar] [CrossRef] [PubMed]
  33. Arslan, S.; Korkmaz, Y.N.; Buyuk, S.K.; Tekin, B. Effects of reverse headgear therapy on mandibular trabecular structure: A fractal analysis study. Orthod. Craniofacial Res. 2022, 25, 562–568. [Google Scholar] [CrossRef] [PubMed]
  34. Darawsheh, A.F.; Kolarovszki, B.; Hong, D.H.; Farkas, N.; Taheri, S.; Frank, D. Applicability of Fractal Analysis for Quantitative Evaluation of Midpalatal Suture Maturation. J. Clin. Med. 2023, 12, 4189. [Google Scholar] [CrossRef]
  35. Muftuoglu, O.; Karasu, H.A. Assessment of mandibular bony healing, mandibular condyle and angulus after orthognathic surgery using fractal dimension method. Med. Oral Patol. Oral Cir. Bucal 2024, 29, e620–e625. [Google Scholar] [CrossRef]
  36. Esperouz, F.; Ciavarella, D.; Lorusso, M.; Santarelli, A.; Lo Muzio, L.; Campisi, G.; Lo Russo, L. Critical review of OCT in clinical practice for the assessment of oral lesions. Front. Oncol. 2025, 15, 1569197. [Google Scholar] [CrossRef]
  37. Ciavarella, D.; Lorusso, M.; Fanelli, C.; Cazzolla, A.P.; Maci, M.; Ferrara, D.; Lo Muzio, L.; Tepedino, M. The Correlation between Mandibular Arch Shape and Vertical Skeletal Pattern. Medicina 2023, 59, 1926. [Google Scholar] [CrossRef]
  38. Gili, T.; Di Carlo, G.; Capuani, S.; Auconi, P.; Caldarelli, G.; Polimeni, A. Complexity and data mining in dental research: A network medicine perspective on interceptive orthodontics. Orthod. Craniofacial Res. 2021, 24, 16–25. [Google Scholar] [CrossRef]
  39. Cuschieri, S. The STROBE guidelines. Saudi J. Anaesth. 2019, 13, S31–S34. [Google Scholar] [CrossRef]
  40. World Medical Association (AMM). Helsinki Declaration. Ethical principles for medical research involving human subjects. Assist. Inferm. Ric. 2001, 20, 104–107. [Google Scholar]
  41. Alharbi, H.; Almutairi, M.S.; Alrajhi, S.; Almotairy, N. Effect of Orthodontic Movement on the Periapical Healing of Teeth Undergone Endodontic Root Canal Treatment: A Systematic Review. J. Clin. Med. 2025, 14, 7292. [Google Scholar] [CrossRef]
  42. Consolaro, A.; Miranda, D.A.O.; Consolaro, R.B. Orthodontics and Endodontics: Clinical decision-making. Dent. Press J. Orthod. 2020, 25, 20–29. [Google Scholar] [CrossRef]
  43. Installation & Operating Instructions, DBSWIN 5.17 Dental Imaging Software; Dürr Dental SE: Bietigheim-Bissingen, Germany; Air Techniques, Inc.: Melville, NY, USA, 2022.
  44. Schneider, C.A.; Rasband, W.S.; Eliceiri, K.W. NIH Image to ImageJ: 25 years of image analysis. Nat. Methods 2012, 9, 671–675. [Google Scholar] [CrossRef]
  45. McHugh, M.L. Interrater reliability: The kappa statistic. Biochem. Medica 2012, 22, 276–282. [Google Scholar] [CrossRef]
  46. Schindelin, J.; Arganda-Carreras, I.; Frise, E.; Kaynig, V.; Longair, M.; Pietzsch, T.; Preibisch, S.; Rueden, C.; Saalfeld, S.; Schmid, B.; et al. Fiji: An open-source platform for biological-image analysis. Nat. Methods 2012, 9, 676–682. [Google Scholar] [CrossRef]
  47. Choi, Y.H.; Lee, H.J. Surgical extrusion of a maxillary premolar after orthodontic extrusion: A retrospective study. J. Korean Assoc. Oral Maxillofac. Surg. 2019, 45, 254–259. [Google Scholar] [CrossRef]
  48. Bruhnke, M.; Beuer, F.; Bose, M.W.H.; Naumann, M. Forced orthodontic extrusion to restore extensively damaged anterior and premolar teeth as abutments for single-crown restorations: Up to 5-year results from a pilot clinical study. J. Prosthet. Dent. 2023, 129, 61–68. [Google Scholar] [CrossRef]
  49. Curtin, F.; Schulz, P. Multiple correlations and Bonferroni’s correction. Biol. Psychiatry 1998, 44, 775–777. [Google Scholar] [CrossRef]
  50. Argueta, J. Surgical extrusion: A reliable technique for saving compromised teeth. A 5-years follow-up case report. G. Ital. di Endod. 2018, 32, 25–30. [Google Scholar] [CrossRef]
  51. Conserva, E.; Fadda, M.; Ferrari, V.; Consolo, U. Predictability of a New Orthodontic Extrusion Technique for Implant Site Development: A Retrospective Consecutive Case-Series Study. Sci. World J. 2020, 2020, 4576748. [Google Scholar] [CrossRef]
  52. Hayek, E.; Aoun, G.; Bassit, R.; Nasseh, I. Correlating Radiographic Fractal Analysis at Implant Recipient Sites with Primary Implant Stability: An In Vivo Preliminary Study. Cureus 2020, 12, e6539. [Google Scholar] [CrossRef]
  53. Azzi, L.; Maurino, V.; Vinci, R.; Croveri, F.; Boggio, A.; Tagliabue, A.; Silvestre-Rangil, J.; Tettamanti, L. ADULT syndrome: Dental features of a very rare condition. J. Biol. Regul. Homeost. Agents 2017, 31, 61–65. [Google Scholar]
  54. Azzi, L.; Croveri, F.; Vinci, R.; Maurino, V.; Boggio, A.; Mantegazza, D.; Farronato, D.; Tagliabue, A.; Silvestre-Rangil, J.; Tettamanti, L. Oral manifestations of selective IgA-deficiency: Review and case-report. J. Biol. Regul. Homeost. Agents 2017, 31, 113–117. [Google Scholar] [PubMed]
  55. Frost, H.M. A 2003 update of bone physiology and Wolff’s Law for clinicians. Angle Orthod. 2004, 74, 3–15. [Google Scholar] [CrossRef] [PubMed]
  56. Teichtahl, A.J.; Wluka, A.E.; Wijethilake, P.; Wang, Y.; Ghasem-Zadeh, A.; Cicuttini, F.M. Wolff’s law in action: A mechanism for early knee osteoarthritis. Arthritis Res. Ther. 2015, 17, 207. [Google Scholar] [CrossRef]
  57. Kaitsas, R.; Paolone, M.G.; Paolone, G. Guided orthodontic regeneration: A tool to enhance conventional regenerative techniques in implant surgery. Int. Orthod. 2015, 13, 539–554. [Google Scholar] [CrossRef] [PubMed]
  58. Cucchi, A.; Bettini, S.; Fiorino, A.; Maglio, M.; Marchiori, G.; Corinaldesi, G.; Sartori, M. Histological and histomorphometric analysis of bone tissue using customized titanium meshes with or without resorbable membranes: A randomized clinical trial. Clin. Oral Implant. Res. 2024, 35, 114–130. [Google Scholar] [CrossRef]
  59. Sivolella, S.; Meggiorin, S.; Ferrarese, N.; Lupi, A.; Cavallin, F.; Fiorino, A.; Giraudo, C. CT-based dentulous mandibular alveolar ridge measurements as predictors of crown-to-implant ratio for short and extra short dental implants. Sci. Rep. 2020, 10, 16229. [Google Scholar] [CrossRef]
  60. Berkhout, W.E. The ALARA-principle. Backgrounds and enforcement in dental practices. Ned. Tijdschr. Tandheelkd. 2015, 122, 263–270. [Google Scholar] [CrossRef]
  61. da Silva, M.E.B.; Dos Santos, H.S.; Ruhland, L.; Rabelo, G.D.; Badaro, M.M. Fractal analysis of dental periapical radiographs: A revised image processing method. Oral Surg. Oral Med. Oral Pathol. Oral Radiol. 2023, 135, 669–677. [Google Scholar] [CrossRef]
  62. 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 Surg. Oral Med. Oral Pathol. Oral Radiol. Endod. 2005, 100, 467–472. [Google Scholar] [CrossRef] [PubMed]
  63. Clark, D.; Levin, L. In the dental implant era, why do we still bother saving teeth? Dent. Traumatol. 2019, 35, 368–375. [Google Scholar] [CrossRef]
  64. Weinans, H.; Huiskes, R.; Grootenboer, H.J. The behavior of adaptive bone-remodeling simulation models. J. Biomech. 1992, 25, 1425–1441. [Google Scholar] [CrossRef] [PubMed]
  65. Kang, H.-J.; Jeong, S.-W.; Jo, B.-H.; Kim, Y.-D.; Kim, S.S. Observation of trabecular changes of the mandible after orthognathic surgery using fractal analysis. J. Korean Assoc. Oral Maxillofac. Surg. 2012, 38, 96–100. [Google Scholar] [CrossRef]
Fractalfract 09 00818 g001
Figure 1. (a,b) Pre- and post-treatment orthodontic extrusion.
Figure 1. (a,b) Pre- and post-treatment orthodontic extrusion.
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Figure 2. (a,b) Pre- and post-treatment surgical extrusion.
Figure 2. (a,b) Pre- and post-treatment surgical extrusion.
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Figure 3. ROI selection on ImageJ (National Institute of Health, Bethesda, MD, USA).
Figure 3. ROI selection on ImageJ (National Institute of Health, Bethesda, MD, USA).
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Figure 4. (a–c) Image Crop, Gaussian Blurring, and Binary.
Figure 4. (a–c) Image Crop, Gaussian Blurring, and Binary.
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Figure 5. Changes in apical FD values registered over time: the blue line indicates OE and the orange line indicates SE.
Figure 5. Changes in apical FD values registered over time: the blue line indicates OE and the orange line indicates SE.
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Figure 6. Changes in proximal FD values registered over time: the blue line indicates OE and the orange line indicates SE.
Figure 6. Changes in proximal FD values registered over time: the blue line indicates OE and the orange line indicates SE.
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Table 1. Demographic distribution of study participants and analyzed teeth.
Table 1. Demographic distribution of study participants and analyzed teeth.
NumberMale (%)Female (%)Mean Age (SD)Single-Rooted Teeth (%)Multi-Rooted Teeth (%)Maxillary Teeth (%)Mandibular Teeth (%)
OE group2212 (54.5%)10 (45.4%)36.6 (7.7)21 (95.5%)1 (4.5%)15 (68.2%)7 (31.8%)
SE group2211 (50%)11 (50%)46.1 (9.2)16 (72.7%)6 (27.3%)15 (68.2%)7 (31.8%)
Table 2. Inclusion and exclusion criteria.
Table 2. Inclusion and exclusion criteria.
Inclusion CriteriaExclusion Criteria
Adult subjects > 18 years with permanent dentitionGrowing patients or patients with deciduous teeth
Presence of pre- and post-extrusive treatment and follow-up periapical radiographsAbsence of radiographic records of the extrusive treatment
Extrusive (orthodontic or surgical) treatment (with a minimum quantity of extrusion of 2 mm), performed in the presence of structurally compromised teethPatients undergoing the surgical crown lengthening technique (SCC) to achieve sufficient ferrule and biological width
Signed informed consent form to participate in the studyPatients not willing to participate in the study
Table 3. Baseline (before extrusion).
Table 3. Baseline (before extrusion).
VariableOrthodontic Extrusion
N = 22		Surgical Extrusion
N = 22		p-Value
Gender (female)10 (45%)11 (50%)1.0 a
Age (years)42.1 ± 7.746.1 ± 9.20.121 b
Smokers8 (36%)9 (41%)1.0 a
Upper teeth15 (68%)16 (73%)1.0 a
Molars1 (5%)5 (23%)0.185 b
Apical FD1.833 ± 0.0461.775 ± 0.0640.001 b*
Proximal FD1.743 ± 0.0561.701 ± 0.0570.018 b*
Qualitative data expressed as frequency (percentage) and quantitative data expressed as mean ± Standard Deviation. a—Fisher’s exact test; b—Student’s t-test for independent data; * statistical significance.
Table 4. Apical post-extrusion FD values. * = statistical significance.
Table 4. Apical post-extrusion FD values. * = statistical significance.
Orthodontic Extrusion
N = 22		Surgical Extrusion
N = 22
Post-extrusion apical FD1.877 ± 0.0471.825 ± 0.054
Apical baseline FD vs. post-extrusion FD0.044 ± 0.0540.049 ± 0.050
95%CI (intra-group)0.020; 0.0680.027; 0.072
p-value (intra-group)0.001 *<0.001 *
Effect size (intra-group)0.48 0.43
Table 5. Proximal post-extrusion FD values. * = statistical significance.
Table 5. Proximal post-extrusion FD values. * = statistical significance.
Orthodontic Extrusion
N = 22		Surgical Extrusion
N = 22
Post-extrusion proximal FD1.789 ± 0.0441.743 ± 0.051
Proximal baseline FD vs. post-extrusion FD0.046 ± 0.0310.042 ± 0.045
95%CI (intra-group)0.032; 0.0600.022; 0.062
p-value (intra-group)<0.001 *<0.001 *
Effect size (intra-group)0.41 0.84
Table 6. Three-month apical FD values. * = statistical significance.
Table 6. Three-month apical FD values. * = statistical significance.
Orthodontic Extrusion
N = 22		Surgical Extrusion
N = 22		Adjusted Difference95%CI
(Inter-Group)		p-Value ANCOVA
3-month apical FD1.872 ± 0.0551.833 ± 0.044---
Apical baseline FD vs. 3 months0.039 ± 0.0620.058 ± 0.0490.016−0.016; 0.0470.303
95%CI (intra-group)0.011; 0.0660.036; 0.080---
p-value (intra-group)0.008 *<0.001 *---
Effect size (intra-group)0.39 0.54
Table 7. Three-month proximal FD values. * = statistical significance.
Table 7. Three-month proximal FD values. * = statistical significance.
Orthodontic Extrusion
N = 22		Surgical Extrusion
N = 22		Adjusted Difference95%CI
(Inter-Group)		p-Value ANCOVA
3-month proximal FD1.792 ± 0.0511.748 ± 0.048---
Proximal baseline FD vs. 3 months0.050 ± 0.0340.047 ± 0.0420.017−0.005; 0.0380.122
95%CI (intra-group)0.035; 0.0650.029; 0.066---
p-value (intra-group)<0.001 *<0.001 *---
Effect size (intra-group)0.43 0.2
Table 8. Six-month apical FD values. * = statistical significance.
Table 8. Six-month apical FD values. * = statistical significance.
Orthodontic Extrusion
N = 22		Surgical Extrusion
N = 22		Adjusted Difference95%CI
(Inter-Group)		p-Value ANCOVA
6-month apical FD1.868 ± 0.0541.827 ± 0.044---
Apical baseline FD vs. 6 months0.034 ± 0.0720.051 ± 0.0530.027−0.007; 0.0600.113
95%CI (intra-group)0.003; 0.0660.028; 0.075---
p-value (intra-group)0.036 *<0.001 *---
Effect size (intra-group)0.350.48
Table 9. Six-month proximal FD values. * = statistical significance.
Table 9. Six-month proximal FD values. * = statistical significance.
Orthodontic Extrusion
N = 22		Surgical Extrusion
N = 22		Adjusted Difference95%CI
(Inter-Group)		p-Value ANCOVA
6-month proximal FD1.803 ± 0.0531.758 ± 0.056---
Proximal baseline FD vs. 6 months0.060 ± 0.0310.057 ± 0.0440.014−0.009; 0.0370.228
95%CI (intra-group)0.046; 0.0730.037; 0.076---
p-value (intra-group)<0.001 *<0.001 *---
Effect size (inter-group)0.470.1
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Staderini, E.; Guglielmi, F.; Alessandri Bonetti, A.; Cavalcanti, I.; Grande, N.M.; Castagnola, R.; Gallenzi, P. Fractal Analysis of Trabecular Bone Before and After Orthodontic and Surgical Extrusion: A Retrospective Case–Control Study. Fractal Fract. 2025, 9, 818. https://doi.org/10.3390/fractalfract9120818

AMA Style

Staderini E, Guglielmi F, Alessandri Bonetti A, Cavalcanti I, Grande NM, Castagnola R, Gallenzi P. Fractal Analysis of Trabecular Bone Before and After Orthodontic and Surgical Extrusion: A Retrospective Case–Control Study. Fractal and Fractional. 2025; 9(12):818. https://doi.org/10.3390/fractalfract9120818

Chicago/Turabian Style

Staderini, Edoardo, Federica Guglielmi, Anna Alessandri Bonetti, Irene Cavalcanti, Nicola Maria Grande, Raffaella Castagnola, and Patrizia Gallenzi. 2025. "Fractal Analysis of Trabecular Bone Before and After Orthodontic and Surgical Extrusion: A Retrospective Case–Control Study" Fractal and Fractional 9, no. 12: 818. https://doi.org/10.3390/fractalfract9120818

APA Style

Staderini, E., Guglielmi, F., Alessandri Bonetti, A., Cavalcanti, I., Grande, N. M., Castagnola, R., & Gallenzi, P. (2025). Fractal Analysis of Trabecular Bone Before and After Orthodontic and Surgical Extrusion: A Retrospective Case–Control Study. Fractal and Fractional, 9(12), 818. https://doi.org/10.3390/fractalfract9120818

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