Trabecular bone remodelling following lateral window maxillary sinus augmentation with allograft versus xenograft: a retrospective one-year comparative fractal dimension analysis

Abstract

Background

Maxillary sinus augmentation is widely performed to enable implant placement in the atrophic posterior maxilla, and the radiographic remodelling patterns of different graft materials remain a topic of clinical interest. This retrospective study compared trabecular bone remodelling following lateral window maxillary sinus augmentation with allograft versus xenograft materials using FD analysis of panoramic radiographs over a one-year follow-up.

Methods

One hundred patients (50 allograft, 50 xenograft) treated between 2015 and 2023 were included. Panoramic radiographs obtained immediately postoperatively and at 3 months, 6 months, and 1 year were analyzed using ImageJ software according to the White and Rudolph box-counting method. Intragroup temporal changes were evaluated with the Friedman test and Bonferroni-corrected Wilcoxon signed-rank tests; intergroup comparisons were performed using the Mann–Whitney U test or independent samples t-test according to data distribution. Interobserver reliability was assessed using the intraclass correlation coefficient (ICC).

Results

Age and sex distributions were comparable between groups (p = 0.250 and p = 0.288, respectively). FD values changed significantly over time in both the allograft (p = 0.021) and xenograft (p < 0.001) groups. In the allograft group, only the 3-month versus 6-month comparison reached significance (p = 0.001), whereas in the xenograft group all pairwise comparisons except 6 months versus 1 year were significant. Intergroup comparisons revealed significantly higher FD values in the allograft group immediately postoperatively (p = 0.010) and at 3 months (p < 0.001), but no differences were detected at 6 months (p = 0.107) or 1 year (p = 0.751). Interobserver reliability was good across most measurements (ICC 0.794–0.856), with moderate reliability for the 6-month xenograft measurement (ICC = 0.744).

Conclusions

Allografts produced higher early-phase FD values, while both materials achieved comparable radiographic trabecular complexity by the 6-month and 1-year follow-up periods. These findings suggest convergent radiographic remodelling over time. Further histomorphometric and clinical studies are needed to confirm these FD-derived findings.

Trial registration

Not applicable.

Introduction

The posterior maxilla is considered a clinically challenging region for dental implant placement due to insufficient bone volume resulting from alveolar ridge resorption and maxillary sinus pneumatization. When the residual bone height is less than 5 mm, implant placement is generally not feasible without additional surgical intervention. Therefore, the sinus augmentation procedure has become one of the most widely used techniques to achieve successful implant-supported rehabilitation in the posterior maxilla. By elevating the sinus membrane and placing graft material on the sinus floor, sinus augmentation promotes new bone formation, increases vertical bone height, and enhances long-term implant stability [1–3].

The selection of graft material plays a critical role in determining the quality of bone regeneration and long-term clinical success. Among the materials commonly used in sinus augmentation, allografts and xenografts are the most widely preferred. Allografts contain various biological growth factors and demonstrate both osteoconductive and partially osteoinductive properties, thereby supporting integration with host tissue. Xenografts, in contrast, are characterized by high volumetric stability, low resorption rates, and favourable mechanical strength [4, 5]. Nevertheless, their ability to induce new bone formation, maintain long-term structural stability, and contribute to implant success remains a topic of ongoing debate.

Bone regeneration following sinus augmentation can be assessed using histological evaluation and advanced imaging modalities such as computed tomography (CT), cone-beam computed tomography (CBCT) or micro-CT. However, in routine clinical practice, there is an increasing need for less invasive, accessible, and cost-effective evaluation tools. Fractal geometry describes complex structures that exhibit self-similarity and cannot be adequately characterized by conventional Euclidean dimensions; because trabecular bone displays such irregular, self-repeating architecture, it is well suited to fractal characterization. Fractal analysis quantifies this complexity as a single numerical index, the fractal dimension (FD), which reflects the density, branching, and connectivity of the trabecular network. In dental radiology, FD is most commonly derived using the box-counting method, in which the binarized and skeletonized trabecular pattern within a defined region of interest is overlaid with grids of progressively decreasing box size; the slope of the log–log regression of box count against box size yields the FD value [6, 7]. Higher FD values are generally interpreted as indicating greater radiographic trabecular complexity, whereas lower values may reflect reduced structural complexity associated with bone resorption, delayed remodelling, or immature bone formation. Owing to its objectivity, low cost, and applicability to conventional two-dimensional radiographs, fractal analysis has been widely used to monitor bone microarchitectural changes in various clinical contexts, including dental implant osseointegration, periodontal bone loss, post-extraction healing, graft maturation, and systemic conditions such as osteoporosis. Previous studies have also reported favorable reproducibility of FD measurements, particularly when standardized image acquisition, ROI selection, and image-processing protocols are applied [8–14].

Comparing the effects of different graft materials on bone quality using fractal analysis may address a meaningful gap in the current literature. Specifically, a comparative evaluation of allograft and xenograft materials in terms of long-term bone regeneration has the potential to provide clinicians with objective, evidence-based guidance for graft selection.

Therefore, this study aimed to evaluate radiographic trabecular remodelling following lateral window sinus augmentation with allograft and xenograft materials using fractal analysis. We hypothesized that allograft and xenograft materials would exhibit temporally distinct patterns of trabecular remodelling during the healing process. This approach may provide additional radiographic information regarding graft-related trabecular microarchitectural changes and support future evidence-based radiographic evaluation of graft material–associated remodelling patterns.

Materials and methods

Study design and ethical approval

This study was designed as a retrospective clinical investigation and was approved by the Clinical Research Ethics Committee of Tokat Gaziosmanpaşa University (Project No: 25-MOBAEK-298; Date: 26.09.2025).

Patient selection

Patients who underwent lateral window maxillary sinus augmentation at the Department of Oral and Maxillofacial Surgery, Tokat Gaziosmanpaşa University Faculty of Dentistry, between 2015 and 2023 were retrospectively screened.

Initially, a total of 600 sinus lift sites were reviewed. Patient files and radiographic records were evaluated according to the inclusion and exclusion criteria. Cases with incomplete or unsuitable records regarding smoking status, diabetes mellitus or glycemic control in diabetic patients, vitamin D levels, alcohol consumption, parafunctional habits, systemic diseases, or medication use that could affect bone metabolism were excluded. Cases with insufficient follow-up radiographs, inadequate radiographic quality, or the use of additional graft materials or biomaterials other than allograft or xenograft alone were also excluded.

Inclusion criteria

• Age ≥ 18 years,

• Residual bone height < 5 mm in the posterior maxilla,

• Use of either allograft or xenograft material exclusively during sinus augmentation,

• Availability of postoperative, 3-month, 6-month, and 1-year panoramic radiographs,

• Absence of systemic disease or medication use known to affect bone metabolism.

Exclusion criteria

• Insufficient or missing postoperative radiographic records,

• Poor-quality panoramic radiographs unsuitable for fractal analysis,

• Smoking,

• Diabetes mellitus or inadequate/unknown glycemic control,

• Abnormal or unavailable vitamin D status,

• Alcohol consumption,

• Parafunctional habits,

• Systemic diseases or medication use known to affect bone metabolism,

• Use of additional graft materials, platelet concentrates, hyaluronic acid, autogenous bone, or other bioactive materials.

• Intraoperative complications, including Schneiderian membrane perforation.

After this screening process, 100 systemically healthy patients with complete radiographic follow-up of at least one year were included and divided into two groups based on the graft material used:

• Group 1: Patients who underwent sinus augmentation with allograft (Atident^®, Ankara, Türkiye; particle size 0.5–1.0 mm).

• Group 2: Patients who underwent sinus augmentation with xenograft (Cerabone^®; Botiss Biomaterials GmbH, Zossen, Germany; particle size 0.5–1.0 mm).

Surgical procedure

All surgical procedures were performed by oral and maxillofacial surgeons of the same department, each with a minimum of five years of clinical experience, following a standardized lateral window sinus augmentation protocol. Throughout the study period (2015–2023), the surgical approach, instrumentation, and perioperative clinical protocols were maintained without modification, thereby minimizing operator-related variability.

Sinus augmentation was conducted under local anesthesia (4% articaine with 1:100,000 epinephrine). Following antisepsis, a crestal incision with two vertical releasing incisions was made to elevate a full-thickness mucoperiosteal flap, providing adequate exposure of the lateral maxillary sinus wall. A lateral window was created using a round bur under copious irrigation, and the Schneiderian membrane was carefully elevated with sinus curettes. No autogenous bone, platelet concentrates, hyaluronic acid, or additional bioactive materials were used in any case.

After placement of the selected graft material, the lateral window was covered with a native resorbable collagen membrane derived from porcine pericardium (Jason^® membrane, botiss biomaterials GmbH, Zossen, Germany). The flap was then repositioned and sutured with 3 − 0 silk. Owing to the limited residual bone height, a staged (delayed) protocol was applied in all cases; dental implants were placed approximately 6 months after sinus augmentation.

Radiographic evaluation

All panoramic radiographs were acquired using the same digital panoramic imaging unit (Veraviewepocs 2-D, J. Morita Mfg. Corp., Kyoto, Japan). The device operated under automatic exposure conditions adjusted to patient size, with parameters of 67 kVp, 5 mA, and an exposure time of 7.4 s. During image acquisition, all patients were positioned according to a standardized protocol, with the Frankfort horizontal plane parallel to the floor and the sagittal plane aligned with the vertical reference line. The device underwent routine calibration and quality-control procedures throughout the study period, and only radiographs with adequate image quality and contrast were included in the analysis. Panoramic radiographs obtained immediately after surgery and at 3-month, 6-month, and 1-year postoperative intervals were evaluated.

Fractal analysis

Trabecular bone microarchitecture was analyzed using ImageJ software (NIH, Bethesda, USA) following the method described by White and Rudolph [15], which has been widely adopted for fractal evaluation of jaw trabecular bone on conventional radiographs:

Although a lossless format such as TIFF is theoretically preferable for texture-based image analysis, FD calculation has been reported to be relatively robust against lossy JPEG compression [16], and JPEG format has been used in previous dental FD studies [17]. Moreover, because all images were processed under identical conditions using the same file format, ROI size, software settings, and image-processing workflow, any potential compression-related effect was expected to be consistent across groups and follow-up periods. A Gaussian blur filter (σ = 35 pixels) was applied to minimize brightness variations caused by soft tissues or cortical thickness. The blurred image was subtracted from the original (“Subtract”), and a gray value of 128 was added to each pixel (“Add”) to enhance trabecular contrast. The image was converted to binary format using a threshold of 128. Noise reduction was performed using sequential “Erode” and “Dilate” functions. The image was then inverted and skeletonized using the “Skeletonize” command. FD was calculated using the Fractal Box Count method. The number of boxes containing trabecular structures was recorded, and the slope of the log–log plot of box size versus box count was taken as the FD value.

Each ROI was standardized as a 50 × 50-pixel square positioned within the central augmented sinus region and anchored to fixed anatomical references unaffected by graft remodelling, ensuring that the same anatomical area was sampled in each patient. In dentate patients, the ROI was positioned medio-distally at a standardized distance from the roots of the teeth bordering the augmented site; in edentulous patients, where dental landmarks were unavailable, it was positioned medio-distally at a standardized distance from the maxillary tuberosity. In both groups, the ROI was positioned vertically with reference to the native (pre-existing) sinus floor. Because these landmarks were outside the grafted region and were expected to remain relatively stable over time, the ROI was repositioned using the identical landmark relationship on each serial radiograph (postoperatively, 3 months, 6 months, and 1 year), ensuring that the same anatomical area was sampled as consistently as possible across all follow-up periods. Previous maxillary sinus lift and panoramic FD studies have used similar anatomically referenced ROI standardization to enhance reproducibility across serial images [3, 5, 18, 19]. Residual native bone, the Schneiderian membrane, and radiopaque artifacts were excluded. All FD measurements were independently performed by two oral and maxillofacial surgeons, both of whom had at least five years of clinical experience in the field of oral and maxillofacial surgery. Both observers were blinded to the graft type and time point (Figs. 1 and 2).

Fig. 1.

Examples of ROI selection on panoramic radiographs at different healing stages (postoperative, 3 months, 6 months, 1 year) in a patient treated with xenograft. The ROI was placed at a standardized distance referenced to the native sinus floor and the FD value calculated for each ROI is shown; fractal analysis was performed according to the method described by White and Rudolph [15]. A Postoperative, B 3 months, C 6 months, D 1 year

Fig. 2.

Examples of ROI selection on panoramic radiographs at different healing stages (postoperative, 3 months, 6 months, 1 year) in a patient treated with allograft. The ROI was placed at a standardized distance referenced to the native sinus floor and the FD value calculated for each ROI is shown; fractal analysis was performed according to the method described by White and Rudolph [15]. A Postoperative, B 3 months, C 6 months, D 1 year

Statistical analysis

All statistical analyses were performed using IBM SPSS Statistics version 27.0. Continuous variables were presented as mean ± standard deviation, median, and minimum–maximum values, while categorical variables were expressed as frequencies and percentages. The normality of continuous variables was assessed using the Shapiro–Wilk test. A two-tailed p-value of < 0.05 was considered statistically significant. Age was compared between the allograft and xenograft groups using the Mann–Whitney U test, and sex distribution was compared using Pearson’s chi-square test. These demographic comparisons were performed to confirm the baseline comparability of the two graft groups with respect to age and sex, rather than to model the independent effects of these variables on FD. Intragroup temporal changes were analyzed using the Friedman test, followed by Wilcoxon signed-rank tests with Bonferroni correction for pairwise comparisons. With six pairwise comparisons per group, the Bonferroni-adjusted significance threshold was set at p < 0.0083. Intergroup comparisons of FD values were performed using the Mann–Whitney U test or independent samples t-test according to data distribution. For the independent samples t-test, Cohen’s d was reported as the effect size measure, with values of 0.2, 0.5, and 0.8 considered small, medium, and large effects, respectively.

Radiological measurement reliability was assessed using measurements performed by two independent observers. The single-measure intraclass correlation coefficient ICC (2,1) and its 95% confidence intervals were calculated based on a two-way random-effects model with absolute agreement.

The required sample size was calculated using G*Power 3.1.9.7. Based on previous research evaluating FD changes following sinus augmentation [5], a moderate effect size (Cohen’s d = 0.6) was conservatively assumed for the between-group comparison, taking into account the expected variability between cohorts and measurement protocols. With a two-tailed independent samples t-test, a significance level of α = 0.05, and a statistical power of 80%, the minimum required sample size was estimated as 45 patients per group. To compensate for a potential dropout rate of approximately 10%, the final target was set at 50 patients per group (100 patients in total).

Results

Demographic findings

A total of 100 patients were included in the study, with 50 patients in the allograft group and 50 patients in the xenograft group. The mean age was 56.10 ± 9.38 years in the allograft group and 57.60 ± 9.97 years in the xenograft group. No statistically significant difference was found between the groups in terms of age (Mann–Whitney U = 1083.500; Z = -1.149; p = 0.250). Sex distribution also did not differ significantly between the groups (χ² = 1.131; df = 1; p = 0.288) (Table 1).

Table 1.

Comparison of demographic characteristics between the study groups

Variable	Allograft (n = 50)	Xenograft (n = 50)	p-value
Age (years), mean ± SD	56.10 ± 9.38	57.60 ± 9.97	0.250
Age, median (min–max)	57.50 (36–73)	60.00 (30–74)	—
Sex, M / F, n (%)	31 (62.0%) / 19 (38.0%)	36 (72.0%) / 14 (28.0%)	0.288

Age was compared using the Mann–Whitney U test. Sex distribution was compared using Pearson’s chi-square test.

Descriptive findings of FD values

In the allograft group, the mean FD value was 1.3005 ± 0.0897 postoperatively, 1.2705 ± 0.0975 at 3 months, 1.3061 ± 0.0903 at 6 months, and 1.3054 ± 0.0948 at 1 year. In the xenograft group, the mean FD value was 1.2505 ± 0.1056 postoperatively, 1.1949 ± 0.1046 at 3 months, 1.2900 ± 0.0759 at 6 months, and 1.3011 ± 0.0909 at 1 year (Table 2).

Table 2.

Descriptive statistics of FD values according to time points

Postoperative	Group	Mean ± SD	Median	Min–Max
	Allograft	1.3005 ± 0.0897	1.3227	1.0203–1.4644
	Xenograft	1.2505 ± 0.1056	1.2674	1.0065–1.4716
3 months	Allograft	1.2705 ± 0.0975	1.2752	1.0604–1.4737
	Xenograft	1.1949 ± 0.1046	1.2231	0.9034–1.4558
6 months	Allograft	1.3061 ± 0.0903	1.3342	1.0569–1.4433
	Xenograft	1.2900 ± 0.0759	1.3026	1.0913–1.4265
1 year	Allograft	1.3054 ± 0.0948	1.3190	0.9683–1.4448
	Xenograft	1.3011 ± 0.0909	1.3146	1.0226–1.4429

SD standard deviation, FD Fractal Dimension, Min–Max, minimum–maximum

Intragroup comparisons over time

In the allograft group, the Friedman test showed a statistically significant difference in FD values across time points (χ² = 9.720; df = 3; p = 0.021). According to the Bonferroni-adjusted pairwise comparisons, only the difference between 3 months and 6 months was statistically significant.

In the xenograft group, the Friedman test also showed a statistically significant difference in FD values across time points (χ² = 56.688; df = 3; p < 0.001). According to the Bonferroni-adjusted pairwise comparisons, all pairwise comparisons except 6 months versus 1 year were statistically significant (Table 3).

Table 3.

Intragroup Comparison of FD Values Between Time Points

Comparison	Allograft p-value	Xenograft p-value
Friedman test, overall	0.021	< 0.001
Postoperative vs. 3 months	0.029	< 0.001
Postoperative vs. 6 months	0.508	0.005
Postoperative vs. 1 year	0.881	< 0.001
3 months vs. 6 months	0.001	< 0.001
3 months vs. 1 year	0.018	< 0.001
6 months vs. 1 year	0.534	0.025

Intragroup temporal changes were evaluated using the Friedman test. Pairwise comparisons were performed using the Wilcoxon signed-rank test. Bold values indicate statistical significance. Bonferroni correction was applied for six pairwise comparisons, and p < 0.0083 was considered statistically significant for pairwise comparisons. FD Fractal Dimension

Intergroup comparisons

Postoperative FD values were significantly higher in the allograft group than in the xenograft group (p = 0.010). Similarly, at 3 months, FD values were significantly higher in the allograft group than in the xenograft group (p < 0.001), with a medium-to-large effect size (Cohen’s d = 0.747, 95% CI: 0.340–1.151). However, no statistically significant difference was found between the groups at 6 months or 1 year (p = 0.107 and p = 0.751, respectively) (Table 4).

Table 4.

Intergroup comparison of FD values at each time point

Postoperative	Allograft, mean ± SD	Xenograft, mean ± SD	Test	p-value
	1.3005 ± 0.0897	1.2505 ± 0.1056	Mann–Whitney U	0.010
3 months	1.2705 ± 0.0975	1.1949 ± 0.1046	Independent samples t-test	< 0.001
6 months	1.3061 ± 0.0903	1.2900 ± 0.0759	Mann–Whitney U	0.107
1 year	1.3054 ± 0.0948	1.3011 ± 0.0909	Mann–Whitney U	0.751

Test selection was based on the Shapiro–Wilk normality test results

FD fractal dimension, SD standard deviation

Interobserver reliability analysis

Interobserver reliability was evaluated in both graft groups at all time points. In the allograft group, good reliability was achieved across all time points, with ICC values ranging from 0.802 to 0.842 and 95% confidence intervals ranging from 0.68 to 0.91.

In the xenograft group, good reliability was observed for the postoperative, 3-month, and 1-year measurements, with ICC values of 0.856, 0.804, and 0.794, respectively. Moderate reliability was detected for the 6-month measurement, with an ICC value of 0.744 and a 95% confidence interval of 0.59–0.85.

Discussion

In this retrospective study, temporal changes in trabecular bone microarchitecture were evaluated using fractal analysis on panoramic radiographs in patients who underwent lateral window sinus augmentation with allograft or xenograft materials. The findings showed an early decrease in FD values that reached statistical significance in the xenograft group, whereas in the allograft group this early decrease represented a non-significant numerical trend after Bonferroni correction; both groups subsequently showed an increase at the 6-month and 1-year follow-up periods. Notably, the within-group temporal kinetics differed markedly between groups: the allograft group displayed comparatively modest and gradual changes across time points, whereas the xenograft group exhibited a more pronounced and dynamic remodelling pattern. This temporal sequence may be consistent with radiographic changes associated with early graft remodelling, graft particle resorption, subsequent new bone formation, and trabecular maturation.

Alveolar ridge augmentation is widely employed to enhance the success of implant-supported prosthetic rehabilitation, particularly in the posterior maxilla, where inadequate bone height commonly results from alveolar resorption and maxillary sinus pneumatization [20]. Although autogenous bone remains the “gold standard” graft material [21], the absence of donor-site morbidity and the predictable outcomes associated with allografts and xenografts have made them popular alternatives. Bone allografts are characterized by their osteoconductive matrix, which provides a scaffold for host cell adhesion and differentiation, and by their osteoinductive potential derived from bone morphogenetic proteins (BMPs) [22]. Xenografts, in contrast, are valued for their favorable biocompatibility, structural stability, and slow resorption rate, contributing to long-term volume maintenance [23].

Beyond the material-related characteristics of graft materials, the resulting bone quality is a critical determinant of implant treatment success [24]. Although histological examination and advanced imaging modalities such as computed tomography (CT) and micro-computed tomography (micro-CT) yield highly accurate assessments of bone structure, their high cost, limited accessibility, and radiation exposure restrict their routine clinical use [6]. Micro-CT is considered one of the most accurate techniques for assessing trabecular bone microarchitecture owing to its high-resolution, non-destructive, three-dimensional evaluation capability [25]. Fractal analysis, on the other hand, offers a non-invasive, low-dose, and highly sensitive method for quantifying trabecular bone microarchitecture using conventional radiographs [10]. Although FD demonstrates acceptable reliability and reproducibility under standardized conditions, FD measurements can be affected by variations in exposure parameters, projection angle, and ROI positioning; methodological standardization is therefore essential to obtain reproducible results [6, 7, 11]. For these reasons, FD represents a valuable tool for objectively assessing radiographic trabecular changes following sinus augmentation.

In the present study, panoramic radiographs were chosen over CBCT for FD evaluation. This preference was based on their lower radiation dose, wide anatomical field, and consistent availability across the retrospective study period. Although CBCT provides three-dimensional volumetric data, some comparative investigations have suggested that panoramic radiographs may yield comparable results in FD-based assessment of trabecular architecture under certain conditions [26, 27]. Nevertheless, it should be acknowledged that CBCT remains the more sensitive imaging modality for evaluating trabecular bone microstructure, and the choice of panoramic radiography in the present study was primarily dictated by its routine clinical availability, lower radiation dose, and retrospective data accessibility rather than by methodological superiority.

Previous studies evaluating grafted regions with fractal analysis have reported heterogeneous results. Some investigations have demonstrated lower FD values in grafted areas compared with native bone [19]. Sancar et al., using a fractal-based assessment of ossification after open sinus lift, observed a progressive reduction in xenograft-related radiographic density between the 3rd and 9th postoperative months, which they attributed to ongoing graft resorption preceding mature trabecular reorganization [1]. The temporal pattern observed in our xenograft cohort showed partial concordance with these findings, in that the lowest FD values were also identified during the early postoperative phase; however, the subsequent recovery in our cohort began earlier (at the 6-month follow-up) and continued progressively up to the 1-year time point. These differences may be explained by methodological factors, including the use of panoramic versus periapical radiographs, distinct ROI placement strategies, variations in graft particle composition and resorption kinetics between the xenograft brands used, and differences in the postoperative time points evaluated. Conversely, Molon et al. reported increased FD values six months after sinus augmentation, associating this with new trabecular formation and improved bone density [28], a pattern more consistent with our findings. In another study comparing autografts and xenografts, mean gray values—representing radiographic density—decreased in both groups at 6 months, although the difference between groups was not significant [29].

Comparable biphasic FD patterns have also been reported in other maxillofacial surgical contexts. Heo et al. demonstrated an initial decrease followed by a gradual increase in FD after bilateral sagittal split osteotomy using panoramic radiographs [30], whereas Çolak et al. similarly reported early postoperative reductions in FD at the osteotomy and condylar regions, with recovery toward preoperative levels between 6 and 12 months [31]. These patterns align closely with the present study’s findings, in which early postoperative FD reduction was followed by progressive increases during healing.

The biological basis for this trend may be partly related to osteoclastic activity. Osteoclast-mediated resorption may create structural irregularities on bone surfaces that could be reflected in FD values. A previous histological study reported a positive relationship between osteoclast number and FD. Consistent with this, modulation of osteoclastic activity has been reported to alter trabecular architecture and the resulting FD values [32], suggesting that fractal analysis may be sensitive to radiographic structural changes associated with bone remodeling processes.

From an osteoblastic perspective, FD changes correlate with new bone formation and increasing architectural complexity during remodelling [12]. Variations in trabecular connectivity, density, and organizational patterns correspond to shifts in resorption and formation dynamics, resulting in measurable fluctuations in FD. Although fractal analysis provides quantitative information about trabecular complexity, it should be interpreted as an indirect surrogate of bone microarchitectural changes rather than a direct measure of bone biology. FD reflects geometric and textural patterns that correlate with — but do not directly quantify — biological properties such as mineral density, porosity, and elasticity. Therefore, its findings should be considered as complementary to, rather than a substitute for, histological or volumetric assessments [12–14]. In the present study, the xenograft group exhibited a statistically significant reduction in FD values at the 3-month follow-up compared with the immediate postoperative measurement, whereas the allograft group displayed a more modest numerical decrease that did not reach statistical significance after Bonferroni correction. Both groups subsequently demonstrated recovery at 6 months and 1 year. The initial decrease may be attributed to the lower structural complexity of graft materials compared with native bone and the immature nature of early trabecular tissue. The subsequent increase in FD likely reflects ongoing bone regeneration and progressive improvement in trabecular organization.

The present findings indicate that allograft and xenograft materials followed distinct temporal remodelling patterns. In the allograft group, intragroup changes were relatively limited, with a significant difference observed only between the 3- and 6-month time points. In contrast, the xenograft group showed significant differences across all pairwise comparisons except between 6 months and 1 year, suggesting a more pronounced recovery phase following the early reduction in FD. This pattern may be consistent with the slower resorption and delayed integration characteristics of high-temperature–sintered xenografts [33–36]. Nevertheless, intergroup differences were significant only in the early postoperative and 3-month measurements, whereas no significant differences were observed at 6 months or 1 year. These findings suggest that, despite distinct early remodelling trajectories, both materials tend to converge toward comparable radiographic trabecular architectures over time.

Previous studies have reported that increases in FD may be associated with new bone formation, osseointegration, and greater trabecular microdensity [12, 37–39]. In addition, positive correlations between pre-implant FD values and post-implant ISQ measurements have been reported [40, 41]. However, FD reflects radiographic trabecular complexity rather than direct biological activity. Therefore, the higher early FD values observed in the allograft group should not be interpreted solely as evidence of more active remodelling, as intrinsic differences in graft radiographic texture and particle morphology may also have contributed to the early intergroup differences. The comparable FD values observed at mid- and long-term follow-up therefore indicate convergence in radiographic trabecular complexity rather than direct evidence of equivalent biological performance.

Limitations

This study has several limitations that should be acknowledged. First, it should be emphasized that the combination of retrospective data collection and two-dimensional panoramic radiography inherently limits the strength of the conclusions, as 2D imaging cannot capture volumetric changes in trabecular architecture and is subject to the superimposition of anatomical structures. This may reduce the sensitivity of fractal analysis. Furthermore, histological validation could not be performed, and the evaluation was based solely on radiographic fractal analysis findings. In addition, ROI images were stored in JPEG rather than a lossless format. Although FD has been reported to be relatively robust against lossy compression and all images were processed identically using the same file format and image-processing workflow, a minor influence of compression on grayscale texture information cannot be entirely excluded.

Another important methodological limitation is related to ROI reproducibility across serial panoramic radiographs. Although ROI placement was standardized using patient-specific anatomical landmarks, panoramic radiography is inherently affected by projection geometry, magnification, and patient-positioning variability. Therefore, despite these standardization procedures, minor differences in ROI localization between follow-up periods could not be completely eliminated. Since FD values may be influenced by ROI selection, positioning, and image acquisition parameters, temporal changes in FD should be interpreted with caution.

The exact graft volume (cc) used in each patient could not be fully standardized; however, because all cases were treated using similar surgical approaches and comparable clinical indications, the potential impact of this variable on the overall results is considered minimal. Additionally, clinical parameters such as implant stability, insertion torque, and postoperative complications could not be directly assessed, as these data were not consistently available in the retrospective records.

Future research should focus on prospective studies with larger sample sizes, incorporating CBCT-based fractal analysis and histomorphometric validation. Correlating fractal analysis findings with histological parameters would further strengthen the clinical relevance and diagnostic validity of FD measurements.

Conclusion

Both allograft and xenograft materials showed progressive radiographic trabecular remodelling following lateral window maxillary sinus augmentation. Although early FD values differed between the groups, FD values became comparable at the 6-month and 1-year follow-ups, indicating convergence of radiographic trabecular complexity over time. Since this study was based solely on FD-derived radiographic analysis and did not include histological, histomorphometric, implant stability, or clinical outcome assessments, the findings should not be interpreted as evidence of biological or clinical equivalence between the materials. Further histomorphometric and clinical studies are needed to confirm these FD-derived findings.

Abbreviations

FD

Fractal Dimension

ROI

Region of Interest

CT

Computed Tomography

CBCT

Cone-beam Computed Tomography

Authors’ contributions

Göksal Keldal: investigation, data curation, writing–original draft, methodology, writing–review and editing. Sefa Çolak: conceptualization, supervision, writing–review and editing.

Funding

This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors.

Data availability

The datasets generated and/or analyzed during the current study are not publicly available due to ethical and privacy restrictions but are available from the corresponding author upon reasonable request and with permission from the relevant ethics committee.

Declarations

Ethics approval and consent to participate

This study was designed as a retrospective clinical investigation and was approved by the Clinical Research Ethics Committee of Tokat Gaziosmanpaşa University (Project No: 25-MOBAEK-298). The study was conducted in accordance with the principles of the Declaration of Helsinki. The requirement for informed consent was waived by the Clinical Research Ethics Committee of Tokat Gaziosmanpaşa University, due to the retrospective nature of the study.

Consent for publication

Not applicable.

Competing interests

The authors declare no competing interests.